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THEORY OF SURFACE ELECTRON ENERGY LOSS FINE STRUCTURE (S.E.E.L.F.S.) SPECTROSCOPY : RELATIONSHIP TO EXAFS AND PERSPECTIVES
F. Mila, Claudine Noguera
To cite this version:
F. Mila, Claudine Noguera. THEORY OF SURFACE ELECTRON ENERGY LOSS FINE STRUC- TURE (S.E.E.L.F.S.) SPECTROSCOPY : RELATIONSHIP TO EXAFS AND PERSPECTIVES.
Journal de Physique Colloques, 1986, 47 (C8), pp.C8-539-C8-542. �10.1051/jphyscol:19868101�. �jpa-
00225996�
JOURNAL DE PHYSIQUE
Colloque C8, suppl6ment au n o 1 2 , Tome 47, dgcembre 1986
THEORY OF SURFACE ELECTRON ENERGY LOSS FINE STRUCTURE (S.E.E.L.F.S.) SPECTROSCOPY : RELATIONSHIP T O EXAFS AND PERSPECTIVES
F. M I L A and C. NOGUERA*
DPHG, SPAS, CEN S a c l a y , F-91191 Gif-Sur-Yvette Cedex, F r a n c e
" ~ a b o r a t o i r e d e P h y s i q u e d e s S o l i d e s , (LAOOZ), U n i v e r s i t 6 d e P a r i s - S u d , F-91405 Orsay Cedex, F r a n c e
RESUME : Nous donnons une e x p r e s s i o n a n a l y t i q u e du c o u r a n t mesure d a n s une e x p e r i e n c e de S.R,F,.L.F.S. A l ' a i d e d ' u n c a l c u l numerique d a n s un c a s r C a l i s t e , nous montrons q u e , b i e n que l e s v a r i a t i o n s du c o u r a n t a v e c l ' g n e r g i e s o i e n t p l u s complexes que c e que l ' o n pense a & n & r a l e - ment, une a n a l y s e numerique d e t y p e EXAFS permet d e d e t e r m i n e r l e s d i s t a n c e s a v e c beaucoup de p r e c i s i o n . Nous proposons une a n a l y s e du s i g n a l p l u s a p p r o f o n d i e , 2 l ' a i d e d ' u n e seconde t r a n s f o r m e e de Fourier, q u i t dans d e s c o n d i t i o n s e x p s r i m e n t a l e s que nous s p 6 c i f i o n s , permet d ' o b t e n i r , de p l u s , l e s v a l e u r s d e s a n g l e s d e s l i a i s o n s .
ABSTRACT : We d e r i v e an a n a l y t i c e x p r e s s i o n f o r t h e c u r r e n t measured i n a S.E.E.L.F.S. experiment. With t h e h e l p o f a computation p e r f o r - med i n a r e a l i s t i c c a s e , we show t h a t , a l t h o u g h t h e e n e r g y dependence o f t h e c u r r e n t i s more i n v o l v e d t h a n what i s g e n e r a l l y b e l i e v e d , a s i m p l e EXAFS-like F o u r i e r a n a l y s i s a l l o w s d i s t a n c e d e t e r m i n a t i o n w i t h a h i g h a c c u r a c y . W e propose a d e e p e r a n a l y s i s o f t h e s i g n a l , based on a second t y p e o f F o u r i e r t r a n s f o r m , which, under s p e c i f L e d experimen- t a l c o n d i t i o n s , a l l o w s i n a d d i t i o n t h e d e t e r m i n a t i o n o f bond a n a l e s .
INTRODUCTION
I n p a r a l l e l t o t h e development of photon-induced s u r f a c e EXAFS t e c h - n i q u e s , s e v e r a l s u r f a c e s e n s i k i v e e l e c t r o n - i n d u c e d s p e c t r o s c o p i e s were shown t o d i s p l a y o s c i l l a t i o n s above t h r e s h o l d s , b e a r i n ? i n f o r m a t i o n on d i s t a n c e s , such a s t h e a p p e a r a n c e p o t e n t i a l t e c h n i q u e s ( 1 ) and, more r e c e n t l y , t h e S.E.E.L.F.S. s p e c t r o s c o p y ( 2 ) . I n t h i s l a s t t e c h n i q u e , primary e l e c t r o n s o f low energy (800 t o 2000 eV) a r e s e n t on s u r f a c e s and t h e e n e r g y l o s s spectrum i s r e c o r d e d i n t h e r e f l e c t i o n mode : t h e s h o r t mean f r e e p a t h f o r i n e l a s t i c s c a t t e r i n g i s r e s p o n s i b l e f o r t h e enhancement of t h e s u r f a c e r e s p o n s e . The f i r s t e x p e r i m e n t s have under- l i n e d t h e r e l a t i o n s h i p between t h e observed o s c i l l a t i o n s and t h e
c r y s t a l l o g r a p h y of t h e sample, and t h e h i g h s i g n a l t o n o i s e r a t i o which a l l o w s a s t u d y of a d s o r b a t e p o s i t i o n s i n submonolayer q u a n t i t i e s . The g o a l o f t h i s paper i s t o d e r i v e an a n a l y t i c e x p r e s s i o n f o r t h e c u r r e n t and t o s t r e s s which k i n d o f a n a l y s i s s h o u l d b e performed.
EXPRESSION OF THE DETECTED CURRENT
L e t u s c o n s i d e r an i n c i d e n t e l e c t r o n of e n e r g y Eo which e x c i t e s a ' p h o t o e l e c t r o n ' o f e n e r g y E from a deep l e v e l o f b i n d i n g energy EB. I n t h e f i n a l s t a t e , i t s e n e r g y E ' obeys t h e e n e r g y c o n s e r v a t i o n law E ' = Eo
-
EB-
E and t h e c u r r e n t d e t e c t e d a t t h e e n e r g y Ef i n a s o l i d a n g l e dR around8
c o n t a i n s two t e r m s a c c o r d i n g t o whether E' = Ef( d e t e c t i o n of t h e i n c i d e n t e l e c t r o n a f t e r i t s i n e l a s t i c s c a t t e r i n g ) o r
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19868101
C8-540 JOURNAL DE PHYSIQUE
E=Ef ( d e t e c t i o n of t h e p h o t o e l e c t r o n )
.
3 e n o t i n g @ C(1)
t h e deep h o l e wave f u n c t i o n , $ i ( i ? ) t h e i n c i d e n t e l e c t r o n wave f u n c t l o n , @,(?) t h e LEED wave f u n c t i q n o f t h e d e t e c t e d e l e c t r o n ( i n g o i n u boundarv c o n d i t i o n s ) and $ n ( E n ,r)
t h e wave f u n c t l o n of t h e o t h e r e l e c t r o n a t e n e r g y En, t h e s e two t e r m s a r e r e s p e c t i v e l y p r o p o r t i o n a l t o :-
-E( a ) B ( b ) -E3
F i g u r e 1 : Energy level diagram. (a) for the Ol term, (b) for the fi2 term.
+ -+
V ( r l
-
1 2 ) i s t h e Coulomb i n t e r a c t i o n r e s p o n s i b l e f o r t h e deep h o l e excitation. I n each of t h e s e e x p r e s s i o n s , two q u a n t i t i e s v a r y w i t h E f , namely t h e LEED f u n c t i o n @,(i!) and t h e imaginary p a r t o f t h e G r e e n ' s f u n c t i o n o f t h e e l e c t r o n i n t h e f i n a l s t a t eI m G
(q;'
) =1
$n (~ ~
$:(E~,?')~ $ 1
6 (En+Ef+Eh3-Eo ),
c u r r e n t l y e n c o u n t e r e d i n t h e EXAFS t h e o r y . Aside from t h i s G r e e n ' s f u n c t i o n , n i t i s w e l l known t h a t @,(;), a l s o b e a r s s t r u c t u r a l i n f o r m a t i o n s , s i n c e + i $ i s met i n j LEED and PhD ( p h o t o e l e c t r o n d i f f r a c t i o n ) t h e o r i e s . G ( r,r'
) and I$, ( r ) may be e x p r e s s e d a n a l y t i c a l l y w i t h i n a s i n q l e s c a t t e r i n a f o r m a l i s m , and c o n t a i n w e l l d e f i n e d o s c i l l a t i n q f a c t o r s p r o v i d e d t h a t t h e y a r e e v a l u a t e d w i t h i n t h e m u f f i n - t i n s p h e r e o f ' t h e e x c i t e d atom ( 3 , 4 ) . With t h e same n o t a t i o n s and a p p r o x i m a t i o n s a s i n r e f . ( 3 - 4 ) , t h e y r e a d( f i g . 2) :
2iI~R.-Fi6~+i$
~ai:,;.) =
I
( 1,
( 1 ) ra,.+r~l m(-i)'+l1y ( ~ R . ) Y " . (&.I:. ( d e 3L I L 1 1 )
LL' i
R ~ ( $ ) a r e a t o m i c wave f u n c t i o n s and t h e two e l e c t r o n s have n o t t h e same wave v e c t o r . I n e q u a t i o n s (1) and ( 2 ) t h e v e c t o m P l a r e o b v i o u s l y i n s i d e t h e p o t e n t i a l of t h e e x c i t e d a t o m d u e t o t h e l o c a l i z a t i o n o f t h e c o r e l e v e l wave f u n c t i o n b u t t h i s i s n o t t h e c a s e f o r
P2
i f ~ ( i ? ~ - i ? ~ ) i s l o n g r a n q e . I n such c i r c u m s t a n c e s t h e o s c i l l a t i o n s a r e washed o u t i n p e r f o r m i n g t h e i n - t e g r a t i o n upon p2. Two c a s e s , t h a t we have b o t h s t u d i e d , may t h u s be d i s -" i g u r e 2: Geometry f o r t h e t i n g u i s h e d a c c o r d i n g t o whether
p h o t o e l e c t r o n d i f f r a c t i o n v(F1-?2) i s l o n g range o r s h o r t r a n g e . ( t e r n )
We p r e s e n t h e r e t h e r e s u l t s r e l a t i v e t o t h e long r a n g e c a s e b u t t h e con- c l u s i o n s t h a t we draw a p p l y a s w e l l t o t h e s h o r t r a n g e one. The f l u x e s
a1
and Q 2 may be w r i t t e n :(k a j
-
~EB-
~E;, K a~mi, fi
i n ( t h e d i r e c t i o n R -+ ) :ALL',
i s t h e s q u a r e of a Coulomb m a t r i x e l e m e n t and t h e r e i s no s i m p l e s e l e c t i o n r u l e on t h e a n g u l a r momenta L and L ' . The q u e s t i o n o f knowing which L and L' g i v e t h e l a r g e r v a l u e s o f A L L , i s u n s e t t l e d : i t depends upon t h e momentum'transfer i n t h e e x c i t a t i o n p r o c e s s and upon t h e atomic wave f u n c t i o n s : f u r t h e r i n v e s t i g a t i o n s a r e needed t o o b t a i n more p r e c i s e answers b u t t h i s i s d e f i n i t e l y beyond t h e s c o p e of t h i s p a p e r . We w i l l o n l y u s e t h e r e s u l t ( 5 ) t h a t s m a l l a n g u l a r momenta a r e p r e f e r r e d , and f o r t h e s a k e o f n u m e r i c a l e v a l u a t i o n we have chosen L = L' = 0. The d e t e c t e d s i g n a l h a s t h u s t h e f o l l o w i n g p r o p e r t i e s : i ) it c o n t a i n s two t e r m s which b e a r s t r u c t u r a l i n f o r m a t i o n , namelv t h e EXAFS l i k e t e r m and t h e PhD l i k e one '2, which b o t h v a r y w i t h E f . ii) One o s c i l l a t e s w i t h k = J Eo-
EB- and
t h e o t h e r w i t h K =w.
iii) the EXAS term contains t h e c e n t r a l atom phase s h i f t s b u t n o t t h e PhD one. i v ) The PhD t e r m depends upon t h e a n g l e o f d e t e c t i o n and upon t h e bond a n g l e s ; and even a 4a a n g u l a r i n t e g r a t i o n o f t h e c u r r e n t c a n n o t d e s t r o v i t s o s c i l l a t i o n s . s i n c e . t o l o w e s t o r d e r i n s c a t t e r i n u ( 4 ) :
PRECISION I N THE DETERMINATION OF BOND LENGTHS :
U n t i l now t h e Q 2 c o n t r i b u t i o n t o t h e c u r r e n t h a s always been f o r q o t t e n and t h e a n a l y s i s o f t h e s i g n a l were performed w i t h t h e h e l p o f t h e EXAFS formula. I n o r d e r t o l e g i t i m a t e t h i s p r o c e d u r e we have made a n u m e r i c a l s i m u l a t i o n of t h e o s c i l l a t i n g p a r t
X
o f t h e s i g n a l @1+e2 i n t k g r a t e d upon a n q l e s w i t h L = L' = 0i n a r e a l i s t i c c a s e : t h e K edge o f 0 i n a C(2 x 2) monolayer on a N i c k e l (100) s u r f a c e ( 6 ) . Then we have performed a s t a n d a r d EXAFS ana- l y s i s of t h e s i g n a l ( 3 ) ( L e t t i n g a s u s u a l t h e r e f e r e n c e energy t o v a r y ) and we have t r i e d t o u n d e r s t a n d under which c i r c u m s t a n c e s t h e p r e s e n c e of @2 g i v e s r i s e t o s y s t e m a t i c e r r o r s i n t h e d e t e r m i n a t i o n o f d i s t a n c e s . The answer depends upon two f a c t o r s : i ) t h e r a n g e Ak = km,,
-
k m i n i n which t h e o s c i l l a t i o n s a r e r e c o r d e d ; Ak i s n o t a t u n a b l e p a r a m e t e r s i n c e it i s a f u n c t i o n of t h e d e g r e e of d i s o r d e r o f t h e sample, and of t h e n a t u r e of t h e b a c k s c a t t e r i n g atoms ; and ii) t h e minimum v a l u e of K , Kmin-
- J Eo-
EB-
kiabx which d e t e r m i n e s t h e i m p o r t a n c e o f t h e PhD. . . . . . .
o s c i l l a t i o n s t h r o u g h t h e f a c t o r f ( a ) / K ; given. kma,, K m i n may be chosen
JOURNAL DE PHYSIQUE
by changing t h e primary e l e c t r o n e n e r g y Eo. We f i n d t h a t , when Kmin i s l a r g e (Kmin > 1 0 A - ~ )
,
i . e . when E, i s l a r g e and p r o v i d e d t h a t t h e r e a r e a t l e a s t t h r e e EXAFS o s c i l l a t i o n s (Ak > 4 i n t h e p r e s e n t c a s e ) 'the p e r t u r b i n g e f f e c t ofa 2
i s s m a l l and t h e f i r s t n e i g h b o u r d i s t a n c e may be d e t e r m i n e d w i t h an a c c u r a c y b e t t e r t h a n .02f ~ .
I t i s n o t i c e a b l et h a t , i n most o f t h e s t u d i e s p u b l i s h e t i u n t i l now, t h e s e two c o n d i t i o n s were f u l f i l l e d . I f K m i n g e t s s m a l l e r t h e e r r o r i s s t i l l s m a l l i f t h e p e r t u r b e $ y a r t of t h e k spectrum i s
mall,
i. e . i f Ak i s l a r g e enough(Ak > 6 A- ) . But i f b o t h Kmin < 10 A-I and Ak < 6 &-1 t h e i m p r e c i s i o n s on R i n c r e a s e , a l t h o u g h t h e y g e n e r a l l y d o n o t exceed - 0 5 o r - 0 6
A.
I n c o n c l u s i o n of t h i s p a r t , we have checked t h a t , i n most o f t h e experimen- t a l s i t u a t i o n s , a s i m p l e EXAFS a n a l y s i s of t h e SEELFS s i g n a l may r e a s o - n a b l y a p p l y , a l t h o u g h t h e d e t e c t e d c u r r e n t h a s a non EXAFS e x p r e s s i o n .POSSIBILITY OF BOND ANGLE DETERMINATION :
I n t h e p r e c e d i n g s e c t i o n t h e g u i d i n g i d e a was t h a t Q1 was t h e u s e f u l s i g n a l and t h e unwanted one. We have f u r t h e r looked under which c o n d i t i o n s one i s a b l e t o e x t r a c t i n f o r m a t i o n from 02. For t h i s purpose we have performed a F o u r i e r t r a n s f o r m w i t h r e s p e c t t o K of t h e a n g l e i n t e g r a t e d c u r r e n t on t h e same system o f oxygen on N i c k e l and we have d e t e r m i n e d t h e p r e c i s i o n A9 o b t a i n e d on t h e f i r s t neighbour d i s t a n c e a s a f u n c t i o n of e x p e r i m e n t a l c o n d i t i o n s . A s p r e v i o u s l y AR depends upon kma, and Eo, b u t t h e r e q u i r e m e n t i s now t h a t t h e e x t e n t A K , on which i s done t h e a n a l y s i s , h a s t o be l a r g e enough. T h i s may be a c h i e v e d by de- c r e a s i n g t h e i n c i d e n t e n e r g y Eo ; n e v e r t h e l e s s t h e minimum v a l u e of K c a n n o t b e chosen s m a l l e r t h a n 5 &-1 (Ef&fOO eV) s o t h a t i n t h e e n e r - gy l o s s spectrum t h e o s c i l l a t i o n s do n o t mix w i t h t h e Auger o r seconda- r y e l e c t r o n peaks. I n t h e c a s e o f t h e K e x c i t a t i o n o f Oxyqen (EB=525eV) and t a k i n g i n t o a c c o u n t t h e above r e q u i r e m e n t s , a t q i v e n kmax v a l u e s , t h e s m a l l e s t i n c i d e n t e n e r g y Eo min t h a t may b e chosen i s r o u q h l y q i v e n by Eo min = EB
+
kka,+
100 eV. For t h i s v a l u e of E,
t h e K - F ~ u r i e r a n a l y s i s g i v e s t h e b e s t p r e c i s i o n on d i s t a n c e s A R ' L . ~ ~ t o .03 A. I f Eo becomes much l a r g e r t h a n Eo mint AR i n c r e a s e s , u n t i l e v e n t u a l l y t h e f i r s t neighbour peak i n t h e F o u r i e r t r a n s f o r m d i s a p p e a r s .T h i s s t u d y on t h e a n g l e i n t e g r a t e d s f g n a l was performed i n o r d e r t o check t h e p o t e n t i a l i t y of t h e method ; a s such
,
it i s o f no p r a c t i c a l u s e s i n c e t h e s t a n d a r d k - F o u r i e r method a l r e a d y g i v e s R w i t h a s a t i s f a c - t o r y a c c u r a c y . But i f an a n g l e r e s o l v e d SEELFS e x p e r i m e n t c o u l d be p e r - formed, f o r example a t normal d e t e c t i o n , it i s c l e a r from e q u a t i o n s 5 , 6 t h a t t h e k - F o u r i e r t r a n s f o r m would g i v e t h e v a l u e s of t h e d i s t a n c e s , w h i l e t h e K-Fourier t r a n s f o r m would a l l o w t h e d e t e r m i n a t i o n o f R(1-case).Within t h e e x p e r i m e n t a l c o n d i t i o n s s p e c i f i e d above, we have e v a l u a t e d t h a t t h e a c c u r a c i e s would be o f t h e o r d e r o f -02
3
f o r R and 3 t o 4 O f o r 0 . To o u r knowledge, i t i s t h e f i r s t t i m e t h a t one s t r e s s e s t h e pos- s i b i l i t y o f bond l e n g t h s & bond a n g l e s d e t e r m i n a t i o n t h r o u g h a s i m p l e and s t r a i g h t f o r w a r d a n a l y s i s o f a s i n g l e s i g n a l . Both t h e o r e t i c a l and e x p e r i m e n t a l works a r e i n p r o g r e s s t o prove more q u a n t i t a t i v e l y t h e f e a s i b i l i t y of t h i s method.REFERENCES
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( 4 9 7 9 ) , 432) M. D e C r e s c e n z i , L. Papagno, G. C h i a r e l l o , R. Scarmozzino, E . C o l a v i t a , R . Rosei : S o l . S t . Comm.
2
($984) 6133 ) P. A . Lee, P. H. C i t r i n , P. E i s e n b e r g e r , B. M. Kinkaid : Rev. Mod.
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(1981) 7694) P. A. Lee : Phys. Rev. B 13 (1976) 5261
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R o e l o f s , G. E . Laramore : Phys. Rev. L e t t . 44 (4980) 496
6 ) M. De C r e s c e n z i , F. A n t o n a n g e l i , C. ~ e l l i n i , ~ . Rosei : Phys. Rev.
L e t t .
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(1983) 4949Acknowledgements : We a r e i n d e b t e d t o J. S z e f t e l f o r f r u i t f u l comments.
