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Submitted on 1 Jan 1983
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DIFFERENTIAL ELLIPSOMETRY
T. Sandström
To cite this version:
T. Sandström. DIFFERENTIAL ELLIPSOMETRY. Journal de Physique Colloques, 1983, 44 (C10),
pp.C10-75-C10-78. �10.1051/jphyscol:19831015�. �jpa-00223472�
JOURNAL DE PHYSIQUE
Colloque C10, supplciment
au n012,Tome 44, d k e m b r e 1983 page C10-75
DIFFERENTIAL ELLIPSOMETRY
Research Laboratory o f EZectronics, ChaZnrers U n i v e r s i t y
of
Technology, S-412 96 Gothenburg, SwedenRESUME
-
Les d i f f g r e n t e s mgthodes d t e l l i p s o m 6 t r i e d i f f e r e n t i e l l e d a n s l a l i t t d r a t u r e o p t i q u e s o n t p a s s d e s e n r e v u e . On p r g s e n t e une n o u v e l l e m6thode q u i p e u t O t r e r d a l i s 6 e p a r une c o n v e r s i o n mdcanique s i m p l e d'un e l l i p s o m 5 t r e d e l t a - p s i . L t u t i l i t d d e 1 ' e l l i p s o m Z t r i e v r a i m e n t d i f f e r e n - t i e l l e e s t d6montrGe. E l l e c o n s t i t u e un moyen d e m e s u r e r d e s d i f f g r e n c e s e n t r e s u r f a c e s f a i b l e s , mais s e s a p p l i c a t i o n s n e s o n t p a s nombreuses.ABSTRACT - A s u r v e y of w a y s t o a c h i e v e d i f f e r e n t i a l e f l i p s o m e t r y is m a d e , a n d a n o v e l p u r e l y d i f f e r e n t i a i s c h e m e i s p r e s e n t e d . T h e n e w s c h e m e c a n b e e m p l o y e d t h r o u g h a r e i a t i v e i y s i m p l e m e c h a n i c a l c o n v e r s i o n of a d e l t a - p s i e l I i p s o m e t e r . A l t e r n a t i v e l y i t c a n b e u s e d t o b u i l d s i m p l i f i e d a u t o m a t i c i n s t r u m e n t s f o r p a r t i c u l a r a p p l i c a t i o n s . T h e u s e f u l n e s s o i t r u l y d i f f e r e n t i a i e l l i p s o m e t r y is a s s e s s e d . I t i s s h o w n t h a t s m a i i d i f f e r e n c e s b e t w e e n s u r f a c e c a n be measured i n some c a s e s , b u t t h a t d i f f e r e n t i a l e l l i p s o m e t r y h a s t o be c o n s i d e r e d a s a special technique with a limited number of applications.
INTRODUCTION
F i r s t of a l l i t i s n e c c e s s a r y t o d e f i n e t h e term d i f f e r e n t i a l e l l i p s o m e t r y . Two d i f f e r e n t m e a n i n g s c a n be d i s t i n g u i s h e d : I n d i v i d u a l m e a s u r e m e n t s of t h e compared s a m p l e s a n d s u b s e q u e n t n u m e r i c a l s u b t r a c t i o n of t h e r e s u l t s , o r t r u l y d i f f e r e n t i a l t e c h n i q u e s where o n l y t h e d i f f e r e n c e i n p h y s i a c a l p r o p e r t i e s i s m e a s u r e d b y t h e i n s t r u m e n t . Although t h e f i r s t type of measurement is obvious and c a n be performed with any instrument g i v i n g n u m e r i c a l o u t p u t , o n e d e s i g n s h o u l d be m e n t i o n e d , t h e Azram t w o - r e f l e c t i o n e l l i p s o m e t e r C I I w h i c h m e a s u r e s d e l t a a n d p s i of t w o s u r f a c e s s i m u l t a n e o u s l y . T h e instrument w a s concieved for use in t h e f a r IR where good transmission c o m p e n s a t o r s c a n n o t be f o u n d a n d u s e s a n a u x i l i a r y r e f l e c t i n g s u r f a c e f o r c o m p e n s a t i o n . A t h o r o u g h a n a l y g i s s h o w s t h a t t h e p r o p e r t i e s of b o t h s a m p l e a n d a u x i l i a r y s u r f a c e c a n b e m e a s u r e d simultaneously.
D i f f e r e n t i a l e l l i p s o m e t r y h a s a l s o b e e n performed w i t h f a s t modulated e l i i p s o m e t e r s with two s a m p l e s a t t a c h e d t o a s p i n n i n g d i s c By means of double l o c k - i n d e t e c t i o n b o t h t h e a v e r a g e a n d d i f f e r e n c e e l i i p s o m e t r i c p r o p e r t i e s of t h e t w o s u r f a c e s a r e f o u n d . I n p r i n c i p l e s u c h t e c h n i q u e s h a v e t h e s a m e g e n e r a l property a s t h e PSSA e l l i p s o m e t e r : t h e i n s t r u m e n t m a k e s a f u l l i n d i v i d u a l c h a r a c t e r i z a t i o n of two s u r f a c e s s i m u l t a n e o u s I y A purely d i f f e r e n t i a l ellipsometer h a s been s k e t c h e d by l r e u E33. A non-polarised beam i s s p l i t i n t o t w o complementarily polarised beams by a Wollaston p r i s m . T h e p o l a r i s a t i o n of t h e two beams i s modulated by a n acousto-optical device and e a c h beam is made t o f a i l o n t o o n e of t h e s a m p l e s . T h e r e f l e c t e d b e a m s a r e a n a l y s e d a n d t h e i r i n t e n s i t i e s , n o t a m p l i t u d e s , a r e added i n t h e d e t e c t o r . T h e e l l i p s o m e t r i c d i f f e r e n c e b e t w e e n t h e t w o s u r f a c e s c a n be found through a s p e c t r a 1 a n a i y s i s of t h e output voltage from t h e d e t e c t o r . A completely d i f f e r e n t s c h e m e is used i n t h e c o m p a r i s o n e l l i p s o m e t e r C 4 . S 1 , w h i c h i s a f i x e d - p o i a r i s e r f i x e d - a n a l y s e r i n s t r u m e n t f o r e l l i p s o m e t r i c c o m p a r i s o n , f i g . I . T h i s i n s t r u m e n t g i v e s e x t i n c t i o n of t h e l i g h t when t h e two c o m p a r e d s u r f a c e s h a v e i d e n t i c a l e I I i p s o m e t r i c a l p r o p e r t i e s . A full-color image of t h e s a m p l e s superimposed i s s e e n i n t h e e y e - p i e c e a n d a r e a s w i t h e q u a l p r o p e r t i e s a p p e a r b l a c k . Apart from b e i n g a n I m a g i n g i n s t r u m e n t , t h e c o m p a r i s o n e l l i p s o m e t e r i s unique i n i t s u s e of w h i t e l i g h t . Ambiguities normally found i n eiiipsometry on films above 250 nm t h i c h n e s s a r e a b s e n t b e c a u s e of t h e non-periodic propertv of white iight
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19831015
JOURNAL DE PHYSIQUE
a,
Fig. 1 Comparison el lipsometer.
F i g . 2Change
o fbase states.
I t s h o u l d b e p o i n t e d o u t t h a t t h e c o m p a r i s o n e l L i p s o m e t e r i s n o t a d i f f e r e n t i a e l l i p s o m e t e r in t h e s e n s e of t h i s a r t i c l e s i n c e i t does not give a q u a n t i t a t i v e m e a s u r e o t h e d i f f e r e n c e b e t w e e n t h e s u r f a c e s . N o r m a l l y i t i s u s e d t o g e t h e r w i t h calibrated r e f e r e n c e s u r f a c e s w i t h fiims of v a r y i n g , b u t k n o w n , t h i c k n e s s . T h e i m p o r t a n c e of t h ~ c o m p a r i s o n e l l i p s o m e t e r i n t h i s c o n t e x t is t h a t i t s h a r e s i t s g e o m e t r y w i t h t h e neb differential ellipsometer in neat paragraph
h N E W DIFFERENTIAL SCHEME
When a beam of I i g h t i s r e f l e c t e d a t a n oblique a n g l e a t a s u r f a c e , i t s p o l a r i s a t i o n s t a t e i s changed by t h e reflection. Under some g e n e r a l a s s u m p t i o n s t h a t t h e s u r f a c e i s i s o t r o p i c and o p t i c a l l y n o n - a c t i v e , t h e r e f l e c t i o n c a n be d e s c r i b e d a s t h e independent reflection of t w o s p e c i f i c p o i a r i s a t i o n c o m p o n e n t s , t h e l i n e a r l y p o l a r i s e d s t a t e s p a r a l l e l a n d p e r p e n d i c u l a r t o t h e plane of i n c i d e n c e , denoted by t h e symbols p a n d s . The a t t e n u a t i o n a n d r e t a r d a t i o n t h a t t h e c o m p o n e n t s of t h e l i g h t i n c u r from t h e r e f l e c t i o n c a n b e r e p r e s e n t e d by m u l t i p l i c a t i o n o f t h e a m p l i t u d e s by c o m p l e x s c a l a r s Vp a n d Vg i t i s s h o w n i n 553 t h a t if t w o s u r f a c e s 51 a n d 52 a r e s o a r r a n g e d , F i g . 2 , t h a t t h e p l a n e s of i n c i d e n c e of a l i g h t b e a m f o r m a r i g h t a n g l e , t h e p a n d s s t a t e s a r e rnterchanged between t h e s u r f a c e s T h e t o t a i action of t h e two s u r f a c e s o n t h e p component of t h e f i r s t s u r f a c e i s VsZVpl
,
w h e r e i a n d 2 d e n o t e t h e s u r f a c e s . Correspondingly t h e s component i s a f f e c t e d b y VpipzV51 If t h e ensemble of t h e two s u r f a c e s i s put i n t h e p l a c e of t h e s a m p l e i n a d e l t a - p s i e l l i p s o m e t e r , F i g . 3 , t h e i n s t r u m e n t w i l l m e a s u r e t h e ellipsomtric differenceFig. 3 Differential ellipsometer.
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Any d e l t a - p s i e l l i p s o m e t e r c a n be modified t o make d i f f e r e n t i a l measurements a s o u t l i n e d a b o v e . T h e main probiem i s t h e mechanical alignment of t h e o p t i c a l c o m p o n e n t s a n d t h e s a m p l e s In o n e - r e f l e c t i o n e l l i p s o m e t r y a l i g n m e n t s c a n be made by means of t h e Iight beam i t s e l f With two r e f l e c t i o n s t h e r e a r e more d e g r e e s of freedom a n d t h e alignment i s more d i f f i c u l t . I t i s p r e i e r a b i e t h a t t h e c o a r s e a l i g n m e n t i s b u i l t i n t o t h e o p t i c a l b e n c h . A i t h o u g h a c o n s t r u c t i o n w i t h m o v a b l e j o i n t s is p o s s i b l e , i t i s a d v i s a b l e t o u s e a o n e - p i e c e r i g i d b e n c h . T h e p l a n e s of i n c i d e n c e on t h e t e s t s u r f a c e s c a n be defined by iixed sample h o i d e r s . Small c h a n g e s t o t h e a n g l e s of i n c i d e n c e o r t h e a n g l e b e t w e e n t h e p l a n e s of i n c i d e n c e c a n be pccomplished by small t i l t s of t h e sample h o l d e r s o r by s l i g h t movements of t h e pinhoie in t h e coIIimator. For f i n e a d j u s t m e n t i t i s s u g g e s t e d t h a t a n a u x i i i a r y p o l a r i s e r be i n t r o d u c e d i n t h e o p t i c a l p a t h between t h e two s u r f a c e s . If A of t h e samples a r e n o t z e r o , t h e p o l a r i s e r a n d t h e a u x i i i a r y p o l a r i s e r c a n e x t i n g u i s h t h e I i g h t only w h e n t h e y a r e p a r a l l e l a n d p e r p e n d i c u l a r t o t h e plane of i n c i d e n c e a t t h e f i r s t s u r i ~ c e . If t h e a u x i l i a r y p o l a r i s e r i s a d j u s t e d t o s u c h a p o s i t i o n , i t w i l l g i v e e x t i n c t i o n fo t h e Iight t o g e t h e r w i t h t h e a n a l y s e r only when t h e plane of incidence of t h e second s u r f a c e i s p e r p e n d i c u l a r t o t h a t of t h e f i r s t o n e . Now t h e p i a n e s of i n c i d e n c e a r e p e r p e n d i c u l a r , and t h e zero azimuths of t h e polarizer and analyzer a r e f o u n d . To e n s u r e t h a t t h e a n g l e s of i n c i d e n c e a r e e q u a l , o n e c a n m e a s u r e t h e d i f f e r e n c e of t w o s u r f a c e s known t o b e e q u a l , e . g . two c l e a n - e t c h e d s i l i c o n s u r f a c e s . When t h e s e t u p i s o n c e well a d j u s t e d a n alignment l a s e r o r a n auto-coliimator c a n be a r r a n g e d s o a s t o f a c i l i t a t e t h e future alignment of t e s t surfaces
ASSESSMENT
T h e s e n s i t i v i t y a n d r u g g e d n e s s of e l l i p s o m e t r y a s compared t o i n t e r f e r o m e t r y come i n p a r t f r o m t h e f a c t t h a t a b s o i u t e p h a s e a n d i n t e n s i t y a r e d i s c a r d e d i n t h e m e a s u r e m e n t . While t h i s i s a g r e a t a d v a n t a g e in making a c c u r a t e m e a s u r e m e n t s i t makes t h e m a t h e m a t i c a i m s n i p u l a i i o n a n d i n t e r p r e t a t i o n o f t h e r e s u l t s m o r e d i f f i c u l t . I n p a r t i c u l a r a n d a r e n o n - l i n e a r f u n c t i o n s of t h e p h y s i c a l p a r a m e t e r s of a s u r f a c e . B e c a u s e of t h e n o n - l i n e a r i t i e s t h e i n t e r p r e t a t i o n o f s m a I I d i f f e r e n c e s A d a n d Yd b e t w e e n t w o s u r f a c e s d e p e n d s on t h e a c t u a l v a l u e s of f', a n d q . T o be a b l e t o u s e a d i f i e r e n t i a l d e l t a - p s i e l l i p s o m e t e r , a s d e s c r i b e d a b o v e , t o m e a s u r e s m a l l d i f f e r e n c e s i n p h y s i c a l p a r a m e t e r s , o n e must c a l c u l a t e t h e p a r t i a l d e r i v a t i v e s of Ad a n d Y'd w i t h r e s p e c t t o t h e p h y s i c a l p a r a m e t e r s , a n d t o d o t h i s o n e m u s t k n o w t h e a p r o x i m a t e p r o p e r t i e s o i t h e s u r f a c e a p r i o r i
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O t h e r s c h e m e s w h e r e two s u r f a c e s a r e measured independellily a n d t h e d a t a a r e s u b t r a c e d n u m e r i c a l l y do i n t h i s r e s p e c t h a v e t h e a d v a n t a g e o i p r o v i d i n g t h e v a l u e s of and?2, T h e P S S A e l l i p s o m e t e r i n C11 a n d s p i n n i n g d i s k e I l i p s o m e t e r s a r e f a v o r a b l e , s i n c e t h e y r e t a i n t h e s i m u I t a n e i t y c h a r a c t e r i s t i c of differential techniquesA11 example of t h e p o t e n t i a l of d i f i e r e n t i a l e l l i p s o m e t r y i s s h o w n i n F i g . 4 . I t s h o w s a n u m e r i c a l l y s i m u l a t e d s p e c t r o s c o p i c c o m p a r i s o n of two samples c o n s i s t i n g of s u b s t r a t e s with wavelength-dependent, but e q u a l , r e f r a c t i v e i n d i c e s c o v e r e d w i t h t h i n f i l m s S nm i i ~ i c k . T h e f i l m s h a v e r e a l r e f r a c t i v e i n d i c e s of 1 . 5 0 , a n d o n e of t h e films h a s a weak a b s o r b t i o n s p e c t r u m . T h e maximum a b s o r b t i o n c o e f f i c i e n t i n t h e film i s 0.01, w h i l e t h e index of t h e s u b s t r a t e m a t e r i a l v a r i e s t h r e e hundred t i m e s a s m u c h . T h e s p e c t r u m of t h e s u b s t r a t e s i s c h o s e n to be reasonably r e a l i s t i c , w h i l e t h a t of t h e f i l m h a s b e e n g i v e n a c h a r a c t e r i s t i c p e r l o d i c w a v e l e n g t h d e p e n d e n c e i n o r d e r t o make any d i s t o r t i o n s visible 3 0 t h spectra obey t h e Cramers-Cronrg r e l a t i o n .
i t i s s e e n from t h e f i g u r e t h a t t h e d i f f e r e n c e s p e c t r u m of t h e f i l m s i s d e t e c t e d , only s i i g h t i y d i s t o r t e d by t h e v e r y much s t r o n g e r s p e c t r u m of t h e s u b s t r a t e s T h e r e a l a n d i m a g i n a r y p a r t s of t h e d i f f e r e n c e s p e c t r u m came o u t a s A d a n d
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r e s p e c t i v e l y . T h e s p e c t r a a r e d i s t o r t e d i n t h e s h o r t w a v e l e n g t h e n d d u e t o t h e s m a l l r e a I p a r t of t h e s u b s t r a t e index.n o w e v e r p r o m i m i s i n g t h i s s i m u l a t i o n may a p p e a r , t h e r e a d e r i s c a u t i o n e d t o n o t i c e some f a c t o r s c o n t r i b u t i n g t o t h e r e s u l t . T h e f i l m s h a v e i d e n t i c a l t h i c k n e s s a n d t h e f i l m s p e c t r a a r e w e a k . i n a s i m u l a t i o n r u n w i t h s l i g h t l y d i f f e r e n t f i l m t h i c k n e s s e s t h e s u b s t r a t e s p e c t r u m a p p e a r e d i n Ad a n d \Yd
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a n d t h e film s p e c t r u m w a s d r o w n e d T h e s e p a r a t i o n o i r e a I a n d i m a g i n a r y p a r t s of t h e i n d e n d i f f e r e n c e i n t h e s i m u l a t i o n i s incidental.T h e p r i n c i p l e i s b e t t e r s u i t e d t o t h e m e a s u r e m e n t of s m a l l i n d e x d i f f e r e n c e s t h a n t o d i i f e r e n c e s i n t h i c k n e s s . R e f r a c t i v e i n d e x d i f f e r e n c e s i n t h i n f i l m s a r e m e a s u r e d w i t h greater e a s e and accurately when t h e r e is no thickness d i f f e r e n c e .
k n a d v a n t a g e with d i f f e r e n t i a l eIiipsometry of t h e s u g g e s t e d t y p e i s t h a t t h e a d j u s t m e n t s of t h e p o l a r i s i n g c o m p o n e n t s a r e s m a l l a n d c a n b e a c c o m p l i s h e d w i t h r e l a t i v e l y simple e l e c t r o - o p t i c a l d e v i c e s a n d m o d e r a t e d r i v i n g For a p p l i c a t i o n s l i k e p r o d u c t i o n c o n t r o l where small v a r i a t i o n s of p r e d i c t a b l e c h a r a c t e r a r e t o be measured or monitored, t h e u s e
CIO-78 JOURNAL DE PHYSIQUE
W a . o h r t b [ r l
Fig. 4 Numerical simulation.
of t h e d i f f e r e n t i a l scheme above c a n sxmpiify t h e i n s t r u m e n t a t i o n c o m p a r e d t o p r e v i o u s instruments.
Applications for t h e d e s c r i b e d t e c h n i q u e a r e measurements of difference s p e c t r a where film t h i c i c i ~ e s s d i f f e r e n c e s a r e unliiteiy t o o c c u r e e . g . r a d i a t i o n induced o p t i c a l e f f e c t s , weak a i l o y s o r i o n i n p i a n t e d m e t a l s o r s e m i c o n d u c t o r s . I n c o n c i u s i o n t h e t r u l y d i f f e r e n t i a l e i i i p s o m e t e r i s n o i a g e n e r a i - p u r p o s e i n s t r u m e n t l i k e t h e o r d i n a r y e i l i p s o m e t e r , b u t rat1;ier a s i m p l e s o l u t i o n to problems of m e a s u r i n g small d i f f e r e n c e s w i t h h i g h r e s o i u t i o n in p a r t i c u i a r a p p l i c a t i o n s w h e r e t h e p r o p e r t i e s of t h e s u r f a c e s a r e approximately known.
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MiIier , Ph . D . T h e s i s , Princeton University, (1974) 3 . Treu J I, Rev. S c i . I n s t r . 45 (1974) 14644. Stenberg if, Sandstrom T , S t i b i e r t L , H a t . S c i . Eng. 42 (1980) 65 5. Sandstrom, Ph . D . T h e s i s , Gothenburq (I982), I S B N 91-7032-073-X
