THEORETICAL APPROACH TO FIELD DESORPTION, TIGHT BINDING CALCULATION OF N2 ON Fe(111)

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THEORETICAL APPROACH TO FIELD

DESORPTION, TIGHT BINDING CALCULATION OF N2 ON Fe(111)

D. Tomanek, H. Kreuzer, J. Block

To cite this version:

D. Tomanek, H. Kreuzer, J. Block. THEORETICAL APPROACH TO FIELD DESORPTION,

TIGHT BINDING CALCULATION OF N2 ON Fe(111). Journal de Physique Colloques, 1986, 47

(C2), pp.C2-139-C2-144. �10.1051/jphyscol:1986220�. �jpa-00225653�

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JOURNAL DE PHYSIQUE

Colloque C2, supplbment au n03, Tome 47, mars 1986 page c2-139

THEORETICAL APPROACH TO FIELD DESORPTION, TIGHT BINDING CALCULATION OF N, ON Fe(ll1)

D. TOMANEK, H.J. KREUZER* and J.H. BLOCK'

Inst. f. Theoretische Physik, F.U. ~ e r l i n , Arnimallee 14, 0-1000 Berlin 33, F.R.G.

+ Fritz-Haber-Institut der ax-Planck-Gesellschaft, Faradayweg 4-6.

0-1000 Berlin 3 3 , F.R.G.

Rksumk

-

Nous avons dkveloppk une approche microscopique de l a d k s o r p t i o n de champen employant un c a l c u l de l i a i s o n s d ' l a g r k g a t s bask l e p r i n c i p e de su- p e r p o s i t i o n atomique e t de d k l o c a l i s a t i o n des k l e c t r o n s , comme il a k t & de- veloppg par A.B. Anderson. Pour de f a i b l e s champs k l e c t r i q u e , l ' a c c r o i s s e m e n t d ' a d s o r p t i o n du au champ e s t c a l c u l k pour une gkometrie l i n k a i r e d ' a d s o r p t i o n vers un atome de Fe du p l a n ( I l l ) , k t a i t approximke par un agrkgat Fe

.

A p a r t i r de 1 'Gnergie p o t e n t i e l l e t o t a l e de surface, nous pouvons e x t r a t r e l a forme de l a b a r r i e r e de Schottky e t d6terminer l a f o r c e de champ de dksorp- t i o n . La dkpendance en champ de l a v i b r a t i o n i n t e r n e de l a molkcule adsorbke e s t p r g d i t e e t donne, avec des champs c r o i s s a n t s , d ' a b o r d une c o n t r a c t i o n p u i s une extension de l a longueur de l a l i a i s o n N-N.

A b s t r a c t

-

We have developed a microscopic approach t o f i e l d desorption, em- p l o y i n g a t i g h t - b i n d i n g c l u s t e r c a l c u l a t i o n based on t h e atomic s u p e r p o s i t i o n and e l e c t r o n d e l o c a l i z a t i o n scheme as developed by A.B. Anderson. A t weak e l e c t r i c f i e l d s t h e field-enhanced adsorption i s c a l c u l a t e d f o r a 1 in e a r ad- s o r p t i o n geometry on a topmost Fe atom of a (111) surface, approximated by an Fe - c l u s t e r . From t h e t o t a l p o t e n t i a l energy surfaces we can e x t r a c t t h e shipe o f t h e Schottky b a r r i e r and determine t h e d e s o r p t i o n f i e l d s t r e n g t h . The f i e l d dependence o f t h e i n t e r n a l v i b r a t i o n o f the adsorbed molecule i s p r e d i c t e d which r e s u l t s , w i t h i n c r e a s i n g f i e l d strength, f i r s t i n a con- t r a c t i o n and then i n an extension o f t h e N-N bond l e n g t h .

I

-

INTRODUCTION

The phenomenon of f i e l d desorption, f i r s t observed by E.W. Wuller, has since then been i n v e s t i g a t e d by many authors. T h e o r e t i c a l discussions considered t h e image hump model /1,2/, t h e charge exchange model / 3 , 4 / and a two-stage mechanism, i .e. t h e p o s t - i o n i z a t i o n process 151. The model p o t e n t i a l s f o r t u n n e l i n p have been e i t h e r a simple t r i a n g u l a r p o t e n t i a l b a r r i e r /5/ o r a three-dimensional t u n n e l i n g p o t e n t i a l / 6 / . An a p p r o p r i a t e value o f t h e e f f e c t i v e charge number o f ions has been introduced by o t h e r authors / 7 , 8 / o r image terms f o r t h e p o t e n t i a l energy o f t u n n e l i n g e l e c - t r o n s have been i n v o l v e d /9/. From t h e f i e l d evaporation data bonding distances and

'permanent address : Dept. of Physics, Dalhousie University, Halifax, Nova Scotia, Canada

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986220

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CZ-140 JOURNAL

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v i b r a t i o n f r e q u e n c i e s o f s u r f a c e atoms have been c o n s i d e r e d /10,11/.

A l l t h e s e t h e o r i e s o f f i e l d d e s o r p t i o n o r f i e l d e v a p o r a t i o n processes a r e phenomeno- l o g i c a l i n n a t u r e and assume a s i m p l e a n a l y t i c a l f o r m f o r t h e p o t e n t i a l energy which a c t s on t h e t u n n e l i n g e l e c t r o n . These phenomenological p o t e n t i a l energy d e s c r i p t i o n s do n o t account f o r charge r e d i s t r i b u t i o n s and t h e h y b r i d i z a t i o n changes i n t h e ap- p l i e d e l e c t r o s t a t i c f i e l d .

In t h i s c o n t r i b u t i o n a t i g h t - b i n d i n g c l u s t e r c a l c u l a t i o n i s p r e s e n t e d f o r t h e f i e l d - induced a d s o r p t i o n and d e s o r p t i o n o f N2 on F e ( l l 1 ) . I n o u r model, a l i n e a r adsorp- t i o n geometry o f N2 on t h e topmost Fe atoms i s chosen. The 1 in e a r f o r m seems p l a u - s i b l e s i n c e i n t h e f i e l d f r e e case N2 has t h i s p o s i t i o n on F e ( l l 1 ) a t l o w tempera- t u r e s /12,13/. We approximate t h e s u b s t r a t e by an Fe4 c l u s t e r c o n s i s t i n g o f one t o p l a y e r Fe-atom and i t s 3 n e a r e s t neighbours i n t h e second l a y e r , hence c o n s e r v i n g t h e l o c a l CjV a d s o r p t i o n symmetry (Fig. 1). It has been shown by Tomanek and Bennemann /13/ t h a t i n c l u d i n g p o r e F e - s u b s t r a t e atoms ( u p t o t w e l v e ) has no remarkable e f f e c t on t h e energy s u r f a c e i n t h e f i e l d f r e e case.

F i g . 1

-

P o t e n t i a l e n e r g i e s f o r N 2 / F e ( l l l ) i n presence o f e l e c t r o s t a t i c f i e l d s F.

The e q u i - d i s t a n t c o n t o u r s a r e separated b y 0.2 eV, t h e p r e f e r e n t i a l d e s o r p t i o n p a t h i s marked b y an arrow.

The c l u s t e r c a l c u l a t i o n f o l l o w s t h e f o r m a l i s m which was developed by A l f r e d

B.

Anderson /14/ and i s c a l l e d ASED = Atomic S u p e r p o s i t i o n and E l e c t r o n D e l o c a l i z a t i o n .

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I t i s an extended Huckel method which i s adding a two-body r e p u l s i v e energy, t a k i n g t h e He1 lmann Feynman theorm i n t o a c c o u n t ( v a l i d i t y o f c l a s s i c a l e l e c t r o s t a t i c s ) . T h i s method has been proven t o p r e d i c t f a i r l y w e l l t h e bond l e n g t h and f o r c e con- s t a n t d a t a o f d i a t o m i c m o l e c u l e s 1 1 4 1 and has r e c e n t l y been a p p l i e d w i t h success t o p r e d i c t p r o p e r t i e s of chemisorbed m o l e c u l e s 1151, i .e. CC on P t (111) i n t h e p r e s - ence o f potassium.

The t i g h t - b i n d i n g H a m i l t o n i a n as used i n t h e ASED scheme /14/ reads

where a and 6 enumerate t h e n u c l e i o f charge (Z,e) a t p o s i t i o n s R,= (x,, y,, z,) and i and j denote t h e e l e c t r o n e i g e n s t a t e s i n t h e f r e e atoms.

e

i s t h e a n g l e between t h e N2 a x i s and t h e s u r f a c e normal. The t h i r d sum r e p r e s e n t s t h e p a i r - w i s e r e p u l s i o n between a n u c l e u s 8 and t h e t o t a l e l e c t r o n i c and n u c l e a r charge d e n s i t y p,(r) a t atom a and t h e l a s t sum shows t h e f i e l d e f f e c t on t h e i o n s . I n t h e p r e s - ence o f an e l e c t r i c f i e l d F t h e energy e i g e n v a l u e s on t h e n i t r o g e n s a r e s h i f t e d

E ; ( F ) = E; (F=O)

+

eF IR,l cos ⁸

,

^{( 2 )}

and t h e hopping i n t e g r a l s change as

Table 1

Atomic parameters used i n t h e c a l c u l a t i o n : p r i n c i p a l quantum number

(n),

a t o m i c l e v e l s ( E ) and o r b i t a l exponents ( 5 ) ; d o u b l e - z e t a S l a t e r b a s i s ( w i t h o r b i t a l c o e f - f i c i e n t s C) has been used f o r t h e d l e v e l s o f Fe

Atoms s P

n &(eV) 5 n c(eV) 5

Fea ) 4 -9.37 1.70 4 -5.83 1.40

Atoms d

n ~ ( e v )

c1 5z

a ) ~ e f . 1171; paramagnetic Fe.

L \

')2 eV a t o m i c l e v e l i n c r e a s e and 0.1 i n c r e a s e i n exponents a p p l i e d t o p a r a r e t e r s from r e f . 1181.

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aB d r ⁰

*

⁶

t . . (F) = tgy (F=O)

+

eF J qi ( r ) (z-z,) v j ( r ) d r .

1 J _z-z

The S l a t e r exponents i n the ( f i e l d - f r e e ) atomic o r b i t a l s

$7

and the e l e c t r o n i c energy l e v e l s &: are given i n t a b l e 1. We have chosen the N exponents t o y i e l d good gas phase N2 p r o p e r t i e s ; t h i s causes t h e Fe-N bond l e n g t h s t o be a b i t s h o r t . The f i e l d - - f r e e hopping i n t e g r a l s are approximated by t h e Wolfsberg-Helmholtz /16/ formula

where Ka8 = 2.25 exp(-0.13

8-I

IR,

-

R B I ) . Because t h e atomic o r b i t a l s 'D: a r e non- orthogonal, we cannot account f o r t h e atomic p o l a r i z a t i o n e f f e c t s i n ( 3 ) b u t o n l y i n c l u d e f i e l d e f f e c t s w i t h t h e energy s h i f t i n ( 2 ) .

I n our c a l c u l a t i o n we keep t h e geometry of the Fe4 c l u s t e r f i x e d and v a r y t h e n i t r o - gen p o s i t i o n s f o r a f i e l d F perpendicular t o t h e surface (e=O) t o c a l c u l a t e the po- t e n t i a l energy surfaces V(z,S). Here, z i s t h e c e n t r e o f mass p o s i t i o n w i t h respect t o t h e topmost Fe and 5 i s t h e i n t r a m o l e c u l a r d i s t a n c e o f t h e N2 c l u s t e r .

I n F i g . 1 we present p o t e n t i a l surfaces o f N2 i n t e r a c t i n g w i t h F e ( l l 1 ) p l o t t e d as contour maps. F i g . l a represents t h e f i e l d - f r e e case. We see t h a t i n t h e a d s o r p t i o n minimum t h e N-N d i s t a n c e 5 has been widened from t h e value i n t h e gas phase

<0 =

1.1

8

t o approximately 5= 1.2

8.

The c e n t r e o f mass o f N2 i s a t about ~ ~ 2 . 1 3

8

^above

t h e topmost Fe. We should note t h a t t h e charge on the i n n e r N i s Q

+

0.4 e and on the o u t e r one i s about -0.7 e as i n f e r r e d from a (basis-dependent) p o p u l a t i o n ana- l y s i s . As i n d i c a t e d by a schematic desorption path, t h e N2 molecule c o n t r a c t s and s t i f f e n s t o i t s gas phase p r o p e r t i e s a t distances l a r g e r than about 4

8

above the surface. Applying a f i e l d F = 0.5

V / f i

( F i g . l b ) t h e h i g h e s t occupied N2 o r b i t a l s o f antibonding c h a r a c t e r a r e l i f t e d biyond EF and drained o f e l e c t r o n s , causing t h e adsorbed N2 molecule t o c o n t r a c t and t o s t i f f e n a l r e a d y i n i t s e q u i l i b r i u m p o s i t i o n . I n a f i e l d F = 1.0

v/8

( F i g . I c ) f u r t h e r l a r g e upward s h i f t o f adsorbate o r b i t a l s , and t h e concurrent r e d u c t i o n i n t h e hopping s t r e n g t h l e a d t o an expansion and s o f - t e n i n g o f t h e N2 bond. A d i a b a t i c d e s o r p t i o n now leads t h e N2 molecule through an energy maximum a t z

-

^2.5

^fi

beyond which t h e N2 i s accelerated away from t h e surface and d i s s o c i a t e d . The l a t t e r i s caused by t h e f a c t t h a t by now t h e bonding o r b i t a l s of N2 have been l i f t e d beyond t h e Fermi energy EF and thus drained o f e l e c t r o n s . I t i s worth n o t i n g t h a t t h i s phenomenon i s a f e a t u r e o f a ground s t a t e c a l c u l a t i o n . As long as we are o n l y i n t e r e s t e d i n e q u i l i b r i u m p r o p e r t i e s , we a l l o w t h e t o t a l system t o r e l a x t o i t s e l e c t r o n i c s t a t e o f minimum energy; t h i s e.g. i m p l i e s t h a t beyond the energy b a r r i e r t h e n i t r o g e n s a r e accelerated away t o i n f i n i t y l o o s i n g a l l e l e c - t r o n s t o t h e s u b s t r a t e . I n p r a c t i c e t h i s w i l l n o t happen due t o t h e low t u n n e l i n g p r o b a b i l i t i e s from t h e N's t o the s u b s t r a t e . To determine t h e i o n y i e l d i n f i e l d de- s o r p t i o n one t h e r e f o r e has t o know both t h e energy surfaces and t h e t u n n e l i n g pro- b a b i l i t i e s ( t h e l a t t e r as a f u n c t i o n o f d i s t a n c e ) .

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I n a f i e l d F=1.5 V/8 ( F i g . I d ) we f i n d t h a t t h e n i t r o g e n m o l e c u l e i s s t r e t c h e d t o gw 1.5

8

and t h e N ' s c a r r y charges +2e. The S c h o t t k y b a r r i e r has been reduced sub- s t a n t i a l l y s u g g e s t i n g t h a t

-

b y ground s t a t e arguments a l o n e

-

t h e c r i t i c a l e l e c t r i c f i e l d necessary f o r d e s o r p t i o n i s somewhat l a r g e r t h a n 1.5

~ / 8 .

T h i s easy d i s s o c i a -

F i g . 2

-

P o t e n t i a l energy E o f N molecules d e s o r b i n g f r o m F e ( l l 1 ) a l o n g t h e a r - rows p l o t t e d i n F i g . 1 i n a i g z n c e o? a p p l i e d e l e c t r i c f i e l d s F. (Energy g i v e n w i t h r e s p e c t t o t h e desorbed N2 i n t h e f i e l d - f r e e case.)

t i o n i s a d i r e c t consequence o f t h e f a c t t h a t o u r o n e - e l e c t r o n c a l c u l a t i o n does n o t i n c l u d e i n t r a - a t o m i c Coulomb r e p u l s i o n i n t h e f o r m a t i o n o f i o n s which e.g. l e a d s on- l y t o charge s t a t e s +2e, +4e,

. . .

f o r t h e desorbed N2 complex.

F i g . 2 we have p l o t t e d t h e p o t e n t i a l energy a l o n g t h e d e s o r p t i o n paths marked by arrows i n F i g . 1. F o r weak f i e l d s energy s u r f a c e s a r e s h i f t e d upwards as a r e s u l t o f t h e s h i f t i n t h e a d s o r b a t e o r b i t a l s . I n s t r o n g e r f i e l d s (F? 1

~ / 8 )

t h e s e o r b i t a l s a r e r a i s e d above EF and d r a i n e d o f e l e c t r o n s c a u s i n g t h e t o t a l energy o f t h e system t o decrease a g a i n . The b i n d i n g energy o f t h e adsorbed molecule, i . e . t h e energy d i f - f e r e n c e between t h e minimum and t h e t o p o f t h e S c h o t t k y b a r r i e r , i n c r e a s e s i n weak f i e l d s l e a d i n g t o f i e l d - e n h a n c e d a d s o r p t i o n as found e x p e r i m e n t a l l y . F o r t h e l a r g e r f i e l d s t h e S c h o t t k y b a r r i e r i s reduced and moves c l o s e r t o t h e s u r f a c e . I n t h e s e model c a l c u l a t i o n s f i e l d d e s o r p t i o n o c c u r s beyond f i e l d s t r e n g t h s Fcrit> 1.5

V / 8

f o r which t h e S c h o t t k y b a r r i e r disappears. T h i s magnitude o f f i e l d s t r e n g t h has a l s o been observed e x p e r i m e n t a l l y .

From t h e p o t e n t i a l energy s u r f a c e s o f F i g . 1 we can a l s o c a l c u l a t e t h e f i e l d dependence o f t h e N2 v i b r a t i o n a l f r e q u e n c y ^V. I n t h e absence o f a f i e l d , t h e v i b r a - t i o n i n t h e adsorbed m o l e c u l e i s reduced f r o m i t s gas phase v a l u e v0=2359 cmml t o v(F=0)=1339 cm-I m a i n l y due t o a p a r t i a l o c c u p a t i o n o f N2 a n t i b o n d i n g o r b i t a l s . The amount o f t h e f r e q u e n c y s o f t e n i n g i s caused by t h e N2 i n t e r a c t i o n w i t h t h e r e a c t i v e i r o n ( h a l f f i l l e d d-band) a t a s i t e w i t h t h e most u n s a t u r a t e d bonds. F o r f i e l d s l e s s t h a n 0 . 5

v/X

i n c r e a s e s a g a i n up t o a v a l u e o f about 1850 cm-I due t o t h e f a c t t h a t

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t h e a n t i - b o n d i n g o r b i t a l s i n N2 a r e d r a i n e d . The a b r u p t decrease i n v a t F

2

0.75

~ / 8

i s accompanied b y an a b r u p t widening o f t h e N-N d i s t a n c e and a decrease i n t h e N2 f o r c e c o n s t a n t . A t t h i s v a l u e of F group o r b i t a l s which were p a r t i a l l y l o c a l i z e d on N2 have been d r a i n e d l e a v i n g t h e N2 m o l e c u l e w i t h a bonding o r b i t a l o c c u p a t i o n decreased by 0.3 e. The d r a m a t i c decrease i n v beyond F

-

^0.9

^{~ / 8}

i s i n d i c a t i v e of f i e l d - i n d u c e d d i s s o c i a t i o n .

Recent c a l c u l a t i o n s concerned r a r e gases

He,

Ne, A r on W { l l l } s u r f a c e s . I t was found t h a t t h e f i e l d i n d u c e d b i n d i n g energy o f He i n c r e a s e d f r o m 5 meV t o

-

500 meV a t 5

v/N

due t o a charge d r a i n o f ^w0.3 e. The f i e l d b i n d i n g energy o f Ne, on t h e o t h e r hand, i n c r e a s e d o n l y s l i g h t l y w i t h i n c r e a s i n g f i e l d .

I n summary, a m i c r o s c o p i c approach t o f i e l d d e s o r p t i o n has been developed employing a t i g h t - b i n d i n g c l u s t e r c a l c u l a t i o n . We f i n d f i e l d - e n h a n c e d a d s o r p t i o n i n weak e l e c - t r i c f i e l d s . From t h e t o t a l p o t e n t i a l energy s u r f a c e s we can e x t r a c t t h e shape o f t h e S c h o t t k y b a r r i e r and determine t h e d e s o r p t i o n f i e l d s t r e n n t h . We f u r t h e r p r e d i c t t h e f i e l d dependence o f t h e i n t e r n a l v i b r a t i o n o f t h e adsorbed molecule.

ACKNOWLEDGEMENT

P a r t i a l s u p p o r t b y t h e Sonderforschungsbereich S f b 6 / ' 8 1 i s g r a t e f u l l y acknowledged.

We a r e g r a t e f u l t o A.B. Anderson f o r p r o v i d i n g t h e ASED programme. One o f us (H.J.K.) thanks t h e Max-Planck-Society f o r a f e l l o w s h i p .

REFERENCES

/1/ M u l l e r , E.W., Naturwissensch.

-

29 (1941) 533.

/2/ M u l l e r , E.W., Phys. Rev.

102

(2956) 618.

/3/ Gomer, R., and Swanson, L.W., J. Chem. Phys.

38

(1963) 1613.

/4/ Tsong, T.T., and K i l l e r , E.W., Phys. S t a t u s S o l i d i ( a ) - 1 (1970) 513.

/5/ E r n s t , N., S u r f . S c i . - 87 (1979) 469.

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