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SURFACE CORE LEVEL SHIFT OF BERYLLIUM.
X-RAY RAMAN SPECTRUM OF A Be THIN FILM
A. Zdetsis
To cite this version:
A. Zdetsis. SURFACE CORE LEVEL SHIFT OF BERYLLIUM. X-RAY RAMAN SPEC- TRUM OF A Be THIN FILM. Journal de Physique Colloques, 1987, 48 (C9), pp.C9-839-C9-842.
�10.1051/jphyscol:19879149�. �jpa-00227260�
SURFACE CORE LEVEL SHIFT OF BERYLLIUM. X-RAY RAMAN SPECTRUM OF A Be THIN FILM
A.D. ZDETSIS
Department of Physics, University of Crete and Research Center of Crete, PO Box 1527, 711 10 Heraklio, Crete, Greece
A b s t r a c c
-
The bonding c h a r a c t e r i s t i c s and t h e i n n e r c o r e I s b i n d i n g energy o f an one-dimensional Be f i l m i s s t u d i e d i n comparison t o t h e b u l k Be m e t a l . The d i f f e r e n c e i n t h e I s b i n d i n g energy i s c a l c u l a t e d v e r y a c c u r a t e l y t o g e t h e r w i t h t h e v a r i a t i o n o f t h e bonding c h a r a c t e r i s t i c s r e s p o n s i b l e f o r t h e appearance o f anomalous peaks i n t h e x - r a y Raman spectrum o f Be m e t a l .The c a l c u l a t e d c o r e l e v e l s h i f t between t h e b u l k and t h e f i l m a f t e r t h e a d j u s t - laent o f t h e Fermi l e v e l p r o v i d e s t h e chemical s h i f t f o r t h e Is c o r e b i n d i n g e n e r g i e s between b u l k and s u r f a c e atoms i n Be m e t a l . The c a l c u l a t e d v a l u e f o r t h e c o r e s u r f a c e chemical s h i f t i s 0.55eV i n e x c e l l e n t agreement w i t h t h e e x p e r i m e n t a l v a l u e o f 0.5eV.
E a r l i e r c a l c u l a t i o n based on t h e small c l u s t e r u n r e s t r i c t e d Hartree-Fock (UHF) method have p r o v i d e d a v e r y good p i c t u r e pf t h e bonding c h a r a c t e r i s t i c s and i n n e r c o r e e l e c t r o n p r o p e r t i e s o f Be metal
[I ,21.
I n a d d i t i o n t o some s t a n d a r d bonding and b i n d i n g p r o p e r t i e s , t h e n a t u r e o f t h e anomalous peaks i n t h e x - r a y Raman spectrum [I] and t h e I s c o r e b i n d i n g energy121
were g i v e n an e x c e l l e n t d e s c r i p t i o n . Rased on t h e success o f t h e s e e a r l i e r UHF c a l c u l a t i o n s , t h e p r e s e n t work extends t h i s method t o t h e d e s c r i p t i o n o f t h e I s c o r e b i n d i n g energy and x - r a y Raman spectrum o f a Be t h i n f i l m f o r which s e v e r a l c o n t r o v e r s i e s s t i l l e x i s t131.
A t t h e same t i m e t h i s work i l l u s t r a t e s a v e r y s u c c e s s f u l scheme f o r c a l c u l a t i n g a c c u r a t e l y t h e chemical s h i f t observed i n e l e c t r o n i c b i n d i n g e n e r g i e s between b u l k and s u r f a c e atoms i n a m e t a l ; Be i n t h e p r e s e n t case [4].The c h o i c e o f Be f o r t h i s s t u d y i s based on i t s s i m p l i c i t y and p e c u l i a r i t y i n t h e p h y s i c a l p r o p e r t i e s . T h i s s i m p l i c i t y (Be atom i s l i g h t and has a c l o s e d s h e l l l s 2 2 s 2 c o n f i g u r a t i o n ) and p e c u l i a r i t y , due m a i n l y t o i t s l a r g e d e p a r t u r e f r o m f r e e c ? l e c t r o n b e h a v i o r , makes Be more amenable t o a UHF s m a l l c l u s t e r t y p e o f c a l c u l a t i o n . T h i s t y p e o f c a l c u l a t i o n f o r Be m e t a l has been proven v e r y s u c c e s s f u l n o t o n l y i n computing t h e bonding c h a r a c t e r i s t i c s and t h e i r s i g n a t u r e i n t h e x - r a y Raman spectrum
[I] ,
b u t a l s o i n v e r y a c c u r a t e l y c a l c u l a t i n o i n n e r c o r e ( I s ) e l e c t r o n b i n d i n n c?nt?rais and phonon p r o p e r t i e s as w e l lk,].
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19879149
C9-840 JOURNAL DE PHYSIQUE
Depending on t h e p r o p e r t y u n d e r study, a s m a l l a t o m i c c l u s t e r comprised o f a r e f e r e n c e atom and i t s n e a r and a t l e a s t n e x t n e a r n e i g h b o r s can be s a t i s f a c t o r y f o r s i m u l a t i n g t h e i n f i n i t e c r y s t a l . One t h e n s h o u l d be c a r e f u l enough t o c o r r e c t l y d i s t i n g u i s h t h e r e a l i s t i c c h a r a c t e r i s t i c s f r o m t h e s p u r i o u s e f f e c t s r e s u l t i n g f r o m t h e f i n i t e s u r f a c e o f t h e c l u s t e r . Q u e s t i o n s a b o u t t h e s u i t a b i l i t and l i m i t a t i o n s o f s m a l l c l u s t e r s c a l c u l a t i o n s have been d i s c u s s e d elsewhere [5,67. B u l k Be m e t a l and Be t h i n f i l m a r e d e s c r i b e d i n t h i s c a l c u l a t i o n by a 13-atom c l u s t e r comprised o f a r e f e r e n c e atom and i t s 12 n e a r e s t neighbors, i n hexagonal c l o s e d packed ( h c p ) geometry. Seven atom c l u s t e r s , i n c l u d i n g o n l y t h e a b s o l u t e l y n e a r e s t n e i g h b o r s were a l s o q u i t e s u c c e s s f u l i n d e s c r i b i n g most o f t h e e l e c t r o n i c p r o p e r t i e s ( e x c e p t t o t a l b i n d i n g e n e r g i e s ) o f b o t h b u l k and p l a n a r systems. D e t a i l s a b o u t t h e e x a c t c l u s t e r geometry and t h e b a s i s s e t a r e g i v e n i n Ref. 1 and i n a f o r t h c o m i n g p u b l i c a t i o n b y t h i s a u t h o r . The geometry o f t h e Be7 p l a n a r c l u s t e r can be seen i n f i g u r e 1 which a l s o d i s p l a y s i n a c o n s t a n t a m p l i t u d e c o n t o u r , t h e wave f u n c t i o n a t t h e Fermi l e v e l .
F i g u r e 1
Constant a m p l i t u d e c o n t o u r s f o r t h e s t a t e a t t h e Fermi l e v e l o f t h e Be7 t h i n f i l m c l u s t e r . S o l i d c u r v e s r e p r e s e n t p o s i t i v e ampl i t u d e s , d o t t e d c u r v e s r e p r e s e n t n e g a t i v e a m p l i t u d e s and dashed c u r v e s z e r o ampl i tudes. The p o s i t i o n s o f t h e Be n u c l e i can be e a s i l y seen as l a r g e dots.
T h i s wave f u n c t i o n was c a l c u l a t e d ab i n i t i o by t h e UHF method, which has been reco- n i z e d as t h e most a c c u r a t e s i m p l e Hartree-Fock t y p e o f method f o r metal c l u s t e r s 7 7 l T h e s t a n d a r d POLVATOM computer code was used i n e v a l u a t i n g t h e i n t e g r a l s and a m o d i f i e d v e r s i o n o f t h e program UHFABK o f A.B. Kunz was employed t o p e r f o r m t h e UHF c a l c u l a t i o n s . T h i s l a s t program i s c a p a b l e o f s e l e c t i v e 1 y d e p o p u l a t i n g o c c u p i e d o r b i t a l s , so t h a t s t a t e s p e c i f i c s e l f - c o n s i s t e n t - f i e l d d i f f e r e n c e s (ASCF) i n t o t a l e n e r g i e s can be c a l c u l a t e d t o o b t a i n s p e c i f i c o n e - e l e c t r o n b i n d i n g e n e r g i e s ( E ~ ) . These b i n d i n g e n e r g i e s a r e g i v e n as:
E b = Et ( N - I )
-
Et ( N ) ( 11
where E t ( W - I ) and E t (N) a r e t h e t o t a l e n e r g i e s o f t h e f i n a l and i n i t i a l s t a t e s o f t h e I1 e l e c t r o n system. N i n t h e Bel3 c l u s t e r s i s equal t o 52. T h i s c l u s t e r ASCF v a l u e accounts f o r s mmetry, exchange and complete r e l a x a t i o n o f t h e o r b i t a l s . I t has been argued [2,7f t h a t t o a good a p p r o x i m a t i o n c o n t r i b u t i o n s o f a t o m i c l i k e e l e c t r o n c o r r e l a t i o n and r e l a t i v i t y e f f e c t s , AEa, can be i n c o r p o r a t e d s e p a r a t e l y by s i m p l e s u p e r p o s i t i o n t o t h e c l u s t e r ASCF r e s u l t s . The f i n a l c o r r e l a t e d b i n d i n g energy cb, i s t h u s g i v e n by C
&; =
The r e s u l t s f o r Ce b u l k m e t a l a r e i n e x c e l l e n t agreement w i t h experiment, as can be seen i n t h e second raw o f t a b l e I . F o r t h e t h i n f i l m , s i n c e t h e a t o m i c c o r - r e l a t i o n i s t h e same, i t i s expected t h a t t h e a b s o l u t e v a l u e , and n o t o n l y t h e r e l a t i v e magnitude, o f t h e I s - b i n d i n g energy s h o u l d be v e r y a c c u r a t e as i t i s f o r t h e b u l k . Of course, t h i s i m p l i e s t h a t t h e p l a n a r c l u s t e r i s p r o p e r l y d e s c r i b i n g
T A B L E I
Comparison o f t h e c a l c u l a t e d p h y s i c a l q u a n t i t i e s f o r t h e one monolayer t h i n f i l m and b u l k Be systems. The f i s t v a l u e f o r t h e Fermi energy and work f u n c t i o n i s s i m p l y t h e Koopman's value. The second v a l u e i s o b t a i n e d by ASCF d i f f e r e n c e s .
As can be seen i n t h e t a b l e I, n o t o n l y t h e I s b i n d i n g energy, b u t a l s o t h e ASCF v a l u e s o f t h e work f u n c t i o n , ( 0 , and o f t h e Fermi energy, &
,
a r e i n good agreement w i t h experiment f o r t h e b u l k Be m e t a l . The c o r r e s p o n d i n g v g l u e s f o r t h e t h i n f i l m a r e expected t o be o f t h e same accuracy, s i n c e t h e same b a s i s s e t , number o f n e a r n e i g h b o r s and method o f c a l c u l a t i o n were employed. The Koopman's v a l u e s f o r t h e same q u a n t i t i e s a r e w e l l o v e r e s t i m a t e d as i s expected, due t o poor screening.The 0.7eV I s b i n d i n g energy d i f f e r e n c e between t h e b u l k and t h e t h i n f i l m i s an i m p o r t a n t q u a n t i t y on i t s own m e r i t . However, t h e same q u a n t i t y p r o p e r l y r e f e r e d t o t h e Fermi l e v e l d i f f e r e n c e , can p r o v i d e t h e s u r f a c e c o r e l e v e l s h i f t between b u l k and s u r f a c e atomsdthe same c r y s t a l . T h i s l a s t q u a n t i t y , which has a t t r a c t e d a l o t o f i n t e r e s t r e c e n t l y , i s c o n s i d e r e d as a v e r y i m p o r t a n t and u s e f u l measure o f t h e d i f f e r e n c e i n chemical environment between b u l k and s u r f a c e atoms of a g i v e m a t e r i a l
Lq.
W i t h i n t h e framework o f e q u a t i o n s (I) and ( 2 ) , t h e c o r e l e v e l s h i f t LC!', can be expressed as AaES = E!'~-
E ; ~ ~( 3 ),
where and E;'~ r e p r e s e n t t h eB u l k observed
115.6
b i n d i n g e n e r g i e s
EL
f o r t h e b u l k ( B ) and s u r f a c e (s)-atoms r e s p e c t i v e l y w i t h r e s p e c t t o t h e Fermi l e v e l ( F ) . The c o r r e s p o n d i n g q u a n t i t i e s w i t h r e s p e c t t o t h e vacuum ( V ) a r e d e s i g n a t e d r:" and&zyv
r e s p e c t i v e l y . The b i n d i n g e n e r g i e s w i t h r e s p e c t t oB u l k c a l c u l a t e d
115.4 I s b i n d i n g energy
(eV
( r e l a t i v e t o vacuum)
vacuum b a r e t h e ' q u a n t i t i e s coming o u t o f t h e c a l c u l a t i o n , whereas t h e e n e r g i e s w i t h r e s p e c t t o t h e Fermi l e v e l a r e t h e e x p e r i m e n t a l l y measured b i n d i n g e n e r g i e s . The two a r e connected t h r o u g h t h e work f u n c t i o n to ( o r
Q B
and @S f o r b u l k and s u r f a c er e s p e c t i v e l y . E q u a t i o n ( 3 ) can t h e n be r e w r i t t e n as:
B S
Ap;S = &B.V
-
E 2 . V-
(Q - (? )b ( 4 )
T h i n f i l m c a l c u l a t e d
114.7
Using t h e r e s u l t s o f t a b l e I , e q u a t i o n ( 4 ) g i v e s =
-
0.50eV, i n e x c e l l e n tP
10.3 15.0 7.10 3.50
p
(eV) Work f u n c t i o n
(eV)
agreement w i t h t h e e x p e r i m e n t a l v a l u e o f -0.55eV
[41.
9 . 7
14.5 5.60 2.25
Another i n n e r c o r e c h a r a c t e r i s t i c o f Be metal which has been d e s c r i b e d q u i t e we1 1 by t h e UHF c l u s t e r technique, i s t h e n a t u r e o f t h e anomalous peaks i n t h e x - r a y Raman spectrum
[I].
These peaks a r e n o t p r e s e n t i n t h e t h i n f i l m t h e o r e t i c a l x - r a y Raman spectrum. T h i s i s i n a c c o r d w i t h t h e p r e d i c t e d o r i g i n o f t h e s e peaks, as due t o t h e q u i t e l a r g e 3spxpy-3sp, s p l i t t i n g o f t h e 3sp band[I].
A s i m i l a r s p l i t t i n g o f t h e ?sp o r b i t a l was c o n s i d e r e d r e s p o n s i b l e f o r t h e d i p i n t h e d e n s i t y of s t a t e s c u r v e a t t h e F e r ~ i l e v e l [I]. T h i s t y p e o f s p l i t t i n g i s n o t p r e s e n t i n t h e two dimensional (2D) f i l m and as a consequence t h e x - r a y Kaman spectrum o f a 20 Be f i l m i s p r e d i c t e d h e r e t o have no anomalous peaks, s i m i l a r t o t h o s e observed i n b u l k BeC9-842 JOURNAL DE PHYSIQUE
metal. S i m i l a r l y t h i s c a l c u l a t i o n p r e d i c t s a good m e t a l l i c c h a r a c t e r f o r t h e Be 2D f i l m as suggested a l s o by more e l a b o r a t e d L o c a l D e n s i t y Approximation (LDA) c a l c u l a ' t i o n s [3].
Concluding t h i s p r e s e n t a t i o n , i n o r d e r t o g a i n more i n s i g h t i n t h e s u r f a c e c o r e l e v e l s h i f t r e s u l t s , a s h o r t comparison w i t h o t h e r c a l c u l a t i o n s i s given. The LDA c a l c u l a t i o n based on Koopman's v a l u e s f o r a t h r e e l a e r s Be f i l m p r e d i c t s a s h i f t o f -0.21eV L3], whereas Niedemala e s t i m a t e procedure 181 g i v e s o n l y -0.15eV. The s h i f t of-0,50eV p r e d i c t e d h e r e i s i n e x c e l l e n t agreement w i t h t h e e ~ p e r i m e n t a l v a l u e o f -0.55eV. P r e l i m i n a r y c a l c u l a t i o n s f o r o t h e r l i g h t m e t a l s have g i v e n r e s u l t s o f s i m i - l a r q u a l i t y , i n d i c a t i n g t h a t t h i s t y p e o f agreement i s n o t p u r e l y f o r t u i t o u s . I t appears t h a t a predominance o f i n i t i a l s t a t e e f f e c t s and an a l m o s t l a c k o f s i g n i f i - c a n t p o s t - c o l l i s i o n e v e n t s c o u l d be m a i n l y r e s p o n s i b l e f o r t h e success o f t h e propo- sed method' I~ere.An e x a m i n a t i o n o f t h e p h y s i c a l and mathematical f a c t o r s i n f l u e n c i n g t h e success and t h e p o s s i b l e l i m i t a t i o n s o f t h e p r e s e n t method, t o g e t h e r w i t h a d d i t i o n a l d e t a i l s and complete c a l c u l a t i o n s f o r s e v e r a l s i m p l e m e t a l s w i l l be g i v e n i n a f o r t h c o m i n g p u b l i c a t i o n .
References
[I]
A.D. Z d e t s i s and D , I l i l i o t i s , S o l i d S t a t e Commun. 42 (1382) 227[2] C.A. l i i c o l a i d e s , A.D. Z d e t s i s and A.N. A n d r i o t i s , S o l i d S t a t e Commun. 50 (1984) 857
[3J J.C. B o e t t g e r , S.B. T r i c k e y , Phys. Rev. B34 (1986) 3604
[4] R, Piyholm, A.S. Flodstrom, L.I. Johansson, S.E. Hornstrom and 3.N. Schmidt- flay, S u r f . S c i . 149 (1985) 449
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[6] A.B. Kunz and D.L. K l e i n , Phys. Rev. B17 (1978) 4614; A.D. Z d e t s i s and A.B.
Kunz, 832 (1985) 6358
[7] A.D. Z d e t s i s , Phys. Rev. 834 (1986) 7666; R.F. M a r s h a l l , R.J. B l i n t and A.U. Kunz, Phys. Rev. 613 (1976) 3333
[8J A.R. Flidema, Z. t l e t a l l k . 69 (1978) 287
