Characterization of Stresses in Polymer Films for Microelectronics

Chapter 29

Characterization of Stresses in Polymer Films for Microelectronics Applications Rolf W. Biernath and David S. Soane

Polymeric Materials for Electronics Packaging and Interconnection Downloaded from pubs.acs.org by YORK UNIV on 12/17/18. For personal use only.

Department of Chemical Engineering, University of California at Berkeley, Berkeley, CA 94720

Experimental results and modeling strategy for the determination of stresses in thermosets used in microelectronics are presented. The bending beam technique for in situ stress measurement i s particularly emphasized. This technique is here extended to determine the glass transition temperature, Tg, and the product of the elastic modulus and coefficient of thermal expansion, Eα, above and below Tg. Three case studies illustrate the range of applicability of the bending beam setup and factors contributing to the stress state. The f i r s t is a comparison of two polymers for interlayer dielectrics: PMDA -ODA (pyromellitic acid dianhydride - oxydiamine) and a bis-benzocyclobutene. The second is of a neat epoxy resin commonly used for microelectronics encapsulation (epoxidized ortho-cresol novolac cured with a phenolic novolac). The third is a screen-printable polyimide coating used for protection of the integrated-circuit chip. An outline of our stress model is sketched, and example results are presented. P o l y m e r s a r e u s e d e x t e n s i v e l y i n t h e f a b r i c a t i o n and e n c a p s u l a t i o n o f m i c r o e l e c t r o n i c s (1). They f u n c t i o n as photoresists, intermetallic d i e l e c t r i c layers, passivation c o a t i n g s , d i e a t t a c h a d h e s i v e s , and e n c a p s u l a n t s f o r t h e packaging o f i n d i v i d u a l chips. Polymer-impregnated c o m p o s i t e s a l s o s e r v e as p r i n t e d c i r c u i t b o a r d s f o r m o u n t i n g and i n t e r c o n n e c t i o n o f i n t e g r a t e d c i r c u i t s . Since polymers g e n e r a l l y e x h i b i t d i f f e r e n t thermal expansion b e h a v i o r from o t h e r m a t e r i a l s commonly employed i n m i c r o e l e c t r o n i c s , s i g n i f i c a n t s t r e s s e s a r e c a u s e d by t e m p e r a t u r e t r a n s i e n t s d u r i n g m a n u f a c t u r i n g and i n u s e ( 2 ) . 0097^6156/89/0407-0356$06.00/0 o 1989 American Chemical Society

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Stresses in Polymer Films

357

Even i f f a i l u r e s such as c h i p c r a c k i n g o r s p a l l i n g a r e a v o i d e d , r e p e a t e d s t r a i n i n g o f i n t e g r a t e d c i r c u i t s may a l t e r t h e i r e l e c t r i c a l c h a r a c t e r i s t i c s through m e t a l l u r g i c a l f a t i g u e and g e o m e t r i c a l d i s t o r t i o n . It i s t h e o b j e c t i v e o f our r e s e a r c h t o e s t a b l i s h mechanisms by w h i c h s t r e s s e s a r e c r e a t e d i n p o l y m e r l a y e r s d e p o s i t e d on s i l i c o n , q u a r t z , and o t h e r s u b s t r a t e s . Once t h e dependence o f t h e r m o - v i s c o e l a s t i c s t r e s s e s on m a t e r i a l p r o p e r t i e s and p r o c e s s i n g p a r a m e t e r s i s f i r m l y u n d e r s t o o d , we p l a n t o d e v e l o p m a t e r i a l d e s i g n and p r o c e s s o p t i m i z a t i o n g u i d e l i n e s t o minimize s t r e s s e s i n packaged i n t e g r a t e d c i r c u i t s . Stress i s r e l a t e d to s t r a i n through c o n s t i t u t i v e equations. M e t a l s and c e r a m i c s t y p i c a l l y p o s s e s s a d i r e c t r e l a t i o n s h i p between s t r e s s and s t r a i n : t h e e l a s t i c modulus Q). P o l y m e r s , however, may e x h i b i t complex v i s c o e l a s t i c b e h a v i o r , p o s s e s s i n g c h a r a c t e r i s t i c s o f b o t h l i q u i d s and s o l i d s (4.) . T h e i r s t r e s s - s t r a i n b e h a v i o r depends on t e m p e r a t u r e , d e g r e e o f c u r e , and t h e r m a l h i s t o r y ; t h e b e h a v i o r i s made even more c o m p l i c a t e d i n c u r i n g systems s i n c e m a t e r i a l p r o p e r t i e s change from a low m o l e c u l a r weight l i q u i d t o a h i g h l y c r o s s l i n k e d s o l i d polymer (ϋ). When a d i m e n s i o n a l change i n a p o l y m e r c o a t i n g does not match t h a t o f i t s c o n s t r a i n t (such as t h e s u b s t r a t e t o which i t adheres), the r e s u l t i n g s t r a i n generates s t r e s s i n b o t h t h e p o l y m e r and t h e s u b s t r a t e . Strain arises in p o l y m e r s by t h e r m a l e x p a n s i o n and c o n t r a c t i o n (£) , from s o l v e n t and b y - p r o d u c t e v a p o r a t i o n ( 2 ) , from m o i s t u r e a b s o r p t i o n (£), from c u r e (£), and from p h y s i c a l a g i n g (1Û) . Polymer p r o p e r t i e s a r e h i g h l y s e n s i t i v e t o t e m p e r a t u r e w i t h t r a n s i t i o n s between p h y s i c a l s t a t e s t y p i c a l l y o c c u r r i n g o v e r many t e n s o f d e g r e e s C e l s i u s (A) . A d d i t i o n a l l y , the p r o p e r t i e s are s e n s i t i v e t o the r a t e at w h i c h t h e t e m p e r a t u r e changes. F o r example, t h e a p p a r e n t g l a s s t r a n s i t i o n t e m p e r a t u r e o f a g i v e n p o l y m e r sample i n c r e a s e s with the r a t e of temperature scan. For t h e r m o s e t s (such as e p o x i e s and p o l y i m i d e s ) t h e t h e r m a l h i s t o r y i s e s p e c i a l l y important because of i t s coupled e f f e c t on t h e p h y s i c a l s t a t e o f t h e p o l y m e r and t h e r e a c t i o n k i n e t i c s (XL) . O t h e r f a c t o r s h a v i n g a s u b s t a n t i a l i n f l u e n c e on p o l y m e r p r o p e r t i e s a r e s o l v e n t and b y - p r o d u c t concentrations. Here, an i n c r e a s e i n s o l v e n t concentration d e c r e a s e s t h e g l a s s t r a n s i t i o n t e m p e r a t u r e (12.) . R e p e a t e d t h e r m a l c y c l i n g a l s o i m p a c t s t h e p o l y m e r p r o p e r t i e s and t h e s t a t e o f s t r e s s (13) . The c o n v e r s i o n o f s t r a i n mismatch i n t o s t r e s s i s a f u n c t i o n o f t h e s t r e s s r e l a x a t i o n modulus e x h i b i t e d by t h e polymer. A p r e d i c t i v e s t r e s s model must i n c o r p o r a t e t h e complex d e p e n d e n c i e s o f t h e modulus and s t r e s s r e l a x a t i o n b e h a v i o r on t e m p e r a t u r e , g l a s s t r a n s i t i o n t e m p e r a t u r e , degree o f cure, c r o s s l i n k d e n s i t y , s o l v e n t - p l a s t i c i z a t i o n , and r e a c t i o n k i n e t i c s .

358

POLYMERS FOR ELECTRONICS PACKAGING AND INTERCONNECTION

Experimental Method The s t r e s s measurement t e c h n i q u e employed i n o u r l a b o r a t o r y i s b a s e d on t h e p r i n c i p l e o f a b e n d i n g c a n t i l e v e r beam. The method was f i r s t d e v e l o p e d f o r s t r e s s measurement i n m e t a l f i l m s ( l i b 1 5 ) , b u t has r e c e n t l y been e x t e n d e d t o p o l y m e r s ( £ , 1 £ ) due t o t h e a v a i l a b i l i t y o f u l t r a - t h i n q u a r t z s t r i p s (~ 80 μιη t h i c k ) . When two m a t e r i a l l a y e r s a d h e r e t o one a n o t h e r and one l a y e r d i f f e r e n t i a l l y expands o r c o n t r a c t s r e l a t i v e t o t h e o t h e r , t h e l a y e r s bend i n o r d e r t o m i n i m i z e t h e s t r a i n energy. S u b j e c t t o v a r i o u s c o n s t r a i n t s , s u c h as l o c a l l y u n i f o r m l a y e r t h i c k n e s s e s , and t h a t t h e s t i f f e s t l a y e r be l i n e a r e l a s t i c , t h e l o c a l b e n d i n g can be d e s c r i b e d by t h e a r c o f a c i r c l e o f r a d i u s , R. I f t h e c o n s t r a i n t s a r e v a l i d a c r o s s an e n t i r e sample, t h e e n t i r e sample w i l l i n d e e d bow i n t h e form o f an a r c o f a c i r c l e . This i s the o p e r a t i n g p r i n c i p l e o f t h e b e n d i n g beam a p p a r a t u s and i s i l l u s t r a t e d i n F i g u r e 1. Depicted i n Figure 1 i s a b i - m a t e r i a l s t r i p subject to b e n d i n g by i n t e r n a l s t r e s s e s a f t e r c o o l i n g from i t s c u r e temperature t o below the g l a s s t r a n s i t i o n temperature o f the polymer l a y e r . L a y e r 1 r e p r e s e n t s a low modulus, h i g h thermal expansion polymer; l a y e r 2 represents a high m o d u l u s , low t h e r m a l e x p a n s i o n s u b s t r a t e . The p o l y m e r s e e k s t o c o n t r a c t a l o n g i t s l e n g t h more t h a n does t h e s u b s t r a t e because o f i t s g r e a t e r t h e r m a l expansion coefficient. The s u b s t r a t e r e s i s t s t h e c o n t r a c t i o n o f t h e polymer, thereby i n d u c i n g a t e n s i l e s t r e s s i n the polymer and a c o m p r e s s i v e s t r e s s i n t h e s u b s t r a t e n e a r t h e interface. The t e n s i l e s t r e s s i n t h e p o l y m e r l a y e r w i l l c a u s e t h e s u b s t r a t e t o bow i n t h e d i r e c t i o n o f t h e p o l y m e r . The b o w i n g o f t h e s u b s t r a t e i n d u c e s a t e n s i l e s t r e s s a t i t s o u t s i d e edge. A typical linear elastic stress profile is s u p e r i m p o s e d on t h e d i a g r a m ; t e n s i o n i s d e n o t e d by "+", c o m p r e s s i o n by " - " . As w i l l be shown l a t e r , t h e b o w i n g o f the s u b s t r a t e i s d i r e c t l y p r o p o r t i o n a l to the s t r e s s f e l t by t h e p o l y m e r c o a t i n g . The b e n d i n g beam a p p a r a t u s o f f e r s s e v e r a l s p e c i f i c a d v a n t a g e s f o r s t r e s s measurement. F i r s t , the experiment measures d i r e c t l y t h e t r u e a v e r a g e s t r e s s i n t h e m a t e r i a l (lu, 1 2 ) . T h e r e f o r e , r e s u l t s from d i f f e r e n t l a b o r a t o r i e s can be m e a n i n g f u l l y compared. Secondly, the s t r e s s i s measured d u r i n g p r o c e s s i n g , e n a b l i n g i n d i v i d u a l f a c t o r s c o n t r i b u t i n g t o t h e s t r e s s s t a t e t o be d i s c e r n e d and quantified. T h i r d l y , the experiment r e q u i r e s o n l y a m i n i m a l amount o f m a t e r i a l ( l e s s t h a n a g r a m ) , and t h u s can be v e r y v a l u a b l e i n s c r e e n i n g and c o m p a r i n g low s t r e s s r e s i n s i n a development l a b o r a t o r y e n v i r o n m e n t . A d d i t i o n a l l y , s e v e r a l m a t e r i a l p r o p e r t i e s o f t h e r e s i n can be d e t e r m i n e d - t h e s e i n c l u d e t h e g l a s s t r a n s i t i o n t e m p e r a t u r e , T g , and t h e p r o d u c t o f t h e e l a s t i c modulus and t h e r m a l c o e f f i c i e n t o f e x p a n s i o n , E a , b o t h b e l o w and above

29. BIERNATH & SOANE


Tg. Effects of stress relaxation, c y c l i n g c a n a l s o be q u a n t i f i e d .

359

a g i n g , and t h e r m a l

A p p a r a t u s D e s c r i p t i o n . A s c h e m a t i c o f t h e b e n d i n g beam a p p a r a t u s i s g i v e n i n F i g u r e 2. The p o l y m e r b e i n g s t u d i e d i s s p i n - c o a t e d onto a t h i n s t r i p o f s i l i c o n o r q u a r t z (1). The r e s u l t i n g sample i s p l a c e d i n a s m a l l e n v i r o n m e n t a l chamber, which houses a s t u r d y r e f e r e n c e beam h e l d p a r a l l e l t o t h e sample beam. T h i s r e f e r e n c e beam p r o v i d e s an e x a c t measure o f sample d i s p l a c e m e n t due t o chamber and h o l d e r e x p a n s i o n o r c o n t r a c t i o n , which c a n t h e n be a c c o u n t e d f o r in the curvature c a l c u l a t i o n . The e n v i r o n m e n t a l chamber, w h i c h has d u a l q u a r t z windows t o a l l o w sample o b s e r v a t i o n , i s h e a t e d by e l e c t r i c a l r e s i s t a n c e h e a t e r s and c o o l e d by a circulating fluid. A d i g i t a l ramp t e m p e r a t u r e controller e n s u r e s p r e c i s e c o n t r o l o f h e a t i n g and c o o l i n g r a t e s (up t o 10°C/min). The t e m p e r a t u r e i s measured by a t h e r m o c o u p l e p o s i t i o n e d n e a r t h e sample, and i s u n i f o r m t o w i t h i n 3°C a c r o s s t h e sample. The t h e r m o c o u p l e t i m e l a g i s a c c o u n t e d f o r i n the data a n a l y s i s . The chamber m a i n t a i n s a vacuum and o f f e r s a c o n t r o l l e d atmosphere. Most e x p e r i m e n t s a r e r u n w i t h t h e chamber s l i g h t l y p r e s s u r i z e d w i t h an i n e r t g a s , a l t h o u g h sometimes a h u m i d i f i e d o r o x y g e n a t e d atmosphere i s employed. The h i g h - t e m p e r a t u r e l i m i t o f t h e chamber i s 280°C. The d e f l e c t i o n o f t h e sample beam i s measured by a 200x m i c r o s c o p e f i t t e d w i t h a c r o s s h a i r , and mounted on a p r e c i s i o n x-y-z t r a n s l a t o r . The m i c r o s c o p e i s d e s i g n e d t o achieve h i g h m a g n i f i c a t i o n , yet t o m a i n t a i n a l a r g e working d i s t a n c e (50 mm) . D i s p l a c e m e n t s on t h e o r d e r o f 3μπι c a n be r e a d i l y d e t e c t e d w i t h t h i s system, by u s i n g a s t e p p e r micrometer. R e p e a t a b i l i t y o f a s i n g l e d e f l e c t i o n measurement ( d i s t a n c e between r e f e r e n c e beam and sample beam) i s on t h e o r d e r o f 1 μπι. T y p i c a l p r o c e d u r e s o f t h e b e n d i n g beam e x p e r i m e n t s were as f o l l o w s . R e s i n c o a t i n g s were a p p l i e d t o one s i d e o f a c l e a n q u a r t z s t r i p by s p i n - c o a t i n g from an a p p r o p r i a t e s o l v e n t a t 2000 t o 8000 rpm f o r about 30 s e c o n d s . Coatings were t h e n e v a l u a t e d f o r u n i f o r m i t y , and a c c e p t a b l e beams were t h e n i n s e r t e d i n t o t h e b e n d i n g beam a p p a r a t u s . Stress measurements were t a k e n d u r i n g t e m p e r a t u r e ramps and h o l d s . The s p e c i f i c c u r e s c h e d u l e f o l l o w e d f o r e a c h m a t e r i a l depended on t h e m a n u f a c t u r e r s recommendations o r t h e r e s u l t s o f m i c r o d i e l e c t r i c c u r e s t u d i e s (IS.) . Upon c o m p l e t i o n o f a l l s t r e s s e x p e r i m e n t s , t h e beam was removed and t h e f i l m t h i c k n e s s measured by an A l p h a s t e p profilometer. The q u a r t z beams were 82 ± 2 μπι t h i c k , 3.8 cm l o n g , and 0.31 cm wide. T h e i r e l a s t i c modulus and t h e r m a l c o e f f i c i e n t o f e x p a n s i o n a r e 74,500 MPa and 5.7 χ 1 0 " ° C ~ (12) . 7

1

360


Figure

1. B i - m a t e r i a l

internal

strip

subject

t o b e n d i n g by

s t r e s s e s a f t e r c o o l i n g from i t s c u r e

t e m p e r a t u r e t o below t h e g l a s s t r a n s i t i o n t e m p e r a t u r e o f the

polymer

layer

1 .

Temperature Controller

F i g u r e 2. S c h e m a t i c o f b e n d i n g beam a p p a r a t u s .

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361


B e n d i n g Beam T h e o r y A w e l l known e q u a t i o n by Timoshenko (14.) i s employed t o d e t e r m i n e t h e l a y e r s t r e s s e s f r o m t h e measured r a d i i o f c u r v a t u r e o f a b i m a t e r i a l s t r i p ( F i g u r e 1 ) . The s t r e s s i n l a y e r 1 as a f u n c t i o n o f d i s t a n c e y from t h e c e n t e r o f t h e layer i s :

1

R6(l+m)m

1

X

1

Η—— η m Η—— η m + 1

6

y

|

n

m

3

X

6

y

n

m

2

X

1

(1)

where t ^ , t2, and E2 a r e t h e r e s p e c t i v e l a y e r t h i c k n e s s e s and e l a s t i c m o d u l i o f l a y e r s 1 a n d 2, m i s t h e r a t i o of the thicknesses ( t i / t 2 ) , η i s the r a t i o of the m o d u l i (E1/E2), and R i s t h e measured r a d i u s o f c u r v a t u r e . T h i s r e l a t i o n f o r s t r e s s r e q u i r e s knowledge o f t h e m o d u l i of both l a y e r s . The s t r e s s - r e l a t i o n f o r l a y e r 2 i s s i m i l a r t o t h a t f o r l a y e r 1, o n l y t h e s u b s c r i p t s a r e i n t e r c h a n g e d . A l s o , t h e h i g h e s t s t r e s s i n each l a y e r i s f e l t a t t h e interface. F o r a t h i n p o l y m e r l a y e r ( i . e . , t]_ « t2> / E q u a t i o n 1 reduces t o :

1 n

σ

E

2

t

2

m

»"ϊΓΤΪΓ

T h i s e q u a t i o n has s e v e r a l i m p o r t a n t f e a t u r e s . The m a t e r i a l p r o p e r t i e s o f l a y e r 1 are absent. Also, the thickness of the s u b s t r a t e , t2, i s the parameter o f g r e a t e s t s e n s i t i v i t y - t y p i c a l l y t h i s i s an e a s i l y measured q u a n t i t y . In addition, the stress p r o f i l e i n the t h i n layer i s f l a t f o r a l i n e a r e l a s t i c layer, i . e . , the e n t i r e f i l m i s subjected to a uniform s t r e s s . By a l g e b r a i c m a n i p u l a t i o n , i t c a n be shown t h a t f o r a c a n t i l e v e r beam o f l e n g t h L, t h e r a d i u s o f c u r v a t u r e c a n be d e t e r m i n e d from t h e d e f l e c t i o n , δ, o f t h e beam t i p :

when δ « R; t y p i c a l magnitudes f o r δ and R a r e i n t h e m i c r o n and meter r a n g e . T h i s e q u a t i o n i s employed f o r o b t a i n i n g R f r o m d e f l e c t i o n d a t a i n t h e b e n d i n g beam experiment. A c t u a l e x p e r i m e n t s a r e r u n by m e a s u r i n g t h e d e f l e c t i o n a t a p o i n t χ < L, i n o r d e r t o a v o i d edge e f f e c t s w h i c h a r e e s t i m a t e d t o be o p e r a t i v e w i t h i n an o r d e r o f two t o t h r e e beam t h i c k n e s s e s ( 2 Û ) . The p r o d u c t o f t h e e l a s t i c modulus and t h e r m a l e x p a n s i o n c o e f f i c i e n t f o r t h e t h i n p o l y m e r c o a t i n g , Ea, can be c a l c u l a t e d from t h e s t r e s s - t e m p e r a t u r e c u r v e by t h e

362


r e l a t i o n s h i p of the t h e r m a l l y induced s t r e s s , Aa t h i n l a y e r t o t h e t h e r m a l e x p a n s i o n mismatch and t e m p e r a t u r e change, ΔΤ: (21)

Αο

λ

= Ε Δα λ

l f

in a

( 4 )

ΔΤ

where i s t h e e l a s t i c modulus o f t h e f i l m , Δα = α^ i s t h e mismatch between t h e l i n e a r t h e r m a l e x p a n s i o n c o e f f i c i e n t s o f t h e f i l m and s u b s t r a t e , and Δσχ i s t h e i n c r e a s e i n f i l m s t r e s s r e s u l t i n g from a t e m p e r a t u r e d e c r e a s e ΔΤ. F o r most p o l y m e r s on q u a r t z o r s i l i c o n , 1 2' giving, α

> > (

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Δ Τ Thus, Ea o f t h e polymer i s p r o p o r t i o n a l t o t h e s l o p e o f t h e s t r e s s - t e m p e r a t u r e c u r v e i n t h e r m a l - e x p a n s i o n dominated regimes. A d e c r e a s e i n Ea r e s u l t s i n a l o w e r t h e r m a l expansion-mismatch induced s t r e s s . Thus, a l o w e r Ea s h o u l d a l s o endow t h e m a t e r i a l w i t h t h e a b i l i t y t o s u s t a i n a g r e a t e r number o f t h e r m a l c y c l e s b e f o r e f a t i g u e - i n d u c e d f r a c t u r e because o f a s m a l l e r c y c l i c a l s t r e s s a m p l i t u d e . The e l a s t i c modulus o f t h e polymer can be c a l c u l a t e d f r o m Ea w i t h knowledge o f a^ from t h e r m a l m e c h a n i c a l a n a l y s i s (TMA), when s t r e s s r e l a x a t i o n e f f e c t s a r e n e g l i g i b l e . It s h o u l d a l s o be p o s s i b l e t o c a l c u l a t e c r o s s l i n k d e n s i t y from t h e r u b b e r y modulus (above Tg) by u s i n g r u b b e r e l a s t i c i t y theory. The g l a s s t r a n s i t i o n t e m p e r a t u r e , Tg, can a l s o be c a l c u l a t e d from t h e s t r e s s - t e m p e r a t u r e p r o f i l e . I t can be t a k e n as t h e i n t e r s e c t i o n o f two l i n e s drawn from t h e l i n e a r r e g i o n s o f t h e g l a s s y and r u b b e r y r e g i m e s , i n a manner s i m i l a r t o Tg d e t e r m i n a t i o n from TMA. Here, however, t h e measured Tg c o r r e s p o n d s more w i t h t h o s e d e r i v e d f r o m dynamic m e c h a n i c a l methods b e c a u s e o f t h e s t r o n g dependence o f s t r e s s on t h e modulus t r a n s i t i o n between t h e r u b b e r y and g l a s s y s t a t e s . O t h e r ways t o measure Tg would be t o t a k e t h e d e r i v a t i v e o f t h e σ(Τ) c u r v e t o o b t a i n E a ( T ) ; t h e Tg c o u l d t h e n be d e t e r m i n e d as e i t h e r t h e i n f l e c t i o n p o i n t o r t h e midway p o i n t i n t h e t r a n s i t i o n between g l a s s y Ea and r u b b e r y Ea. The Timoshenko e q u a t i o n h o l d s o n l y f o r e l a s t i c f i l m s on e l a s t i c s u b s t r a t e s . Polymer l a y e r s , however, a r e v i s c o e l a s t i c , i n p a r t i c u l a r near t h e i r g l a s s t r a n s i t i o n temperatures. The e x p e r i m e n t a l raw d a t a can be d e c o n v o l u t e d t o o b t a i n s t r e s s measurements, even i f t h e v i s c o e l a s t i c e f f e c t s are important. T h i s i s b e c a u s e we use t h e t h i n - f i l m e q u a t i o n , where t h e v i s c o e l a s t i c modulus o f t h e polymer i s not needed f o r t h e s t r e s s c o m p u t a t i o n . For



363

the case o f t h i c k c o a t i n g s , indeed, the proper v i s c o e l a s t i c modulus s h o u l d r e p l a c e t h e e l a s t i c m o d u l u s . R e s u l t s and D i s c u s s i o n T h r e e c a s e s t u d i e s a r e examined w h i c h i l l u s t r a t e t h e use o f t h e b e n d i n g beam s t r e s s e x p e r i m e n t . The f i r s t i s a c o m p a r i s o n o f two p o l y m e r s f o r i n t e r l a y e r d i e l e c t r i c s . The s e c o n d i s o f a n e a t epoxy r e s i n commonly u s e d f o r microelectronics encapsulation. The t h i r d i s a p o l y i m i d e c o a t i n g u s e d f o r p r o t e c t i o n o f an i n t e g r a t e d - c i r c u i t c h i p . PMDA-QDA and B C B . S t r e s s e s i n d u c e d d u r i n g p r o c e s s i n g o f a PMDA-ODA p o l y i m i d e ( p y r o m e l l i t i c a c i d d i a n h y d r i d e o x y d i a m i n e , Dupont P y r a l i n 2545) and a b i s - b e n z o c y c l o b u t e n e (BCB, Dow p r o p r i e t a r y ) were s t u d i e d u s i n g t h e b e n d i n g beam apparatus. B o t h m a t e r i a l s were u s e d as s u p p l i e d by t h e m a n u f a c t u r e r : t h e PMDA-ODA s o l v a t e d i n n - m e t h y l p y r r o l i d i n o n e and t h e BCB i n x y l e n e . F i n a l c o a t i n g t h i c k n e s s e s , as measured by p r o f i l o m e t r y , were 2 . 8 μπι f o r t h e PMDA-ODA and 3.2 μπι f o r t h e BCB on f u s e d q u a r t z s t r i p s . B o t h m a t e r i a l s were s u b j e c t e d t o t h e same p r o c e s s i n g conditions. The c u r e p r o f i l e c o n s i s t e d o f h e a t i n g from room t e m p e r a t u r e t o 2 60°C a t 5°C/min, h o l d i n g a t 260°C f o r 2 h o u r s , t h e n c o o l i n g t o room t e m p e r a t u r e a t 5 ° C / m i n . As can be seen i n F i g u r e 3, t h e i r s t r e s s - t e m p e r a t u r e p r o f i l e s are q u i t e d i f f e r e n t . Both f i l m s l e f t the s p i n - c o a t e r w i t h approximately zero s t r e s s . Upon h e a t i n g , t h e p o l y i m i d e f i l m d e v e l o p e d s u b s t a n t i a l t e n s i l e s t r e s s due t o f i l m c o n t r a c t i o n from s o l v e n t e v a p o r a t i o n w h i l e t h e BCB f i l m e x h i b i t e d o n l y m i l d t e n s i l e s t r e s s b u i l d u p . The s t r e s s i n t h e BCB f i l m r e l a x e d a t 260°C w h i l e t h e s t r e s s i n t h e polyimide d i d not. The d i f f e r i n g b e h a v i o r can be e x p l a i n e d on t h e b a s i s o f t h e i r r e s p e c t i v e c h e m i s t r i e s and t h e i r i n i t i a l p h y s i c a l states. The p o l y i m i d e p o l y m e r i z a t i o n o c c u r s v i a a two s t e p mechanism ( F i g u r e 4 ) . F i r s t , t h e PMDA r e a c t s w i t h t h e ODA t o y i e l d a p o l y a m i c a c i d p o l y m e r . The p o l y i m i d e i s t h e n formed by a r i n g c l o s u r e r e a c t i o n and y i e l d s w a t e r as a condensation by-product. Both r e a c t i o n s take p l a c e f a i r l y r a p i d l y a t t h e t e m p e r a t u r e s a t w h i c h t h e PMDA-ODA i s manufactured. The b e n z o c y c l o b u t e n e r e a c t i o n a l s o t a k e s p l a c e v i a a two s t e p r e a c t i o n ( F i g u r e 5 ) ; however, t h e p o l y m e r i s n o t formed u n t i l t h e s e c o n d s t e p . F i r s t , the cyclobutene r i n g i s d e s t a b i l i z e d upon h e a t i n g above 200°C p r o d u c i n g h i g h l y r e a c t i v e methylene groups. These, i n t u r n , r e a c t w i t h one a n o t h e r t o y i e l d l i n e a r o r network p o l y m e r . Unsaturation i n t h e i n t e r v e n i n g g r o u p , X , may a l s o r e s u l t i n i t s participation i n curing v i a Diels-Alder reactions. The p o l y i m i d e , as s u p p l i e d , was i n a s l i g h t l y advanced s t a t e , a moderate m o l e c u l a r w e i g h t p o l y m e r , w i t h a d i s t i n c t l y h i g h e r v i s c o s i t y t h a n t h e B C B . The advanced s t a t e o f t h e p o l y i m i d e i s a consequence o f t h e h i g h -

364


Temperature (C)

F i g u r e 3.

Comparison o f s t r e s s - t e m p e r a t u r e

profiles for

BCB and PMDA/ODA.

F i g u r e 4. R e a c t i o n o f PMDA w i t h ODA t o form

polyimide.

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365

temperature manufacturing process. It f a c i l i t a t e s p o l y i m i d e p r o c e s s i n g under s p i n - c o a t i n g c o n d i t i o n s ; however, i t a l s o i m p a r t s g r e a t e r s o l i d - l i k e c h a r a c t e r t o the p o l y i m i d e . C o n s e q u e n t l y , when t h e f i l m c o n t r a c t s due t o s o l v e n t e v a p o r a t i o n , t h e s t r a i n does not r e l a x . Rather, i t t r a n s l a t e s t o s i g n i f i c a n t t e n s i l e s t r e s s i n the f i l m . In o r d e r f o r t h e p o l y i m i d e t o have such a h i g h modulus t h r o u g h o u t t h e c o u r s e o f t h e h e a t i n g c y c l e , t h e Tg o f t h e p o l y i m i d e must i n c r e a s e v i a c u r i n g t o remain n e a r o r above t h e sample t e m p e r a t u r e . Note a l s o t h a t a c o m p e t i t i o n e x i s t s between f i l m c o n t r a c t i o n due t o s o l v e n t e v a p o r a t i o n and f i l m e x p a n s i o n due t o t h e r m a l e x p a n s i o n d u r i n g t h e h e a t i n g ramp t o t h e cure temperature. T h i s c o m p e t i t i o n becomes a p p a r e n t as t h e s o l v e n t i s d r i v e n out o f t h e p o l y i m i d e f i l m . The s l o p e o f t h e s t r e s s - t e m p e r a t u r e c u r v e becomes z e r o as t h e mechanisms b a l a n c e e a c h o t h e r (~100°C) . I t becomes n e g a t i v e as thermal expansion dominates. At 180°C f i l m c o n t r a c t i o n due t o water e v a p o r a t i o n , t h e i m i d i z a t i o n b y - p r o d u c t , b e g i n s t o compete w i t h t h e r m a l e x p a n s i o n . S t r e s s r e t e n t i o n a t 2 60°C i n d i c a t e s t h a t t h e p o l y i m i d e has g e l l e d , and p o s s e s s e s a Tg s i g n i f i c a n t l y h i g h e r t h a n 2 60°C. These r e s u l t s appear t o be i n agreement w i t h t h e c u r e c h a r a c t e r i s t i c s r e p o r t e d f o r a s i m i l a r p o l y i m i d e s y s t e m (22.) . The BCB e x h i b i t s m i n i m a l s o l i d - l i k e c h a r a c t e r upon h e a t i n g ; c o n t r a c t i o n due t o s o l v e n t e v a p o r a t i o n o n l y s l i g h t l y outpaces thermal expansion. The Tg r e m a i n s s i g n i f i c a n t l y below t h e sample t e m p e r a t u r e , resulting in a low modulus and t h u s low s t r e s s . Upon r e a c h i n g 2 60°C, t h e t e n s i l e s t r e s s i n t h e BCB f i l m r e l a x e s b e c a u s e o f o n l y m i n i m a l network f o r m a t i o n , which would i n h i b i t t h e r e l a x a t i o n , d u r i n g the h e a t i n g c y c l e . Upon c o o l i n g , a f t e r a 2 hour c u r e , b o t h m a t e r i a l s e x h i b i t l i n e a r stress-temperature p r o f i l e s . This indicates t h a t t h e g l a s s t r a n s i t i o n t e m p e r a t u r e i s a t o r above t h e c u r e t e m p e r a t u r e , and t h a t measurements have been made i n the g l a s s y e l a s t i c regime. The g l a s s y - s t a t e Ea can be c a l c u l a t e d from t h e s l o p e s o f t h e s e c u r v e s . For the p o l y i m i d e i t i s 0.13 MPa/°C and f o r t h e BCB i t i s 0.16 MPa/°C. Note t h a t t h e p o l y i m i d e b e a r s a h i g h e r c u m u l a t i v e s t r e s s a t room t e m p e r a t u r e b e c a u s e o f t h e s t r e s s i n d u c e d by s o l v e n t e v a p o r a t i o n , i n s p i t e o f i t s lower Ea. Encapsulant Resin. F i g u r e 6 shows t h e s t r e s s t r a c e o f an epoxy r e s i n t y p i c a l l y u s e d i n e n c a p s u l a n t f o r m u l a t i o n s . The r e s i n c o n s i s t s o f e p o x i d i z e d o r t h o - c r e s o l n o v o l a c (EOCN, S h e l l DPS-164) c u r e d w i t h a p h e n o l i c n o v o l a c (PN, B o r d e n 1731), c a t a l y z e d by t r i p h e n y l p h o s p h i n e (TPP, Aldrich). I t was s p i n c o a t e d o n t o a q u a r t z s t r i p from a m i x t u r e o f m e t h y l e t h y l k e t o n e and Dowanol PM y i e l d i n g a f i n a l c o a t i n g t h i c k n e s s o f 5.3 um. The c u r e s c h e d u l e c o n s i s t e d o f h e a t i n g t o 160°C, h o l d i n g f o r 1 hour, c o o l i n g t o -30°C, h e a t i n g t o 210°C, h o l d i n g f o r 1 hour, t h e n c o o l i n g t o room t e m p e r a t u r e ; h e a t i n g and c o o l i n g was done a t

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5°C/min. M i c r o d i e l e c t r o m e t r y was u s e d t o d e t e r m i n e t h a t t h e r e s i n had c e a s e d r e a c t i n g a t t h e c u r e t e m p e r a t u r e s before cooling. The i n i t i a l h e a t i n g i s u n e v e n t f u l , as t h e r e s i n i s i n s u f f i c i e n t l y advanced t o s u s t a i n s t r e s s . Upon c o o l i n g from 160°C, s t r e s s i n c r e a s e s n e a r l y l i n e a r l y , i n d i c a t i n g t h a t t h e g l a s s t r a n s i t i o n t e m p e r a t u r e i s a t o r above t h e c u r e t e m p e r a t u r e , and y i e l d i n g an Ea o f 0.24 MPa/°C. Upon c o o l i n g below 0°C, anomalous b e h a v i o r due t o c o n d e n s a t i o n o f m o i s t u r e on t h e sample beam i s n o t e d . Such c o n d e n s a t i o n weighs t h e beam downward, d e c r e a s i n g t h e a p p a r e n t beam d e f l e c t i o n , and t h u s a n o m a l o u s l y d e c r e a s e s t h e measured stress. The m o i s t u r e e v a p o r a t e s d u r i n g t h e s e c o n d h e a t i n g c y c l e , g i v i n g normal b e h a v i o r upon r e a c h i n g 50°C. This demonstrates t h a t a s u b s t a n t i a l l y m o i s t u r e - f r e e environment must be employed i n o r d e r t o use t h e b e n d i n g beam t e c h n i q u e a t s u b - z e r o t e m p e r a t u r e s ( i . e . , t h e dew p o i n t o f t h e ambient gas must be below t h e l o w e s t d e s i r e d t e m p e r a t u r e ) . As t h e beam i s h e a t e d towards 210°C, t h e r e s i n e x h i b i t s a c o m p r e s s i v e s t r e s s above i t s c u r e t e m p e r a t u r e o f 160°C. The s t r e s s p a s s e s t h r o u g h a minimum a t 170°C where t h e r a t e o f s t r e s s i n d u c t i o n due t o t h e r m a l e x p a n s i o n i s b a l a n c e d by s t r e s s r e l a x a t i o n . Stress r e l a x a t i o n i s the dominant mechanism u n t i l 210°C. T h e r e a r e no d e t e c t a b l e c u r e - s h r i n k a g e i n d u c e d s t r e s s e s d u r i n g t h e 210°C c u r e . The s t r e s s i n c r e a s e s n o n - l i n e a r l y upon c o o l i n g , i n d i c a t i n g t h a t t h e g l a s s t r a n s i t i o n t e m p e r a t u r e i s below t h e c u r e temperature. Under 150°C, t h e s t r e s s i n c r e a s e s l i n e a r l y , y i e l d i n g an Ea o f 0.22 MPa/°C. T h i s Ea i s lower t h a n t h a t f o l l o w i n g t h e 160°C c u r e , and a g r e e s w i t h b e h a v i o r e x p e c t e d below Tg from an i n c r e a s e i n c r o s s l i n k d e n s i t y . The Ea r e d u c t i o n i s due t o a d e c r e a s e d t h e r m a l e x p a n s i o n c o e f f i c i e n t r e s u l t i n g from a more h i g h l y c r o s s l i n k e d network. F i g u r e 7 shows t h e b e h a v i o r o f t h e same sample h e a t e d t o 280°C a t 5°C/min. The c u r e d sample f o l l o w s t h e same s t r e s s - p r o f i l e as t h e p r i o r c o o l i n g c u r v e , w i t h t h e p o i n t o f z e r o s t r e s s o c c u r r i n g s l i g h t l y above t h e c u r e t e m p e r a t u r e a t 214°C. The s t r e s s becomes m i l d l y c o m p r e s s i v e w i t h f u r t h e r h e a t i n g , and a g l a s s t r a n s i t i o n t e m p e r a t u r e o f 190°C i s n o t e d . The s l o p e o f t h e l i n e a r r e g i o n above t h e g l a s s t r a n s i t i o n t e m p e r a t u r e y i e l d s a r u b b e r y Ea o f 0.014 MPa/°C upon h e a t i n g , and 0.02 6 MPa/°C upon c o o l i n g from 280°C. The h i g h e r r u b b e r y Ea upon c o o l i n g i s b e s t e x p l a i n e d by t h e v i s c o e l a s t i c n a t u r e o f t h e t h e r m o s e t c o a t i n g . The h e a t i n g r a t e o f t h e e n v i r o n m e n t a l chamber d e c r e a s e s r a p i d l y above 200°C b e c a u s e i t i s n e a r i n g i t s h i g h t e m p e r a t u r e l i m i t s , s u c h t h a t t h e f i n a l a p p r o a c h t o 280°C o c c u r s a t about 0.5°C/min. The c o o l i n g , however, o c c u r r e d a t a w e l l c o n t r o l l e d 5°C/min. This ten-fold difference i n heating rates i s quite s i g n i f i c a n t , having allowed s i g n i f i c a n t l y more t i m e f o r v i s c o e l a s t i c s t r e s s - r e l a x a t i o n upon h e a t i n g t h a n upon c o o l i n g . S i n c e Ea i s d e t e r m i n e d from t h e s l o p e

368


of the stress-temperature curve, a r e d u c t i o n of s t r e s s s t r e s s r e l a x a t i o n w i l l d e c r e a s e t h e a p p a r e n t Ea.

by

Screen-Printable Polyimide. B e n d i n g beam r e s u l t s f o r a s c r e e n - p r i n t a b l e p o l y i m i d e used f o r c h i p p r o t e c t i o n are p r e s e n t e d i n F i g u r e 8. The EPO-TEK 600 p o l y i m i d e p a s t e was a p p l i e d t o a q u a r t z beam, t h e n t h e beam was spun a t 5000 rpm t o a c h i e v e h i g h u n i f o r m i t y . R e s u l t s a r e p r e s e n t e d as i n v e r s e r a d i u s o f c u r v a t u r e , 1/R, b e c a u s e t h e 50 μπι c o a t i n g t h i c k n e s s on t h e 84 μπι s u b s t r a t e v i o l a t e s t h e t h i n f i l m c r i t e r i o n o f E q u a t i o n 2. We have no knowledge o f t h e p o l y i m i d e s v i s c o e l a s t i c modulus, w h i c h i s needed i n o r d e r t o c o n v e r t 1/R i n t o i n t e r f a c i a l s t r e s s u s i n g E q u a t i o n 1. The p o l y i m i d e i s known t o bow s i l i c o n w a f e r s (~450 μπι t h i c k ) v e r y l i t t l e ; i t bows t h e t h i n q u a r t z s t r i p s i g n i f i c a n t l y b e c a u s e o f t h e lower b e n d i n g modulus o f t h e thin strip. The p o l y i m i d e was c u r e d as f o l l o w s : one hour a t 160°C t o d r i v e o f f t h e s o l v e n t , and 1 hour a t 280°C t o c u r e t h e p o l y i m i d e , w i t h t e m p e r a t u r e ramps o f 5°C/min. The EPO-TEK d e v e l o p s a s i g n i f i c a n t modulus as i t i s h e a t e d t o 160°C, as can be seen from t h e bowing i n d u c e d by s o l v e n t e v a p o r a t i o n . An i n f l e c t i o n i n t h e 1/R c u r v e i s n o t e d a t 178°C on h e a t i n g t o 280°C - t h i s c o r r e s p o n d s t o t h e g l a s s t r a n s i t i o n temperature. Again i t i s noted that the g l a s s t r a n s i t i o n t e m p e r a t u r e can r i s e h i g h e r t h a n t h e c u r e t e m p e r a t u r e . The c o a t i n g s u s t a i n s a m i l d l y c o m p r e s s i v e s t r e s s as i t c u r e s a t 280°C; n e g l i g i b l e s t r e s s i n d u c e d by c u r e s h r i n k a g e i s n o t e d for t h i s polyimide. Upon c o o l i n g , s t r e s s i n c r e a s e s i n p r o p o r t i o n t o t h e t e m p e r a t u r e change. 1

Modeling

Thermoset

Properties Purina

Cure

These s t u d i e s p o i n t e d out t h a t a c o m p r e h e n s i v e model o f t h e r m o s e t c u r e f o r s t r e s s c a l c u l a t i o n s must a c c o u n t f o r a l a r g e number o f p r o c e s s i n g i n f l u e n c e s and m a t e r i a l properties. Mass t r a n s f e r (22.), c h e m i c a l k i n e t i c s , network s t r u c t u r e f o r m a t i o n , and m a t e r i a l p r o p e r t y development a r e e s s e n t i a l i n g r e d i e n t s . Induced s t r a i n s must be a c c u r a t e l y c a l c u l a t e d , as must s t r e s s r e l a x a t i o n . Properties d e p e n d e n c i e s on t e m p e r a t u r e a r e s i g n i f i c a n t and must be a c c o u n t e d f o r , as must t h e i n t e r - r e l a t i o n s h i p between r e a c t i o n k i n e t i c s and d i f f u s i o n . F i g u r e 9 o u t l i n e s t h e t h e r m o s e t c u r e model b e i n g d e v e l o p e d i n t h i s l a b o r a t o r y t o d e s c r i b e p r o p e r t y changes and s t r e s s b u i l d u p d u r i n g p r o c e s s i n g . The i n t e n t o f t h i s model i s t o d e v e l o p p r o c e s s i n g and m a t e r i a l g u i d e l i n e s f o r minimizing residual stresses. A f o r t h c o m i n g p a p e r w i l l be devoted t o t h i s t o p i c . However, i t i s i n s t r u c t i v e t o b r i e f l y summarize t h e m o d e l i n g s t r a t e g y employed. A c u r e t e m p e r a t u r e p r o f i l e i s i n p u t i n t o t h e model. The p h y s i c a l s t r u c t u r e o f t h e p o l y m e r i s t h e n computed from knowledge o f t h e c h e m i c a l k i n e t i c s , u t i l i z i n g t h e s t a t i s t i c a l methods d e v e l o p e d by Macosko and M i l l e r (2A,

29.

BIERNATH & SOANE


Temperature (C)

Figure

8. Beam r a d i u s o f c u r v a t u r e

as a f u n c t i o n o f

t e m p e r a t u r e f o r 50 urn t h i c k EPO-TEK 600.

369

370


At

Temperature Profile T(t)

Kinetics Degree of cure - Bond formation

1 Material Parameters Crosslink density, Molecular Weight, Glass transition temperature, free volume

Stress Model Parameters Glassy and Rubbery components: Relaxation times and Moduli

Strains Thermal, Cure, Aging

Stress Model Viscoelastic

Figure

9. F l o w c h a r t o f t h e r m o s e t

c u r e model.

29.

BIERNATH & SOANE


371

25.) . The g l a s s t r a n s i t i o n t e m p e r a t u r e and r e s u l t i n g f r e e volume a r e c a l c u l a t e d from t h e D i B e n e d e t t o e q u a t i o n (2£) o r by an a p p r o a c h which i n c o r p o r a t e s t h e e f f e c t o f c r o s s l i n k d e n s i t y on t h e g l a s s t r a n s i t i o n t e m p e r a t u r e (22). This p a r t o f t h e model i s i t e r a t i v e i n o r d e r t o a c c o u n t f o r d i f f u s i o n - l i m i t a t i o n s on t h e r e a c t i o n r a t e i n t h e l a t e r s t a g e s o f t h e r m o s e t c u r e (2d) . The m a t e r i a l p r o p e r t i e s (moduli and r e l a x a t i o n t i m e s ) a r e t h e n c a l c u l a t e d from knowledge o f network s t r u c t u r e and f r e e volume. S t r a i n s i m p a r t e d by p r o c e s s i n g and r e a c t i o n are determined. These i n p u t s a r e t h e n a p p l i e d t o a v i s c o e l a s t i c b i - M a x w e l l model, whereby s t r e s s i n t h e polymer i s determined. Time i s t h e n i n c r e m e n t e d and t h e procedure repeated u n t i l the cure p r o f i l e i s complete. Sample model r e s u l t s a r e p r e s e n t e d i n F i g u r e 10. R e a l i s t i c model p a r a m e t e r s were s e l e c t e d t o d e m o n s t r a t e t h e model c a p a b i l i t i e s f o r a g e n e r i c t h e r m o s e t r e s i n s i m i l a r t o t h e EOCN-based r e s i n . The c u r e s c h e d u l e s i m u l a t i o n c o n s i s t e d o f h e a t i n g t o 125°C, h o l d i n g f o r 1 hour, c o o l i n g t o 60°C, h e a t i n g t o 200°C, h o l d i n g f o r 1 hour, t h e n c o o l i n g t o room t e m p e r a t u r e . A l l h e a t i n g and c o o l i n g was done a t 5°C/min. The model c o r r e c t l y s i m u l a t e s t h e q u a l i t a t i v e b e h a v i o r e x h i b i t e d by t h e EOCN. S t r e s s r e t e n t i o n upon c o o l i n g a f t e r b o t h t h e 125°C and 200°C c u r e s i s n o t e d , w i t h a d e c r e a s e d Ea when more f u l l y c u r e d . A compressive s t r e s s w h i c h r e l a x e s o u t i s o b s e r v e d on h e a t i n g t h e p a r t i a l l y c u r e d r e s i n t o 200°C. B o t h cool-down c u r v e s e x h i b i t c u r v a t u r e n e a r t h e c u r e t e m p e r a t u r e s due t o t h e dependency o f modulus, t h e r m a l e x p a n s i o n , and s t r e s s r e l a x a t i o n on t e m p e r a t u r e , Tg, and c r o s s l i n k d e n s i t y . S o l v e n t and b y - p r o d u c t e v a p o r a t i o n can be a c c o u n t e d f o r i n a manner a n a l o g o u s t o t h e methods u s e d p r e v i o u s l y

(22) . Conclusions S t r e s s e s i n p o l y m e r s f o r m i c r o e l e c t r o n i c s a r e v e r y complex f u n c t i o n s of time, temperature, thermal h i s t o r y , s o l v e n t and b y - p r o d u c t e v a p o r a t i o n , degree o f c u r e , c u r e k i n e t i c s , c r o s s l i n k d e n s i t y , and v i s c o e l a s t i c i t y . The b e n d i n g beam e x p e r i m e n t e n a b l e s t h e s e e f f e c t s t o be o b s e r v e d and quantified. I t measures a t r u e s t r e s s i n t h e polymer, a l l o w i n g t h e p r o d u c t o f t h e e l a s t i c modulus and t h e r m a l e x p a n s i o n c o e f f i c i e n t , Ea (both above and below T g ) , and t h e g l a s s t r a n s i t i o n t e m p e r a t u r e , Tg, t o be d e t e r m i n e d from a small quantity of material. Modeling e f f o r t s are underway t o d e t e r m i n e p r o c e s s i n g and m a t e r i a l s g u i d e l i n e s for minimizing residual stresses.

372


Temperature (C)

Figure curing.

10. Example model p r e d i c t i o n s

f o r thermoset



373

Acknowledgment s This work was supported by the O f f i c e of Naval Research under N00014-87-K-0211.

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.

Soane, D.; Martynenko, Z. Polymers in Microelectronics: Fundamentals and Applications; Elsevier: New York, 1989. Bolger, J. C. In Polyimides: Synthesis, Characterization, and Applications II; Mittal, K. L., Ed.; Plenum: New York, 1984; p 871. Popov, E. P. Introduction to the Mechanics of Solids; Prentice-Hall, Inc.: Englewood C l i f f s , 1968. Ferry, J. D. Viscoelastic Properties of Polymers, 3rd ed.; John Wiley & Sons, Inc.: New York, 1980. Aronhime, M. T.; Gillham, J. K. J. Coat. Tech. 1984, 56, 35. Timoshenko, S. J. Opt. Son. Am. 1925, 11, 233. Croll, S. G. J. Coat. Tech. 1979,51,64. Berry, B. S.; Pritchet, W. C. IBM J. Res. Develop. 1984, 28, 662. Srivastava, A. K.; White, J. R. J. Appl. Polym. Sci. 1984, 29, 2155. Chow, T. S. J. Rheol. 1986,30,729. Wisanrakkit, G.; Gillham, J. K.; Enns, J. B. Polym. Mat. Sci. Eng. 1987,57,87. Duda, J. L.; Vrentas, J. S.; Ju, S. T.; Liu, H. T. AIChE J. 1982,28,279. van den Bogert, W. F.; Molter, M. J.; Belton, D. J.; Gee, S. Α.; Aklas, V. R. Polym. Mat. Sci. Eng. 1988, 59, 642. Timoshenko, S. J. Opt. Son. Am. 1925,11,233. Wilcock, J. D.; Campbell, D. S. Thin Solid Films 1969, 2, 3. Hu, C.-K.; Tong, H. M.; Feger, C.; Ho, P. S. In IEEE V-MIC Conf., 1985, p 280. Scherer, G. W. Relaxation in Glass and Composites; Wiley-Interscience: New York, 1986. Senturia, S. D.; Jr., N. F. S. Adv. Polym. Sci. 1986, 80, 1. Hibshman Corp. 1988. Scherer, G. W. J. Am. Cer. Soc. 1982,66,135. Mahrenholtz, O.; Johnson, W. Int. J. Mech. Sci. 1962, 4, 35. Feger, C. Polym. Mat. Sci. Eng. 1988,59,51. Biernath, R. W.; Soane, D. S. In Polymeric Materials for Electronic Packaging and High Technology Applications; The Electrochemical Society: Honolulu, 1987; p 147.

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POLYMERS FOR ELECTRONICS PACKAGING AND INTERCONNECTION Macosko, C. W.; M i l l e r , D. R. Macromolecules 1976, 9, 199. M i l l e r , D. R.; Macosko, C. W. Macromolecules 1976, 9, 206. Nielsen, L. E. J . Macromol. S c i . 1969, C3, 69. Hale, A. Doctoral D i s s e r t a t i o n , U n i v e r s i t y of Minnesota, 1988. Chern, C.-S.; Poehlein, G. W. Polym. Eng. S c i . 1987, 22, 788.

RECEIVED February 10,1989

Characterization of Stresses in Polymer Films for Microelectronics

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