DEPTH DISTRIBUTION OF CHARACTERISTIC X-RAYS OF NICKEL AND COPPER EXCITED BY ELECTRON BOMBARDMENT

(1)

HAL Id: jpa-00227281

https://hal.archives-ouvertes.fr/jpa-00227281

Submitted on 1 Jan 1987

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.

DEPTH DISTRIBUTION OF CHARACTERISTIC X-RAYS OF NICKEL AND COPPER EXCITED BY

ELECTRON BOMBARDMENT

G. Wiech, W. Zahorowski

To cite this version:

G. Wiech, W. Zahorowski. DEPTH DISTRIBUTION OF CHARACTERISTIC X-RAYS OF NICKEL

AND COPPER EXCITED BY ELECTRON BOMBARDMENT. Journal de Physique Colloques,

1987, 48 (C9), pp.C9-935-C9-938. �10.1051/jphyscol:19879167�. �jpa-00227281�

(2)

Sektion Physik, Ludwig-Maximilians Universitat Miinchen, 0-8000 Miinchen 22, F.R.G.

A b s t r a c t

The peak i n t e n s i t y o f t h e N i L a and t h e Cu Ka l i n e s e x c i t e d by e l e c - t r o n bombardment was m e a s u r e d a s a function o f t h e t h i c k n e s s o f t h e t a r g e t and a t d i f f e r e n t i n c i d e n t e l e c t r o n e n e r g i e s . The r e s u l t s a r e compared w i t h c a l c u l a t i o n s b a s e d on a G a u s s i a n e x p r e s s i o n d e s c r i b i n g t h e d e p t h d i s t r i b u t i o n o f x - r a y p r o d u c t i o n .

The d e p t h d i s t r i b u t i o n o f x - r a y p r o d u c t i o n i s a n i m p o r t a n t f u n c t i o n i n 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 and i t i s a l s o n e c e s s a r y f o r t h e i n - t e r p r e t a t i o n o f x - r a y s p e c t r o s c o p i c r e s u l t s ( s e e , f o r i n s t a n c e / I / ) . I n t h i s p a p e r we r e p o r t o n r e s u l t s o f measurements o f t h e peak i n - t e n s i t y I o f t h e N i L a and Cu Ka l i n e s r e c o r d e d a s a f u n c t i o n o f t h e t h i c k n e s s x o f t h e c o p p e r and n i c k e l t a r g e t s . The t a r g e t s were p r e - p a r e d by e v a p o r a t i o n and t h e i r t h i c k n e s s was d e t e r m i n e d by t h e T o l a - n s k y method / 2 / . For n i c k e l t h e i n c i d e n t e l e c t r o n e n e r g i e s w e r e v a r - i e d from 4 t o 9 keV, and f o r c o p p e r from 1 1 . 4 t o 2 3 . 9 keV. The I ( x ) d a t a , n o r m a l i s e d t o I , . , t h e p e a k i n t e n s i t y e m i t t e d from t h e " t h i c k "

s a m p l e , a r e p r e s e n t e d I n F i g . 1 . A number o f q u a n t i t i e s c a n b e de- r i v e d from t h e I ( x ) / I m c u r v e s . These i n c l u d e t h i c k n e s s o f l a y e r s e f f e c t i v e i n x - r a y p r o d u c t i o n , a v e r a g e d d e p t h s o f x - r a y p r o d u c t i o n and e l e c t r o n r a n g e s / 3 / .

I n t h i s p a p e r we s h a l l p o i n t o u t a n o t h e r a p p r o a c h t o t h e I ( x ) / I , c u r v e s .

I n t h e a b s e n c e o f f l u o r e s c e n c e e f f e c t s , t h e r a t i o I ( x ) / I , c a n be w r i t t e n a s t h e r a t i o o f t h e i n t e n s i t y e m i t t e d from t h e s a m p l e o f t h e t h i c k n e s s x t o t h e i n t e n s i t y e m i t t e d from t h e " t h i c k " s a m p l e

("on leave from the Institute of Physics. Polish Academy of Sciences, PL-02 668 Warsaw, Poland

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19879167

(3)

JOURNAL DE PHYSIQUE

1 1 1 1 , 1 1 1 , 1 1 1 , , 1 , , , , 1 , , 1 ,

500 loo0 $500 RMO 1500 ⁱ ^, ^r

FlLM THICKNESS

( A ) --

I Î Î Î Î Î Î Î Î

1000 ZOO0 GOO0 6000 8000 10000 12000 UOOO

FlLM THICKNESS ( A ) --m

F i g . 1 . E x p e r i m e n t a l I ( x ) / I m c u r v e s f o r N i L a ( u p p e r p a r t ) and Cu Ka l i n e s ( l o w e r p a r t ) r e c o r d e d f o r d i f f e r e n t i n c i d e n t e l e c t r o n e n e r g i e s .

FlLM THICKNESS ( A ) ^--#-

F i g . 2 . C a l c u l a t e d I ( x ) / I c u r v e (

- -

- ) and e x p e r i m e n t a l v a l u e s o f t h e r a t y o I ( x ) / I m f o r t h e N i L a l i n e ( open c i r c l e s ) . The i n c i d e n t e l e c t r o n e n e r g y E o = 7 . 5 keV.

(4)

e l e c t r o n s c a t t e r i n g and e:ergy l o s s . The s u r f a c e x - r a y p r o d u c t i o n ( i o n i s a t i o n ) f u n c t i o n @ ( 0 ) was c a l c u l a t e d by Love e t a l . / 6 / u s i n g a Monte C a r l o method. The e q u a t i o n s f o r a , 6 a n d y o and f o r @ ( 0 ) a r e g i v e n i n / 5 / and / 6 / , r e s p e c t i v e l y .

The I ( x ) / I _ c u r v e s w e r e c a l c u l a t e d u s i n g t h e e q u a t i o n s ( 1 ) a n d ( 2 ) f o r t h e i n c i d e n t e l e c t r o n e n e r g i e s 7 . 5 a n d 23.9 keV f o r N i La and Cu Ka, respectively. The i n t e g r a l s I ( x ) a n d I w e r e c a l c u l a t e d n u m e r i c a l l y . The l e n g h t s o f t h e i n t e r v a l s w e r e cons'?ant f o r a l l I ( x ) i n t e g r a l s o f e a c h e l e m e n t . The l e n g h t s w e r e c h o s e n s m a l l enough ( 3 8 f o r N i a n d 1 5 2 f o r Cu) i n o r d e r t o m i n i m i z e i n t e g r a t i o n e r r o r s f o r I ( x ) w i t h x c l o s e t o z e r o . The I _ i n t e g r a l s w e r e e v a l u a t e d w i t h i n r a n g e s which r e p r e s e n t a t h i c k s a m p l e .

The r e s u l t s f o r N i La a n d Cu Ka a r e shown i n F i g . 2 a n d F i g . 3 , r e - s p e c t i v e l y . Only a q u a l i t a t i v e a g r e e m e n t w i t h t h e e x p e r i m e n t a l v a l u e s o f t h e r a t i o I ( x ) / I (open c i r c l e s i n F i g . 2 and F i g . 3) h a s b e e n a c h i e v e d . ~ u a n t i t a t y v e l ~ , t h e c a l c u l a t e d c u r v e s l i e w e l l below t h e ex- p e r i m e n t a l v a l u e s . T h i s i s e v i d e n t e s p e c i a l l y f o r l o w e r v a l u e s o f x.

I n t e r e s t i n g l y e n o u g h , t h e d i s a g r e e m e n t i s s i m i l a r f o r b o t h c u r v e s i n s p i t e o f d i f f e r e n c e s i n t h e i n c i d e n t e l e c t r o n e n e r g i e s and t h e c h a r a c - t e r i s t i c l i n e s u s e d (K and L l i n e s ) . T h i s d i s a g r e e m e n t c a n n o t b e c a u - s e d by t h e two a p p r o x i m a t i o n s which h a v e b e e n made i n e x p r e s s i o n ( 1 ) : ( i ) t h e n e g l e c t of f l u o r e s c e n c e e f f e c t s . The c h a r a c t e r i s t i c L-L f l u o - r e s c e n c e c o u l d r e d u c e t h e d i f f e r e n c e b e t w e e n t h e e x p e r i m e n t a l d a t a a n d t h e c a l c u l a t e d I ( x ) / I a c u r v e i n t h e N i La c a s e where a c o p p e r s u b s t r a - t e was u s e d . M o r e o v e r , t h i s e f f e c t i s e x p e c t e d t o b e s t r o n g e r f o r t h i n f i l m s o f n i c k e l

-

j u s t where t h e d i s c r e p a n c y o c c u r s . But i n t h e c a s e o f Cu Ka a s i m i l a r e x p l a n a t i o n i s n o t p o s s i b l e . An aluminum s u b - s t r a t e was u s e d i n t h i s c a s e a n d f l u o r e s c e n c e c o u l d b e e x c i t e d by t h e c o n t i n u o u s s p e c t r u m o n l y . The c o n t i n u u m f l u o r e s c e n c e , h o w e v e r , d o e s n o t e x c e e d 1 % i n most c a s e s / 7 / a n d t h e r e f o r e c a n b e n e g l e c t e d f o r b o t h N i La a n d Cu Ka. ( i i ) e x p r e s s i o n ( 2 ) was d e r i v e d f o r n o r m a l

i n c i d e n c e o f e l e c t r o n s w h e r e a s t h e i n c i d e n t a n g l e i n t h e e x p e r i m e n t a l s e t - u p f o r Cu Ka was 75'. T h i s , a g a i n , c a n n o t b e a c a u s e f o r t h e d i s - a g r e e m e n t s i n c e t h e e l e c t r o n t r a j e c t o r i e s , f o l l o w i n g t h e f i e l d l i n e s , t e n d t o w a r d s t h e n o r m a l i n t h e c l o s e v i c i n i t y o f t h e s p e c i m e n s u r f a c e . A p o s s i b l e e x p l a n a t i o n i s t h a t t h e d i s c r e p a n c y b e t w e e n c a l c u l a t e d c u r v e s a n d t h e e x p e r i m e n t a l d a t a i s c a u s e d by t h e f u n c t i o n @ ( p x ) i t - s e l f . A l t h o u g h t h e p a r a m e t e r s a , B and y o f t h e G a u s s i a n ( 2 ) w e r e d e r i v e d from t h e o r e t i c a l s c a t t e r i n g e q u a t i o n s / 4 / , t h e p a r a m e t e r s

(5)

JOURNAL DE PHYSIQUE

I , , , ,

1000 5000 10000 ^I ^" ^" ^I ^" ^' 15000 FILM THICKNESS

( A )

4

F i g . 3 . C a l c u l a t e d I ( x ) / I c u r v e ( - -

-

) and e x p e r i m e n t a l v a l u e s o f t h e r a t i o 1 ( x ) ? I m f o r t h e Cu Ka l i n e (open c i r c l e s ) . The i n c i d e n t e l e c t r o n e n e r g y Eo = 2 3 . 9 keV.

were t h e n a d j u s t e d t o f i t a l a r g e amount o f p u b l i s h e d a n a l y s e s o f s t a n d a r d s p e c i m e n s . A n a r r o w i n p o f e r r o r h i s t o g r a m s was u s e d a s t h e o n l y c r i t e r i o n f o r a d j u s t i n g t h e G a u s s i a n e x p r e s s i o n . The method, a l t h o u g h j u s t i f i e d i n 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 , seems t o b e i n - a d e q u a t e f o r r e a d j u s t m e n t s o f t h e G a u s s i a n p a r a m e t e r s . A more d i r e c t c o m p a r i s o n w i t h e x p e r i m e n t a l d a t a i s n e e d e d . I ( x ) / I m c u r v e s c o u l d be u s e d f o r s u c h a c o m p a r i s o n . M o r e o v e r , t h e I (x) / I m c u r v e s , i n t e r p r e t e d a s shown above o f f e r a n a l t e r n a t i v e method t o t h e " t r a c e r method" / 7 / f o r d e t e r m i n i n g @ (px)

.

Acknowledgments

We t h a n k M . Wimmer and H . M i c h e l f o r t h e i r a s s i s t a n c e i n a c q u i r i n g t h e s p e c t r o s c o p i c d a t a . W.Z. k i n d l y a c k n o w l e d g e s f i n a n c i a l s u p p o r t by t h e German F e d e r a l M i n i s t e r f o r R e s e a r c h and Technology BMFT.

R e f e r e n c e s

/ I / R . S . C r i s p , J.Phys.F:Met.Phys.l3,1325 (1983)

/ 2 / J . E . T o l a n s k y , M u l t i p l e Beam I F f e r f e r o m e t r y o f S u r f a c e s and F i l m s , O x f o r d , 1948

/ 3 / L. Hoffmann, G . Wiech a n d E . Zopf, Z . P h y s . 2 2 9 , 131 (1969) / 4 / J . D . Brown and R . H . Packwood, X-Ray S p e c t r K l l , 187 (1982) / 5 / R . H . P a c k w ~ o d and J . D . Brown, X-Ray Spectrom.TB, 138 (1981) / 6 / G . Love and V . D . S c o t t , J . P h y s . D : A p p l . P h y s . l 1 ~ 1 3 6 9 (1978)

G . Love, M . G . Cox and V . D . S c o t t , J . P h y s . D : % p l . P h y s . l l , 23 (1978) / 7 / S . J . B . Reed, 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 , London : Cambridge UP,

1975