X-RAY STUDIES RELATED TO COATING THICKNESS MEASUREMENTS

HAL Id: jpa-00223764

https://hal.archives-ouvertes.fr/jpa-00223764

Submitted on 1 Jan 1984

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

X-RAY STUDIES RELATED TO COATING THICKNESS MEASUREMENTS

D. Sewell, I. Hall, G. Love, J. Partridge, V. Scott

To cite this version:

D. Sewell, I. Hall, G. Love, J. Partridge, V. Scott. X-RAY STUDIES RELATED TO COATING THICKNESS MEASUREMENTS. Journal de Physique Colloques, 1984, 45 (C2), pp.C2-33-C2-36.

�10.1051/jphyscol:1984208�. �jpa-00223764�

JOURNAL

D E PHYSIQUE

Colloque C2, supplCment

au

n02, Tome 45, fCvrier

1984

page

C2-33

X-RAY S T U D I E S RELATED TO COATING T H I C K N E S S MEASUREMENTS

D.A. Sewell, I.D. H a l l , G. Love, J . P . P a r t r i d g e and V.D. S c o t t SchooZ of Materiazs Science, University of Bath, U . K .

Resume

-

Des mesures d ' i n t e n s i t g d e s rayons X s o n t f a i t e s s u r une s e r i e de s u b s t r a t s avec d e s couches soigneusement c a l i b r e e s . On propose une formule pour l a d e t e r m i n a t i o n de l ' g p a i s s e u r des couches ; e l l e p e u t e t r e a u s s i u t i l i s g e pour donner l a profondeur maximale de g e n e r a t i o n d e s rayons X . A b s t r a c t

-

X-ray measurements a r e c a r r i e d o u t on a s e r i e s of s u b s t r a t e s with c a r e f u l l y p r e s c r i b e d c o a t i n g s . An equation i s developed f o r determining c o a t i n g t h i c k n e s s and c a n a l s o b e used t o g i v e v a l u e s f o r t h e x-ray range.

1. INTRODUCTION

It i s o f t e n n e c e s s a r y t o know the depth i n t h e sample f r o m which x-rays a r e b e i n g g e n e r a t e d , e s p e c i a l l y when c a r r y i n g o u t e l e c t r o n - p r o b e m i c r o a n a l y s i s on specimens having an a b r u p t change of chemical composition w i t h i n a micrometre o r s o of t h e s u r f a c e , e.g. p r e c i p i t a t e s , s u r f a c e r e a c t i o n p r o d u c t s and c o a t i n g s on s u b s t r a t e s . Moreover, i f t h e depth of x-ray g e n e r a t i o n , i . e . t h e x-ray r a n g e , ca_n b e formulated i n terms of such parameters a s mean atomic number o f t h e specimen ( Z ) , i n c i d e n t e l e c t r o n energy ( E ) and c r i t i c a l e x c i t a t i o n energy of t h e measured x-ray l i n e

(E ) , it t h e n becoges f e a s i b l e t o o b t a i n q u a n t i t a t i v e d a t a on c o a t i n g s . I n p r ? n c i p l e t h i s means t h a t i f t h e t h i c k n e s s i s known, t h e chemical composition can b e determined o r , a l t e r n a t i v e l y , i f t h e composition i s known, t h e t h i c k n e s s may b e e s t a b l i s h e d . Although, however, v a r i o u s formulae f o r t h e x-ray range have been proposed which embody t h e above p a r a m e t e r s , many g i v e widely d i v e r s e r e s u l t s which, i n extreme c a s e s , may d i f f e r by a f a c t o r of two ( 1 ) .

2 . PRINCIPLE OF THE PROPOSED METHOD

Our method i n v o l v e s t h e development of a n equation which may b e a p p l i e d t o any c o a t i n g / s u b s t r a t e combination. The procedure may b e summarised a s f o l l o w s .

( i ) X-ray i n t e n s i t y measurements a r e made on t h e c o a t e d s u b s t r a t e and a s t a n d a r d of t h e same composition a s t h e c o a t i n g . The beam energy i s t h e n determined a t which t h e g e n e r a t e d x-rays a r e j u s t c o n f i n e d t o t h e c o a t i n g m a t e r i a l . I n t h i s s i t u a t i o n t h e c o a t i n g t h i c k n e s s ( p t ) w i l l equal t h e x-ray range (pz ) a p p r o p r i a t e f o r t h e s e experimental c o n d i t i o n s . Such an approach has been used s r e v i o u s l y by Reuter e t a 1 ( 1 ) i n s t u d i e s of t h e x-ray range.

(ii) We choose t h e n t o e x p r e s s p t i n terms of t h e mean depth of x-ray g e n e r a t i o n

(z)

r a t h e r t h a n pz f o r two r e a s o n s . F i r s t l y , a s i n d i c a t e d by t h e t a i l s of Bishop's ( 2 ) norrnalfsed x-ray depth d i s t r i b u t i o n s , ( f i g u r e 1) it appears t h a t a simple p r o p o r t i o n a l r e l a t i o n s h i p may e x i s t between pzr and

z.

Secondly an expression f o r i s a l r e a d y a v a i l a b l e ( 3 ) which has been shown t o work w e l l f o r a very wide range of experimental c o n d i t i o n s .

The method h a s t h e advantage t h a t t h e r e s u l t s a r e n o t i n f l u e n c e d by t h e s u b s t r a t e . Thus,, atomic number c o r r e c t i o n s a r e n o t r e q u i r e d because any e l e c t r o n s b a c k s c a t t e r e d from t h e s u b s t r a t e w i l l have i n s u f f i c i e n t energy t o e x c i t e t h e x-ray l i n e from t h e c o a t i n g which i s being measured. Furthermore, s i n c e no e n e r g e t i c x-rays a r e

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984208

C2-34 JOURNAL

DE

PHYSIQUE

g e n e r a t e d i n t h e s u b s t r a t e a c h a r a c t e r i s t i c f l u o r e s c e n c e c o r r e c t i o n i s unnecessary, w h i l s t a continuum f l u o r e s c e n c e c o r r e c t i o n i s l i k e l y t o b e very small because continuum c o n t r i b u t i o n s w i l l be almost i d e n t i c a l i n specimen and s t a n d a r d . This l e a v e s u s with p o s s i b l e e r r o r s due t o x-ray a b s o r p t i o n . These may a r i s e i n h e a v i l y absorbing systems because t h e depth i n t h e t a r g e t from which x-rays a r e emitted w i l l t h e n b e somewhat l e s s t h a n t h e x-ray range ( t h e depth i n which x-rays a r e

g e n e r a t e d ) .

For p r e s e n t purposes, however, a b s o r p t i o n w i l l b e ignored and r e f e r r e d t o a g a i n a t t h e end of t h e paper.

3. EXPERIMENTAL

c o a t i n g / s u b s t r a t e combinations used i n t h e i n v e s t i g a t i o n were aluminium/magnesium, copper/iron and g o l d / l e a d , a l l m a t e r i a l s b e i n g of high p u r i t y . Samples of each c o a t i n g / s u b s t r a t e combination were mounted t o g e t h e r i n b a k e l i t e and p o l i s h e d down t o a m i r r o r f i n i s h . A f t e r thorough d e g r e a s i n g , t h e p o l i s h e d mount was p o s i t i o n e d on t h e p l a t f o r m i n a vacuum e v a p o r a t i o n u n i t t o g e t h e r with two g l a s s c o v e r s l i p s , one of which was p a r t i a l l y masked. Care was taken t o e n s u r e t h a t a l l items were e q u i d i s t a n t from t h e metal evaporation s o u r c e , t h e p l a t f o r m being r o t a t e d d u r i n g e v a p o r a t i o n t o a c h i e v e u n i f o r m i t y of d e p o s i t . A s a guide t o t h e amount of m a t e r i a l being d e p o s i t e d a q u a r t z c r y s t a l monitor was included w i t h i n t h e vacuum chamber but t h e a c t u a l c o a t i n g t h i c k n e s s was determined from t h e amount d e p o s i t e d on t h e g l a s s c o v e r s l i p s . I n t e r f e r o m e t r i c measurements were c a r r i e d o u t on t h e p a r t i a l l y masked c o v e r s l i p t o g i v e t h e t h i c k n e s s d i r e c t l y , whiLe atomic a b s o r p t i o n spectroscopy was used t o determine t h e mass of m a t e r i a l d e p o s i t e d on t h e second cover s l i p . Mass t h i c k n e s s given by t h e s e two methods agreed t o w i t h i n a few p e r c e n t f o r a l l systems s t u d i e d .

X-ray i n t e n s i t y measurements were c a r r i e d o u t using a JEOL JXA-50A electron-probe microanalyser f i t t e d with wavelength-dispersive and energy-dispersive x-ray s p e c t r o m e t e r s . The energy-dispersive s p e c t r o m e t e r was used p r i m a r i l y f o r

measuring a c c u r a t e l y t h e probe v o l t a g e , i . e . r e c o r d i n g t h e short-wave l e n g t h c u t - o f f of t h e x-ray continuum.

X-ray i n t e n s i t y measurements were o b t a i n e d from c o a t e d specimen and r e s p e c t i v e s t a n d a r d and p l o t t e d a s a f u n c t i o n of beam energy. The beam energy (Ed) a t which t h e x-ray range c o i n c i d e s w i t h t h e c o a t i n g t h i c k n e s s was given by t h e v a l u e where t h e i n t e n s i t y r a t i o s t a r t e d t o d e p a r t from u n i t y .

4. RESULTS AND DISCUSSION

A t y p i c a l s e r i e s of x-ray i n t e n s i t y measurements from aluminium l a y e r s of d i f f e r e n t t h i c k n e s s d e p o s i t e d upon magnesium a r e shown i n f i g u r e 2 , p l o t s of I /I v e r s u s beam energy ( E o ) , where I and I a r e x-ray i n t e n s i t i e s from coatingcan8 s t a n d a r d r e s p e c t i v e l y . The p o i n t s C l i e onSa s e r i e s of s t r a i g h t l i n e s , t h e i n t e r s e c t i o n of each with t h e a x i s g i v i n g t h e beam energy (E ) a t which x-rays a r e j u s t c o n f i n e d w i t h i n t h e p a r t i c u l a r c o a t i n g t h i c k n e s s . ~ i g i l a r d a t a were o b t a i n e d f o r a l l t h r e e s u b s t r a t e c o a t i n g combinations.

Using t h e s e v a l u e s of Ed, t h e mean depth of x-ray g e n e r a t i o n

(F)

was c a l c u l a t e d from ( 3 )

-

pz = ps ^(0.49269

-

1.098711

+

0.7855711~) 1nU

m 0:70256

-

1.0986511

+

1 . 0 0 4 6 1 1 2 + l n ~ ( 1 )

where U i s given by E /E and E is t h e c r i t i c a l e x c i t a t i o n energy; ps i s t h e

d c m

e l e c t r o n range and i s expressedCby

Z i s atomic number and A t h e atomic weight of t h e c o a t i n g m a t e r i a l ; J i s t h e mean i o n i s a t i o n p o t e n t i a l and e q u a l s 0.01352.

These c a l c u l a t e d v a l u e s f o r were t h e n compared with t h e r e s p e c t i v e c o a t i n g t h i c k n e s s e s a s determined d i r e c t l y by o p t i c a l i n t e r f e r o m e t r y and/or atomic

a b s o r p t i o n spectroscopy. The s e t s o f d a t a f o r t h e aluminium c o a t i n g s a r e p l o t t e d i n f i g u r e 3 and t h e p o i n t s l i e on a s t r a i g h t l i n e with g r a d i e n t 2 . 8 4 i 0 . 0 6 , i . e . we may w r i t e

p t = k p = (2.84f 0 . 0 6 ) p .

Values of k were c a l c u l a t e d f o r a l l systems s t u d i e d and a l s o f o r t h e c o a t i n g s i n v e s t i g a t e d by Reuter e t a 1 ( I ) . The r e s u l t s i n d i c a t e t h a t k i s r e l a t i v e l y independent of atomic number b u t i s s t r o n g l y i n f l u e n c e d by u ( = E ~ / E ~ ) . This e f f e c t is i l l u s t r a t e d i n f i g u r e 4 ; above U 2. 5 , k remains approximately c o n s t a n t a t 2.7, b u t below U 2 . 3 i t r i s e s r a p i d l y .

Least-squares a n a l y s i s of t h e compiled d a t a g i v e s

from which we o b t a i n

Values of p t were c a l c u l a t e d and compared with t h o s e o b t a i n e d by o p t i c a l and atomic a b s o r p t i o n measurements. By i n c l u d i n g R e u t e r ' s systems with our own, some f i f t y d a t a p o i n t s were provided w i t h c o a t i n g t h i c k n e s s e s r a n g i n g from 50 t o 800nm.

I t was found t h a t our e q u a t i o n performed w e l l when U

>

2 . 5 , with a r o o t mean square (RMS) e r r o r of 6.7%;below U = 2.5, however, t h e e r r o r was s i g n i f i c a n t l y h i g h e r a t 15%.

Before concluding, it i s of i n t e r e s t t o compare o u r method f o r determining c o a t i n g t h i c k n e s s with t h e e q u a t i o n proposed by Reuter ( I ) , v i z

T h i s expression i s a l i t t l e simpler t h a n our own b u t g i v e s RMS e r r o r s of 22% and 36% r e s p e c t i v e l y , i n d i c a t i n g t h a t i t s performance i s s i g n i f i c a n t l y l e s s s a t i s - - f a c t o r y .

5. CONCLUSIONS

AII e q u a t i o n h a s been developed f o r c a l c u l a t i n g c o a t i n g t h i c k n e s s which g i v e s s a t i s f a c t o r y r e s u l t s when a p p l i e d t o systems c o v e r i n g a wide range of atomic number. To use t h e method a s t a n d a r d c o n s i s t i n g o f t h e c o a t i n g m a t e r i a l i s needed and then t h e beam energy is determined a t which t h e g e n e r a t e d x-rays a r e j u s t c o n t a i n e d w i t h i n t h e c o a t i n g ; t h e s e measurements need only t a k e t e n minutes t o c a r r y o u t i n p r a c t i c e . Best accuracy i s achieved when t h e beam energy exceeds 2.5 t i m e s t h e c r i t i c a l e x c i t a t i o n energy of t h e measured x-ray l i n e a n d , i f t h i s c r i t e r i o n i s t o b e met, low energy x-ray l i n e s ( s a y 1 t o 3keV) must b e recorded.

P r e s e n t r e s u l t s s u g g e s t t h a t a b s o r p t i o n e f f e c t s a r e n o t s e r i o u s , e s p e c i a l l y f o r c o a t i n g s l e s s t h a n 500nm t h i c k . However, with multi-element c o a t i n g s t h e s e e f f e c t s may no l o n g e r b e n e g l i g i b l e and it c o u l d prove n e c e s s a r y t o extend equation 2 by i n t r o d u c i n g an a b s o r p t i o n term c o r r e c t i o n .

F i n a l l y , t h e equation may b e r e a d i l y used t o p r o v i d e v a l u e s f o r t h e x-ray range a p p r o p r i a t e t o any s e t of experimental c o n d i t i o n s .

Acknowledgements

Thanks a r e due t o AERE and SERC f o r supporting t h i s work.

REFERENCES

1. REUTER,W., KMTSIS,J.D., LURI0,A. and KYSER,D.F., J . P h y s . D : A p p l . ~ h y s . Z (1978) 2633.

2. BISHOP,H.E., J.Phys.D:Appl.Phys. 7 (1974) 2009.

3. LOVE, G . , COX, M.G.C. and SCOTT,

V.D.,

J.Phys.D:Appl.Phys. - 10 (1977) 7.

JOURNAL

DE

PHYSIQUE

Fig.2. X-ray i n t e n s i t y r a t i o s ( 1 ~ 1 1 s ) p l o t t e d a s a f u n c t i o n o f e l e c t r o n beam energy f o r s i x d i f f e r e n t c o a t i n g t h i c k n e s s e s .

F i g . 1 . Normalised x-ray d e p t h d i s t r i b u t i o n s a f t e r Bishop. H o r i z o n t a l a x i s s c a l e d i n terms o f t h e mean d e p t h and a l l c u r v e s n o r m a l i s e d t o t h e same t o t a l a r e a .

Fig.3. P l o t of c o a t i n g t h i c k n e s s ( p t ) v e r s u s mean d e p t h

(5)

f o r aluminium c o a t i n g s .

~ i g . 4 . Graph of k ( = @ I F ) v e r s u s U (=Ed/Ec) f o r a l l systems s t u d i e d .