Plasma-Polymerized Organosilicon Thin FilmsâStructure and

13 Plasma-Polymerized Organosilicon T h i n F i l m s -

Downloaded by UNIV OF CALIFORNIA IRVINE on October 25, 2014 | http://pubs.acs.org Publication Date: September 24, 1979 | doi: 10.1021/bk-1979-0108.ch013

Structure and Properties M. KRYSZEWSKI, A. M. WROBEL, and J. TYCZKOWSKI Centre of Molecular and Macromolecular Studies, Polish Academy of Sciences, 90-362 Lodz, Poland

Numerous recent developments i n advanced technology have drawn attention to t h i n films produced by low temperature plasma polymerization. One of the outstanding advantages of plasma polymerization for preparation of thin polymer films i s the wide variety of organic compounds that may be polymerized by this technique eg. monomers which do not polymerize using conventional methods. Among the numerous monomers which have been used i n plasma polymerization the organosilicons were found to form films of unique properties. The plasma polymerized organosilicon films show: a) high thermal s t a b i l i t y ( 1 , 2 ! ) , b) high d i e l e c t r i c constant ( 3 . ) , c) outstanding o p t i c a l properties which may be u t i l i z e d i n conventional and integrated optics ( 4 ) , d) they may be applied as p r o t e c t i v e coatings for many materials and as d i e l e c t r i c s i n microelectronics. The mechanism of formation of those films and t h e i r structure are very complex due to many elementary reactions taking place i n a glow discharge. These films are insoluble i n common solvents due to the high degree of c r o s s l i n k i n g ; thus to characterize t h e i r structure complex methods must be used. Preparation of t h i n films by plasma polymerization of organosilicons and e s p e c i a l l y of organosilazanes and

0-8412-0510-8/79/47-108-219$05.00/0 © 1979 American Chemical Society

In Plasma Polymerization; Shen, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1979.

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some a s p e c t s o f t h e mechanism o f t h e s e r e a c t i o n s were d i s c u s s e d i n o u r p r e v i o u s p a p e r s (5-J7). The aim o f t h i s p a p e r was t o s t u d y t h e s t r u c t u r e and c r o s s l i n k i n g me chanism o f p o l y m e r s o b t a i n e d by low t e m p e r a t u r e plasma p o l y m e r i z a t i o n o f h e x a m e t h y l c y c l o t r i s i l a z a n e (HMCTSN) and o f h e x a m e t h y l c y c l o t r i s i l o x a n e (HMXTSO) as w e l l as some problems r e l a t e d t o t h e changes o f t h e i r s t r u c t u r e due t o t h e r m a l treatment. Me Si

Me Si

?

9

'NH

HN Me Si 2 \

SiMe^

9

Me Si 9

SiMe.

NH HMCTSN

HMCTSO

The p r e s e n t p a p e r r e p o r t s a l s o some r e s u l t s o f d.c. c o n d u c t i v i t y s t u d i e s o f f i l m s o b t a i n e d from some mono mers and e s p e c i a l l y from HMCTSN. The i n v e s t i g a t i o n s seem t o be a s t e p i n t h e a t t e m p t s t o r e a c h a c o r r e l a t i o n between t h e s t r u c t u r e o f t h e s e t h i n f i l m s and their electrical properties. Complex r e a c t i o n s o c c u r i n g d u r i n g glow d i s c h a r g e p o l y m e r i z a t i o n l e a d to the formation of m a t e r i a l s which s h o u l d n o t be s i m p l y c a l l e d polymers o b t a i n e d from g i ven monomers; i t w o u l d be more a p p r o p r i a t e t o use t h e expression: plasma-polymerized h e x a m e t h y l c y c l o t r i s i l a zane e t c . f o r o t h e r monomers b u t f o r t h e sake o f simp l i c i t y t h e terms p o l y s i l a z a n e s and p o l y s i l o x a n e s w i l l be used i n t h i s p a p e r .

EXPERIMENTAL H e x a m e t h y l c y c l o t r i s i l a z a n e and h e x a m e t h y l c y c l o t r i s i l o x a n e were p u r i f i e d by r e c t i f i c a t i o n i n vacuum f o l l o w i n g w h i c h t h e i r p u r i t y was t e s t e d by gas chromato graphy. Plasma p o l y m e r i z a t i o n s were c a r r i e d o u t i n an e l e c t r o d e system d e s c r i b e d p r e v i o u s l y ( 5_). T h i n f i l m were d e p o s i t e d i n a 20 kHz glow d i s c h a r g e on t h e s u r f a ce o f s t a i n l e s s s t e e l e l e c t r o d e s o r on g o l d o r s i l i c o n e l e c t r o d e s i n t h e case o f t h i n l a y e r s i n t e n d e d f o r f u r ther studies of e l e c t r i c a l properties. A l l polymeriza t i o n s were c a r r i e d o u t a t c o n s t a n t d i s c h a r g e parame t e r s : c u r r e n t d e n s i t y j = 1 mA/cm2, d i s c h a r g e d u r a t i o n t = 30 s e c , monomer vapour p r e s s u r e ρ = 0.3 T o r r .



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F o r f u r t h e r a n a l y t i c a l i n v e s t i g a t i o n s 0.2 mg p o l y mer samples were removed from e l e c t r o d e s and p y r o l y s e d i n a J e o l p y r o l y s e r u n i t , Model 727. P y r o l y s e s were c a r r i e d o u t i n a h e l i u m atmosphere a t a t e m p e r a t u r e o f 400° C f o r 30 s e c . The v o l a t i l e p y r o l y s i s p r o d u c t s were f e d d i r e c t l y t o t h e i n j e c t i o n p a r t o f a J e o l gas c h r o matography Model JGC 1100, e q u i p p e d w i t h a flame i o n i z a t i o n d e t e c t o r ; the apparatus i n c o r p o r a t e d a 2.5 m χ 2 mm s t a i n l e s s s t e e l s e p a r a t i o n column f i l l e d w i t h 0V 101 10 % s u p p o r t e d on V a r a p o r t 80/100 mesh. The v o l a t i l e p y r o l y s i s p r o d u c t s , i s o l a t e d by gas chromato g r a p h y , were a n a l y s e d u s i n g a LKB mass spectrometer,Mo d e l 2091, e q u i p p e d w i t h a PDP11 computer. Mass s p e c t r o m e t r i c a n a l y s e s were c a r r i e d o u t w i t h an e l e c t r o n beam energy o f 70 eV. Studies o f the e l e c t r i c a l p r o p e r t i e s o f t h i n poly mer f i l m s were c a r r i e d o u t i n a s t a n d a r d e l e c t r o m e t r i c system. The f i l m s under i n v e s t i g a t i o n were p r e p a r e d un der t h e same c o n d i t i o n s as t h o s e used f o r t h e i r s t r u c t u r e s t u d i e s . They were p r e p a r e d on t h e s u r f a c e s o f d i f f e r e n t vacuum d e p o s i t e d m e t a l e l e c t r o d e s o r on t h e s u r f a c e o f S i - s i n g l e c r y s t a l s . The a p p r o p r i a t e upper e l e c t r o d e was vacuum d e p o s i t e d on t h e s u r f a c e o f a t h i n polymer l a y e r . F i l m t h i c k n e s s was d e t e r m i n e d by double beam i n t e r f e r e n c e method.

RESULTS AND DISCUSSION S t r u c t u r e o f Polymer F i l m s . P r e v i o u s s t u d i e s o f p l a s m a - p o l y m e r i z e d o r g a n o s T l i c o n f i l m s have shown t h a t t h e i r c h e m i c a l s t r u c t u r e i s v e r y complex (6-1_3) . I n o r der t o o b t a i n more d e t a i l e d i n f o r m a t i o n about t h e che m i c a l s t r u c t u r e o f t h e s e f i l m s , t h e y were examined u s i n g combined a n a l y t i c a l t e c h n i q u e s o f p y r o l y s i s - g a s chromatography-mass s p e c t r o m e t r y (PGCMS). Gas chromatograms o f v o l a t i l e p y r o l y s i s p r o d u c t s formed from p l a s m a - p o l y m e r i z e d HMCTSN and HMCTSO a r e shown i n F i g s . 1 and 2, r e s p e c t i v e l y . They were i d e n t i f i e d by mass s p e c t r o m e t r y and w i t h t h e a i d o f c e r t a i n s t a n d a r d compounds. F o r t h e sake o f b r e v i t y i t i s n o t p o s s i b l e t o d i s c u s s t h e mass s p e c t r a h e r e . The s t r u c t u res o f p y r o l y s i s products corresponding t o the respec t i v e c h r o m a t o g r a p h i c peaks a r e p r e s e n t e d i n T a b l e I f o r b o t h p o l y m e r s . I t s h o u l d be n o t e d t h a t t h e peaks marked by X ( F i g s . 1 and 2) c o r r e s p o n d t o u n s e p a r a t e d m i x t u r e o f l i g h t h y d r o c a r b o n s . As c a n be seen from T a b l e I , t h e p y r o l y s i s p r o d u c t s i n t h e case o f b o t h polymers c o n s i s t o f low m o l e c u l a r c y c l i c o r g a n o s i l i c o n compounds.



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Figure 1. Gas chromatogram of the volatile cyclic products of pyrolysis at 400°C of phsma-polymerized hexamethylcyclotrisilazane

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Figure 2. Gas chromatogram of the volatile cyclic products of pyrolysis at 400°C of phsma-polymerized hexamethylcyclotrisiloxane

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> 2 ( F i g . 3 ) . I t i s u s e l e s s , however, t o l o o k i n t h i s case f o r the t h i c k n e s s dependence o f the c o n d u c t i n g c u r r e n t i n o r d e r t o e l i m i n a t e SCLS. I t was shown, by means o f n u m e r i c a l c o m p u t a t i o n , t h a t f o r such h i g h f i e l d s even S c h o t t k y o r P o o l e - F r e n k e l c u r r e n t s p l o t t e d i n l n j - d " c o o r d i n a t e s y i e l d a dependence, w h i c h can be a p p r o x i m a t e d by a s t r a i g h t l i n e w i t h η > 3, w h i c h i n t u r n i s e x p e c t e d f o r space charge l i m i t e d c u r r e n t s ( 2 5 ) . However the second and the t h i r d b r a n c h e s o f l n j - I n V p l o t f o r t h i s p o l y m e r merge i n t o one s t r a i g h t l i n e when r e p l o t t e d i n l n j - v 1 ' c o o r d i n a t e s , thus s u g g e s t i n g t h a t a l s o the t h i r d b r a n c h may be due to the same p r o c e s s , i . e . S c h o t t k y o r P o o l e - F r e n k e l . I t can thus be assumed t h a t one o f these two mechanisms does p l a y a d e c i s i v e r o l e i n the e l e c t r i c c o n d u c t i v i t y o f the f i l m s under d i s c u s s i o n . However, i t i s n o t easy t o d i s t i n g u i s h between the two mechanisms, e s p e c i a l l y i n the case o f p o l y m e r systems. The s i m p l e s t t e s t , usu a l l y a p p l i e d t o c r y s t a l s e m i c o n d u c t o r s , i s the c o m p a r i son o f e x p e r i m e n t a l c o e f f i c i e n t s 3 d e t e r m i n e d form the s l o p e o f the l i n e a r p a r t o f the j - V c h a r a c t e r i s t i c drawn i n the l n j - V«/2 system w i t h t h e o r e t i c a l v a l u e s o f t h a t c o e f f i c i e n t (the v a l u e s o f the c o e f f i c i e n t are c o l l e c t e d i n T a b l e I I ; the t h e o r e t i c a l v a l u e s were c a l c u l a t e d f o r d i e l e c t r i c c o n s t a n t ε = 3.5).


s

n

2

Table I I . The values o f coefficients 3 obtained from experiments and calculated according to Schottky and Poole-Frenkel mechanisms. 3 exp Plasma-Polymerized:

3

PooleFrenkel χ 10 eV(m/V)' /2 ^Schottky 5

Styrene (29) Hexamethyldisiloxane(21) Hexamethyldisilazane(25) Hexamethylcyclotrisilazane(24)

2.4 1.8 2.3±0.4 1.7±0.3

2.03


4.06

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Properties

I t f o l l o w s (Table I I ) t h a t t h e e x p e r i m e n t a l v a l u e s a r e i n good agreement w i t h t h e t h e o r e t i c a l a s s u m p t i o n s o f t h e S c h o t t k y mechanism. However, t h i s cannot be t r e a t e d as a d e f i n i t e s o l u t i o n , i f o n l y because o f t h e f a c t t h a t i n some cases gs 3P-F (32,3_3), and i n sim p l e models v a l u e s o f t h e c o e f f i c i e n t d i f f e r by a f a c t o r o f 2 o n l y , which i s i n s u f f i c i e n t f o r unequivocal d i f f e r e n t i a t i o n between t h e two mechanisms. In view o f t h e above, c o n d u c t i v i t y measurements were conducted i n asymmetric systems: A u - p o l y m e r - S i f o r p o l y s t y r e n e and p o l y s i l a z a n e , and A u - p o l y m e r - I n f o r p o l y s i l o x a n e . The d i f f e r e n c e i n b a r r i e r h e i g h t between Au-polymer and S i - p o l y m e r e s t i m a t e d on t h e b a s i s o f measurements o f t h e A u - S i b a r r i e r i s c a . 0.5 eV (34) w h i c h , i n t h e case o f t h e c o n d u c t i v i t y l i m i t e d by the e l e c t r o d e s , s h o u l d produce a d i f f e r e n c e i n t h e i n t e n s i t y o f the currents o f opposite p o l a r i z a t i o n s equal t o about 8 o r d e r s o f magnitude. The d i f f e r e n c e i n work f u n c t i o n o f Au and I n , on t h e o t h e r hand, i s c a . 1 eV s o , on t h e a s s u m p t i o n o f t h e S c h o t t k y mechanism o f con d u c t i v i t y , the d i f f e r e n c e i n the i n t e n s i t y o f opposite p o l a r i z a t i o n s s h o u l d amount t o 17 o r d e r s o f magnitude (35) . As c a n be seen i n F i g . 4 i n t h e case o f an asym m e t r i c p o l y s i l a z a n e sample t h e r e i s a d i f f e r e n c e i n t h e i n t e n s i t y o f the c u r r e n t s ; although t h i s d i f f e r e n c e does t a k e t h e e x p e c t e d c o u r s e , i t i s s e v e r a l times s m a l l e r t h a n e x p e c t e d , and i s thus v i r t u a l l y n e g l i g i b l e . A s i m i l a r r e s u l t was o b t a i n e d f o r the p o l y s t y r e n e sample, w h i l e i n t h e case o f t h e asymmetric system b a sed on p o l y s i l o x a n e t h e r e was no d i f f e r e n c e i n t h e i n t e n s i t y o f t h e o p p o s i t e - b i a s s e d f i e l d s over the e n t i r e range o f f i e l d s used - up t o 3 χ 1 0 V/m. I t c a n thus be assumed t h a t t h e c o n d u c t i v i t y i n t h e f i l m s under s t u d y i s dominated by t h e P o o l e - F r e n k e l volume genera t i o n i n d e p e n d e n t o f t h e c o n t a c t e f f e c t s . Such were a l s o the c o n c l u s i o n s o f the w o r k e r s who s t u d i e d t h e conduc t i v i t y i n p o l y s t y r e n e (29) and p o l y s i l o x a n e ( 2 J J . A more s e a r c h i n g a n a l y s i s o f t h e P o o l e - F r e n k e l me chanism p e r f o r m e d f o r p o l y s i l o x a n e on t h e b a s i s o f t h e H i l l model (36) showed t h a t charge c a r r i e r e m i s s i o n s h o u l d p r o c e e d from t h e i s o l a t e d Coulomb c e n t r e and s h o u l d t a k e p l a c e i n t h e hemisphere r e l a t e d t o t h a t c e n t r e . The depth o f t h e c e n t r e s , d e t e r m i n e d form t h e a c t i v a t i o n dependence o f t h e t e m p e r a t u r e , was E ^ = = 0.76 eV. I t has been shown r e c e n t l y t h a t t h e p r e s e n c e o f P o o l e - F r e n k e l c e n t e r s i n t h e sample s h o u l d l e a d t o t h e appearance i n TSC s p e c t r a o f peaks f o r w h i c h t h e tem p e r a t u r e T c o r r e s p o n d i n g t o t h e i r maxima a r e e l e c t r i c a l f i e l d strenght-dependent according t o the f o l l o w i n g


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4.

Schottky plot for asymmetric system zane)-Si; (A) Au electrode positive, (O)Au

Au-poly(hexamethylcyclotrisihelectrode negative.


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ET AL.

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r e l a t i o n T - F / 2 ( 3 7 ) . The e x p e r i m e n t a l y o b t a i n e d TSC s p e c t r a i n p o l y s i l a z a n e measured i n the f i e l d range o f 10" - 10^ V/m d i d not show f i e l d dependent maxima. These r e s u l t s e n a b l e d us t o e x c l u d e the p r e s e n c e o f P o o l e F r e n k e l c e n t e r s i n the i n v e s t i g a t e d f i l m s g i v i n g a s t r o n g argument a g a i n s t t h e o p p e r a t i o n o f the P o o l e F r e n k e l mechanism o f c o n d u c t i v i t y i n p o l y s i l a z a n e s . T h i s l e a d s t o a r e c o n s i d e r a t i o n o f the s i g n i f i c a n c e o f the S c h o t t k y mechanism. The r e s u l t s o f c u r r e n t d e n s i t y s t u d i e s i n samples s u p p l i e d w i t h asymmetric e l e c t r o d e s mentioned above d i d not c o n f i r m i t s i m p o r t a n c e u n e q u i v o c a l l y , b u t assuming t h e e x i s t e n c e o f s u r f a c e s t a t e s one has t o t a k e i t i n t o a c c o u n t . I n f a c t , M i z u t a n i a t a l . (38) have shown t h a t the b a r r i e r h i g h t s a t the met a l - p o l y m e r c o n t a c t s as e s t i m e t e d by p h o t o i n j e c t i o n f o r two d i f f e r e n m e t a l s may d i f f e r o n l y by 0.07 eV, w h i l e t h e o r e t i c a l p r e d i c t i o n s a r e 1.1 eV. T h i s d i s a p p e a r a n c e o f the b a r r i e r h i g h t s d i f f e r e n c e i s r e l a t e d t o t h e s u r f a c e s t a t e s . S i m i l a r e f f e c t s may be e x p e c t e d i n the c a se o f p o l y s i l a z a n e f i l m s . Measurements o f t h e r m a l a c t i v a t i o n e n e r g i e s i n the system A u - p o l y s i l a z a n e - S i f o r o p p o s i t e b i a s e d f i e l d s have shown a s m a l l b u t d i s t i n c t d i f f e r e n c e : f o r p o l a r i z a t i o n o f +50 V E ^ = 0.980 ± ± 0.005 eV and f o r p o l a r i z a t i o n o f -50 V E = 1.01 ± 0.01 eV. These d i f f e r e n c e s a r e s i m i l a r t o those r e p o r t e d i n ( 3 8 ) . These r e s u l t s seem t o show t h a t f o r pol y s i l a z a n e s - i n the range o f the i n v e s t i g a t e d f i l m t h i c k n e s s e s and f i e l d s t r e n g t h s - i n j e c t i o n from e l e c t r o d e s dominates when c o n s i d e r i n g t h e r o l e o f s u r f a c e states. I t would be i n t e r e s t i n g t o o b t a i n a c t u a l systems w i t h asymmetric c o n t a c t b a r r i e r s on p o l y m e r . I t seems t h a t heat t r e a t m e n t o r plasma m o d i f i c a t i o n by c h e m i c a l l y a c t i v e gases may l e a d t o such systems from plasma p o l y m e r s . One c o u l d e x p e c t f o r such systems an i n c r e a s e o f the a c t i v a t i o n energy d i f f e r e n c e f o r two o p p o s i t e p o l a r i z a t i o n s o f the f i l m . 1


m

A

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ABSTRACT The chemical structure of thin films formed by plasma polymerization of hexamethylcyclotrisilazane (HMCTSN) and hexamethylcyclotrisiloxane (HMCTSO) was studied. The investigations were carried out using combined techniques of pyrolysis - gas chromatography - mass spectrometry. The results showed that the pyrolysis products of highly crosslinked plasma polymers contained low-molecular weight compounds trapped in the



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polymer film during its growth. The distinct difference between the structure of the pyrolysis products of both polymers showed silazane and siloxane monomers to undergo polymerization according to two different mechanisms. It was found that heat treatment of plasma-polymerized HMCTSN films leads to the formation of thermally stable materials of almost inorganic structure. D.C. conductivity and thermally stimulated currents examinations showed that Schottky effects were of importance for the elucidation of the electrical conductivity mechanism of plasma polymer films.


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LITERATURE CITED 1. Tuzov L . S . , Kolotyrkin V.M. and Tunitskij N.N., Vysokomol.Soed., (1970) A12,849. Tkatschuk B.W., KolotyrkinV.M. and Smetankina N.P., Vysokomol.Soed., (1970) A12, 1458. 2. Wrobel A.M. and Kryszewski M . , Bull.Acad.Pol.Ser. Sci.Chim. (1974) 22, 471. 3. Maisonneuve M., Segui Y. and Bui Α . , Thin Solid Films, (1976) 33, 35. 4. Tien P.K., Riva-Senseverion S., Martin R.J. and Smolinsky G . , Appl.Phys.Lett., (1974) 24, 547. 5. Wrobel A.M., Kryszewski M. and Gazicki M., Polymer, (1976) 17, 673. 6. Wrobel A.M., Kryszewski M. and Gazicki M., Polymer, (1976) 17, 678. 7. Gazicki M . , Wrobel A.M. and Kryszewski M . , J.Aggl.Polym.Sci., (1977) 21, 2013. 8. Tkatschuk B.W., Bushin U . V . , KolotyrkinV.M. and Smetanskina N.P., Vysokomol.Soed., (1967) A9, 2018. 9. Tkatschuk B.W., Koloryrkin V.M. and Kirey G.G., Vysokomol.Soed. (1968) A10, 585. 10. Vasile M.J. and Smolinsky G . J . , J.Electrochem.Soc., (1972) 119, 451. 11. Denes F . , Ungutenasu C. and Hajduc J . , J.Europ. Polym.,(1970) 6, 1155. 12. Tkatschuk B.W. and Kolotyrkin V.M, "Formation of Thin Polymer Films from Gase Phase" Izd.Khimia, Moscow 1977. 13. Möller W. and Schmidt M . , Beitr.Plasmaphys., (1977) 17, (2), 121. 14. T i l l e r H . J . , Berg D., Herzberg D. and Dumke Κ., J.Macromol.Sci.Chem. (1977) A11, 547. 15. Wrobel A.M., Gazicki M. and Kryszewski M . , IUPAC Macromolecular Symposium, Taskent 1978. 16. Wrobel A.M. and Kryszewski M . , IUPAC-International Round Table for PlasmaPolymerizationandSurface Treatment, Limoges 1977. 17. Wrobel A.M. and Kryszewski M . , Polymer Preprints, (1978) 19, 521. 18. Bradley A. and Hammes P., J.Electrochem.Soc. (1963) 110, 15. 19. Mearns A.M., Thin Solid Films, (1969) 3, 201. 20. Pechonik H. and Seebacher G., Thin Solid Films, (1974) 38, 343. 21. Desbarax Ν . , These de Doctorat, Universite Paul Sabatier, Toulouse, France 1975.



236

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POLYMERIZATION

22. Desbarax N . , Lacoste R., et Segui Y . , Colloque "Phenomenes de vieillissement dans les dielectri ques solides et methodes d'essais", Toulouse 1975. 23. Maisonneuve M . , Segui Y. and Bui Α . , Thin Solid Films (1977) 44, 209. 24. Tyczkowski J., Zielinski M. and Kryszewski M. Thin Solid Films, in press. 25. Tyczkowski J., unpublished data. 26. Morita S. and Shen M . , J.Polym.Sci.,(1977) 15, 981. 27. Tkatschuk B.W., Ganiuk L.J., Laurs E . P . , Khim.Vys. Energ. (1977) 11, 350. 28. Simmons J.G., J.Phys.D.,(1971) 4, 613. 29. Carchano H. and Valentin M . , Thin Solid Films, (1975) 30, 335. 30. Chybicki M . , Phys.Stat.Sol., (1977) a39, 271. 31. Kryszewski M. and Szymanski M . , Macromol.Rev., (1970) 4, 245. 32. Simmons J.G., Phys.Rev., (1967) 155, 657. 33. Hall R.B., Thin Solid Films, (1971) 8, 263. 34. Deal B . E . , Snow E.H. and Mead C . A . , J.Phys.Chem. Solids, (1966) 27, 1873. 35. Wintle H . J . , J.Non-Cristalline Solids, (1974) 15 471. 36. H i l l R.M.,Phil. Mag. (1971) 23, 59. 37. Zielinski M. and Samoc M . , J.Phys.D. (1977) 10, L. 105. 38. Mizutani T . , Takai, Osawa T. and Ieda M . , J.Phys.D.,(1976) 9, 2253. Received March 29, 1979.


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