Solvent Concentration Profile of Poly(methyl methacrylate) Dissolving

Chapter 23

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Solvent Concentration Profile of Poly(methyl methacrylate) Dissolving in Methyl Ethyl Ketone A Fluorescence-Quenching Study 1

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William Limm , Mitchell A. Winnik , Barton A. Smith , and Deirdre T. Stanton 2

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U.S. Army CRDEC, Attn: S M C C R - R S C - A (E3220), Aberdeen Proving Ground-Edgewood Arsenal, MD 21010-5423 Lash Miller Chemistry Laboratory and Erindale College, University of Toronto, Toronto, Ontario M5S 1A1, Canada IBM Research Division, Almaden Research Center K91/801, San Jose, CA 95120-6099 2

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A novel approach to determine the solvent concentration profile in a photoresist undergoing dissolution viafluorescencequenching and laser interferometry is introduced. Fluorescence arising from phenanthrene dye labels in a 1-μm-thick poly(methylmethacrylate) (PMMA) film is quenched by permeation of methyl ethyl ketone (MEK), a good solvent for PMMA. A steady-state MEK concentration profile has been estimated from quenching data with existing sorption and light scattering data. The profile contains all the features of Case II diffusion: the Fickian precursor, the solvent front, and the plateau region. However, the solventfrontis not so steep as those observed in systems where penetrant diffusion is much slower. We account for thesefindingsin detail. D i s s o l u t i o n o f p o l y m e r s i n o r g a n i c s o l v e n t s a t t r a c t e d much a t t e n t i o n r e c e n t l y (1-11) d u e t o t h e i m p o r t a n c e o f t h e photoresist d i s s o l u t i o n process i n manufacturing i n t e g r a ted c i r c u i t s (IC's). As t h e i r s o p h i s t i c a t i o n and c i r c u i t d e n s i t y i n c r e a s e , t h e u n d e r s t a n d i n g o f fundamental a s p e c t s of p h o t o r e s i s t d i s s o l u t i o n becomes more c r i t i c a l . Cur r e n t l y , t h e s t a t e - o f - t h e - a r t I C ' s h a v e t h e minimum f e a t u r e s i z e o f l e s s t h a n 1 μ ι α . On t h i s s c a l e , p h o t o r e s i s t s w e l l i n g , which u s u a l l y accompanies i t s d i s s o l u t i o n , i s o f t e n the l i m i t i n g f a c t o r i n obtaining higher c i r c u i t density. T h e r e f o r e , a r e d u c t i o n o f p h o t o r e s i s t s w e l l i n g upon e x p o s u r e t o d e v e l o p i n g s o l v e n t i s of v i t a l i n t e r e s t t o t h o s e who a r e d e v e l o p i n g new p h o t o r e s i s t m a t e r i a l s . E x t e n t o f p o l y m e r s w e l l i n g i s o f t e n gauged by g r a v i m e t r i c method - one m o n i t o r s t h e w e i g h t - g a i n o f a p o l y 0097-6156/89/0412-0385$06.00/0 ο 1989 American Chemical Society

Reichmanis et al.; Polymers in Microlithography ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

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mer sample when i t i s immersed i n s o l v e n t . Thus, the s o l v e n t p e r m e a t i o n r a t e (SPR) a n d , t h e r e f o r e , p e r m e a t i o n mechanism c a n be d e t e r m i n e d from t h i s m e t h o d . However, i t p r o v i d e s no i n f o r m a t i o n on how a p o l y m e r s w e l l s s p a t i ally. F u r t h e r m o r e , i f s o l v e n t permeation i s accompanied by p o l y m e r d i s s o l u t i o n , as i n t h e c a s e o f p h o t o r e s i s t , the g r a v i m e t r i c method i s i n a c c u r a t e . A more u s e f u l a p p r o a c h i s to determine the thickness of the g e l l a y e r during the polymer d i s s o l u t i o n experiment s i n c e the g e l l a y e r i s formed due t o t h e s w e l l i n g o f b u l k p o l y m e r . However, t h e determination of the g e l l a y e r thickness i s not t r i v i a l . Krasicky et a l . ( 4 ) estimated the thickness of the t r a n s i t i o n l a y e r , w h i c h encompasses a l l i n t e r p h a s e s b e t w e e n t h e b u l k g l a s s y p o l y m e r f i l m and t h e b u l k p o l y m e r s o l u t i o n , by m e a s u r i n g t h e change i n o p t i c a l i n t e r f e r e n c e i n t e n s i t y d u r i n g and a f t e r t h e p o l y m e r d i s s o l u t i o n p r o c e s s . To e s t i m a t e t h e t h i c k n e s s o f t h e g e l l a y e r from t h i s m e t h o d , a s o l v e n t c o n c e n t r a t i o n p r o f i l e (SCP) a c r o s s t h e t r a n s i t i o n l a y e r h a s t o be a d o p t e d . Conversely, i f the c o r r e c t SCP c a n be d e t e r m i n e d b y some e x p e r i m e n t a l m e t h o d , t h e SCP w o u l d y i e l d n o t o n l y t h e g e l l a y e r t h i c k n e s s , b u t t h e manner o f s o l v e n t d i f f u s i o n i n t o t h e p o l y m e r f i l m as w e l l . T h e r e f o r e , the best approach to i n v e s t i g a t e photo r e s i s t s w e l l i n g i s t o d e t e r m i n e , i n - s i t u , t h e SCP i n a polymer undergoing d i s s o l u t i o n . A l t h o u g h C r a n k (12) p r o p o s e d a d e s c r i p t i v e SCP i n 1953, f i r m e x p e r i m e n t a l d a t a s t a r t e d to appear only r e c e n t l y . Thomas a n d W i n d l e ' s m i c r o d e n s i t o m e t r y (13-16) a n d K r a m e r ' s R u t h e r f o r d b a c k s c a t t e r i n g (17-18) p r o d u c e d SCP o f s e v e r a l s o l v e n t - p o l y m e r combinations. However, t h e s e e f f o r t s were l i m i t e d b y t h e s p a t i a l r e s o l u t i o n o f t h e i r t e c h n i q u e s ( c a . 30 nm). In a d d i t i o n , t h e s e t e c h n i q u e s have been a p p l i e d t o systems where t h e S P R ' s a r e on t h e o r d e r o f 1 μ ι η / h o u r o r l e s s . The S P R s a r e much g r e a t e r f o r s y s t e m s where s o l v e n t p e r meation i s accompanied by polymer f i l m d i s s o l u t i o n . T h e r e f o r e , t h e d e t e r m i n a t i o n o f SCP i n s u c h s y s t e m s w o u l d r e q u i r e a t e c h n i q u e t h a t i s q u i c k e r a n d l e s s cumbersome f o r r e p e a t e d measurements. I n o u r p r e v i o u s p a p e r ( H ) , we i n t r o d u c e d a n o v e l e x p e r i m e n t a l method t o s t u d y t h e m e c h a n i s t i c d e t a i l s o f s o l v e n t permeation i n t o t h i n polymer f i l m s . T h i s method i n c o r p o r a t e s a f l u o r e s c e n c e q u e n c h i n g t e c h n i q u e (19-20) and l a s e r i n t e r f e r o m e t r y ( £ ) . The f o r m e r , i n e f f e c t , m o n i t o r s t h e movement o f v a n g u a r d s o l v e n t m o l e c u l e s ; t h e l a t t e r monitors the d i s s o l u t i o n process. We t o o k t h e t i m e d i f f e r e n c e s between t h e s e two t e c h n i q u e s t o e s t i m a t e b o t h t h e n a s c e n t and t h e s t e a d y - s t a t e t r a n s i t i o n l a y e r t h i c k n e s s e s o f PMMA f i l m u n d e r g o i n g d i s s o l u t i o n i n 1:1 MEKisoproanol solution. The s t e a d y - s t a t e t h i c k n e s s was i n good agreement w i t h t h e e s t i m a t e o f K r a s i c k y e t a l . ( 2 - 8 ) . I n t h i s p a p e r , t o d e t e r m i n e t h e s t e a d y s t a t e SCP a c r o s s t h e t r a n s i t i o n l a y e r , we a n a l y z e t h e fluorescence i n t e n s i t y d e c a y o f dye m o l e c u l e s c o v a l e n t l y bound t o t h e polymer c h a i n s . The d e c a y i s due t o t h e p e r m e a t i o n o f 7


23. LIMM ET AL.

Solvent Concentration Profile ofPoly (methyl methacrylate)

s o l v e n t , w h i c h quenches dye f l u o r e s c e n c e , i n t o the polymer film. The d i f f u s i o n c o e f f i c i e n t s o f MEK, t h e q u e n c h e r , were a v a i l a b l e from a l i g h t s c a t t e r i n g e x p e r i m e n t (21) at h i g h MEK c o n c e n t r a t i o n s . F o r t h e low c o n c e n t r a t i o n r e g i m e , i n d i r e c t e x p e r i m e n t a l d a t a were a v a i l a b l e (22). Once t h e d i f f u s i o n c o e f f i c i e n t i s d e t e r m i n e d a t a g i v e n c o n c e n t r a t i o n , t h e e x t e n t o f f l u o r e s c e n c e q u e n c h i n g c a n be predicted. T h e r e f o r e , by w o r k i n g b a c k w a r d , one c a n d e t e r mine t h e s o l v e n t d i f f u s i o n c o e f f i c i e n t and t h e s o l v e n t c o n c e n t r a t i o n i n a p o l y m e r f i l m from f l u o r e s c e n c e q u e n c h ing data. Consequently, i f a polymer f i l m d i s s o l v e s i n a s o l v e n t w i t h a c o n s t a n t d i s s o l u t i o n r a t e (DR)% t h e s o l v e n t c o n c e n t r a t i o n s a t d i f f e r e n t p a r t s o f t h e SCP c a n be d e t e r mined. F i n a l l y , a SCP i s c o n s t r u c t e d f r o m t h e s e d a t a . P o l y ( m e t h y l m e t h a c r y l a t e ) [PMMA] i s a n e x c e l l e n t polymer f o r s t u d y i n g p h o t o r e s i s t d i s s o l u t i o n because o f i t s minimal s w e l l i n g c h a r a c t e r i s t i c . F o r t h i s w o r k , PMMA m o l e c u l e s were l a b e l l e d w i t h p h e n a n t h r e n e (Phe) d y e s i n c e i t s f l u o r e s c e n c e i s quenched b y MEK. In a d d i t i o n , t h i s dye h a s t h e a d v a n t a g e o f f o r m i n g few e x c i m e r s (23-24) which r e s u l t s i n s e l f - q u e n c h i n g . Thus, the r e d u c t i o n i n f l u o r e s c e n c e i n t e n s i t y o f PMMA-Phe* i s v i r t u a l l y s o l e l y due t o MEK q u e n c h i n g . C o n s e q u e n t l y , t h e p e r m e a t i o n o f MEK i n t o a PMMA f i l m c a n be m o n i t o r e d f r o m f l u o r e s c e n c e intens i t y decay. The i n t e r f e r o m e t r y t r a c e shows t h e c h a n g e i n t h e o p t i c a l t h i c k n e s s of the polymer f i l m w i t h r e s p e c t t o time. Both the completion o f the polymer f i l m d i s s o l u t i o n and t h e D R c a n be d e t e r m i n e d . Experimental The PMMA-Phe s y n t h e s i s , c h a r a c t e r i z a t i o n , f i l m p r e p a r a t i o n , a p p a r a t u s and e x p e r i m e n t a l scheme a r e d e s c r i bed elsewhere (11). B r i e f l y , t h e PMMA c h a i n s , c o p o l y m e r i z e d from MMA and P h e - l a b e l l e d monomers, were c h a r a c t e r i z e d v i a g e l permeation chromatography (GPC): M = 4 1 1 , 0 0 0 , M - 1 9 7 , 0 0 0 and M / M - 2 . 0 8 . UV-absoïfption measurements i n d i c a t e d t h a t c a . Ï % o f a l l monomer u n i t s were P h e - l a b e l l e d . T h e s a m p l e was d i s s o l v e d i n t o l u e n e and was s p i n - c o a t e d o n t o 1 - i n c h d i a m e t e r q u a r t z d i s k s . T h e n , t h e f i l m s ( c a . 1 μπι t h i c k ) were a n n e a l e d a t 160 C f o r 60 m i n u t e s u n d e r vacuum. A PMMA-Phe f i l m was s e a t e d i n t h e f l o w c e l l a n d was c o n t i n u o u s l y e x p o s e d t o 290 nm r a d i a t i o n t h r o u g h o u t the experiment (Figure 1). The Phe f l u o r e s c e n c e was mon i t o r e d a t 3 65 nm maximum w h i c h d i d n o t s h i f t a p p r e c i a b l y w i t h a c h a n g e i n MEK c o n c e n t r a t i o n i n PMMA-Phe. There f o r e , t h e d e c a y i n t h e Phe f l u o r e s c e n c e i n t e n s i t y p r o v i d e s an a c c u r a t e measure o f MEK d i f f u s i o n and i t s S C P . The s o l v e n t pump was t u r n e d o n a t t » 0 s e c . It t a k e s c a . 20 s e c f o r t h e s o l v e n t t o r e a c h t h e f l o w c e l l c o n t a i n i n g t h e PMMA-Phe s a m p l e . A significant reduction in fluorescence i n t e n s i t y signals the a r r i v a l of solvent a t t h e PMMA-Phe s u r f a c e .


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Solvent outlet

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Figure 1. Flow C e l l f o r Monitoring Solvent Permeation and PMMA F i l m D i s s o l u t i o n Simultaneously. The c e l l i s placed i n the sample chamber of a fluorescence spectrometer. (Reproduced with permission from Ref. 11. Copyright 1988 Wiley & Sons.)


23.

LIMMETÀL.

Solvent Concentration Profile of Poly (methyl methacrylate)

Results A t y p i c a l time p r o f i l e o f the e x c i t e d PMMA-Phe* fluorescence i n t e n s i t y decay i s shown i n Figure 2. The MEΚ permeation commences a t 24 sec. The SPR increases during the p l a s t i c i z a t i o n p e r i o d u n t i l i t becomes con stant, the onset o f the steady s t a t e . I t i s c h a r a c t e r i z e d by a l i n e a r r e l a t i o n s h i p between the amount o f solvent absorbed and time. I t was determined from a l i n e a r r e g r e s s i o n a n a l y s i s t h a t the PMMA-Phe fluorescence i n t e n s i t y s t a r t s t o d e v i a t e from l i n e a r i t y a t 197 sec. T h i s i n d i cates a decrease i n the SPR and/or the unquenched PMMAPhe*. The decrease i n SPR i s unexpected a t t h i s f i l m thickness s i n c e the SPR i n t h i c k e r PMMA-Phe f i l m s show no anomaly a t 1 μ ι . A more p l a u s i b l e explanation i s the r e d u c t i o n i n a v a i l a b l e PMMA-Phe*, which i s expected when the f r o n t end o f the SCP reaches the s u b s t r a t e . The PMMA d i s s o l u t i o n was monitored v i a l a s e r i n terferometry. The r e s u l t i n g s i n u s o i d a l p a t t e r n (Figure 3) can be transformed t o i l l u s t r a t e the l o s s i n PMMA f i l m t h i c k n e s s with respect t o time ( ϋ ) . The d i s s o l u t i o n com mences a t 27 sec and ends a t 222 sec. By comparing the l a t t e r with the fluorescence d e v i a t i o n a t 197 sec, one obtains the t r a n s i t i o n l a y e r time-thickness i s 25 sec. Since the f i l m i s 1.0 μια t h i c k , i t s o v e r a l l DR i s ca. 5.1 nm/sec. Then, the s p a t i a l thickness o f the t r a n s i t i o n l a y e r i s ca. 130 nm. Figure 3 a l s o i n d i c a t e s t h a t the DR changes l i t t l e during the course o f d i s s o l u t i o n . This c o n t r a s t s with the permeation process which possesses a r a t h e r lengthy p l a s t i c i z a t i o n p e r i o d as seen from the curvature i n the i n t e n s i t y versus time data a t e a r l y times i n Figure 2. Data A n a l y s i s We wish t o use the fluorescence decay data i n F i g ure 2 t o c o n s t r u c t the SCP as i t propagates through the PMMA f i l m , f o c u s i n g on data a t the f i n a l phase o f the d i s s o l u t i o n process. T h i s a n a l y s i s w i l l i n v o l v e the f o l l o w i n g three assumptions: 1) the SCP advances a t a constant r a t e 2) the shape o f the p r o f i l e does not change and 3) the assumptions above hold even a f t e r the s o l v e n t molecules have reached the s u b s t r a t e . In Figure 4 we present a p i c t u r e o f t h i s model i l l u s t r a t ing the propagation o f the SCP through the f i l m . Accord ing t o assumptions 1) and 2), the SCP maintains i t s shape as i t advances a t a constant r a t e . These assumption are i n accord both with the data (Figures 2 and 3) and with the c u r r e n t l e v e l o f understanding o f Case I I d i f f u s i o n . The t h i r d assumption i s more troublesome but necessary f o r e v a l u a t i o n o f the data. As depicted i n Figures 4b and 4c, we ignore the f a c t t h a t the f r o n t i e r s o l v e n t molecules accumulate as they reach the substrate, and assume t h a t


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Figure 2 . PMMA-Phe* Fluorescence Decay i n MEK. I n i t i a l contact o f MEK and PMMA-Phe* produces a sharp drop i n i n t e n s i t y . T h i s i s followed by the p l a s t i c i z a t i o n p e r i o d , the steady s t a t e and the termination.

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Figure 3 . Interferometry Trace o f a PMMA F i l m D i s s o l v i n g i n MEK.


23. LIMM ET Al*

Solvent Concentration Profile ofPoly (methyl methacrylate)

the S C P maintains i t s shape. T h i s i s tantamount t o assum i n g t h a t t h e number o f m o l e c u l e s a l r e a d y a t t h e s u b s t r a t e s u r f a c e i s s m a l l compared t o t h e number a r r i v i n g a t e a c h increment i n time. T h i s model a l l o w s u s t o u s e t h e f l u o r e s c e n c e inten s i t y o b t a i n e d n e a r t h e end o f t h e d i s s o l u t i o n p r o c e s s i n F i g u r e 2 t o c o n s t r u c t t h e SCP i n t h e PMMA f i l m . The s t r a t e g y i s t o measure t h e i n c r e m e n t a l change i n f l u o r e s c e n c e i n t e n s i t y , Δ Ι , o c c u r r i n g i n a one s e c o n d i n t e r v a l i n t h e c u r v e d r e g i o n o f F i g u r e 2 and t o r e l a t e t h i s t o t h e amount of r e s i d u a l fluorescence, I , ' i n the A t s l i c e . The t i m e p r o f i l e o f I ' c o n t a i n s i n f o r m a t i o n about t h e SCP. The t i m e p r o f i l e c a n be t r a n s f o r m e d t o t h e d i s t a n c e p r o f i l e b e c a u s e t h e SCP p r o p a g a t e s a t a c o n s t a n t r a t e t h r o u g h t h e PMMA f i l m . I n a d d i t i o n , one needs t o know I o ' , t h e t o t a l ( u n quenched) f l u o r e s c e n c e i n t e n s i t y c o r r e s p o n d i n g t o t h e A t s l i c e s from w h i c h I ' i s d e t e r m i n e d . The r a t i o lo'/l' is related to a s p e c i f i c concentration of solvent (quencher) t h r o u g h i n d e p e n d e n t knowledge o f t h e f l u o r e s c e n c e q u e n c h ing process. L e t u s c o n s i d e r what happens t o t h e fluorescence i n t e n s i t y o f a t h i n PMMA-Phe f i l m a t t h e PMMA-quartz i n terface. F o r t h e s a k e o f s i m p l i c i t y , we f o c u s on t h e r e g i o n t h a t l i e s between t h e s u b s t r a t e and 5 . 1 nm away from i t , w h i c h we name t h e " Q - z o n e " . 5 . 1 nm i s t h e d i s t a n c e t h e s t e a d y s t a t e SCP t r a v e l s i n one s e c o n d . In F i g u r e 4 a , i t e x p e r i e n c e s no q u e n c h i n g . A f t e r one s e c o n d , F i g u r e 4 b , q u e n c h i n g commences. The change i n f l u o r e s c e n c e i n t e n s i t y i n t h a t one s e c o n d i s c o m p l e t e l y due t o q u e n c h i n g a t the "Q-zone", which c o n t a i n s i n f o r m a t i o n about t h e MEK c o n c e n - t r a t i o n a t t h e f i r s t 5 . 1 - n m o f t h e S C P . A f t e r a n o t h e r s e c o n d , we h a v e t h e s i t u a t i o n i l l u s t r a t e d i n Figure 4c. S i m i l a r l y , t h e Δ Ι between F i g u r e s 4b a n d 4c r e p r e s e n t s t h e amount o f q u e n c h i n g due t o t h e s e c o n d 5 . 1 -nm o f t h e S C P . T h e r e f o r e , a s t h e SCP p r o p a g a t e s t h r o u g h t h e " Q - z o n e " ( F i g u r e s 4c and 4 d ) , t h e MEK c o n c e n t r a t i o n a t e a c h 5 . 1 - n m p o r t i o n o f t h e SCP c a n be d e t e r m i n e d . F l u o r e s c e n c e Quenching F l u o r e s c e n c e quenching i s d e s c r i b e d i n terms o f two mechanisms t h a t show d i f f e r e n t d e p e n d e n c i e s on q u e n cher concentration. I n dynamic q u e n c h i n g , t h e quencher c a n d i f f u s e a t l e a s t a few n a n o m e t e r s on t h e t i m e s c a l e o f the e x c i t e d s t a t e l i f e t i m e (nanoseconds). In s t a t i c quen c h i n g , mass d i f f u s i o n i s s u p p r e s s e d . O n l y t h o s e dye m o l e c u l e s w h i c h a r e a c c i d e n t a l l y c l o s e t o a q u e n c h e r w i l l be affected. T h o s e f a r from a q u e n c h e r w i l l f l u o r e s c e n o r m a l l y , unaware o f t h e p r e s e n c e o f q u e n c h e r s i n t h e s y s t e m . These p r o c e s s e s a r e d e s c r i b e d below f o r t h e s p e c i f i c c a s e o f PMMA-Phe* q u e n c h e d b y MEK. I n low v i s c o s i t y m e d i a , t h e q u e n c h i n g o f Phe* f l u o r e s c e n c e b y MEK i s d y n a m i c i n n a t u r e a n d f o l l o w s t h e Stern-Volmer equation (25):


391

392

POLYMERS I N MICROLITHOGRAPHY

I /I = 1 + k r° o

q

(1)

c

where τ° i s the unquenched l i f e t i m e o f the Phe, c i s the molar c o n c e n t r a t i o n o f MEK and k i s the phenomenological second-order r a t e constant f o r t8e quenching process: k Phe* + MEK • Phe + MEK* (2) 3

Studies on the quenching o f photoexcited 9-phenanthrylmethyl p i v a l a t e by MEK, a model f o r - t h e PMMA-Phe/MEK system, provide a value o f k = 7.3 X 10 M~ s " i n c y c l o hexane (11). T h i s value i s S e a r l y one order o f magnitude lower than the d i f f u s i o n - c o n t r o l l e d r a t e . For r e a c t i o n s i n which a d i f f u s i o n step precedes a chemical step, t h e r e l a t i o n s h i p between k and ^ ^ i s given by: q

1 k

d

_1

=

k

q

+

f f

_ k

diff

i

(3)

chem

where k , i s the second-order r a t e constant f o r the quenching process under s t r i c t l y chemical c o n t r o l ( k oo ) . Since k , . _ = 5.0 X 10%M s i n cyclohexafiè" (11), we o b t a i n RtZZ = 8.6 X 10* M~ s . Values o f U ® J i n PMMA-MEK mixtures can be c a l c u l a t e d from the Smoluchowski expression: d i f f

Ί

X

m

f f

k

diff

=

4

TN R D/1000, A

(4)

O

where N i s Avogadro's number, R i s the capture r a d i u s f o r the quenching and D i s the d i f f u s i o n c o e f f i c i e n t o f MEK i n PMMA-MEK mixtures. Values o f D over the PMMA weight f r a c t i o n range o f 0 t o 0.75 are a v a i l a b l e from l i g h t s c a t t e r i n g experimentation (21). No data are a v a i l able a t higher PMMA concentrations f o r MEK, but D values i n g l a s s y PMMA have been reported f o r methyl acetate (MeAc) (22.) which i s i s o s t e r i c with MEK. These values are p l o t t e d i n F i g u r e 5 and are combined by drawing a smooth l i n e through both s e t s o f data. With R * 5 A (11), we have a l l the data necessary t o c a l c u l a t e k j f and k values over the e n t i r e range o f PMMA-MEK compositions. MEK d i f f u s i o n i s too slow t o make a s i g n i f i c a n t c o n t r i b u t i o n t o quenching i n mixtures r i c h i n PMMA. Quenching occurs only i f a MEK molecule i s c l o s e enough t o a Phe group a t the moment i t absorbs l i g h t . S t a t i c quenching i s d e s c r i b e d by the P e r r i n equation (26-27): A

d

f

In ( I / I ) = 4 *N R [MEK]/3000 Q

A

Q

(5)

where R , the r a d i u s o f the a c t i v e sphere, i s 5 A f o r Phe* quenchea by a l i p h a t i c ketones ( H ) . At an MEK c o n c e n t r a t i o n g r e a t e r than 1 M, both the dynamic and the s t a t i c quenching mechanisms have t o be taken i n t o account. Therefore, Frank and V a v i l o v ' s model of combined s t a t i c and dynamic quenching model (28),


23.

LIMMETAK

Solvent Concentration Profile of Poly (methyl methacrylate) 393

Distance from the Substrate

[MEK]

b, quenching commences

a, no quenching

[MEK]

c, more quenching F i g u r e 4.

Propagation

d, SPC forges ahead of

Solvent Concentration

Profile.

Do (MEK) = S.11 E-5 cm2/sec

-6 Hwang & Cohen, Macromol. 17, 2890 (1984)

log D

Wang & Kwei, Macromol. β, 919 (1973)

-12 10

[MEK] F i g u r e 5. MEK D i f f u s i o n MEK C o n c e n t r a t i o n .

Coefficient

as

a Function


of

POLYMERS IN

394

V

1

=

MICROLITHOGRAPHY

(V^STATIC^V^DYNAMIC

= β χ ρ ( 4 π N R [MEK]/3000) · (1 + k A

Q

6

g

r°[MEK]/1000)

i s used t o c a l c u l a t e the solvent c o n c e n t r a t i o n . At an MEK c o n c e n t r a t i o n g r e a t e r than 7 M, quenching i s too extensive to determine the r e s i d u a l fluorescence i n t e n s i t y . Solvent Concentration P r o f i l e The most complete model t o date f o r d e s c r i b i n g Case I I d i f f u s i o n i s t h a t of Thomas and Windle (13-16). They e n v i s i o n the process as a coupled s w e l l i n g - d i f f u s i o n problem i n which the s w e l l i n g r a t e i s t r e a t e d as a l i n e a r v i s c o e l a s t i c deformation d r i v e n by osmotic pressure. T h i s model leads t o the idea of a precursor phase propagating ahead of a moving boundary, as we have d e p i c t e d i n F i g u r e 4. While Thomas and Windle have used numerical methods t o examine i n d e t a i l the p r e d i c t i o n s of t h e i r model, t h i s model i s d i f f i c u l t t o t e s t with the data obtained here. Consequently, we w i l l f o l l o w the example of M i l l s e t a l . (29) who r e c e n t l y presented the f i r s t measurements of l o c a l s o l v e n t c o n c e n t r a t i o n using the Rutherford backs c a t t e r i n g technique. They analyzed the case o f 1,1,1t r i c h l o r o e t h a n e (TCE) d i f f u s i n g i n t o PMMA f i l m s i n terms of a simpler model developed by P e t e r l i n (30-31), i n which the propagating s o l v e n t f r o n t i s preceded by a F i c k i a n p r e c u r s o r . The P e t e r l i n model d e s c r i b e s the f r o n t end of the steady s t a t e SCP as: c(x) = c

Q

exp

(-vx/D)

(7)

where c i s the l i m i t i n g c o n c e n t r a t i o n of F i c k i a n d i f f u s i o n , ν i s the f r o n t v e l o c i t y , χ i s the d i s t a n c e ahead of the moving f r o n t and D i s the d i f f u s i o n c o e f f i c i e n t of penetrant. We determine the SCP as i t i s terminated at the s u b s t r a t e i n the f o l l o w i n g manner. F i r s t , we c a l c u l a t e I ' = d l / d t f o r the l i n e a r p o r t i o n of the i n t e n s i t y decay. A l i n e a r l e a s t squares f i t t o the data i n the time i n t e r v a l 170 - 190 sec produces a value of d l / d t = 1150 counts/sec. T h i s represents the steady s t a t e quenching r a t e which i s i n t i m a t e l y r e l a t e d t o the steady s t a t e SPR. Secondly, we c a l c u l a t e I ' = d l / d t at one-second i n t e r v a l s as the steady s t a t e ends with the a r r i v a l o f the SCP a t the s u b s t r a t e . For example, f o r the data i n Figure 2, I. 's have been c a l c u l a t e d commencing at 197 sec. Finally, we use these values of i ,-//!*.') i n conjunction with eq. (6) t o c a l c u l a t e the c o n c e n t r a t i o n of MEK, c ( x ) , a t each i n t e r v a l by a numerical method and, thereby, c o n s t r u c t a histogram of the SCP (Figure 6). F i g u r e 7 i l l u s t r a t e s the f r o n t end of the SCP as a semilogarithmic p l o t with respect t o time. The p l o t i s l i n e a r , i n accord with eq. (7). Each second corresponds Q

1


23. LIMMETAL.

Solvent Concentration Profile ofPoly (methyl methacrylate) 395

10 Total

tau(Phe') = 46 nsec

8

Ro (Phe*-MEK) = 4.9 A Co (Phc^-MEK) = 3.3β M —

Dynamic

6 In (Io/I) 4

2

-^^^static

—-

1

0

^

1

2

4

1

1

6

8

10

[MEK]

Figure 6. C a l c u l a t e d PMMA-Phe* Fluorescence I n t e n s i t y from S t a t i c and Dynamic Quenching Theory as a Function of MEK Concentration.

ι

0

ο From C(x) = Co cxp (-vx/D), In C(x) = In Co - vx/D

-

D = 1.30 £-12 cm2/sec

-2

Co = 1.27 M ο

-3

where C(x) = M E K cone, at distance χ ahead of front Co = limiting M E K cone, for Fickian DiiT.

0

and ν = velocity of front

1

1

200

204

1

1 208

1

I 212

ι

1 216

TIME (sec)

Figure 7 . F i c k i a n Precursor i n the MEK Solvent Concen tration Profile.



396

to a distance o f 5.1 nm. The span o f the p l o t i n Figure 7 covers ca. 16 seconds corresponding t o a permeation depth of a t l e a s t 80 nm f o r the F i c k i a n precursor ahead o f the moving f r o n t . I t i s i n t e r e s t i n g t o compare t h i s value with that o f the t r a n s i t i o n l a y e r which we determined t o be ca. 130 nm t h i c k . T h i s i n d i c a t e s that the F i c k i a n pre cursor takes up the major p o r t i o n o f the t r a n s i t i o n l a y e r f o r the PMMA-MEK system. The r e p t a t i o n model f o r polymer d i f f u s i o n would p r e d i c t t h a t the thickness o f the g e l phase r e f l e c t s the dynamics o f disentanglement. The important f a c t o r s here are chain length, solvent q u a l i t y and temperature s i n c e they a f f e c t the dimensions o f the polymer c o i l s i n the g e l phase. The precursor phase, on the other hand, depends upon solvency and temperature only through the osmotic force i t can generate i n the system and the v i s c o e l a s t i c response o f the system i n the region o f the f r o n t . These f a c t o r s should be independent o f the PMMA molecular weight. From the s l o p e o f the p l o t i n Figure 7, we c a l c u l ate D = 1.3 X 10 cm /sec and c = 1.3 M, which i s ca. 0.11 i n MEK mole f r a c t i o n * ^ By comparison, Wang and Kwei (22) reported D = 5 X 10 cm /sec f o r MeAc vapor a t 30 C. In a d d i t i o n , M i l l s e t a l . (29)-reported, f o r TCE d i f f u s i n g i n t o PMMA f i l m , D = 3 X 10 cm /sec and c = 0.09 i n TCE mole f r a c t i o n from t h e i r Rutherford bacKs c a t t e r i n g experiment. Therefore, our f i n d i n g s are i n good agreement with other i n v e s t i g a t o r s ' r e s u l t s . In the high concentration regime, our SCP i s d i f f e r e n t from a t y p i c a l SCP observed i n Case I I d i f f u s i o n . S p e c i f i c a l l y , our SCP l a c k s the sharp s o l v e n t f r o n t (£jLg.8). The abrupt i n c r e a s e i n s o l v e n t c o n c e n t r a t i o n normally ob served i s due t o the long r e l a x a t i o n time o f the polymer chain i n response t o s o l v e n t p l a s t i c i z a t i o n . Then, the absence of t h i s f e a t u r e p o i n t s t o a very r a p i d r e l a x a t i o n of PMMA chains by MEK. This i s probably due t o a good match i n the s o l u b i l i t y parameters o f PMMA and MEK ( =9.3 f o r both). Tne molar concentration o f pure MEK i s ca. 11.2 M. One might question why the concentration o f MEK does not reach 11.2 M on the SCP. T h i s i s mostly due t o the slow process o f untangling PMMA chains. For the c o n c e n t r a t i o n of MEK t o reach 11.2 M, the swollen polymer g e l phase has t o be untangled and removed from the v i c i n i t y o f the quartz s u b s t r a t e . T h i s i s d r i v e n by the e n t r o p i e f o r c e which works r a t h e r slowly i n the absence o f high s o l v e n t flow. For example, M i l l s e t a l . (29) r e p o r t , f o r TCE d i f f u s i n g i n t o PMMA f i l m , t h a t the SCP o f TCE s t a b i l i z e s at a mole f r a c t i o n o f l e s s than 0.2. By comparison, our r e s u l t s o f [MEK] = 3.2 M corresponds t o a mole f r a c t i o n o f ca. 0.3. T h i s , again, r e f l e c t s the b e t t e r s o l u b i l i t y o f MEK i n PMMA r e l a t i v e t o TCE ( δ « 9.6). 2

2


UMMETAL

Solvent Concentration Profile of Poly(methyl methacrylate) 397

Q

Distance from the 5p ψ

Substrate ψ

(nm) Ζψ-

4 -

Time

(sec)

Figure 8. Estimation of the MEK P r o f i l e i n a PMMA F i l m .

Solvent

Concentration



398

Summary Experiments are reported on the d i s s o l u t i o n r a t e and permeation r a t e f o r t h i n (1 μια) PMMA f i l m s exposed t o l i q u i d MEK. The f i l m s contain ca. 1 % o f covalently-bound Phe, a f l u o r e s c e n t dye. By monitoring the d i s s o l u t i o n rate by l a s e r interferometry and the fluorescence quench ing of Phe* by MEK, we can determine: 1) the thickness of the g e l l a y e r 2) the shape and the thickness of the F i c k i a n pre cursor and 3) the d i f f u s i o n c o e f f i c i e n t of MEK i n the g l a s s y PMMA matrix. Acknowledgments The authors wish t o thank the IBM SUR program, NSERC Canada and NRC Research A s s o c i a t e s h i p program f o r t h e i r support o f t h i s work.

Literature Cited 1. 2. 3. 4.

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23. LIMMETAL.

Solvent Concentration Profile oj'Poly'(methyl methacrylate)

18. Hui, C.-Y.; Wu, K.-C.; Lasky, R. C . ; Kramer, E. J. J. Appl. Phys. 1987, 61, 5137. 19. Forster, Th. Faraday Soc. Disc. 1959, 27, 7. 20. Dexter, D. L. J . Chem. Phys. 1953, 21, 836. 21. Hwang, D.-H.; Cohen, C. Macromol. 1984, 17, 2890. 22. Wang, T. T.; Kwei, T. K. Macromol. 1973, 6, 919. 23. Birks, J . B.; Georghiou, S. J . Phys. B. 1968, 1, 958. 24. Stevens, B.; Dubois, J . T. Trans. Faraday Soc. 1966, 62, 1525. 25. Birks, J . B. Photophysics of Aromatic Molecules, p.443, Wiley-Interscience, New York, 1970. 26. Perrin, F. Compte. Rend. 1924, 178, 1978. 27. Perrin, F. Ann. Chem. Phys. 1932, 12, 283. 28. Frank, J . M.; Vavilov, S. I. Z. Physik 1931, 69, 100. 29. Mills, P. J.; Palmstrom, C. J.; Kramer, E. J . J . Mater. Sci. 1986, 21, 1479. 30. Peterlin, A. J . Polym. Sci. 1965, B3, 1083. 31. Peterlin, A. J . Res. NBS 1977, 81A, 243. RECEIVED June29,1989


39

Solvent Concentration Profile of Poly(methyl methacrylate) Dissolving

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