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ELLIPSOMETRY OF THICK (d>λ) TRANSPARENT FILMS USING CHANNELLED SPECTRUM
M. Yamamoto
To cite this version:
M. Yamamoto. ELLIPSOMETRY OF THICK (d>λ) TRANSPARENT FILMS USING CHAN- NELLED SPECTRUM. Journal de Physique Colloques, 1983, 44 (C10), pp.C10-35-C10-38.
�10.1051/jphyscol:19831006�. �jpa-00223455�
JOURNAL DE PHYSIQUE
Colloque ClO, supplkment a u n012, Tome 44, d6cembre 1983 page C10- 35
E L L 1 PSOMETRY OF T H I C K ( d > h ) TRANSPARENT F I L M S USING CHANNELLED SPECTRUM
M . Yamamoto
Research I n s t i t u t e f o r S c i e n t i f i c Measurements, 'I'ohuku U n i v e r s i t y , Sendai 980, Jupan
Resume
-
On d e c r i t dans c e t a r t i c l e une methode e l l i p s o m e t r i q u e d ' e x t i n c - t i o n s i m p l e e t de h a u t e p r e c i s i o n p o u r des f i l m s Ppais (d.h), q u i u t i l i s e l e s p e c t r e cannele de l a l u m i P r e p o l a r i s e e . On donne des r e s u l t a t s expe- rimentaux pour des f i l m s de MgF.
C e t t e methode s ' a v e r e u t i l e pour l ' e t u d e d e t a i 1 le e des p r o p r i e t e s o p t i q u g s de f i l m s e p a i s t r a n s p a r e n t s ou f a i b l e - ment absorbants.A b s t r m
-
A s i m p l e method o f p r e c i s i o n n u l l - e l 1 ip s o m e t r y f o r t h i c kTd';j;r
f i l m s , i n which use i s made o f p o l a r i z e d - l i g h t - c h a n n e l l e d - s p e c t r u m , i s described. Experimental r e s u l t s w i t h MgF2 f i l m s a r e given. The method i s u s e f u l f o r t h e d e t a i l e d s t u d y o f t h e o p t i c a l p r o p e r t i e s o f t r a n s p a r e n t o r weakly a b s o r b i n g t h i c k f i l m s .51. I n t r o d u c t i o n
I n t h e e l l i p s o m e t r i c s t u d y o f f i l m s t h i c k e r than t h e wavelength o f t h e probe l i g h t h,a d i f f i c u l t y may a r i s e i n d e t e r m i n i n g t h e t h i c k n e s s d owing t o t h e h i g h o r d e r o f i n t e r f e r e n c e i n v o l v e d . Another d i f f i c u l t y , which i s perhaps more e s s e n t i a l , i s o f t e n caused by t h e n o n u n i f o n n i t y o f t h e f i l m , t y p i c a l l y t h e change i n r e f r a c t i v e i n d e x n i n t h e d i r e c t i o n normal t o t h e f i l m s u r f a c e . The method d e s c r i b e d h e r e w i l l p r o v e u s e f u l i n s o l v i n g such d i f f i c u l t i e s .
92. P r i n c i p l e
L e t S i n F i g . 2 be a sample ( f i l m / s u b s t r a t e ) as shown i n F i g . 1
P
r 1 p , r 1 s S
W t e l i g n t
r o s *
r 2 P , r 2 S Parallel
n s s u b s t r a t e beam
F i g . 1 - F i l m / s u b s t r a t e system ( & A ) : r ' s a r e Fresnel c o e f f i c i e n t s . S u b s c r i p t s p and s denote p a r a l l e l and p e r p e n d i c u l a r v i b r a t i o n components.
F i g . 2 - O p t i c a l system.
The p r i n c i p l e o f t h e p r e s e n t method w i l l most r e a d i l y be understood i n t h e c a s e where t h e f i l m and s u b s t r a t e a r e t r a n s p a r e n t , n o n - d i s p e r s i v e and homogeneous. I n such a case, i f one examines t h e o u t p u t spectrum a t v a r i o u s a z i m u t h a l angles o f t h e a n a l y z e r OA, one w i l l f i n d a t two v a l u e s o f O A t h a t t h e spectrum i s accompanied by a s e r i e s o f d i s t i n c t d a r k 1 in e s l o c a t e d w i t h s y s t e m a t i c i n t e r v a l s (chunneZZed s p e c t m /1,2/); a t o t h e r v a l u e s o f O A no c l e a r dark l i n e s a r e o b s e r v a b l e . L e t us
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19831006
C10-36 JOURNAL DE PHYSIQUE
denote by (em, X ) t h e values o f 0 and
X
a t which e x t i n c t i o n occurs (Om = Omt2 i n rnt h e s i m p l e s t case now under c o n s i d e r a t i o n ) . As w i l l be seen below, rn corresponds t o t h e o r d e r o f i n t e r f e r e n c e o f l i g h t .
I f t h e f i l m and/or s u b s t r a t e a r e / i s absorbing, d i s p e r s i v e a n d / o r inhomogeneous, t h e i n t e r v a l s between t h e v a l u e s o f Om, and o f Am, f o r d i f f e r e n t o r d e r s become apparent- l y l e s s s y s t e m a t i c . Through a l l t h e cases however, t h e e x t i n c t i o n c o n d i t i o n s a r e g i v e n by t h e s t a n d a r d e l l i p s o m e t r i c f o r m u l a e
Im(R /R ) = t a n Y s i n A = 0,
P s ( 1 )
Re(R /R ) = t a n Y cos A = - t a n 8 t a n €IA,
P s P ( 2 )
w i t h
-
RP = t a n W eiA = f(e-iS) where f ( g ) : (3)Rs
I n t h e case where 6 = -45" and R
t
0, t h e e x t i n c t i o n c o n d i t i o n s (1) and (2) a r eP P
s a t i s f i e d i f
X
= Am and 0 = Om, where t h e v a l u e s o f Xrn and Om a r e such t h a t s i n a(Xm) = 0,t a n Om = t a n Yrn: t a n Y(Am).cos a(Xm)
.
The s i g n o f
ern
i s d e t e r m i n e d by t h a t o f cos A(Xrn). The r e g u l a r i t y o f t h e i n t e r v a l s between t h e values o f Am, o r o f Om, determined by t h e above e q u a t i o n s i s e v i d e n t i f n and ns ( t h e s u b s t r a t e i n d e x ) a r e r e a l , independent o f X and homogeneous; and i sl e s s so i f n o t .
I t w i l l be seen by t h e above r e l a t i o n s t h a t t h e method d i s c u s s e d h e r e i s a p p l i c a b l e a l s o t o weakly a b s o r b i n g f i l m s .
I n t h e case where n and n s a r e r e a l and homogeneous, rlp. r2p, rls, r2s and 6 be- come r e a l and eqs. (5) and ( 6 ) can be r e w r i t t e n as
s i n 6 = 0, ( 7)
t a n Om = t a n Ym = f ( c o s 6) (8)
Note t h a t i n eq. (8) YNl i s d e f i n e d i n t h e r e g i o n -n < Ym
2
n. These two e q u a t i o n s can f u r t h e r be r e w r i t t e n as f o l l o w s .A m p l i t u d e c o n d i t i o n
F o r even values o f rn(=22): t a n 8 2 2 = t a n W 2 2 = f ( 1 ) = rop/roS ( 9 ) F o r odd v a l u e s o f m(=22+1) : t a n 822+1 = f ( - 1 ) ( 1 0 ) Phase c o n d i t i o n
E q u a t i o n ( 9 ) shows t h a t i s independent o f t h e f i l m i n d e x and determined* s o l e l y
53. Experiments w i t h MgF7 F i l m s
W i t h t h e purpose o f d e m o n s t r a t i n g t h e c a p a b i l i t y o f t h e c h a n n e l l e d s p a c t m e l - iipsorneLmJ d e s c r i b e d above, a p r o v i s i o n a l experiment was c a r r i e d o u t w i t h MgF2 f i l m s
*
I f t h e f i l m i s p e r f e c t l y homogeneous. I f n o t , i s v e r y s e n s i t i v e t o t h e f i l m i n - homogeneity / 3 / .vacuum-deposited a t Pa onto wedge-type BK7 substrates. A 150 W Xe lamp was employed as the l i g h t source (Fig. 2). UV prism p o l a r i z e r s were used f o r P and A.
The beam t r a n s m i t t e d by A was focussed on t h e entrance s l i t o f a NlKON G 500 spectrometer.
- -
10.04 h r ~-
XI? short arc'5 -
2
~ O O
LOO 6 00 800 h(nm)F i g . 3 Channelled spectra f o r even and odd orders observed f o r a MgF2 f i l m . Figure 3 shows t h e channel l e d spectra observed a t O A = -10.04"
-
Y21 ( s o l i d 1 ine) and a t OA = -0.60' Y21+1 (broken 1 in e ) . The observed exact values of ( Y ~ ~ , AZZ) and ( Y ~ ~ + ~ , A21+1) are given i n Table 1. The probable e r r o r s can be reduced s u b s t a n t i a l l y by l o w e r i n g t h e s t r a y l i g h t l e v e l i n t h e spectrometer.200 400 60
o
800 h ( n r n )Table 1
-
Exact e x t i n c t i o n p o s i t i o n sobserved f o r t h e spectrum shown i n Fig.4
-
Simulated channelled spectraFig. 3. corresponding t o t h e experimental ones
i n Fig. 3.
I n Fig. 4 a r e shown the t h e o r e t i c a l curves f o r B A = YZ1 = -10.04' and BA = Yel+,
= -1.15" which correspond t o F i g . 3. The c a l c u l a t e d Am's ( f o r m = 21 as w e l l as f o r m = 21
+
1) agree s a t i s f a c t o r i l y w i t h the experiment except a t h 5 300 nm.The values o f n(X21+1) can be evaluated by s u b s t i t u t i n g t h e observed Y2L+,1s i n t o eq.(lO). They a r e g i v e n i n Fig. 5, t o g e t h e r w i t h those evaluated f o r another f i l m f o r which measurements were made a t two incidence angles. S u b s t i t u t i n g t h e n(A21+1) values i n t o e q . ( l l ) , one may o b t a i n the f i l m thickness d ( F i g . 6 ) . The order o f i n t e r f e r e n c e m , which i s r e q u i r e d i n t h i s c a l c u l a t i o n , can be found as m = Am+l/
(A,
-
A w l ) . The gradual change i n d a tX
> 300 nm i s due t o t h e f i l m inhomogeneity.The sudden drop a t
X
s 300 nm i s caused by t h e a b s o r p t i o n by t h e BK7 substrate.ClO-38 JOURNAL
DE
PHYSIQUEI I I
LOO 500 600
A ( n m ) Fig.5 Evaluated values o f n(A 1 ' s f o r two t y p i c a l samples. Films a r v assumed t o be homogeneous.
-
-a__ --
---065.2.+
d(nrn)0 65.23' x 50.17. 597
experimental
50.25' 653
4
obsorptlon In BK7- - - -
colculoled0 65.2'
5 9 6
-
594 dunt = 590 nrn
400 5 0 0 6 0 0
X tnm) Fig. 6 - E v a l u a t e d d ' s f o r data shown i n Fig. 5. Films a r e assumed t o be homo- geneous. Thickness measured by m u l t i p l e beam i n t e r f e r o m e t r y dMBI a r e a l s o shown.
1
o~ filmL
I I I 1300 400 500 600 Fig. 8 - n dependence o f Y2z+1
A(nml Fig. 7
-
1Y2t's observed showing p a r a l l e l s h i f t s from t h e homogeneous curve.The values o f n(h2z) given i n Fig. 5 have been obtained from eq. ( 4 ) , employing t y p i c a l values o f d f o r the r e s p e c t i v e f i l m s ( F i g . 6 ) .
As s t a t e d before, Y2z should be determined s o l e l y by nS (eq. ( 9 ) ) p r o v i d e d t h e f i l m i s homogeneous. I n Fig. 7, the broken curves g i v e t h e values o f Y ~ Z c a l c u l a t e d by eq. (9) u s i n g t h e t a b l e values of nS(h) f o r BK7, w h i l e t h e s o l i d ones g i v e t h e ob- served Y2;. The d i s t a n c e between the s o l i d and broken curves gives a measure f o r the f i l m ~nhomogeneity.
F i g u r e 8 gives an idea o f the c a p a b i l i t y o f t h e channelled spectrum e l l i p s o m e t r y as a means o f d e t e n i n i n g t h e f i l m index. The curves represent eq.(10). A change as small as 0.01 i n n w i l l r e s u l t i n a change as l a r g e as l o i n Y22+1 i n c a s e MgFZ f i l m s on BK7 are examined a t @ 50
-
70°.54 Discussion
The p r e c i s i o n and accuracy of t h e channelled spectrum e l l i p s o m e t r y compares w i t h the usual e x t i n c t i o n e l l i p s o m e t r y . I t w i l l f i n d many a p p l i c a t i o n s , i n c l u d i n g t h e study o f f i l m inhomogeneity u t i l i z i n g measurements a t many incidence angles.
Reference
1. M.Born and E.Wolf, P r i n c i p l e s o f Optics (Pergamon, Oxford, 1959) p.265
2. L.Chaumont, Ann. Phzjs. 4 (1915) 61; H.G. Jerrard, J. Opt. Soc. Am. 42 (1952) 159 3. Y .Doi, Oyo Buturi 25 (1956) 133; Y. Doi, Rep. Meeh. Eng. Lab. Jpn. 27 (1958) 26
