SURFACE STATES AND ADSORPTION IN AN EXTERNAL ELECTRIC FIELD

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HAL Id: jpa-00224390

https://hal.archives-ouvertes.fr/jpa-00224390

Submitted on 1 Jan 1984

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SURFACE STATES AND ADSORPTION IN AN EXTERNAL ELECTRIC FIELD

M. Stwślicka, M. Radny

To cite this version:

M. Stwślicka, M. Radny. SURFACE STATES AND ADSORPTION IN AN EXTERNAL ELECTRIC FIELD. Journal de Physique Colloques, 1984, 45 (C9), pp.C9-65-C9-70. �10.1051/jphyscol:1984912�.

�jpa-00224390�

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SURFACE STATES AND ADSORPTION I N AN EXTERNAL ELECTRIC FIELD M. ~t~llicka' and M. Radny*

IntemationaZ Centre for Theoretical Physics, Trieste, I t a l y

* ~ n s t i t u t e of Experimental Physics, CybuZskiego 36, 50-205 Wroc2aw, PoZand Resume

-

On a e t a b l i que l e s n i v e a u x s u p e r f i c i e l s trees p a r l e s atomes adsorbes, Fi l ' o p p o s g d e s niveaux d e Tamm, s o n t extrsmement s e n s i b l e s 2 l a p r e s e n c e d ' u n champ g l e c t r i q u e ex- t e r n e . Le champ e l e c t r i q u e p o s i t i f ne change p a s l a l o c a l i s a - t i o n d e s niveaux ; t a n d i s que l e champ n e g a t i f t r a n s f o r m e l e s niveaux c r 6 6 s p a r l e s atomes a d s o r b e s e t l e s niveaux d e T a m en niveaux v i r t u e l s .

A b s t r a

-

^Iti s f o u n d t h a t t h e a d s o r p t i o n - l i k e s t a t e s c o n t r a - Tamm-like s t a t e s a r e v e r y s e n s i t i v e t o t h e p r e s e n c e of a n e x t e r n a l e l e c t r i c f i e l d . A p o s i t i v e e l e c t r i c f i e l d d o e s n o t r e a l l y i n f l u e n c e t h e l o c a l i z a t i o n p r o p e r t i e s of t h e s t a - t e s ; a n e g a t i v e e l e c t r i c f i e l d , however, c h a n g e s t h e Tamm- and a d s o r p t i o n - l i k e s t a t e s i n t o v i r t u a l s t a t e s .

INTRODUCTION

I n o u r p r e v i o u s / I / we have s t u d i e d t h e b e h a v i o u r of s u r f a c e s t a t e s i n t h e p r e s e n c e of a d s o r b e d atoms and we have o b t a i n e d Tamm-like

e l e c t r o n l o c a l i z e d a t t h e c r y s t a l s u r f a c e and a d s o r p t i o n - l i k e e l e c t r o n i c s t a t e s e l e c t r o n l o c a l i z e d n e a r t h e adatom

.

^{Here we}

i n v e s t i g a t e t h e e f f e c t of a p o s i t i v e e x t e r n a l e l e c t r i c f i e l d EEF and of a n e g a t i v e EEF on s u r f a c e s t a t e s of a s e m i i n f i n i t e

6

- w e l l c r y s t a l model w i t h t h e s u r f a c e c o v e r e d by f o r e i g n atoms.

MODEL AND NOTATION

The model p o t e n t i a l i s ehovm i n F i g . l a ( c r y s t a l model w i t h p o s i t i - v e EEF) and i n Fig. I b ( c r y s t a l model w i t h n e g a t i v e EEF).

x-0 (SURFACE)

F i g s 1

-

Schematic p l o t of t h e model p o t e n t i a l s V(x) ( f o r n o t a t i o n s e e t h e t e x t ) .

+ Permanent address : Institute of Experimental Physics, Cybulskiego 36, 50-205 Wrocaaw, Poland.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984912

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C9-66 JOURNAL DE PHYSIQUE

The e l e c t r i c i n t e n s i t y F, ( f o r 0

<

x

<

d ) i s assumed t o be s m a l l e r t h a n Fz ( f o r x

>

d). The p r e s e n c e of a n adatom n e a r t h e c r y s t a l s u r f a c e (x = 0 ) i s t a k e n i n t o aocount v i a t h e s u i t a b l e u m o d u l a t i o n v of t h e s u r f a c e p o t e n t i a l b a r r i e r V,

,<

V, (V, b e i n g .the work f u n c - t i o n ) and t h e c h a n e of t h e a r a m e t e r p (the s t r e n g t h of t h e paten-

t i a l of t h e adatom? (cf. /1/f. ¹

Numerical c a l c u l a t i o n s were c a r r i e d o u t w i t h c r x s t a l r a m e t e r s a a p p r o p r i a t e f o r s i l i c o n , i . e . Vo = 4.8 eV, b = 5.44

%:

^p⁼¹^.?

^.

The " i n t e r n a l w f i e l d i n t e n s i t g F was t a k e n from t h e i n t e r v a l 10' V/cm

-

¹

o5

V/cm ( f o r F 4 19' \/em t h e dependence 3 = f (d) wes t h e same a s f o r Fi = l o s ?/cm

.

FXERGY EXPRESSIOIJS AND LOCALIZATION PROPERTIES

Using t h e s t a n d a r d m a t c h i n g procedure we have o b t a i n e d t h e f o l l o v r i n g e x p r e s s i o n s f o r t h e s u r f a c e s t a t e s energy I?

where

w i t h

**M * ~ z ~ , z ~ )** =

B(2:)

- ^8'03 ^,

M:

( ~ ~ ~ 2 : )

-

^A(ze,

^B(zg1- A(zt)B~b>

⁹

N' - A'(z~)-A'(zB'(z~) , D

' = A

( z z ) d.,

(lit Zp4 ^{/ b} ^{i dl} " ) ' 1 ,

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The l o c a l i z a t i o n p r o p e r t i e s of a n e l e c t r o n occupying t h e s u r f a c e s t a t e s were d i s c u s s e d u s i n g t h e r e l a t i v e p r o b a b i l i t y d e n s i t g func- t i o n P(x) d e f i n e d by / 2 /

.

where v ( x ) i s t h e wave f u n c t i o n f o r a s u r f a c e s t a t e ( t h e c r y s t a l s u r f a c e i s always l o c a t e d a t x = 0

-

s e e F i g s l a and l b ) . ~ n s i d e t h e c r y s t a l (-b 4 x 4 0 ) P(x) i s g i v e n by

where

O u t s i d e t h e c r y s t a l f o r O d x i d P(x) o' Pll(x) and

where z-

+

= z o

+_

^4,x. F o r x 2 d , P(x)=

Pill

(x) and i s g i v e n by

NUMERICAL RESULTS

The e f f e c t of a n e x t e r n a l e l e c t r i c f i e l d on b o t h t h e energy dependen- c e E = f (d) of t h e Tamm-like and a d s o r p t i o n - l i k e s t a t e s and on t h e r e l a t i v e p r o b a b i l i t y P(x) c a n be summarized a s f o l l o w s .

P o s i t i v e ( ~ i ~ . 2 ) and n e g a t i v e EEF1s (3'ig. 3 ) change d r a s t i c a l l y t h e energy dependence E = f ( d ) of t h e a d s o r b e d - l i k e s t a t e s ( d o t t e d dashed l i n e s f o r EEF and dashed l i n e s f o r z e r o f i e l d a p p l i e d ) .

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C9-68 JOURNAL DE PHYSIQUE

The energy of t h e Tamm-like s t a t e s ( ~ i g s 2 and 3 ) is a l m o s t indepen- d e n t of t h e f i e l d i n t e n s i t i e s F and Fz ( d o t t e d l i n e s f o r EEF and s o l i d l i n e s f o r z e r o f i e l d

applied).

I n t h e model w i t h a n e g a t i v e f i e l d t h e Tamrn- and a d s o r p t i o n - l i k e s t a t e s a r e r e p l a c e d by v i r t u a l s u r f a c e s t a t e s [cf, /3/ and /4/) a s c a n b e s e e n i n F i g . 3 ( i n s e r t f o r p o i n t s A and B),

1.0

TAMM STATE 0.8

0.6 0.4 0.2

2 4 6 10 12 14 16 18 dIh1

Fig. 2

-

^E⁼^f(d) f o r p o s i t i v e EEF ( f o r n o t a t i o n s e e t h e t e x t ) The l o c a l i z a t i o n p r o p e r t i e s of t h e Tamm-like and a d s o r p t i o n - l i k e s t a t e s a r e a l m o s t n o t s e n s i t i v e t o t h e p r e s e n c e of a n EEP ( p i g s 4 and 5). F o r t h e n e g a t i v e f i e l d , however, P(x) h a s o s c i l l a t o r y c h a r a c t e r o u t s i d e t h e c r y s t a l ( ~ i g . 5 ) , i , e . e l e c t r o n s from v i r t u a l s t a t e s c a n t u n n e l t h r o u g h t h e p o t e n t i a l b a r r i e r .

TAMM STATE 0.8

0.6 0.4 0.2

2 4 6 8 10 12 14 16 18 d [ A ]

Fig. 3

-

^E⁼f ( d ) f o r t h e n e g a t i v e

Em

( f o r n o t a t i o n s e e t h e t e x t )

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SUGGESTED INTZRPRETATION OF THE RESULTS based on t h e V o l k e n s t e i n of c h e m i s o r p t i o n /5/

With no e l e c t r i c f i e l d a p p l i e d , t h e c u r v e s E(d) f o r t h e a d s o r p t i o n - - l i k e and T a m - l i k e s t a t e s i n t e r s e c t ( s e e F i g s 2 and 3). The ground s t a t e h a s a n i o n i c c h a r a c t e r (an e l e c t r o n from adatom i s t u n n e l l i n g i n t o empty s u r f a c e s t a t e ) . There i s a p o s s i b i l i t y of a d i r e c t i o n i c e v a p o r a t i o n w i t h o u t a f i e l d .

I n a s t r o n g p o s i t i v e e l e c t r i c f i e l d , t h e " a d s o r p t i o n " c u r v e i s s t r o n - g l y deformed and t h e c u r v e s E(d) do n o t i n t e r s e c t (3?ig. 2). Thus t h e ground s t a t e i s p u r e l y i o n i c a t any d i s t a n c e from t h e c r y s t a l s u r f a c e . I n p r i n c i p l e , t h e r e f o r e , a n e l e c t r o n of t h e image g a s e c a n t u n n e l i n t o t h i s s t a t e ( t h e c o r r e s p o n d i n g c a l c u l a t i o n s a r e i n pro- g r e s s ) . F o r I? 2 5 - l o 8 V/cm, * 9 a d s o r p t i o n w c u r v e merge i n t o t h e c o n d u c t t o n ban% (no l o c a l i z e d s t a t e s

-

t h e c a s e c o r r e s p o n d i n g t o t h e f i e l d d e s o r p t i o n ) .

I n a n e g a t i v e e l e c t r i c f i e l d , t h e a d s o r p t i o n and Tamm E(d) c u r v e s i n t e r s e c t a t s m a l l e r surface-adatom d i s t a n c e ( n e g a t i v e f i e l d seems t o "pushw adatom t o w a r d s t h e c r y s t a l s u r f a c e ) .

We b e l i e v e t h a t o u r r e s u l t s might form t h e s t a r t i n g p o i n t f o r more r e a l i s t i c model of c h e m i s o r p t i o n i n v o l v i n g s u r f a c e s t a t e s , t h u s becoming e x t e n s i o n of V o l k e n s t e i n 9 s t h e o r y of c h e m i s o r p t i o n ( s e e /5/).

b

1

A

--

b 0 b

f

3 b x

A DATOM

Fig. 5

-

^P(x) f o r t h e n e g a t i v e EXF: a) T a m - l i k e s t a t e s , b) A d s o r p t i o n - l i k e s t a t e s .

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JOURNAL DE PHYSIQUE

PEFERENCES

111 M. S t e S l i c k a and N.Radny, Physica

u,

239 (1984).

121

A,J. Thakkar and hl.Steglicka, S u r f a c e S c i .

u,

168 (1974).

131 A. l o d i n o s , S u r f a c e S c i .

41,

425 (1 974).

141 I . S t g 8 l i c k a and Z. P e r k a l , S o l . S t a t e Comm.

2,

349 (1980).

151 F.F, V o l k e n s t e i n , " E l e c t r o n i c t h e o r y of c a t a l y s i s of sernicon- d u c t o r s w , ( F i z m a t z i g , ?+!Iosco:~~) (1960) ( i n Russian).

SURFACE STATES AND ADSORPTION IN AN EXTERNAL ELECTRIC FIELD

HAL Id: jpa-00224390

https://hal.archives-ouvertes.fr/jpa-00224390

Submitted on 1 Jan 1984

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

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.