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The anodization of silicon in an r.f. plasma Scholz, Frank Joseph 1971

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THE ANODIZATION OF SILICON IN AN R.F. PLASMA by FRANK JOSEPH SCHOLZ B.Sc., University of Missouri, 1967 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF- APPLIED .SCIENCE i.n the Department of El e c t r i c a l Engineering We accept this thesis as conforming to the required standard Research Supervisor Members of the Committee , Head of the Department , Members of the Department of E l e c t r i c a l Engineering THE UNIVERSITY OF BRITISH COLUBMIA February, 1971 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e 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 s t u d y . I f u r t h e r ag ree 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 c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y pu rpo se s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . 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 o r p u b l i c a t i o n o f t h i s t h e s i s f o r 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 my w r i t t e n p e r m i s s i o n . Depa r tment The U n i v e r s i t y o f B r i t i s h Co l umb i a Vancouve r 8, Canada ABSTRACT ' The work contained in this thesis i s concerned with the elucidation of the growth mechanism responsible for the formation of s i l i c o n dioxide by plasma anodization. Three possible theories for the growth mechanism have been considered; namely, (1) the rate-limiting diffusion theory (2) the class i c a l theory of high-field ionic conduction and (3) the impact ionization theory. The v e r i f i c a t i o n of the applicability of any of the above three theories required the design and construction of (a) an in s i t u film thickness measuring system and (b) a plasma anodization system capable of controlling the substrate temperature. The experimental data could not be accounted for by either the rate-limiting diffusion or high-field ionic conduction theories, but good agreement was found with predicted results from an impact ionization theory. The development of a suitable impact ionization theory yielded a value for the electron mobility in SiO^ which was almost identical to the average value calculated from recent Hall effect measurements. i TABLE OF CONTENTS Page I. INTRODUCTION 1 I I . POSSIBLE THEORIES FOR THE ANODIZATION GROWTH MECHANISM 3 1. R a t e - l i m i t i n g d i f f u s i o n theory 3 2. C l a s s i c a l theory of h i g h - f i e l d i o n i c conduction 4 3. Impact i o n i z a t i o n theory 5 4. Summary 13 I I I . APPARATUS 14 1. The i n - s i t u f i l m thickness measuring system 14 2. The discharge c e l l , sample holder and anodization c i r c u i t 21 3. Sample preparation 25 IV. EXPERIMENTAL PROCEDURE 25 1. Setti n g up the o p t i c a l system 25 2. Sample temperature measurement 30 3. Anodization at constant voltage ' 30 4. Double probe measurements 32 V. EXPERIMENTAL RESULTS 32 1. R e f l e c t i v i t y data 32 2. Ionic current density as a function of time and f i l m thickness 3.3 3a. C a l c u l a t i o n of impact i o n i z a t i o n theory parameters 40 3b. T h e o r e t i c a l dependence of i o n i c current density on 46 thickness f o r an impact i o n i z a t i o n mechanism 4a. Double probe c h a r a c t e r i s t i c s 45 4b. Comment on the t h e o r e t i c a l and actual change i n voltage 49 drop and e l e c t r i c f i e l d i n the oxide under conditions of constant voltage anodization i i • . Page VI. DISCUSSION . 49 VII. CONCLUSION 52 APPENDIX ^ . < 54 The problem of maintaining a constant voltage across the oxide film REFERENCES . 64 i i i LIST OF ILLUSTRATIONS Figures Page 2.1 The s i l i c o n - s i l i c o n dioxide interface and the s i l i c o n dioxide- 6 plasma interface 2.2 Graphical solution to (2.24) (limiting thickness) H 3.1 The arrangement of the optical film thickness measuring system 15 ' F l ' 3.2 Graphs of the form of log i r i(R ) vs. D and l o g l A ( — ) vs. D 18 v 10 power &10 F^ 3.3 Photograph of the angle measuring device 20a. 3.4 Construction of the plasma anodization system 22 3.5 Detailed drawing of the water-cooled sample holder and 23 temperature measuring thermocouple 3.6 Anodizing ci r c u i t 24 4.1a Through 4.3b photographs of the waveforms seen on the 27-29 differential oscilloscope for the optical thickness measuring system F l 5.1 Plot of l o g ^ Q ( — ) - -299 vs. D for different values of time 34 5.2 Graph of D vs. t 35 5.3 Graph of |^ vs. t 36 5.4 Graph of j . vs. t 37 v ion 5.5 Graph of j t . vs. t 38 r J t o t a l 5.6 Graph of n vs. J t o t a l 41 5.7 Graph of j . vs. 1/D 42 v ion 5.8 Graph of l o g 1 0 ( J i o n ) vs. 1/D 43 5.9 Graph of j . vs. D 44 v J ion 5.10 Graphical solution for limiting thickness 47 5.11 Graph of probe current vs. voltage 48 iv Figures Page 1 Potential diagram for sample and return electrode ' 55 2a through 2g Potential diagrams for the double probe system with one probe grounded and with different applied potentials 57.-T-59 3 Double probe characteristic 61 4 Potential diagram of the plasma for two different film 61 thicknesses LIST OF TABLES Table Page I Values of D, 1/D, 4T> j . » j _ _ i a n d u for fifteen values 39 ' ' dt J i o n -'total of time II Calculated values of j , , and q for different point sets 40 III Calculated sets of (D, v t^) a n d corresponding values of D/vt^ 45 IV The caluculated values of u n and T U taken for five different 46 e i combinations of sets of points in Table III v ACKNOWLEDGEMENT The author i s deeply indebted for the encouragement and guidance received from his research supervisor Dr. D. L. Pulfrey and also for the valuable suggestions and help received from Dr. L. Young. The author also wishes to thank Mr. G. Olive for many valuable discussions. Grateful acknowledgement is made to senior technician Mr. J. Stuber for the major assistance in the construction of the apparatus and to Mr. J. Lees (Physics Department) for the fabrication of the quartz discharge tube. The author i s also grateful for the technical assistance received from Mr. C. G. Chubb, Mr. D. G. Daines and from Mr. H. H. Black for the photographic work. The author also wishes to thank Miss Linda Morris for typing the manuscript and Mr. S. Graf, Mr. G. Olive and Mr. B. Wilbee for their careful proofreading of the fi n a l draft. The author is grateful for the financial support received from the U. S. Air Force (contract F33615-70-C-1225), and the National Research Council (operating grants 67-7248 and 3392). v i I. INTRODUCTION In s i l i c o n integrated device technology i t would be desirable to limit the temperature required for the growth of s i l i c o n dioxide films. The present commerically used technique of growing s i l i c o n dioxide films is by thermal oxidation which requires temperatures in the range of 700 to 1200°C. It would also be desirable to be able to grow s i l i c o n dioxide films by a technique that would be compatible with present thin film vacuum technology. A technique which satisfies the above two requirements is plasma anodization which may be described as the growing of an oxide film on a metallic or semiconducting substrate by the application of a positive potential to the substrate when i t is immersed in a plasma. The technique of plasma anodization has been used to grow oxides on many metals and semiconductors e.g. A l , Ta, Mg, Cr, Sb, Bi, Zr, Mn, U, Nb, T i , Be, Ge, Si and GaAs. Reviews covering the work on plasma anodization up to about the end of 1969 are a v a i l a b l e ' . This investigation w i l l be restricted to the plasma anodization of s i l i c o n because of the importance of the s i l i c o n dioxide film on s i l i c o n in integrated device technology. Ut i l i z a t i o n of the technique of plasma anodization on s i l i c o n was f i r s t reported by Nazarova^3^ . Ligenza^^ investigated the growth mechanism for anodization in a microwave discharge and reported obtaining a parabolic growth rate that was dependent en the oxygen pressure in the discharge tube. Subsequently Kraitchman^"^ , using a similar microwave discharge, obtained a growth rate that deviated from a parabolic form by a constant that could be attributed to sputtering of the film occurring ( 6^  simultaneously with i t s growth. Jorgensen . has reported this same parabolic growth mechanism f o r f i e l d a s s i s t e d thermal oxidation of s i l i c o n . In the i n v e s t i g a t i o n s of Ligenza and Kraitchman no provisions were made for cooling the s i l i c o n sample and temperatures as high as 600°C were believed to have been present. These high temperatures besides negating one of the a t t r a c t i o n s of the low temperature anodization process also suggest the p o s s i b i l i t y that f i e l d a s s i s t e d thermal oxidation may have been the operative growth mechanism i n these cases a l s o . The primary aim of t h i s i n v e s t i g a t i o n , therefore, i s the e l u c i d a t i o n of the growth mechanism responsible for the plasma anodization of s i l i c o n . Because of the apparent high growth rates i n high frequency plasmas, as opposed to d.c. p l a s m a s ^ , t h i s i n v e s t i g a t i o n was undertaken using a plasma induced by an r . f . generator. In Chapter II the theories f o r three growth mechanisms that have been previously considered responsible f o r the anodization of s i l i c o n under various conditions are outlined and modified, where necessary, to f i t the conditions of plasma anodization. Chapter I I I describes the apparatus used and the experimental procedures followed are outlined i n Chapter IV. The experimental r e s u l t s are presented i n Chapter V and a d i s c u s s i o n of these, i n r e l a t i o n to the theories presented i n Chapter I I , follow i n Chapter VI. Chapter VII gives the conclusions which may be drawn from t h i s i n v e s t i g a t i o n as w e l l as suggestions for f u r t h e r research. 3 II. POSSIBLE THEORIES FOR THE ANODIZATION GROWTH MECHANISM 1. R a t e - l i m i t i n g d i f f u s i o n theory The r a t e - l i m i t i n g d i f f u s i o n process besides being invoked to explain the microwave plasma anodization of s i l i c o n ^ ^ ' i s known to take place during the thermal oxidation of s i l i c o n ^ ' ^  . The theory assumes that some type of oxygen s p e c i e s d i f f u s e across the oxide layer and react with the s i l i c o n at the o x i d e - s i l i c o n i n t e r f a c e . The growth mechanism may be expressed mathematically as dt " - D ( 2 < l a ) where D i s the f i l m thickness, t i s time and K i s the pressure dependent rate constant. In the work of K r a i t c h m a n ^ a sputtering rate constant was introduced i n t o (2.1a), to take account of sputtering of the f i l m occurring simultaneously with i t s growth, giving dD _ K d T-D"- s ( 2 ' l b ) Kraitchman showed (2.1b) to be appli c a b l e for. anodization under conditions of constant voltage, constant current and also f o r the case of no applied p o t e n t i a l . (This l a t t e r condition i s further i n d i c a t i o n of the p o s s i b i l i t y of thermal oxidation having taken place.) By the a p p l i c a t i o n of Faraday's Law of e l e c t r o l y s i s the i o n i c current density necessary to produce a growth rate 4^ " > f ° r a n oxide of dt formula A 0 , i s given by x y J j _ £2yF dD J i o n M dt ' K l - L ) where 3 i o n i s the i o n i c current density, p i s the density of the oxide, M i s the molecular weight of the oxide and F i s the Faraday (9.65 x 10^ coulombs). 4 By the s u b s t i t u t i o n of (2.1b) in t o (2.2) one obtains p2yFK . 1 p2yFS . . . , i . = — TT - — i ~ , — which can be w r i t t e n as J i o n M L> M 'i  u M j i o n = c l ( ^ " C2 ' ( 2 ' 3 ) where c^ and are constants. If the r a t e - l i m i t i n g d i f f u s i o n mechanism describes the f i l m growth i n the present i n v e s t i g a t i o n , then a p l o t of j ^ o r l v s . 1/D w i l l be a s t r a i g h t l i n e 1 2. C l a s s i c a l theory of h i g h - f i e l d i o n i c conduction For high resistance anodic oxide films (e.g. Ta^O^ prepared by s o l u t i o n ^ ^ and d.c. plasma a n o d i z a t i o n ^ ^ and SiO^ by s o l u t i o n a n o d i z a t i o n ) the i o n i c current density flowing through an oxide f i l m due to the a p p l i c a t i o n of an e l e c t r i c f i e l d can be expressed a s ^ ^ ' ^ ^ n 0 -w/KT aOaE/KT . BE i . = aQ2anve e = Jne , (2.4) J i o n 0 where w i s the height, with zero applied f i e l d , of the p e r i o d i c p o t e n t i a l b a r r i e r of half-width a, v i s the v i b r a t i n g frequency of i n t e r s t i t i a l ions i n the f i l m , n i s the mobile ion density, K i s Boltzmann's constant, T i s the temperature and E i s the e l e c t r i c f i e l d i n the oxide. For a constant voltage, U, applied across the oxide f i l m , of thickness D, the e l e c t r i c f i e l d E i n the oxide w i l l be U/D so that (2.4) becomes j . = V B U / D . (2.5) J i o n 0 Taking the common logarithm of (2.5)gives 108io(W = logio(Jo) +^logioe- ( 2'6 ) 5 A plot of l°S^o^ion^ V S ' ^ D b e a s t r a i S n t line provided that U and T remain constant. 3. Impact ionization theory This theory was put forward by F r i t z s c h e ^ ^ ' ^ ^ to explain his data obtained in the solution anodization of s i l i c o n . The basic assumption of the theory is that every ionizing c o l l i s i o n produces one extra free electron and one mobile ion. This suggests that the film may grow by cation migration, the cations being s i l i c o n ions. Fritzshe has derived an equation (6.3) relating total current density to the inverse of the time, the latter being measured from the instant of application of constant voltage. This equation is based on the assumptions that the film grows l i t t l e , relative to the i n i t i a l film thickness, after constant voltage is applied and that the film thickness is equivalent to many electron mean-free paths. These" assumptions, as w i l l be shown in Chapter VI, are not applicable to the plasma anodization results presented in this thesis. Thus in this section modifications of the impact ionization theory have been made to make i t relevant to r.f. plasma anodization. The impact ionization theory can be developed in the following way. Figure 2.1 shows the s i l i c o n - s i l i c o n dioxide interface and the sil i c o n dioxide-plasma interface. the concentration of electrons excited thermally in the SiC^ film n. . c o l l e l xon E D the concentration of electrons injected into the SiO^ film from the plasma the concentration of mobile ions produced by c o l l i s i o n in the Si0 2 film absolute "value of an electronic charge the number of electronic charges carried by a cation the mobility of electrons in the SiC^ film the mobility of ions in the SiO^ film the electric f i e l d in the oxide film the oxide film thickness S i j i o n = a Q ^ SiO 2 Q A G l ( i v n h j + n c o U ) E ion c o l l s — o — P L A S M A ( J H V O L T A G E A C R O S S O X I D E Fig. 2.1 % 7 Due to impact ionization there w i l l be a postive ion current density toward the oxide surface given by j . = aO'y. n . ,E. (2.7) J i o n Mxon c o l l v ' There w i l l also'be an electron current density at the Si0 2 - Si interface given by j _ i = Qvi_i (n + n- • + n 1 1 ) E. (2.8) el r e l o inj c o l l The total current density measured in the external circuit w i l l be given by the sum of i . and i , or J J i o n J e l j ^ ^ i = Qy T (n + n. . + n _.)E + aQy. n ..E. (2.9) J t o t a l e l o inj c o l l H H i o n c o l l v ' The ionic current efficiency, n , is thus defined by j . aQy. n ,.E ion v t M i o n c o l l j^^t-oi QP i ( n + n. . + n ..)E + aQy. n _. E total el o inj c o l l Hion c o l l y e l Defining the mobility ratio by q =. , and the leakage current density ^ion by _ j . = Qy ( n + n. .)E*. (2.10) Jleak el o in_ The ionic current efficiency can thus be written as n = — (2.11) j , , + j . • (1+ a ) Jleak Jxon a Hence the ionic current density can be expressed as 3 total ~ 3 leak  3 i o n (2.12) and n can be expressed as • n = • a 1 3 leak U+*> ( 1 + f ) 3 t Q t a l (2-13) a *. This is not the usual definition of leakage current, but is the total current density that would result i f no ionization collisions took place, 8 The next step in developing the theory i s to find a relation-ship between n .., and the film thickness. The time for an electron to c o l l obtain ionization energy while being accelerated in the oxide film i s denoted by t^ and the average velocity of an electron through the oxide. film i s denoted by v. The distance an electron w i l l travel i n time t. i s vt. and the expression for n ..., can be shown to be 1 1 r c o l l n c o l l - ( n o + n i n j ) ( I 2 D / V t l - 1 ) - ( 2 ' 1 4 ) , ,(13) t. can be expressed as l t. = v , where t^ is the time required for an electron to acquire an energy QI under free acceleration and T is the mean time between collisions of a l l types in the SiC^ film. The electron free acceleration time t can be expressed i n terms of the ionization potential, I, and the electronic mass, m, by t = >/2IQm 'I QE Fritzsche has not expressed the average electron velocity, v, in terms of the electric f i e l d and he has also assumed that vt^ can be taken as constant during constant voltage anodization. In this thesis the average electron velocity w i l l be taken as v = u e lE . r (2.15) Thus vt. i s written as I y e l ^ " v^IQm/xQE vt. = e or for a constant voltage U applied across the oxide film vt^ can be expressed as 9 vt. = P e l e T (2.16) Using (2.7), (2.10), (2.14), (2.16) and the definition of q the ionic current density can be expressed as a function of D for a constant voltage u as [ QD e^UQ ] u p l/2HM =r2 -1 3 ion 'leak (2.17) (12) Fritzsche has suggested that j ^ e a k a n d 1 w i l l remain constant over a sizeable range of values of i ., . If we follow this & J t o t a l assumption then the values of j 1 . and (-^-) can be calculated from an leaK. a experimental plot of nvs. j by taking two points (i _ .. .. , n-,) and r v J t o t a l J b J t o t a l 1 '1 (j +. i o' no) a n d substituting these points into (2.13) and solving these two simultaneous equations for j n . and (% giving ( n 1 n 2 ) j t o t a l total 2 (2.18) l e a k V t o t a l f V total 2 and £L = a 'total 1 total 2 7 11 J total 1 - 1 n 2 J t o t a l 2 In order to use (2.17) i t w i l l be necessary to obtain values (2.19) of y ^  and TU which can be calculated as follows. Using (2.7), (2.10), (2.14) and the definition of q one can obtain the expression 3 ion 3 + 1 leak. a = 2 D/vt. x (2.20) By taking two points on the experimental curve of i . vs. D i.e. (D„, i . ,) v ion 1' Jxon r 10 and (D„, i . „) one can calculate two other sets of points of D and vt. 2' J i o n 2 i ^ D l ' V t i 1^  a n d ^°2' V t i 2^  u s i n g (2-20)• T n e two sets of points of D and vt_^ can be substituted into (2.16) giving two equations which can be solved for u ^ and rU giving (vt, 1Q a e l /2IQm " D l . r ( v t i V ln [ ] ( v t . ) 2 ^ e ° r D2 (2.21) and TU /2IQm (D1-D2) < v ti>l (2.22) Note that i t is not necessary to know the value of U in order to calculate u ^ and TU, though the value of x cannot be determined independently of U. Substituting u and TU into (2.17) gives D r D n r ( v t i > i . In [-ion 'leak {-D D r D 2 ^ 2 i , ( v V i 2 } -1 (2.23) which can be used to draw a graph of j . vs. D in order to see i f the ion impact ionization theory agrees with the experimental plot of J ^ o n vs. D. Two features of (2.17) should be noted. First-the ionic current density w i l l be zero when De D u . /2IQ¥ TU el (2.24) Equation (2.24) can be solved graphically, as shown in Fig. (2.2), giving the limiting oxide film thickness, D , and the minimum oxide 0 0 max thickness, D . , for which impact ionization can take place for a given mm r e . 12 constant value of voltage. It w i l l be shown that U w i l l not be completely constant, for a constant voltage applied to the sample, and may increase by about 21% of i t s i n i t i a l value, for the range of current considered in this investigation, resulting in a higher value of D than would be max predicted for a constant voltage. For the second feature of (2.17) i t is necessary to take the derivative of i . with respect to D. To simplify the expression for J i o n the derivative l e t A = I^Qm ^ that the derivative becomes ion dj leak dD dD -AD b.— e ] l Io y e l A 2 -1 +• j l e a k * n 2 2 y e l A 2(f) a -AD r D xU , -AD xU el A xU (2.25) This derivative was taken with U assumed to be constant which may, as pointed out above, not be completely true in practice. If j is Jleak constant with D then — — = 0 and (2.25) becomes dD -AD dj ion dD J l e a k l n 2 . 2 " e l A r D XU , A T S [- e ] -AD xU 2<Xl I _ _D A xU dj ion dD has a value of zero when D xU ^ (i.e. x = tj). This is equivalent to saying that the maximum ionic current density is obtained when the time between collisions is equal to the time required for an electron to acquire an energy QI under free acceleration which would be the condition for the most efficient impact ionization. Let us consider the situation of a constant total current density applied to the sample. The total current density may be written as 13 j , = j , , + (1 + . • J t o t a l J l e a k a / J i o n By using (2.17) with ^ = E the t o t a l current density can be w r i t t e n as j = Qu .(n„ + n. .)E J t o t a l H H e l 0 i n j ' { QD e-/2IQm j y /nQm" T Q E 1 + + 1) (±2 6 1 1 } q 2 (2.26) For a constant t o t a l current density (2.26) must be constant. Inspection of (2.26) shows that the condition of a constant current density cannot be attained by keeping the f i e l d constant across the oxide f i l m f o r as the f i l m grows D w i l l increase and the t o t a l current density would increase even i f E were kept constant. The v a r i a t i o n of (n„ + n. .) with D i s also 0 m j an unknown fa c t o r which must be considered. 4. Summary The three anodization theories considered i n t h i s chapter can be dis t i n g u i s h e d by the predicted dependencies of J ^ o n o n D o r l/D-_ To te s t whether the r a t e - l i m i t i n g d i f f u s i o n theory i s app l i c a b l e i t does not matter i f constant current or constant voltage anodization i s used, whereas the h i g h - f i e l d i o n i c conduction theory and the impact i o n i z a t i o n theory are analyzed more e a s i l y under conditions of constant voltage anodization. Thus constant voltage anodization has been used i n t h i s i n v e s t i g a t i o n . In addition attempts have been made to keep the substrate temperature and the discharge pressure constant during oxide f i l m growth. 14 III APPARATUS 1. The in situ film thickness measuring system For a l l of the three theories l i s t e d i n Chapter II a knowledge of the dependence of film thickness on time is required. A simple method of obtaining film thickness data i s through (21) optical r e f l e c t i v i t y measurements The power reflection coefficient, R , for light incident at r power an angle <j>o from the normal to a non-absorbing film of thickness D located on a substrate is given by R = R. . , R* . , , (3.1) " power total t o t a l ' where R , is the total amplitude reflection coefficient for the total (14) electric f i l e d vector and is given by -2i6 r l + r 2 e R t o t a l " . ^  -216 • ( 3 ' 2 ) 1 + r i r 2 e The Fresnel amplitude reflection coefficient at the ai r - f i l m interface is denoted by r^ and the Fresnel coefficient at the film-substrate interface i s denoted by r^. The change in phase of the light on traversing the 2TT film is denoted by 6 and is given by 6 = -r— nnD costj). , where X is the wave-length of the light used, n^ is the refractive index of the film, D is the film thickness, and <j>^  i s the angle of refraction of the light i n the film given by Snell's Law as sind> = n, sind).. . ° o 1 r l Equations (3.1) and (3.2) form the basis for the method of film thickness measurement used in this investigation. Figure 3.1 shows the arrangement of the optical film thickness measuring system. By following the signals through the apparatus shown in Fig. 3.1 i t can be seen that the input voltage pulse amplitude to nqngT9l9Tw1Tw1Pi USHT SHIELD WATER-COOLED SAMPLE HOLDER SAMPLE Wg TgWXi<HwPi DISCHARGE CELL LIGHT SHIELD RCA 7102 PHOT OMUL TIPUER TUBE NO.1 —OPTICALLY FLAT OUARTZ WINDOW ^Vs T 9^0w 2 T w2* R *~ f i RCA 7102 PHOT OMUL TIPLIER TUBE NO.2 X-Y MICRO-MANIPULATOR \ i low pass cathodo followor filter >T I I cathode follower low pass filter 1 UNIVERSITY LABORATORIES MODEL 340 ImW 6328A He-No LASER J L T L T t i g . 3.1 DIFFERENTIAL OSCILLOSCOPE irLTL o s c i l l o s c o p e input #2 i s 0 * * * (3.3) and the input voltage pulse amplitude to o s c i l l o s c o p e input / / l i s 01 l l l l x g g (3.4) R denotes the amplitude r e f l e c t i o n c o e f f i c i e n t of the beam s p l i t t e r and g the T's are amplitude transmission c o e f f i c i e n t s with the subscripts r e f e r r i n g t o : - g, the beam s p l i t t e r , wl the entry window and w2 the e x i t window, n i s the r e f r a c t i v e index of the beam s p l i t t e r , n i s the g q r e f r a c t i v e index of the quartz windows, F^ and F^ are the readings f o r voltage d i v i d e r s ill and #2 r e s p e c t i v e l y , and are the p r o p o r t i o n a l i t y constants of photomultipliers #1 and #2, r e s p e c t i v e l y , A^ and A^ are the gains of the two cathode followers and f ^ andf are the factors by which the amplitudes of the rectangular pulses are attenuated i n passing through the low pass f i l t e r . By adjusting voltage d i v i d e r #2 such that v A ^ = V Q 2 > which gives a zero output on the o s c i l l o s c o p e , one obtains R power (3.5) f,A,K R R 1 1 g g By taking the logarithm of (3.5) one obtains 2 * * * •)+ l o g i n ( R 10 power )• (3.6) f, A,K,R R 1 1 1 g g The f i r s t term on the r i g h t hand side of (3.6) i s a constant of the o p t i c a l system so that (3.6) may be wr i t t e n as F l l o g ( — ) - (constant of system) = l o g i n ( R 10 power (3.7) 17 The r i g h t hand side of (3.7), l ° g 1 0 ^ R p o w e P ' C a n b e P l o t t e d against D, the f i l m thickness, for a measured angle <j>o and for d i f f e r e n t values of n, . For a non-absorbing f i l m n. w i l l be r e a l and log,_.(R ) w i l l be 1 6 1 &10 power a p e r i o d i c function of D having maxima and minima as shown i n F i g . 3.2. The value of n.. may be obtained by taking the d i f f e r e n c e between the F l maxima and minima values of l o g i n ( — ) , defined by i u 12 F F F A l o 8 1 0 ( F ^ " [ 1 ° 8 1 0 ( F ^ ) ] m a x ' [ 1 ° 8 1 0 ( F ^ ]min', and then determining what value of n, w i l l give a p l o t of log. r i(R ) ° 1 10 power vs. D with a d i f f e r e n c e between i t s maxima and minima, defined by Alog. n(R ) =. [log . n ( R )] - [log. n(R )] . ,, 10 power 10 power max 10 power min'.' such that A l o g 1 0 ( ^ ) = A l o g 1 ( ) ( R p o w e r ) . The value of the o p t i c a l system constant can be determined by taking the F l -average value of the dif f e r e n c e s between the maxima of l o g 1 A ( — ) and the ±U r 2 F l maxima of loe,„(R ) or the minima of log^_(^—) and the minima of to10 power 10 F^ l o e i r i ( R ) or the average value of both differences so that &10 power " F l (constant of the system) = [ l o g 1 0 ( j - ) ^ - f l o g 1 0 ( R p o w e r ) ] m a x = f l o 8 1 0 ( F 7 ) ] m i n - [ l o 8 1 0 ( R P o w e r ) ] m i n ' ^ 3 ' 8 ) where the value of n, i n the equation of l o g 1 _ ( R ) was determined from 1 °10 power the procedure explained above. The f i l m thickness vs. time curve can be obtained by the following procedure: one f i r s t subtracts the system constant from each 19 F l measured value of log 1 n(—-) and determines what film thickness would make -LU h 2 log.„(R ) have the same value, that is what value of D w i l l satisfy 10 power J (3.7). There are many values of D that w i l l satisfy (3.7), but there is l i t t l e chance of ambiguity in determining the correct value of D i f one starts growing the film from a known i n i t i a l film thickness and also consults an interference colour-thickness t a b l e ^ ^ . After having F l determined the correct value of D for each value of log (—)-(constant of 10 F 2 F l system) and having recorded the time at which each measurement of log n ( — ) iO i 2 was made then one has available the necessary points for plotting a curve of D vs. time. In the practical thickness measuring system extensive e l e c t r i c a l and optical shielding was necessary in order to permit measurement with the plasma on. The photomultipliers were screened from most of the plasma by aluminium sheet metal painted matt black and narrow band optical f i l t e r s , centered at the laser frequency, were used on each photomultiplier and the light was allowed to reach them only after traveling down 2" long, 1/4" i.d. copper tubes that had been painted matt black. E l e c t r i c a l interference from the r.f. generator, being received by the di f f e r e n t i a l oscilloscope, was eliminated by the installation of 6-element Butterworth low pass f i l t e r s . Cathode follower circuitry was used to prevent loading of the decade voltage divider boxes by the f i l t e r s . A detailed analysis of the percentage error involved in this method of thickness measurement is d i f f i c u l t to carry out, but some of the possible sources of error and ways to minimize these errors are b r i e f l y 20 discussed below. Greatest inaccuracy in estimating D w i l l occur when the r e f l e c t i v i t y is near a maximum or minimum on the curve of log.._(R ) J • °10 power vs. :D, since in these maxima and minima regions the reflected light intensity w i l l be much less sensitive to changes in the film thickness. This error can be reduced by restricting measurements to those regions on the log i n(R ) vs. Dcurve that are not in the v i c i n i t y of maxima or 10 power J minima. Another possible way of reducing this error is to use shorter (22) wavelengths thereby causing the maxima and minima to be narrower. A second source of error is that the sample holder may move due to thermal expansion and thus not permit the f u l l laser beam to shine into the 1/4" i.d. tube attached to the photomultiplier. This error was corrected for by mounting photomultiplier #2 on an x-y micromanipulator which can be adjusted to compensate for the movement of the laser beam. A third source of error is inaccurate measurement of the angle of incidence. This error was reduced by a method of replacing the sample by a rotating mirror and measuring the angle through which the mirror must be rotated to make the laser beam move from being reflected back into the laser to being reflected into photomultiplier ill. Figure 3.3 shows a photograph of the angle measuring device which can be read to 0.4 degree accuracy. A fourth source of error is incorrect polarizer adjustment. In this investigation S-light was used and the beam s p l i t t e r was positioned so that i t s plane of incidence was parallel to the sample plane of incidence. For the range of film thicknesses in which the polarizer was adjusted the sample had a larger power reflection coefficient for S-light than P-light. Also the decrease in the power transmission coefficient of the beam sp l i t t e r when going from P-light to s-light was much less than the increase in the power 20a. Fig. 3.3 21 reflection coefficient of the sample in going from P-light to s-light. Thus when S-light was present maximum signal amplitudes were obtained from photomultipliers #1 and #2. A f i f t h source of error is an incorrect value of refractive index of the substrate. The value of refractive index of the substrate was interpolated from a table of refractive index vs. wavelength . A sixth source of error i s a non-linear intensity response of the photomultipliers, but for the fixed wavelength used the photomultipliers had good linearity over the intensity levels used. 2. The discharge c e l l , sample holder and anodization ci r c u i t The construction of the apparatus is shown in Fig. 3.4. The quartz discharge tube has side-arms with optically f l a t windows positioned at angles of approximately 36° with respect to the discharge tube axis. Stainless steel end caps, with viton '0' ring seals, allow sorption pumping of the system at one end and oxygen and sample holder entry from the other. Figure 3.5 shows a detailed drawing of the water-cooled sample holder and temperature measuring thermocouple. An octal header feedthrough allows connection of the sample to the anodizing ci r c u i t of Fig. 3.6. This ci r c u i t permits the switching from constant current to constant voltage operation and also a continual measurement of the current drawn by the sample. A s i l i c o n electrode at ground potential was used as the anodizing current return electrode. The r . f . power to the plasma is coupled in from a Philips PH1012-02-10-20 model, 12KW, 0.5-l.OMHz, generator by a two turn water-codled c o i l around the quartz tube. It is conceivable that the growth conditions could be changed to a considerable extent by using alternative coupling arrangements, but this po s s i b i l i t y was not investigated in this thesis. PHILIPS 12 KW 23 T H E R M O C O U P L E S I L I C O N W A F E R M I C A M A S K T H E R M O C O U P L E P y r o x T U B E C H R O M E L W I R E A L U M E L W I R E S L I G H T L Y T A P E R E D W A T E R - C O O L E D C O P P E R T U B E W A T E R O U T L E T T U B E V 'E f i g . 3 . 5 P L U N G E R F O R E L E C T R I C A L C O N T A C T T O B A C K O F S I L I C O N W A F E R S P R I N G P y r e x T U B E F O R I N S U L A T I O N N I C K E L P L A T E D C O P P E R C Y L I N D E R - P y r e x T U B I N G W I R E F O R E L E C T R I C A L C O N N E C T I O N T O W A F E R S T A I N L E S S S T E E L T U B E W A T E R E N T R Y T U B E Pa V W A T E R I N L E T T U B E PERMANENT-MAGNET MOVING-COIL GALVANOMETER DOUBLE POLE DOUBLE THROW-SWITCH REGULATED D.C. VOLTAGE SUPPLY 0-500 VOLTS 0-100 ma SILICON SAMPLER 6 t o m 3.6 HEWLETT PACKARD D.C. CONSTANT CURRENT SOURCE 0-100ma 0-300 VOLTS R.E COIL SILICON ELECTRODE OSCILLOSCOPE MOSELY MODEL 7100 JCHART RECORDER JOHN FLUKE HIGH IMPEDANCE D.C. DIFFERENTIAL VOLTMETER 25 3. Sample preparation The specimens that were anodized were s i l i c o n wafers having 15 3 n-type impurity concentrations of 3 x 10 /cm . The wafers, purchased from Monsanto, had been polished.by an electrochemical technique ... -• to mirror fini s h . Onto the unpolished back sides of the wafers was evaporated gold doped with 1% antimony. The gold-antimony was then alloyed into the s i l i c o n at 425°C i n nitrogen with a flow rate of 1000 c c . per hour for 5 minutes in order to make an ohmic contact. The wafers were cleaved to a size that would f i t the sample holder and were then mounted to the sample holder between two mica sheets, the sheet on the polished side of the wafer having a hole in i t which exposed the required 2 area (usually 1-2 cm ). IV EXPERIMENTAL PROCEDURE 1. Setting up the optical system The sample holder was positioned a distance of 6" from the r.f. c o i l ; this caused the sample to be in the weaker outer edge of the plasma for pressures i n the range of 25-35 m i l l i t o r r when the generator output was 2 kilowatts. The laser beam was aligned to give a reflected beam into photo-multiplier ill. The VacSorb pump was then opened to the system, pumping i t down to 10 m i l l i t o r r . The variable leak valve was then opened to allow flushing of the system with oxygen for about 15 minutes. The pressure was then reduced to about 30 mtorr and the r . f . discharge was struck with the i n i t i a l aid of a Tesla c o i l . The system was allowed to reach a state of thermal equilibrium which was determined by observing when the sample holder temperature, measured by the thermocouple, reached a constant value and also when thermal expansion of the sample holder tube 26 ceased (i.e. when the x-y micromanipulator no longer required adjustment). After reaching thermal equilibrium the pressure was adjusted to 32 m i l l i t o r r where i t was kept constant throughout the entire experiment. The x-y micromanipulator was again adjusted to obtain a maximum output from photomultiplier #2. This adjustment was necessary to compensate for any possible movement of the sample holder due to a change in pressure. The polarizer was then adjusted to obtain maximum signals from photomultipliers #1 and #2 which corresponds to the condition of S-light. The polarizer was adjusted twice, the f i r s t time without the beam sp l i t t e r in the optical system and the second time with the beam spl i t t e r present; the reason being to see i f the beam spl i t t e r would lead to an erroneous adjustment of the polarizer i f i t were not aligned with i t s incident plane perfectly parallel to the plane of incidence of the sample. There was no noticeable difference between the two adjustments? of the polarizer. The quartz windows did not interfere with the polarizer adjustment since the laser beam was practically at normal incidence to the windows and at normal incidence - s-light and P-light are indistinguishable. Decade voltage divider #1 was adjusted to give a reference signal pulse amplitude of about 20 or 25 mV. Decade voltage divider #2 was then adjusted for a n u l l , of the reference and reflected signals, on the differential oscilloscope. These waveforms are shown in Figures 4.1a through 4.3b. Figures 4.1a and 4.1b show the rectangular wave voltages at the inputs #1 and #2 to the d i f f e r e n t i a l oscilloscope. Figure 4.2 shows the voltage waveform on the differential oscilloscope when ~VQ-^VQ2 for the case where F^- has deviated from i t s balanced value by 0.035. Figures 4.3a and 4.3b show the voltage waveform on the di f f e r e n t i a l fig.(4.1 a) roferonce s ignal sensitivity 5mv/cm fig.(4.3a) s on s i t i v i t y 5mv/cm 30 oscilloscope for the case of a balance where = VQ2 ^ o r t w o different voltage s e n s i t i v i t i e s . 2. Sample temperature measurement The sample temperature was estimated by the use of a chromel-alumel thermocouple having a reference junction at 0°C. Figure 3.5 shows the location of the thermocouple next to the sample holder. The thermocouple reading when thermal equilibrium was reached was 200°C. Thus i t can be inferred that the substrate temperature was also approximately the same. Furthermore the spring that made the el e c t r i c a l contact to the s i l i c o n substrate did not loose i t s elastic properties indicating that i t s temperature remained below 200°C. 3. Anodization at constant voltage The sample, which had been e l e c t r i c a l l y floating during the time when the system was reaching thermal equilibrium, was allowed to draw a small constant current of about 1 to 2 ma. The current as a function of time was recorded on a chart recorder. The current was increased in constant current steps of about 3 to 4 ma to a f i n a l value of usually around 12 ma. The film was grown at constant current u n t i l i t reached a thickness that passed the f i r s t minima on the curve of l o g10^ Rpower^ V S* ° ±' e" s o t h a t t h e c o n s t a n t o f t h e optical system could be evaluated, so that the f i r s t maxima could probably be reached even i f the film grew very l i t t l e under constant voltage and to be i n the range of highest accuracy. After passing the f i r s t minima of reflected intensity the sample was switched to constant voltage. The value of constant voltage applied, 129 volts for results presented here, was the value of voltage measured across the terminals of the constant current 31 generator at the time i t was switched to constant voltage. In switching from constant current to constant voltage there was a transient increase i n current of 0.6 ma, which was probably due to error i n measuring the voltage across the constant current source before switching. The current measured with a permanent-magnet-moving-coil galvanometer was i n good agreement with that as measured on the chart recorder. This suggests that the chart recorder was responding only to the d.c. anodizing current being drawn and not j u s t to some l e v e l which might include a r e c t i f i e d component of the r . f . voltage. This check was necessary as an o s c i l l o s c o p e , connected across the one ohm r e s i s t o r used to measure the current, showed an a.c. s i g n a l at the frequency of the r . f . generator with a peak amplitude of 1.5 ma. The recorded anodizing current decayed slowly with time which (12) was contrary to the current decay for s o l u t i o n grown films . This suggested the p o s s i b i l i t y of large leakage currents masking the actual current decay. This was l a t e r checked by masking o f f the front face of the sample and applying the same constant voltage that had been applied during constant current growth. Only a small leakage current of .8 ma was measured. This value of leakage current was subtracted from a l l the values of current measured on the chart recorder thus t y p i c a l l y g i v i n g an i n i t i a l current when constant voltage was applied of 12 ma. As the f i l m grew the o p t i c a l system became unbalanced and was n u l l e d with decade voltage d i v i d e r #2 each time the imbalance became large enough to require a .01 to .02 change i n the decade voltage d i v i d e r reading i n order to r e - e s t a b l i s h balance. The values of F^ and were * The PMMC galvanometer has e s s e n t i a l l y zero frequency range. 32 recorded along with the time when the balance was made. It was possible to see the interference colours of the oxide f i l m through the quartz tube. These colours changed as the f i l m grew and were recorded along with F^ and o F^ for d i f f e r e n t times. The films were grown to thickness of about 3800A. o The f i l m thicknesses when constant voltage was applied were about 1400A o with growth rates of about .277 A/sec. The f i n a l growth rates were about o .088 A/sec. The angle of incidence of the l a s e r beam was measured by the method described i n Chapter I I . 4. Double probe measurements To use the probe technique, explained i n the appendix, the s i l i c o n wafer was removed from the sample holder and replaced by a s t a i n l e s s s t e e l d i s c masked o f f to the same surface area as that of the oxide f i l m . The s t a i n l e s s s t e e l d i s c was biased for a ser i e s of values of voltages with respect to the grounded electrode and the d.c. current through the external c i r c u i t was measured. The same pressure and power conditions were used during t h i s measurement as were used during the constant voltage growth of the Si02 f i l m s . V. EXPERIMENTAL RESULTS 1. R e f l e c t i v i t y data F l From the measured values of F n and F Alog ) was c a l c u l a t e d J- 2 IL) r 2 to be .682. Using the measured angle of incidence, 4>Q = 34.4°, and the value of the r e f r a c t i v e index of the substrate, i n t e r p o l a t e d from a table of r e f r a c t i v e index vs. w a v e l e n g t h = 3 . 8 6 - j.017 for o X = 6328A), the r e f r a c t i v e index of the f i l m was c a l c u l a t e d , by the 33 method of Chapter III, to be = 1.428. The usual range of refractive index for SiO^ films ranges from 1.43 to 1.46^'^. Using the value of n the constant of the optical system was determined to be 0.299. The F l optical constant was subtracted from a l l the values of log^C--—) . An enlarged graph of log..~(R ) vs. D was made having a modulus of the ° 10 power o ordinate of 50 cm/unit and a modulus for the abscissa of .1 millimeter/A. F l The values of log i n(——) - .299 were placed on this graph along with their 10 £ 2 corresponding values of time. A photographic reduction of this graph is shown i n Figure 5.1. 2. Ionic current density as a function of time and film thickness From the information contained in Figure 5.1 a large graph of D vs. t was made starting from the time when the constant voltage was o applied. The ordinate of the D vs. t curve had a modulus of .1 mm/A and i t s abscissa had a modulus of .05 mm/sec. Figure 5.2 shows a photographic reduction of the graph of D vs. t. The derivative of the D vs. t curve was determined by graphical differentiation using the Chordal Method ' . The modulus of the ordinate o was 400 mm/(A/sec) and the'modulus for the abscissa was .05 mm/sec. dD Figure 5.3 shows a photographic reduction of the graph of -j— vs. t. 3(17) By using (2.2), with p = 2.2 gm/cm and M = 60 gm/mole for Si0„, and the graph of ~- vs. t a graph of i . vs. t was made and is 2 o r ^ j . o r J i o n shown in Figure 5.4. In Figure 5.4 the time scale has been changed to minutes with the zero reference corresponding to the instant of switching to constant voltage operation. The total current density was calculated, by dividing the total measured current minus the leakage current (.8 ma) by the area of the sample, and a graph of _ t o t a ^ v s • fc» f° r constant voltage 4500 4000 3500 3000 2500 O (/) CO Iii ^ 2000 u 1500 1000 500 f i g . 5 . 2 CONSTANT VOLTAGE APPUED AT THIS TIME 1 7000 8000 9000 1QD00 11000 12JD00 13O00 14000 15000 16D00 17000 18pOO 19DO0 2Q000 TIME (SECONDS) fi±H 7— 0 , 0 20 ZO 40 50 60 ™ BOlOioO 110 HO 130. 140 .50 / TIME(minutes) fig.5.4 < Jo no Tso Tw zoo zio 10 10 30 40 50 TO 80 $0 loo JlO {ZO BO TIME (minutes) 150 160 170 180 190 ZOO f ig.5.5 00 P T . T I M E T I M E D (I) 1/D dD / d t J I O N J T O T A L E T A N O . S E C . M I N . l/K M I C 4 0 - 1 M I L L I -A / S E C . A M P S . / C M A M P S . / C M 1 7 , 7 0 0 0 . 0 1 4 3 0 7 . OOE » 0 4 . 2 7 7 3 9 . 2 0 6 . 9 0 5 . 70E< ° 0 3 2 8 , 0 6 4 6 .1 1 5 3 0 6 . 5 4 E - 0 4 . 2 7 2 3 8 . 6 0 6 . 6 7 5 . 8 0 E - 0 3 3 8 , 7 9 6 1 8 . 6 1 7 3 0 5 . 7 8 E « 0 4 . 2 6 5 3 7 . 5 0 6 . 6 1 5 . 6 7 E ' - 0 3 4 9 , 9 8 7 3 8 . 2 2 0 4 0 4 . 9 0 E - 0 4 . 2 5 4 3 5 . 9 0 6 . 4 4 5 . 5 7 E - 0 3 5 1 1 , 0 1 2 5 5 . 2 2 3 0 0 4 . 3 5 E - 0 4 . 2 4 5 3 4 . 6 0 6 . 2 9 5 . 5 0 E' - 0 3 6 1 2 , 3 4 0 7 7 . 3 2 6 1 5 3 . 8 3 E - 0 4 . 2 2 5 3 1 . 8 0 6 . 1 2 5 . 2 0 E ' " 0 3 7 1 3 , 1 3 3 9 0 . 5 2 7 8 0 3 . 6 0 E - 0 4 . 2 1 0 2 9 . 7 5 5 . 9 8 4 . 9 7 E ' » 0 3 8 1 3 , 6 7 2 9 9 . 6 2 8 9 0 3 . 4 6 E - 0 4 . 1 9 2 2 7 . 2 0 5 . 8 6 4 . 6 4 E - 0 3 ' 9 1 4 , 4 2 8 1 1 2 . 0 3 0 2 5 3 . 3 I E - 0 4 . 1 7 5 2 4 . 8 0 5 . 3 5 4 . 6 4 E - 0 3 1 0 1 5 , 4 0 4 1 2 8 . 0 3 1 9 0 3 . 1 4 E - 0 4 . 1 6 0 2 2 . 6 0 5 . 2 3 4 . 3 2 E - 0 3 1 1 1 6 , 7 5 6 1 5 1 . 0 3 4 0 0 ' 2 . 9 4 E - 0 4 . 1 4 0 1 9 . 3 0 5 . 0 0 3 . 9 6 E - 0 3 1 2 1 7 , 9 3 9 1 7 1 . 0 3 5 7 0 2 . 8 0 E - 0 4 . 1 1 8 1 6 . 6 5 4 . 8 2 3 . 4 6 E =»03 1 3 1 8 , 4 4 1 1 7 9 . 0 3 6 3 0 2 . 7 6 E - 0 4 . 1 1 0 1 5 . 6 0 4 . 7 1 3 . 3 1 E - 0 3 1 4 1 9 , 3 0 7 1 9 3 . 0 3 7 2 0 2 . 6 9 E - - 0 4 . 0 9 5 1 3 . 4 5 4 . 3 7 3 . 0 8 E - 0 3 1 5 2 0 , 0 0 0 2 0 5 . 0 3 7 9 0 2 . 6 4 E - 0 4 . 0 8 8 1 2 . 3 9 4 . 2 8 2 . 9 0 E - » 0 3 TABLE 1 40 operation is given in Figure 5.5. Fifteen values of i , were taken, for different times during J t o t a l ' ° the constant voltage anodization and the current efficiency, n, was calculated for these points. Table I gives the values of D, 1/D, ~ , j . , ° dt ion i ., and n that correspond to each of the fifteen points. From the J t o t a l i f r points of Table I plots of n vs. j -, s j . vs. 1/D, log._(j. ) vs. 1/D ^ total' J i o n 10 ion and i . vs. D were made and are shown in Figures 5.6 through 5.9 respectively, ion 3a. Calculation of impact ionization theory parameters " j.leak and q were calculated using (2.18), (2.19) and different sets of points from Table I. These point sets are li s t e d in Table II along with the corresponding values of j 1 1 and ^~ calculated for each leak a point set. Note that j and ^- remained reasonably constant over the leak a constant voltage growth range considered, thus justifying the assumption made in Section II. Table II Point Set 3 leak m . 2&11 87.9 3.26 2&15 89.8 3.15 4&11 89.0 3.24 5&10 87.4 3.23 4&13 84.6 3.39 ( I O N I C C U R R E N T E F F I C I E N C Y )X I t f * e • e 6 ? g. . — ' e 1*7 60 45 The average values of ^- and , obtained from.Table II are (^-) =87.7 6 a Jleak a ave 2 and ( j . . , ) = 3.25 ma/cm . Substituting these values in (2.13) gives the graph shown by the curve in Figure 5.6. Using (2.20), with the average values o"f j . . i a n d ^ , sets o f values of (D, vt.) were calculated j. e aK a x for different sets of points from Table I. These calculated sets of (D, vt_^) as well as D/vt_^  are l i s t e d in Table III along with the corres-ponding point from which each set was calculated. Table III Point o D A o vt. A X D/vtj, 1 1430 700 2.04 4 2040 1030 1.98 6 2615 1380 1.89 7 2780 1500 1.85 11 3400 2100 1.62 15 3790 2680 1.42 Different pairs of the points of Table III were taken two at a time and were substituted into (2 .21) and (2. 22) from which were calculated and TU. The value of the ionization L potential, I, for S i 0 2 used in (2.21) and (2.22) was 11 eV. as has been determined by Fritzsche from break-down measurements on SiO 2 films. Table IV l i s t s the calculated values of u , and TU taken for el five different combinations of sets of points in Table III. Note that u , and el UT remain reasonably constant over the constant voltage growth range considered. 46 Table IV Pairs of Points y ncm / v o l t sec e l 1&7 16.15 4&15 6&15 4&11 27.9 27.7 30.2 28.2 31.6 Ux v o l t sec 1.98 x 10 -12 1.96 x 10 -12 2.05 x 10 -12 1.98 x 10 -12 2.14 x 10 -12 The average values' of p , and Ux determined from TABLE IV are (y ,) = ° e l e l ave 2 -12 29.1 cm / v o l t sec and (Ux) = 2.02 x 10 v o l t sec. ave 3b. T h e o r e t i c a l dependence of i o n i c current density on thickness f o r impact i o n i z a t i o n The. average values of j , , , y , and Ux were s u b s t i t u t e d b J l e a k a e l into (2.17) and a graph of i . vs. D was made which i s the curve i n b t- J 1 0 n Figure 5.9. The l i m i t i n g thickness of the oxide f i l m was cal c u l a t e d by s u b s t i t u t i n g (u •,) and (xU) in t o (2.24) a graph of which i s shown & el'ave ave o i n Figure 5.10. The value of D was estimated to be I) = 4900 A 6 max max o while the value of D . was estimated to be D . = 400 A. I t i s noteworthy m m m m that the l a t t e r value was f a r below the value of f i l m thickness when the constant voltage was applied. 4a. Double probe c h a r a c t e r i s t i c s From the probe measurement of Section 4, Chapter IV a graph was made of probe current vs. voltage and i s shown i n Figure 5.11. The i n t i t a l t o t a l current drawn by the sample was 1^ = 12 ma, obtained from point 1 of Table I by mu l t i p l y i n g J t o t a i k y the a r e a of the sample, and 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 fig.5.10 D (A) 4>-48 fig. 5.11 49 the f i n a l t o t a l current was 1^ = 7.45 ma. Thus from Figure 5.11 V,. = 35 v o l t s and V," = 15 v o l t s (see Appendix), d l dz 4b. Comment on the t h e o r e t i c a l and actual change i n voltage drop and  e l e c t r i c f i e l d i n the oxide under conditions of constant voltage  anodization Using the values of V „ and V,„ of Section 4a. Chapter V, the d l al value of V ' (129 v o l t s ) and (1) and (2) of the Appendix the i n i t i a l supply and f i n a l values of the voltage across the oxide are U^ = 94 v o l t s and U 2 = 114 v o l t s r e s p e c t i v e l y . The percentage voltage r e g u l a t i o n was, from (4) of the Appendix, 21%. The value of y c a l c u l a t e d from (10) of the Appendix was 7.92%. The average v e l o c i t y of electrons crossing the f i l m can be estimated by using the average value of m o b i l i t y and the i n i t i a l value U l 6 of the e l e c t r i c . f i e l d (E1 = —— = 6.57 x 10 volts/cm). Using the r e l a t i o n 1 8 v = u ,E., the e l e c t r o n v e l o c i t y v obtained was 1.9 x 10 cm/sec, while e l 1 the v e l o c i t y of l i g h t i s approximately 3 x 10"^ cm/sec. Thus v/c = .006 and the theory of r e l a t i v i t y has not been v i o l a t e d . VI DISCUSSION If the r a t e - l i m i t i n g d i f f u s i o n theory i s a p p l i c a b l e the graph of 3 ^ o n v s - 1/D, shown i n Figure 5.7, should be a s t r a i g h t l i n e given by (2.3). I t can be seen from Figure 5.7 that no s i n g l e s t r a i g h t l i n e can account f o r the data. A po s s i b l e source of deviation from a s t r a i g h t l i n e could occur i n p r a c t i c e due to a change i n the value of the pressure_ dependent rate constant K, but since the pressure was held constant i t appears that the r a t e - l i m i t e d d i f f u s i o n theory does not explain the experimental r e s u l t s . 50 For high-field ionic conduction, the graph of log-^y ^  ^  ior? VS' Figure 5.8, should be a straight line according to (2.6). Again the experimental data is not accounted for by a single straight l i n e , but as has been pointed out in the Appendix the value of U would increase some-what as the film grew. The possibility arises therefore that the deviation of the curve in Figure 5.8 from a straight line i s due to an increasing voltage with increasing film thickness. Writing (2.6) as y = mx + b , (6.1) where y = l o g i r i ( j . ), x = 1/D, m = BU log-.-.e and b = log.--.J_, we have J "10 ion &10 °10 0 the equation of a straight line of slope m and y intercept b. The curve in Figure 5.8 may be divided up into two straight lines one line from point 1 to point 5 with slope m^  and another line from point 12 to point 15 with slope ir^. The line from points 1 to 5 is where the voltage has a constant value U^ and the line from points 12 to 15 is where the voltage has a constant value V^. The percent voltage regulation during the growth of the film can be expressed in terms of the slopes m^  and by (6.2). U2 ~ U l m2 ~ m l (percentage voltage regulation) = x 100 = x 100 (6.2) 1 m l °-l Theslopesm^ and ir^ were calculated giving m^  = 204 units/(A ) and t = n i i l l l u m t - c m„ = 8100 units/(A" ). The required voltage regulation to f i t the high-f i e l d ionic conduction theory is thus 3870%! However the predicted percentage voltage regulation from probe measurements is only 21%. It should also be noted that the two lines have greatly different y intercepts which would mean that the value of b changed greatly during the growth of the film, but this is very unlikely. Thus these results seem to indicate that the high-field ionic conduction mechanism is not responsible 51 for the growth of SiC^ films in an r . f . plasma. Having shown that the rate-limited diffusion theory and the high-field ionic conduction theory are not applicable to this investi-gation, the impact ionization:, theory i s next considered. The graph of n V S ' j t o t a l > ' ( 2 - 1 3 ) ' u s i n § t h e v a l u e s o f ( f ) a v e a n d ^ l e a k ^ v e a § r e e s w e l 1 with the experimental points as can be seen from Figure 5.6. The average value of U >^ calculated from Table IV was 29.1 2 (19) cm /volt sec and i t is worth noting that Goodman obtained an average 2 value of 29 cm /volt sec for the electron mobility in SiC^ films using a modified Hall measurement technique especially suited for use with insulator films. The fact that the average value of electron mobility obtained from Table IV is the same as the average value of electron mobility measured by Goodman is a strong factor for suggesting that the impact ionization theory is responsbile for the growth of the film. Furthermore, considering the graph of J^ o n v s« D (2.17), which is shown in Figure 5. 9 , i t is noted that there i s good agreement with the experimental points. There is thus strong evidence in support of the impact i o n i -zation theory as presented here being responsible for the growth process in r .f. plasma anodization of s i l i c o n . However i t is perhaps of interest to remark on the differences in current decay rate that result from (12) consideration of the above theory and Fritzsche's original theory Fritzshe derived an equation giving the current density time decay at constant voltage as 1 _ - L - B ( t _ t ), ( 6.3) J t o t a l Jleak J t o t a l Q J l e a k Q where the constant voltage was applied at time t^ when the total current 52 density was j - and the leakage current density was j , . B is totaJ-Q J_eaiCQ a constant independent of voltage. Equation (6.3) was derived for the case of solution anodization of SiC^ where the assumptions were made that D/vt^>>l and that the primary electrons could be neglected. In the present experiment the values of D/vt^ varied from 2.04 to 1.42 which does not satisfy the above requirements. Therefore (6.3) could not be valid for this experiment. The total current density can be written in terms of the leakage current density and the ionic current density as j total = ^leak + ^ 1 + a ) ; j i o n ' By assuming that j . . and are constant one< can expect the total leatc a current to vary with time in the same manner as the ionic current density varies. The film thickness D can be expressed as a function of time in terms of the ionic current density by (2.2) as D = D_ + (constant) ft j . dt, " (6.4) 0 t _ Q Jxon ' where the constant voltage was applied at time t=0 when the film thick-ness was D_. If (2.17) is substituted for i . i n (6.4) an implicit 0 Jxon function in D i s obtained which is d i f f i c u l t or perhaps impossible to solve for D as a function of time. Thus in this investigation no explicit expression has been given for D or j . as a function of time. v & Jxon VII CONCLUSION Silicon dioxide thin films were grown on single crystal s i l i c o n wafers by the plasma anodization technique in an r . f . excited oxygen plasma. Film thicknesses were measured in situ by a technique u t i l i z i n g the variation of the intensity of a laser beam reflected from a growing 53 film as a function of film thickness. The optical system was so designed that i t was possible to make thickness measurements continuously with the plasma on. To elucidate the nature of the growth mechanism films were grown under conditions of constant pressure (-32 m i l l i t o r r ) , constant sample temperature (~200°C) and with an anodizing voltage held constant o o for film growth in the typical thickness range of 1400 A to 4000 A. A double probe method was used to estimate the voltage regulation of the voltage across the oxide film with a constant bias voltage applied to the sample and i t was found to be 21%. However for the purposes of comparing the experimental data the error in electric f i e l d change is more important; this error was only 7.9%. Three different theories of anodization were investigated: (1) the rate-limiting diffusion theory (2) the classical theory of high-f i e l d ionic conduction in solids and (3) the impact ionization theory. Of the three theories proposed, the experimental results strongly indicate that the impact ionization theory is applicable over the film thickness range considered in this experiment. The electron mobility in the Si02 film was calculated from the experimental data using the value of ionization (18") 2 potential given by Fritzsche for Si02 films, and found to be 29 cm /volt-(19) sec which agreed very well with the value determined by Goodman from modified Hall measurements for insulators. The following is a l i s t of topics suggested for further research: (a) The verification of the upper limits of oxide film thickness, as predicted by the impact ionization theory, for given sets of conditions; (b) The optimization of the growth rate by investigation of the effects of gas pressure, position of the sample and type of r . f . power coupling.. (c) The detailed study of the dielectric properties of SiC^ films grown by r.f. plasma anodization to assess the applicability of this technique to integrated circuit technology APPENDIX The problem of maintaining a constant voltage across the oxide film The need arose for a method of maintaining a constant voltage, U, across the oxide film while the film was growing. The simpleist biasing arrangement is to apply a constant voltage, ^SUppi_y> t o t n e sample with respect to the grounded electrode (see Figure 3.6), but this may not necessarily mean that U remains constant. In this Appendix an estimate is made of the constancy of U for a given constant V . . J supply A method of analyzing this problem is to consider the system of Figure 3.6 as that of a double probe system with one of i t s probes grounded. Johnson and M a l t e r ^ ^ analyzed the double floating probe arrangement, which differs from the arrangement in this experiment in that here one of the probes is grounded and instead of the potentials on both of the probes changing the plasma potential is forced to move with respect to the grounded probe. The surface of the oxide film can be considered as probe number (1) having an area, A^, the same as the surface area of the oxide film. The electrode can be considered as probe number (2) having an area k^' Figure (1) shows the potential diagram between probes (1) and (2) with a positive potential applied to probe (1) with respect to probe (2) which is grounded. The potential V c represents the difference in the plasma potentials due to non-uniformity of the plasma. Fig. (1) 56 To simplify the analysis of the probes assume that = A^ and that V =0. Furthermore assume that V, has no effect on the ion current c d to the probes. This is a reasonable approximation as the heavy ions are much less influenced by a potential on the probe than are the lighter electrons. In order to better understand how the probes work i t is worth considering the following five cases. Case 1 occurs when V, = 0 so that the number of electrons d arriving at each probe is the same. The electron current flowing to each probe w i l l balance the positive ion current flowing to each probe and no net current w i l l flow in the external c i r c u i t . Figure 2a. shows the potential diagram for case 1. Case 2 occurs when is a small positive voltage so that probe (1) draws more electrons than probe (2). Since probe (2) is grounded i t cannot go more negative in order to make a deficiency of electrons at probe (2) to compensate for the increase in electrons being drawn by probe (1). Thus the electrons drawn from the plasma by probe (1) cause the plasma potential to rise so that probe (2) is now more negative with respect to the plasma potential and thus draws fewer electrons. The excess electrons at probe (1) then flow through the external circuit to probe (2) to compensate for the deficiency of electrons at probe (2) and a net current, 1^, flows through the external cir c u i t . The potential diagram for case 2 is shown in Figure 2b. Case 3 occurs when V, is made large and positive. Now probe (1) d draws a large number of electrons from, the plasma so that the plasma potential i s forced quite far upward making probe (2) highly negative with respect to the plasma potential so that probe (2) no longer draws electrons 57 ,PROBE N P g« V, v d = o Case 1 Fig. 2a PROBE /<PR0BE N0.2 NO.1 w Vpi ^Plasma 2. Case 2 Fig. 2b yPROBE PROBE P M r > i M H O PROBE PROBE N0.2 N0.1 V, 58 from the plasma. Thus half of the electrons arriving at probe (1) pass through the external circuit to make up for the deficiency of electrons at probe (2). Any further positive increase in the value of V, w i l l not d cause any further increase in the current through the external c i r c u i t because probe (1) is already drawing enough electrons from the plasma to balance a l l the ion current flowing in the system. The further increases in w i l l only raise the plasma potential higher, but w i l l not change the potential difference between the plasma potential and probe (1). Probe (2) thus becomes more negative with respect to the plasma potential and is thus saturated with respect to positive ions. The potential diagram for case 3 is shown in Figures 2c and 2d. Case 4 occurs when is slightly negative so that probe (1) draws less electrons than probe (2). With fewer electrons leaving ,the plasma than ions the plasma potential drops so that more electrons reach probe (2) and the excess of electrons which arrive at probe (2) pass through the external circuit to compensate for the deficiency of electrons at probe (1). The potential diagram for case 4 is shown in Figure 2e. Case 5 occurs when is made strongly negative such that probe (1) does not draw any electrons from the plasma causing the plasma potential to f a l l as more positive ions are leaving the plasma than are electrons. Due to the f a l l in the plasma potential probe (2) draws more electrons, half of which flow through the external circuit to compensate for the deficiency of electrons at probe (1). If is made more strongly negative the potential difference between the plasma and probe (2) w i l l not change, as probe (2) is already drawing enough electrons from the plasma to balance a l l the ion current flowing i n the system. Thus by 59 PROBE NO.1 Plasma 5 PROBE N 0 2 ^ Case 4 Fig. 2e PROBE N0.1 PROBE N0.1 PROBE NO.2 N V, Plasma 6 Case 5 Fig. 2f V, Plasma 7 PROBE NO. 2 I Case 5 Fig. 2g 60 going further negative the potential of probe (1) w i l l become further negative with respect to the plasma potential, but the plasma potential w i l l not change. The potential diagram for case 5 is shown in Figures 2f and 2g. Figure 3 shows the curve of I ,vs. V, for the cases discussed d d above. For the experiment explained in this thesis the part of Figure 3 where i s negative was not needed. When the probe areas are not equal and or V ^ 0 the curve w i l l not cross the V, axis where V, =0, but i t c d d w i l l s t i l l have the same form. Figure 4 shows the potential diagram, for two different film thicknesses, when a constant voltage, V , , i s applied to the sample. supply-In Figure 4 a constant voltage was applied when the film thickness was and the oxide drew an i n i t i a l current 1^. The film was allowed to grow to a thickness where i t drew a fi n a l current I ^ . By replacing the oxide film by a metal electrode of the same area as the film surface area a curve can be obtained as in Figure 3. The values of and can then be obtained from Figure 3 by finding the voltages corresponding to 1^ and l2« Since electrode number 2 is grounded and at zero voltage, the i n i t i a l voltage across the oxide film, when the film thickness i s , is and the f i n a l voltage across the oxide film i s U^, when the film thickness is D2, where and are given by (1) and (2) respectively. U = V . - V „ (1) 1 supply dl U = V . - V , 0 (2) 2 supply d2 The change in voltage across the oxide film in growing from i t s i n i t i a l to f i n a l thickness i s defined by AU which is given by (3). SATURATION Fig. (3) Fig. (4) 62 A U 3 U 2 - U l = V d l - V d 2 (3) The voltage regulation during the film growth from to i s given by (4). V - V (percent voltage regulation) = — x 100 = — — - — x 100 (4) 1 supply dl If V ' >>V,1 and i f the difference between V,, and V,„ i s small compared supply dl dl d2 ^ to Vg ^ the voltage regulation w i l l be quite small. The condition that ^ s upp^y > >^ r (j^ c a n ^ e obtained by having a film of good insulating quality and the condition that V,, - V,„<<V . can be obtained by ^ J dl d2 supply J not operating in the saturation region of Figure (3). It is useful to consider also the electric f i e l d in the oxide film. The i n i t i a l f i e l d in the oxide film is the slope of the line AB in Figure <&)which is given by (5). U l E l " IT <5> The actual final f i e l d in the oxide film i s ( E j , and is the slope 2 actual of the line AD in Figure (4) which is given by (6). U2 ( E2 )actual " D^ ( 6 ) It is of interest to define the f i e l d that would be in the oxide film i f did not change with film thickness so that the f i e l d change in the oxide was only due to the change in the thickness of the film and not also to a change in voltage across the oxide film. This f i e l d is defined as (E-) , . ., and is the slope of line AC in Figure (4) which is given 2 theoretical by (7). ^ E2^theoretical = D^ ^ 63 The theoretical f i e l d change due only to the change in thickness of the film i s denoted by (AE) , ^. , and is given by (8). theoretical ( A E ^ theoretical = E l ~ (1V theoretical = U1 (D^ " (8) The actual f i e l d change due to the combination of a film thickness change and the change in the potential across the film is denoted by ( ^ ^ ) a c t u a ^ and i s given by (9). ( A E ) a c t u a l " E l " f a c t u a l = IT " ^ <9> The percent error between the theoretical f i e l d change and the actual f i e l d change, denoted by the Greek letter y, is given by (10). (AE), . . - (AE) _ . D. U. - U. D- percent Y theoretical actual . _ n 1 2 1 . n n 1 s v . _ , / i n N i = x 100 = — x 100 = — {voltage } (10) 1 2 1 2 regulation The value of y is a measure of whether the voltage regulation took place over a small or large interval of film thickness. For a fixed voltage regulation y w i l l be larger i f the regulation took place over a small Interval of film thickness than over a large interval of film thickness. 64 REFERENCES 1. C.J. Dell'Oca, D. Pulfrey and L. Young, Physics of Thin Films, 6^  (in press). 2. J.F. O'Hanlon, J. Vac. Sci. and Tech., ]_, 330 (1970). 3. R. I. Nazarova, Russ J. Phys. Chem., _36_, 522 (1962). 4. J. R. Ligenza, J. Appl. Phys., 36, 2703 (1965). 5. J. Kraitchman, J. Appl. Phys., _38, 4323 (1967). 6. P.J. Jorgensen, J. Chem. Phys., 37, 874 (1962). 7. W.L. Lee, G. Olive, D.L. Pulfrey, and L. Young, J. Electrochem. Soc, 11, 1172, (1970). 8. B.E. Deal and A.S. Grove, J. Appl. Phys., 36, 3770 (1965). 9. L. Young, Anodic Oxide Films, Academic press: London (1961). 10. L. Young and F.G.R. Zobel, Electrochm. Soc, 113, 277 (1966). 11. CR. Fritzshe, Solid State Comm., j5, 341 (1968). 12. CR. Fritzsche, J. Phys. Chem. Solids, 30, 1885 (1969). 13. S. Whitehead, Dielectric Breakdown of Solids, Oxford: London (1951). 14. O.S. Heavens, Optical Properties of Thin Solid Films, Butterworths: London (1955). 15. I. Franz and W. Langheinrich, Sol. Stat. Electr., 11_, 63, (1968). 16. T.E. French and C.J. Vierck, Graphic Science, McGraw-Hill, 1st. ed., 676, (1958). 17. R.M. Burger and R.P. Donovan, Fundamentals of Silicon Integrated  Device Technology, Prentice Hall: New York, 5^  (1967). 18. CR. Fritzshe, Z. Angew. Phys., 24, 48 (1967). 19. A.M. Goodman, J. Electrochem. Soc, 115, 281, (1968). 20. E.O. Johnson and L. Malter, Phys. Rev., 80, 58, (1950). 65 21. L. Maslng, J.E. Orme, and L. Young, J. Electrochem. Soc, 108, 428, (1961). 22. M.J. Rand, J. Appl. Phys., 41, 787 (1970). 

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