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

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PROPERTIES OF THIN YTTRIUM OXIDE DIELECTRIC FILMS by ERNEST B. RIEMANN B. Eng . (Physics).., McMaster U n i v e r s i t y , 1969 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department o f E l e c t r i c a l E n g i n e e r i n g We a c c e p t t h i s t h e s i s as c o n f o r m i n g to the r e q u i r e d s t a n d a r d R e s e a r c h S u p e r v i s o r . Members o f t he Committee Head o f t h e Department Members o f t h e Department o f E l e c t r i c a l E n g i n e e r i n g THE UNIVERSITY OF BRITISH COLUMBIA December, 1971 In presenting 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 requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that 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 reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood that copying 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 gain s h a l l not be allowed without my w r i t t e n permission. Department of The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada 'ABSTRACT A study has been made of the properties of thin yttrium oxide dielectric films prepared by the electron beam evaporation of high purity Y2 U3 powder* 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 Y2^3* 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 interstitial 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 in different frequency ranges. 3tnte:rnal photoemission measurements were made on Al-Y^O^-Al sand-wiches. 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 . i v -ACKNOWLEDGEMENT v i I. Introduction........ •• i II. Sample Preparation ." • 3 III. Electron Microscopy of Thin Films. 7 1. Introduction 7 2. Procedure • 8 3. Results.. •• 8 4. Analysis 12 5. Discussion 17 IV. Conduction in Thin Y 2°3 Films 1. Introduction. . . . 19 2. Experimental procedures. 27 3. Experimental results 27 4. . Discussion... 34 V. Step Response and Loss Factor in ^2 U3 1. Introduction 44 2. Experimental procedures 46 3. Results 3.1 Step response.... 46 3.2 Loss factor 52 4. Discussion.. 52 VI. Barrier Height Determination by Interanl Photoemission..... 1. Introduction 54 2. Experimental Procedures 57 3. Experimental Results .". • • 58 Page 4. D i s c u s s i o n 64 APPEND IX . . . . 67 REFERENCES .' 71 L I ST OF ILLUSTRATIONS Page I I . 1 MIM S t r u c t u r e 6 I I . 2 MIS S t r u c t u r e 6 I I I . 3 F r e s h l y d e p o s i t e d Y 2 0 3 f i l m . . .... 9 I I I . 4 R e c r y s t a l l i z e d . Y ^ f i l m : 9 I I I . 5 D i f f r a c t i o n s t r u c t u r e o f r e c r y s t a l l i z e d f i l m . 9 I I I . 6 D i f f r a c t i o n p a t t e r n 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 . 10 I I I . 7 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 f rom ^ O ^ on n - t y p e p o l i s h e d s i l i c o n 10 I I I . 8 D i f f r a c t i o n p a t t e r n o f Au f i l m ... 10 I I I . 9 Jh2+k2+i2 v s . r i n g d i a m e t e r f o r Y ^ 13 T V . 1 T rap p o t e n t i a l w e l l . . 21 IV. 2 P o o l e - F r e n k e l l o w e r i n g o f t r a p ene r gy b a r r i e r . . 22 IV. 3 Ene r gy band d i a g r am f o r Simmons' model 24 IV. 4 D.C. 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 28 IV. 5 Log I v s . /V f o r d i f f e r e n t t e m p e r a t u r e s (d = 4680 A ) 29 IV. 6 D e t e r m i n a t i o n o f 8 . . 30 IV. 7 E f f e c t o f p o l a r i t y r e v e r s a l on D.C. c o n d u c t i o n . 32 IV. 8 D e t e r m i n a t i o n o f a c t i v a t i o n e n e r g y 33 IV. 9 D.C. C o n d u c t i o n a t Low P r e s s u r e (p = 50u) 35 IV . 10 D e t e r m i n a t i o n o f 6..... 36 IV . 11 D e t e r m i n a t i o n o f a c t i v a t i o n e n e r g y . . 37 IV. 12 R e p r o d u c i b i l i t y o f D.C. c o n d u c t i o n c u r r e n t (p = 50 uHg) .... 38 V . 1 A l - Y ^ O ^ - A l s t e p r e s p o n s e c h a r g i n g c u r r e n t . 47 V. 2 : A l - ^ O ^ - A l s t e p r e s p o n s e d i s c h a r g i n g c u r r e n t . 48 V. 3 Log ( I / I Q ) V S . l o g (t/rQ) f o r d i s c h a r g e a f t e r 3V s t e p . . . . . 50 Page V. 4 D i e l e c t r i c l o s s e s v s . f r e q u e n c y 51 V I . 1 S i m p l i f i e d MIM band s t r u c t u r e 54 V I . 2 Monochromator c a l i b r a t i o n c u r v e ( d e u t e r i u m s o u r c e ) 56 V I . 3 Monochromator i n t e n s i t y c a l i b r a t i o n ( v i s i b l e range) 59 V I . 4 Monochromator c a l i b r a t i o n (200 0 - 5 0 0 0 A°) 60 V I . 5 P h o t o r e s p o n s e o f A l - Y ^ - A l 61 V I . 6 F o w l e r P l o t s f o r A l - Y ^ - A l 63 V I . 7 Y 2 0 3 b a r r i e r shape 64 A . l M0S C H y s t e r e s i s ( f=0.1Hz) 68 A .2 M0S C H y s t e r e s i s ( f=0.05Hz) 69 A. 3 MOS C H y s t e r e s i s ( f=0.01Hz) . .• . 70 v ACKNOWLEDGEMENT I w i s h t o thank my r e s e a r c h s u p e r v i s o r , D r . L. Young , f o r h i s encouragement and gu i dance i n the c o u r s e o f t h i s i n v e s t i g a t i o n . G r a t e f u l acknowledgement i s g i v e n t o the N a t i o n a l R e s e a r c h C o u n c i l f o r s u p p o r t i n g t h i s work w i t h a S c i e n c e S c h o l a r s h i p . Thanks a re a l s o due to Mr. B. Wong f o r d o i n g some o f t h e D.C. c o n d u c t i o n measurements , and M i s s L . M o r r i s f o r t y p i n g t h i s t h e s i s . v i •I. INTRODUCTION High quality thin dielectric films are v i t a l to the fabrication of many solid state devices. The films provide insulation, and are used for diffusion masking, surface passivation and hermetic sealing. To date, S i 0 2 > Si-jN^, AlpO^, T a 2^5 a n c* evaporated SiO have been the principal dielectrics used in electronic devices. It is desirable to find 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 desirable in a dielectric used for device fabrication. Some of these are: (1) Good insulating properties (low pinhole density, high breakdown f i e l d strength-, high permittivity, low losses.) (2) Low ionic mobility at adequate operating fields and, temperatures. (3) Low surface-state density when deposited on semiconductor material. (4) Ease of production. In this thesis, the properties of thin yttrium oxide dielectric films have been investigated. Previous work by Campbell^ had shown these films to have low losses and interesting dielectric properties. In the next chapter, the techniques used in sample preparation are discussed. Chapter III is concerned with the study of thin yttrium oxide films by electron microscopy, in order to determine their physical structure. Chapter IV deals with the D.C. conduction properties of these films, and how these properties may be understood by considering the structure of the Y2°3 crystal l a t t i c e . In Chapter V, the results of step response and A.C. loss measurements are given. 2 C h a p t e r V I d e a l s w i t h the energy b a r r i e r h e i g h t d e t e r m i n a t i o n a t t h e A l - Y ^ O ^ i n t e r f a c e i n A l - Y ^ O ^ - A l d e v i c e s . F i n a l l y , i n C h a p t e r V I I t h e c o n c l u d i n g remarks and recommendat ions f o r f u r t h e r r e s e a r c h a r e g i v e n . • I I , SAMPLE PREPARATION The y t t r i u m oxide f i l m s were evaporated i n an e l e c t r o n beam apparatus w i t h a 10-inch d i f f u s i o n pump capable of reaching pressures as low as 10 ^ torr without l i q u i d n i t r o g e n c o o l i n g . A Brad-Thomson type 776 W 9kW water-cooled e l e c t r o n gun provided the e l e c t r o n beam used f o r hea t i n g the compressed Y^O^ powder. I t was p o s s i b l e to apply beam powers of up to 800 watts ( 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 cu r r e n t ) to an area 2 as small as 25 mm. . The evaporation procedure was s i m i l a r to that used by C a m p b e l l ^ . 99.99% p u r i t y y t t r i u m oxide powder was packed f i r m l y i n t o a boron n i t r i d e c r u c i b l e before i n s e r t i o n i n t o the vacuum system. The m a t e r i a l was outgassed 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 the vacuum reached 1 X 10 t o r r , oxygen was b l e d i n t o the system and _5 the pressure was hel d at 5 x 10 torr by t h r o t t l i n g back the high vacuum va l v e . The f i l m t hickness was monitored during evaporation by d e p o s i t i n g Y^O^ simultaneously on the su b s t r a t e and a quartz c r y s t a l o s c i l l a t i n g at a 5 MHz r a t e . The mass deposited on the c r y s t a l decreased the o s c i l l a t i n g frequency, which was mixed w i t h the output of a v a r i a b l e o s c i l l a t o r set near 5 MHz. The frequency 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 of f i l m t h i c k n e s s , assuming constant f i l m d e n s i t y . The constant of p r o p o r t i o n a l i t y was found by measuring the thickness of a number of deposited f i l m s w i t h a T a l y s u r f . The equation d * 3.24Af where d = f i l m t h i c k n e s s (&)and Af = change i n frequency (Hz), was found to be accurate 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 thickness measurements were made by T a l y s u r f or A Made by Ta y l o r Hobson L t d . A n g s t r o m e t e r . The T a l y s u r f i s a m e c h a n i c a l d e v i c e t h a t measures t h e a m p l i f i e d m e c h a n i c a l movement o f a s t y l u s w i t h r e s p e c t t o a r e f e r e n c e p l a n e . The A n g s t r o m e t e r measures a f r i n g e d i s p l a c e m e n t c a u s e d by t h e i n t e r f e r e n c e o f monochromat ic l i g h t (Na y e l l o w , 5890 i ) between t h e f i l m t o be measured and a F l z e a U f l a t i n c o n t a c t w i t h the f i l m . A l a y e r o f h i g h l y r e f l e c t i n g a luminum was d e p o s i t e d on the i n s u l a t i n g f i l m to f a c i l i t a t e measurement. The t h i c k n e s s i s g i v e n by . _ d _X (1) D 2 where t H f i l m t h i c k n e s s D = d i s t a n c e between f r i n g e s d = f r i n g e s t e p X = 5890 1 Both methods were c o n s i d e r e d to be a c c u r a t e to about +100 JL A f t e r d e p o s i t i o n the f i l m s were a l l o w e d to c o o l s l o w l y i n an oxygen ambient f o r f i f t e e n m i n u t e s . The f i l m s were then baked i n a i r f o r s i x t e e n hour s at 1 5 0 ° C . Some prob lems were e n c o u n t e r e d w i t h the f i r s t f i l m s , w h i c h had many p i n h o l e s . The cause was f ound to be s p a t t e r i n g o f m a t e r i a l f rom the c r u c i b l e d u r i n g e v a p o r a t i o n . T h i s was c o n t r o l l e d by f i r s t f u s i n g t h e s u r f a c e o f t he ^2^3 P o W ^ e r a n c ^ b e g i n n i n g the e v a p o r a t i o n , t h e n r o t a t i n g the s u b s t r a t e i n t o p o s i t i o n o v e r the c r u i c i b l e . Two t y p e s o f s u b s t r a t e s were u sed , Dottf C o r n i n g 7059 a l u m i n o s i l i c a t e g l a s s and s i l i c o n w a f e r s . The f o rmer were c l e a n e d w i t h p r o p y l a l c o h o l , c h r o m i c o a c i d and d i s t i l l e d w a t e r , then d r i e d i n a i r . A m e t a l f i l m t y p i c a l l y 2000 A t h i c k was e v a p o r a t e d on to the s u b s t r a t e i n an Edwards d i f f u s i o n pump vacuum s y s t e m . A luminum, i n d i u m and g o l d were u s e d . The 99.999% p u r i t y A l w i r e was cleaned i n KOH solution before placement on the tungsten heater wire. The aluminum was melted car e f u l l y and a small quantity was evaporated with the shutter i n place between the heater and substrate. This allowed impurities to b o i l o f f . The shutter was opened for the evaporation, then shut again before a l l the aluminum had evaporated to minimize the evaporation of tungsten and other impurities from the heater wire. Evaporation rates as high as 1500 2/min were found to give good films. The thickness was monitored with another quartz c r y s t a l o s c i l l a t o r . Similar precautions were used i n evaporating the other metals, except that propyl alcohol was used for cleaning. Y^O^ films 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 highly stressed films that cracked on cooling. 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 studies, the counterelectrode films were made between 100 and 150 A* thick. For other measurements, more durable counterelectrodes of several thousand angstroms thickness were employed. The structures 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 polished s i l i c o n wafers one inch i n diameter, purchased from the Monsanto Company. Yttrium oxide films were evaporated onto the s i l i c o n s l i c e s as before. A layer of antimony doped gold one to two thousand angstroms thick was evaporated onto the unpolished (reverse) side of the wafer. The antimony was driven into 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 + for f i v e minutes. The re s u l t i n g heavily doped n region permitted ohmic contact to be made to the s i l i c o n . 6 m e t a l c o u n t e r e l e c t r o d e 7059 g l a s s s u b s t r a t e F i g . 1 MIM S t r u c t u r e m e t a l c o u n t e r e l e c t r o d e s n t y p e s i l i c o n w a f e r / - "+ AuSb F i g . 2 MIS S t r u c t u r e 7 I I I . ELECTRON MICROSCOPY Of THIN.Y 0 FILMS 1. I n t r o d u c t i o n A p o l y c r y s t a l l i n e m a t e r i a l y i e l d s a r i n g d i f f r a c t i o n p a t t e r n f o r wh i ch i t can be shown t h a t Dd = 2LX, where (1) D = d i f f r a c t i o n r i n g d i a m e t e r Lx E camera c o n s t a n t d B i n t e r p l a n a r s p a c i n g i n c r y s t a l l a t t i c e . B r a g g ' s law f o r d i f f r a c t i o n i s nX = 2d s i n 6, where (2) n E an i n t e g e r 5 1 6 E a n g l e between the i n c i d e n t beam and the c r y s t a l p l a n e . In a c u b i c l a t t i c e , t he i n t e r p l a n a r s p a c i n g d c o r r e s p o n d i n g t o a s e t o f M i l l e r i n d i c e s {hkl} i s d - a i k 1 + k 2 + I 2 < 3 ) o where a i s t he l a t t i c e c o n s t a n t , o Combin ing e q . ( l ) and (3) g i v e s a ^ 2 U ^ D = + k 2 + l 2 » W h i c h ( 4 ) r~2~ 2 2 i s a s t r a i g h t l i n e o f s l o p e a Q / 2 L X when / h + k + 1 i s p l o t t e d a g a i n s t D. Two t e c h n i q u e s were u sed to o b t a i n d i f f r a c t i o n p a t t e r n s : s e l e c t e d a r e a d i f f r a c t i o n and 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 . The s e l e c t e d a r e a method b e g i n s w i t h an image of t h e f i l m . The s e l e c t e d a r e a a p e r t u r e ( l o c a t e d i n t h e o b j e c t i v e l e n s image p l a n e ) d e f i n e s t he a r e a o f the o b j e c t t h a t can be s e e n . In n o r m a l o p e r a t i o n , t he o b j e c t i v e l e n s and i n t e r m e d i a t e l e n s image p l a n e s a r e c o n j u g a t e f o c i , so t h a t an 8 enlarged image of the film is produced. To obtain a diffraction pattern, the focal length of'the intermediate lens is decreased U n t i l 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 distilled 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 f i lm. Fig. « Recrystallized Y 0 f i lm. F i g . 5 Diffraction Structure of Recrystall ized film F i g . 7 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 from Y 0 , on n-type po l i shed s i l i c o n F i g . 8 D i f f r a c t i o n pa t te rn of gold f i l m 11 because of d i f f r a c t i o n by crystals of several orientations stacked v e r t i c a l l y i n the f i l m . When the films were heated with an intense electron beam, they were observed to r e c r y s t a l i z e . An attempt was made to find the r e c r y s t a l l i z a -tion temperature with a heating stage, but nothing W a s observed below 800°C, the thermal l i m i t of the stage. Fig. A shows the structure of a r e c r y s t a l l i -zed f i l m at a magnification of ,X46,O0O. A d i f f r a c t i o n pattern for t h i s f i l m i s shown i n Fig. 5. The pattern was observed to be more d i s t i n c t , probably because of reduced random scattering of electrons from near-amorphous regions. The strong lines have diameters i n the same ra t i o s as i n Fig. 3, but more rings can be resolved. This pattern was photographed using lOOkV as the accelerating p o t e n t i a l , resulting i n larger diameter rings (due to the shorter electron wavelength.) than Fig. 3. After further r e c r y s t a l l i z a t i o n by the beam, the pattern of Fig. 6 was obtained. The continuous d i f f r a c t i o n rings of Fi g . 5 are broken into rings of d i f f r a c t i o n spots because of the smaller number of cry s t a l s i n the path of the beam. Fig . 7 shows a r e f l e c t i o n electron d i f f r a c t i o n pattern for yttrium oxide deposited on polished n-type s i l i c o n . The ring diameters again are i n the same ra t i o s as the brightest rings i n Fig. 5, but the size of the o v e r a l l pattern i s reduced because of the proximity of the specimen and the photo-graphic plate 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 pattern for a thin gold f i l m that was used to determine the camera constant of the electron microscope for the p a r t i c u l a r control.settings used. The value of the camera constant varies with the lens settings, and so the same settings must 1 2 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 accuracy of the f i n a l r e s u l t s depends on the accuracy with which the camera constant i s determined. A gold f i l m was used because the c r y s t a l structure of gold and i t s l a t t i c e constant are w e l l known. 4. Analysis The camera constant of the electron microscope was determined with equation (4) to be LX = 5.82 + 0.02, using the Value of 4.087 £ f o r the l a t t i c e constant of g o l d . ^ Table 1 shows an analysis of the d i f f r a c t i o n pattern of yttrium oxide based on F i g . 5. The^ring diameter r a t i o s were found to be consistent with a simple cubic structure. The r i n g i n t e n s i t i e s were compared to e x i s t i n g data for p o l y c r y s t a l l i n e ^O^ powder and were found to be i n e x c e l l e n t agreement. A few f a i n t rings (consistent with the c r y s t a l structure) were observed i n the electron d i f f r a c t i o n but not i n the X-ray pattern. n ' 2 2 F i g . 9 shows a p l o t of /h + k + 1 vs. r i n g diameter. The r e s u l t i s a s t r a i g h t l i n e passing through the o r i g i n , i n d i c a t i n g a good f i t of the data to the simple cubic structure. From F i g . 9 , the l a t t i c e constant was determined to be a = 10.58 + 0.05 A, o -which i s i n excellent agreement with the value 10.605 +' 0.001 obtained by (4) X-ray d i f f r a c t i o n . The f i r s t four rings of F i g . 3 and F i g . 7 are.analyzed i n Tables 2 and 3. The ring diameters were found to be i n the same r a t i o s and have the same r e l a t i v e i n t e n s i t i e s as the br i g h t ^ r a c t i o n rings of F i g . 5, within experimental erro r . TABLE 1 ELECTRON DIFFRACTION RESULTS R i n g R a t i o X-Ray D i amete r D R D R2 h k l i n t e n s i t y * I n t e n s i t y ( 5 ) (cm) 1.10 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 v f -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 31 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 v f 2 TABLE 1 ( C o n t i n u e d ) D(cm) R R 2 2 2 2 h k l I X-Ray I 6.78 6.17 38,0 38 6 U 532 m 8 6.95 6.33 40.1 40 620 v f 2 7.13 6.48 42.1 42 541 m 8 7.30 6.64 44.1 44 622 b 43 7.46 6.78 4 6 . 0 46 631 m 11 7.62 6.93 48 .0 48 444 m 10 7.78 7.08 50.1 50 550 710 543 f 4 7.93 7.22 52.0 52 640 v f 3 8.08 7.36 54.2 54 633 552 721 m 6 8.23 7.46 55.8 56 642 f 4 * v f v e r y f a i n t f f a i n t m medium b b r i g h t vb v e r y b r i g h t 16 TABLE 2 YgO^ on NaCl. ' , Un re'cry's t a l l i z e d D (cm) R- D 0.707 R 2 2 2 2 h +k +SL P l a n e I n t e n s i t y 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 . 0 5 TABLE 3 Y^O^ On S i l i c o n D D 2 2 2 2 (cm) R= - ,,Q R h +k + £ P l a n e I n t e n s i t y 0 . 4 0 0 1.62 3.46 12.0 12 222 vb 1.90 3.96 , 15.7 16 400 b 2.66 5.66 32 .0 32 440 b 3.12 6.65 44.2 44 622 m ± 0 . 0 5 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 polycrystalline, with a crystal size of the order of 100 A°. Thus, i t can be concluded that the crystal structure of the substrate material has l i t t l e effect 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 is in good agreement with the existing data for bulk Y 2 0 3 . Thus, i t is evident that the metastable reduced oxide Y0 is present in^ only small quantities or not at a l l in the films. The results found are in essential agreement with those of Hass, Ramsey and Thun^, who examined the structure of I^O^ in the course of their work on optical coatings. However, their films were somewhat more amorphous than those studied here, possibly because they did not evaporate in an oxygen ambient. Also, they evaporated from tungsten boats, a lower temperature process than electron gun evaporation. As a result, their structure determination of I^O^ showed a hexagonal l a t t i c e with a c/a ratio of 1.63 instead of the value of 1.56 accepted for the bulk material. No such distor-tions of the crystal l a t t i c e were observed in this work. The unit c e l l of the Y^O^ structure contains 32 yttrium and 48 oxygen i o n s ^ . The structure consists of subunits containing one cation centered within a cube of eight anion sites, of which only six are occupied. Half the cations are in subunits which have the unoccupied anion sites on the face diagonal, the other half have unoccupied sites on a body diagonal. The subunits f i t together so that the unoccupied anion s i t e s form nonintersecting st r i n g s along the <111> d i r e c t i o n s ' o f the c r y s t a l . These s t r i n g s provide pathways along which the d i f f u s i o n of oxygen ions would meet with r e l a t i v e l y l i t t l e resistance. F u l l y one-fourth of the anion s i t e s i n the s u b l a t t i c e are unoccupied, so that a high s o l u b i l i t y of CL i n Y„0„ would be expected. 19 IV. CONDUCTION IN THIN FILMS 1. I n t r o d u c t i o n In t h i n i n s u l a t i n g f i l m s , a v a r i e t y o f mechanisms can be r e s p o n s i b l e f o r c a r r i e r t r a n s p o r t . F o r w ide bandgap m a t e r i a l s (E > 3 e V ) , c o n d u c t i o n i s o f t e n due to the t r a p p i n g and d e t r a p p i n g o f c a r r i e r s . T h i s i s p a r t i c u l a r l y t r u e f o r f i l m s more than a few hundred angs t roms t h i c k . S e m i c o n d u c t o r t h e o r y g i v e s t h e f o l l o w i n g e x p r e s s i o n f o r t h e e l e c t r o n c u r r e n t d e n s i t y i n an i n t r i n s i c i n s u l a t o r : J = aE = neuE = e y / N ^ E e x p ( - E g / 2 k T ) . (1) where E = e l e c t r i c f i e l d J B c u r r e n t d e n s i t y 'a = c o n d u c t i v i t y n H c a r r i e r c o n c e n t r a t i o n • y = c a r r i e r m o b i l i t y E g = 2 ( E p - E c ) = bandgap N ,N = i n s u l a t o r e f f e c t i v e d e n s i t y o f s t a t e s i n c o n d u c t i o n and v a l e n c e C V bands T = a b s o l u t e t e m p e r a t u r e A. 19 - 3 F o r f a v o u r a b l e r o o m - t e m p e r a t u r e v a l u e s o f vN N^ = 3 x 10 cm , 2 6 E = 3eV, y = 100 cm /V s e c , and E = 10 V /cm, t h e c u r r e n t d e n s i t y i s o n l y —18 2 (7) about 10 A/cm , w h i c h i s much l e s s t h a n t h e magn i tude o f the c u r r e n t s n o r m a l l y o b s e r v e d i n t h i n f i l m i n s u l a t o r s . F u r t h e r m o r e , t h e o b s e r v e d a c t i v a t i o n e n e r g i e s f o r c o n d u c t i o n a r e u s u a l l y much s m a l l e r t h a n E / 2 , so s t h a t i n t r i n s i c c o n d u c t i o n cannot be t h e t r a n s p o r t mechani sm. The c o n d u c t i v i t y o f vacuum d e p o s i t e d t h i n f i l m s can b e a t t r i b u t e d to t h e un ique n a t u r e o f such f i l m s . Compounds a r e d i f f i c u l t to e v a p o r a t e s t o i c h i o m e t r i c a l l y becau se o f the d i f f e r i n g e v a p o r a t i o n r a t e s o f t h e c o n s t i -20 t u e n t atoms. O f t e n , i n t he case o f o x i d e s , t h e f i l m s a r e r e d u c e d somewhat. D u r i n g the e v a p o r a t i o n o f ^O^v f i l m s d e p o s i t e d r a p i d l y showed a brown d i s -c o l o r a t i o n t h a t r e s e a r c h e r s on b u l k Y^O^ have a t t r i b u t e d to c o l o r c e n t e r s a s s o c i a t e d w i t h oxygen v a c a n c i e s and t r a p p e d e l e c t r o n s . C o n t a m i n a t i o n w i t h c r u c i b l e m a t e r i a l c o u l d a l s o be a source, o f f i l m d e f e c t s . E v a p o r a t i o n o f t he c r u c i b l e m a t e r i a l many o r d e r s o f magn i tude s l o w e r than the e v a p o r a n t can p r o d u c e s i g n i f i c a n t d e f e c t d e n s i t i e s i n d i e l e c t r i c f i l m s , s i n c e t h e s e m a t e r i a l s have such a s m a l l i n t r i n s i c c a r r i e r c o n c e n t r a t i o n . F i n a l l y , t he amorphous o r near -amorphous n a t u r e o f t h i n e v a p o r a t e d i n s u l a t i n g f i l m s makes i t l i k e l y t h a t a h i g h t r a p d e n s i t y w i l l e x i s t . In vacuum e v a p o r a t e d CdS, 21 3 (9) t r a p p i n g d e n s i t i e s as h i g h as 10 /cm have been r e p o r t e d h i g h d e n s i t y o f t r a p s and a c c e p t o r o r donor c e n t e r s , and hence t h e c o n d u c t i o n p r o p e r t i e s o f t h e s e f i l m s must be s t u d i e d w i t h t h i s d e f e c t s t r u c t u r e i n m i n d . A number o f c o n d u c t i o n mechanisms have been p r o p o s e d f o r i n s u l a t i n g f i l m s betx^een m e t a l c o u n t e r e l e c t r o d e s . The t u n n e l e f f e c t ( f rom m e t a l t o m e t a l ) i s a p o s s i b l e mechanism o n l y f o r i n s u l a t o r s l e s s than 100 A* t h i c k , and w i l l n o t be c o n s i d e r e d h e r e . The S c h o t t k y e f f e c t i s f i e l d enhanced t h e r m i o n i c e m i s s i o n o v e r the b a r r i e r a t a m e t a l - i n s u l a t o r i n t e r f a c e . I f t he b a r r i e r a t t h e i n t e r f a c e i s assumed to be C o u l o m b i c , then t h e image f o r c e b a r r i e r l o w e r i n g f o r an e l e c t r o n has been shown to be T h u s , i t i s l i k e l y t h a t e v a p o r a t e d i n s u l a t i n g f i l m s w i l l have a (2) and t h e c o n d u c t i o n c h a r a c t e r i s t i c i s J = AT exp{-e V 6 s ^ } (3) kT where A = c o n s t a n t ii> = b a r r i e r h e i g h t I t i s u n l i k e l y t h a t t h i s mechanism can a c c o u n t f o r c o n d u c t i o n i n f i l m s w i t h a h i g h d e f e c t d e n s i t y , u n l e s s t h e f i l m s a r e q u i t e t h i n , s i n c e t r a p p i n g and space charge e f f e c t s wou ld be e x p e c t e d to dominate the c o n d u c t i o n p r o c e s s i n t h i c k f i l m s . The P o o l e - F r e n k e l e f f e c t , o r f i e l d - a s s i s t e d t h e r m a l e m i s s i o n o f c a r r i e r s o v e r t h e Cou lomb ic b a r r i e r o f a donor c e n t e r , was f i r s t a p p l i e d by F r e n k e l t o s e m i c o n d u c t o r s . In F i g . 1, t h e p o t e n t i a l w e l l a s s o c i a t e d w i t h a t r a p o f d e p t h E f c i s i l l u s t r a t e d . F i g . 1 The n e x t d i a g r am shows how the p o t e n t i a l i s m o d i f i e d by the p r e s e n c e o f a u n i f o r m e l e c t r i c f i e l d E. The b a r r i e r i s l o w e r e d i n ene r gy by A<j>, w h i c h can be d e t e r m i n e d by f i n d i n g t h e d i s t a n c e f rom t h e c e n t e r o f t h e p o t e n t i a l d i s t r i b u t i o n t o the maximum i n the ene rgy f u n c t i o n . The Coulomb b a r r i e r has t h e p o t e n t i a l X Fig. 2 In the presence of the field E, this becomes 2 E = - eEx (4) Jn 4TTEX The dielectric constant e is the high frequency value, since the electron motion is too rapid for the lattice ions to follow. At x , o dE e^ •~~r~ = 0, so , 2 dx 4irex o - eE = 0, or Xo /4ireE (5) Thus, A<f> is A* ./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 = euNcE exp-{ [ ( E g - B p F ^ ) ]/2kT} = Jo 6 X P ( _2kT- )' (7) Mead (1962) ^ \ in his work on Ta^ O,. thin films, used the equation J = GQE exp{[(B p F^-V)]/kT} (8) to e x p l a i n h i s r e s u l t s . He assumed the c o n d u c t i o n mechanism t o be f i e l d -enhanced t h e r m a l e m i s s i o n from t r a p s o f dep th V i n t h e i n s u l a t o r f o r b i d d e n bandgap. He d e r i v e d (8) by assuming t h a t t h e e x p o n e n t i a l dependence o f J on E was s i m i l a r t o t h a t o f t he S c h o t t k y e f f e c t , e x c e p t t h a t t h e b a r r i e r l o w e r i n g was t w i c e as l a r g e (as can be seen by compar ing (2) and ( 6 ) ) . H i s e q u a t i o n i s s i m i l a r t o F r e n k e l ' s , e x c e p t t h a t the c o e f f i c i e n t o f i s B ™ / kT . Mead ' s Jrr d a t a gave a f i t o f 21 and 27' f o r t h e d i e l e c t r i c c o n s t a n t . T h e s e v a l u e s a r e t oo l a r g e f o r t he h i g h - f r e q u e n c y d i e l e c t r i c c o n s t a n t o f Ta20,.. O t h e r worker s who u sed (8) to e x p l a i n t h e i r r e s u l t s have t y p i c a l l y f ound t h a t v a l u e s o f e about f o u r t imes t oo l a r g e were n e c e s s a r y to f i t t h e i r (12) d a t a . Hartman et a l c o n c l u d e d t h a t (8) d i d no t a d e q u a t e l y f i t t h e d a t a on ^^2^S a n c * f i l m s becau se o f t h e d i f f i c u l t y w i t h t h e p e r m i t t i v i t y . A l t h o u g h t h e S c h o t t k y c o n d u c t i o n e q u a t i o n gave a .much b e t t e r f i t f o r e, i t c o u l d no t e x p l a i n the v a r i a t i o n o f c u r r e n t w i t h f i l m t h i c k n e s s t h a t was o b s e r v e d . (13) Simmons has s u g g e s t e d a t h e o r y o f P o o l e - F r e n k e l e m i s s i o n t o r e s o l v e t h e d i f f i c u l t y . In t h i s t h e o r y , Simmons c o n s i d e r e d an i n s u l a t o r model w i t h deep donor c e n t e r s and s h a l l o w n e u t r a l t r a p s , as i l l u s t r a t e d be low. I f we assume t h a t t he number o f e l e c t r o n s i n t h e c o n d u c t i o n band i s n e g l i g i b l y s m a l l compared to t h e number o f t r a p p e d e l e c t r o n s , t h e n we can equa te t h e number o f e l e c t r o n s m i s s i n g f rom donor c e n t e r s t o t h e number o f * I f e q . (8) i s c o r r e c t , i t wou ld be p o s s i b l e t o d i f f e r e n t i a t e between S c h o t t k y e m i s s i o n ( eq . (3 ) ) and P o o l e - F r e n k e l e m i s s i o n by the d i f f e r e n c e i n s l o p e o f . t he l o g T v s . v^ E p l o t s . The P o o l e - F r e n k e l s l o p e wou ld be t w i c e t h e S c h o t t k y s l o p e . F i g . 3 o c c u p i e d t r a p s , f o r E - E >> kT and E „ - E_ >> k T : r 1J I r N D e x p { - ( E F - E D ) / k T } = e x p { - ( E ^ E p ) / k T > (9) where = e f f e c t i v e donor d e n s i t y o f s t a t e s N ,^ = e f f e c t i v e t r a p d e n s i t y o f s t a t e s . S o l u t i o n o f (9) f o r the Fe rm i ene r gy g i v e s E F = i ( E D + V + \ k T ln<VV <10> T h u s , at z e r o f i e l d , the number o f f r e e e l e c t r o n s i s n = N c e x p - { [ E c - E F ] / k T } = N c % / N T e x p - { [ 2 E c - ( E T + E D ) ] / 2 k T } (11) and the z e r o f i e l d c o n d u c t i v i t y i s a = neu o = eyN /N /N exp{ [2E - ( E +E ) ] / 2 k T } ( 1 2 ) c D 1 c ID When an e l e c t r i c f i e l d i s a p p l i e d , the donor e n e r g y b a r r i e r E c ~ E D i s l owered by the P o o l e - F r e n k e l v a l u e . Because the t r a p s a r e assumed to be n e u t r a l , t h e i r ene r gy b a r r i e r i s n o t a f f e c t e d , so t h a t t he number o f f r e e e l e c t r o n s i n the c o n d u c t i o n band i s n = N c v / N D / N T e x p { t ( E c - E T ) + ( E c - E D ) - 3 p F v a T ) ] / 2 k T } (13) Hence, a = a Q exp (B p F v T T /2kT) . (14) We see t h a t t he c o n d u c t i v i t y v a r i e s w i t h the f i e l d i n a manner n o r m a l l y a s s o c i a t e d w i t h the S c h o t t k y e f f e c t at a n e u t r a l b a r r i e r . The c u r r e n t i s J » aE = a E exp{BT3„vaY/2kT} (15) O r r S t u a r t ^ ^ and H i l l et a l ^ ^ have explained their conduction data on SiO with equation (15). The f i t for e was found to be good in the high-field region of conductivity. There are several d i f f i c u l t i e s with Simmons' theory. First, the calculation of the electron concentration using the Fermi level requires that the insulator be in equilibrium. Poole-Frenkel emission, however, is a non-equilibrium effect, and so the methods used to derive (15) are somewhat contradictory. It is also unrealistic to assume that the trap energy barrier w i l l remain unaffected by the presence of an electric f i e l d . The barrier height for emission from traps is smaller than that for emission from donors in Simmons' model, and the trap barrier 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 activation 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 level and the insulator conduction band is 3eV or more (the bandgap is 6-8eV). The Poole-Frenkel barrier lowering for E = 10^V/cm (near break-down), and e f = 3 i s only 0.44 eV. This amount of barrier lowering is not nearly large enough to allow a significant number of donors below the Fermi energy to be ionized at room temperature. The activation energies usually observed for Poole-Frenkel currents are about 0.5 eV. Stuart found 0.4 eV fitt e d the results for SiO, and 0.6 eV was found for Y2^3 fil™ 8 . Thus, Simmons' theory suggests higher activation energies than are found in practise. An e q u a t i o n t h a t g i v e s b e t t e r r e s u l t s can be f ound by c o n s i d e r i n g t h e methods o f F r e n k e l ' s o r i g i n a l p a p e r . C o n s i d e r an i n s u l a t o r w i t h s h a l l o w donors t h a t a r e n o r m a l l y f i l l e d w i t h e l e c t r o n s at room t e m p e r a t u r e . I f i s the t o t a l number o f donors and n^ t h e number o f o c c u p i e d donor s we can d e f i n e an occupancy f a c t o r by The r a t e o f r e l e a s e o f e l e c t r o n s f rom donor s i n t h e p r e s e n c e o f a f i e l d (assuming P o o l e - F r e n k e l b a r r i e r l o w e r i n g ) w i l l be R = f N D v e x p - { [ ( E c - E D ) - 3 p F v ^ E ] / k T } (17) where v = v i b r a t i o n f r e q u e n c y of t r a p p e d e l e c t r o n s . The r a t e o f c a p t u r e o f e l e c t r o n s w i l l be c = (1 ~ - f ) N J s / e , where (18) J = c u r r e n t d e n s i t y s E c a p t u r e c r o s s - s e c t i o n o f empty d o n o r s . F o r s h a l l o w d o n o r s , we wou ld e x p e c t t h e occupancy f a c t o r f t o be f i e l d - d e p e n d e n t . In e q u i l i b r i u m , t h e r a t e s o f e l e c t r o n c a p t u r e and r e l e a s e a r e e q u a l , so t h a t ^ = ev e x p - { [ ( E c - E D ) - e p p v ^ ] } / J s (19) I f we assume t h a t t h e number o f e l e c t r o n s r e l e a s e d f r om donor s by t h e f i e l d i s s m a l l , t h e n f 1, and the c u r r e n t i s g i v e n by J = neuE = ( l - f ) N eyE 2 • N e uEv = e x p - { t ( E c - E D ) - 6 p F / E " ] / k T } (20) S o l v i n g f o r t h e c u r r e n t g i v e s H V E e x p - { [ ( E - E j - B ^ ^ E j ^ k T } (21) s ^ c D " PF .27 This equation i s s i m i l a r to Simmons', and i t gives the same slope on a log J vs. plot as the Schottky conduction law. The pre-exponential v a r i a t i o n with the f i e l d i s v^E rather than E. This i s unimportant at high f i e l d s , where the exponential term dominates. 2. Experimental Procedures The D.C. conduction cha r a c t e r i s t i c s were measured with a Keithley 417 high-speed picoammeter i n series with a variable voltage supply.. Shielded cables were used to minimize transients. 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 characteristics were found to d r i f t over a period of time, probably because of step response effects i n the d i e l e c t r i c material. I t was found necessary to wait for anywhere between a few minutes to an hour (depending on the applied V o l t a g e ) for the conduction to approach i t s l i m i t i n g value to within a few percent. Space charge effects or i o n i c currents are also a possible explanation of the observed d r i f t . 3. Experimental Results The thi n Y^O^ films were found to have bulk-limited conduction characteristics roughly s i m i l a r to those found for SiO films by Stuart. In Fig. 4, log I i s plotted against vA/ for three di f f e r e n t thicknesses of f i l m . The plots 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 films 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 with temperature i s plotted. . Higher currents were observed at higher temperatures. - 6 . 0 0 S O R T I V / V O L T ) Fig. 5 Log I vs. V 1^ 2 for Different Temperatures(d = 4680A°.) 0.60-1 104 3/TCDEG. KELVINJ Fig. 6 8 1 F i g . 6 shows a p l o t o f (— ) / (2.303 kT) v s . d e r i v e d . f r o m F i g . 5. A f i t f o r 3 i n t he e q u a t i o n 1 • h ex»-{2#' (22) was made w i t h F i g . 6, and the r e l a t i v e p e r m i t t i v i t y o f t he f i l m was f ound u s i n g 3 3 < 2 3> T T E d o The f i l m t h i c k n e s s was measured to be 4680 + 200 A on t h e S l o a n M100 A n g s t r o m e t e r . The d i e l e c t r i c c o n s t a n t was found t o be e r = 3.2 + 0.2 (24) The r e f r a c t i v e i n d e x o f a Y 2 ^ 3 o n s i l i c o n was d e t e r m i n e d by e l l i p s o m e t r y a t a w a v e l e n g t h o f 6328 A ° to be n = 1.75 + 0.01 (25) T h i s r e s u l t was f o u n d by s o l v i n g the e l l i p s o m e t r y . equa t i on on t h e U .B .G . IBM 360 computer w i t h i t e r a t i v e methods . T h i s g i v e s the. p e r m i t t i v i t y 2 e r = n = 3 .05 , wh i ch i s i n good agreement w i t h the V a l u e o f t h e p e r m i t t i v i t y f ound f rom the c o n d u c t i o n measurements . The e f f e c t o f p o l a r i t y r e v e r s a l on t h e c o n d u c t i o n measurements i s i l l u s t r a t e d i n F i g . 7 f o r a f i l m w i t h g o l d and i n d i u m c o u n t e r e l e c t r o d e s . These m e t a l s were s e l e c t e d b e c a u s e o f t h e i r l a r g e work f u n c t i o n d i f f e r e n c e . The f o r w a r d and r e v e r s e 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 were f ound t o be v i r t u a l l y i d e n t i c a l . Thu s , t h e c o n d u c t i v i t y o f ^ O ^ i s b u l k - l i m i t e d r a t h e r than e m i s s i o n l i m i t e d . The v e r y s l i g h t asymmetry i n c o n d u c t i v i t y o b s e r v e d i s p r o b a b l y due to an i n t e r n a l f i e l d i n t h e o x i d e , as Xtfould be e x p e c t e d f o r c o n t a c t s w i t h d i f f e r e n t work f u n c t i o n s . -8.00-, -.9.00 -a. tx u -10.00 o -11.00--12.00 0.0025 T r T~ R T r 0.0030 3/TtDEG. KELVINJ Fig. 8 D e t e r m i n a t i o n o f A c t i v a t i o n E n e r g y T 1 0.0035 34 The activation energy of the conduction process was found to be independent of temperature, as can be seen from the straight line plot of log I vs. — shown in Fig. 8. The activation energy was found to be 0.58 + 0.05eV. The low pressure D.C. conduction characteristics are plotted for different temperatures in Fig. 9. The pressure was about 50uHg. The film 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. Fig. 10 shows a plot of (3/2)/(2.303kT) based on the slopes of Fig. 9. The value of the relative permittivity that was found to f i t the conduction characteristics was E = 11.2 + 0.7, or roughly four times the high-pressure value. The activation energy was found from Fig. LV to be 0.63 + 0.05eV, almost the same as the high-pressure value. Fig. 12 gives the D.C. conduction of three different counterelectrodes on the same Y^O^ film. The reproducibility i s seen to be f a i r l y good. The variation observed can be attributed to thickness variations in the thin film. 4. Discussion The conduction characteristics of thin Y^O^ films were found to f i t equation (21) quite well. The non-linearity observed at low fields i s similar to that reported by Kartman et a l ^ (1966) and S t u a r t ^ (1967) for SiO films. The conductivity in this region is believed to be partly bulk-limited and p a r t l y ohmic. This view is supported by the fact that the current for a l l three thicknesses begins to approach the same limiting value at low applied 5 voltages. In the high-field region where E a p p i i e ( 3 ^ 1° volts/cm, the 35 -12.00H - 1 3 . 0 0 T — i — r 3.00 ' I 1 ' 4.00 i—|—i—i—I—i—|—i—i—i—i—I—i—i—i—i—I—r 5.00 6.00 7.00 a.00 SQRTIV/VOLT) T 1 1 | 1 I 1 1 1 9.00 10.00 Fig. 9 D.C. Conduction at Low Pressure (P=50u) 0.40 - i 1/TlOEG. KELVIN) Fig. 1 0 37 -n.oo-i 31 -lO.OO-i 00 SQRTlV/VOLT) Fig. 12 R e p r o d u c i b i l i t y o f D.C. C o n d u c t i o n C u r r e n t (P=50uHg) P o o l e - F r e n k e l e m i s s i o n p r o c e s s d o m i n a t e s . The p o s s i b i l i t y o f i o n i c , c o n d u c t i o n was c o n s i d e r e d . However, t he movement o f d i f f e r e n t i o n s t h rough wou ld be e x p e c t e d t o g i v e d i f f e r e n t c u r r e n t s a t t he same p o t e n t i a l . F i g . 7 showed t h a t t he e l e c t r o d e m e t a l had l i t t l e e f f e c t on the c o n d u c t i o n p r o c e s s , so i o n i c c o n d u c t i o n i s u n l i k e l y . F i g . 7 a l s o e l i m i n a t e s S c h o t t k y e m i s s i o n as a p o s s i b l e c o n d u c t i o n mechanism, s i n c e the d i f f e r e n t b a r r i e r h e i g h t s at t he two m e t a l - i n s u l a t o r i n t e r f a c e s wou ld g i v e d i f f e r e n t c u r r e n t s f o r S c h o t t k y c o n d u c t i o n , and t h i s was n o t o b s e r v e d . The most l i k e l y mechanism i s P o o l e - F r e n k e l e m i s s i o n o f e l e c t r o n s i n t o the v a l e n c e band f rom donor c e n t e r s 0 .6eV be l ow the i n s u l a t o r c o n d u c t i o n b a n d . A f a i r l y h i g h c o n c e n t r a t i o n o f oxygen v a c a n c i e s o r y t t r i u m i n t e r s t i t i a l s i s p o s s i b l e , even though the f i l m s were e v a p o r a t e d i n an oxygen a m b i e n t . B a k i n g the f i l m s r e d u c e d the d i e l e c t r i c l o s s e s , p r o b a b l y by t h e f i l l i n g o f v a c a n c i e s by d i f f u s i o n o f oxygen t h r o u g h the f i l m s . Hass e t a l ^ f o u n d , i n t he c o u r s e o f t h e i r work on o p t i c a l p r o p e r t i e s o f r a r e e a r t h f i l m s , t h a t o n l y f i l m s d e p o s i t e d on a h e a t e d s u b s t r a t e d i d no t change p r o p e r t i e s on s u b -sequent b a k i n g . They a t t r i b u t e d t h i s t o r e d u c t i o n o f t h e o x i d e d u r i n g e v a p o r a -t i o n on to c o l d s u b s t r a t e s (as were u s e d i n t h i s w o r k ) . They f o u n d t h a t b a k i n g r e d u c e d the o p t i c a l a b s o r p t i o n c o e f f i c i e n t , b u t no t t o t h e v a l u e o b t a i n e d f o r f i l m s d e p o s i t e d on h e a t e d s u b s t r a t e s . T h u s , b o t h y t t r i u m i n t e r s t i t i a l s ( u n a f f e c t e d by b a k i n g ) and oxygen V a c a n c i e s ( p a r t l y f i l l e d by b a k i n g ) a r e p r o b a b l y p r e s e n t i n t h e p a r t i a l l y r e d u c e d c o o l - s u b s t r a t e f i l m s . The s l o w d r i f t i n t h e f i l m p r o p e r t i e s w i t h t ime o b s e r v e d f o r e l e c t r o n beam e v a p o r a t e d ^2^2 £ ^ m s c a n a^-s0 be e x p l a i n e d by t h e s l ow f i l l i n g o f v a c a n c i e s w i t h oxygen atoms. C o n t a m i n a t i o n by c r u i c i b l e m a t e r i a l i s an u n l i k e l y s o u r c e o f d o n o r s . The b o r o n n i t r i d e c r u c i b l e was h e l d i n a w a t e r - c o o l e d b l o c k and hence was unab le t o r e a c h the v e r y h i g h t e m p e r a t u r e s n e c e s s a r y f o r e v a p o r a t i o n . S u b s t a n t i a l c o n t a m i n a t i o n w i t h s u b s t r a t e m a t e r i a l i s a l s o u n l i k e l y , s i n c e t h e s e were C o r n i n g 7059 a l u m i n o s i l i c a t e g l a s s , w h i c h has a low c o n c e n t r a t i o n o f m o b i l e a l k a l i i o n s . The p r e s s u r e dependence o f 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 i s no t e a s i l y u n d e r s t o o d . B e r a r d et a l , i n t h e i r work on oxygen d i f f u s i o n i n s i n g l e c r y s t a l r a r e e a r t h s e s q u i o x i d e s found t h a t ^2^2 ^ a s 3 ^ i g h o x y § e n d i f f u s i v i t y —6 2 ^ (6.06 x 10 cm / s e c ) and a low a c t i v a t i o n energy ( 0 . 8 5 e V ) . They e x p l a i n e d t h e s e r e s u l t s by a m i g r a t i o n mechanism b a s e d on t h e i n h e r e n t l y d e f e c t i v e n a t u r e o f the a n i o n s u b l a t t i c e o f t h e s e m a t e r i a l s . As d i s c u s s e d i n C h a p t e r I I , pathways e x i s t i n t he Y^O^ c r y s t a l s t r u c t u r e a l o n g wh i ch oxygen i o n s can m i g r a t e r e a d i l y . The u n u s u a l l y open a n i o n s u b l a t t i c e p r o v i d e s ample s i t e s f o r t h e s o l u t i o n o f i n t e r s t i t i a l oxygen . In d e t e r m i n i n g t h e d i f f u s i o n c o n s t a n t o f oxygen i n ^2^3' G e r a r d assumed f u l l s o l u b i l i t y o f oxygen i n t he c r y s t a l l a t t i c e , s i n c e no d a t a were a v a i l a b l e on the s o l u b i l i t y o f oxygen i n Y^O^. The d i f f u s i o n c o n s t a n t c o u l d be s e v e r a l o r d e r s o f m a gn i tude h i g h e r , and i n p o l y c r s t a l l i n e e v a p o r a t e d f i l m s , t he p o r o s i t y wou ld make d i f f u s i o n even e a s i e r . Assuming B e r a r d ' s w o r s t - c a s e V a l u e s g i v e s t h e f o l l o w i n g r e s u l t s f o r d i f f u s i o n f o r 1000 seconds at room t e m p e r a t u r e : » = D o e x p ( - £ ) ~10 -19 * Measured at a t e m p e r a t u r e o f 1200 C. However, i f Berard's diffusion constant is too low by two orders of magnitude (as he indicated to be possible) and the average activation energy in the thin films is 0.6eV rather than 0.85eV, the diffusion distance becomes x /-v/ Jt> x lO-"*"^ xlO^ cm = 7700 A, or more than the film thickness. Thus, oxygen diffusion cannot be eliminated as a possible cause of the reduced conductivity at lower pressures. Tallan and Vest , in their high temperature (1400-1800 C) measurement of the conductivity of bulk polycrystalline Y^O^ found that the material was an amphoteric semiconductor. The region of predominant hole conduction had the conductivity a = 1.3 x 10 3 P Q 2 3 / 1 6 exp(-1.94/kT) (26) They explained their results by assuming the presence of fu l l y ionized Y vacancies. In the films studied here, the trap density for holes is probably too great for hole conduction to occur. Also, yttrium i n t e r s t i t i a l s are more li k e l y to be present than yttrium vacancies. They did observe a strong dependence of a on the oxygen partial pressure, as observed in this 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 interaction of yttrium i n t e r s t i t i a l s , oxygen vacancies and dissolved oxygen atoms. Reducing the oxygen partial pressure would reduce the number of oxygen atoms in solution and increase the number of oxygen V a c a n c i e s , and this may be the cause of the conductivity change with p r e s s u r e . The presence of more oxygen vacancies, which act as deep electron t r a p s , w o u l d r e d u c e t h e number o f e l e c t r o n s i n t he donor l e v e l s a v a i l a b l e f o r P o o l e - F r e n k e l e m i s s i o n . I f oxygen v a c a n c i e s and y t t r i u m i n t e r s t i t i a l s a re c l o s e l y a s s o c i a t e d as n e u t r a l d e f e c t pairs> the p r e s e n c e o f deep t r a p s (oxygen v a c a n c i e s ) wou ld r e d u c e t h e number o f donor s a v a i l a b l e f o r e m i s s i o n f rom to n D = N D - N T (27 Then e q u a t i o n ( 21) wou ld be m o d i f i e d to The empty donors p r o d u c e d by N v a c a n c i e s wou ld no t a c t as t r a p p i n g c e n t e r s arguments l e a d i n g to e q u a t i o n (21) a r e s t i l l v a l i d . E q u a t i o n (28) does p r e d i c t a l o w e r c o n d u c t i v i t y a t r e d u c e d oxygen p a r t i a l p r e s s u r e s , a s suming s u f f i c i e n t l y r a p i d oxygen d i f f u s i o n . However, (28) does no t e x p l a i n t h e h i g h v a l u e o f t h e p e r m i t t i v i t y found a t low p r e s s u r e s f rom the c o n d u c t i o n d a t a (11.7 v s . 3.2 at a t m o s p h e r i c p r e s s u r e ) . I t i s l i k e l y t h a t t he r e d u c e d c o n c e n t r a t i o n o f oxygen atoms and the i n c r e a s e d oxygen Vacancy c o n c e n t r a t i o n at low p r e s s u r e caused some change i n t h e r e f r a c t i v e i n d e x o f t he o x i d e , b u t a change o f t h e magn i tude o b s e r v e d seems d o u b t f u l . The Y^O^ f i l m s were found to have 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 q u i t e s i m i l a r t o t h o s e o f S iO t h i n f i l m s B o t h have b u l k - l i m i t e d 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 a t f i t t h e e q u a t i o n (28) b e c a u s e o f t h e i r c l o s e a s s o c i a t i o n w i t h oxygen v a c a n c i e s \ so t h a t t h e 1 2kT ' ) A c ompar i s on i s made i n t h e f o l l o w i n g t a b l e : TABLE 1 Activation _ I at E = MATERIAL Energy n , ..5 t,, ' O J 3x10 V/cm. W SiO 0.4eV 3.6 10~5 amps. Y 20 3 0.6eV 3.05 10~8 amps. Y^O^ has much smaller conduction currents at the same electric f i e l d . The higher activation energy and different doping levels are l i k e l y the cause of this 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 ' C W) = C~1{/°°(j)(t)cosa)t dt + C } (1) a ° o e"Cw) = C~1{/D<t>(t)sinu)t dt + Guf1}, ( 2 ) a o where C 5 capacitance with vacuum between the capacitor plates, cl C =• capacitance at high frequencies, G = steady-state D.C. Conductivity, and co = angular 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 m a (19) holds for many materials at a fixed temperature . Use of this expression in ( 2 ) yields, after a contour integration convergent for 2 > m > 0 , cos ( m T r / 2 ) ] + G/CJC , ( 3 ) a * For materials with a Cole-Cole distribution of relaxation energies, *The Cole-Cole distribution function has the form ( 2 0 ) T./ \ J 1 sin aTr , . - F(s)ds = — r—7- r ds, 2TT cosn (l-a)s-cos arr where a and a are constants. The distribution.is similar to the Gaussian distribution, but i t is less peaked. Many materials have a Cole-Cole distribution of relaxation times. the permittivity has been determined to be e = e ' - j e " - e+' { t e ^ O / U ^ ^ ) " 1 } CO .C" Here the high-frequency dielectric constant is - yj— , E q is the static a dielectric constant, T is the most probable relaxation time and n = 1 - a, ' o r where a is a factor determining the distribution width. Both n and a V a r y between 0 and 1. The reversible transient current <f>(t) flowing at a time t after a step in voltage can be found by taking the inverse Fourier transform of (1) and (2) giving <t>(t) = ~ TeCjw) exp(ju)t)dw (5) ir o On substitution of (4) into (5), expanding in a series and integrating, two limiting cases arise: > ( t ) = [te -e ) / T ] [ l / r ( n ) ] ( t / T )-<l-n) (6) O 0 0 o o for t<<x , and o + ( t ) = [ C e 0 - e , ) / T 0 J [ n / r a - n ) 3 ( ^ - ) " ( 1 + n ) (7) o for t>>t,where x is a characteristic time. Hence, for a given material the o o 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 o,and a slope o f s 2 = -Cl+n) = -(2-a) (9) at times very long compared to T o . At times near T q , the curve bends over. This i s the dispersion region where a peak in e"occurs. The dielectric loss factor for a Cole-Cole distribution has been found for the two l i m i t i n g cases to be e"Cu) - (e -eJCiot ) nsin(nTr/2) (10) o *° o for (urr )<<1, and o £ " ( U ) = (c -e ) ( ( 0 T j ' n s i n ( n f f / 2 ) (11) O 0 0 0 at high frequencies where tox » 1 . 2. Experimental Procedures Step response measurements were carried out with the same c i r c u i t used for conduction measurements, except for the addition of a switch. Currents were measured with the Keithley 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 for the current ranges used. Capacitance and loss measurements were made with 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 Typical results for charging and discharging currents are shown i n o the double log plots of Fig. 1 and 2 for an yttrium oxide f i l m 1250 + 50 A thick. The counterelectrode metals were aluminum and indium. The two plots are very s i m i l a r for the same voltage step, except that the D.C. conduction current eventually dominates the charging c h a r a c t e r i s t i c . In F i g . 3, a plot i s made of l o g ( l / I Q ) against log(t/,x o) f o r d i s -charge currents after a voltage step of 3 v o l t s . I and T q are the current and time at the point where the 3 Volt curve i n F i g . 2 bends over. From Fig. 3 the slopes determined i n the two regions are -8.00-1 -9.00H 10.D0H l l . D O H 12.00- T r T — 1 r 1.00 T 1 f— 1 1 1 1 1 r~ 1 1 1 1 2.00 3.00 4.00 LOG IT/SEC) Fig. 1 kl-Y^O^-Al Step Response Charging Current V o l t s T 1 T 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1.00 2.00 3.00 4.00 L0GU7SECJ Fig. 2 kl-Y^O^-kl S t ep Response D i s c h a r g i n g C u r r e n t 0.014-1 0.012H 0.030H o.ooaH 0.006H 0.004H 0.002H -0.000-10 11 u IIIHIIUM niiuiimiii i 11111IIIIHIII IIIIM'III'H ' ' ' ' | ' " l " H " l ' W i 1 " I ' " I ' l ' V l M ' l i 2 3 4 6 1 2 3 4 6 10 2 3 4 6 . 10 2 3 4 6 30 FREQUENCY IKHZ J Fig. 4 . Dielectric Losses vs. Frequency 52 s, = -0.49 + 0.03 for t«f 1 - o and s 2 = -1.49 + 0.03 for t > > T O < Use of equations (8) and (9) gives an average value for n of 0.50 + 0.03. The ch a r a c t e r i s t i c time t was 200 seconds. Use of the following parameters i n equation (11) gives the v a r i a t i o n of the high-frequency d i e l e c t r i c loss with frequency: * em = 3 .'05 + 0.02 (opt real-measurements) e Q = 12.4 + 1.0 (capacitance measurements) n = 0.50 + 0.03 e"(f) + 10%. (12) r r -3.2 Loss Factor The d i e l e c t r i c loss factor for a Y ^ f i l m 1950 + 80 1 thick with indium and aluminum counterelectrodes i s shown i n Fig. 4. This result i s si m i l a r to that found by C a m p b e l l ^ for ^ O^ fi l m s , although the magnitude of his dissipation factor was somewhat smaller at low frequencies. 4. Discussion The agreement between the loss factor calculated from step response measurements and that determined by bridge methods was only approximate. This suggests that two different loss mechanisms are operative. The mechanism responsible for 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 relaxation energies. An estimate of the most probable relaxation energy can be made using T = v*"1 exp(E /kT) (13) o p where T Q E most probable relaxation time v s atomic v i b r a t i o n frequency Ep = most probable relaxation energy. A reasonable estimate for 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 with the di f f u s i o n results of Berard et a l (1968) who found an activation energy of 0.85 eV for 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 activation energies i s quite good. Thus, the loss peak may be due to the relaxation of oxygen atoms dissolved i n the Y^O^ l a t t i c e . Campbell (1970) found a strong dependence of d i e l e c t r i c losses on temperature i n his ^O^ films. He f e l t that t h i s dependence was i n d i c a t i v e of an activation energy process, but for 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 activation energies. The proposed loss mechanism i s i n agreement with these conclusions. At higher frequencies, the losses were independent of frequency, indicating that a different loss mechanism i s dominant. This view i s support by the poor agreement between the measured values of e" and the calculated values predicted by the theory i n the introduction 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 diff e r e n t substrates or some small difference i n evaporation technique. 54 •VI. BARRIER HEIGHT DETERMINATION BY INTERNAL PHOTOEMISSION 1. I n t r o d u c t i o n I n t e r n a l p h o t o e m i s s i o n i s t h e e m i s s i o n o f p h o t o e x c i t e d c a r r i e r s o v e r the energy b a r r i e r a t t he i n t e r f a c e between a m e t a l ( o r s e m i c o n d u c t o r ) and an i n s u l a t o r . From p h o t o c u r r e n t measurements as a f u n c t i o n o f t h e w a v e l e n g t h o f i n c i d e n t l i g h t , t h e energy b a r r i e r h e i g h t may be d e t e r m i n e d . (21) F o w l e r has g i v e n ah a p p r o x i m a t e c l a s s i c a l t r e a t m e n t o f t he p h o t o -e l e c t r i c e f f e c t (.emission of e l e c t r o n s f rom a m e t a l i n t o Vacuum) . The e x a c t (22) quantum m e c h a n i c a l t h e o r y i s g i v e n by M i t c h e l l . F o r t h e p u r p o s e s o f t h i s work , t h e two t r e a t m e n t s g i v e e s s e n t i a l l y i d e n t i c a l r e s u l t s , so t h e s i m p l e r t h e o r y o f F o w l e r w i l l be r e f e r r e d t o . C o n s i d e r t he s i m p l i f i e d ene r gy band s t r u c t u r e o f a m e t a l - i n s u l a t o r -m e t a l d i o d e shown i n F i g . 1. 4> E c • * \ / \ ^ hv M e t a l M e t a l 1 i n s u l a t o r 2 F i g . 1 The e f f e c t i v e work f u n c t i o n $ i s the d i f f e r e n c e i n e n e r g y be tween t h e F e r m i l e v e l and t h e i n s u l a t o r c o n d u c t i o n b a n d . E l e c t r o d e 2 i s v e r y t h i n . and hence s e m i - t r a n s p a r e n t . F o r an e l e c t r o n to be e x c i t e d f r o m m e t a l 1 i n t o t h e i n s u l a t o r c o n d u c t i o n band by an i n c i d e n t p h o t o n o f energy h v , t h e c o n d i t i o n hv + E > <j) (1) must be met . E i s t h e i n i t i a l k i n e t i c e n e r g y o f t h e e l e c t r o n . The l o w e s t 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 <}>.  In a first approximation, the other velocity components may be neglected. 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 will be absorbed by the electron velocity component normal to the metal surface, and the probability that the electron will 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 2T 2 , x e 2 x , e 3 x ,,«. R- o ' {e 9— + — 0 - ...} (4) for x = ( * g % * 0, and 2„2 2 2 ~2x - 3 x 4Trmk T • ,Tf , -x e , e , \ /t-s for x 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 is I = C(hv - <j>)2 (6) Monochromator C a l i b r a t i o n Curve ( D e u t e r i u m S o u r c e ) where C is a constant. A plot of the square root of the current against the photon energy hv w i l l give a straight line for large values of x. In the presence of att electric f i e l d , the barrier height w i l l be lowered by because of the Schottky effect. 2. Experimental Procedures The photocurrents were measured with the circuit shown below. motor c h o p p e r spec imen D r i v e w £ ? e l jj-j Monochromator C h a r t r e c o r d e r 417 p i coammeter L o c k - i n A m p l i f i e r EXT Photodiode Light from the Bausch and Lomb precision 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 in i t s most sensitive range. The currents developed in the specimen were detected by the Keithley 417 picocammeter, amplified in the Princeton HR-8 lock-in amplifier and plotted on a Moseley Chart recorder. The lock-in amplifier was used in the selective external mode, with the. external signal"'being, derived . from the output of a photodiode in the path of the chopped light. This method of detection was found superior to the D.C. method because errors due to slow transient currents in the dielectric film were eliminated, as were some of the noise problems associated with measuring currents of less 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 in 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. A typical run took 45 minutes. The slow scan rate eliminated slow transient effects from the data. The.monochromator entrance and exit slits 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 in 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 tn s 200.00 loo.ooH 0 —I if i » — i — I — r 2000.00 3000.00 5000.00 ' ' 6000. WAVELENGTH IRNGSTRQHS) T — i — | — r 4000.00 i— 00 Fig. 3 Monochromator Intensity Calibration (Visible Range) 7.00-j 00 WAVELENGTH IflNGSTRCMSJ F i g . 4 Monochromator C a l i b r a t i o n (2000-5000 A ° ) Y^O^ photo-emission is shown in Fig. 4, which shows the incident photon flux. Fig. 5 shows the photoresponse of an aluminum-yttrium oxide-aluminum M1M structure. The insulating film was measured to be 880"^°^ with the Sloan M-100 Angstrometer. The aluminum counterelectrode was o about 100 A thick and had a transmission coefficient of 0.04 for white light. The response .was observed to f i r s t go negative, then positive with increasing v. Since no potential was applied across the insulating film, 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 = c2(hv-<f>2)2 - c1(hv-<f>1)2 (8) where the constants c^ and, c 2 are different because the light intensities are different in the two metal films. If <t>2 >~4>^i then for hv < Q^* c 2 = 0; similarly, for hv < <}>, c^ = 0 also. For cf>^  < hv < <f>2> /|R| = »^(hv-(j,l) (9) The f i r s t points in the negative portion of Fig. 5 were plotted in Fig. 6 to give /J~. The barrier height was found to be = 3.14 +0.06eV. (10) The positive current / l j = /cj(hv-<f>2) (11) was found using equation (8) and the result plotted in Fig. (6). The work function <j>2 was found to be <t>2 = 3.72 + 0.07 eV. (12) The electric f i e l d in the insulator i s E = *2-*l W = (6.7 + 2.2) x 10 volts/cm. The Schottky barrier lowering i s A<}> = 0.0056 + 0.00015 eV, which is much smaller than the errors in <fi and <j) , so i t may be neglected. 4. Discussion The barrier determined for ^ O^ was found to have the following shape: tj> =3.14 eV <J>2 = 3.72 eV hv Fig. 7 A simple explanation of the observed currents can be given. For c j ^ < hv < <j»2» only ^ flows in the insulator. Because the intensity of light in metal (1) is low, and because is attenuated by the electric f i e l d in the insulator, the current observed is small. When hv > ty^* both and flow, but J 2 rapidly becomes dominant because i t i s .assisted by the in t r i n s i c f i e l d and the intensity of light in metal (2) is large. In the region hv or hv-v^,' a curvature i s observed in the Fowler plot. This is due to the spread in the occupation probability of electron energy states near the Fermi level because the temperature is greater than absolute zero. A more e x a c t model wou ld t a k e o t h e r f a c t o r s i n t o a c c o u n t . When hv > <j>, t h e e l e c t r o n s w i l l be i n j e c t e d i n t o t h e o x i d e w i t h t h e ene r gy P 2 E = — + hv - <(>, where P 2 2^ was t h e i n i t i a l e l e c t r o n k i n e t i c energy w i t h a momentum no rma l t o t h e m e t a l s u r f a c e . The o t h e r components o f momentum have been n e g l e c t e d , as .was done i n . F o w l e r ' s d e r i v a t i o n . When h v -(j>--is s u f f i c i e n t l y l a r g e , t h e e l e c t r o n s i n j e c t e d w i l l be ho t e l e c t r o n s , w h i c h have d i f f e r e n t t r a n s p o r t p r o p e r t i e s t h a n t h e r m a l e l e c t r o n s . The i n t e r f e r e n c e o f l i g h t between 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 a c c o u n t , as i t a f f e c t s t h e i n t e n s i t y o f l i g h t i n t he m e t a l f i l m s . The a b s o r p t i o n o f l i g h t by t h e m e t a l f i l m s must a l s o be c o n s i d e r e d . The e f f e c t s o f s c a t t e r i n g j u s t i n s i d e the i n s u l a t o r pay a l s o be s i g n i f i c a n t Some o f t h e i n j e c t e d e l e c t r o n s w i l l s i m p l y be s c a t t e r e d back i n t o the m e t a l . Some o f t h e s e f a c t o r s have been c o n s i d e r e d by a number o f r e s e a r c h e r s ( 2 5 , 2 6 , 2 7 , 2 8 ) ^ n Q c o m p r e h e n s i v e mode l has y e t been d e v e l o p e d . C 2 c 27) The most p r o m i s i n g r e s u l t s have been o b t a i n e d w i t h Monte C a r l o c a l c u l a t i o n s o f i n t e r n a l p h o t o e m i s s i o n y i e l d s , w h i c h gave a good f i t t o e x p e r i m e n t a l d a t a On A l - A ^ O ^ - A l . • The d a t a o b t a i n e d f o r ^ O ^ appear t o f i t t h e s i m p l e mode l w e l l , b u t t he f a i r l y l a r g e e x p e r i m e n t a l e r r o r s wou ld mask any second o r d e r e f f e c t s . The b a r r i e r h e i g h t s f ound a r e comparab le t o t h o s e f ound f o r o t h e r w i d e bandgap i n s u l a t o r s . The d i f f e r e n c e i n work f u n c t i o n s a t t he two b a r r i e r s i s due to the p r e p a r a t i o n method. The f i r s t a luminum f i l m was exposed o f o r a s h o r t t ime to a i r and l i k e l y had about 50A o f ^2^3 o n ^ e s u r f a c e . The o t h e r f i l m was e v a p o r a t e d d i r e c t l y on to the ^ O ^ f i l m , so a d i f f e r e n t e f f e c t i v e b a r r i e r h e i g h t c o u l d r e s u l t . V I I . CONCLUSIONS The t h i n Y^O^ f i l m s i n v e s t i g a t e d were found to have many o f t h e p r o p e r t i e s e s s e n t i a l f o r d e v i c e f a b r i c a t i o n . -The i n s u l a t i n g p r o p e r t i e s o f t he f i l m s were e x c e l l e n t , and t h e e v a p o r a t i o n o f Y^O^ w a s a r e a s o n a b l y s i m p l e , n o n - c r i t i c a l p r o c e s s . The i o n i c m o b i l i t y was found t o be q u i t e h i g h i n t h e f i l m s , l e a d i n g to l o w - f r e q u e n c y l o s s e s , and h y s t e r e s i s i n t h e MOS c a p a c i t a n c e c u r v e s . I t may be p o s s i b l e to improve t h e p e r f o r m a n c e o f t he f i l m s by d e p o s i t i n g on a h e a t e d s u b s t r a t e i n o r d e r to p r e v e n t r e d u c t i o n o f t h e e v a p o r a n t . A number o f o t h e r e x p e r i m e n t s can be s u g g e s t e d . I t wou ld be d e s i r a b l e to know more about the p r e s s u r e dependence o f t he c o n d u c t i o n p r o c e s s i n Y^O^, i n o r d e r to check t h e mechanism p r o p o s e d . A l s o , s t e p r e s p o n s e d a t a t a k e n at d i f f e r e n t t e m p e r a t u r e s wou ld be u s e f u l . A p l o t o f t he most p r o b a b l e r e l a x a t i o n f r e q u e n c y a g a i n s t r e c i p r o c a l t e m p e r a t u r e w o u l d then g i v e a more a c c u r a t e e s t i m a t e o f t h e mean a c t i v a t i o n ene r gy o f the l o s s mechanism. F u r t h e r i n v e s t i g a t i o n o f the p r o p e r t i e s o f ^ O ^ i n MOS s t r u c t u r e s wou ld be d e s i r e a b l e . In v i e w o f t he ease o f d e p o s i t i o n , Y^O^ may be a u s e f u l m a t e r i a l f o r d o u b l e - d i e l e c t r i c d e v i c e f a b r i c a t i o n . F u r t h e r work on m o d e l l i n g the i n t e r n a l p h o t o e f f e c t i s n e c e s s a r y , w i t h p a r t i c u l a r emphas i s on t h e ho t n a t u r e o f p h o t o e l e c t r o n s at l i g h t e n e r g i e s w e l l above the p h o t o e l e c t r i c t h r e s h o l d . APPENDIX P r e l i m i n a r y i n v e s t i g a t i o n of the MOS c a p a c i t a n c e c u r v e s o f A u - ^ O ^ - S i d e v i c e s showed h y s t e r e s i s i n t he 1 MHz d i f f e r e n t i a l C-V c u r v e s . F i g s . 1-3 were g e n e r a t e d on an X-Y p l o t t e r by the a p p l i c a t i o n o f a v o l t a g e o f t r i a n g u l a r waveform and low f r e q u e n c y a c r o s s the spec imen w h i l e m e a s u r i n g the MOS c a p a c i t a n c e w i t h a Boonton model 71A c a p a c i t a n c e -i n d u c t a n c e m e t e r . The spec imen had a Y20^ f i l m 1500 + 2 0 0 A ° t h i c k on n - t y p e s i l i c o n o f 0 .4 +.05fi - cm r e s i s t i v i t y . The h y s t e r e s i s o b s e r v e d was more p ronounced a t l ower s c a n f r e q u e n c i e s . Compar i son w i t h the i d e a l MOS c a p a c i t a n c e , as c a l c u l a t e d (29) u s i n g the MOS d e p l e t i o n a p p r o x i m a t i o n mode l• , i n d i c a t e d a s u r f a c e 11 2 s t a t e d e n s i t y o f about 3 x 10 /cm . T h i s i s s u r p r i s i n g l y l ow, c o n s i d e r i n g the h i g h e n e r g i e s i n v o l v e d i n t he e l e c t r o n beam e v a p o r a t i o n ( i . e . , x - r a y s ) t h a t w o u l d be e x p e c t e d t o g i v e h i g h e r d e f e c t d e n s i t i e s and h e n c e h i g h e r s u r f a c e s t a t e d e n s i t i e s . T h u s , Y^O^ appear s t o be a u s e f u l m a t e r i a l f o r MOS d e v i c e s f rom s u r f a c e s t a t e d e n s i t y c o n s i d e r a t i o n s . The h y s t e r e s i s o b s e r v e d may be cau sed by the s l ow movement o f e i t h e r e l e c t r o n i c o r i o n i c cha rges n e a r the Y20 . j - S i i n t e r f a c e . I f i o n i c m o t i o n i s the cause (as seems l i k e l y , c o n s i d e r i n g the s t r u c t u r e o f t he o x i d e f i l m s and t h e A - C l o s s e s o b s e r v e d ) , t h e m o t i o n o f oxygen i o n s i s p r o b a b l y the mechanism. 68 C ( p f ) -5 F i g . 1 MOS C H y s t e r e s i s (Sweep F r e q u e n c y = 0.1 Hz) 69 70 71 REFERENCES 1. Campbell, K.C. Thin Solid Films , 6(1970) pp. 197-202. 2. Marshak, R.E., Fundamental' of Transmission Electron Microscopy , Wiley Interscience, p. 179 (1964). ~ ' 3. American Institute of Physics Handbook, McGraw-Hill (1967) p. 9-4. 4. Staritzky, E., Analytical Chemistry, 28(1956) p. 2023 5. Hass, G., J.B. Ramsey and R. Thun, J. Optical Soc. Am., 2, 49 p. 116 (1959). 6. Berard, M.F. , CD. Wirkus and D.R. Wilder, J. Am. Cer. Soc, 11, Vol. 51, 643 (1968). 7. Simmons, J.G., Handbook of Thin Film Technology, McGraw-Hill Co., 19 70, p. 14-3. 8. Miller, A. and A. Daane, J. Inorg. Nucl. Chem., 9, 27 p. 1955-60 (1965). 9. Dresner, J. and F.V. Shalcross, Solid-State Electron , 5, 205 (1962). 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. Blair and R. Bauer, JAP 37, p. 2468 (1968). 13. Simmons, J.G. Phys. Rev. 3, 155 (1967). 14. Stuart, M., Phys. Stat. Solid!, 23, 595 (1967). 15. H i l l , A.G., A.M. Phahle and J.H. Calderwood, Thin Solid Films 5(1970), p. 278-95. 16. Archer, R.J. "Determination of the Properties of Films on Silicon by the Method of Ellipsometry", J. Optical Soc. Am., Vol. 52, No. 9, . pp. 970-977, Sept. 1962. 17. Tallan, N.M. and R.W. Vest, J. Amer. Cer Soc. 8, 49, p. 401 (1966). 18. Frohlich, H., 'Theory of Dielectrics, Oxford University Press, London, 1949. ,19. Baird, M.E., Reviews of Modern"Physics, 1, 40, p. 219 (1968). "20. Cole, K.S. and R.H. Cole, J. Chem Phys. 10, 98 (1942). 21. Fowler, R.H., S t a t i s t i c a l Mechanics, Cambridge University Press, 1936 p. 358. . 72 22. M i t c h e l l , K., P r o c . R o y a l Soc . Am. , V o l . 146 p. 442 (1924 ) . 23. S chuermeyer , F . , J . A p p l . Phy s . 37 (5) p. 1998 (1966 ) . 24. Goodman, A.M., E l e c t r o c h e m . Sdc . , V o l . 15 No. 9 p. 276C ( 1 9 6 8 ) . 25. S c h u e r m e y e r , F . , JAP 37 No. 5, p . 1998 ( 1 9 6 6 ) . 26. S c h u e r m e y e r , F . , C.K. Young and J . M . B l a s i n g a m e , JAP 39 No. 3, p. 1971 (1968 ) . 27. S t u a r t , R. and F. Wooten, P h y s . Rev. 156 No. 2, p. 364 ( 1 9 6 7 ) . 28. P o w e l l , R . J . , J A P , 40 No. 13, p. 5093 (1969 ) . 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 o f S e m i c o n d u c t o r D e v i c e s , John W i l e y and Son s , 1967, p. 271. 

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