ELECTROREFLECTANCE SPECTROSCOPY IN THE STUDY OF METAL-ELECTROLYTE INTERFACES

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ELECTROREFLECTANCE SPECTROSCOPY IN THE STUDY OF METAL-ELECTROLYTE INTERFACES

D. Kolb

To cite this version:

D. Kolb. ELECTROREFLECTANCE SPECTROSCOPY IN THE STUDY OF METAL-

ELECTROLYTE INTERFACES. Journal de Physique Colloques, 1983, 44 (C10), pp.C10-137-C10-

146. �10.1051/jphyscol:19831029�. �jpa-00223486�

JOURNAL DE PHYSIQUE

Colloque CIO, supplément au n°12, Tome M, décembre 1983 page C10-137

E L E C T R O R E F L E C T A N C E S P E C T R O S C O P Y IN T H E STUDY OF M E T A L - E L E C T R O L Y T E INTERFACES

D.M. Kolb

Fr-itz-Haber-Institut der Max-Planak-Gesellsohaft, Faradayweg 4-6, 1000 Bevlin 33, F.R.G.

Résumé - L'électroréflectance des surfaces monocristal!inés de Cu, Ag et Au en contact avec une solution aqueuse est brièvement passée entrevue et discutée. On montre que les états de surface à l'interface métal- électrolyte contribuent de façon significative à l'effet global d'électroreflectance et peuvent fournir des renseignements sur la distribution du champ électrique à l'intérieur de la double couche électrochimique. L'électroreflectance infrarouge peut être utilisée pour détecter directement certaines contributions des composants de la double couche. Finalement le rôle de l'optique non-locale pour l'interprétation des spectres d'électroreflectance est mis en valeur.

Abstract - Electroreflectance of Cu, Ag and Au single crystal surfaces in contact with an aqueous electrolyte is briefly reviewed and discussed. It is shown that surface states at the metal-electrolyte interface contribute significantly to the overall electroreflectance effect, and they can provide information on the electric field distribution inside the electrochemical double layer. Infrared electroreflectance may be used to detect

contributions from the double layer constituents directly. Finally, the role of non-local optics for interpretation of electroreflectance spectra is emphasized.

1 - Introduction

Classical electrochemical techniques which are based on charge and potential measurements, yield in essence a thermodynamic description of the electrochemical

interface /l/. However, in order to derive a microscopic picture, information regarding the electronic and geometric structure of the double layer region is very important. In this respect, reflectance spectroscopy promises a better understanding by investigation of the optical and hence electronic properties of the bare and adsorbate-covered electrode surfaces. It is applicable in-situ, specific at an atomic or molecular level, and sensitive enough to characterize in detail electrode-electrolyte interfaces. Among the various spectroscopic techniques, electroreflectance (ER) was regarded as the most appropriate tool for investigation of the metal-electrolyte interface. In the absence of any electrochemical reaction, this interface behaves like a capacitor which can be charged or discharged by appropriate potential variations. Since the double layer capacity ranges between 20 and 100 yFcm"2 and the potential region for double layer charging for a metal like silver is about 1 V, large surface charges (say, 20yCcm"2, corresponding to about 0.1 electron per surface atom!) and high electric fields (~107Vcm"£) can be obtained with ease and their values modulated by simple potential modulation / 2 / . Such a potential variation in the double layer charging region has been found to cause a noticeable change in the reflectance of the metal-electrolyte interface / 3 / . This change in reflectance with electrode potential is called electroreflectance (ER). In contrast to semiconductor ER where the static or low frequency electric field penetrates into the bulk several thousand Angstroms, thus probing the bulk band structure / 4 / , the perturbing electric field is screened within the first atomic layer of the metal because of the htgh charge carrier density (the Thomas-Fermi screening

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19831029

ClO-138 JOURNAL DE PHYSIQUE

3

-

-

tn +- -

C l e n g t h i s about 0.5

8 ) .

Hence ER f o r

= ! 2 -

-

m e t a l s s h o u l d be e x t r e m e l y surface

? s e n s i t i v e . T h i s i s demonstrated i n F i g .

\ 1, where f o r a j e l l i u m m e t a l , t h e s u r f a c e

T '

- - ^-

charge d e n s i t y induced by a weak e x t e r n a l

a 01 e l e c t r i c f i e l d i s shown 151. I n t h e

f o l l o w i n g , v a r i o u s c o n t r i b u t i o n s t o m e t a l ER a r e b r i e f l y discussed, r e s t r i c t i n g t h e examples t o s t u d i e s o f s i n g l e c r y s t a l s u r f a c e s o n l y .

- 8 - 6 - L - 2 0 2 L 6 x /A

F i g . 1

-

Surface charge d e n s i t y A 3

of a metal, induced by a weak 2

-

ER S p e c t r a o f Cu and Ag Surfaces e x t e r n a l e l e c t r i c f i e l d . x = 0

denotes t h e edge of t h e p o s i t i v e - E a r l y e x p e r i m e n t s were performed w i t h charge background. A f t e r r e f . / 5 / . p o l y c r y s t a l l i n e s u r f a c e s / 6 / . The

r e s u l t s , m a i n l y f o r Ag and Au, were i n t e r p r e t e d i n terms of t h e " f r e e - e l e c t r o n " model developed by Hansen /7,8/ and r e f i n e d by M c I n t y r e 191. T h i s model assumes t h a t t h e change i n t h e f r e e - e l e c t r o n c o n c e n t r a t i o n a t t h e s u r f a c e , induced by t h e p o t e n t i a l change, i s m a i n l y r e s p o n s i b l e f o r t h e observed e f f e c t . Bound e l e c t r o n s a r e t a k e n t o be p e r f e c t l y screened by t h e f r e e e l e c t r o n s , hence t h e y do n o t respond t o t h e a p p l i e d e l e c t r i c f i e l d . The f r e e - e l e c t r o n model has p r o v e n t o reproduce t h e main f e a t u r e s o f an ER spectrum, e s p e c i a l l y f o r p o l y c r y s t a l l i n e s u r f a c e s (e.g., t h e peak a t 3.9 eV f o r Ag and 2.5 eV f o r Au); however, t h e s e gross f e a t u r e s i n AR/R a r i s e m a i n l y f r o m t h e 1/R e f f e c t , which i s always p r e s e n t f o r m e t a l s w i t h r a p i d l y v a r y i n g r e f l e c t i v i t y . Many d e t a i l s i n t h e s p e c t r a c o u l d n o t be e x p l a i n e d by t h i s s i m p l e model, i n d i c a t i n g t h a t t h e r e a r e o t h e r sources which c o n t r i b u t e s i g n i f i c a n t l y t o t h e ER and which had been n e g l e c t e d so f a r . The marked d i f f e r e n c e s which a r e observed f o r t h e v a r i o u s c r y s t a l l o g r a p h i c f a c e s o f one and t h e same m e t a l s t r o n g l y suggested t h a t t h e bound e l e c t r o n s do f e e l t h e m o d u l a t i n g p o t e n t i a l / l O , l l / . T h i s i m p l i e s t h a t t h e ER s p e c t r a o f s i n g l e c r y s t a l s u r f a c e s c o n t a i n i n f o r m a t i o n a b o u t t h e band s t r u c t u r e i n t h e s u r f a c e r e g i o n and i t s dependence on t h e e l e c t r o d e p o t e n t i a l .

The f a i l u r e o f t h e f r e e - e l e c t r o n model t o reproduce even pronounced e f f e c t s i n ER i s demonstrated i n F i g . 2 1121. Here t h e ER s p e c t r a f o r C u ( l l 1 ) on mica a r e shown f o r s- and p- p o l a r i z e d l i g h t a t 45'. Note t h a t t h e s i g n o f ARIR i s such t h a t a p o s i t i v e v a l u e r e f e r s always t o a r e f l e c t i v i t y i n c r e a s e w i t h p o s i t i v e l y g o i n g p o t e n t i a l . The pronounced peaks i n t h e s p e c t r a a t 2.2 eV, a t t h e o n s e t o f t h e i n t e r b a n d t r a n s i t i o n , cannot be reproduced by t h e f r e e - e l e c t r o n model alone.

However, s a t i s f a c t o r y agreement between t h e o r y and experiment was o b t a i n e d when a s h i f t o f t h e i n t e r b a n d t r a n s i t i o n energy w i t h e l e c t r o d e p o t e n t i a l was t a k e n i n t o account. T h i s s h i f t amounts t o about 0 . 1 eV f o r a 0.5 V p o t e n t i a l change /12/.

The experiment cannot y e t answer t h e q u e s t i o n whether t h i s change i n band s t r u c t u r e i s s o l e l y caused by t h e p o t e n t i a l i n f l u e n c e o r whether t h e s u r f a c e r e g i o n a l r e a d y i n t h e absence o f an e x t e r n a l f i e l d possesses an e l e c t r o n i c s t r u c t u r e which d i f f e r s f r o m t h a t o f t h e b u l k because o f s u r f a c e r e c o n s t r u c t i o n . Besides an a c t u a l change i n t h e e l e c t r o n i c s t a t e s a t t h e s u r f a c e due t o t h e v e r y h i g h e l e c t r i c f i e l d which l e a d s t o a m o d u l a t i o n o f t h e i n t e r b a n d c o n t r i b u t i o n t o ER, t h e r e can be a n o t i c e a b l e m o d u l a t i o n o f t h e i n t e r b a n d t r a n s i t i o n pCoper. As was p o i n t e d o u t by Lynch 1131, t h i s may o c c u r v i a f i e l d - i n d u c e d i n d i r e c t "

i n t e r b a n d t r a n s i t i o n s . Because o f t h e h i g h f i e l d s t r e n g t h a t t a i n a b l e a t m e t a l - e l e c t r o l y t e i n t e r f a c e s , t h e u n c e r t a i n t y i n t h e wave v e c t o r p a r a l l e l t o t h e a p p l i e d f i e l d can be a p p r e c i a b l y l a r g e ( u p t o 0 . 1

W - L ) ,

hence a l l o w i n g f o r k - c o n s e r v i n g i n t e r b a n d t r a n s i t i o n s o v e r a l a r g e r v a r i e t y o f f i n a l s t a t e s t h a n i n t h e absence o f t h e f i e l d 1131.

Fig. 2

-

^ER spectra of Cu(ll1) at 45O and Fig. 3

-

Normal-incidence ER spectra s- and p-polarized light. (-) Experi- of Cu(ll0) in 1 N H,SO, for two mental curves for AU=500 mV.(---) different directions of the electric Calculated by the free-electron model. vector of the linearly polarized

(0000) Adding to the free-electron model light. U,= -0.3 V vs. SCE. AU,,=100 mV.

a O.leV shift with potential of the inter- After ref. /12/.

band transition. After ref. /12/.

I n F i g . 3 t h e n o r m a l - i n c i d e n c e ER s p e c t r a f o r C u ( l l 0 ) a r e shown f o r two d i f f e r e n t c r y s t a l l o g r a p h i c d i r e c t i o n s . T h i s p o l a r i z a t i o n a n i s o t r o p y , w h i c h was f i r s t r e p o r t e d f o r A g ( l l 0 ) by F u r t a k and Lynch /10,14,15/, r e f l e c t s t h e t w o - f o l d symmetry o f t h e surface and has been observed f o r t h e (110) f a c e s o f Cu /12/, Ag

/ l o /

and Au /16,17/. I t demonstrates a g a i n t h a t band s t r u c t u r e e f f e c t s and c r y s t a l symmetries i n f l u e n c e t h e ER e f f e c t . The dependence o f t h e p o l a r i z a t i o n a n i s o t r o p y on t h e s u r f a c e c r y s t a l l o g r a p h i c d i r e c t i o n i s shown i n F i g . 4 f o r Ag (110) as t h e e l e c t r i c v e c t o r o f t h e l i n e a r l y p o l a r i z e d l i g h t i s r o t a t e d by 360'.

I t i s i n t e r e s t i n g t o n o t e t h a t f o r Cu and Ag, A R / R i s l a r g e s t f o r e 11[001] (i.e., a c r o s s t h e a t o m i c r a i l s ) and s m a l l e s t f o r Z 11 E l 1 0 1 ( i .e., a l o n t h e d e n s e l y packed a t o m i c r a i l s ) w h i l e t h e o p p o s i t e b e h a v i o r i s found f o r AuqllO) /16,17/.

Secondly, we f i n d t h a t t h e p o l a r i z a t i o n a n i s o t r o p y i s f o u n d o v e r a wide range o f photon energy and n o t a t a l l l i m i t e d t o t h e i n t e r b a n d t r a n s i t i o n r e g i o n /18/.

The p o t e n t i a l dependence o f t h e p o l a r i z a t i o n a n i s o t r o p y i s reproduced i n F i g . 5 f o r A g ( l l O ) , where t h e h i g h e s t a n i s o t r o p y i s f o u n d a t p o t e n t i a l s p o s i t i v e o f t h e p o t e n t i a l o f z e r o charge (pzc: -1.0 V ) , w h i l e t h e a n i s o t r o p y t e n d s t o d i s a p p e a r r a t h e r q u i c k l y f o r A g ( l l 0 ) as t h e surface becomes n e g a t i v e l y charged /15/.

COO11

8

6 Fig. 4

-

^{Normal LLI}

incidence ER for Ag

2

(110) as a function

2

⁴

of surface crystall- 2 ographic direction;

'

two different 2 wave lengths.

C1lO' 0 . 1 N HC10,

.

U, = -0.4v.

0

I 1 I

1

Ag (110)

-

h = 318nm

-

-

_{Zll LllOI}

',

^/

'%-/'

I 1

- 1 2 -0 8 - 0 4 0

USCE I V

Fig. 5

-

Potential dependence of the polarization anisotropy for Ag(ll0). Normal incidence.

0.5 M NaF. AU,, = 100 mV.

CiO-140 JOURNAL DE PHYSIQUE

F i n a l l y we b r i e f l y d i s c u s s how t h e ER e f f e c t s f o r v a r i o u s c r y s t a l l o g r a p h i c s u r f a c e s compare /19,20/. T h i s was done i n t h e case o f Cu by t h e use o f a s i n g l e c r y s t a l c y l i n d e r whose a x i s was p a r a l l e l t o [110]. The v a r i o u s h i g h and l o w i n d e x f a c e s were t h e n s t u d i e d o p t i c a l l y by t h e a p p r o p r i a t e r o t a t i o n o f t h e c y l i n d e r . The r e s u l t s f o r two d i f f e r e n t wave l e n g t h s a r e shown i n F i g . 6. W h i l e t h e a n i s o t r o p y i s l a r g e s t f o r t h e (110) and a d j a c e n t faces, t h e l a r g e s t e f f e c t i n AR/R i s c l e a r l y observed f o r t h e (113) face. F o r A = 570 nm, t h e p o l a r i z a t i o n

a n i s o t r o p y a c t u a l l y i s marked o n l y around

10 (110). Since t h e h i g h i n d e x f a c e s o f t h e

0 8 t y p e ( h h l ) (h23) can be c o n s i d e r e d as

stepped s u r f a c e s w i t h (110) t e r r a c e s , i t seems t h a t t h e a n i s o t r o p y i s a

0 s c h a r a c t e r i s t i c o f t h e (110) s u r f a c e

LL p r o p e r r a t h e r t h a n o f a s u r f a c e o f

P

^{O L} t w o - f o l d symmetry i n g e n e r a l .

o 2 The r e s u l t s of F i g . 6 seem t o i n d i c a t e

t h a t t h e more open t h e s u r f a c e s t r u c t u r e i s , t h e l a r g e r t h e ER s i g n a l i s . AR/R

0 o ^{60 120 180} i s i n g e n e r a l f o u n d s m a l l e s t f o r t h e most d e n s e l y packed (111) face. T h i s has been t e n t a t i v e l y e x p l a i n e d by a smoothing Cu-cyl~nder e f f e c t f o r t h e more open s u r f a c e s , which

causes l a r g e r changes i n t h e o p t i c a l p o l a r i z a b i l i t y o f t h e s u r f a c e l a y e r w i t h (

b 1-

p o t e n t i a l /12,18/. The e l e c t r o n d e n s i t y

c o n t o u r s f o r an open s u r f a c e s h o u l d reproduce t h e wavy s t r u c t u r e o f t h e p o s i t i v e background p a r a l l e l t o t h e surface. However, as was p o i n t e d o u t by Smoluchowski /21/, t h e smoothing e f f e c t tends t o reduce any s t r u c t u r e i n t h e d e n s i t y p r o f i l e p a r a l l e l t o t h e s u r f a c e by a c c u m u l a t i n g n e g a t i v e charge i n t h e

C 60 120 180 v a l l e y s . Charging t h e m e t a l e l e c t r o d e

3

\

.

z 1 -

0

a l d e q e a p o s i t i v e p o t e n t i a l s t h e p o s i t i v e

background c o n t o u r s s h o u l d appear more Fig. 6

-

Normal-incidence ER for Cu as s t r o n g l y . Hence, t h e p o t e n t i a l induced a function of crystallographic orien- change i n t h e o p t i c a l p o l a r i z a b i l i t y o f a tation (a,b) and polarization anisotropy s u r f a c e s h o u l d be l a r g e r f o r more open (C). 1 N H2SO4. U o = -0.3 V. bur,, = 100 m ~ . s u r f a c e s t r u c t u r e s , c a u s i n g l a r g e r AR/R- After ref. /19,20/. v a l u e s as f o u n d i n t h e experiment. T h i s

e f f e c t , however, does n o t seem t o be t h e o n l y source f o r t h e p o l a r i z a t i o n a n i s o t r o p y , as i t cannot a c c o u n t f o r d e t a i l s such as t h e observed p o t e n t i a l o r wave l e n g t h dependencies o f t h e a n i s o t r o p y . F o r example, i t has been shown t h a t s u r f a c e s t a t e s a t t h e m e t a l - e l e c t r o l y t e i n t e r f a c e can p l a y a s i g n i f i c a n t r o l e f o r

I I I 1

I

I

CU-cyltnder (

C j

axis 11 t1101 h=570 nm

(1121

' 2 -

& -

--

---

t t t t t t t t

7

(111) (113) (1001 (1131 (1111 (3311(1101 (3311 (1111

I

I I

1

1 1

-

s u r f a c e w i l l a f f e c t t h e e l e c t r o n d e n s i t y d i s t r i b u t i o n n o t o n l y p e r p e n d i c u l a r t o t h e s u r f a c e b u t a l s o p a r a l l e l t o i t . While f o r a d e n s e l y packed s u r f a c e o r surface d i r e c t i o n , t h e e l e c t r o n t a i l may b e

c h a r g i n g j u s t pushed w i t h o u t outward much change w i t h n e g a t i v e i n shape, i t may change t h e d e n s i t y c o n t o u r s a t a more open s u r f a c e o r s u r f a c e d i r e c t i o n by changing t h e degree o f smoothness. A t n e g a t i v e p o t e n t i a l s t h e i n c r e a s e o f charge s h o u l d smooth o u t t h e s p a t i a l v a r i a t i o n o f t h e e l e c t r o n d e n s i t y o 60 120 180 p a r a l l e l t o t h e s u r f a c e , w h i l e a t

t h e o b s e r v a t i o n o f p o l a r i z a t i o n a n i s o t r o p y f o r 1 ow-symmetry s u r f a c e s , as w i 11 be d i s c u s s e d i n t h e f o l l o w i n g .

3

-

S u r f a c e S t a t e s a t t h e M e t a l - E l e c t r o l y t e I n t e r f a c e

The r o l e o f e l e c t r o n i c s u r f a c e s t a t e s i n e l e c t r o r e f l e c t a n c e was f i r s t p o i n t e d o u t by Ho, Harmon and L i u 1221. When c a l c u l a t i n g t h e two-dimensional ( s u r f a c e ) band s t r u c t u r e of a m e t a l , i.e., t h e p r o j e c t i o n o f t h e b u l k band s t r u c t u r e o n t o a p l a n e p a r a l l e l t o t h e s u r f a c e , energy gaps a r e f o u n d i n c e r t a i n c r y s t a l l o g r a p h i c d i r e c t i o n s . I n a s e l f - c o n s i s t e n t p s e u d o - p o t e n t i a l c a l c u l a t i o n f o r A g ( l l O ) , Ho e t a l . 1221 have shown t h a t s u r f a c e s t a t e s e x i s t i n t h e s e energy gaps, which a r e s p l i t o f f t h e volume s t a t e s a t t h e upper and l o w e r band edge o f t h e gap. Such a s i t u a t i o n i s s c h e m a t i c a l l y shown f o r Ag(100) i n F i g . 7 1231. The s u r f a c e s t a t e s A and B a r e s t r o n g l y l o c a l i z e d a t t h e s u r f a c e , and r a p i d l y decay a l o n g t h e s u r f a c e normal. As a consequence, t h e e n e r g e t i c p o s i t i o n o f t h e s u r f a c e s t a t e s w i l l depend on an a p p l i e d e x t e r n a l f i e l d i n a way which i s d i s t i n c t l y d i f f e r e n t f r o m t h a t o f t h e b u l k s t a t e s . Hence, o p t i c a l t r a n s i t i o n s f r o m t h e b u l k s t a t e s t o a s u r f a c e s t a t e s h o u l d be i n f l u e n c e d i n t h e i r energy by t h e e l e c t r o d e p o t e n t i a l . T h i s dependency can be used t o d e t e c t and i d e n t i f y s u r f a c e s t a t e s a t t h e m e t a l - e l e c t r o l y t e i n t e r f a c e . I n a c a r e f u l s t u d y /23,24/ o f t h e ER s p e c t r a o f Ag(100), two s p e c t r a l f e a t u r e s were i n d e e d observed, t h e e n e r g e t i c p o s i t i o n s o f which v a r i e d s t r o n g l y w i t h t h e e l e c t r o d e p r t e n t i a l (see F i g . 8 ) .

When t h e e l e c t r o d e p o t e n t i a l o f a metal e r e c t r o d e i s changed by 1 V p o s i t i v e l y o r n e g a t i v e l y , t h e n t h e whole b u l k band s t r u c t u r e ( i n c l u d i n g t h e Fermi l e v e l ) i s s h i f t e d w i t h r e s p e c t t o t h e vacuum l e v e l by e x a c t l y 1 eV downward ( t o h i g h e r work f u n c t i o n ) o r upward (towards l o w e r work f u n c t i o n ) . Since t h e s u r f a c e s t a t e s p e n e t r a t e somewhat i n t o t h e d o u b l e l a y e r , t h e y e x p e r i e n c e o n l y a c e r t a i n f r a c t i o n o f t h e t o t a l p o t e n t i a l d r o p across t h e Helmholtz l a y e r , as t h e e l e c t r o c h e m i c a l d o u b l e l a y e r i s f r e q u e n t l y c a l l e d . Hence t h e s u r f a c e s t a t e s a r e s h i f t e d l e s s i n energy t h a n t h e b u l k s t a t e s . As a r e s u l t , t h e o p t i c a l t r a n s i t i o n f r o m an o c c u p i e d b u l k s t a t e i n t o an empty s u r f a c e s t a t e v a r i e s w i t h p o t e n t i a l such t h a t t h e t r a n s i t i o n energy i n c r e a s e s as t h e p o t e n t i a l moves i n t h e p o s i t i v e d i r e c t i o n . Such a b e h a v i o r i s n o t i c e d f o r t h e s p e c t r a l f e a t u r e s around 3 and 1 eV i n t h e ER s p e c t r a o f Ag(100) ( F i g . 8 ) . A comparison o f t h e e x p e r i m e n t a l l y observed t r a n s i t i o n e n e r g i e s and t h e i r dependence on t h e e l e c t r o d e p o t e n t i a l (see i n s e r t o f F i g . 8 ) w i t h t h e c a l c u l a t i o n by Ho and L i u gave an almost p e r f e c t agreement, which a l l o w e d

Wave Vector

Fig. 7

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The Ag(100) pro- Fig. 8

-

Normal-incidence ER spectra of jected band structure with Ag(100) in 0.5 M NaF for various bias surface states A and B. potentials. After ref. /24/. Insert:

After ref. /23/. transition energies as a function of electrode potential.

JOURNAL DE PHYSIQUE

f o r a s a f e assignment o f t h e above mentioned s p e c t r a l f e a t u r e s i n t h e ER spectrum o f Ag(100) t o t r a n s i t i o n s from occupied b u l k s t a t e s i n t o t h e s u r f a c e s t a t e s A and B, r e s p e c t i v e l y /23/. Even t h e disappearance o f t h e t r a n s i t i o n i n t o B around -0.6 V i s f o u n d t o be i n f u l l agreement w i t h t h e o r y which p r e d i c t s t h e s u r f a c e s t a t e B t o be s h i f t e d below t h e Fermi l e v e l a t t h a t p o t e n t i a l /23/.

O p t i c a l t r a n s i t i o n s i n t o empty s u r f a c e s t a t e s have a l s o been p r e d i c t e d f o r A g ( l l 0 ) /22/. However, based on symmetry c o n s i d e r a t i o n s , such t r a n s i t i o n s s h o u l d b e p o s s i b l e o n l y f o r

T

11[001], b u t n o t f o r

5

11[110]. T h i s was i n d e e d c o n f i r m e d b y e x p e r i m e n t /24/. The p o t e n t i a l dependence o f o p t i c a l t r a n s i t i o n s i n t o empty s u r f a c e s t a t e s can a l s o be seen q u i t e c l e a r l y , when AR/R i s r e c o r d e d as a f u n c t i o n o f b i a s p o t e n t i a l f o r d i f f e r e n t wave l e n g t h s . Such curves a r e shown i n F i g . 9 f o r A g ( l l 0 ) f o r b o t h p o l a r i z a t i o n d i r e c t i o n s . Two s u r f a c e s t a t e f e a t u r e s a r e i m m e d i a t e l y r e c o g n i z e d f o r ~ l l [ 0 0 1 ] , around 1000 nm a t 0 V and around 800 nm a t -1.1 V, and t h e i r s h i f t w i t h p o t e n t i a l i s marked. No such f e a t u r e s a r e f o u n d f o r 5 \ ] [ 1 1 0 ] , where t h e s t r u c t u r e s i n AR/R do n o t s h i f t w i t h wave l e n g t h ( F i g . 9b). I t i s e v i d e n t f r o m a comparison o f F i g s . 9a and 9b, t h a t s u r f a c e s t a t e s c o n t r i b u t e i n a p r o m i n e n t way t o t h e observed p o l a r i z a t i o n a n i s o t r o p y o f A g ( l l O ) , as d i s c u s s e d i n t h e p r e v i o u s s e c t i o n .

As t h e e n e r g e t i c p o s i t i o n o f t h e s u r f a c e s t a t e s s e n s i t i v e l y depends on t h e e x t e r n a l e l e c t r i c f i e l d , i n f o r m a t i o n about t h e p o t e n t i a l d i s t r i b u t i o n near t h e metal s u r f a c e s h o u l d be o b t a i n a b l e f r o m an a n a l y s i s o f t h e s h i f t i n e x c i t a t i o n energy. I n o u r s i m p l e p i c t u r e o f t h e e l e c t r o c h e m i c a l i n t e r f a c e , which we t r e a t as a condenser w i t h 0.3 nm p l a t e d i s t a n c e /25/, we assume a l i n e a r p o t e n t i a l d r o p a c r o s s t h e d o u b l e l a y e r . I f we f u r t h e r assume t h a t t h e s u r f a c e s t a t e s probe t h e r e g i o n j u s t o u t s i d e t h e m e t a l s u r f a c e , say 0.1 nm away /22/, t h e n t h i s w o u l d y i e l d a r e l a t i v e s h i f t o f about 0.3 eV/V. Such a s h i f t has indeed been observed f o r Au(100) /17,24,26/. F o r Ag s i n g l e c r y s t a l s u r f a c e s , however, much h i g h e r s l o p e s were found, up t o 4 eV/V f o r t h e A g ( l l 0 ) s u r f a c e /24/. T h i s i n d i c a t e s t h a t t h e p o t e n t i a l d i f f e r e n c e between b u l k and s u r f a c e s t a t e s i s much l a r g e r t h a n t h a t d e r i v e d f r o m a l i n e a r p o t e n t i a l d r o p a c r o s s t h e H e l m h o l t z l a y e r . The l a r g e s h i f t s may be e x p l a i n e d by assuming a n o n - l i n e a r , s t r o n g l y v a r y i n g p o t e n t i a l d i s t r i b u t i o n w i t h i n t h e H e l m h o l t z l a y e r , caused by t h e m i c r o s c o p i c s t r u c t u r e o f t h e i n t e r f a c i a l w a t e r o r by s p e c i f i c a l l y adsorbed ions. F o r example, t h e f i n i t e s i z e o f t h e w a t e r d i p o l e s may l e a d t o

Fig. 9a

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ER signals of Ag(ll0) Fig. 9b

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ER signals of Ag(ll0) in 0.5 M NaF as a function of in 0.5 M NaF as a function of electrode potential for electrode potential for two various wave lengths. Normal different wave lengths. Normal incidence. [ O O l ] . A U p p = 100 mV. incidence.

ZI I

^{[llO]. AU,,} =

100mV. AI=double layer charging current. pzc: -1.0 V.

r e g i o n s o f o v e r s c r e e n i n g and underscreening, as has been p o i n t e d o u t i n c o r r e s p o n d i n g model c a l c u l a t i o n s 1271. The u n i t y s l o p e which i s f o u n d f o r Ag(100) i m p l i e s t h a t t h e p o t e n t i a l d i f f e r e n c e between b u l k and s u r f a c e s t a t e s , i.e., between m e t a l s u r f a c e and l o c a t i o n o f maximum d e n s i t y o f s u r f a c e s t a t e s , i s as l a r g e as t h e t o t a l p o t e n t i a l drop across t h e H e l m h o l t z l a y e r . T h i s l e a d s t o a p i c t u r e w i t h a s t r o n g l y v a r y i n g p o t e n t i a l i n t h e double l a y e r , s i m i l a r t o t h a t f o r s p e c i f i c a d s o r p t i o n where an " o v e r s h o o t i n g " o f t h e p o t e n t i a l o c c u r s 1251. The v e r y h i g h s l o p e s of 3

-

4 eV/V observed f o r A g ( l l O ) , however, a r e d i f f i c u l t t o r a t i o n a l i z e i n such a p u r e l y e l e c t r o s t a t i c d e s c r i p t i o n , and o t h e r e f f e c t s , such as chemical i n t e r a c t i o n , may have t o be c o n s i d e r e d i n a d d i t i o n .

F i n a l l y , we b r i e f l y f o c u s o u r a t t e n t i o n on t h e l i n e shape o f t h e a b s o r p t i o n band f o r t h e o p t i c a l e x c i t a t i o n i n t o s u r f a c e s t a t e s . As a consequence o f t h e m o d u l a t i o n t e c h n i q u e a p p l i e d f o r d e t e c t i n g e l e c t r o r e f l e c t a n c e s i g n a l s , t h e o p t i c a l t r a n s i t i o n s f r o m b u l k t o s u r f a c e s t a t e s g i v e r i s e t o a d e r i v a t i v e - l i k e s t r u c t u r e i n t h e ER s p e c t r a , which s h i f t s w i t h b i a s p o t e n t i a l . I n t e g r a t i o n o f t h i s s t r u c t u r e l e a d s t o t h e a c t u a l a b s o r p t i o n band, t a k i n g a reasonable background s u b t r a c t i o n i n t o account. T h i s a b s o r p t i o n band f o r s u r f a c e s t a t e B has been shown t o b e s u r p r i s i n g l y wide (about 1 eV) f o r t h e m e t a l - e l e c t r o l y t e i n t e r f a c e 1281, much w i d e r t h a n expected t o be f o r t h e metal-vacuum i n t e r f a c e ( a b o u t 0.3 eV /29/). The s m a l l v a l u e i n t h e l a t t e r case a r i s e s f r o m t h e f a c t t h a t t h e o p t i c a l t r a n s i t i o n i n t o t h e s u r f a c e s t a t e does n o t s t a r t r i g h t a t t h e t o p o f t h e b u l k band, as t h e r e b u l k and s u r f a c e s t a t e s have t h e same p - l i k e symmetry 1231. W i t h i n c r e a s i n g photon energy d e e p e r - l y i n g b u l k s t a t e s become i n v o l v e d i n t h e t r a n s i t i o n , which have a d m i x t u r e s of a l l o w e d c h a r a c t e r , and hence a b s o r p t i o n i s observed. The broadening o f t h e s u r f a c e s t a t e l e v e l up t o 1 eV r e f l e c t s t h e t i m e l y f l u c t u a t i o n s o f t h e w a t e r d i p o l e s i n t h e double l a y e r . Hence, a l i n e shape a n a l y s i s s h o u l d t h r o w some l i g h t o n t o t h e m i c r o s c o p i c s t r u c t u r e o f t h e i n t e r f a c i a l w a t e r and i t s p o t e n t i a l dependence /30,31/.

4

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C o n t r i b u t i o n s t o t h e ER from t h e Double Layer

The ER e f f e c t i s u s u a l l y dominated by c o n t r i b u t i o n s f r o m t h e metal s u r f a c e , e s p e c i a l l y i n t h e i n t e r b a n d t r a n s i t i o n r e g i o n . The p o t e n t i a l - i n d u c e d changes i n t h e o p t i c a l p r o p e r t i e s o f t h e Helmholtz l a y e r proper, which c o n s t i t u t e s a p u r e l y d i e l e c t r i c f i l m i n t h e photon energy range under study, a r e expected t o g i v e r i s e t o ARIR v a l u e s which a r e o r d e r s o f magnitude s m a l l e r t h a n t h o s e o f t h e m e t a l s u r f a c e 191. Attempts have been made i n t h e p a s t t o u n r a v e l t h e s e two t y p e s o f c o n t r i b u t i o n s f o r p o l y c r y s t a l l i n e s u r f a c e s 132,331, b u t t h e assumptions used a r e l i k e l y t o be wrong because o f o v e r - s i m p l i f i c a t i o n o f t h e m e t a l ' s r o l e i n ER.

When e x t e n d i n g t h e wave l e n g t h range f o r t h e o p t i c a l s t u d i e s i n t o t h e i n f r a r e d r e g i o n , i.e., w e l l below t h e o n s e t o f i n t e r b a n d t r a n s i t i o n s , o p t i c a l e f f e c t s o r i g i n a t i n g f r o m a p o t e n t i a l m o d u l a t i o n o f t h e H e l m h o l t z l a y e r may be seen. I n t h i s r e g i o n t h e f r e e - e l e c t r o n c o n t r i b u t i o n o f t h e m e t a l g i v e s r i s e t o a smooth and u n s t r u c t u r e d background o n l y , and e f f e c t s f r o m s u r f a c e s t a t e s can be a v o i d e d by choosing t h e a p p r o p r i a t e c r y s t a l l o g r a p h i c s u r f a c e o r s u r f a c e d i r e c t i o n (e.g., T l l [ 1 1 0 ] f o r A g ( l l 0 ) ; see p r e v i o u s s e c t i o n ) . Such a s i t u a t i o n i s shown i n F i g . 9b, where we f i n d a d e r i v a t i v e - l i k e s t r u c t u r e i n AR/R r i g h t around t h e pzc (-1.0 V), which does n o t s h i f t w i t h wave l e n g t h . T h i s s t r u c t u r e , which i s observed a l s o f o r t h e o t h e r s i n g l e c r y s t a l f a c e s o f Ag, has been i n v e s t i g a t e d i n more d e t a i l f o r t h e A g ( l l 1 ) s u r f a c e , because f o r t h i s f a c e t h e metal ER i s h a r d l y seen i n t h e i n f r a r e d . I n F i g . 10, t h e d o u b l e l a y e r c a p a c i t y o f A g ( l l 1 ) i n 0.5 M NaF i s shown and compared w i t h t h e c o r r e s p o n d i n g r e f l e c t i v i t y change a t 1000 nm w i t h p o t e n t i a l . The l a t t e r c u r v e was o b t a i n e d by i n t e g r a t i o n o f t h e ER s i g n a l -(AR/R)/ A U . The c l o s e s i m i l a r i t y between b o t h c u r v e s l e d us t o b e l i e v e t h a t t h i s d e r i v a t i v e - l ' i k e s t r u c t u r e i n t h e ER s i g n a l i s indeed o r i g i n a t i n g f r o m t h e H e l m h o l t z l a y e r . The s i g n of t h e o p t i c a l response i s such t h a t t h e r e f l e c t i v i t y o f t h e i n t e r f a c e i s l o w e s t a t t h e pzc (more s t r i c t l y speaking, a t t h e maximum o f C ~ L ) and i t i n c r e a s e s w i t h p o t e n t i a l on e i t h e r s i d e . T h i s b e h a v i o r i s r a t h e r d i f f i c u l t t o r a t i o n a l i z e i n a s i m p l e three-phase model w i t h a p u r e l y d i e l e c t r i c f i l m 1341. F o r example, a t

CIO-144 JOURNAL DE PHYSIQUE

Fig. 10

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Double layer capacity (a), Fig. 11

-

Normal-incidence ER signals integrated ER signal (b, see text) for Au(ll0) in 0.5 M NaF as a function and ER signal (c) for Ag(ll1) in 0.5 of-potential. Two different directions M NaF as a function of potential. of the electric vector. X = 800 nm.

Normal incidence. A = 1000 nm. PZC: -0.09 V.

AUpp= 112 mV. pzc:-0.67 V.

1000 nm, t h e e f f e c t i n AR/R i s t o o l a r g e t o be e x p l a i n e d s o l e l y by a change i n t h e r e f r a c t i v e index o f t h e i n t e r f a c i a l water. However, we c o u l d account f o r t h e observed e f f e c t by assuming s l i g h t l y a b s o r p t i v e p r o p e r t i e s o f t h e double l a y e r water a t t h e p o t e n t i a l o f t h e hump. Such a m o d i f i c a t i o n o f t h e water p r o p e r t i e s , which a r e p u r e l y d i e l e c t r i c f o r b u l k water a t 1000 nm, c o u l d a r i s e from a s p e c i f i c

i n t e r a c t i o n o f water w i t h t h e Ag surface, as invoked by T r a s a t t i f o r metals w i t h l a r g e i n n e r - l a y e r c a p a c i t y a t t h e pzc 1351. An a l t e r n a t e e x p l a n a t i o n may be sought i n t h e s p e c i f i c adsorption o f f l u o r i d e which was r e p o r t e d by V a l e t t e /36/ t o occur on Ag s i n g l e c r y s t a l surfaces.

A q u i t e d i f f e r e n t behavior was observed f o r gold. The p o t e n t i a l dependence o f AR/R f o r A u ( l l 0 ) a t 800 nm i s shown i n Fig. 11 f o r t h e two main c r y s t a l l o g r a p h i c d i r e c t i o n s . There i s a pronounced a n i s o t r o p y around t h e pzc (-0.09 V), which i s n o t a f f e c t e d i n shape by a wave l e n g t h change. Hence, surface s t a t e s can be excluded as a cause o f t h e anisotropy. The o p t i c a l p r o p e r t i e s o f t h e double l a y e r seem t o undergo marked changes around t h e pzc, which a r e seen o n l y w i t h l i g h t f o r

Z ] l

[OOl].

5

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The Role o f Non-Local Optics i n ER

One o f t h e g r e a t v i r t u e s o f ER a t t h e m e t a l - e l e c t r o l y t e i n t e r f a c e i s t h e h i g h s e n s i t i v i t y w i t h which r e f l e c t a n c e changes can be detected. Hence, t h e o r i e s on metal o p t i c s can be t e s t e d a g a i n s t experiment w i t h h i g h accuracy. It has been shown t h a t standard o p t i c s ( t r a n s v e r s e electromagnetic waves o n l y ) should f a i l i n d e s c r i b i n g t h e r e f l e c t i v i t y o f metal surfaces near t h e volume plasma frequency, when p - p o l a r i z e d l i g h t i s used 137,381. I n t h i s frequency r e g i o n (e.g., 3.8 eV f o r Ag), l o n g i t u d i n a l waves (plasma waves) are eigenmodes o f t h e metal which a r e o p t i c a l l y e x c i t e d w i t h p - p o l a r i z e d 1 ig h t because t h e e l e c t r i c f i e l d component normal t o t h e surface induces p e r i o d i c charge-density f l u c t u a t i o n s 1391. The l o n g i t u d i n a l waves propagate i n t o t h e metal, i n a d d i t i o n t o t h e transverse waves, and t h e r e f o r e c o n t r i b u t e t o t h e r e f l e c t a n c e and t r a n s m i t t a n c e o f t h e metal surface.

I t has been shown f o r Ag t h a t around 3.8 eV t h e ER spectra f o r p - p o l a r i z e d l i g h t c o u l d n o t be reproduced by standard o p t i c s , unless one were w i l l i n g t o assume r a t h e r p e c u l i a r o p t i c a l p r o p e r t i e s f o r t h e surface l a y e r . This discrepancy was removed by using proper metal o p t i c s , i.e., by i n c l u d i n g s p a t i a l d i s p e r s i o n

( n o n - l o c a l e f f e c t s ) i n t h e c a l c u l a t i o n /40,41/. I n t h e f o l l o w i n g t h e i n f l u e n c e o f n o n - l o c a l e f f e c t s on t h e ER s p e c t r a o f m e t a l s i s demonstrated by two examples.

When t h e ER s p e c t r a o f Au a r e c a l c u l a t e d by s t a n d a r d o p t i c s , u s i n g t h e f r e e - e l e c t r o n model, a pronounced peak i n -(AR/R) below t h e volume plasma f r e q u e n c y o f g o l d (2.5 eV) i s p r e d i c t e d f o r p - p o l a r i z a t i o n , e s p e c i a l l y f o r p o s i t i v e b i a s p o t e n t i a l s (see F i g . 12b, d o t t e d l i n e ) 1421. Such a f e a t u r e has n e v e r been observed i n experiment, and i t i s o b v i o u s l y an a r t i f a c t a r i s i n g f r o m t h e use o f an improper m e t a l o p t i c s . The e x p e r i m e n t a l s p e c t r a i n t h i s wave l e n g t h r e g i o n have about t h e same shape f o r s- and p - p o l a r i z e d l i g h t , w i t h a d i f f e r e n c e i n magnitude o f a b o u t a f a c t o r o f two f o r 45" a n g l e o f i n c i d e n c e /6,9/. When c a l c u l a t i o n s w i t h n o n - l o c a l o p t i c s a r e performed, t h e f e a t u r e d e s c r i b e d above i s no l o n g e r f o u n d i n t h e t h e o r e t i c a l spectrum ( F i g . 12, s o l i d l i n e ) , and a s p e c t r a l shape emerges w h i c h i s i n v e r y good agreement w i t h e x p e r i m e n t 1431. I n l o c a l o p t i c s i t i s assumed t h a t t h e surface l a y e r has a plasma f r e q u e n c y o f i t s own, which d i f f e r s f r o m t h e b u l k plasmon f r e q u e n c y because o f t h e f ie l d - i n d u c e d change i n t h e s u r f a c e e l e c t r o n d e n s i t y . Charging t h e Au s u r f a c e p o s i t i v e l y reduces t h e f r e e - e l e c t r o n c o n t r i b u t i o n t o t h e r e a l p a r t o f t h e Au d i e l e c t r i c c o n s t a n t E ' t o such an e x t e n t t h a t E ' o f t h e s u r f a c e l a y e r becomes z e r o a t l o w e r p h o t o n e n e r g i e s 1421. The l o c a l t r e a t m e n t o f t h e s u r f a c e l a y e r , f o r w h i c h now t h e plasmon resonance c o n d i t i o n (sl=O) i s f u l f i l l e d a t e n e r g i e s below 2.5 eV, l e a d s t o t h e pronounced peak i n -AR/R around 2.3 eV ( F i g . 12b). The c o r r e c t , n o n - l o c a l o p t i c s t r e a t s t h e s u r f a c e charge d e n s i t y n o t as s i n g u l a r i t y b u t a l l o w s a s p r e a d i n g normal t o t h e s u r f a c e , which couples t h e plasmon waves o f t h e s u r f a c e l a y e r t o t h o s e o f t h e b u l k . T h i s makes t h e ARIR v a l u e s r a t h e r i n s e n s i t i v e t o t h e s u r f a c e charge d e n s i t y , a t l e a s t i n t h e r e g i o n o f t h e plasma frequency, i n agreement w i t h e x p e r i m e n t a l f i n d i n g s .

The second example r e f e r s t o t h e ER o f a t h i n Ag o v e r l a y e r on A u ( l l 1 ) 1441. I n F i g . 13, AR/R i s shown f o r s e v e r a l wave l e n g t h s around t h e plasma frequency o f Ag as a f u n c t i o n o f t h i c k n e s s D o f t h e Ag f i l m , which was d e p o s i t e d o n t o A u ( l l 1 ) under d i f f u s i o n c o n t r o l l e d c o n d i t i o n s . We n o t e pronounced o s c i l l a t i o n s i n AR/R f o r p - p o l a r i z e d l i g h t , w h i l e f o r s - p o l a r i z a t i o n a smooth c u r v e i s f o u n d (we i g n o r e f o r t h i s c o n s i d e r a t i o n t h e t h i c k n e s s r e g i o n below 0.5 nm because t h e o p t i c a l p r o p e r t i e s o f t h e f i r s t monolayer a r e s t r o n g l y coverage dependent and hence cause s t r u c t u r e s i n ARIR f o r &tJp o l a r i z a t i o n s ) . The o s c i l l a t i o n s i n AR/R f o r p - p o l a r i z e d l i g h t a r e caused b y t h e f o r m a t i o n o f s t a n d i n g plasma waves as t h e Ag f i l m a c q u i r e s c e r t a i n m u l t i p l e t h i c k n e s s values. These f e a t u r e s have been reproduced b y n o n - l o c a l o p t i c s assuming b u l k o p t i c a l p r o p e r t i e s f o r t h e A g - f i l m 1441. An

3 1 1 1 1 1 1 1

Fig. 12

-

Calculated ER spectra for Au at 45' for two different potential steps. (---) s-polarization; ⁽⁷⁾p-polarization with plasma waves ; (.--- ) p-polarization with local optics. 0.4 nm thick surface layer;

free electron density change from (a) 0.82 to 0.77, and (b) 0.70 to 0.65 of n

(pzc: 1~0.75). After ref. / 4 3 / .

Fig. 13

-

^ER signals for Au(ll1) during deposition of an Ag over- layer of thickness D. % = 45O- (-) p- and (---) s-polarization.

AUpP= 100 mV. After ref. /44/.

CIO-146 J O U R N A L DE PHYSIQUE

e v a l u a t i o n o f t h e curves i n F i g . 13 by c l a s s i c a l o p t i c s c l e a r l y would be m i s l e a d i n g as we would be f o r c e d t o assume strange, o s c i l l a t i n g o p t i c a l p r o p e r t i e s o f t h e Ag f i l m , which i s n o t t h e case.

Acknowledgement: T h i s a r t i c l e was w r i t t e n w h i l e t h e a u t h o r was a V i s i t i n g S c i e n t i s t a t t h e IBM Thomas 3. Watson Research Center, Yorktown H e i g h t s , U.S.A.

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