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SEMICONDUCTOR MATERIALS ANALYSIS
A. Rosencwaig
To cite this version:
A. Rosencwaig. APPLICATIONS OF THERMAL-WAVE PHYSICS TO SEMICONDUCTOR MATERIALS ANALYSIS. Journal de Physique Colloques, 1983, 44 (C6), pp.C6-437-C6-452.
�10.1051/jphyscol:1983671�. �jpa-00223230�
J O U R N A L DE P H Y S I Q U E
C o l l o q u e C6, supplement a u nO1O, T o m e 44, o c t o b r e 1983 page C6- 437
A P P L I C A T I O N S OF THERMAL-WAVE P H Y S I C S T O SEMICONDUCTOR M A T E R I A L S ANALYS I S
A. Rosencwaig
Therma-Wave, Inc., Fremont, CA 94539, U.S.A.
RGsum6 - On d 4 c r i t l e s a p p l i c a t i o n s d e s ondes t h e r m i q u e s 2 l ' i m a g e r i e e t aux m e s u r e s q u a n t i t a t i v e s d ' 4 p a i s s e u r d e f i l m s m i n c e s p a r d e s m a t 4 r i a u x s e m i c o n d u c t e u r s e t d e s composants.
A b s t r a c t - N o n s p e c t r o s c o p i c a p p l i c a t i o n s o f thermal-wave p h y s i c s , i n p a r t i c u l a r t h o s e i n v o l v i n g m a t e r i a l s a n a l y s i s t h r o u g h t h e r - mal-wave i m a g i n g , and q u a n t i t a t i v e t h i n - f i l m t h i c k n e s s measure- m e n t s , a r e d e s c r i b e d f o r t h e s t u d y o f semiconductor m a t e r i a l s and d e v i c e s .
I - INTRODUCTION
Thermal-wave p h y s i c s i s p l a y i n g a n e v e r - i n c r e a s i n g r o l e i n t h e s t u d y of m a t e r i a l p a r a m e t e r s . I t h a s been employed i n o p t i c a l i n v e s t i g a - t i o n s o f s o l i d s , l i q u i d s and g a s e s w i t h p h o t o a c o u s t i c 1 and t h e r m a l - l e n s 2 s p e c t r o s c o p y . Thermal waves have a l s o been used t o s t u d y t h e t h e r m a l and thermodynamic p r o p e r t i e s 1 f 3 o f m a t e r i a l s , and f o r imaging t h e r m a l and m a t e r i a l f e a t u r e s w i t h i n a s o l i d sample. 4
Thermal waves a r e p r e s e n t whenever t h e r e i s p e r i o d i c h e a t g e n e r a t i o n and h e a t f l o w i n a medium. There a r e , t h e r e f o r e , a m u l t i t u d e o f mechanisms by which t h e s e waves c a n be p r o d u c e d , w i t h t h e two most common i n v o l v i n g t h e a b s o r p t i o n by t h e sample o f e n e r g y from e i t h e r a n i n t e n s i t y - m o d u l a t e d o p t i c a l beam,' o r from an i n t e n s i t y - m o d u l a t e d e l e c t r o n S e v e r a l mechanisms a r e a l s o a v a i l a b l e f o r d e t e c t i n g , d i r e c t l y , o r i n d i r e c t l y , t h e r e s u l t i n g t h e r m a l waves. These i n c l u d e ; gas-microphone p h o t o a c o u s t i c d e t e c t i o n o f h e a t flow from t h e sample t o t h e s u r r o u n d i n g g a s i n which p r e s s u r e c h a n g e s a r e m o n i t o r e d ; l r 5 p h o t o t h e r m a l measurements o f i n f r a r e d r a d i a t i o n e m i t t e d from t h e h e a t - ed sample s u r f a c e ; 6 - 8 0 p t i c a l beam d e f l e c t i o n o f a l a s e r beam t r a v e r s i n g
t h e p e r i o d i c a l l y h e a t e d g a s e o u s o r l i q u i d l a y e r j u s t above t h e sample s u r f ace ; 9-11 .
l n t e r f e r o m e t r i c d e t e c t i o n o f t h e t h e r m o e l a s t i c d i s p l a c e - ments o f t h e s u r f a c e ; 12'13 o p t i c a l d e t e c t i o n o f t h e t h e r m o e l a s t i c d e f o r m a t i o n s o f t h e s u r f a c e ; 13-16 and p i e z o e l e c t r i c d e t e c t i o n o f t h e r m o a c o u s t i c s i g n a l s g e n e r a t e d i n t h e sample. 1 , 1 7 , 1 8
To d a t e , o n l y t h i s l a s t t e c h n i q u e i n v o l v i n g t h e r m o a c o u s t i c d e t e c t i o n h a s been used r o u t i n e l y f o r d e t e c t i n g h i g h - f r e q u e n c y ( i . e . MHz regime) t h e r m a l waves. The t h e r m o a c o u s t i c d e t e c t i o n methodology has. t h e r e -
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983671
14,19,20 at f o r e found i m p o r t a n t a p p l i c a t i o n s i n thermal-wave imaging
h i g h s p a t i a l r e s o l u t i o n where micron-sized t h e r m a l waves a r e needed, a s i n t h e s t u d y of semiconductor m a t e r i a l s and d e v i c e s .
I s h a l l h e r e d i s c u s s some n o n s p e c t r o s c o p i c a p p l i c a t i o n s o f h i g h f r e - quency t h e r m a l waves f o r imaging and t h i n - f i l m t h i c k n e s s measurements i n semiconductor m a t e r i a l s a n a l y s i s .
11. THERMAL-WAVE I M A G I N G
Thermal-wave imaging i s a new t e c h n i q u e whereby m i c r o s c o p i c t h e r m a l f e a t u r e s on o r b e n e a t h t h e s u r f a c e o f a sample c a n be d e t e c t e d and imaged. Thermal f e a t u r e s a r e t h o s e r e g i o n s o f an o t h e r w i s e homogen- e o u s m a t e r i a l t h a t e x h i b i t v a r i a t i o n s , r e l a t i v e t o t h e i r s u r r o u n d i n g s , i n e i t h e r t h e d e n s i t y t h e s p e c i f i c h e a t , o r , most i m p o r t a n t l y , t h e t h e r m a l c o n d u c t i v i t y of t h e sample. V a r i a t i o n s i n t h e s e t h e r m a l p a r a - m e t e r s c a n a r i s e from changes i n b a s i c m a t e r i a l c o m p o s i t i o n , from t h e p r e s e n c e of mechanical d e f e c t s such a s m i c r o c r a c k s , v o i d s and delam- i n a t i o n ~ , from changes i n c r y s t a l l i n e o r d e r o r s t r u c t u r e , and evenfrom t h e p r e s e n c e o f s m a l l c o n c e n t r a t i o n s o f f o r e i g n i o n s o r l a t t i c e d e f e c t s i n a n o t h e r w i s e p e r f e c t c r y s t a l .
I n thermal-wave microscopy a l a s e r 2 1 o r e l e c t r o n beam 2 2 1 2 3 i s i n t e n s i - ty-modulated i n t h e 100 kHz-10 MHz r a n g e , f o c u s e d , and scanned o v e r t h e s u r f a c e o f a sample. The p e r i o d i c s u r f a c e h e a t i n g t h a t r e s u l t s from t h e a b s o r p t i o n of t h e i n c i d e n t beam g e n e r a t e s t h e r m a l waves t h a t p r o p a g a t e from t h e i n i t i a l l y h e a t e d r e g i o n s . These d i f f u s i v e t h e r m a l waves a r e c r i t i c a l l y damped and p r o p a g a t e o n l y one t o two wavelengths b e f o r e t h e i r i n t e n s i t y becomes n e g l i g i b l y s m a l l . N e v e r t h e l e s s , w i t h i n t h e i r p r o p a g a t i o n r a n g e , t h e t h e r m a l waves w i l l s c a t t e r and r e f l e c t from t h e r m a l f e a t u r e s much l i k e c o n v e n t i o n a l p r o p a g a t i n g waves do from o p t i c a l o r a c o u s t i c f e a t u r e s . Imaging of t h e t h e r m a l f e a t u r e s t h u s r e - q u i r e s d e t e c t i o n o f t h e s c a t t e r e d and r e f l e c t e d thermal-waves. A Therma-Wave , 1nc. 2 4 thermal-wave microscope u s e s t h e e l e c t r o n beam i n a scanning e l e c t r o n mircoscope t o g e n e r a t e t h e t h e r m a l waves and d e t e c t s t h e s c a t t e r e d and r e f l e c t e d t h e r m a l waves t h r o u g h t h e i r e f f e c t on t h e t h e r m o a c o u s t i c s i g n a l s g e n e r a t e d i n t h e bulk o f t h e sample. The thermo- a c o u s t i c s i g n a l s a r e d e t e c t e d i n t u r n w i t h a s u i t a b l e p i e z o e l e c t r i c t r a n s d u c e r i n a c o u s t i c c o n t a c t w i t h t h e sample. The magnitude and phase of , t h e t h e r m o a c o u s t i c s i g n a l s a r e d i r e c t l y a f f e c t e d by t h e p r e s e n c e of s c a ' t t e r e d and r e f l e c t e d t h e r m a l waves. 25 Thus by measuring t h e magnitude and/or phase o f t h e t h e r m o a c o u s t i c s i g n a l a s a f u n c t i o n o f e l e c t r o n beam p o s i t i o n on t h e s u r f a c e of t h e sample, an image i s g e n e r a t e d t h a t d e p i c t s
t h e v a r i o u s thermal-wave s c a t t e r i n g and r e f l e c t i o n e v e n t s t h a t o c c u r a t e a c h p o i n t on t h e sample.
SUBSURFACE DEFECTS
S u b s u r f a c e mechanical d e f e c t s such a s v o i d s , c r a c k s and d e l a m i n a t i o n s r e p r e s e n t s u b s t a n t i a l t h e r m a l f e a t u r e s and t h u s a r e r e a d i l y d e t e c t e d w i t h a thermal-wave microscope. 4 ' 2 0 One i l l u s t r a t i o n o f t h i s a p p l i c a - t i o n i s shown i n F i g u r e 1. F i g u r e l a i s t h e e l e c t r o n image o f a GaAs d e v i c e , where t h e o n l y v i s i b l e d e f e c t s a r e two seemingly i n s i g n i f i c a n t c h i p - o u t s a t t h e edge o f t h e d e v i c e , one a l o n g t h e r i g h t - h a n d e d g e , and t h e o t h e r a l o n g t h e bottom. The thermal-wave image i n F i g u r e l b shows, however, t h a t t h e s m a l l c h i p - o u t a l o n g t h e r i g h t - h a n d s i d e i s a much l a r g e r s u b s u r f a c e d e l a m i n a t i o n which e x t e n d s i n t o t h e lower g a t e of t h e d e v i c e where it r e s u l t s i n a " l o o p - l i k e " s u b s u r f a c e f l a w . The s m a l l c h i p - o u t a l o n g t h e bottom i s a l s o s e e n t o be t h e o r i g i n o f a long s u b s u r f a c e c r a c k . T h e r e f o r e , where o p t i c a l and e l e c t r o n images show o n l y two i n s i g n i f i c a n t d e f e c t s , t h e thermal-wave image shows t h e p r e s e n c e of s e r i o u s s u b s u r f a c e d e f e c t s .
F i g . 1 - Examples o f s u b s u r f a c e d e f e c t s i n a GaAs d e v i c e . The e l e c - t r o n micrograph ( a ) shows o n l y 2 s m a l l edge c h i p - o u t s , one a l o n g t h e r i g h t - h a n d s i d e , t h e o t h e r a t t h e bottom. The thermal-wave image ( b ) shows more s e r i o u s d e f e c t s - t h e c h i p - o u t a l o n g t h e r i g h t - h a n d s i d e i s s e e n a s a s u b s t a n t i a l d e l a m i n a t i o n e x t e n d i n g i n t o t h e lower g a t e r e - g i o n where a " l o o p - l i k e " d e f e c t i s v i s i b l e ; t h e c h i p - o u t a t t h e bottom i s t h e o r i g i n of a l o n g s u b s u r f a c e microcrack r u n n i n g up i n t o t h e d e v i c e . ( M a g n i g i c a t i o n 220x)
CRYSTALLINE VARIATIONS
When a c r y s t a l l a t t i c e i s h i g h l y o r d e r e d , minor changes i n l a t t i c e s t r u c t u r e can produce measurable changes i n t h e l o c a l t h e r m a l conduc- t i v i t y of t e m a t e r i a l and t h u s c a n be imaged w i t h a thermal-wave microscope. T h i s c a p a b i l i t y i s i l l u s t r a t e d i n F i g u r e s 2 and 3 which show GaAs d e v i c e s . The o p t i c a l and e l e c t r o n micrographs image
t h e v i s i b l e f e a t u r e s of t h e g a t e s t r u c t u r e s i n t h e d e v i c e s . The t h e r - mal-wave images show, i n a d d i t i o n , t h e Si-doped r e g i o n s o f t h e G a A s ,
s i n c e t h e s e r e g i o n s have a d i f f e r e n t t h e r m a l c o n d u c t i v i t y t h a t t h e un- doped r e g i o n s . Such images p e r m i t a r a p i d and n o n d e s t r u c t i v e a n a l y s i s of t h e e f f e c t s of l a t e r a l d i f f u s i o n s o f d o p a n t s i n semiconducting c r y s t a l s .
F i g . 2 - Images o f GaAs d e v i c e . The o p t i c a l ( a ) and e l e c t r o n micro- g r a p h s ( b ) show t h e v i s i b l e f e a t u r e s . The thermal-wave image ( c ) shows i n a d d i t i o n t h e Si-doped r e g i o n s o f t h e GaAs. ( M a g n i f i c a t i o n 4 0 0 x 1
.
F i g . 3 - Images o f a g a t e r e g i o n i n a GaAs d e v i c e . The o p t i c a l ( a ) and e l e c t r o n micrographs ( b ) show t h e v i s i b l e f e a t u r e s . The thermal- wave image ( c ) shows i n a d d i t i o n t h e l a t e r a l l y d i f f u s e d S i doped
r e g i o n around t h e g a t e s t r u c t u r e . ( M a g n i f i c a t i o n 500x).
Another i n t e r e s t i n g example o f thermal-wave d e t e c t i o n of l a t t i c e p e r - t u r b a t i o n s i s shown i n F i g u r e 4 . A sample o f GaAs was f i r s t masked i n a p a t t e r n and t h e n bombarded w i t h e n e r g e t i c p r o t o n s (40KeV) a t a f l u x
15 2
o f 10 /cm . These p r o t o n s p r o d u c e d a c o n t r o l l e d d e f e c t zone o f va- c a n c i e s and i n t e r s t i t i a l s a b o u t 0.5pm b e n e a t h t h e s u r f a c e wherever t h e GaAs was n o t p r o t e c t e d by t h e mask. The e l e c t r o n micrograph o f t h e GaAs shows, a f t e r removal o f t h e mask, no v i s i b l e p a t t e r n s ( F i g . 4 a ) . However, t h e thermal-wave image o f t h e same a r e a ( F i g . 4b) c l e a r l y shows t h e masking p a t t e r n ( w h i t e r e g i o n s ) . The image c o n t r a s t a r i s e s from t h e f a c t t h a t t h e proton-bombarded GaAs ( d a r k r e g i o n s ) now h a s a lower t h e r m a l c o n d u c t i v i t y t h a t t h e u n p e r t u r b e d GaAs ( w h i t e r e g i o n s ) .
F i g . 4 - Images o f a proton-bombarded GaAs w a f e r ; (a) e l e c t r o n m i c r o - g r a p h of t h e GaAs sample a f t e r removal o f t h e mask, showing no e v i - d e n c e of t h e masking p a t t e r n : ( b ) thermal-wave r e g i o n o f same re- g i o n s showing proton-bombarded ( d a r k ) r e g i o n s and u n p e r t u r b e d ( w h i t e ) r e g i o n s . ( M a g n i f i c a t i o n 100x) .
The imaging of c r y s t a l l i n e v a r i a t i o n s c a n a l s o be u s e f u l . i n m e t a l l o - graphy , 4 1 1 8 f 2 7 s i n c e d i f f e r e n t m e t a l l i c p h a s e s o r g r a i n s c a n be r e a d - i l y imaged w i t h no s p e c i a l sample p r e p a r a t i o n . We i l l u s t r a t e t h i s i n F i g u r e 5 where t h e columnar g r a i n s and t r a n s i t i o n zone i n a weld r e g i o n , o f an aluninum a l l o y a r e c l e a r l y v i s i b l e i n t h e thermal-wave image.
F i g . 5 - Thermal-wave image o f a weld r e g i o n i n an aluminom a l l o y . The columar g r a i n s i n t h i s r e g i o n a r e c l e a r l y v i s i b l e . ( M a g n i f i c a t i o n 30x).
Another example, F i g u r e 6 , shows t h e e l e c t r o n and thermal-wave images o f an Al-Zn a l l o y . The e l e c t r o n image ( a ) shows only topographical.
f e a t u r e s , w h i l e t h e thermal-wave image ( b ) c l e a r l y shows both t h e q r a i n s t r u c t u r e and, a t h i g h m a g n i f i c a t i o n , t h e p r e s e n c e o f Fe or Sn pre- c i p i t a t e s . Other s t u d i e s w i t h m e t a l s i n d i c a t e a p p l i c a t i o n s i n i n v e s t - i g a t i o n s of mechanical deformation2' and g r a i n boundaries. 19
F i g . 6 - E l e c t r o n ( a ) and thermal-wave (b) micrographs a t 50x o f an Al-Zn a l l o y . The thermal-wave micrqgraph shows t h e Al-Zn
g r a i n s , and t h e p r e s e n c e of F e o r Sn p r e c i p i t a t e s .
B O N D I N G INTEGRITY
Microscopic d e t a i l s i n a thermal-wave image a r e due t o r e f l e c t i o n and s c a t t e r i n g o f t h e r m a l waves from s u r f a c e and s u b s u r f a c e t h e r m a l f e a - t u r e s . I n a d d i t i o n , thermal-wave images o f t e n e x h i b i t l a r g e b r i q h t and d a r k a r e a s which r e p r e s e n t t h e a c o u s t i c modes o f t h e sample. 19 The i n c i d e n t e l e c t r o n beam i s v e r y e f f e c t i v e i n e x c i t i n g t h e p l a t e modes o f v i b r a t i o n s i n t h i n samples such a s I C c h i p s and w a f e r s . Thus, a t c e r t a i n r e s o n a n t f r e q u e n c i e s , v i b r a t i o n p a t t e r n s a r e s e t up on t h e sample c h a r a c t e r i z e d by r e g u l a r l y spaced nodes and a n t i n o d e s . When t h e e l e c t r o n beam i s a t a p l a t e node on t h e sample s u r f a c e , t h e r e i s no enhancement o f t h e t h e r m o a c o u s t i c s i g n a l . However, a t t h e a n t i - nodes t h e r e i s a c o n s i d e r a b l e enhancement, w i t h t h e enhancement b e i n g 180 0 out-of-phase between a p o s i t i v e and n e g a t i v e a n t i n o d e . Thus t h e p l a t e mode v i b r a t i o n i s s e e n a s a p a t t e r n o f b r i g h t and dark r e g i o n s i n t h e thermal-wave image, c o r r e s p o n d i n g t o t h e p o s i t i v e and n e g a t i v e a n t i n o d e r e g i o n s on t h e sample s u r f a c e . I f t h e sample i s a w i r e , t h e n t h e thermal-wave image d i s p l a y s t h e r a d i a l a c o u s t i c modes i n t h e w i r e .
Because of t h e i r s h o r t wavelength ( g e n e r a l l y <20pm), h i g h f r e q u e n c y t h e r m a l waves a r e u n a b l e t o p e n e t r a t e t h r o u g h an I C d i e t o probe t h e bonding between t h e d i e and i t s s u p p o r t s t r u c t u r e . However, I C d i e s a r e t h i n p l a t e s and t h u s w i l l e x h i b i t p l a t e mode v i b r a t i o n p a t t e r n s i n t h e i r thermal-wave images. The i n t e n s i t y of t h e s e v i b r a t i o n s i s a s e n s i t i v e f u n c t i o n o f t h e t h i c k n e s s of t h e sample, d e c r e a s i n g a s t h e t h i c k n e s s i n c r e a s e s . The same e f f e c t o c c u r s when t h e sample i s bonded t o a t h i c k e r s u b s t r a t e . The combination of t h e two s t r u c t u r e s now c o n s t i t u t e s a much t h i c k e r sample and t h e v i b r a t i o n i n t e n s i t i e s w i l l now d e c r e a s e . How s t r o n g t h i s e f f e c t w i l l be i s dependent on t h e
i n t e g r i t y and u n i f o r m i t y o f t h e bond between t h e d i e and i t s s u p p o r t - i n g s t r u c t u r e . The p l a t e mode p a t t e r n s s e e n i n t h e thermal-wave image can t h u s be used f o r comparative e v a l u a t i o n o f d i e a t t a c h .
F i g u r e s 7a and 7b show t h e thermal-wave images of two l a r g e s i l i c o n I C d i e s mounted i n l a r g e ceramic DIP packages. The d i e i n F i g u r e 7a i s known t o have a "poor" d i e - a t t a c h , w h i l e t h a t i n F i g u r e 7b i s a
"good" d i e - a t t a c h . I n agreement w i t h t h i s , t h e d i e i n F i g u r e 7a shows a s t r o n g p l a t e mode p a t t e r n i n d i c a t i v e o f a " t h i n - p l a t e " sample, t h a t i s , of a d i e t h a t i s p o o r l y a t t a c h e d . On t h e o t h e r hand, t h e d i e i n F i g u r e 7b shows l i t t l e e v i d e n c e o f a p l a t e mode p a t t e r n t h e r e b y i n d i c a t i n g a " t h i c k - p l a t e " sample, t h a t i s , a d i e f i r m l y and uniformly bonded t o i t s s u p p o r t s t r u c t u r e .
F i g . 7 - Examples o f a bonding i n t e g r i t y s t u d y . Thermal,-wave image of l a r g e IC d i e i n D I P package w i t h ( a ) p o o r d i e - a t t a c h a n d ex- h i b i t i n g s t r o n g p l a t e mode p a t t e r n ; and ( b ) b g o o d d i e - a t t a c h e x h i - b i t i n g no p l a t e mode p a t t e r n ( M a g n i f i c a t i o n '40x1.
Although s t i l l i n i t s f o r m a t i v e s t a g e , thermal-wave imaging h a s a l - ready demonstrated s e v e r a l i n t e r e s t i n g and u s e f u l a p p l i c a t i o n s f o r a v a r i e t y of m a t e r i a l s t u d i e s .
111. LASER BEAM DEFLECTION
The examples above were o b t a i n e d w i t h an e l e c t r o n beam t o g e n e r a t e t h e thermal waves. C l e a r l y t h e same images could have been o b t a i n - ed w i t h a l a s e r beam a s However i n b o t h c a s e s t h e u s e of a thermoacoustic probe t o d e t e c t t h e r e f l e c t i o n and s c a t t e r i n g of t h e thermal waves from t h e t h e r m a l f e a t u r e s s u f f e r s from t h e major draw- back of r e q u i r i n g a c o u s t i c ~ 0 u p l i n q between t h e sample and an u l t r a - s o n i c t r a n s d u c e r . I n t h e a n a l y s i s of semiconductor m a t e r i a l s and d e v i c e s , one would l i k e t o o p e r a t e i n a n open environment, employ completely c o n t a c t l e s s methods f o r thermal-wave g e n e r a t i o n and de- t e c t i o n , and be a b l e t o make measurements o r o b t a i n images a t high s p a t i a l r e s o l u t i o n . T h i s l a s t requirement n e c e s s i t a t e s t h e u s e of a h i g h l y focused beam f o r thermal-wave g e n e r a t i o n and t h e c a p a b i l i t y
f o r d e t e c t i n g high-frequency (>100kHz) thermal waves.
To s a t i s f y a l l of t h e above c o n d i t i o n s one needs t o u t i l i z e l a s e r s f o r both g e n e r a t i n g and d e t e c t i n g t h e t h e r m a l waves. The genera-, t i o n i s , of course, s t r a i g h t f o r w a r d . The d e t e c t i o n i s performed e i t h e r by l a s e r i n t e r f e r o m e t r i c d e t e c t i p n o f t h e t h e r m o e l a s t i c d i s - placements of t h e sample s u r f a c e , 12114*15 o r by l a s e r d e t e c t i o n of t h e l o c a l t h e r m o e l a s t i c d e f o r m a t i o n s o f t h e s u r f ace. 13-16 Both t e c h n i q u e s a r e analogous t o t h e o p t i c a l methods used f o r d e t e c t i n g
2 9 , 30
s u r f ace a c o u s t i c waves, a l t h o u g h h e r e t h e s u r f a c e d i s p l a c e m e n t s and deformations a r e due t o t h e thermal waves. A l l of t h e o t h e r methods f o r thermal-wave d e t e c t i o n s u f f e r from e i t h e r b e i n g l i m i t e d t o low modulation f r e q u e n c i e s o r from r e q u i r i n g c o n t a c t t o t h e sample.
There have been some i n i t a l s t u d i e s of thermal-wave d e t e c t i o n u s i n g t h e l a s e r techniques d e s c r i b e d above. Ameri e t a 1 have performed a rudimentary imaging experiment w i t h t h e l a s e r i n t e r f e r o m e t r i c t e c h n i - q u e , 1 2 while Arner and h i s c o l l e a g u e s have used both t h e l a s e r d e f l e c - t i o n ( s u r f a c e deformation d e t e c t i o n ) t e c h n i q u e and t h e l a s e r i n t e r - f e r o m e t r i c technique f o r s p e c t r o s c o p i c ~ t u d i e s . ' ~ - ~ ~ These i n v e s t i - g a t i o n s have a l l been performed a t low t o moderate modulation frequen- c i e s (<100kHz) only. We have employed t h e l a s e r d e f l e c t i o n t e c h n i q u e i n a somewhat d i f f e r e n t e x p e r i m e n t a l c o n f i g u r a t i o n a t h i g h thermal-wave f r e q u e n c i e s (up t o 10MHz) f o r q u a n t i t a t i v e measurements of t h i n - f i l m t h i c k n e s s e s . 1 6
I V . DEPTH-PROFILING AND THIN-FILM THICKNESS MEASUREMENTS
Semiconductor d e v i c e s a r e composed o f a c o m p l i c a t e d t h r e e - d i m e n s j o n a l a r r a y o f t h i n f i l m s . Thermal-wave p h y s i c s p r o v i d e s an i d e a l t o o l t o s t u d y s u c h s y s t e m s b e c a u s e o f i t s u n i q u e d e p t h - p r o f i l i n g c a p a b i l i t y . 3 1 We have employed t h e l a s e r d e f l e c t i o n method a t f r e q u e n c i e s a s h i g h a s lOMHz t o measure t h e t h i c k n e s s o f opaque and t r a n s p a r e n t f i l m s used i n s e m i c o n d u c t o r p r o c e s s i n g . 1 6 Using an i n c i d e n t h e a t i n g l a s e r beam o f a p p r o x i m a t e l y 30mW a t lMHz, we a r e a b l e t o d e t e c t l o c a l s u r - f a c e d e f o r m a t i o n s t h a t c o r r e s p o n d t o s u r f a c e d i s p l a c e m e n t s o f approx- i m a t e l y 10-*2/&, a s e n s i t i v i t y t h a t i s c o n s i d e r a b l y b e t t e r t h a n t h a t r e p o r t e d p r e v i o u s l y . 12,13-15
To make q u a n t i t a t i v e t h i n f i l m t h i c k n e s s measurements w i t h t h e l a s e r probe t e c h n i q u e we e x t e n d e d t h e Opsal-Rosencwaig thermal-wave d e p t h - p r o f i l i n g t o t h r e e d i m e n s i o n s , a n d i n c l u d e d t h e r m o e l a s t i c s u r f a c e d e f o r m a t i o n s , t h e r m a l l e n s e f f e c t s , o p t i c a l e f f e c t s and non- l i n e a r e f f e c t s a r i s i n g from t h e t e m p e r a t u r e dependence of t h e v a r i o u s m a t e r i a l p a r a m e t e r s . When a l l o f t h e s e e f f e c t s a r e p r o p e r l y i n c l u d e d i n t h e model, q u a n t i t a t i v e measurements on s i n g l e and m u l t i p l e f i l m s a r e t h e n p o s s i b l e . T h i s i s i l l u s t r a t e d i n F i g u r e 8 w h e ~ e we show t h e o r e t i c a l c u r v e s and d a t a o b t a i n e d f o r s i n g l e f i l m s of A 1 on S i and f o r f i l m s o f A 1 on S i 0 2 on S i . We have u s e d t h e magnitude of t h e thermal-wave s i g n a l r a t h e r t h a t t h e p h a s e i n t h e s e measure-
ments s i n c e t h e magnitude h a s a g r e a t e r r a n g e and c a n be measured more p r e c i s e l y . The d a t a i n F i g u r e 8 i s a n e x c e l l e n t agreement w i t h t h e t h e o r y b o t h f o r t h e s i n g l e and t h e d o u b l e fi.lms. The p r e c i s i o n of t h e r e a d i n g s o b t a i n e d w i t h a 1 - s e c a v e r a g i n g t i m e o v e r t h e t h i c k n e s s r a n g e o f 5002 - 1 5 , 0 0 0 8 i s 2 2 % f o r t h e s e A 1 f i l m s .
I n F i g u r e 9 , we show t h e t h e o r e t i c a l c u r v e s and t h e d a t a f o r a s e r i e s o f t r a n s p a r e n t S i 0 2 f i l m s on S i . Although o n l y a s i n g l e f i l m problem, t h e t h e o r y i n t h i s c a s e must i n c l u d e t h e r m o e l a s t i c d e f o r m a t i o n s a t b o t h t h e Si-SiO2 and t h e S i 0 2 - a i r i n t e r f a c e s , t h e r m a l l e n s e s i n b o t h t h e S i 0 2 and t h e a i r , and o p t i c a l i n t e r - f e r e n c e s e f f e c t s i n t h e S i 0 2 ( s e e R e f e r e n c e 1 6 ) . The f i t be- tween t h e o r y and e x p e r i m e n t i s s t i l l , w i t h a l l t h i s c o m p l e x i t y , q u i t e good, i n d i c a t i n g t h a t t r a n s p a r e n t a s w e l l as opaque f i l m s c a n be measured w i t h thermal-wave t e c h n o l o s v . -- The t h i c k n e s s s e n s i t i v i t y f o r S i 0 2 f i l m s o n S i a p p e a r s t o be 5 2 % o v e r t h e r a n g e 500g - 15,OOOg.
0 .5 1 .O 1.5 2.0 2.5 THICKNESS (microns)
F i g . 8 - R e l a t i v e a m p l i t u d e a t 1 MHz o f l a s e r beam d e f l e c t i o n s i g n a l a s a f u n c t i o n of A 1 f i l m t h i c k n e s s f o r a s e r i e s o f Al-on-Si and A l - on-Si02-on S i f i l m s . C i r c l e s a r e e x p e r i m e n t e d d a t a and c u r v e s a r e
from t h e extended Opsal-Rosencwaig model.
THICKNESS (microns)
F i g . 9 - R e l a t i v e amplitude a t 1 MHz of l a s e r beam d e f l e c t i o n s i g n a l a s a f u n c t i o n of S i 0 2 f i l m t h i c k n e s s f o r a s e r i e s of Si02-on-Si f i l m s . C i r c l e s a r e e x p e r i m e n t a l d a t a and c u r v e s a r e from t h e extended Opsal- Rosencwaig model.
V. CONCLUSIONS
Thermal-wave p h y s i c s h a s b e e n a p p l i e d , f o r s e v e r a l y e a r s , t o t h e s t u d y of many m a t e r i a l s i n c l u d i n q s e m i c o n d u c t o r m a t e r i a l s . U n t i l r e c e n t l y , t h e s e s t u d i e s h a v e b e e n c o n f i n e d p r i m a r i l y t o s p e c t r o - s c o p i c i n v e s t i g a t i o n s . The e x a m p l e s p r e s e n t e d above i l l u s t r a t e t h a t thermal-wave p h y s i c s c a n a l s o p l a y a m a j o r r o l e i n o t h e r i m - p o r t a n t a p p l i c a t i o n s r e l a t e d t o s e m i c o n d u c t o r m a t e r i a l s , s u c h a s
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