POLYPHASE SUBSTRATE ELLIPSOMETRY - A KINETIC INVESTIGATION

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POLYPHASE SUBSTRATE ELLIPSOMETRY - A KINETIC INVESTIGATION

E. Roberts-Sengier, M. Hamilton, R. Hunt

To cite this version:

E. Roberts-Sengier, M. Hamilton, R. Hunt. POLYPHASE SUBSTRATE ELLIPSOMETRY - A KI- NETIC INVESTIGATION. Journal de Physique Colloques, 1983, 44 (C10), pp.C10-199-C10-203.

�10.1051/jphyscol:19831041�. �jpa-00223498�

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POLYPHASE SUBSTRATE ELLIPSOMETRY - A KINETIC INVESTIGATION

E.F.I. Roberts-Sengier, M.A. Hamilton and R. Hunt

Department of Metallurgy and Materials Engineering, City of London Polytechnic, Whiteehapel High Street, London El 7PF, U.K.

Résumé - L'utilité de 1'ellipsométrie est augmentée si on peut travailler sur des substrats inhomogènes. On présente un modèle et on l'expérimente par une étude cinétique du système Ti/TiH .

Abstract - The usefulness of ellipsometry is enhanced if it is able to work on inhomogeneous substrates. A model is presented and tested by an investigation of the kinetics of the Ti/TiH system.

1. Introduction. Optical techniques have been central to the qualitative and quantitative characterisation of solids. Interest in the solid state focused attention upon techniques capable of analysing the reflected beam spectroreflectometry and spectroellipsometry. The examination of mixed or inhomogeneous substrates has been accepted as a concommitant aspect of using spectroreflectometry but has received little attention in ellipsometry.

Despite their apparent simplicity optical studies of solids have been beset by experimental and analytical problems. Non-ideality has been critical, nevertheless there has been reasonably good agreement among the optical constants for solids if some concessions are made to purity, modes of preparation and methods of measurement. These results have, in the main, been conducted upon fairly pure polycrystal- line or single crystal elements or solid solutions. Occasionally mention is made of substrate quality, thus Hayfield (1) working on titanium said "For polycrystal- line materials...there is some possibility that provided both films and substrate are fine grained and randomly orientated, the effects of anisotropy are likely to be cancelled out". This would appear to be the pragmatic solution adopted by most el- lipsometrists working on the diagnosis of filmed systems. Inhomogeneity has mainly been considered as a function of substrate/film depth and has been dealt with since Drude (2), Vasicek (3), Abeles (4), Theeten and Aspnes (5).

In the course of applying spectroellipsometry to the optical characterization of jewellery alloys (6) that were, in some cases, composed of two discrete phases two phenomena were observed a) the nulling ellipsometer always found a stable null, b) the colour characteristics of the two-phase alloys were displaced from their predicted loci in the CIE colour space. That sensible optical spectra were being produced was not in doubt and importantly»in the case of immiscible phases,the spectra demonstrated classical mixture behaviours (7) (ie. edges remained fixed but their height varied with volume fraction). Several models for mixed phase optical behaviour were tested (8).

Following Maxwell—Garnett and assuming the Clausius-Mossotti relation to hold in a completely metallic environment we attempted to analyse the phase mixture through the relation

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19831041

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CIO-200 JOURNAL

DE

PHYSIQUE

where q i s t h e volume f r a c t i o n of t h e second phase. This was assumed t o h o l d when was complex, and was s o l v e d f o r E e f f . The M-G assumptions i n t h i s

E m a t r i x

i n s t a n c e , i e . small m e t a l l i c p a r t i c l e s i n a d i e l e c t r i c environment, were u n l i k e l y , however, t o hold.

The second model assumed t h a t i n t e r f e r e n c e took p l a c e between coherent beams from a d j a c e n t phases ( a and B)

-

a weighted average of t h e amplitude r e f l e c t i o n coef- f i c i e n t s (Pp and Ps) i s then measured when l i g h t i s focused a t t h e d e t e c t o r t o a small s p o t .

T h i r d l y t h e e f f e c t i v e d i e l e c t r i c c o n s t a n t i e f f was formed by a l i n e a r a d d i t i o n of weighted d i e l e c t r i c c o n s t a n t s of t h e two phases (Ea a 1 E B r e s p e c t i v e l y ) .

When d i f f e r e n c e s between $a and

2'

a r e small t h i s does n o t g i v e v a s t l y d i f f e r e n t r e s u l t s from t h e M-G o r i n t e r f e r e n c e models. However none of t h e s e models gave r e f l e c t a n c e curves w i t h i n 5% of t h e e x p e r i m e n t a l l y d e r i v e d r e f l e c t a n c e s f o r t h e c o p p e r - s i l v e r a l l o y system.

F i n a l l y a m a t r i x f o r m u l a t i o n (9) was devised and s u c c e s s f u l l y a p p l i e d t o t h i s system and i t i s w i t h t h e a p p l i c a t i o n of t h i s model t o a k i n e t i c experiment, i n which t h e second phase appears d u r i n g t h e course of t h e experiment, t h a t t h i s paper d e a l s .

2. The polyphase e l l i p s o m e t r i c model. The d e r i v a t i o n of t h i s model h a s been pub- l i s h e d and s o only t h e o u t l i n e and necessary r e s u l t s w i l l be p r e s e n t e d h e r e . A duplex phase mixture of phases ru and 6 a r e r e p r e s e n t e d by volume f r a c t i o n s Q, and QB, (Q, + QB = 1 ) . The s u r f a c e i s f l a t and s p e c u l a r l y r e f l e c t i n g and t h e a r e a f r a c t i o n s a r e considered t o e q u a l t h e volume f r a c t i o n s . When l i g h t of known e l l i p t i c i t y i s i n c i d e n t upon t h e phase mixture two wavefronts of d i f f e r i n g e l l i p t - i c i t y a r e r e f l e c t e d , t h e s e two wavefronts combine t o form a n average of t h e two p o l a r i z a t i o n s t a t e s . The i n c i d e n t l i g h t i s assumed t o be i n c o h e r e n t and t h e r e f - l e c t e d beam can be d e s c r i b e d by a Stokes v e c t o r (SR) e q u a l t o t h e weighted sum of t h e normalized Stokes v e c t o r s of t h e r e f l e c t i o n s from each phase ( i e . Sru and S ) ( I S )

B

It can be shown t h a t :

and t a d S = Q tan$ .sinA + QBtan+@.sinA

a a a B

Qatan$,.cosAa + QBtan@B.cosA

B

3 . The formation of t i t a n i u m hydride by c a t h o d i c e l e c t r o l y s i s . E l e c t r o l y t i c t i t a n i u m hvdride w i t h a c o m ~ o s i t i o n somewhat l e s s than t h e s t o i c h i o m e t r i c TiH? - may be formed on and w i t h i n a t i t a n i u m cathode i n aqueous s u l p h u r i c acid(O.O5M)(lO).

S u i t a b l y mounted a m e a l e d t i t a n i ~ & ~ l a ~ u e t t e s (2 x 1 cm) were m e t a l l o g r a p h i c a l l y p o l i s h e d , cleaned and measured by automatic null-method s p e c t r o e l l i p s o m e t r y i n a i r . The sample was t h e n c a t h o d i c a l l y charged a t c o n s t a n t temperature, pH and ambient

*Titanium(Goodfellow Metals Ltd Cambridge) average p u r i t y 99.6%. I m p u r i t i e s (ppm) : A1500;Co2;Cr500;Cu500;Cu200;Fe300;Mg2P;Mn500;Ni500;Si200;Sn200;Ta10;V5OO;C200;H30;

N80;0200.

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s t r u c t u r e of t h e h y d r i d e ( 1 2 ) . The h y d r i d e s u r f a c e was t h e n r e p o l i s h e d and t h e s p e c t r a l c h a r a c t e r i s t i c s of t h e ' b u l k ' h y d r i d e d e t e r m i n e d . These measurements were a l s o i n a i r b u t l o n g t e r m o b s e r v a t i o n of t h e h y d r i d e s u r f a c e confirmed t h a t i t d i d change w i t h t i m e s u g g e s t i n g t h a t t h e h y d r i d e i s u n r e a c t i v e ( o r h i g h l y r e a c t i v e and s t a b l e ) . Furthermore r e p e a t e d p r e p a r a t i o n s and measurements of t h e h y d r i d e showed a remarkable r e p r o d u c i b i l i t y , T h i s b e h a v i o u r was r e m i n i s c e n t of measurements o n c e r a m i c s , g l a s s e s and c e r t a i n m i n e r a l s , and encouraged us t o u s e t h e i n a i r hyd- r i d e v a l u e s . The r e p r o d u c i b i l i t y of t h e t i t a n i u m (A,$) p a i r s was p o o r b u t a c o r r e c t e d e v a l u a t i o n of t h e t i t a n i u m s u b s t r a t e (A ,$ o)Ti

,

was computed. T h i s computation assumed t h e v a l i d i t y of r e s u l t s o b t a i n e d f o r t i t a n i u m i n u l t r a h i g h yacuum (n = 1.975 k = 2 . 7 3 3 ) ( 1 3 ) and a t s e v e r a l wavelengths

.

The t h i c k n e s s o f a r u t i l e f i l m (n = 2.421 k = 0.013 a t 400 nm) conforming t o (A, $)

e x p e r i m e n t a l computed u s i n g n u m e r i c a l f i t t i n g . T h i s f i l m confirmed an air-formed t h i c k n e s s of 3.4 nm on t h e p o l i s h e d t i t a n i u m . Using t h i s t h i c k n e s s of t h e f i l m a c o r r e c t e d s p e c t r a l s e t of t h e o p t i c a l c o n s t a n t s o f t i t a n i u m was computed, t h u s complementing t h e s e t d e r i v e d f o r t h e h y d r i d e ( F i g u r e 1 ) . A wavelength (400 nm) f o r i n s i t u

1 0

300 Xnm

.

⁸⁰⁰ ³⁰⁰ _Xnm

_.

⁸⁰⁰

i ) i i )

F i g . 1

-

O p t i c a l c o n s t a n t s of A T i t a n i u m ( e x p e r i m e n t a l ) , B T i t a n i u m ( c a l c u l a t e d ) , C T i t a n i u m h y d r i d e ( e x p e r i m e n t a l ) , D T i t a n i u m d i o x i d e ( r u t i l e ) ; i ) n

-

v a l u e s , i i ) k

-

v a l u e s .

s t u d i e s of t h e h y d r i d e f o r m a t i o n was chosen t h a t o p t i m i s e d t h e u s a b l e d i f f e r e n c e s between t h e h y d r i d e and t h e t i t a n i u m ( % ( T i ) = 49% and % ( T i n 2 ) = 43% a t 400 nm).

It was, of c o u r s e , i m p e r a t i v e t o c o n s i d e r t h e p o s s i b i l i t y t h a t t h e h y d r i d e d i d grow as a f i l m a t l e a s t a t t h e s u r f a c e . E l e c t r o n t h i n f o i l e x p e r i m e n t s had shown t h a t t h e h y d r i d e forms d i s c o n t i n u o u s l y a l t h o u g h g r a i n - b o u n d a r i e s and f r e e s u r f a c e s were enhanced n u c l e a t i o n s i t e s ( F i g u r e 2 ) .

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CIO-202 JOURNAL DE PHYSIQUE

The f i l m models e s t a b l i s h e d ( A , $ ) l o c i i ( F i g u r e 3B) t h a t were c l e a r l y i n c o n s i s t e n t w i t h t h e e x p e r i m e n t a l r e s u l t s ( F i g u r e 3A).

2 3

4 5 5 0 A deg. 60 65 70

F i g . 3

-

A , $ l o c i o f v a r i o u s t i t a n i u m / t i t a n i u m h y d r i d e models and e x p e r i m e n t a l r e s u l t s . A E x p e r i m n t a l p o i n t s ( 0 ) ; B T i t a n i u m s u b s t r a t e + t i t a n i u m h y d r i d e f i l m

(numbers = nm); C Mixed t i t a n i u m / t i t a n i u m h y d r i d e s u b s t r a t e ; D T i t a n i u m + r u t i l e * o v e r l a y e r (no,= nm)

.

I n s i t u n

e n v i r o n ⁼1.333, A = 400 nm, = 75'.

A much b e t t e r f i t of t h e e x p e r i m e n t a l d a t a w i t h t h e o r e t i c a l c u r v e s a p p e a r e d when t h e polyphase s u b s t r a t e models were employed ( F i g u r e 3C). I n t h i s c a s e i t was a l s o p o s s i b l e t o examine t h e e f f e c t s o f a r u t i l e f i l m superimposed o n t h e mixed s u b s t r a t e ( F i g u r e 3D). T h i s i s i n t e r e s t i n g s i n c e a number of workers have prop- osed t h a t p r o t o n s t r a v e r s e any o x i d e f i l m and combine, a s hydrogen a t t h e i n n e r s u r f a c e ( 1 4 ) . The r e s u l t s p r e s e n t e d h e r e s u g g e s t t h a t t h e o r i g i n a l 3.4 n m f i l m of r u t i l e h a s t h i n n e d i f n o t c o m p l e t e l y d i s s o l v e d i n t h e e l e c t r o l y t e . Indeed l o n g t e r m immersion o f an a n o d i s e d t i t a n i u m sample w i t h o u t an impressed c u r r e n t r e v e a l e d t h a t t i t a n i u m i o n s d i d e n t e r s o l u t i o n and ( f r o m i n t e r f e r e n c e c o l o u r s ) t h e f i l m changed t h i c k n e s s .

We s u g g e s t t h e r e f o r e t h a t o x i d e s o l u t i o n does o c c u r and t h a t hydrogen e n t e r s t h e s u b s t r a t e e i t h e r d i r e c t l y o r a s p r o t o n s . There i t d i s s o l v e s i n t h e t i t a n i u m b u t where t h e s o l u b i l i t y i s exceeded i t forms n o n - s t o i c h i o m e t r i c h y d r i d e

T i H x , x = 1 . 4 8 ) .

Using t h e r e l a t i v e q u a n t i t i e s (volume f r a c t i o n s ) of h y d r i d e formed at i n c r e a s i n g t i m e s i t was t h e n p o s s i b l e t o s u g g e s t a growth curve f o r t h e h y d r i d e t h e growth conformed t o a l o g a r i t h m i c f u n c t i o n

6

= .34

+ .

1 2 l n r t h e c o r r e l a t i o n f o r t h i s e q u a t i o n b e i n g r2 = 0.981. S o l u b i l i t y measurements ( 1 1) have i n d i c a t e d t h a t s o l u - t i o n f o l l o w s a l i n e a r f u n c t i o n and t h a t h y d r i d e t h i c k e n i n g f o l l o w s a p a r a b o l i c f u n c t i o n ( i b i d ) . These measurements were n o t s e n s i t i v e t o t h e q u a n t i t y of h y d r i d e formed i n t h e f i r s t s t a g e s ( i e . b e f o r e s u r f a c e c o v e r a g e was complete) and i t i s c o n s i s t e n t w i t h a d i f f u s i o n c o n t r o l l e d r e a c t i o n t h r o u g h a n i n t e r v e n i n g b a r r i e r . There was, however, a n i n d i c a t i o n t h a t t h e mean composition of t h e h y d r i d e was lower i n t h e i n i t i a l p e r i o d and t h i s may v e r y w e l l have been due t o a n o v e r e s t i - mate of t h e q u a n t i t y of h y d r i d e formed o r t h e f a i l u r e t o t a k e i n t o a c c o u n t t h e h e t e r o g e n e o u s two-phase n a t u r e of t h e system.

4. Conclusion. There a r e f r e q u e n t o c c a s i o n s when e l l i p s o m e t r i c o b s e r v a t i o n s a r e made on p o l y p h a s e , inhomogeneous s u b s t r a t e s , l i k e w i s e t h e r e may b e r e a c t i o n s which modify a s u b s t r a t e ( s i c induce phase c h a n g e s ) . These m o d i f i c a t i o n s o r t h e inhomo- g e n e i t y may be u s e f u l l y s t u d i e d a s f u n c t i o n s of o t h e r i n d e p e n d e n t v a r i a b l e s . I n t h i s p a r t i c u l a r c a s e a model f o r polyphase s u b s t r a t e , e l l i p s o m e t r i c c h a r a c t e r i s t - i c s h a v e b e e n employed i n a dynamic s t u d y o f i n s i t u h y d r o g e n a t i o n of t i t a n i u m and c o n f i r m t h a t t i t a n i u m h y d r i d e d e v e l o p s n o t a s a f i l m b u t a s a p r e c i p i t a t e which grows w i t h t i m e t o g i v e complete s u r f a c e conversion.The h y d r i d e a p p e a r s t o grow e i t h e r a f t e r complete o r p a r t i a l d i s s o l u t i o n o f t h e air-formed f i l m

in

d i l u t e

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a fine specular surface.

The optical model has thus provided evidence of its application in a) using known spectra to quantify the proportion of phases present and b) that it can be inver- ted to provide an unknown spectra if the proportions of several alloys (with identical phases) are previously known.

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2,

^{532, 865.}

3. Vasicek, A., "Optics of thin films". North Holland (1960).

4. ~belhs, F., "Ellipsometry in the measurement of surfaces and thin films".

NBS Misc.Publn.256 (1963) pp 41.

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1683-1689.

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177-183.

11. Philips, I I., Poole, P, Shreir, L L. Corrosion, 1972,

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^855-866.

12. Hamilton, M A. MSc Report (CNAA), City of London Polytechnic, 1980.

13. T Smith. J Opt.Soc.Am., 1972, 62, 774-780.

14. Matsuda, S., Sugimoto, K. J.Jap.Inst.Met.,l981, 45, 203-209.

15. Klein, M.V., "Optics", John Wiley (New York) 1970.