ELECTROREFLECTANCEOFSINGLECRYSTALMETALS

Thomas Elton Furtak

I

Ph. D. Thesis Submitted to Iowa State Unive~sity

. .

Arnes Laboratory, ERDA Iowa State University

Ames, Iowa 5001 1

PREPARED FOR THE U. S. ENERGY RESEARCH AND DEVELOPMENT ADMINISTRATION UNDER CONTRACT NO. W-7405-g-82

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iii

Electroreflectance of single crystal metals

Thomas.Elton Furtak

, ' .

A Dissertation Submitted to the

Graduate Faculty in Partial Fulfillment of . . . .

The Requirements for the Degree of . .

DOCTOR OF PHILOSOPHY

Department: Physics , . Major: Sol id State Physics

. .

Approved : . .

. .

. . . . . . .

. For t h p a j o r ~epaitment .. .

Iowa state University . . . . Ames ,. .Iowa . .. .

Abstract

CHAPTER I. INTRODUCTION

CHAPTER I I . EXPERIMENTAL

CHAPTER I l l . RESULTS

CHAPTER I V . DISCUSSION

APPEND l X A. ANOMALOUS RESULTS

APPENDIX B. ELECTRONIC AND OPTICAL PROPERTIES OF THE NOBLE METALS

APPEND1X.C. ELECTROCHEMISTRY

APPEND I x D. L I NEAR APPROX I MAT I ON THEORY FOR S T R A T I F I E D MEDIA

REFERENCES

ACKNOWLEDGMENTS

P a g e v

1

:> E lec t ro re f l ec tance o f s i n g l e c r y s t a l metals

Thomas E l t o n Fur tak

Under the superv is ion o f David W. Lynch From the Department o f Physics

Iowa Sta te U n i v e r s i t y

Measurements o f t h e normal incidence, po la r i zed l i g h t e l e c t r o -

r c f lectance o f clean, s t r a i n f r e e ( 1 10) and (100) Ag, from' 3 e~ t o 4.2

eV, and ( 1 10) Au, from 1.6 eV t o 4.0 e ~ , were performed us ing t h e

e l e c t r o l y t e technique i n a novel drop conf igura t ion . A t 3.9 eV i n A g . . . .

a dramatic rep roduc ib le anisotropy i n t h e negat ive peak ~ ~ R - ' A R / A P , ' ' .

': t h a t was unquest ionably c o r r e l a t e d w i t h t h e o r i e n t a t i o n o f t h e c r y s t a l , . .

was observed' on l y on t h e ( 1 10) face. No anisotropy was detected i n

t h e e lec t ro re f l ec tance of A". A d e t a i l e d s tudy of t h e an iso t rop ic

spectrum was conducted as a func t ion of surface preparat ion, s o l u t i o n , .

composition, sample b ias p o t e n t i a l , and modulat ion amplitude.

The resu 1 t s of t h i s research have demonstrated beyond doubt t h a t

t he e lec t ro re f l ec tance on the (110) surface o f Ag invo lves a modulat ion '

o f e l e c t r o n s ta tes t h a t possess t h e c r y s t a l sur face symmetry. The most

p l a u s i b l e i n te rp re ta t i on , excluding such e x o t i c mechanisms as i n t r i n s i c

sur face s ta tes o r an an iso t rop ic e l e c t r o n gas, involves a combined

e f f e c t o f a Mclntyre-Aspnes-l ike charge modulation, which i s respon-

s i b l e f o r t h e gross d e t a i l s , and f i e l d asq is ted i n d i r e c t in terband

t r a n s i t i o n s which add an an iso t rop ic con t r i bu t i on .

-1.

"USERDA Report IS-T-697. This work was performed u n d e f c o n t r a c t W-7405-eng-82 w i t h t h e Energy Research, and Development Admi n i s t ra ' t ion.

1

CHAPTER I. INTRODUCTION

Preambl e

~ r a d i t i o n a l ' l y 1 i q u i d ma te r ia l s science has been t h e i n t e r e s t o f

chemistry and s o l i d ma te r ia l s science has been i n t h e realm.of physics.

E lec t ro re f 1 ectance o f metals us ing t h e e l e c t r o l y t e technique imp1 ies

t h e presence o f t h e j u n c t i o n o f a . s o l i d and a l i q u i d a t an interphase

boundary. To understand p roper l y and i n t e r p r e t such s tud ies requ i res

. . a background i n s o l i d s t a t e physics as w e l l as e lec t roch& is t r y .

This d i , sse r ta t i on i s presented w i t h a b i a s toward s o l i d s t a t e

phys ica l ideas bu t i t i s meant t o represent the.complete r n u l t i - d i s c i -

p l inary e f f o r t . To a i d t h e understanding o f concepts and d e f i n i t i o n s

which are p e c u l i a r t o chemistry o r physics, Appendices B and C have . . .

been included. They g i ve a t u t o r i a l d iscuss ion o f what i s appropr ia te

from each o f the'se f i e l d s t o t h e i n t e r p r e t a t i o n o f t h i s research. I ' .

w i l l assume t h a t the reader i s f a m i l i a r w i t h t h e ma te r ia l i n these

appendices. However s p e c i f i c r e f e r r a l w i l l be made i n several places

f o r emphasi s.

Although some e f f o r t has been d i r e c t e d a t t h e experimental and

theore t ic 'a l study o f metal 1 i c e l e c t r o r e f lectance [ER) , i t has remained a

poor l y understood phenomenon. Involv ing, as i t does, a r & l t i d i s c i p l i-

nary approach, i t s in terpr .e, tat fon has n o t ,received t h e a t t e n t i o n o f

e i t h e r chemistry o r physics. I n t he c u r r e n t surge o f a c t i v l t y concern-

i n g surface s tud ies i t i's becoming more important t o decipher t h e

myster ies o f t h e sol i d / s o l u t ion boundary. Metal 1 i c ER holds a

of revea l i ng in format ion on t h e e l e c t r o n i c s t r u c t u r e o f t h e i n t e r f a c e

as we l l as t h e energet ics o f c a t a l y s i s and chemical bonding. I t may '

be one o f t h e few ways t o modify and thereby study the sur face region

o f metals where i n t r i n s i c o r more complex surface s ta tes might e x i s t .

I t was t h e purpose of my research p r o j e c t t o perform proper ly

c o n t r o l l e d e lec t rochemis t ry and sur face prepara t ion on metal s i n g l e

c r y s t a l s i n u t i l i z i n g the e l e c t r o l y t e method o f s tudy ing e l e c t r o r e -

f lectance. I t was planned t o use normal ly inc ident , po la r i zed l i g h t

t o t r y t o observe t h e symmetry breaking character o f t h e f i ' e ld . ' .

An attempt would be made t o i d e n t i f y ER due t o e l e c t r o n i c i n t e r a c t i o n s . ' .

, w i t h t h e p e r i o d i c l a t t l ce , thus demonstrat ing t h e p a r t i c i p a t i o n o f

bound electrons.

.E 1 e c t r o r e f 1 ectance 192

Modulat ion techniques3 have proven usefu l i n o p t i c a l s tud ies by , . ,

t h e i r a b i l i t y t o enhance s t ruc ture . E l e c t r i c f i e l d modulat ion o f . t h e

r e f l e c t i v i t y , o r e l e c t r o r e f lectance (ER), a ids t h e assignment o f

c r i t i c a l p o i n t energies i n semiconductors w i t h i t s uncommonly h igh

reso lu t ion . With o ther modulat ions such as s t r a i n and heat, e lec t ron

momentum i s s t i 1 1 a good quantum number, t o w i t h i n a rec ip roca l 1 a t -

t i c e vector, even when t h e symmetry i s lowered by t h e modulation. The

e l e c t r i c f i e l d (a Imposes a c o n t r i b u t i o n t o t h e one e l e c t r o n Hamil-

t on ian w h i c h . i s n0.L t r a n s l a t i o n a l l y i nva r ian t . The ' e lec t ron momentum

p a r a l l e l t o t h e f i e l d i s no longer a good quantum number i n an e l e c t r i c

f i e l d per turbed c r y s t a l . This causes m ix ing o f t he one-el ec t ron B'loch

funct ions. The r e s u l t i s equ iva lent t o spreading a fo rmer l y sharp

t r a n s i t i o n over a r a n g e o f ' i n i t i a l and f i n a l momenta. I f ? i s small,

t h e m ix ing i s r e s t r i c t e d t o wave func t i ons w i t h momenta near t h a t o f

t h e o r i g i n a l l y v e r t i c a l allowed t r a n s i t i o n . Th is produces a compli-

cated pe r tu rba t ion i n t h e d i e l e c t r i c funct ion, s, t h a t approximates

4 i t s t h i r d d e r i v a t i v e w i t h respect t o photon energy. For t h i s reason

ER i n semiconductors and i n s u l a t o r s d i sp lays extremely sharp spectra.

For h igher f ields,,changes i n t h e d i e l e c t r i c f u n c t i o n ' c a n be expressed

i n terms o f e l e c t r o - o p t i c func t i ons t h a t are der ived us ing t h e now

c l a s s i c Franz-Keldysh theory.' Th is f i e ld -ass i s ted absorp t ion i s an

even f u n c t i o n o f t h e f i e l d -- independent o f t h e sign.

Experimental ly, two basic techniques are employed t o apply an

e l e c t r i c f i e l d t o a so l id .3 Provided t h e ma te r ia l has a h i g h enough

r e s i s t i v i t y , t h e f i e l d can be imposed by b r u t e f o r c e t ransversely,

perpendicular t o t h e d i r e c t i o n o f t h e i nc iden t photon beam, v i a ohmic

contac ts o r c a p a c i t i v e coupl ing. The advantage o f t h i s c o n f i g u r a t i o n

i s t h a t t h e photon f i e l d can be a l igned perpendicular o r p a r a l l e l t o

t h e p e r t u r b i n g f i e l d making poss ib le a v a r i e t y of symmetry studies.

The second technique i s t o apply t h e pe r tu rb ing f i e l d normal t o t h e

sample sur face by employing some type O F o p t i c a l l y t ransparent e lec-

trode. One way t o do t h i s i s w i t h a ' c a p a c i t o r - l i k e package us ing an

Insu la to r , a n a t i L e o r deposited oxide, t o separate t h e f i e l d e lec t rode

f rvm t h e sample. The magnitude o f t h e e l e c t r i c f i e l d p o s s i b l e w i t h

t h e capac i to r package i s l i m i t e d by t h e breakdown s t reng th (about

5 10 ~ / c m ) o f a v a i l a b l e i n s u l a t i n g mater ia ls . The o the r l o n g i t u d i n a l

method uses t h e intense e l e c t r i c f i e l d a t t h e i n t e r f a c e between a

sol i d and an e l e c t r o l y t i c so lu t ion . The " t ransparent e lectrode" i n .

t h i s c o n f i g u r a t i o n i s a l aye r o f ions i n t h e e l e c t r o l y t e which come

very c lose t o the s o l i d surface. I t i s poss ib le t o achieve f i e l d s

up t o l o 7 V/cm by ,app ly ing o n l y a few v o l t s across t h e in ter face. The "

e l e c t r o l y t e method i s l i m i t e d by t h e transparency and temperature

range imposed by t h e e l e c t r o l y t e , and by I n t e r f e r i n g compl icat ions

due t o t h e e lec t rochemis t ry o f t h e system. I t is, nevertheless, t h e

o n l y way t o apply such intense e l e c t r i c f i e l d s t o a large, f l a t o p t i c a l

sur face and i s t h e most e f f e c t i v e technique i n t h e extension o f e lec-

t r o r e f lectance t o metals.

The q u a n t i t y o f i n t e r e s t t h a t i s exper imenta l ly access ib le i s

t h e l oga r i t hm ic d e r i v a t i v e o f t h e r e f l e c t i v i t y , m/R. The most com-

monly used procedure i s . t o impose a p e r i o d i c a l l y va ry ing f i e l d by one

o f t h e p rev ious l y mentioned methods. The p e r i o d i c component o f t h e

r e f l e c t e d i n t e n s i t y , which i s p ropor t i ona l t o AR, i s e x t r a c t e d . w i t h

phase s e n s i t i v e e lec t ron ics . By d i v i d i n g ' t h i s by t h e average va lue

of t h e . r e f lea ted in tens i t y , which i s propo.rtfona1 t o R,. AR/R i s obtained.

E l e c t r o r e f lectance i n Metals . .

The penef r a t i o n depth o f t h e e l e c t r i c f i e l d beyond t h e sur face

of an absorbing semicandiic.Lor I s o f t h e same order o f magnitude as t h e

penet ra t ion depth o f i nc iden t plroLons. I n metals, however, due t o t h e

h i g h dens i t y o f mob i le e lectrons, a s t a t i c e l e c t r i c f i e l d i s screened

o u t w i t h i n a sho r t d is tance of t h e surface. The Thomas-Fermi screening I

l ength f o r t y p i c a l m e t a l l i c parameters i s l ess than 1 i. Since t h e

photon penetrates up t o 10,000 A, i t was not expected t o be an ef fec-

t i v e probe o f any pe r tu rba t ion due t o a s t a t i c f i e l d a t t h e sur face . ,

o f a metal. However, apparent ly due t o t h e importance o f t h e sur.face

i n determining the r e f l e c t i v i t y , exper imental ly observed .e lec t rore-

f l ec tance i s a rea l ' i t y . An exce l l en t review o f t h e s i t u a t i o n up t'o

6 1972 i s o f f e r e d by Mclntyre, who himself has con t r i bu ted ex tens ive ly

t o the understanding o f t h i s phenomenon.

Experimental evidence

Well-documented e lec t ro re f l ec tance experiments have been per-

formed on Au, Ag, Cu, Pb, and P t . Most of t he work employs t h e ,

e l e c t r o l y t e technique on t h i n f i l m samples. Many i n v e s t i g a t i o n s in -

volved poor o r unspec i f ied chemical technique. A l l t h e ER s tud ies

on b u l k metals have been performed w i t h polish-damaged surfaces.

7 The f i r s t spectroscopic repor t of metal 1 i c ER was by ~ e i n l e i b .

He looked a t poli 'shed bu lk Ag, and Films of Au. Using an aqueous

KC1 e l e c t r o l y t e and app ly ing a 2 V p-p modulat ion between t h e sample

and a P t a u x i l i a r y electrode, he observed a AR/R o f t h e order o f a

few tenths of a percent. Peaks i n OR/R vs photon energy were reported

a t 3.9 eV i n Ag and a t 2.35 eV i n Au. The quant i t a t i ve . ' s ign i f i cance

of t h i s work i s i n doubt s ince t h e modulat ion p o t e n t i a l excurs ions

probably encompassed cond i t i ons whe,re reac t lohs were modi fy ing t h e

in ter face. Since proper techniques were no t fo l lowed i t i s dangerous

t o base any conclus ions on h i s data.. The appearence o f F e i n l e i b ' s

paper, however, a t t r a c t e d t h e i n t e r e s t o f chem,ists and p h y s i c i s t s a l i ke .

6

8 Buckman and together w i t h ~ashara ' a p p l i e d t h e technique o f modu-

l a ted e l l i psomet ry t o t h e ER o f Au and Ag f i l m s i n 1 M KCl. The output

o f t h e i r experiment was a spect ra l representa t ion o f t h e changes i n the

d i e l e c t r i c funct ion. The i r data were n o t causal ly , (Kramers-Kronig)

cons is ten t however, which can be blamed on t h e . s e n s i t i v i t y and as-

sumptions t h a t go i n t o e l l i p s o m e t r i c analysis.

The most r e l i a b l e ER experiments t i l l now were performed by

Mclntyre, who es tab l ished c a r e f u l l y c o n t r o l l e d electrochemi.ca1 condi-

t ions . F igure l a shows h i s ER o f a t h i n f i l m of us ing photons

inc ident on t h e sample a t an angle o f 45". The photon f i e l d was

po la r i zed perpendicular (I) o r para1 l e l ( 1 1 ) t o t h e p lane of incidence.

There i s a sharp peak a t 3.9 eV and some weaker s t r u c t u r e near 3.3 eV.

The ER of a Au t h i n f i l m as measured by ~ c l n t ~ r e ' l i s shown i n F igu re

lb. Th is spectrum i s dominated by a broad peak a t 2.5 eV and some

smal ler s t r u c t u r e near 3.5 eV. Although i t i s no t i nd i ca ted i n

F igure 1, the peaks a re i n t h e negat ive d i r e c t i o n . That is, t h e

r e f l e c t i v i t y i s a decreasing f u n c t i o n o f e lec t rode potent ia l . .

Yeager and co-workers measured r e f l e c t i v i t y i n a m u l t i p l e r e f l e c -

t i o n c e l l as a f u n c t i o n o f e lec t rode p o t e n t i a l ( I ) then numer ica l ly

ca l cu la ted R " ~ R / ~ I . ~ ~ ' ~ ~ Thei r samples were Au f i l m s i n e l e c t r o -

l y t e s o f HC104, H2S04, and NaC104. By per forming t h e i r ana lys is a t

var ious pliuton energies they obta ined spect ra l in fo rmat ion. Due t o

t h e uncer ta in ty involved i n t h i s technique compared t o t h e e l e c t r o n i c

d e r i v a t i v e method, t h e i r r e s u l t s a re tenuous. They observed t h e broad

peak near 2.5 .eV and 'reported tha t . i t s h i f t e d t o lower photon energies

Figure 1. E lec t ro re f l ec tance o f m e t a l l i c t h i n f i l m s as measured by Mc lny t re w i t h 45" inc iden t 1 i g h t po la r i zed para1 l e l ( 1 1 ) and perpendicular (L) t o . t he p lane o f i-ncidence. ( a ) Ag f i l m i n 1 M NaC 104, QDC = -0.5 V (sCE) , QAC = 100 mV rms a t 27 Hz ; (b) AU f i l m i n 1 N ~ ~ 1 0 ~ ~ QDC = O.l.6 v (SCE), ~q = 1.91

'kcoul/cm2 a t 270 Hz, dot ted 1 i ne calculat ,ed w i t h Mc ln ty re- . Aspnes model.

as the average va lue of t he e lec t rode p o t e n t i a l increased. They a l so

noted t h e s i m i l a r i t y between t h e ER spectra and a d i f f e r e n c e spectrum

ca lcu la ted between an ox id i zed and a c lean Au f i l m .

Russian e l e c t r o c h e m i , ~ t s ~ ~ ' ~ ~ inves t iga ted t h e i n f l uence o f i on

t h e ER o f Au and P t bu l k samples i n 1N H2S04. They experienced con-

taminat ion problems which caused unreproi luc ib le resu l t s . On a ' g i v e n . : *

sample they repor t t he peak a t 2.5 eV i n Au but i t d i d n o t s h i f t w i t h

changing @. The d i f f e r e n t i a l capacitance of t he double layer (Cdl),.

which they a lso monitored as a func t i on of @, showed no obvious

s i m i l a r i t y i n form t o the R-I AR(@) data. Th is they i n te rp re ted as

imp ly ing t h a t t he ER e f f e c t d i d not scale w i t h charge. A secondary

s t r u c t u r e appeared i n the Au spect ra l r e s u l t s near 3.6 eV f o r @ g reater

than zero v o l t s SCE which disappeared when t h e e lec t rode was c a t h o d i c a l l y

t reated. This was expla ined as an ox ide e f fec t .

A considerable e f f o r t o f doubt fu l va lue has been con t r i bu ted by

Garr igos and associates. Over a per iod o f f ou r years they have in -

16 ves t iga ted Eb o f b u l k samples of Ag and Au. l7 They have always

mechanical ly po l ished t h e i r surfaces, even w i t h s i n g l e c r y s t a l samples,

and have r insed them i n I1degreaser" j u s t p r i o r t o p l a c i n g them i n t h e i r

c e l l . ~ h e ~ ' m a k e no attempt t o e l i m i n a t e t h e work damage. . E a r l i e r ex-

periments were performed.under undefined e lec t rochGica1. cond i t ions .

Even more recent, p roper ly c o n t r o l l e d . work shows evidence o f severe ,

18 contamination. A Kramers-Kronig invers ion was used i n one paper 17

t o attempt an e x t r a c t i o n of t h e e f f e c t i v e change i n t h e d i e l e c t r i c

. f u n c t i o n due t o t h e pe r tu rb ing f i e l d . They assumed t h a t t h e

semiconductor data ana lys is techniques were appl icable. ~odever , '

s ince these equations apply on ly t o a uniform, deeply pene t ra t i ng

per turbat ion, t h e i r extension t o ER i n metals i s c l e a r l y incor rec t .

Anderson and an sen" e x p l o i t e d t h e at tenuated i n t e r n a l r e f l e c t ion

(ATR) scheme on t h i n f i l m s (< 200 i) o f Au and Cu i n 0.1 M Na2S04.

They reported broad s t r u c t u r e a t 2.5 eV i n gold .but t h e data q u i t a t

3.0 eV. I t i s d i f f i c u l t t o assess t h e s i g n i f i c a n c e o f t h e i r work s ince

.a lmost no in format ion was o f f e r e d on t h e i r experimental procedure.

A very recent d e s c r i p t i o n has appeared by Abelbs e t a l .20 o f re-

l i a b l e ATR experiments u t i l i z i n g t h e e x c i t a t i o n of a non- rad ia t i ve

sur face plasma resonance a t 2.034 eV between a Au f i l m and e l e c t r o l y t e s

o f H2S04 and HC104. By observ ing how changes i n t h e surface plasmon

wave vec tor wi t'h e lec t rode charge va r ied between t h e two so lu t ions ,

they c l a i m t o have separated t h e e f f e c t due t o t h e metal from t h a t oc-

c u r r i n g i n the e l e c t r o l y t e . The ana lys i s depends on an o v e r s i m p l i f i e d

t reatment o f t h e o p t i c a l e f f e c t o f ' t h e double layer. due t o Stedman

(see next sect ion) ,

One e a r l y attempt was made t o perform m e t a l l i c ER w i thou t r e s o r t -

2 1 i n g t o t h e e l e c t r o l y t e technique. S tad ler t r i e d evaporat ing t h i n

f i l m s of Au on t h e sur face of a f e r r o e l e c t r i c c r y s t a l (BaTiO ). The 3 atomic displacement i n t h i s ma te r ia l causes l o c a l l y in tense e l e c t r i c

8 . f i e l d s (10 V/cm) which are a v a i l a b l e a t t h e Au inter face. -The photon

beam was i nc iden t from t h e a i r s ide and supposedly sampled t h e e l e c t r i c

f i e l d per turbed region on the f e r r o e l e c t r i c s ide o f t h e Au f i l m .

P i e z o e l e c t r i c e f fec ts were e l im ina ted as a cause o f t h e s t r u c t u r e a t

2.5 eV by comparing t h e e f f e c t o f a one-signed . d r i v i n g vo l tage w i t h

t h a t of t h e synimetric waveform used t o reverse t h e f e r r o e l e c t r i c d i s -

placement.

I n view o f t h e v a r i e t y o f methods and l e v e l s o f s o p h i s t i c a t i o n

which have been employed t o study ER i n metals, i t i s remarkable t h a t

t he data a re so s im i la r . V i r t u a l l y every attempt us ing Au as a sample

has revealed some s t r u c t u r e i n a R / R near 2.5 eV w h i l e t h e work on Ag

always shows something a t 3.9 eV. A c lose r study of t h e cond i t i ons

which apply a t t h e e l e c t r i p f i e l d per turbed metal sur face suggests an

explanat ion f o r t h i s resemblence. The t h i n per turbed reg ion o f t h e

metal imposes an e f f e c t i v e ' i n t e r m e d i a t e phase between t h e b u l k metal

and the so lu t i on . The r e f l e c t i v i t y o f t h e system i s a func t i on o f t h e

o p t i c a l p roper t i es o f a l l t h ree phases, and i n p a r t i c u l a r , o f t h e

o p t i c a l coup1 ing a t each phase boundary. A t 2.5 eV i n Au and 3.9 eV

i n Ag, t h e b u l k metal o p t i c a l p roper t i es a re changing r a p i d l y w i t h

photon energy. I t seems l o g i c a l tha t , i n such a mul t iphase assembly,

these a re t h e l oca t ions o f s t ruc ture , regardless o f t h e modulat ion

mechanism i n t h e intermediate layer , Th is makcs a t h e o r e t i c a l I n t e r -

p r e t a t i o n d i f f i c u l t .

Theore t ica l i n t e r p r e t a t i o n s

. Ea r l y ideas The f i r s t attempt t o exp la in m e t a l l i c ER was pro-

posed by ~ e i n l e i b.7 T h ~ t model, however, was based on a two phase op-

t i c a l system which i s n o t v a l i d s ince i t ignores t h e ex is tence of t h e

double l aye r i n t h e e l e ~ t r o l ~ t e ' ~ t h e metal. A phenomenological

d e s c r i p t i o n was presented by Prostak and ans sen^' based on a f i e l d i n -

duced r i g i d s h i f t i n energy o f t h e o p t i c a l p roper t i es o f a 0.5 a . layer

o f metal. No j u s t i f i c a t i o n f o r t h e s h i f t was given. Later, Hansen and

~ r o s t a k ~ ~ expla ined t h a t a change i n e lec t ron dens i t y i n t h e surface re-

g ion induces a sh i . f t of t h e Fermi l e v e l w i t h respect t o t h e b u l k band

s t ruc ture . This, they argued, was t h e source o f t h e r i g i d s h i f t . Th is

forma.lism p r e d i c t s A R / R o f bo th s igns f o r a ma te r ia l such as Ag, which

exper imenta l ly e x h i b i t s on l y a negat ive peak (F igure la) .

E l e c t r o l y t e e f fec ts 24

Stedman has ca l cu la ted t h e o p t i c a l e f -

f.ect of changes i n i o n i c concent ra t ion i n t h e d i f f u s e laye r o f t h e

e l e c t r o l y t e due t o changes i n e lec t rode charge. There was no spec t ra l

in fo rmat ion i n her resu l ts , which pred ic ted a c o n t r i b u t i o n t o normal

2 inc idence A R / R o f up t o 3 x 1 0 - ~ f o r a charge v a r i a t i o n of 10 pcoul/crn . A "speculat ive" extensionz5 o f t h e theory t o inc lude inner l aye r e f -

f e c t s was based on t h e compression o f water and an a d d i t i o n t o t h e

concent ra t ion mechanism due t o s p e c i f i c a l l y adsorbed ions, Th is added

a A R / R as h igh as 10-' f o r o b l i q u e incidence, ma.inly due t o t h e adsorp-

t i o n con t r i bu t i on . The model on which these conclusions were based

contained many doubt fu l assumptions, i nc lud ing t h e use o f ion re-

f r a c t i v i t i e s der ived from measurements on d i l u t e b u l k so lu t ions .

Assuming no specia l mechanism bu t employing t h e l i n e a r approxima-

6 t i .on (LA) theory (Appendix D) f o r a th ree phase system, Mc ln ty re has

shown t h a t a simple d i s c r i m i n a t i o n between metal 1 i c and s o l u t i o n

e f f e c t s can be made. I f the modulat ion occurs i n t h e e l e c t r o l y t e ,

w i t h an angle of inc idence o f 45", A R / R i s small and f i n t t e f o r

s - p o l a r i z a t i o n (perpendicular t o t h e plane of incidence) bu t zero

f o r p - p o l a r i z a t i o n ( p a r a l l e l t o t h e plane o f incidence). The reason

2 6 f o r t h i s i s t h a t t h e Brewster angle between two t ransparent media

w i t h n e a r l y t h e same o p t i c a l constants i s very near 45". The modu-

l a t e d e l e c t r o l y t e l aye r becomes l l i nv i s ib le l l under these cond i t i ons

w i t h p-po lar ized l i g h t . Whereas, us ing t h e LA theory, if t h e modula-

t i o n occurs i n a l a y e r which has o p t i c a l p roper t i es which s l i g h t l y

dev ia te from' t h e metal 1 i c values, then a t 45', AR/R f o r p - p o l a r i z a t i o n

i s approximately t w i c e t h e va lue of AR/R f o r s -po lar iza t ion . Th is

app l ies regardless o f t h e modulat ion mechanism. From F igu re 1 i t i s

ev ident that , i f these arguments apply, t h e change occurs i n t h e

metal, n o t t he e l e c t r o l y t e . i t i s expected t h a t e l e c t r o l y t e e f fec ts

a re no t important.

Surface s t a t e theo ry 12

Cahan, Horkans, and Yeager proposed

an explanat ion of ER i n Au t h a t hypothesized t h e ex is tence o f i n -

t r i n s i c surface states. These s ta tes were claimed t o be present due . '

t o t h e t r u n c a t i o n o f t he l a t t i c e and were sa id t o be caused by a d i s -

t o r t i o n of t h e d-band toward t h e Fermi l eve l i n t h e sur face region.

They o f fe red as proof, t h e presence o f a t a i l i n g o f a,bsorption i n

unmodulated Au t o lower energies than t h e expected d-band t o Fermi

l e v e l gap. (This, however, can be a t t r i b u t e d t o ' l o w e r energy i n t e r -

band t r a n s i t i o n s i n t h e bulk. Appendix B) The i r idea f o r modulat ion

comes from a s h i f t i n g o f these sur face s ta tes w i t h @. It , i s more

1 i k e l y t h a t any sur face s ta tes are caused because o f a complex i n t e r -

act. ion between t h e metal and s o l u t i o n sides o f t h e double layer. These

6 are best re fer red t o as e x t r i n s i c surface states. The energy

spec i f i ca t ion o f surface states, whether i n t r i n s i c o r ex t r ins ic , i s

a complicated problem and cannot be t reated by simply assuming bu lk

band d i s t o r t i o n i n the surface region.

The Mclntyre-Aspnes theory - The most successful theory o f

metal l ' i c ER has been formulated by Mclntyre and Aspnes 6~11,27528 (H-A).

The basic assumption i s t ha t the bound electrons are = i t he r " s t i f f a l . o r

we1 1 shielded by the f ree-electrons so that, t o 1 s t order, the on ly ,

modi f ica t ion of the o p t i c a l proper t ies of the metal i n the surface re-

gion involves the f r ee e lec t ron component. Their evidence f o r th. is . \

i s tha t d-states have small o r b i t s compared t o sp-states o f comparable

energy. There a re ' e r ro r s of constant fac to rs i n the presentat ion o f

the M-A theory i n references 6 and 28. A cor rec t reproduct ion' o f the

, bas i c ideas i s presented here.

The l i nea r approximation (LA) theory fo r a s p a t i a l l y vary ing

per turbat ion o f a substrate (s) i n contact w i t h an ambient medium (a)

i s used t o describe the 'opt ica l i n te rac t ion w i t h the inter face. Eqs.

( D - 1 ) . (D-2), and (0-4) appiy.. This y i e l d s a formula f o r AR/R i n

terms of t h e . s p a t i a l l y averaged change i n the substrate d i e l e c t r i c

function, (AoS). The substrate f r e e e lec t ron d i e l e c t r i c funct ion . ' .

f E (w) f o r photon energy 'hw, which depends on the e lec t rnn densi.ty, N, . .

S

through the plasma frequency, w i s given by Eq. ( B - 5 ) . According P'

t o the theory, the only source o f modulation i s Au, /w = ( ~ / ~ ) A N / N . When P P

the f l uc tua t i on i n ' e l e c t r o n densi ty i s expressed i n terms of a change

i n t h e charge on t h e electrode, a concise form f o r t h e M-A (asS) i s

obtained.

When t h i s i s s u b s t i t u t e d i n t o t h e LA theory, t h e r e s u l t i s

The f i n a l form i s independent of t h e screening length, d, and

scales w i t h t h e charge modulat ion amplitude. When T i n Eq. (8-5)

i s small, as i s t h e case f o r , t h e noble metals i n t h e v i s i b l e and uv

r e g i o n s o f the spectrum, sz i s dominated by i t s l a r g e , negat ive rea l .

par t . Under these condi-t ions, f o r w << w AR/R i s negative. Since P'

f s i s devoid of s t ruc ture , t h e mai.n source o f t h e exper imental ly ob-

s - 1

served peaks, according t o t h e M-A theory, i s due t o - I m ( o S - sa) . I t fo l lows t h a t t h e ER spectra should have a s i m i l a r i t y w i t h t h e l oss

- 1 funct ion, -Im(eS) .

MC l n ty re l ' has extended t h i s theory t o non-normal incidence and

has compared it t o h i s measured ER on Au. The do t ted l i n e s i n F igu re

l b are t h e . resu l t o f t h a t ca l cu la t i on . The agreement, w i t h no ad jus t -

ab le parameters, i s s u r p r i s i n g l y good. The 2.5 eV peak i s exper i -

mental 1 y broader and ' extends t o lower energy. Mc ln ty re has i d e n t i f i e d

th . i s e x t r a s t r u c t u r e w i t h sur face plasma modulat ion (see .Appendix B) .

I n t h e Au/solut ion system, t h e cond i t i ons f o r sur face p1,asma

\ o s c i l l a t i o n s are met a t about 2.5 eV. The surface plasma mechanism

was also blamed f o r the s t ruc tu re near 3.2 eV i n Ag (Figure la ) . The

agreement between experiment and theory i s be t t e r yet f o r Ag near

3.9 eV but poor f o r Cu.

Bewick and ~ o b i n s o n ~ ' have i d e n t i f i e d the region o f a p p l i c a b i l i t y

o f the M-A theory i n very ca re fu l l y performed experiments on Pb. They

demonstrated t ha t ARlR scaled w i t h Aq k i t h an angle o f incidence o f

45' (where no e l e c t r o l y t e e f f ec t s should be v i s i b l e ) . A dev.iat ion

from t h i s behavior was observed f o r la rge negative charge changes which

was i d e n t i f i e d by them as being caused by bound electrons.

Other theor ies Hansen together w i t h ~nderson" has attempted

t o improve on the M-A theory by inc lud ing the con t r i bu t i on o f bound

electrons. As i n previous theor ies inf luenced by Hansen, they were

looking f o r a way t o "sh i f t " the op t i ca l propert ies. A band-bending

which a f f ec t s the interband energy separation Aw was hypothesized n ' n

but improperly exploited. The formula they employed f o r the d i e l e c t r i c

funct ion was obtained f roni the work by Ehrenreich and Phi 1 ipp30 where

the o s c i l l a t o r st rength i s used but not defined. I n an e a r l i e r paper

Ehrenreich and cohen3' have shown t h a t t h e i r osci 1 l a t o r st rength

ac tua l l y depends on w n ' no

Hansen and Anderson have apparently over-

looked th is , s ince they t reated the o s c i l l a t o r s t rength as a constant.

They a lso l e t the damping parameter, T, go t o zero before tak ing t h e

rea l and imaginary par ts o f Ehrenreich's resu l t . This means they l o s t

information about any modulation o f the imaginary p a r t o f the d ie lec-

t r i c function. I n addit ion, they neglected the z-space dependence o f

Awn,,. The i r f i n a l computer-generated r e s u l t had so many ad jus tab le

parameters t h a t they were ab le t o f i t t h e i r own data.

Rely ing on band s h i f t i n g as a source o f s t ruc ture , even when

p roper l y employed, seems exper imental ly u n j u s t i f i e d . A s u p e r f i c i a l

study o f t h e band s t ruc tu res o f t h e noble metal s ( ~ ~ p e n d i x 0) i n t h e

reg ion o f t h e f i r s t s t rong interband t r a n s i t i o n s reveals t h a t any

change i n in terband energy must come about by a s h i f t i n t h e bands

w i t h respect t o each o the r o r by a s h i f t o f t h e Fermi leve l . Wi th

both cases, t r a n s i t i o n s from t h e Fermi surface t o h igher s ta tes are

af fected oppos i te l y than t r a n s i t i o n s from lower l y i n g s ta tes t o unoc-

cupied s ta tes a t t h e Fermi leve l . This w i l l i n general cause peaks o f

bo th s ign i n t h e d i f f e r e n t i a l o p t i c a l p roper t ies . One can get an idea

o f t h i s e f f e c t by look ing a t t h e r m o m ~ d u l a t i o n ~ ~ ~ ~ ~ ' ~ ~ a t low tempera-

ture, where t h e major m o d i f i c a t i o n i s a broadening o f t h e Fermi leve l .

This produces peaks o f both s ign i n AR/R. The prime example i s Ag,

whose ER i s one sided and located a t 3.9 eV. This i s t h e energy loca-

t i o n f o r t he onset of t r a n s i t i o n s from t h e Fermi l eve l (p -s ) . There - i s no s i y n i f i c a n t s t r u c t u r e i n t h e energy region where t h e much st ronger

(producing a greater c o n t r i b u t i o n t o t h e interband j o i n t dens i ty o f

s ta tes) t r a n s i t i o n - t o the Fermi l e v e l (d +p) should produce a peak o f

oppos i te sign.

Garr igos e t - a ~ . ~ ' - have presented an obscure theo ry which appears

t o have no l o g i c a l i n t e r p r e t a t i o n . They ca l cu la ted t h e modi f ied re-

f l e c t i v i t y o f a m e t a l l i c surface w i t h a phenomenological sur face

current . The i r j u s t i f i c a t i o n was t h a t t h e s t a t i c e l e c t r i c f i e l d

induces a charge dens i ty which i s acted upon by the e l e c t r i c f i e l d

of t h e sampling l i g h t , thus producing t h e surface cur rent . Due t o the

l a rge number o f parameters, they were ab le t o f i t t h e i r own data.

Bower36 has attempted t o inc lude bound e l e c t r o n e f f e c t s by devel-

oping a theory f o r a s p a t i a l l y d i spe rs i ve d i e l e c t r i c constant. His

conclusians, . however, were, based on improper reasoning connected' w i t h

the use o f s p a t i a l l y dependent response funct ions.

Preface t o Th is Research

. .

3 7 Symmetry cons idera t ion

+ The e l e c t r i c displacement, D, i s r e l a t e d t o t h e e l e c t r i c f i e l d o f . .

t he photon, z, by t h e d i e l e c t r i c tensor o f t he medium, = C s E V PY v *

The d i e l e c t r i c tensor must t ransform i n t o i t s e l f when operated on by , .

t h e symmetry opera t ions o f t he p o i n t group o f t h e l a t t i c e . I f t h e

p o i n t group has a symmetry a t l 'east as h i g h as the orthorhombic system,

then w i t h t h e proper choice o f coord inate axes, s can be d iagonal- /.W

ized. I n a medium o f m3m symmetry, such as a face-centered cub ic

c r y s t a l , a l l t h ree diagonal components are equal. The o p t i c a l i n t e r -

act ion, described by t h e displacement, i s i s o t r o p i c under these con-

d i t ions.

I n t h e sur face, reg ion o f a normal ly i so t rop ic . c rys ta1 , t h e sym-

metry i s lower due t o t h e presence o f a pre fer red d i r e c t i o n perpendicu-

l a r t o the surface. Th is s i t u a t i o n may e x i s t f o r o n l y a few atomic

layers beyond which t h e bu lk symmetry appl ies. The sur face symmetry,

and the re fo re t h e d i e l e c t r i c tensor i n t h e surface region, depends on

t he p a r t i c u l a r c r y s t a l lograph ic plane which forms t h e surface. Table 1

summarizes t h e s i t u a t i o n f o r t h e t h r e e p r i n c i p a l cub ic d i rec t i ons .

Table 1. Surface d i e l e c t r i c tensor i n cubic c r y s t a l s

Crys ta l l og raph ic surf ace .

Surf ace symme t r y

Surface d i e l e c t r i c tensor d iagonala

a z i s perpendicular t o t h e surface.

With normal ly i n c i d e n t l i g h t , f i s always p a r a l l e l t o t h e surface.

+ . For t h e (100) and ( 1 1 1 ) surfaces, D i s s t i l l i s o t r o p i c . However, on

t h e (110) sur face t h e symmetry i s low enough t h a t 5 i n t h e sur face

. , reg ion depends on t h e o r i e n t a t i o n o f g.

This argument imp l ies t h a t even I n a cub ic s i n g l e c r y s t a l , t h e

o p t i c a l p roper t i es o f t he (1.10) ' sur face are i nhe ren t l y an iso t rop ic .

The c o n t r i b u t i o n o f t h e sur face region i s so small t h a t t h e e f f e c t i s

normal ly unobservable. However, i f any change i n t h e sur face reg ion

t h a t mainta ins t h e c r y s t a l symmetry i s imposed, and t h e o p t i c a l e f f e c t

of t h a t change detected, then anisotropy w i l l be observed on ly on the

(110) sur face o r one of lower symmetry f o r normal incidence.

. .

These are t h e cond i t i ons t h a t apply t o ER of s i n g l e c r y s t a l s .

The (110) surface o r one of .lower symmetry must be used i f e f fec ts

due t o t h e l a t t i c e p o t e n t i a l o r i e n t a t i o n a re t o be studied.

S t ruc tu re o f t h e i n t e r f a c e

The j u n c t i o n o f a metal and an e l e c t r o l y t e i s charac ter ized by

a d i s t r i b u t i o n o f charge c a r r i e r s ( i n t h e metal, e lec t rons ; i n t h e

e l e c t r o l y t e , ions) which d i f f e r s from t h a t o f t he b u l k phases. F ig-

u r e 2 i l l u s t r a t e s a hypothet ica l union of a metal and an e l e c t r o l y t i c

so lu t i on ; t h e so-cal led double layer. The var ious regions i n t h e

s o l u t i o n are discussed i n ' ~ p p e n d i x C. Here, comments w i 1 1 be re-

s t r i c t e d t o t h e metal phase. A l l t h e p i c t u r e d zones may o r may no t .

e x i s t depending on the condi t ions. The d is tances a re on ly hypo the t i ca l

and are sub jec t t o v a r i a t i o n and reversal .

Penetrat ion of p e r t u r b i n g f i e l d Th is i s t h e depth t o which

t h e metal has knowledge of coulomb forces due t o . t h e presence of solu-

t i ,on ions and d ipoles. I t s ex tent r e f l e c t s t h e a b i l i t y of e lec t rons

i n t h e metal t o screen a s t a t i c charge. I n a f ree e l e c t r o n gas t h e

e l e c t r o n dens i t y f a l l s from 90 percent t o 10 percent o f i t s b u l k

va lue over a d is tance o f 0.34 Fermi wavelength38 (about 1.8 A). Elec-

t rons t h a t p a r t i c i p a t e i n t h e screening a re a l s o expected t o p a r t i c i -

pa te i n i n t e r a c t i o n s w i t h t h e metal cores,

I n t r i n s i c surface Th is i s t h e depth t o which the metal k ~ ~ ~ o w s

about the l a t t i c e te rminat ion. According t o some c a l c u l a t ions3' these

e f f e c t s a r e s t i 1 1 present beyond 20 atomic layers. c e r t a i n l y

t h e f i r s t several layers are involved. Three dimensional rec ip roca l

space i s n o t expected t o be s t r i c t l y v a l i d i n approximating t h e e lec-

t r o n wave func t i ons here s ince l a t t i c e p e r i o d i c i t y i s l i m i t e d perpen-

d i c u l a r t o t h e surface.

Photon penet ra t ion The photons probe a reg ion which can be

- 1 charac ter ized by a , the inverse o f t h e absorpt ion c o e f f i c i e n t . Th is '

i s t h e depth a t which t h e 1 i g h t i n t e n s i t y has dropped t o e-' of i t s

i nc iden t value. I t i s usual ly over 100 and may be a micrometer o r

more.

CHAPTER II. EXPERIMENTAL

S o l i d Electrodes 40

S o l i d e lectrodes are c h a r a c t e r i s t i c a l l y in f luenced by chemical

i n te rac t i ons . They have a tendency t o acqu i re anodic f i l m s i n v o l v i n g

oxygen and layers o f c a t h o d i c a l l y adsorbed hydrogen. There i s s t i l l

some doubt whether an idea l double l aye r reg ion ex i s t s . S p e c i f i c

adsorpt ion i s a more c r i t i c a l fac tor , and t h e geometry on t h e molecu-

l a r l e v e l i s o f t e n unknown. For these reasons, e lec t rochemis t ry has

been based on s tud ies o f t h e mercury e lectrode. I t i s p h y s i c a l l y

smooth and homogeneous, renewable, and chemical ly i n e r t . I t i s pos-

s i b l e t o work w i t h s o l i d electrodes, however, t h e utmost care must be

adopted.

The f i , r s t c r i t e r i o n should be r e p r o d u c i b i l i t y . Minute i m p u r i t i e s

may be s t rong ly adsorbed and thereby concentrated a t t h e i n t e r f a c e

lead ing t o e r ro rs . These i m p u r i t i e s tend t o f a l l I n t o one o f two

categor ies.

1. Inorganic impur i t ies . These may be oxygen o r heavy m e t a l l i c

ca t i ons t h a t could undergo o x i d a t i o n o r reduct ion r e s u l t i n g . i n a

steady f low o f d i r e c t current . The e lec t rode i s then no longer ide-

a l l y polar ized. Although d ramat i ca l l y a f f e c t i n g t h e I(@) resu l t s ,

t h i s type o f impur i t y should n o t a f f e c t t h e capac i ty measurements.

2. Surface a c t i v e contamination. This category inc ludes spe-

c i f i c a l l y adsorbed ions o r o rgan ic molecules. Even concent ra t ions

below normal de tec t i on l e v e l s a re enough t o r u i n t h e surface.

I n a d d i t i o n t o the inherent d i f f i c u l t i e s involved w i t h s o l i d

e lectrodes the re i s t h e haunt ing problem of how t o prov ide f o r an ,

i n e r t e l e c t r i c a l connection. This i s combined w i t h t h e necess i ty

o f mounting t h e sample i n a molecu lar ly t i g h t mount. The c r i t e r i o n

o f iner tness i s q u i t e r e s t r i c t i v e . The o n l y t rus twor thy cons t ruc t i on

ma te r ia l s are quar tz and t e f l o n . Even these have l i m i t a t i o n s . By

t h e t ime t h e demands of o p t i c a l s tud ies a re added t o t h e 1 i st, t h e

experimental d i f f i c u l t i e s have become q u i t e formidable. On t o p o f

a l l t h i s , when s i n g l e c r y s t a l e lectrodes a re studied, t h e requ i re -

ments become almost incompatible.

. With s i n g l e c r y s t a l s , mounting i s p a r t i c u l a r l y c r i t i c a l . The

sample cannot be squeezed s ince t h i s would induce a l a t t i c e per turba-

t i o n i n t h e form of s t r a i n . I n addi t ion, t h e sur face must be prepared

. i n such a way t h a t a l l t h e work-damaged mate r ia l produced i n t h e

p o l i s h i n g process i s completely removed. I n order t o e x p l o i t t h e

s i n g l e c r y s t a l t o advantage, i t must be accura te ly o r i e n t e d w i t h re-

spect t o t h e experimental measurement.

Surface Preparat ion

Mechanical p o l i s h i n g

I t i s known t h a t spark c u t t i n g induces deformation t o a depth o f

100 micrumeters, even w i t h medium energy sparks.41 The r e s u l t i n g

sur faee must be ground f i a t w i t h a s u i t a b l e abrasive such as 600 g r i t

S i c paper. I t i s important i n t h i s step t o prov ide a f l o w i n g stream

of water across t h e surface o f t h e paper t o c a r r y away abrasion debr i s

which could cause a d d i t i o n a l damage beyond t h a t produced by t h e 0-40

micrometer p a r t i c l e s . Th is treatment must then be fol lowed by a

ser ies of successively f i n e r abrasives imbedded i n a p o l i s h i n g c lo th .

The p o l i s h i n g t ime f o r each grade i s much longer than t h a t requ i red

t o remove t h e v i s i b l e scratches l e f t by t h e previous grade. P a r t i c -

u l a r l y w i t h s o f t e r metals, such as t h e noble metals, p o l i s h i n g i s a

combined process o f e ros ion - and f i l l i n g . An apparent ly smooth sur face

a c t u a l l y conta ins p l a s t i c a l l y deformed regions where l tva l leys l l have

been f i l l e d in. These shpw up i n a chemical e t ch ing treatment t h a t

p r e f e r e n t i a l l y a t tacks such regions. Even w i t h 500 s i z e p a r t i c l e s

o 41 the damage can range up t o 11,000 A!

The sur face t reatment fo l lowed i n my experiment i s shown i n

F igu re 3. The d e s c r i p t i o n i s f o r Ag, which was s tud ied more exten-

s i v e l y than Au, however t h e mechanical p o l i s h i n g techniques were

i d e n t i c a l .

The sample of Ag was an ingot of 99.9% p u r i t y , o r i e n t e d w i t h

t h e [ 1101 d i r e c t i o n p a r a l l e l t o t h e long axis, The Au c r y s t a l was

n o t measured f o r composit ion but I s was assumed t h a t i t was o f a t

l e a s t r o u t i n e p u r i t y . Back r e f l e c t i o n Laue x-ray s tud ies ass is ted

i n t h e o r i e n t a t i o n before c u t t i n g t o expose t h e ( 1 10) and (100) planes

of Ag, and t h e (110) p l a n e o f Au.

A f t e r spark c u t t i n g t h e samples i n t o 1/8" wafers, they were

ground f l a t us ing t h e technique described above. A sho r t Ag w i r e

was attached t o t h e back s ide w i t h r a d i o solder. Th is stub was l a t e r

used as a p r o j e c t i o n f o r making e l e c t r i c a l contact . I performed t h e

.I PRELl MINARY TREATMENT I SPARK CUT GRIND FACES oR'ENTED t

FLAT t SOLDER Ag ELECTRICAL

INGOT SAMPLE # 6 0 0 Sic CONNECTION

I I I

MECHANICAL POLISH

RINSE IN POLISH CLEAN IN DOUBLE

ACETONE DISTILLED ALUM I NA ALUM1 NA WATER

5 PARTS NH40H 3 PARTS (30%) H202

BY VOLUME

KCN 37gA IN AgCN 35g/ l DOUBLE K2C03 38911 DIST. H20

500A ALUMINA . .

SLURRY

I I

HEAVY FLUSH WITH DOUBLE DISTILLED WATER - -

INTO NITROGEN CHAMBER

Ag CATHODE; ROOM TEMP

(#A,- +sCE) = -0.25 VOLTS

I, SKID POLISH - 5 MIN

2. 'ETCH ' RINSE '- 15 SEC

Figure 3. Technique for preparing smooth, strain free single ciystal surfaces of Ag.

I. SLOW STIR - 10 MIN. C,D. - 60 M A / C M ~

2. STILL - 5 MIN C.D. - 15 MA/ C M ~

pre l iminary f i n e po l i sh ing on a Beuler I1Vibrometl1 v ib ra to ry po l i sh ing

machine using a s l u r r y o f 3000 1 alumina. I n some o f the runs an

addi t iona l f i n e po l i sh ing step was added i n 500 alumina s l u r r y by

hand. A t t h i s po in t a longer t h i n Cu w i re was fastened t o the pro-

j e c t i n g w i re on the back o f the samples using a conductive glue (l l~ucoll

cement and Ag pa in t ) .

Removal of surface damage

Noble metals, because of t h e i r i n e r t character, are d i f f i c u l t t o

chemical l y o r e lectrochemical ly pol ish. Ag i s p a r t i c u l a r l y temper-

mental. A f t e r many unsuccessful methods were t r i ed , inc lud ing thermal

annealing, a p o t e n t i o s t a t i c a l l y con t ro l led e lec t ropo l i sh ing technique

and an etch-at tack po l i sh ing method were adopted.

As shown i n Figure 3, the etch-at tack involves simultaneous

chemical ac t ion and m i l d abrasion by us ing the etchant instead o f

water i n the s lur ry . I t i s very t r i c k y since the chemical react ion

heats up the surface and dr ives the system i n t o condi t ions which pro-

mote the formation o f contaminating f i lms, With care it c.an produce

a surface o f considerable c rys ta l log raph ic perfect ion. 42

I used a

f i n a l wash o f the c r ys ta l i n the etchant t o ensure t ha t a l l t races o f

abrasion were e l iminated.

I t was necessary to.employ po ten t ia l con t ro l i n the argentocyanide

e lec t ropo l i sh ing o f Ag43 (Appendix C). I used a saturated calomel

reference electrode (SCE) and a Ag w i re counter e lec t rode i n a conven- I

t i ona l , a i r saturated electrochemical conf igurat ion. A con t ro l

c i r c u i t s im i l a r t o t ha t u t i l i z e d i n the ER measurements (described

l a t e r ) maintained the desired Ag sample po ten t ia l w i t h respect t o

the SCE. The whole operat ion was conducted i n a v e n t i l a t i o n hood due

t o the extreme t o x i c i t y o f the e lec t ropo l i sh ing solut ion. The com-

pos i t i on o f t ha t so lu t ion as wel l as the operat ing condi t ions f o r

sa t i s f ac to r y po l i sh ing are ou t l i ned i n Figure 3.

The Au sample was electropol ished under the less sophist icated,

standard cur rent con t ro l conf igurat ion. The electrode po ten t ia l was

not monitored so the SCE was not needed. I used a so lu t ion of 10

par ts g l a c i a l acet ic acid t o 3 par ts s u l f u r i c acid i n a s ta in less

s tee l beaker t ha t acted as the cathode. A cur rent densi ty o f about

2 4 A/cm was passed through the c e l l f o r about 15 seconds. This ra ther

h igh cur'rent densi ty caused vigorous oxygen evo lu t i,on which seemed t o

be requi red f o r sa t i s fac to ry pol ishing. U l t rason ic s t imu la t ion t o

. . break up the oxygen bubbles resu l ted i n .a less perfect surface.

The samples appeared very clean and b r i gh t a f t e r the f i n a l t r e a t -

ment. The Ag c r ys ta l s had a few microscopic p i t s presumably due t o

c rys ta l log raph ic imperfections. This was more pronounced on the etch-

pol ished samples. The Au c r ys ta l exh ib i ted some minor i r r e g u l a r i t i e s

which I a t t r i b u t e d t o act ion due t o the oxygen evolut ion. This was

v e r i f i e d by d i f f e r e n t ag i t a t i on schemes.

Grazing-incidence e lec t ron d i f f r a c t i o n was performed on an etch-

pol ished Ag sample. The spot pa t te rn indicated the surface was f ree

42 from s t ra in ,

I t i s expected t h a t t he microscopic topography of these surfaces

was f a r from t h e idea l s i n g l e c r y s t a l plane. Any o r i e n t a t i o n e r r o r

would have produced a stepped plane. More ser ious i s t h e r e s u l t of

t he mechanical and e l e c t r o p o l i s h i n g procedure. Even if t h e surface

appeared unstra ined by e lec t ron d i f f r a c t i o n , t he re might have been

h i g h and low spots. I do n o t b e l i e v e t h a t t h e non-uni formi ty was

,' severe, bu t t h e sur face was c e r t a i n l y n o t i d e a l l y planar. I do f e e l

t h a t t h e s i n g l e c r y s t a l sur face p e r f e c t i o n achieved i n t h i s research

represented t h e s t a t e of t h e a r t i n electrochemical studies.

. Electrochemical Methods

Drop techn i que

Instead o f t h e usual method o f s tudy ing electrodes, I employed

a technique whereby t h e e l e c t r o l y t e was conf ined t o , a s i n g l e drop

44 which rested on t h e sample top surface. Th is had t h e advantage i n

s i n g l e c r y s t a l s tud ies o f l eav ing t h e sample completely f r e e on a l l

s ides w i thou t t h e s t ra in - i nduc ing mount. Only one face'was exposed

t o the s o l u t i o n so t h a t we l l def ined c r y s t a l l o g r a p h i c s tud ies could

be made. E l e c t r i c a l contact could be made t o the back o f t h e sample

w i thout f e a r o f contamination. However, t he most a t t r a c t i v e f e a t u r e

was t h a t t h e solution-volume-to-electrode-area r a t i o was g r e a t l y re -

duced. I f any contaminat ion were present i n a minute concentrat ion,

t h e t o t a l amount avai lable, even i f i t were a l l adsorbed, would have

no no t i ceab le e f fec t on t h e measurements.

F igu re 4 shows my r e a l i z a t ion o f t h i s technique. The sample (a),

which was about 1/2" dia., was provided w i t h e l e c t r i c a l contac t v i a a

t h i n Cu w i r e (b) which was attached t o t h e back side. i t rested

f r e e l y on a ho l low t e f l o n pedestal (c) which was secured t o an over-

f l ow bas in (d) w i t h a ho l low Kel-F screw (e). The e l e c t r o l y t e contac t -

i n g t h e sample was r e s t r i c t e d t o a drop (about 0.1 ml) r e s t i n g on t h e

h o r i z o n t a l l y exposed upper face. The drop was f l a t t e n e d by a quar tz

o p t i c a l window (f) t h a t was supported from t h e s ide by a quar tz rod

extension (r). E l e c t r i c a l contac t w i t h t h e drop was achieved w i t h - .

so lut ion-bear ing, t h i n bore g lass c a p i l l a r i e s . C a p i l l a r y - g led,

through a c losed stopcock (h) , t o a small reservo i r i n .which a Beckman

asbestos f i b e r j u n c t i o n reference e lec t rode (i) was dipped. C a p i l l a r y -

j led, through a medium-porosity f r i t t e d g lass membrane (!), t o a

c losed compartment which contained t h e counter e lectrode. The counter

e lec t rode was t h e c o i l e d extension o f a P t w i r e (n) t h a t was sealed

i n t h e ou te r h a l f o f a small standard taper j o i n t (m). The e n t i r e

counter e lec t rode chamber could be f i l l e d w i t h so lu t ion , then sealed

shut, t o prevent s o l u t i o n from streaming i n t o t h e drop by capi 1 l a r y

act ion, through a f i l l p o r t and t e f l o n cap (k). Tube-p l ed t o a 100

m l a l l - g l a s s syr inge f i l l e d w i t h f r e s h s o l u t i o n (not shown) and tube-q

led t o a s i m i l a r empty syr inge (a l so no t shown). Th is system was de-

signed t o enable t h e drop t o be renewed w i thou t w e t t i n g t h e s ides o f

t h e c r y s t a l . I n some t r i a l s tube-q was e l im ina ted and t h e excess

s o l u t i o n al lowed t o drop over t h e sides o f t h e c r y s t a l i n t o t h e

Figure 4. . . c a p i 1 1 ary e lec t rode placement and sample mount '(shown w i t h a ( 1 10) Ag sample) used i n t h e drop e lect roc iemist ry configuration. The components marked w i t h l e t t e r s a r e i d e n t i f i e d i n the t e x t .

overf low basin. The l i g h t was inc ident from above and was focused t o

a spot (s) which was 1 x 5 mm i n extent.

This e n t i r e assembly was made t o f i t ins ide a p lex ig las box

w i t h a quartz window i n the top. The f r on t o f the box, provided w i t h

a s i l i c o n e rubber seal, was removable t o permit access t o the i n t e r i o r .

A1 though other invest igators o f meta'l 1 i c E R ~ ~ reported no a f f e c t due

t o oxygen i n the so lu t ion on the AR/R spectra, I be l ieve i t i s im-

por tant t o e l iminate oxygen t o avoid i t s in ter ference i n electrochemi-

ca l monitors and because i n the e l im ina t ion process, one a lso gets r i d

o f other a i rborne contamination. The p lex ig las box was suppl ied w i t h

a f lowing atmosphere o f pu r i f i ed , water-saturated n'i trogen.

E lec t ro l y t e

A su i t ab le e l e c t r o l y t e must meet several c r i t e r i a . I t should

be o f h igh conduct iv i ty . I t should be eas i l y pur i f i ed . Ttie pH va1u.e'

should a l low a wide range o f e lectrode po ten t ia l s wi thout so lu t i on

breakdown. ~ i ' n a l l ~ , i t should contain an anion t ha t has a low tendency

f o r spec i f i c adsorption.

Ideal choices from the chemical po in t o f vicw arc NaF (which i s

the e l e c t r o l y t e w i t h the leas t known tendency f o r adsorption) and

NaC104. These have ra ther low conduc t i v i t i es t ha t cause s t a b i l i t y

problems w i t h the con t ro l c i r c u i t r y (described l a te r ) . In t h i s re-

search I have chosen KOH and HC104.

KOH i s a base. I t permits a moderate negative po la r i za t i on of

the.e lec t rode wi thout hydrogen evolut ion. The hydroxyl ion does not

s p e c i f i c a l l y adsorb t o any great extent, and the s o l u t i o n d i sp lays a

h igh conduc t i v i t y . I n addi t ion, so lu t i ons w i t h OH- as t h e anion are

p a r t i c u l a r l y s u i t a b l e f o r o p t i c a l s tud ies o f t h e electrode. The molar

p o l a r i z a b i 1 i t y and molar volume of OH- a re s i m i l a r t o water,46 t h e

c h i e f c o n s t i t u e n t o f any aqueous e l e c t r o l y t i c so lu t i on . Hence, t h e

r e f r a c t i v e index o f an OH- layer, i f such a l aye r ex is ts , would be

c lose t o t h a t o f water.

HC104 i s an ac id w i t h an anion o f low adsorpt ion c a p a b i l i t y .

The c o n d u c t i v i t y i s very high, and t h e a l lowab le e lec t rode p o l a r i z a t i o n

range t o p o s i t i v e values i s appreciable.

Chemical procedure

A l l t h e glassware and t e f l o n . p a r t s which con tac ted ' the s o l u t i o n

were t r e a t e d w i t h 400" C concentrated s u l f u r i c ac id then r i nsed w i t h

t w i c e - d i s t i l l e d water t i l l no t r a c e o f t h e hydrogen ion was detected

i n t h e r ins ings . Suction, provided w i t h a syringe, was used i n t h i s

process t o insure thorough c lean ing o f t h e f r i t t e d g lass membrane.

A f te r t he a c i d treatment, on l y t h e ' o u t s i d e surfaces o f t h e pieces were

handled, and those w i t h neoprene rubber gloves.

The n i t r o g e n was c o l l e c t e d from the b o i l - o f f o f a l a rge l i q u i d

n i t r o g e n storage tank. I t was passed through an ac t i va ted charcoal

f i l t e r then over Cu tu rn ings a t 200' C. The Cu had p rev ious l y been

ac t i va ted by heat ing i t t o 400' C i n t h e presence o f molecular hydro-

gen. The f i n a l gas treatment was a p resa tu ra t i on w i t h water i n a gas

wash column. The r e s u l t i n g gas should have been f r e e from oxygen and

organ ic impuri t i es .

The water f o r p repara t ion of t h e s o l u t i o n and f i n a l r i n s i n g o f

t h e apparatus was t w i c e - d i s t i l l e d from an a l k a l i n e permanganate solu-

t i o n o f deionized water i n a closed, quar tz s t i l l . The absolute p u r i t y

o f t h e product was not known. However, t h i s water was acquired from a

labora tory engaged i n surface s tud ies o f t h e P t electrode. These i n - .

v e s t i g a t o r s found the same water q u i t e s a t i s f a c t o r y f o r t h e i r c r i t i c a l

appl i c a t ions.

The e l e c t r o l y t e was prepared f rom F i sher "Reagent ACS" grade

70% HC104 and " C e r t i f i e d ACS" grade KOH wi thout f u r t h e r p u r i f i c a t i o n .

Although t r a c e i m p u r i t i e s might be expected w i thout p r e - e l e c t r o l y t i c

t reatment o f t h e prepared solut ions, i t was no t deemed necessary w i t h

the small s o l u t i o n volume a c t u a l l y allowed t o contac t ' the sample. The D

so lu t i ons were pre-saturated w i t h N2 before t h e syr inges were f i l l e d . t

With t h e HC104 e l e c t r o l y t e i t was necessary t o f i l l t h e s a l t

b r i dge chamber of t h e calomel reference e lec t rode w i t h sa tura ted NaCl

r a t h e r than saturated KC1 s o l u t i o n t o avoid t h e formation o f a pre-

c i p i t a t e a t t h e f i b e r junc t ion . When t h i s e lec t rode was used i t ' h a s

been reported as SCE (NaCl). The e q u i l i b r i u m p o t e n t i a l o f t h i s r e f e r -

ence d i d n o t , d i f f e r appreciably from t h e conventional KC1 f i l l e d type.

Opt ics and E lec t ron ics

Op t i ca l system

I placed the p l e x i g l a s box i n s i d e a l i g h t - t i g h r enc1usui.e which

contained t h e focusing and de tec t i on op t i cs . This was a mul t i -braced

s tee l frame covered w i t h rubber sheet ing and sealed w i t h put ty . The

e n t i r e f r o n t o f t he enclosure was removable f o r access . to t h e exper i -

men t . Figure 5 i s a schematic i l l u s t r a t i o n o f t h e i n t e r i o r o f t h e l i g h t

enclosure showing t h e path of t h e l i gh t . ' Not shown . i n t h e f i g u r e i s

t h e compressed a i r cooled 900 wa t t Xenon arc lamp which was a source

f o r t h e Leiss model 9100 double monochromator. Quartz prisms were

used over t h e e n t i r e spect ra l energy range. The monochromator was

c a l i 'brated from 1.6 eV t o 4.5 eV us ing Osram spect ra l lamps. Using

a s l i t w id th of 500 meters my spect ra l r e s o l u t i o n (def ined as t h e

w i d t h of an atomic emission l i n e a t h a l f maximum),was 0.025 eV i n t h e

region of 3.64 eV. The r e s o l u t i o n i s b e t t e r a t h igher photon energies

and worse a t . l o w e r energies f o r t h e constant s l i t w id th used i n t h i s

experiment.

The e x i t s l i t o f t h e monochromator i s shown i n F igu re 5 (a). The

1 i g h t was c 6 l l ec ted by a 5 inch diameter, f/6.4 sphericaSl m i r r o r ' (b), . .

which was masked t o a 2 inch diameter, and d i r e c t e d t o a p lanar m i r r o r

(c) which de f lec ted t h e beam downward. A 2 inch diameter Polacoat

t h i n f i l m p o l a r i z e r was mounted i n a r o t a t a b l e mount a t p o s i t i o n (d).

A gear and index mechanism al lowed t h e o r i e n t a t i o n o f t h e p lane o f

p o l a r i z a t i o n t o be c o n t r o l l e d from o u t s i d e (e) t h e l i g h t enclosure.

I n some experiments a.mechanica1 d r i v e was added i n p lace o f t h e man-

ua l crank a t (e). The p l e x i g l a s box (k) i s a l so shown w i t h a s i m p l i -

f i e d i n t e r i o r (no c o n t r o l l i n g e lectrodes) f o r c l a r i t y . The l i g h t

passed i n t o t h e n i t rogen atmosphere through t h e quar tz p l a t e ( f ) t o

t h e sample (g). . The r e t u r n beam was co l lec ted, as soon a s , t h e r e was . .

F igu re 5 . I n t e r i o r cross sec t i on o f t h e l i g h t enclosure showing o p t i c a l components ( i d e n t i f i e d i n t he t e x t ) .

t h e

a s p a t i a l separat ion of ' the i nc iden t and re f l ec ted beams, by a beveled ,

diagonal m i r r o r (h). A quar tz lens (i) introduced enough convergence

t o concentrate t h e beam so t h a t i t was s l i g h t l y l a r g e r than t h e photo-

cathode'of t h e de tec to r (1 cm dia.). The p h o t o m u l t i p l i e r ( j ) was an

EM1 62560 and i s charac ter ized by a S - 1 3 response (usable from 2 eV t o

7.5 eV).

, I n t h i s diagram the p o s i t i o n of t h e f resh s o l u t i o n (1) and used

s o l u t i o n (n) syr inges i s a l s o shown, as i s t h e n i t rogen gas i n l e t (m).

Contro l e l e c t r o n i c s

The e n t i r e c o n t r o l and de tec t i on e l e c t r o n i c system i s i l l u s t r a t e d

i n b lock form i n F igu re 6,.

The main component of t h e c o n t r o l c i r c u i t was t h e pote 'n t ios ta t

(POT). A schematic o f . t h i s device i s shown i n F igu re 7. A b i p o l a r

opera t iona l power supply (Kepco 72-1 .5~) (BOP) served as t h e adding

a m p l i f i e r as w e l l as t h e power booster. The h i g h impedence opera-

t i o n a l a m p l i f i e r ( ~ n a l o g Devices ~ ~ 5 0 6 ~ ) was employed i n t h e b u f f e r

mode t o p r o t e c t t h e reference e lec t rode (SCE). I n opera t ion t h e BOP

adjusted i t s ou tput t o the counter e lec t rode so as t o keep t h e d i f f e r -

ence between i t s inputs equal t o zero. The sum o f t h e AC and DC i n -

pu ts and t h e feedback vo l tage was present a t t h e i n v e r t i n g Input.

Since t h e non- inve r t i ng input was grounded, t h e output was adjusted

so t h a t t he feedback (which was minus !5CE) was minus the AC and DC

inputs.

The sample cu r ren t was monitored by the vo l tage developed across

a one ohm load r e s i s t o r . The v a r i a b l e feedback elements served t o . .

Figure 6. Block diagram of the control and detection electronics.

POLARIZER L ,f - -- 7

3.w MONO ---L V(fiw) PM

MONO' - DRIVE .

'I ,COUNT A T - . T A

I' . SCE POT + ( t ) REC

1

HV 1 hilm A

T SCOPE

. . A CRYSTAL

I(+) 4 b

REC DC HV SIG SERVO

\ .

V(R) MOD. GEN -

I LIA - M(+,h) - R .

A C SIGNAL - REF* V(AR) REC u

F igu re 7. Schematic diagram1 of t he c o n t r o l po ten t i os ta t .

- v s SCEo 111 =PA

IS1

- -

,,

A w

A

5

h .r I

0 - 4 0 K 0- IFF

AC o-Mh . 4 0 K

INPUT

-

DC COUNTER

4 0 K

ISCE SAMPLE

control the gain and stabi 1 i ty of the control system. External input

to the potentiostat was supplied by one (or both) of two signal gener-

ators. The high frequency modulation potential was developed with a

sine waveform (Hewlett-Packard 200 CD). The DC potential was scanned

with a triangular waveform (Wavetek 142). Not shown is a low voltage

47 4

regulated power supply which was the source of the non-varying DC

bias potential.

Various potential and current monitors were employed to achieve

operation versatility.

Potential 1. An x-t recorder (Varian G-14~-1) provided a con-

tinuous record of the DC potential of the sample.

2 . Visual readout on a digital voltmeter (Fluke

8000~) (not shown) monitored the DC potential.

3. The x-axis of an x-y recorder (Moseley 2 ~ ) w a s

driven as a function of DC potential for I(@)

measurements.

4. The x-axis of another x-y recorder (Hewlett-

Packard 7001~~) was driven versus DC potential for

R-I AR (@) measurements.

5. AC potential waveform was monitored on an oscillo-

scope (~ekt ron i x 535~).

6. AC potential rms values were recorded with a VTVM

(Hewlett-Backard 4000H).

Current The vo l tage across the load r e s i s t o r was monitored.

1. DC values were recorded w i t h a m i l l i - m i c r o v o l t -

meter (Ke i th ley 149). Th is had an a m p l i f i e d out -

pu t which was fed t o t h e y -ax i s of 3 above.

2. AC values were monitored by 5 above and by another

VTVM (Hewlett-Packard 4 0 0 ~ ) . The output o f t h i s

instrument could be fed t o t h e y-axis o f 3 above . .

f o r capacitance versus Q measurements. . .

The e lectrochemical c e l l , which was a load f o r t h e c o n t r o l sys-

tem, acted 1 i k e a low pass f i l t e r t h a t handed back t o t h e BOP, through

t h e feedback loop, on l y the low frequency component of t h e vo l tage .

de l i ve red by the counter e lectrode. The c u t o f f frequency ( f ) was . - CO

- 1 - 1 - I (2fiCdl)e (Rsolut ion + Rfaradaic ), where Cd l i,s t he double

l aye r capacitance, and the res is tances are i n t h e s o l u t i o n from t h e

counter e lec t rode t o t h e reference electrode, and i n t h e double l aye r

due t o faradaic chemical a c t i v i t y . The f a r a d a i . ~ res is tance was . .

u s u a l l y h l g h when double layer opera t ing cond i t i ons held. I n t h i s

case f was determined, ou ts ide of uncon t ro l l ab le var iables, by t h e CO

s o l u t i o n resistance, and t h e e lec t rode area. I n a g iven conf igura-

t i o n the area, which was la rge i n my case, was f ixed. I t was de-

s i r a b l e then t o work w i t h h i g h l y conduct ive so lu t ions . I n p r a c t i c e

my conr ro l system would not pass a square wave t o t h e e lec t rode .w i th -

uuL d i b L u r t l o n when opera t ing a t t < 40'Hz i n 0.94 HC104. To enable

opera t ion a t higher, no ise f r e e frequencies, a s inuso ida l waveform

was used. The modulat ion was conducted a t 1000 Hz i n most cases.

Detect ion e l e c t r o n i c s

A second home-made, regu 1 ated, DC power supply4' provided v o l tage

t o a 10 t u r n rheosta t mounted on t h e monochromator drum. This was se t

t o prov ide a 1 v o l t / t u r n output which was fed t o t h e x -ax is o f t h e HP

recorded f o r AR/R versus photon energy runs. The r e s o l u t i o n o f t h i s

technique was 1 i m i t ed by t h e s i z e of t h e vo l tage steps due t o t h e

windings on t h e rheostat. Th is amounted t o 2 mV o r about 0.025 eV a t

a 3.0 eV photon energy.

The monochromator drum was d r i v e n by a 10 rpm synchronous motor

coupled through a gearbox which usua l l y was se t a t a speed reduct ion

r a t i o o f 1/100. The r e s u l t was a scan r a t e of 1 t u r n per 600 sec.

A t t h i s speed i t was poss ib le t o se t t h e t ime constant of t he l o c k - i n

a m p l i f i e r t o 300 msec, which i s 1/4 t h e t ime r e s o l u t i o n imposed by

t h e rheosta t windings.

48 F igure 8 i s a schematic of t he e l e c t r o n i c servo used t o main-

t a i n t h e average anode cu r ren t of t h e p h o t o m u l t i p l i e r equal t o a

preset value. The h igh vo l tage was suppl ied by an opera t iona l power

supply (Kepco OPS 2000), thro'ugh the 60 kbl p r o t e c t i o n r e s i s t o r , t o

t h e dynode chain which c o n t r o l l e d t h e gain of t h e detector . The anode

current , p ropor t i ona l t o t h e l i g h t i n t e n s i t y , was sent t o ground

through a 100 kS1 load across which a vo l tage was developed. The AC

p o r t i o n of t h i s s igna l was sent d i r e c t l y t o t h e l o c k - i n a m p l i f i e r

v i a a small capac i to r . The D C s igna l was I so la ted by a low-cutof f

f i l t e r and a b u f f e r opera t iona l a m p l i f i e r . It was monitored a t t h i s

Figure 8. Schematic o f t he e l e c t r o n i c gain servo used t o mainta in a constant DC s igna l from t h e photomul t ipl i e r .

PHOTO- CATHODE

OOK

p o i n t as w e l l as sent, i n a feedback mode, t o t h e open loop inpu t o f

t h e OPS. The opera t i ng l eve l o f t h e system could be adjusted by C

e i t h e r o f t h e v a r i a b l e r e s i s t o r s . I used a picoammeter (Ke i th ley 741)

i n a vo l tmeter mode t o moni tor the,DC s ignal . Th is was accomplished

by feeding t h e output of t h e bu f fe r a m p l i f i e r through a 1 megohm re-

s i s t o r t o t h e ammeter. The advantage o f t h i s instrument was a v a r i -

ab le zero supression which was no t avai 1 ab le on o the r conventional

vo l tmeters a t my disposal.

The e n t i r e de tec t i on and c o n t r o l e l e c t r o n i c system had on ly one

cont inuous ground. A l l t h e AC power connect ions were made w i thou t

grounding connections. I n coax ia l cab le t h a t was connected t o an

already grounded chassis the s h i e l d connect ion was broken. Even t h e

i n d i v i d u a l e l e c t r o n i c instruments were i nsu la ted from t h e mounting

rack i n an e f f o r t t o e l i m i n a t e ground loops. The main system ground

was connected t o t h e h igh vo l tage end o f t h e p h o t o m u l t i p l i e r

Operat ing Procedure

The f i n a l sample pre-treatment f o r Ag wa's simply a heavy r i n s e

i n t w i c e - d i s t i l l e d water, f o r gold a qu ick d i p i n concentrated n i t r i c

a c i d was fo l lowed by t h e water r inse. A f t e r t h i s t h e samples were

mounted on t h e t e f l o n pedestal and t h e atmosphere box was placed i n

p o s i t i o n w i t h i n the l i g h t enclosure. The system was al lowed t o sa t -

u r a t e w i t h n i t r o g e n before t h e drop was created.

I t was necessary, w i t h t h e e lec t ropo l i shed Ag samples, t o reduce

c a t h o d i c a l l y t h e contaminat ing viscous laye r l e f t f rom t h e

e l e c t r o p o l i s h i n g action4' (Appendix C ) . Th is was accomplished - i n

s i t u by ho ld ing t h e cond i t i ons a t t h e e lec t rode sur face a t - t he p o i n t - where atomic hydrogen evo lu t i on was j u s t beginning. A one h a l f hour

treatment was u s u a l l y s u f f i c i e n t , a f t e r which t h e drop was renewed.

W i thout t h e reduct i on treatment, anomalous resu l t s were observed

(Appendix A). This was no t necessary w i t h t h e e lec t ropo l i shed Au,

which had an ac id treatment p r i o r t o mounting i n t h e apparatus, nor

w i t h the chemica l ly po l ished Ag.

C y c l i c voltammetry was performed. The c h a r a c t e r i s t i c s o f t h e

I(@) curves i d e n t i f i e d t h e i d e a l l y p o l a r i z a b l e region f o r each sample

and ind i ca ted when e l e c t r o a c t i v e i m p u r i t i e s were present ( ~ p p e n d i x C) .

A slow t r i a n g u l a r vo l tage waveform was de l i ve red t o t h e p o t e n t i o s t a t

i npu t on top o f a steady DC b ias value. The output was recorded

d i r e c t l y on t h e Moseley x-y recorder. Due t o a zero d r i f t problem i n

t h e d i r e c t cu r ren t de tec t i on system the re was an absolute e r r o r o f

2 2 LA.

For capacitance measurements, a small (30 mV rms), h i g h frequency

(1000 Hz), s inuso ida l component was added t o t h e slow t r i a n g u l a r

sweep. The a l t e r n a t i n g current , which was p ropor t i ona l t o t h e double

l aye r capacitance, was detected w i t h one of t h e VTVM1s and t h e output

fed t o t h e y -ax i s o f t h e recorder, w h i l e t h e x -ax is was s t i l l scanning

t h e p o t e n t i a l . I cou ld e a s i l y de tec t a chanqe of 0.5 pF w i t h t h i s

technique. However t h e absolute capacitance may be o f f by as much as

2 o r 3 pF. I n addi t ion, t he re i s an uncer ta in ty i n determining the

coverage of t he e lec t rode by t h e drop which enters i n t o t h e determina-

t i o n o f t h e capacitance per u n i t area.

In' capac i ty data I looked f o r t h e absence o f frequency dependence,

the absence o f hys te res i s w i t h respect t o t h e po ten t ia l , and s i m i l a r i t y

w i t h o the r publ ished resu l t s . When these c r i t e r i a were sa t i s f i ed , I

was reasonably sure t h a t t h e sur face was f r e e from f i l m s o r absorbed

mater ia l .

.The opera t ing ,procedure f o r t a k i n g o p t i c a l data was as fo l l ows :

The p o t e n t i o s t a t maintained a constant b ias w i t h respect t o t h e SCE

reference. A s inuso ida l modulat ion o f frequency f, was app l ied on

top of t ha t . Th is produced a s inuso ida l p o l a r i z a t i o n o f t h e i n t e r -

face. Photons in te rac ted w i t h the modul ated in te r face and c a r r i e d

in format ion t o t h e detector . The s igna l from the de tec to r was s p l i t

. . i n t o a DC component, which was fed d i r e c t l y t o t h e DC monitor, and an

AC s ignal , superimposed on background no'ise. The l o c k - i n a m p l i f i e r

(PAR 186), which was referenced to . t h e modulat ion p o t e n t i a l , ex t rac ted

t h e component o f t h e AC s igna l channel which was i n phase w i t h t h e

modulat ion a t frequency f. The on ly source f o r t h e AC. s igna l was a

modulat ion on t h e r e f l e c t i v i t y o f t h e in ter face. On d i v i d i n g t h e AC

s igna l by t h e DC s ignal , a1 1 constant f a c t o r s canceled ieav ing AR/R

d i r e c t l y . Since t h e e l e c t r o n i c ga in servo on t h e de tec to r maintained

a constant DC s ignal , t h e output of t h e l o c k - i n versus a scanned

parameter had t h e same shape as AR/R versus t h a t parameter.

Several modes o f opera t ion were employed:

Mode A The scanned v a r i a b l e of t h e most i n t e r e s t was t h e

photon energy, hw. The monochromator drum was mechan i c a l 1 y scanned.

The voltage, p ropor t i ona l t o t h e drum pos i t ion , was connected t o t h e

x -ax is of t h e HP recorder, and the l o c k - i n output was de l i ve red to

t h e y-axis. The r e s u l t was a p l o t o f R-I AR ( h w ) . Mode B With t h e monochromator se t a t a f ixed. photon energy,

t h e slow t r i a n g u l a r sweep was imposed on t h e p o t e n t i o s t a t as t h e

scanned var iab le . The DC p o t e n t i a l was de l i ve red t o t h e x -ax is o f

t h e HP recorder and the l o c k - i n output d i r e c t e d t o t h e y-axis. The

- 1 ou tput on t h e recorder was R OR (4 ) f o r t he f i xed photon energy.

Mode c The monochromator se t t . ing and t h e b ias p o t e n t i a l were

he ld constant i n t h i s mode, w h i l e t h e o r i e n t a t i o n o f t h e l i g h t p o l a r i -

z a t i o n was mechanical ly rot.ated as ,a f u n c t . i m of time. The l o c k - i n

output was d i r e c t e d t o t h e y -ax is of t h e recorder w h i l e t h e x -ax is

was being scanned w i t h t ime (a f e a t u r e o f t h e HP 7001AM recorder).

The c h a r t ou tput was OR/R as a f u n c t i o n o f t h e o r i e n t a t i o n o f t h e

p o l a r l z a t ion of t h e 1 ight .

CHAPTER I I I. RESULTS

S ing le c r y s t a l s o f Ag were studied much more ex tens ive ly than

those of Au. I b e l i e v e the r e s u l t s f o r s i l v e r , based on the c r i t e r i o n

o f r e p r o d u c i b i l i t y , a re b e t t e r than any m e t a l l i c e l e c t r o r e f l e c t a n c e

data p rev ious l y published, c r y s t a l o r t h i n f i l m . The r e s u l t s f o r Au,

w h i l e recorded under t h e same opera t ion condi t ions, were no t numerous

enough t o e s t a b l i s h t h e i r r e l i a b i l i t y . I expect t h a t t h e Au data, by

reason o f comparison t o t h e l i t e r a t u r e , a re a t l e a s t as good as the

major i t y o f previous work.

A summary of t h e reported data under t h e d i f f e r i n g cond i t i ons o f

c r y s t a l o r i e n t a t i o n , sur face preparat ion, and s o l u t i o n composit ion i s

given i n Table 2. The numbers i n d i c a t e the f i g u r e where t h e i n d i - ,

cated type o f data appears.

Electrochemical Resul ts

. . S i l v e r

The voltammetry, I(IDC), f o r t h e Ag (110) sur face i s shown i n

F igure 9. A l l p o t e n t i a l s a re expressed versus t h e saturated calomel

e lec t rode (sCE). I n HC104 t h e NaCl f i l l i n g s o l u t i o n was used. The

p o t e n t i a l a x i s i s p l o t t e d w i t h @ increas inq neqat ive t o t h e r i g h t i n

acc~rdance w i t h electrochemical convention. Cathodic cu r ren t i s ~t

p o s i t i v e ordinates.. This i s t h e c o n d i t i o n where e lec t rons are leav-

i n g the e l e c t rode. The zero e r r o r i s L 2uA.

I n curve a, t h e double l aye r region i s i d e n t i f i e d as t h e loca-

t i o n of zero cur rent . : - I t i s d isplaced toward po,s i t i ve p o t e n t i a l due

Table 2. Summary of ' r e s u l t s and the f i g u r e numbers where data are located

tb C Sample so lu t i ona Prep.. I(@) C d , ( @ ) M o d e A Mode C peake

d Mode B d

A9 HC 1 Oh [ 1101 etched 9 13 2 2

Ag KO H [ 110] etched A 1 - 22

Ag KOH [ I 101 e 'po l . 9 10 14, A2 18, 19, 21 16, 20 2 2

10 14 Ag KO H [ l o o ] e 'pol . 16

Au HC 1 O4 [1101 e 'po l , 1 1 1 1 15 16 ,- ul W

al ,molar.

b~ = d i r e c t i o n o f t h e modulat ing f i e l d , normal t o t h e surface.

C Surface prepara t ion by e t ~ h - ~ o l i sh o r - e lec t ropo l i sh.

d Operating modes .are described i n the previous sect ion.

. . e A record o f peak p o s i t i o n as a funct , ion o f QDC.

I 1 I I I 1 I 1 I I 1 I 1 I 1

a C 0

Ag

b

$5, / 0- -c - - - -------- - - - - _ - - - _ _ _

T c

1

I I 1 1 I I I I I I I I I I I I

t 0.2 0.0 -0.2 - 0.4 -0.6 - 0.8 - 1 .O - 1.2 + (vol ts vs SCE)

F igu re 9. Cyc l i c voltammetry on c lean (110) :Ag. Exposed top area = 0.8 t o I cm2. (a) 1 M HC104, . etch-pol i shed, 40 ml/sec; (b) I M KOH, e l e c t ropol i shed and reduced, 20 mV/sec; (c)

I M KOH, e lec t ropo l ished and reduced, wetted bottom i n e l e c t r i c a l contact w i t h top, 50 mvisec.

t o the h igh concent ra t ion of H+ ions i n t h e acid. Hydrogen e v o l u t i o n

+ was beginning a t t h e negat ive end of t h e reg ion as H was converted

t o atomic hydrogen. This can be i d e n t i f i e d from t h e small ca thod ic

upturn near -0.45 V. Due t o t h e low concent ra t ion of OH- i n t h e

ac id so lu t ion , i t was much harder t o form t h e oxide. The anodic t rend

t h a t i s shown beginning near +0.27 V i s an i n d i c a t i o n of some process

i n v o l v i n g oxygen. Th is curve e x h i b i t s idea l behavior. The double

l aye r region i s charac ter ized by an almost undetectable cur rent , a l l

o f which can be a t t r i b u t e d t o charging o f t h e i n te r face .

I n b, bas ic s o l u t i o n a l lows a more negat ive excurs ion o f poten-

+ t i ,a l , due t o t h e low concent ra t ion o f ,H , but makes t h e r i s k o f ox ide

format ion on t h e p o s i t i v e end greater as a r e s u l t o f t h e increased

OH- concentrat ion. The features o f t h i s curve a re a s l i g h t s l a n t

toward t h e cathodic d i r e c t i o n w i t h decreasing +, i n d i c a t i n g t h e pres-

ence o f some t r a c e amount o f oxygen i n t h e so lu t ion , and a l a r g e r

2 cu r ren t i n t h e charging region, al though s t i l l l ess than 5 pA/cm .

Curve c d i sp lays a s t r u c t u r e t h a t I have i d e n t i f i e d w i t h a wet-

t i n g . problem t h a t was troublesome w i t h t h e KOH e l e c t r o l y t e . I n many

samples t h e so lu t ion , due t o t h e super io r w e t t i n g a b i l i t y o f s t rong

bases, c r e p t around s.o as t o cover t h e e n t i r e sur face o f t he c r y s t a l

i nc lud ing the s ides and bottom where the r a d i o so lder contac t was

located. I t seems as though one o f t h e main advantages o f t h e drop

method, i n e r t e l e c t r i c a l contact, had been compromised. I b e l i e v e

t h i s cu r ren t behavior t o be a c h a r a c t e r i s t i c on l y o f reac t ions t h a t

occurred a t t h e so lde r / so lu t i on in ter face. The j u s t i f i c a t i o n f o r

t h i s conclus ion i s t h a t be fore we t t i ng occurred, I observed idea l

voltammetry behavior as i n b. This behavior i n s t a n t l y changed t o

type c, which always d isplayed t h e same shape, when drop renewal

allowed increas ing coverage of t h e sides. When dry n i t rogen.was

pumped through t h e atmosphere' box t o a1 low evaporat ion on t h e wetted

sides of t h e c r y s t a l , thus breaking e l e c t r o l y t i c contact wFth the

bottom, ideal behavior was restored. The s i z e o f t h i s s t r u c t u r e i s . .

much less than impur i t y peaks i n voltammetry repor t s i n con junc t ion

w i t h ER s tud ies by o ther inves t iga tors , where the e n t i r e s o l u t i o n was

17,18 Nevert he1 ess, when homogeneous and con tac t i ng t h e electrode.

t h i s behavior was present t h e r i s k o f m i s i n t e r p r e t i n g charge f l o w data

and the r i s k o f leached impur i t i es passing i n t o the s o l u t i o n from t h e

solder was rea l . I do not t h i n k t h i s was a problem w i t h t h e o p t i c a l

measurements because t h e contaminat ing reac t i on occurred on t h e bottom

o f t h e c r y s t a l whereas the top, which was d i f f u s i o n i s o l a t e d from t h e

bottom, was the on ly sur face sampled by the l i g h t . . .

. . The C d l 0 ) f o r several representa t ive samples o f Ag i s shown i n

F igure 10. The s o l i d l i n e s w i t h superimposed s o l i d symbols are my

data, ex t rac ted from I AC*

The comparison w i t h two studies of Cdl from

the l i t e r a t u r e 50951 are a1 so shown as dot ted 1 ines. These are two of

t h e few r e s u l t s a v a i l a b l e on Ag s o l i d e lectrodes i n concentrated solu-

t ions . Both o f those studies were conducted on renewable surfaces -(by

scraping) w i t h meticulous a t t e n t i o n t o p u r i t y i n a standard e l e c t r o -

chemical apparatus.

Figure 10. Double layer c a ~ a c i t a n c e . o f Ag i n 1 M KOH, e lec t ropo l ished and reduced; 1 kHz; A (110), area = 0.8 crn2, ghc = 30 mV rms; W (110), area = I cm2, %C = 10 mV rms; 0 (100)) area = 0.8 cm2, @ I A C = 30 rnV rrns. L i t e r a t u r e comparison, renewable p o l y c r i s t a l l i ne Ag, + Zel i n s k i i e t 1. ;50 x Nechaev and ~au . tov5 l i n 1 N NaC104.

My data requ i re an est imate o f sur face coverage. I used values

2 o f 1 t o 0.8 cm . There i s a 20 t o 30% margin o f unce r ta in t y i n t h i s

estimate. The shape o f t h e Cdl curves should be true, h0weve.r t h e

absolute va lue i s i n some doubt. The l i t e r a t u r e comparisons were

s t ra ined p o l y c r y s t a l s d"e t o t h e scraping technique. The data shown

as a crossed (+) dot ted l i n e were i n 1 M KOH, the same as t h a t which

I used.

The two (110) sur face curves from my work (square and t r i a n g l e ) '

agree we l l i n shape. The (100) sur face ( c i r c l e ) curve i s . d i s p l a c e d t o

p o s i t i v e @ i n accordance w i t h theo r ies o f t he double layer.87 This

would be explained as due t o a s h i f t o f t h e p o t e n t i a l o f zero charge

(PzC) t o more p o s i t i v e values as t h e packing dens i ty o f atoms on a

s i n g l e c r y s t a l sur face increases. I n a l l .my data I observed no @

hysteresis .

I be l i eve t h a t the e lectrochemical r e s u l t s show t h a t I had

achieved a clean surface w i t h on ly water d ipo les and s o l u t i o n ions

near t h e uncontaminated Ag sample.

Gold - This mate r ia l was observed o n l y i n HC104 s ince t h e PZC l i e s i n a

p o t e n t i a l range accessib le w i t h ac id e lec t ro l y tes , and the . conduct ive

p roper t i es o f t h e ac id promote e f f i c i e n t . o p e r a t i o n o f t h e c o n t r o l

c i r c u i t r y . '

I n t h e I($), shown i n t h e bottom p o r t i o n o f F igu re 11, one can

n o t i c e several features. The hydrogen evo lu t i on reac t i on s t a r t s a t a

Figure 1 1 . Electrochemical monitors on Au v e r s u s @ , SCE (NaCl). Electropol ished ( 1 10) surface, i n 1 M HC104. 0 .8 cm2 coverage; bottom, voltammetry, 400 mV/sec; middle, double l a y e r capacitance, 1 kHz, QAC = 100 mV rms; top, Carr and ~ampson52 i n 0.45 M H2SO4.

I \ \ \ CARR & HAMPSON I

+ ( v o l t s vs SCE)

l ess negat ive p o t e n t i a l than f o r t h e Ag/HC1O4 system i n agreement

w i t h t h e ove rpo ten t ia l d i f f e rences f o r t h i s . r e a c t i o n between t h e two

metal's (0.2 v). I t i s a l s o . p o s s i b l e t o p o l a r i z e t h e Au t o a more

p o s i t i v e potent i a1 before oxygen involvement .becomes a problem. This

i s due t o t h e more i n e r t chemical charac ter o f Au. F i n a l l y , t h e

voltammetry d i sp lays some s t ruc ture , most o f which can be a t t r i b u t e d

t o double l aye r charging s ince t h e p o t e n t i a l was being swept a t a

r a t h e r h i g h r a t e (0.4 V/sec). This i s v e r i f i e d by t h e c u r r e n t i n -

crease i n t h e region where Cdl i s big.

My measured Cdl i s d isplaced downward from t h e o n l y comparison,

i n concentrated a c i d ( H ~ s o ~ ) so lu t ion , a v a i l a b l e i n recent l i t e r a -

t ~ r e . ' ~ Th is discrepancy may be accounted f o r by my area determina-

t i o n e r r o r s and a d i f f e rence i n t h e s o l u t i o n concent ra t ions (0.5 M i n

C and H; 1 M i n t h i s work) I saw no hysteresis , as Carr and Hampson

did. The i r s t r u c t u r e near 0.1 V was dependent on scan d i r e c t i o n i n -

d i c a t i n g t h a t they may have had problems.

E lec t ro re f l ec tance Versus Photon Energy

The data i n t h l s sec t ion were recorded under mode A as described

e a r l i e r . The photon energy was scanned a t f i x e d b i a s p o t e n t i a l and

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

: S i l v e r (110)

F igu re I f shows t h e o r i e n t a t i o n o f t h e sample w i t h respect t o

t h e l i g h t beam. The angle o f inc idence was as c l o s e t o normal as was

possib le, l i m i t e d by t h e s i z e o f t h e l i g h t cone, w i thou t us ing a beam

Figure 12. O r i e n t a t i o n o f t h e plane o f incidence w i t h respect t o the (110) Ag c r y s t a l l o g r a p h i c axes. L i g h t was inc ident i n a range o f angles from 0 " t o 5'.

s p l i t t e r . The c r y s t a l surface, denoted as ( ! l o ) , has th ree p r i n -

- - c i p l 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 s i n i t s face, [TIO], [ 1111, and

LOOT]. The [T10] d i r e c t i o n was a l so i n t h e p lane o f incidence.

No t i ce t h a t p - p o l a r i z a t i o n corresponds t o & along [T10] and t h a t

s-pol a r i z a t ion corresponds t o $ along [ o o ~ ] . whenever' reference i s

made t o t h e o r i e n t a t i o n o f $, i t i s understood t h a t [ 1101, [ 1 1 11, and

[ I 0 0 1 mean than $ i s o r i en ted along a d i r e c t i o n which i s a symmetry

equivalent, i n t h e b u l k c r y s t a l , t o these d i rec t i ons . The t o t a l

o r i e n t a t i o n a l unce r ta in t y o f $ w i t h respect t o the c r y s t a l axes

amounted t o 2 3'.

The ER o f an etch-pol ished sample i n 1 M HC104 f o r t h r e e o r i e n t a -

t i o n s of $ i s shown i n F igu re 13. The o r d i n a t e has been normalized

by d i v i d i n g t h e measured AR/R ( l a r g e s t peak va lue -6.00 k , 0.05 x

by t h e rms d r i v i n g p o t e n t i a l @ (54 mv). The negat ive nature o f t h e AC

peaks were v e r i f i e d by moni to r ing t h e DC s igna l from t h e l i g h t de-

t e c t o r w h i l e the p o t e n t i a l was d iscont inuous ly stepped by 0.15 V.

his check i s an important procedure w i t h any modulat ion experiment

s ince the re i s a phase ambiguity of 180" between t h e s igna l and r e f -

erence channels o f t h e l o c k - i n a m p l i f i e r .

The peak p o s i t i o n (3.88 ev) agrees w i t h M c l n t y r e ' s re1 i a b l e

resul t s l 0 and i s independent of $. The l o c a t ion of s t r u c t u r e occurs

j u s t - a t t h e onset energy f o r in terband t r a n s i t i o n s i n Ag and d ies o u t

a t energies where these t r a n s i t i o n s are strong. The r a p i d i t y o f t he

drop-of f was dependent on s o l u t i o n composit ion and 9 as described DC

l a t e r . The beginning o f t h e peak t a i l s t o low energy where no

PHOTON ENERGY (eV) F igu re 13. ER o f (110) Ag versus photon energy f o r t h ree o r i e n t a t i o n s o f t he l i g h t p o l a r i z a t i o n

^e. Etch-po1,ished sur face i n 1 M HClO4; OIDC = 0 V SCE ( ~ a C l ) , OAC = 54 mV rms a t 1 kHz.

in terband e f f e c t s are expected i n b u l k unperturbed Ag. There i s no

evidence o f low energy s t r u c t u r e near 3.3 eV as seen,by o ther i n -

ves t i ga to rs o f t h i s us ing f i lms a t ob l i que incidence 9 y 1 0 and micro-

s c o p i c a l l y s t ra ined b u l k samples. 7 y 1 5 9 1 6 1 b e l i e v e t h e low energy

s t r u c t u r e i s a product o f . imperfect samples i n those repor t s ( ~ p p e n -

d i x A).

The most s i g n i f i c a n t c h a r a c t e r i s t i c of my data, never before - - -

observed, , i s t h e marked anisotropy i n magnitude. This f e a t u r e \

appears a t a l l photon energies below 4.1 eV t o some degree but i s

much.more pronounced i n the peak region.

The anisotropy i s a r e s u l t o f t h e symmetry o f t h e c r y s t a l sur-

face and not s- and p-po lar ' i za t ion e f f e c t s on t h e re f lec tance f o r

t h ree convinc ing reasons:

1. The experiment was performed w i t h l i g h t i nc iden t i n a range - .

o f angles from 0" t o 5". Under these cond i t i ons po la r i za -

t i o n e f f e c t s on i s o t r o p i c surfaces a re unimportant. I n

r o u t i n e o p t i c a l experiments angles as h igh as 15" are t ' reated

as normal incidence.

2. Oblique inc idence (45O) ER on t h i n f i l m s l 0 shows a p o l a r i z a -

t i o n dependence t o AR/R (F igure la) . ' However, t h e e f f e c t i s

j u s t t h e oppos i te o f what I see. My la rges t pea'k occurs f o r

what would be s - p o l a r i z a t i o n which i s i n c o n t r a s t t o t h e

l a rges t peak f o r p - p o l a r i z a t i o n i n F igu re la .

3. 1 have ro ta ted t h e c r y s t a l 90" w i t h respect t o t h e i nc iden t .

beam (normal t o t h e surface). The r'esul t i s t h a t t h e

anisotropy fo l l ows t h e c r y s t a l , no t t h e s- and p-behavior

o f t h e l i g h t .

S i l v e r (100)

According t o p r e d i c t i o n s o f sur face symmetry arguments (Chapter

I ) , anisotropy should b e ' p e c u l i a r t o t h e (110) and lower symmetry

planes. F igu re 14 shows t h e r e s u l t o f t h e ER on t h e (100) face of Ag

' together w i t h a compar i son of. ER on t h e ( 1 10) face measured under

s i m i l a r condi t ions. Curves.b and c were recorded on t h e (110) face

w i t h two perpendicular o r i e n t a t l o n s o f t h e l i g h t p o l a r i z a t i o n . Curves

a r e s u l t f rom measurements on t h e (100) face wi,th p o l a r i z a t i o n o r i e n t a -

t i o n s along s i m i l a r d i rec t i bns . As predicted, t he re i s no an iso t ropy

i n any region o f t h e spectrum on t h e h igher symmetry surface.

The peak s t r u c t u r e i n t h e (100) data i s s h i f t e d t o h igher energy.

Also n o t i c e t h a t t he peak magnitude i s l a r g e r i n t h i s determinat ion.

Th is i s a r e s u l t o f sample t o sample v a r i a t i o n and a h igher Cdl which,

under t h e same opera t i ng condi t ions, a l lows a greater charging e f fec t .

The appearance of some low energy s t r u c t u r e near 3.3 eV i s a t t r i b u t e d

t o sur face inhomogeneities on t h i s p a r t i c u l a r (110) sample.

Gold (110) - I n c o n t r a s t t o Ag, my r e s u l t s f o r Au, shown i n F igu re 15, d i s p l a y

no anisotropy. The s i z e o f t h e A R / R s t r u c t u r e i s smal l e r than t h a t - -4

observed i n Ag bu t s t i l l w e l l above t h e no ise ( 0 . 5 ~ 1 0 ) As i n Ag,

t h e peak i s negative. That i s , R i s a decreasing f u n c t i o n of @.

A

F e o 100' ooi .a 100 o li b 110 ooi C 110 Ti0

Figu re 14. ER of. Ag f o r two perpendicular o r i e n t a t i o n s o f t h e 1 i g h t p o l a r i z a t i o n $ and two o r i e n t a t i o n s o f t he pe r tu rb ing f i e l d P, perpend i cu 1 a r t o t h e su r f ace, e l ec t ropol i shed and re- * . . duced, 1 M KOH, DC = -0.6 V SCE, IAC = 35 mV rms a t 1 kHz; (a) ( loo) , IAC = 5.4 mA; . ( b , ) (110), I A c = 4.8 mA.

Figure 15. ER a t

-

- e \ -

-

0' I l I 1 1. . I I I I I I

1.6 2.0 2.4 2.8 3.2 3.6 4 -0 PHOTON ENERGY ( e V )

of (1 10) Au; e lec t ropol ished, i n 1 M ~ ~ 1 0 ~ . qDC = 0.6 V SCE (NaCl), 1 kHz.

aAC = 100 mV rms

The broad s t r u c t u r e beginning we1 1 below 2 eV and topping o u t

a t 2.5 eV i n a d d i t i o n t o t h e p la teau a t about 3.6 eV compares favor -

ably w i t h r e p o r t e d t h i n f i l m ER" (F igure lb ) .

The s t r u c t u r e f o r hw > 3.6 eV has been a source of some cont ro-

versy i n ER as w e l l as t h e r e f l e c t i v i t y (Appendix 0 ) . Other i n v e s t i -

gators 14y28 have seen t h i s feature, bu t i t was dependent o n t h e

e lec t rode p o t e n t i a l t o a much l a r g e r degree than I observe. My

r e s u l t s show t h a t t h i s region of t h e spectrum scales roughly i n t h e

same way as t h e major peak w i t h G.

Summary

To emphasize t h e p o l a r i z a t i o n dependence i n a g iven sample,

mode B was used as an opera t ing procedure. With a l l o the r v a r i a b l e s

he ld constant t h e l i g h t p o l a r i z a t i o n d i rec t i on , 2, was scanned w i t h

time. F igu re 16 i s a summary o f t h e r e s u l t s f o r t h e cases i n v e s t i -

gated. The abscissa i s labe led f o r t h e (110) surfaces bu t s t i l l

represents t h e r e l a t i v e angular o r i e n t a t i o n on the (100) surface.

For t h a t surface, each long t i c k mark represents a d i r e c t i o n o f [ l o o ]

symmetry. The photon energies were located a t t h e maxima i n t h e

AR/R major s t ruc ture .

The anisotropy i s on l y observed on t h e Ag (110) sur face t o we l l

w i t h i n t h e experimental e r ror . Although these data rcprcscnt o n l y

one photon energy and b i a s p o t e n t i a l , i t i s s i g n i f i c a n t t o no te t h a t

when t h e p o l a r i z a t i o n anisotropy was absent, i t was absent over t h e

e n t i r e range of G and hw invest igated, t o w i t h i n experimental un-

c e r t a i n t y .

I 1 I I I I I I 1 1 I 1 " ' 1 1 1 " 1 "

- 5 x loo4 2 I IO Ag

T I10 A u

- I I I I I I I I I I 1 1 1 1 1 1 1 1 1 1 1 1

ORIENTATION OF $ F i g u r e 16. ER versus 1 i g h t p o l a r i z a t i o n E ; Abscissa l a b e l s app ly t o ( 1 10) su r faces and represen t

t h e same angu la r r e l a t i o n s h i p s f o r t h e (100) sur face. For Ag, t h e same parameters as i n F i g u r e 14 apply. Top, h w = 3.88 eV; middle, h w = 3.93 eV. For Au, t h e same

'parameters a r F i g u r e 15 apply. hw = 2.45 eV.

Elec t ro re f l ec tance Versus Operat ing Condi t ions

I n the ex tens ive study of Ag (110), several ope ra t i ng parameters

and e lect rochemical cond i t i ons were observed i n r e l a t i o n t o t h e i r e f f e c t

on t h e exper imenta l l y observed ER. The va r iab les o f i n t e r e s t i n . t h i s

.. sec t ion were observed t o have a minor e f f e c t comp.ared t o t h e i n f l u e n c e

' o f t h e th ree major independent va r i ab les ; photon energy, e lec t rode

b i a s p o t e n t i a l , and l i g h t p o l a r i z a t i o n .

Modulat ion ampl i tude

A convenient way t o express t h e e f fec t of a v a r i a b l e which i s n o t

. . expected t o modify t he measurement i s through t h e p o l a r i z a t i o n r a t i o

AR (^e para1 l e l t o [ 100])/AR ( b a r a l l e l t o [ 1101). The r e s u l t o f t h i s

ana lys i s as a f u n c t i o n o f t he modulat ing p o t e n t i a l ampl i tude app l ied

t o t h e i n t e r f a c e i s shown i n F igu re 17. The reg ion o f ampl i tude inde-

pendent e f f e c t s l i e s below 35 mV rms. Most o f t h e repor ted data were

recorded i n t h i s region. The onset of ampl i tude dependent behavior i s

a t t r i b u t e d t o t h e ex ten t o f t he modulat ion encompassing a p o t e n t i a l .

reg ion over which the double l aye r p r o p e r t i e s vary appreciably, o r t o

more complicated pe r tu rba t i ons o f t h e e l e c t r o n t r a n s i t i o n s respons ib le

f o r absorpt ion.

With a l l o t h e r v a r l a b l e s f i xed , AR/R scaled l i n e a r l y w i t h % AC '

which i s d i r e c t l y p ropo r t i ona l t o Aq, t he charge modulat ion f o r ampl i-

tudes below 35 mV rms.

Modulat ion frequency

I d i d no t be l i eve t h a t it was worth a l a rge investment o f t ime t o

study t h e frequency dependence o f t h e s ignal . The upper l i m i t o f t h e

p o t e n t i a l don t ro l c i r c u i t r y was about' 1.5 kHz, depending on t h e solu-

t i on . Th is i s a r e l a t i v e l y low frequency f o r making any determinat ions

as t o t h e dynamic o r i e n t a t i o n a l e f f e c t s o f t h e water d ipoles.

A cursory study o f t h e frequency dependence over t'he l i m i t e d re-

g ion o f poss ib le v a r i a t i o n revealed no change i n t h e p o l a r i z a t i o n r a t i o

AR1OO/aR110 (40 t o 1000 Hz). Th is i nd i ca ted t h a t t h e double l aye r

could respond e f f e c t i v e l y over t h i s frequency range and t h a t no long

t ime constant adsorpt ion o r reac t i on processes were involved. This

in format ion i s la rge ly , redundant t o t h a t provided by t h e double l aye r

capac i tance.

Surface prepara t ion

No major e f f e c t was observed which may have depended on t h e d i f -

ferences between the e tch-a t tack po l ished and the e lec t ropo l i shed sur-

faces. Th is .was t r u e f o r p roper ly prepared and cleaned surfaces

(Figures 1 3 and 14). On samples t h a t s t i l l r e ta ined some sur face

s t r a i n a f t e r t h e f i n a l treatment, anomalous low energy s t r u c t u r e '

appeared (Appendix A). With e lec t ropo l i shed~samp les t h a t were no t

subjected t o t h e ca thod ic reduct ion pretreatment, anomalous h i g h energy

s t r u c t u r e was, seen t h a t rep1 aced t h e normal ER 1 i neshape ( ~ p p e n d i x A).

So lu t i on composit ion

I n previous s tud ies o f e l e c t r i c f i e l d modulat ion o f metal sur-

faces, o n l y ~ b e l s s B t -- a ~ . ' ~ w i t h h i s ATR c o n f i g u r a t i o n on Au a t low

photon energy was ab le t o observe changes a t t r i b u t a b l e t o t h e compo-

s i t i o n o f t he e l e c t r o l y t e . o the r inves t iga t ions '2 '28 show no major

d i f f e r e n c e i n ER s t r u c t u r e due t o d i f f e r e n t e l e c t r o l y t e s . Among my

resu l ts , F igure 13 represents ER i n 1 M HC104 and F igu re 14 b,c

represents the c h a r a c t e r i s t i c s of t h e 1 M KOH so lu t ions . One observes

d i f f e r e n t behavior f o r h w > 4.0 eV as p rev ious l y mentioned. I n addi-

t i on , t h e peak he igh t i n KOH so lu t i ons .never achieved t h e maximum

he ight obta i ,nabl e i n t h e ~ ~ 1 0 ~ so lu t ions .

These two so lu t i ons a re q u i t e d i f f e r e n t and might be expected

t o a f f e c t t h e metal i n t e r f a c e d i f f e r e n t l y . The KOH i s a s t rong base

w i t h a h igh p ropor t i on o f OH' ions whereas t h e HC104 i s a s t rong ac id

+ w i t h a l a r g e concent ra t ion o f H . The OH- anion does not undergo

s p e c i f i c adsorpt ion whereas, w h i l e s t i l l possessing a weak tendency,

- t h e C104 may adsorb t o some degree. I t has already mentioned t h a t

- OH- i s expected t o behave 1 i ke water o p t i c a l l y whi l e C104 may not.

Oxygen e f f e c t s

By opening t h e atmosphere box which contained t h e exposed drop

o f so lu t ion , I could observe t h e e f f e c t o f oxygen, which has t h e

l a rges t concent ra t ion i n a i r , a f t e r n i t rogen. TheAR/R struc ' ture

increased un i fo rmly across t h e spectrum o f photon energies by about

10 percent under these condi t ions.

The e x p l i c i t e f f e c t of an e lec t rochemica l ly generated ox ide

laye r was b r i e f l y invest igated. A shor t anodic t reatment i n t h e

p o t e n t i a l region f o r t h e formation o f Ag20 resu l ted i n t h e disap-

pearance o f t he AR/R s ignal . When t h e p o t e n t i a l was returned t o the

double l aye r region, a f t e r t h e cu r ren t peak associated w i t h ca thod ic

reduct ion of t h e oxide, s t r u c t u r e returned s i t u a t e d roughly a t t h e

same energy as before but severely broadened. There was no pol a r i za -

t i o n dependence t o t h i s broadened s t ruc ture . Th is t e s t . r e i n f o r c e s

t h e c l a i m t h a t t he Ag was o r i g i n a l l y c lean and ox ide f r e e before t h e

anodic treatment.

E lec t ro re f l ec tance Versus E lec t rode Bias Po ten t ia l

The data i n t h i s sec t ion were recorded under mode C. With a l l

o the r va r iab les constant, t h e e lec t rode b i a s p o t e n t i a l , a , was scanned

over the region o f idea l double l aye r behavior. Th is technique was t h e

best f o r @ s tud ies s ince i t insured reproduc ib le electroc'hernical con-

d i t i o n s a t a l l photon energies f o r a given @. I recorded data on t h e

scan toward more p o s i t i v e p o t e n t i a l s only, t o make c e r t a i n t h a t t he

e lec t rode was i n a clean, f r e s h l y reduced s ta te . '

Resul ts a re reported f o r t h e (110) sur face o f Ag only, s ince

t h a t ma te r ia l was t h e on ly one e x h i b i t i n g anisotropy. The p o t e n t i a l

was scanned from -1.5 V (sCE) where atomic hydrogen e v o l u t i o n i s j u s t

beginninq. Before record inq data, t h e sample was maintained a t ' t h i s

negat ive p o t e n t i a l t o e lec t rochemica l ly reduce t h e sur face laye r due

t o e l e c t r o p o l i s h i n g as p rev ious l y described.

F igu re 18 shows rep resen ta t i ve r e s u l t s f o r t h r e e energies;

before t h e peak (3.4 eV), very near t h e peak maximum (3.9 eV), and

a f t e r t he peak (4.07 eV). Note t h a t 9 increases t o the l e f t . The

w i d t h o f t h e no ise i n t h e f i n a l AR/R spectrum was 0.1 x Several

fea tures are worth p o i n t i n g ou t :

1. There i s a b i g v a r i a t i o n i n peak he igh t w i t h Q. This re-

' f l e c t s t h e a b i l i t y o f t he e l e c t r o l y t e t o d e l i v e r charge t o

the metal surface. The charge m o d i f i c a t i o n d u r i n g a h a l f

c y c l e o f t h e 1000 Hz s inuso ida l modulat ion i s r e l a t e d t o t h e

exper imenta l l y measured I (rms) by, A q = 4 . 5 ~ 1 0 ~ ~ AC 'AC

This q u a n t i t y i s p l o t t e d i n F igu re 19 together w i t h t h e

3.9 eV curves from F igu re 18. The o p t i c a l s i gna l scales

roughly w i t h t h e d e l i v e r e d charge b u t i t i s c l e a r t h a t some

a d d i t i o n a l change due t o 9 i s a l so a f f e c t i n g t h e ER.

2. The s c a l i n g of A R / R w i t h capacitance i s on l y apparent a t

photon energies near and beyond t h e peak maximum.

3. The p o l a r i z a t i o n an iso t ropy o f t h e peak disappears f o r

negat ive p o t e n t i a l s (< -0.9 V), and reverses charac ter a t ,

t h e p o s i t i v e end o f t h e 9 axis, Th is behavior can be ex-

pressed by the p o l a r i z a t i o n r a t i o which i s p l o t t e d i n F igu re

20. Th is graph d ramat i ca l l y i l l u s t r a t e s t h e p o t e n t i a l re -

g ion and sense o f t h e an i sotropy.

4. For hw = 3.4 eV t h e p o l a r i z a t i o n dependence reverses near

9 = -0.5 V. and f o r hw = 4.07 eV the an iso t ropy i s constant

w i t h respect t o 4.

- ( vo l t s vs S C E )

F igu re 18. ER o f (110) Ag versus e lec t rode p o t e n t i a l f o r two perpendicular l i g h t p o l a r i z a t i o n s g, and t h r e e representa t ive photon energies. E lec t ropo l ished and reduced surface, 1 M' KOH, QAC = 30 mV rms a t 1 kHz.

F igu re 19. Comparison o f ER on (110) Ag t o experimental charge de l i ve red du r ing a h a l f c y c l modul'ation; AR/R r e p l o t t e d from F igure 18 f o r hur = 3.90 eV; A, ^e 11 [ 1101 ; ., ^e )I

I

0 I 0 0 0.2 0.4 0.6 0.8 1.0 1.2

- + (volts vs SCE)

'- -

I I I. ' .

I

Figure 20. R a t i o . o f AR/R on (110) Ag for two perpendicu1a.r l i g h t p o l a r i z a t i o n s versus e lect rode p o t e n t i a l ; sarne.operating condit ions as Figure 18.

~ h e ' d a t a recorded w i t h mode C f o r t h e two perpendicular pol 'ar iza-

t ' i on o r i e n t a t i o n s and fo r a v a r i e t y of photon energies were r e p l o t t e d

w i t h hw as t h e abscissa f o r a s e l e c t i o n o f constant po ten t ia l s . Th is

in format ion appears i n F igure 21. The region o'f anisotropy i n t h e

.peak magnitude i s c l e a r l y displayed, as i s t h e reversa l o f t h e low

energy an i so t ropy.

An a d d i t i o n a l c h a r a c t e r i s t i c o f t h e data shows up i n t h i s f igure .

The energy p o s i t i o n o f t he maximum o f t h e peak i s observed t o s h i f t

w i t h @. To most accura te ly study t h i s behavior, mode A was employed.

The l o c a t i o n o f t h e maximum i n . t h e peak of AR/Ry f o r ^e pa r ' a l l e l t o

[ l o o ] under a v a r i e t y o f condi t ions, versus e lec t rode b ias p o t e n t i a l

i s shown i n F igu re 22. Each type of symbol represents a given day 's

run. The parameters are l i s t e d i n t h e capt ions o f t h e r e f e r r e d f i g -

ures. The data e x h i b i t some uncer ta in ty from day t o day. The peak

s h i f t , c l e a r l y d iscernab le on a s i n g l e sample, i s very small -- a t

t h e l i m i t s o f my r e s o l u t i o n c a p a b i l i t y . Going from zero v o l t s toward

negat ive b ias p o t e n t i a l , t h e p o s i t i o n f i r s t s h i f t s s l i g h t l y t o lower

energy then bottoms o u t and s h i f t s ,toward h igher energy. The behavior

o f t h i s ' e f f e c t i s s i m i l a r f o r a1 1 samples i n KOH but occurs over a

smal ler p o t e n t i a l range i n HC10,+.

Cahan -- e t a1. l2 have reported a peak s h i f t i n t h e ER o f Au f i lms .

As t h e e lec t rode was made more pos i t i ve , t h e peak was seen t o broaden

and s h i f t batht i - d ramat i ca l l y t o lower energy. However, Mc ln ty re is 2 8

more re1 i a b l e data on AU exh ib i ted no such , s h i f t w i t h i n t h e 1 i m i t s of

h i s reso lu t ion . . .

- I.0V / o * ~ " ' I I I I I I I

I '

3.0. 3.5 4.0 PHOTON ENERGY (eV)

Figure 21. ER o f (1 10) Ag versus photon energy and e l e c t r o d e p o t e n t i a l f o r two perpendicular l i g h t p o l a r i z a t i o n s ; t h i s graph was reconstructed from d a t a taken under the condit ions t h a t apply t o F igure 18.

- (volts vs SCE) - F igure 22. Photon energy l o c a t i o n o f the maximum i n t h e major s t r u c t u r e o f M / R . f o r (110) Ag

versus e lec t rode p o t e n t i a l . For a l l cases $ 1 1 [ 1001. Each type o f symbol represent .'

one day 's resu l t ; under cond i t i ons t h a t apply t o F igure 13 ( ) F igu re 14, ( A ) , and F i gure A2. (x) .

Kramers Kronig Analys is

A Kramers-Kronig invers ion o f t h e experimental, AR/R was performed

f o l lowing standard modulat ion r e f l e c t i v i t y techniques3 t o get t h e d i f -

f e r e n t i a l Fresnel coe f f i c i en ts . These were used w i t h t h e 1 inear

approximat ion theory ( ~ p p e n d i x D) t o get values f o r Acb a t t h e surface. 2

This i nve rs ion depends very s t rong ly on a'ssumptions concerning t h e

o p t i c a l s t r u c t u r e o f t he double layer . I t a l so requ i res knowledge o f

t h e o p t i c a l p roper t i es o f t h e b u l k metal, which vary r a p i d l y i n t h e

region of i n t e r e s t .

I n view o f the many u n c e r t a i n t i e s surrounding the understanding

o f m e t a l l i c ER, I have decided against basing any conclus ions on the

KK resu l ts . Although AR/R i s no t d i r e c t l y p ropor t i ona l t o quantum

mechan i c a l absorpt ion processes, i t does represent the t r u e experimental

phenomenon. Any data processing which depends on t e n t a t i v e assumptions

i s no b e t t e r than an ana lys is of AR/R i t s e l f . The experimental r e s u l t s

w i l l always be a v a i l a b l e f o r comparison t o theory when more complete '

i ; terpretat ions become avai 1 able.

CHAPTER I V.. D I SCUSS I O N

The r e s u l t s o f t h i s i n v e s t i g a t i o n represent t h e f i r s t repro-

d u c i b l e e lectroref . lectance measurements on proper ' ly prepared, s t r a i n

f r e e s i n g l e c r y s t a l metal surfaces. The drop technique avoided most

of t h e sample mounting and s o l u t i o n p u r i t y problems experienced when

conventional electrochemical proc'edures are employed. The improved

method enabled a study o f t h e photon energy and e l ' cc t rsde p o t e n t i a l

dependence-of AR/R. I n addi t ion, t h e a p p l i c a t i o n o f c a r e f u l s i n g l e

. c r y s t a l surface prepara t ion techniques made poss ib le a d e t a i l e d study

o f t h e l i g h t polar izat ion'dependcince which before had never been a t -

'. tempted.

Any explanat ion of t h e e l e c t r o r e f lectance o f Ag and Au must

s a t i s f y a number o f experimental features. These a re summarized i n

t h e f o l lowi'ng 1 i st . several ' o f t h e c h a r a c t e r i s t i c s have been noted

by o the r i n v e s t i g a t o r s (a). he m a j o r i t y a re po in ted ou t f o r t h e

f i r s t t ime i n t h i s work s,ince they represent experimental in fo rmat ion

never before ava i lab le .

-'- 1 . An increase i n p o t e n t i a l across a me ta l / so lu t i on i n t e r f a c e pro-

duces a decrease i n t h e r e f l e c t i v i t y o f t h e metal.

+:2. S t ruc tu re i n t h e spect ra l representa t ion o f AR/R occurs a t t h e

same energy as s t r u c t u r e i n R i n most cases.

;':3. The major peak s t r u c t u r e i n AR/R t a i l s o f f t o low energy..

4 . A h igher energy p lateau i s observed i n ' t h e E R of Au.

5. A v a r i a b l e h i g h energy d ropo f f i s present i n t h e ER o f Ag.

6. Clean, smooth, s t r a i n f ree Ag d isp lays no 'ER s t r u c t u r e near

3.3 eV.

-7. AR/R scales w i t h Aq.

8. AR/R d i sp lays a magnitude v a r i a b i l i t y t h a t depends on t h e e lec-

t rode b i a s p o t e n t i a l .

kg. There i s no dramatic ' d i f f e rence between t h e ER o f a metal re -

corded i n two q u i t e d i f f e r e n t e l e c t r o l y t e s .

10. The magnitude o f AR/R increases s l i g h t l y wi ' th t h e a d d i t i o n of

oxygen t o the so lu t ion .

"11 . The maximum i n t h e major s t r u c t u r e o f AR/R versus photon energy

s h i f t s w i t h e lec t rode b i a s p o t e n t i a l .

12. The character o f t h e peak s h i f t depends on t h e s o l u t i o n cornpo-

s i t i o n .

13. The major s t r u c t u r e i n t h e ER o f (100) Ag i s s h i f t e d t o h igher

energy w i t h respect t o t h e same s t r u c t u r e i n t h e ER of (110)

Ag

14. The ER o f (1 10) Ag d i sp lays an anisotropy, us ing normal i n -

cidence rad ia t i on , t h a t depends on photon energy.

15. There i s no ani sotropy i n t h e ER of (100) Ag.

16. There i s no anis'otropy i n the. ER .of ( 1 10) Au. '

17. The anisotropy i n t h e ER o f (110) Ag disappears w i t h l a r g e

negat ive e lec t rode po ten t ia l s .

18. The anisotropy i n the EK o f (110) Ag'occurs t o some degree a t

a l l photon energies when i t i s present.

19. The angular dependence of the (110) Ag ER anisotropy var ies

w i t h e lectrode potent ia l .

20. The angular dependence of the (110) Ag ER anisotropy i s inde-

pendent o f modulation amplitude fo r small amplitudes.

21. The anisotropy goes away when an oxide layer i s produced on Ag.

Comparison t o the Mclntyre-Aspnes Theory

As ou t l i ned i n the introduct ion, Mclntyre has explained most

of the prev ious ly observed features of m e t a l l i c ER w i t h h i s model,

developed i n co l labora t ion w i t h Aspnes, which i s based on charge modu-

l a t i o n o f the f r e e e lec t ron d i e l e c t r i c func t ion i n a t h i n inhomoge-

neous layer. The loca t ion o f s t ruc tu re i n AR/R w i t h t h i s model i s

dependent on op t i ca l coupl ing between the bu lk so lu t ion and the bu lk

metal and on the loca t ion o f s t ruc tu re i n cb of the bu lk metal. This 2

can explain why AR/R i s less than zero and why peaks i n AR/R appear

near peaks i n R of the bu lk metal ( features 1, 2, and 4). Since

there i s not much change i n the op t i ca l proper t ies o f the bu lk solu-

t i ons r e s u l t i n g from d i f f e ren t e lec t ro ly tes , t h i s theory a lso an-

- t ic ipates the observation of feature 9,

The comparison o f the M-A theory w i t h my data f o r (110) Ag,

shown i n Figure 23, exh ib i t s a remarkable agreement. The symbols are

taken from Figure 21 and have been scaled by the experimental Aq/A.

The ca l cu la t i on uses Eqs. (2) and (8-5). The op t i ca l proper t ies o f

bu lk Ag used i n t h i s beterminat ion were measured on t h i n f i lms by

54 another invest igator .

Figure 23. Comparison of M-A model to my experimental AR'I AR/Aq taken from Figure 21 for cC = -1.0 V SCE). Experimental parameters, Aq = 4.14 ~coul, A = 0.6 cm2. Theoretical parameters, 42 r = 1 . 0 4 ~ 10-14 sec, up = 1.4~ 1016 sec-1,. N = 5.85 x 1022 electrons/cm~, n = 1.36. a

3.0 3.2 3.4 3.6 3.8 4.0 4.2

PHOTON ENERGY (eV)

The M-A theory should be most app l i cab le near t h e p o t e n t i a l o f

zero charge, PZC, s ince t h e i n t e r f a c e . r e g i o n i s f r e e from complicated

d i s t o r t i o n s . This i s the p o t e n t i a l where, i n t h e absence o f spec i , f i c

adsorption, t he re i s no excess i o n i c charge on t h e s o l u t i o n s ide o f

t h e double l aye r ( ~ p p e n d i x C). Th is c o n d i t i o n i s analogous t o t h e

"f 1 a t band" potent i a1 about which semiconductor ER i s con'ducted. 3

The p o t e n t i a l o f I = -1.0 V (sCE), t h e experimental va lue i n , F i g -

u r e 23, i s very c lose t o the accurately 'measured va lue o f t h e PZC f o r

(1 10) Ag o f - 1 . O 1 V (SCE). , The PZC determinat ion i s probably n o t

genera l ly app l i cab le t o the concentrated so lu t i ons employed i n my

experiment where t h e double l aye r s t r u c t u r e i s dominated by t h e char-

ac te r o f t h e inner layer . Even though t h e e l e c t r o l y t e s chosen i n t h i s

work do not s t rong ly adsorb, t he re q u i t e l i k e l y was some minor c o n t r i -

bu t i on t o t h e Inner Helmholtz Plane i n t h e concentrated s o l u t i o n s

employed. Under these cond i t i ons t h e PZC i s expected t o move t o

s i i g h t l y more negat ive p o t e n t i a l s . ,

An a d d i t i o n a l success of t h e M-A theory demonstrated by my r e s u l t s

i s t h e l i n e a r s c a l i n g o f AR/R w i t h Aq ( fea tu re 7). Th is r e f l e c t s t h e

combined e f f e c t o f t h e l i n e a r approximation, LA, theory and t h e e l e c t r o n

dens i t y assumption.

Mc ln ty re invoked a sur face plasmon mechanism t o exp la in t h e low

energy s t r u c t u r e i n Ag near 3.3 eV which I see o n l y under unfavorable

cond i t i ons ( fea tu re 6). An a d d i t i o n a l d iscuss ion o f t h i s behavior i s

conta ined i n Appendix A. ,Sur face plasmons are a l so t h e source o f t h e

low energy t a i l i n g i n Au ( f e a t u r e 3 ) , according t o Mclntyre.

The M-A theory does no t address i t s e l f t o e f f e c t s o f v a r i a t i o n s

i n t h e average e lec t rode p o t e n t i a l ( features 8 and 1 1 ) nor t o any be-

hav ior r e l a t e d t o t h e c r y s t a l l a t t i c e o r i e n t a t i o n ( fea tu res 13 and 21).

Ne i ther does i t t r e a t t h e more s u b t l e evidence o f dependence on the . ,

chemical makeup of t h e i n t e r f a c e ( fea tu res 5, 10, and 12).

The LA theory, which i s independent o f t h e modulat ion mechanism,

can be expanded t o inc lude anisotropy and b ias p o t e n t i a l e f fec ts , i n

simple a d d i t i v e combination. To enable sub t rac t i on o f t h e M-A com-

ponent o f t h e s ignal , however, would requ i re knowledge o f how t h e

an iso t rop ic mechanism depends on Aq, which i s no t a v a i l a b l e w i thout

.a 'de ta i 1 ed theory.

MclntyreZ8 has suggested an explanat ion f o r some o f h i s anomalqus

b i a s p o t e n t i a l e f f e c t s which may serve as . an . exp lanat ion o f t h e poten-

, t i a l dependence o f t h e an iso t ropy t h a t I observe ( f e a t u r e 17). I n

h i s measurements on Au f i lms, he saw t h e appearance o f p o s i t i v e s t ruc -

t u r e near 4 eV which became more pronounced as t h e Au was biased more

p o s i t i v e t h a n . l . 0 V ( s C E ) . Although Mc ln ty re ' s s t ruc ture .may be

quest ionable, s ince t h e p o t e n t i a l region was approaching t h a t where

ox ide format ion begins, h i s i n t e r p r e t a t ion i s i n t e r e s t i n g . He S U . ~ -

gested t h a t t he p o s i t i v e e lec t rode p o t e n t i a l reg ion caused a reducing

o f t h e ef fect iveness w i t h which t h e bound e lec t rons a re shie lded there-

by a l l ow ing t h e i r c o n t r i b u t i o n t o t h e ER t o be not iceable. The

an iso t ropy r e f l e c t s t h e i n t e r a c t i o n o f t h e e lectrons, which, sense t h e

photon probe, and the i on l a t t i c e , which d i sp lays t h e c r y s t a l symmetry.

The modulat ion of t h i s i n t e r a c t i o n probably takes p lace w i t h i n a

shal low region o f t he sample sur face beyond which t h e modulat ing f i e l d

i s screened. By b i a s i n g t h e e lec t rode t o a more negat ive p o t e n t i a l ,

t h e e l e c t r o n dens i t y i n the sur face region increases. The modulat ing . .

f i e l d i s more e f f e c t i v e l y screened and may no t penet ra te t o a depth

where t h e e lec t rons f e e l t he l a t t i c e . w i thou t t h e l a t t i c e , t h e

anisotropy i s absent. As t h e e lec t rode p o t e n t i a l i s increased pos i -

t i v e l y , t h e e lec t rons are "pushed" back i n t o t h e reg ion where t h e l a t -

t i c e e x i s t s and t h e anisotropy appears. The f a c t t h a t t h e angular

dependence o f t h e ani sotropy changes w i t h b ias p o t e n t i a l ( f e a t u r e 1.9)

i l l u s t r a t e s t h e complexi ty o f t h e mechanism.

I n t e r a c t i o n Between Photons and an Adsorbed Layer

I n t h i s sec t ion I consider some of t h e unexplained fea tures o f

t h e experimental ER one might be tempted t o i n t e r p r e t as due t o o p t i - c a l i n t e r a c t i o n s w i t h t h e unmodulated s o l u t i o n phase adjacent t o t h e

sa'mple, I f t h l r e were ions s p e c i f i c a l l y adsorbed-at t h e l ~ p ' w i t h an

o r i e n t a t i o n r e f l e c t i n g the two-dimensional symmetry o f t h e surface,

an iso t ropy might be expected. The OHP ions, which tend t o have hydra-

t i o n sheaths and which are much f a r t h e r from t h e e f f e c t o f t h e l a t t i c e ,

would add a h igher order c o r r e c t ion t o t h i s model.

The LA theory includes t h e c a p a b i l i t y o f desc r ib ing t h e e f f e c t o f

an unmodulated ove r laye r through Eq. (D-3 ) ( ~ p p e n d i x D) . The pos-

b i l i t y o f an i so t rop ic c o n t r i b u t i o n s from such a s t r u c t u r e i n t h e ab-

sence o f anisotropy from t h e metal i s remote f o r several reasons:

a) I t i s n o t expected t h a t t h e c r y s t a l l a t t i c e e f f e c t wou,ld be

s t rong enough t o o r i e n t a sol .ut ion molecule a n d ' a t t he same

t ime be screened o u t so t h a t sur face e lec t rons i n t h e metal

had no knowledge o f t h e l a t t i c e symmetry.

b) I n o r d e r t o e x p l a i n m y experimental resu l ts , t h e o v e r l a y e r

mechanism must be p e c u l i a r t o Ag only. The experiment was

performed w i t h the same e l e c t r o l y t e ( ~ ~ 1 0 ~ ) on both Ag and

Au. One would expect the same ove r laye r e f f e c t t o operate . .

on each metal.

c) There i s no change i n t h e gross p o l a r i z a t i o n dependent be-

hav ior a t t r i b u t a b l e t o s o l u t i o n composit ion (KOH o r ~ ~ 1 0 ~ )

on Ag. The 'so lu t i ons of these e l e c t r o l y t e s have a very

. d i f f e r e n t make-up and consequently would be expected t o

have a very d i f f e r e n t IHP, i f i t i s present a t a1 1.

d) Even i f a sub-monolayer o f ox ide were present, i t has been

shown44 t h a t anodic ox ide f i l m s tend t o be amorphous and do

n o t grow e p i t a x i a l l y . My cursory i n v e s t i g a t i o n of t h e ER

o f Ag i n t h e known presence o f an ox ide ( f e a t u r e 21) seems

t o subs tan t ia te t h i s argument.

e) The c o r r e c t ion term i n Eq. (D-3) i s of t h e same o rde r o f

magnitude as h/do. Th is would be no l a r g e r than I f

present a t a l l , t h e c o r r e c t i o n would be very small and cou ld

not produce such pronounced e f f e c t s as observed i n experiment.

For these reasons I tend t o r e j e c t t h e p o s s i b i l i t y o f an adsorbed

laye r o r f i l m t h a t has an o p t i c a l e f f e c t on AR/R but does n o t pe r tu rb

t h e metal by i t s presence.

Vectora l Pe r tu rba t ion

Several poss ib le explanat ions f o r t h e symmetry p r o p e r t i e s o f t h e

s i n g l e - c r y s t a l ER of metals r e l y on arguments centered around t h e

- symmetry p roper t i es o f t he face-centered cub ic B r i l l o u i n zone. These

ideas depend on the assumption t h a t t he e l e c t r o n energy s ta tes in. t h e

sur face region can be represented by t h e band s t r u c t u r e o f t h e bulk,

o r a t l e a s t t h a t t h e surface e lec t rons a f f e c t e d by t h e modu1,ation

p a r t i c i p a t e t o a l a r g e enough degree i n i n t e r a c t i o n s w i t h bu.lk s tates,

t h a t 'symmetry p roper t i es of t h e ER s igna l r e f l e c t t h e symmetry o f t h e

bulk. This i s n o t expected t o be a good approximation f o r quan t i t a -

t i v e work but may c l a r i f y t h e understanding of. t h e p o l a r i z a t i o n de-

pendent s t r u c t u r e of t h e ER o f Ag.

A formal ism e x i s t s f o r qua1 i t a t i v e ana lys i s of t h e symmetry be-

hav ior o f semiconductor ER which was developed by Bot tka and Fischer 5 5

on a suggestion by ~ h i l l i p s . ~ ~ I t was o r i g i n a l l y intended f o r use

w i t h the Franz-Keldysh e f fec t as a modulat ion mechanism but should be

good f o r any vec to ra l pe r tu rba t ion of t h e j o i n t dens i t y of ' s ta tes

(JDOS). I t i s discussed i n terms of t he e f f e c t on e i f o r a t r a n s i t i o n

between a s i n g l e p a i r of bands, The f i e ld -pe r tu rbed r e s u l t can be

w r i t t e n by modi fy ing Eq. (8-8).

Here, t h e sum i i s over t h e symmetry equ iva lent (be fore t h e app l ica-

t i o n o f t h e f i e l d ) regions of 2 - s p a c e t h e t c o n t r i b u t e t o the t r a n s i -

t i o n of i n t e r e s t . ( t h e s t a r o f T;). I t i s assumed tha't t he re i s no

change i n t h e interband m a t r i x elements so t h a t Mi s t i l l adequately

. . describes t h e way t h e p o l a r i z a t i o n vec tor of t h e photon samples

. -

. . , each region i. Ti, t h e r e s o l u t i o n o f t h e pe r tu rba t ion vec to r f i n

t h e l oca l coord inate system i, has an as y e t unspec i f ied e f f e c t

on the, l oca l JDOS. The o r i e n t a t i o n o f 7 i s d i f f e r e n t i n each system

. i causing d i f f e rences among t h e J(w,f i ) .

Consider t h e f.c.c. B r i l l o u i n zone f o r Ag. I n t h e energy range

o f i n t e r e s t (near 4 eV), interband t r a n s i t i o n s occur between s ta tes

o f A symmetry. Th is I s t h e symmetry o f a cube diagonal. There are . .

8 equ iva lent members t o t h e unperturbed s t a r o f ( i i s summed f rqm

1 t o 8). I n t h e absence o f 7 a1 l J(w,O) are equ iva lent and Eq. (3)

: reduces t o Eq. (8-8), t he i s o t r o p i c r e s u l t . When T i s present, t h e .

J(w,fi) a re no longer equivalent . F igu re 24 shows the f.c.c.

B r i 1 l o u i n zone and t h e symmetry reducing e f f e c t o f a vec to ra l per-

t u r b a t i o n i n t h e [ I 1 0 1 d i r e c t i o n . The 8 p rev ious l y equ iva lent mem-

bers o f t h e s t a r o f A are shown as dot ted l ines . Member d i r e c t i o n s

te rm ina t ing on the zone face ( a t L), shown w i t h a double c i r c l e , a re

-perpendicular t o 7? (2, 4, 7, 8) w h i l e t h e remaining f o u r members

(1, 3, 5, 6) a re o r i e n t e d a t 35.3' w i t h respect t o < Equation (3)

now depends on photon p o l a r i z a t i o n s ince the JDOS must remain i n t h e

sum and ac ts as a weight f a c t o r f o r Mi;

F igu re 24. B r i l l o u i n z o n e , f o r Ag w i t h a vec to ra l per tu rba t ion , 7, app l i ed i n the [ I 1 0 1 d i r e c t i o n . The e i g h t members o f . t h e s t a r o f A a re shown w i t h do t ted l i nes .

As might be expected from t h e general symmetry arguments pre-

sented i n Chapter I, the ana lys is i f repeated f o r 7 para1 1 e l t o [ 1'1 11

o r [ ' l oo ] y i e l d s an i s o t r o p i c r e s u l t when t h e photon p o l a r i z a t i o n vec-

tor i s r e s t r i c t e d t o l i e i n a p lane perpendicular t o 7.

The v a l i d i t y of t h e f i e l d - f r e e m a t r i x element assumption can be

tes ted by observ ing t h e p o l a r i z a t i o n r a t i o AR1OO/aR110 f o r a v a r i e t y

o f modul a t ion amp1 i tudes. (See F igure 17) The demonstrated inde-

pendence o f - t h i s r a t i o f o r iP < 35 mV imp l ies that , f o r small modu- AC

l a t i o n amplitudes, any v a r i a t i o n i n AR due t o 7 occurs equa l ly f o r

[ 1101 and [ 1001 p o l a r i z a t i o n s o f t h e 1 igh t . That is, t h e v a r i a t i o n , .

occurs i n t h e JDOS, not i n Mi t h a t depends on t h e p o l a r i z a t i o n . Th is

provides a good explanat ion f o r fea ture 20.

Franz-Keldysh e f f e c t

The prev ious arguments descr ibe t h e formal ism t h a t can e x p l a i n

t h e anisotropy i n ER o f metals provided a vec to ra l p e r t u r b a t i o n

mechanism can be j u s t i f i e d . The f i r s t guess one might exp lo re would

be t o f o l l o w t h e quantum mechanical theory f o r t h e e f f e c t o f a u n i -

form e l e c t r i c f i e l d on o p t i c a l t r a n s i t i o n s i n a b u l k c r y s t a l . The

r e s u l t would be s i m i l a r t o thoroughly researched semiconductor e lec -

t r i c f i e l d e f fec ts , on l y modi f ied by t h e presence o f a Fermi surface.

Th is ana lys i s i s n o t expected t o be v a l i d under cond i t i ons o f a

s p a t i a l l y vary ing f i c l d . Aspnos and ~ r o v a " have described a method

f o r app ly ing the un i fo rm f i e l d r e s u l t t o an inhomogeneous system.

However, t h e i r ana lys is assumes t h a t a t any depth t h e un i fo rm f i e l d

equations apply. Th is requires, t h a t F) be uniform over many l a t t i c e

58 constants, a c o n d i t i o n t h a t c l e a r l y does not apply i n metal1 i c ER. ,

I n d i r e c t t r a n s i t i o n s

Morr i s and demonst ra ted t h e poss i b i 1 i t y o f i nd i r e c t

in terband t r a n s i t i o n s i n d i l u t e Agln a l loys . This mechanism con-

t r i b u t e s t o absorpt ion a t an energy j u s t below t h e onset o f d i r e c t

t r a n s i t i o n s . ' Sca t te r i ng from t h e I n impur i ty atoms suppl ied enough

momentum i n t h a t c a i e f o r e lec t rons t o become. e x c i t e d from t h e p-

band a t t h e Fermi l eve l near L2 ' t o t h e L1 c r i t i c a l po in t . The change

i n wavevector (p ropor t i ona l t o momentum change) needed t o make t h i s

8 - 1 '

t r a n s i t i o n i s on l y 0 . 2 ~ 1 0 cm , a small Frac t ion o,l: a rec ip roca l

1 a t t i c e vector .

I f an e l e c t r o n could g a i n momentum from an in terac t . ion w i t h t h e

pe r tu rb ing f i e l d i n an e l e c t r i c f i e l d modulated sur face region, a

s i m i l a r i n d i r e c t in terband t r a n s i t i o n may be t h e cause o f p o l a r i z a - \,

t i o n dependent s t r u c t u r e i n t h e ER of AS. To est imate t h e magnitude

o f t h e f i e l d needed I might use t h e equation o f motion f o r an e lec-

t r o n i n t h e presence o f an e l e c t r i c f i e l d : d ( ~ T ; ) / d t = -lei?. With

d t o f t h e order o f an e lec t ron 1 i f e t i m e (10- l4 sec) and dk equal t o

8 - 1 t h e needed wavevector change ( 0 . 2 ~ 1 0 cm ), t he requ i red f i e l d i s

o n l y 14 V/cm. This i s f i v e orders o f magnitude smal ler than t h e f i e l d

expected a t t h e sur face o f t h e metal i n t h e m e t a l / e l e c t r o l y t e double

layer . Even i f t h e f i e l d were exponent ia l l y at tenuated w i t h d is tance

i n t o t h e metal, t he re would s t i 1 1 be enough. momentum avai l a b l e from

100

t h e f i e l d f o r i n d i r e c t t r a n s i t i o n s t o take p l a c e , a t a depth 10 times

t h e Thomas-Fermi screening length. C e r t a i n l y by t h i s depth t h e b u l k

band s t r u c t u r e has more meaning and f i e l d ass is ted i n d i r e c t in terband

t r a n s i t i o n s might be expected.

F igure 25 shows t h e band s t r u c t u r e o f Ag., and Au near L and t h e

c o n t r i b u t i o n s t o eb r e s u l t i n g from interband t r a n s i t i o n s i n t h a t re- 2

g ion of 2-space. I n Ag, t h e p-s gap i s smal l e r than t h e d-p gap. I n

t h e corresponding onset o f absorption, Rwl l i e s a t a lower photon

energy than Rw2. If, i n the 'presence o f an e l e c t r i c f i e l d , t r a n s i -

t i o n s were allowed from the Fermi sur face t o t h e bottom o f t h e s-band . ,

a t L,, then an a d d i t i o n a l c o n t r i b u t i o n t o e i would be expected below

Awl. The s t reng th o f these t r a n s i t i o n s would depend on the d i r e c t i o n

o f t h e pe r tu rb ing f i e l d i n t h e l oca l coord inate system. .This would . .

g,ive r i s e t o t h e anisotropy producing J (w,B~) .

No ind. i rect t r a n s i t i o n s a re allowed a t t h e d-p gap s ince the f i n a l .

. . s ta tes a t L;' are already f i l l e d .

Thi.s model does a good j o b o f exp la in ing the absence o f anisotropy

i n Au ( fea tu re i 6 ) . Since t h e d-p gap i n Au i s sma l 1 e r than t h e p-s

gap, t h e onset o f p + s t r a n s i t i o n s i s swamped by t h e presence o f s t rong

d j p t r a n s i t i o n s . F i e l d induced i n d i r e c t t r a n s i t i o n s i n Au may take

p lace but they are unobservable.

Most recent assignments of t h e onset energy hco2 i n Ag are, about

3.87 eV (Appendix B). Th is i s exac t l y t h e reg ion o f t h e greates t con-

t r i b u t i o n t o t h e anisotropy . i n Ag.

F igu re '25. F i e l d ass is ted . ' i n d i r e c t in terband t r a n s i t i o n s i n Ag and Au. The schematic ~5 r e s u l t i n g from d + p d i r e c t t r a n s i t i o n s , which s t a r t a t hwa, and p + s d i r e c t . t r a n s i t i o n s , which s t a r t at.hwl, a re a l so shown. I n d i r e c t t r a n s i t i o n s are masked i n Au .

A g

Au

f i ~ l f iw2 3%

b € 2

ENERGY BANDS

Stress modulation

Another possible explanation for metallic ER which includes a

mechanism for anisotropy is stress modulktion. In a bulk crystal a

uniaxial stress lowers the crystal symmetry. However, momentum is

still a good quantum number to within a reciprocal lattice vector.

Transitions remain vertical and the dominant effect is due to a shift

of energy gaps or a change in the amplitude of matrix elements. The

differential dielectric function under these conditions approximates

the first derivative of the unperturbed value. Piezoreflectance of '.

Ag exhibits peaksof both signs, unlike the one-signed

experimental ,ER.

If an electric field produces a piezoreflectance signal there

must be a coupling between the field and a stress. This has.been ob-

served in ER of semiconducting crystals with 43m (zinc blende)

symmetry. 61 How,ever, incrystals with inversion symmetry (such as

the noble metals) there is no coup1 ing between the appl ied field and

an induced stress. If it is present in metallic ER, stress modulation

would have to exploit the lower symmetry in the surface region due to

the preferred direction of the surface normal, or the direct piezo-

optic effect due to pressure on the crystal surface transmitted by

double layer compression. Any stress modulation mechanism must ex-

plain the absence ot anisotropy in the ER of Au.

Although I have insufficient information to exclude this mech-

anism completely, the evidence seems to make it an unlikely consider-

at.ion.

103

Anisotropic Electron Gas

The M-A theory assumes t ha t on ly the f ree e lec t ron component o f

c i s modulated and t ha t the f r ee electrons have no in te rac t ion w i t h

the l a t t i c e . Since t h i s model explains many o f the features o f ER i n

metals i t might be p laus ib le t o hypothesize a surface e lec t ron gas

which causes, through planar charge densi ty f luc tuat ion, most o f the

ER e f fec t . I f t h i s c o l l e c t i o n o f e lec t rons were placed on top o f the

per iod ic l a t t i c e o f ion cores one might expect some charge densi ty

concent r a t ion over the 1 a t t i ce s'i tes. To proper1.y describe the many-

body d i e l e c t r i c func t ion o f t h i s gas requires a < dependent formalism. , .

Most o f the larger Four ier components would have perpendicular t o

the surface due t o the severe inhomogeneity i n . t h a t d i rec t ion . How-

ever, some non-zero component .o f ;j* would l i e paral l e l t o the surface

t o describe the e f f e c t o f inhomogeneity due t o e lec t ron concentrat ion

over the ion cores. On a (110) surface one would expect an an isot rop ic

d i e l e c t r i c tensor r e f l e c t i n g the lack of symmetry i n the plane. Sur-

face inhomogeneities, such as bumps and steps i n the l a t t i c e , could be

included by consider lng the1 r c6n t r i but ion t o t.he vector paral l e i , t o

the sur f ace.

The deta i 1 ed formal i sm f o r t h i s phenomenon does not ex i s t so no

addi t iona l discussion i s warranted. However, i t remains' an i n te res t i ng

p o s s i b i l i t y f o r theore t i ca l invest igat ion,

Surface States

One o the r p o s s i b i l i t y e x i s t s which can be invoked t o exp la in

v i r t u a l l y every f e a t u r e of t he experimental ER resu l t s . Th is i s t h e

exis tence o f e l e c t r o n states, e i t h e r i n t r i n s i c o r i n combination w i t h

s o l u t i o n const i tuents , which are l o c a l i z e d i n t h e sur face region and

which have a d i f f e r e n t charecter than t h e b u l k states.

M e t a l l i c sur face s ta tes

I n t u i t i v e l y one might expect l o c a l i z e d s ta tes as an i n t r i n s i c

r e s u l t o f t h e lower symmetry i n the surface region, even i n the ab-

sence o f pe r tu rb ing f i e l d ef fects. Several t h e o r e t i c a l works e x i s t

on t h e c a l c u l a t i o n of sur face energy bands f o r metals. 39,62,63

p e r i o d i c i t y p a r a l l e l t o t h e sur face i s re ta ined so t h a t wave

func t i ons a re B loch - l i ke i n t h a t plane. However, due t o t h e loss of

p e r i o d i c i t y perpendicular t o the surface, t h e wave f u n c t i o n s ' a r e

mo lecu la r - l i ke i n t h a t d i r e c t i o n . No c a l c u l a t i o n s e x i s t f o r low sym-

metry surfaces o f noble metals so no 'discussion o f the-expected t r a n s i -

t i o n s o r t h e i r anisotropy can be conducted.

Such surface s t a t e s werc suggcstcd as s cause o f ER i n Au as

e a r l y as 1970 by Cahan e t a l . l2 (see Chapter I ) . However w i t h t h e

i n t r o d u c t i o n and p a r t i a l success o f t he M-A model and because o f t h e

l ack o f o the r independent work on surface states, t h e idea was more o r

1 ess fo rgot ten .

ln terphase surface s ta tes

These s ta tes would e x i s t because o f a complicated i n t e r a c t i o n

1 1 between the e l e c t r o l y t e and t h e metal. Mc ln ty re has suggested t h a t

i f chemisorbed species a re ab le t o a l t e r eb i n t h e in terphase region,

e i t h e r through s t rong i n t e r a c t i o n w i t h d -e lec t rons i n t he sur face atoms

o f t h e metal o r by i n t r o d u c t i o n o f new t r a n s f e r absorp t ion processes,

they would produce e f f e c t s on t h e ER t h a t might vary non - l i nea r l y

w i t h p o t e n t i a l bias. These e x t r i n s i c surface states, he suggested,

a re expec ted , to add a h igher o rder c o r r e c t i o n t o the M-A theory and'

may be respons ib le f o r t he peak s h i f t phenomenon. MCI n ty re28 elab-

o ra ted on t h i s idea w i t h t h e proposal t h a t v i r t u a l bound s t a t e s a re

c rea ted by the adsorbate-metal i n t e r a c t i o n which r e f l e c t s t h e proper t ' ies

o f t he metal. Such v i r t u a l s ta tes have been observed i n photoemis-

64 s ion.

More recent ly , Bennett and Penn6' have advanced a theory f o r . .

the c a l c u l a t i o n o f t he o p t i c a l p r o p e r t i e s ' o f an adsorbate atom, us ing

a Green's f u n c t i o n technique. The formal ism i s r a t h e r complicated

and i s presented w i t h no comparison tn experiment.

Experimental e l ect'rochemical spectroscopy evidence i nd.icates

t h a t sub-monolayer f i l m s have measurable e f fec ts on t h e o p t i c a l prop-

. e r t i e s o f t h e substrate. Kolb e t a1.66 have shown t h a t TI, Cu, and Pb

adsorbed on Au produce r e f l e c t a n c e changes tha t , t o f i r s t order,

c l o s e l y approximate t h e ER of c lean Au. Takamura e t a1 .45 observed

Au i n t h e presence of M pb2+ and i d e n t i f i e d f o u r d i f f e r e n t

adsorpt ion s ta tes w i t h a combinat ion o f e lectrochemical and o p t i c a l

techniques. The f i r s t adsorpt ion s t a t e produced a re f l ec tance change

t h a t resembles c lean Au ER. This e f fec t has a l so been observed by

Hc l n t y r e and Kol b67 and Takimura -- e t a1. ' i n re f l ec tance measurements

o f t h i n ox ide layers on Au. I t . appears as though t h e i d e n t i t y o f t he

adatom p lays a secondary ro le .

Using t h i s p i c tu re , "cl'ean" metal ER would be caused by a complex

i n t e r a c t i o n between an adsorbed species and t h e metal which could be

approximated t o f i r s t o rder by a two d imensional ly un i fo rm e l e c t r i c

f i e l d . The I n t e r a c t i o n would be present w i t h water d ipoles, hydrated

ions, adsorbed cat ions, and sub-monolayer f ilms, which would a1 1, a t

lowcoverage, .a f fec t t h e m e t a l i n t h e same way. Changes i n the e lec-

t r i c p o t e n t i a l d i f f e rence between t h e metal and t h e s o l u t i o n would

modify the character o f these in terphase-sur face. s ta tes and would

cause the observed.changes i n o p t i c a l i n te rac t i ons .

The interphase sur face s t a t e model could, i n p r i n c i p l e , exp la in

most o f t h e experimental d e t a i 1 s o f metal 1 i c ER.. The energy locat ion,

sign, and shape o f AR/R would simply r e f l e c t t h e charac ter of these

s ta tes ( fea tu res 1, 3-6, 9, 10). The f a c t t h a t t h e s t r u c t u r e appears

where the o p t i c a l p roper t i es o f t h e subst ra te are r a p i d l y changing

( f e a t u r e 2) could be expla ined by a combined e f f e c t o f mul t iphase

o p t i c s and the m e t a l l i c charac ter o f the s t a l e s . Changes i n e l e c t r o n

d e n s i t y i n the sur face region indueed by changes i r ~ p u t e n t l a l would

modify t h e sur face s t a t e occupation and would be manifested t h r u t h e

dependence o f A R / R on Aq ( f e a t u r e 7 ) . As the p o t e n t i a l b a r r i e r

1

imposed by the me ta l / so lu t i on p o t e n t i a l d i f f e r e n c e i s modified, t h e

energy s t r u c t u r e o f t he s ta tes would -change. Th is would cause peak

s h i f t i n g ( fea tures 1.1, 12) as w e l l as o the r b ias p o t e n t i a l dependent

fea tures (8, 13, 18-20). Since t h e interphase sur face s ta tes would

r e f l e c t t he o p t i c a l p roper t i es o f t h e substrate, they would have t h e

symmetry o f t h e two dimensional s i n g l e c r y s t a l sur face region. On

low symmetry planes one would expect anisotropy w i t h normal incidence

photon i n t e r a c t i o n s ( fea tures 14, 15). The absence of anisotropy

under negat ive b ias cond i t i ons on Ag ( f e a t u r e 17) as w e l l as i t s ab-

sence w i t h heavy ox ide coverage ( f e a t u r e 21) suggests t h a t t h e i n t e r -

a c t i o n of t h e sur face s ta tes w i t h t h e l a t t i c e symmetry would be e a s i l y

broken. .The absence of anisotropy on s i n g l e c r y s t a l s o f Au ( fea ture

16) i s no t e a s i l y expla ined w i t h t h i s model. I t may i n d i c a t e t h a t '

these s ta tes would have q b i t e d i f f e r e n t character on Au and Ag.

Although interphase surface s ta tes can be invoked t o exp la in

m e t a l l i c ER, t he re i s danger i n us ing them as t h e un ive rsa l cause.

I n t h e absence o f t h e o r e t i c a l gu ide l ines one can e a s i l y p o i n t t o non-

e x i s t e n t t heo r ies as t h e source of poor ly under,stood phenomena. Th is

i s a s t rong temptation, bu t any concl.usions based on incomplete ideas

should always be considered hypothet ica l .

CHAPTER V. CONCLUS l ON

The r e s u l t s of t h i s research have demonstrated beyond doubt

t h a t t he e l e c t r o r e f l e c t a n c e on the (110) sur face o f Ag involves a

modulat ion o f e l e c t r o n s ta tes t h a t possess t h e c r y s t a l sur face sym-

metry. The most p l a u s i b l e i n t e r p r e t a t i o n , excluding such e x o t i c

mechanisms as i n t r i n s i c sur face s ta tes o r an an iso t rop ic e. lectron gas,

involves a combined e f f e c t o f a Mclntyre-'Aspnes-l ike charge modula-

t ion , which i s responsib le f o r t he gross d e t a i l s , and f i e l d ass is ted

i n d i r e c t interband t r a n s i t i o n s which add an an iso t rop ic con t r i bu t i on .

These i n d i r e c t t r a n s i t i o n s , from t h e Fermi sur face near L t o L,, a re

suppressed by ca thod ic p o l a r i z a t i o n ( l ess than -0.9 V SCE) as ' the e lec-

t r o n dens i ty i n t h e sur face region more e f f e c t i v e l y screens the modu- .

l a t i n g f i e l d , and by over lapping d i r e c t t r a n s i t i o n s (as i n AU) which

mask the observat ion o f t h e i r e f fec t . . These ideas q u a l i t a t i v e l y ex-

p l a i n t h e m a j o r i t y o f t h e fea tures o f m e t a l l i c ER l i s t e d i n Chapter

I V ( fea tures 1, 2, 4, 7-9, 14-17, 19, 20). Surface condi t ions, as

discussed' i n Ap.pendix A, exp la in fea tures 5, 6, and 13; w h i l e ex- . .

t r i n s i c chemical i n t e r a c t i o n s are most successfu l ly invoked t o in , ter-

p r e t t he second'order e f f e c t s represented by fea tures 3, 10-12, 18,

and 21 . Perhaps the most s i g n i f i c a n t c o n t r i b u t i o n o f this work was t h e

experimental demonstration t h a t s i n g l e c r y s t a l m e t a l l i c e l e c t r o r e -

f l ec tance can be c a r e f u l l y c o n t r o l l e d and i s an extremely s e n s i t i v e

probe o f t h e energy s t r u c t u r e o f t h e i n t e r f a c e region. C l e a r l y more

study i s requ i red and should be d i r e c t e d along t h e f o l l o w i n g l ines .

1. ' A.more thorough measurement o f t h e ER of s i n g l e c r y s t a l

nob le metals o ther than Ag should be conducted t o p o s i t i v e l y

v e r i f y t h e unique a n i s o t r o p i c behavior us ing Ag.

2. A I1dryt1 technique should be developed t o permi t simul taneous

intense e l e c t r i c f i e l d a p p l i c a t i o n and o p t i c a l observat ion

on t h e su r face .o f metals. his would a l l o w t h e f i e l d e f f e c t .

t o be s tud ied w i thout i n te r fe rence from a s o l u t i o n and over

a wide temperature range.

3. Other m a t e r i a l s t h a t could be e a s i l y s tud ied w i t h the e lec-

t r o l y t e technique inc lude Pd, Cd, In, and Zn as we l l as

N i . . .

4. The c a l c u l a t i o n o f sur face energy bands f o r low symmetry

planes o f t h e noble metals shou'ld t e s t t h e i n t r i n s i c sur face

s t a t e mechanism.

5. A t h e o r e t i c a l e f f o r t should be undertaken t o c a l c u l a t e t h e

e f f e c t o f an intense, extremely l o c a l i z e d e l e c t r i c f i e l d on

t h e bound s t a t e energy s t r u c t u r e o f a metal surface.

6. A quantum mechanical theory f o r o p t i c a l i n t e r a c t i o n w i t h a

per turbed sur face t h a t inc ludes microscopic inhomogeneities

should be performed t o , p r o v i d e t h e o r e t i c a l support f o r sur-

f ace symmet r y exper i men t s.

APPENDIX A. ANOMALOUS RESULTS

Two types o f spectra t h a t look q u i t e d i f f e r e n t from t h e repro-

duc ib le ER on Ag appeared under i d e n t i f i a b l e cond i t i ons and can be

labeled as anomalous. They a re reported here f o r t he sake of complete-

ness and t o i 1 l u s t r a t e t h e importance of proper surface preparat ion.

Surface F i l m

On e lec t ropo l i shed samples, even though they looked very clean,

i t was necessary t o sub jec t t h e surface t o an i n s i t u cathodic hydro-

gen reduct ion treatment t h a t removed a contaminat ing byproduct layer.

This was a1 so f o u n d necessary i n d i f f e r e n t i a l capaci tance4' and e lec-

t r o n d i f f r a ~ t i o n ~ ~ studies o f e l e c t i o p o l ished s i n g l e c r y s t a l s o f Ag.

Without t h e reduct ion o f t h i s contamination, d i s t i n c t l y d i f f e r e n t ER

and capacitance behavior was observed.

~he 'anomalous ER i s shown i n F igu re A l . Wi th 41 [ I l ' O ] , a nega-

t i v e peak was seen a t 3.93 eV which i s s h i f t e d o n l y 0.03 eV from

where i t appeared on c lean samples. However, w i t h an increasing com-

ponent o f ^e a long [ 100], AR/R became dominated by a p o s i t i v e peak t h a t

appeared a t almost exac t l y t h e same energy as t h e negat ive peak on

c lean samples. when t h e anomalous AR/R was present, t h e double 1 ayer

capacitance exh ib i ted a hys te res i s w i t h p o t e n t i a l and looked noth ing

1 i ke pub1 i stied data. 5 0

This behavior could be e l i~ l~ i r iaLed, and t h e contaminat ion rcmoved,

by b i a s i n g t h e sample t o @ < -1.2 V (SCE), where t h e atomic hydrogen

was j u s t beginning t o evolve,. f o r about 30 minutes. . A f t e r t h i s

PHOTON ENERGY ( e V )

Figure A l . Anomalous ER on (110) Ag due t o a contaminat ing f i 1 m . l e f t from e lec t ropo l i sh ing . The i nse t shows the o r i e n t a t i o n , o f t h e l i g h t p o l a r i z a t i o n w i t h respect t o t h e c r y s t a l . 1 M KOH; CDC = -0.2 V (sCE); bAC = 35 mV rms a t 1 kHz.

treatment, t h e Cdl took on t h e appearence o f t h e publ ished data and

t h e normal ER, c h a r a c t e r i s t i c o f c lean s i n g l e c r y s t a l Ag, returned.

Trace remnants o f coverage may be the cause o'f t h e var ' iab i l i t y i n t h e

h igh energy d ropo f f above 4 eV i n Ag ( f e a t u r e 5, Chapter IV). Such

contamination, i f present would have been below t h e de tec t i on capa-

b i l i t y o f t h e e lectrochemical monitors.

A d e t a i l e d study o f t h i s phenomenon was no t made because i t was

considered as a contaminat ion t o t h e experiment. However, i t e x h i b i t s

i n t e r e s t i n g fea tures o f i t s own t h a t warrant a more thorough t r e a t -

ment. The most i n t r i g u i n g fea ture i s how t h e modulated r e f l e c t i v i t y

changed charac ter so d r a s t i c a l l y when the p lane o f p o l a r i z a t i o n a t

normal incidence was rotated. Contro l 1 ed s t r i p p i n g 'vol tammetry anal - y s i s should be performed t o i d e n t i f y t h e ex tent o f coverage. I t might

a l so be poss ib le t o study t h e chemical makeup o f t h e sur face by such

techniquesj o r w i t h some'high vacuum method l i k e LEED (provided t h e

f i l m would stand t h e vacuum). I . , ,

, .

Surface D i s t o r t i o n

Most of my c a r e f u l l y prepared Ag sur face had ER t h a t d i d no t

'd isp lay any pronpunced b t r u c t u r e i n t h e reg ion 3.2. t o 3.5 eV. Th is

i s i n con t ras t t o o the r work on Ag ER. 2 8 7 1 9 9 10, 15, 16 M c l n t y r e re-

;ported that , i n h i s ob1,ique incidence ER on f i l m s of Ag, s t r u c t u r e a t

3.25 eV was very sample dependent and a t t r i b u t e d t h i s t o t h e genera-

t i o n of surface plasmons ( ~ p p e n d i x B). My normal inc idence ER on

smooth, unstra ined Ag show no such low energy s t ruc ture . However, on .

some samples i t was observed (note t h e s l i g h t tendency i n F igu re 14).

I n the example shown i n Figure A2 the low energy s t ruc tu re was

p a r t i c u l a r l y pronounced. This sample was h a s t i l y t reated w i t h the

etch-pol ish procedure and was l e f t w i t h observable scratches. There

was a dramatic po la r i za t ion dependence i n the low energy s t ruc tu re

and the anisotropy of the high energy peak was .reduced.

I a t t r i b u t e the appearance of the low energy s t ruc tu re t o sur-

, . 7 y 15 ' l7 using unpolarized 1 i gh t on . . face s t ra in . Other invest igators . .

. .

mechanically pol ished bu lk s i l ve r , t o which.no s t r a i n . r e l i e f technique

was appl ied, a1 1 show a r i s e a t about 3.2 eV fol lowed by a d i p near . .

3.4 eV. The unannealed t h i n f i l m data a t ob l ique incidence 9,lO . . . ,

d isp lay t h i s feature. It i s wel l known tha t t h i n f i l m s e x h i b i t a , . .

h igh degree o f s t p a i r b e f o r e annealing. . .

The p re fe ren t i a l o r i en ta t i on may be due t o p r e f e r e n t i a l l y a l igned . . .

d i s t o r t i on . Electron d i f f r a c t i o n studies42 on mechanically pol ished . " . '

(1000 f alumina) s ing le c r ys ta l s o f Ag showed t ha t the rewas a pro-. . ' '

. , . .

nounced o r i en ta t i on o f deformation w i t h the [ l o o ] d i r e c t i o n para l le l . ' . .

. . t o the scratches.

From t h i s evidence i t i s c lea r t ha t m e t a l l i c ER i s a very sensi-

t i v e probe o f the surface s t ruc tu re and w i t h the proper i n t e rp re ta t i on

can be used t o advantage i n crys ta l lographie surface studies.

Figure A2. Anomalous ER on (110) Ag due t o surface inper fect ion for t h r e e o r i e n t a t i o n s o f t h e l i g h t p o l a r i z a t i o n vector 8. 1 M KOH; etch-polished surface; QDC = -0.3 V ( S C E ) ; QAC = 35 mV rms a t 1 kHz.

3.0 3 . 2 3.4 3.6 3.8. PHOTON ENERGY

APPENDIX B. ELECTRONIC AND OPTICAL PROPERTIES OF THE NOBLE METALS

Band S t ruc tu re

The s i n g l e p a r t i c l e e l e c t r o n i c band s t ruc tu res (al lowed e l e c t r o n

energy as a func t ion of e l e c t r o n momentum hS;) of t h e noble metals Cu,

Ag, and Au a re very s im i la r . The i r rea l space l a t t i c e i s ' face-cen-

te red cub ic and the rec ip roca l space u n i t c e l l , t h e B r i l l o u i n zone,

,i s t h e t runcated octahedron. The band s t ruc tu res are charac ter ized

by t h e broad sp-band which crosses and hyb r id i zes w i t h t h e narrow

d-bands. The major d i f f e rences among t h e nob le metal band s t ruc tu res

are t h e p o s i t i o n o f the-d-band w i t h respect t o the sp-band, t h e w id th

o f t he d-band, and t h e l oca t ion of t he Fermi leve l .

S i l v e r

Chri stensen has ca l cu la ted t h e augmented plane wave bands68 as . .

we l l as t h e r e l a t i v i s t i c augmented plane.wave bands6' f o r Ag which a re

shown i n F igure B1. The major changes i n t h e RAPW r e s u l t i s t he .add i -

t i o n of s p i n - o r b i t s p l i t t i n g and the s h i f t o f gap energies. (n con-

s ide ra t i ons o f e l e c t r o n t r a n s i t i o n s from f i l l e d ' s ta tes below t h e Fermi.

l eve l t o unoccupied s ta tes above the Fermi l eve l us ing energy changes

o f less than 5 eV, a t t e n t i o n i s drawn t o t h e region around L. The

bands o f i n t e r e s t i n d iscussions o f t h e o p t i c a l p roper t i es are i n d i -

+5+, L ~ - , and L +. The non-re- c a t 4 i n the r e l a t i v i s t i c n o t a t i o n d s L + 4

l a t i v i s t i c n o t a t i o n f o r these bands i s a c t u a l l y b e t t e r known and w i l l

be used i n t h i s work. The n o t a t i o n r e l a t i o n s are summarizsd i n

Table B1.

F i g u r e B l . RAPW band s t r u c t u r e f o r A ~ . ~ ~ 1 r y d = 1 3 . 6 eV.

Table B1. Equivalent n o t a t i o n f o r t hc bands near L -

Atom i c APW RAPW

The ca lcu la ted p-s gap i s very s e n s i t i v e t o t h e cho ice o f c r y s t a l

p o t e n t i a l . I n addi t ion, t h e APW r e s u l t f o r t h i s gap i n s i l v e r i s

4.34 eV w h i l e t h e RAPW resu l t , which sh.ould be more r i g o r o u s l y cor rec t ,

i s 3.48 eV. The h igher energy, however, i s more i n l i n e w i t h exper i -

men t .

Gold

Christensen and Seraphin7' have ca lcu la ted t h e RAPW bands f o r Au.

The form of t h e bands is, s i m i l a r t o those o f Ag so the re i s no p o i n t

i n reproducing them here. For t h e sake o f t h i s work t h e notab le

changes i n going from Ag t o Au are t h e changes in .gap energies a t L.

. . The ca l cu la ted d-p gap i s a t 1.37 eV compared t o 3.82 i n Ag. The s-p

gap i s ca l cu la ted t o be 3.74 eV compared t o 3.48 e~ i n Ag. Experiments

are used t o ad jus t these assignments, however i n d i c a t i o n s are t h a t t h e

s-p in terband energy i s smal ler than the d-p gap i n Ag, w h i l e t h e

s i t u a t i o n i s reversed i n Au.

Opt i ca l Proper t ies 7 1

L i g h t ac ts as a probe o f t h e e l e c t r o n i c energy s t r u c t u r e o f a

so l i d . By observing t h e photon-electron in te rac t i on , much has been

learned about fundamental p roper t i es o f matter. The e l e c t r i c f i e l d

o f t he i nc iden t l i g h t , E'(3,t) a exp(- iwt), induces a displacement

+ + ~ ( r , t ) which i s t e n s o r i a l l y r e l a t e d t o the e l e c t r i c f i e l d by a d i e l e c -

t r i c tensor. The Four ie r transforms o f these q u a n t i t i e s are connected

through t h e r e l a t i o n D ({,w) = E E ({,w)~~({,w). c (<,m) descr ibes I-L v I-Lv UV

. t h e o p t i c a l p roper t i es o f t h e medium and has t h e same symmetry prop-

e r t i e s as t h e rea l space l a t t i c e . The t e n s o r i a l form can be s i m p l i f i e d

. . . w i t h two assumptions: 1) I n systems o f a t l eas t orthorhombic sym-

.. ,

metry, t he d i e l e c t r i c tensor i s diagonal. 2) I f t h e s p a t i a l dependence . .

o f the f i e l d s i s neglected and t h e d i p o l e approximation made, then we . . .

have the < = 0 l i m i t o f t h e more general resu l t . 72 The s i m p l i f i e d .

r e s u l t i s

I n general t he displacement i s ou t o f phase w i t h t h e f i e l d so t h e d i -

, e l e c t r i c tensor i s 'complex,

Energy absorpt ion i n t h e medium i s p ropor t i ona l t o t h e imaginary

p a r t o f t h e d i e l e c t r i c tensor and can be e a s i l y connected t o quantum

mechanical energy e igensta te t r a n s i t i o n formalism. The exper imenta l ly

measured r a t i o o f r e f l e c t e d t o i nc iden t l i g h t i n t e n s i t y (R) i s a

complicated func t ion o f both el and B (see Appendix D). For tunate ly , 2

c a u s a l i t y imposes an interdependence between c1 and B o f t h e form 2

Therefore i t i s poss ib le t o c a l c u l a t e c2 from quantum mechanics and

then use 8-3 t o get el.

Discussion o f photon-electron i n t e r a c t i o n s w i l l be centered

around two bas ic phenomena: 1 ) S ing le p a r t i c l e e x c i t a t i o n s i nvo lve

t h e absorpt ion o f a quantum o f energy from t h e inc iden t photon and

t h e r e s u l t i n g t r a n s i t i o n o f one e l e c t r o n 'from an i n i t i a l s t a t e t o a

h igher energy f i n a l state. 2) C o l l e c t i v e e x c i t a t i o n s are due t o t h e

incomplete screening o f t he long range coulomb i n t e r i c t ion between

electrons. .These are manifested as a coherent osc i 1 l a t i o n o f charge.

S ing le p a r t i c l e e x c i t a t i o n s

The d i e l e c t r i c tensor t h a t describes t h e medium's response t o a

photon probe by i n d i v i d u a l e l e c t r o n t r a n s i t i o n s can be s p l i t i n t o two

terms, t h e f r e e and bound e lec t ron con t r i bu t i ons .

Free e lec t ron e f f e c t s . These e x c i t a t i o n s i nvo lve the t r a n s i t i o n

o f an e lec t ron from an occupied s t a t e t o an empty s t a t e i n the same

band. For t h i s t o take p lace w i t h momentum conservat,ion, some

s c a t t e r i n g mechanism must be involved. Prime examples are l a t t i c e

v i b r a t i o n s and impur i ty atoms. Th is i s a phenomenon o f an e l e c t r o n

gas which i s t o f i r s t order independent o f the l a t t i c e symmetry. I t

i s t he re fo re expected t o behave i s o t r o p i c a l l y and enters as an a d d i t i v e

c o n t r i b u t i o n t o t h e diagonal o f t h e d i e l e c t r i c tensor. i t s func t iona l

dependence on photon energy hw i s

.where T i s a r e l a x a t i o n t ime t h a t charac ter izes t h e s c a t t e r i n g mech-

anism and w 2 i s 4 1 t ~ e ~ m - l ~ c a l l e d t h e plasma frequency. (N i s the' P

e lec t ron dens i t y w i t h m and -1el t h e e l e c t r o n mass and charge.)

Bound e l e c t r o n e r f e c t s Th is category covers what are commonly

c a l l e d interband t r a n s i t i o n s . They r e s u l t when a quantum o f energy,

hw, i s absorbed and an e lec t ron makes a t r a n s i t i o n between energy

s ta tes t h a t have t h e same momentum h z but are i n d i f f e r e n t bands. Such

e x c i t a t l o n s are c a l l e d d i r e c t s ince they i nvo lve no a d d i t i o n a l momentum

change ou ts ide o f t h a t suppl ied by t h e rec ip roca l l a t t i c e vectors.

Quantum mechanics p r e d i c t s t h e func t i ona l dependence uT Ll.~e imaginary

p a r t o f t he bound d i e l e c t r i c tensor, which depends on c r y s t a l symmetry.

The interband energy d i f f e r e n c e i s a f u n c t i o n o f 2 and can be expressed

1 as hwn,.(Q. The r e s u l t depends on a sum over poss ib le i n i t i a l s ta tes

n and f i n a l s ta tes n'. t

where

i s a u n i t vec tor para1 l e l t o t h e photon f i e l d u

+

'n'n (it) i s t h e interband momentum m a t r i x element

Onln (St) i s . t h e p r o b a b i l i t y n ' i s empty and n i s f i l l e d as def ined,

by t h e Fermi sur face . i

For t r a n s i t i o n s l o c a l i z e d i n rec ip roca l space (n i s a s lowly ' n ' n

va ry ing f u n c t i o n o f i n t h a t region. Under t h i s assumption, due to .

t h e symmetry o f t h e B r i l l o u i n zone, t h e . i n t e g r a 1 can be separated i n t o

' a sumof symmetry equ iva lent l oca l i n teg ra l s ; 5 . Each l o c a l i n t e g r a l

i.s taken over- t h e r e s t r i c t e d region i n 2-space where. t r a n s i t i o n s occur.

For h igh symmetry p o i n t s t h e sum i s over the s t a r o f 6.73 The s i m p l i -

: f i e d r e s u l t i s

b - 2 2 € @ ( w ) ~ = A w C E I M ~ I , J ~ , " ( . )

n ' n i

where

i s t h e interband j o i n t dens i t y of s ta tes (JDOS). I n unperturbed

cub ic c r y s t a l s , such as t h e noble metals, t h e JDOS i s i d e n t i c a l f o r

each symmetry equ iva lent region i. Mi depends on t h e o r i e n t a t ion o f

t h e photon f i e l d ( p o l a r i z a t i o n of t h e l i g h t ) i n each l o c a l system.

For cubic c rys ta l s , when summed over i, t h e o r i e n t a t i o n a l dependence

b cancels out. The r e s u l t i n g r ( w ) ~ i s i s o t r o p i c (independent o f u)..

CL b

The JDOS, which conta ins t h e energy s t r u c t u r e of c ( w ) ~ , can !J

2 be re-expressed as a E s p a c e sur face i n t e g r a l (J 'd k) o v e r t h e con-

s tan t in terband energy d i f f e r e n c e sur face (CEDS) given by Awn,, = hw. .

The r e s u l t i s

The source o f s t r u c t u r e i n t h e JDOS can be i d e n t i f i e d from Eq. (B-10).

The most obvious causes are extrema i n t h e interband 'energy' d i f f e r e n c e

hwnl n . Th is makes o p t i c a l i n t e r a c t i o n s a s e n s i t i v e t e s t o f c r i t i c a l

p o i n t energy gaps. A more s u b t l e cause of s t r u c t u r e can be t raced

t o t h e occupation f a c t o r 0 n 'n '

The JDOS i s b a s i c a l l y the weighted

area o f t h e CEDS. The Fermi sur face def ines how much of t h i s area

. . ,

should count. As hw changes, t h e CEDS varies., I f t h e Fermi sur face

has a shape s i m i l a r t o t h e CEDS f o r some photon energy range, then

w h i l e t h a t range o f energies i s being scanned, t h e e f f e c t i v e CEDS area

changes rap id l y . Th is causes a r a p i d a l t e r a t i o n i n t h e JDOS and there-

b f o r e i n t h e interband d i e l e c t r i c tensor r (w). I t i s t h i s occupation

CL

f a c t o r mechanism t h a t i s t h e source of t h e interband onset s t r u c t u r e

i n the noble metal o p t i c a l p roper t ies .

C o l l e c t i v e e x c i t a t i o n s . .

Included i n t h i s category are b u l k charge f l u c t u a t i o n e f f e c t s

' (plasmons) and surface charge o s c i l l a t i o n s (surface plasmons). Bu lk

plasmons, si'nce they represent a p e r i o d i c b u l k charge concentrat ion,

cannot be exc i ted w i t h the t ransverse f i e l d s present i n l i g h t . Be-

cause o f t h e equivalence o f t h e t ransverse and t h e long i . tud ina l d i -

e l e c t r i c func t i ons i n t h e = 0 1 i m i t , t h e cond i t i ons f o r b u l k plasmon

e x c i t a t i o n s t o ex i s t , i f a l o n g i t u d i n a l probe were ava i lab le , can s t i l l

be determined, This phenomenon i s no t o f obvious concern t o m e t a l l i c

ER. The sur face plasmons, however, can e x i s t i n a v a r i e t y o f modes.

With t h e a id. o f surface.roughness caused by imperfect. p lanar topography

some o f these modes can r a d i a t e and thus can. be exc i ted by l i g h t . The . .

cond i t i ons f o r e x c i t a t i o n of a sur face plasmon can be est.imated from

an elementary study o f the e lectromagnet ic boundary cond i t i ons a t a

s o l i d surface. A t an i n te r face between a subst ra te (s) and an ambi'ent

medium (a, here assumed t o be non-absorbing) the r e s u l t i s t h a t t he re .

must be a photon f i e l d component normal t o the sur face w i t h

- € = 8 s l a ' and C S 2 = smal l . (D-1 I )

~f a simple f r e e e l e c t r o n model w i t h = m ( E ~ . (8-5)) i s used f o r

c t h e sur face plasmon energy requi rement i s s l '

fiw = hiu ( € + 1 ) - 1 / 2 P a

(8- 1.2)

A t a vacuum i n t e r f a c e h~ = h ~ ~ ( 2 ) - " ~ . , I n a more dense ambient medium . ,

t h e sur face plasmon i s s h i f t e d t o lower energy.

Experimental App l i ca t i ons

S i l v e r

The bands near L, t he dark reg ion i n F igu re B1, which a re re-

spons ib le f o r t h e in terband o p t i c a l p r o p e r t i e s o f Ag near 4 eV a.re

shown i n F igu re 82. The assignment o f gap energies and e f f e c t i v e

masses i s due t o Rosei e t a1 .34 and i s based on experimental thermo-

-+ modulat ion a t low temperatures. k i s perpendicular t o A, t h e 3- fo ld

I

r o t a t i o n a l symmetry ax is , and 5, i s para1 l e l t o t h a t ax is . The onset

o f p - s t r a n s i t i o n s , 3.87 eV, occurs be fore the onset o f d + p t r a n s i -

t ions , 4.03 eV. The r e s u l t s o f t h i s assignment ag we1 1 as a repre-

s e n t a t i v e s e l e c t i o n o f o the r experimental assignments can be summarized

i n t a b u l a r form.

Table 82. Assignment of in terband onset energies ( e ~ ) i n s i l v e r

Reference Method hW 1 hW2 hwc

74 piezomodul a t ion 3.8

7 5 a1 l oys 3.88 4.4 . 4.1

76 o p t i c a l p r o p e r t i e s 3.86

5 4 'p iezomodulat ion , 3.98 3.92 4.25

32 thermal v a r i a t i o n 3.87 4.11

34 thermomodulation 3-87 4.03 4.16

7 7 f i t t o da ta of Ref. 74 3.87 4.2

F igu re 82. Band s t r u c t u r e of Ag near L.showing t h e th ree bands responsi- b l e f o r o p t i c a l s t ruc tu re . near 4 eV. 1) and I r e f e r t o o r i - en ta t i on w i t h respect t o t h e r o t a t i o n a l symmetry a x i s A. .The e f f e c t i v e mass i s a measure o f t h e inverse u rva tu re o f t h e .

band. Assignments are due t o ~ o s e i e t a l . 36

the d + p t r a n s i t i o n causes a more dramat ic s t r u c t u r e than t h e p + s

t r a n s i t i o n . 34'78 Recently experimental support f o r Chr i s tensen's 0

ca lcu la ted hwc ( L i - Ll) has been offered7' by an assignment o f

3.33 eV based on d i l u t e a1 l oys o f Cd, Mg, and Sn. This i n t e r p r e t a -

t i o n depends on an ex t rapo la t . ion which niay.become q u i t e tenuous a t

low concent ra t ions due t o the p o s s i b i l i t y o f i n d i r e c t t r a n s i t i o n s .

I t has a l so been suggested32 t h a t t h e onset edge i s n o t conf ined t o ,

a small reg ion around L and t h a t extended regions o f space c o n t r i -

bute. This would make the constant m a t r i x element approximation

i nva l id.

A t t h e Ag/vacuum i n t e r f a c e t h e sur face plasmon energy occurs a t

3.64 eV.80 Th is was demonstrated on rough t h i n f i l m s . The sur face

p 1 asmon was subdued .on smoother f i 1 ms.

Gold

T h e ' o n s e t ' o f in terband t r a n s i t ions i n Au occurs f i r s t from the

d + p gap and has been located near 2.5 eV. 32y81 '.82 tiowever RAP" ca 1 - c u l a t ions o f Chr i stensen and seraphin70 f o r t h e CEDS and t h e Fermi

sur face Ir idicaLe t h a t t he re i s a coinc idence of t h e two a t 2.38 eV

over a l a r g e reg ion o f E-space. Th is would make t h e l o c a l ized t r a n s i -

t i o n i n t e r p r e t a t i o n i n v a l i d .

The absorp t ion edge t a i l s t o lower energy than expected from

thermal broadening o f t he Fermi surface. Th i s has been i d e n t i f i e d 32,83

as being due t o low energy in te rband t r a n s i t i o n s a t X which begin. a t

about 1.7 eV. These t r a n s i t i o n s a re very weak however and a re mani-

fested as a small c o r r e c t i o n t o t h e major s t r u c t u r e near L.

The h igher . energy t r a n s i t i o n s , p-s, .are more' i n doubt. Some

idea o f t h e experimental u n c e r t a i n t y can be appreciated by s tudy ing

t h e f o l l o w i n g tab le .

Table 83. Assignment o f hwc (L; - Ll) i n go ld

Reference Met hod Ass i gnmen t (eV)

8 3 piezomodulat ion 3.55

84 photoemission 4.00

85 thermomodulation 3.60

32 thermal v a r i a t i o n 4.20

7 7 data f i t o f Ref. 83 4.57

The p o s i t i o n of t h i s c r i t i c a l p o i n t a f f e c t s t h e onset energy hw,

which can be loca ted near 3.56 eV. 6 0

7 7 y 3 2 Other i n t e r p r e t a t i o n s . o f

s t r u c t u r e i n piezomodulat ion a t 3.6 eV a s s i g n . t h i s f e a t u r e t o t r a n s i -

t i o n s a t X. However, due t o small m a t r i x elements f o r t h i s t r a n s i -

t ion if i s not expected t o c u n t r i b u l e s t ~ ' o ~ s g l y .

Surface plasmons' ha\;; been observed a t 2.7 eV 81 y 8 6 on roughened

f i l m s and were subdued on f l a t f i l m s under the same cond i t ions .

APPEND l X C. ELECTROCHEM l STRY

The So lu t ion Side o f t h e Double Layer 87,88

The so-ca l led double l aye r occurs when phases con ta in ing charged . .

p a r t i c l e s , permanent dipoles, o r induced d ipo les meet t o form an i n t e r -

face. Macroscopical ly t h e assembly appears l i k e a d i p o l e sheet. Micro-

scop ica l l y t h e s t r u c t u r e o f t h e double l aye r may be q u i t e complex. Th is

sec t ion deals w i t h t h e double l aye r a t t h e i n t e r f a c e between a metal' and

an aqueous e l e c t r o l y t i c s o l u t i o n w i t h t h e emphasis on t h e 'so lu t ion

con t r i bu t i on .

F igu re C 1 dep ic t s a hypothet ica l double layer . The metal regions

are discussed i n Chapter I. I n t h e ' s o l u t i o n , c h a r a c t e r i s t i c regions

are ind ica ted by t h e i r approximate locat ions . The d is tances depend on

t h e makeup of t h e s o l u t i o n so t h e f i ' gu re should be considered schematic

only.

I nner Helmhol t z pl ane ( I HP)

Th is i s designated as t h e l o c a t i o n o f e l e c t r i c a l centers o f

specifically adsorbed ions, The term q p e c i f i c imp l ies t h a t forces

o the r than pure e l e c t r o s t a t i c a t t r a c t i o n main ta in t h e adatom/substrate

bond. These ions a re i n i n t i m a t e contac t w i t h t h e metal surface so

t h e l o c a t i o n o f t he IHP i s approximately t h e rad ius o f a bare ion, less

than 2 A. Even i n t h e presence of heavy s p e c i f i c adsorption, t h e over-

whelming p o r t i o n o f . t h e metal surf.ace i s s t i l l covered w i t h water d i -

poles. The h ighest observed s p e c i f i c adsorpt ion coverage i s less than

40 20 percent. The adsorbed species tend t o be anionsY8' l a rge cat ions,

and organic molecules. Eas i l y adsorbed ions tend no t t o have primary

hydra t ion sheaths. The i o n i c tendency f o r s p e c i f i c adsorpt ion i s

summarized i n t h e f o l l o w i n g tab le .

90 ~ a b l e C 1. Spec i f i c adsorpt ion tendency ( increas ing downward)

a An ions Cat ions

. a There i s no equivalence between t h e ca t i ons and an ions .o f t h i s

table. Only t h e v e r t i c a l o rde r . i s s i g n i f i c a n t . ,

Organic adsorpt ion i s most favorab le when t h e water dipoles,

which cover t h e m a j o r i t y o f t h e metal, a re a t t r a c t e d weakly t o t h e

e lectrode. Th is occurs. when t h e metal charge i s a minimum.

Outer Helmholtz p l a n e (OHP)

This i s t h e d is tance o f c loses t approach ( e l e c t r i c a l centers) of

hydrated ions. These tend t o be cat ions. The d is tance i s approxi-

mately t h e radius o f a solvated ion. The OHP t o IHP length i s less

than about 5 i. The OHP and t h e IHP comprise what i s f requen t l y

' . c a l l e d t h e inner layer . 1.n many e lectrochemical approximations i t

i s t rea ted as a s i n g l e ' s h e e t of charge located, a t some mean d is tance

from t h e e lectrode.

D i f f u s e laye r

The excess charge on t h e e lec t rode ( i n c l u d i n g t h e metal p l u s

inner l aye r adsorbed ions) i s compensated by an i o n i c atmosphere o r

d i f f u s e laye r composed o f ions w i t h concent ra t ion excesses o r d e f i -

c ienc ies w i t h respect t o t h e i r b u l k values, and which are he ld i n

e q u i l i b r i u m by an i n t e r p l a y of coulombic and thermal forces. A con-

c e n t r a t i o n p r o f i l e can be est imated from t h e Poisson-Boltzmann equa-

t i o n . Th is i s t h e essence of the GouyChapman theory of t h e double

l aye r which i s charac ter ized by t h e Debye length, LD. Th is parameter,

which i s independent o f t h e makeup o f t h e e lectrode, i s measured from

t h e OHP i n t o ' t h e so lu t ion . I t i s t h e d is tance w i t h i n which t h e con-

- 1 c e n t r a t i o n excess drops t o e o f i t s va lue a t t h e OHP and i s given

where z i s t h e i o n i c charge and c i s t h e b u l k i o n i c concent ra t ion i n

moles/ l i t e r . For concentrated so lu t i ons where c i s near un i t y , L i

approaches-the s i z e o f 'an unsolvated ion. Th.is.says t h a t t h e d i f f u s e

laye r i n concentrated so lu t i ons i s absent. The b u l k concent ra t ion

i s maintained up t o the OHP where a l l t h e excess charge i s located.

An est imate o f t h e e l e c t r i c f i e l d a t t h e OHP can be made us ing t h e

formalism o f t h e Gouy-Chapman theory.

where q, i n ucoul/cm, i s t h e in tegra ted surface charge from t h e OHP

o u t i n t o t h e so lu t i on . For an in teg ra ted sur face charge o f on l y 20

6 pcoul/cm t h e e l e c t r i c f i e l d s are o f t h e order o f 3 x 10 V/cm! Th is

can be es tab l ished w i t h a me ta l - so lu t i on p o t e n t i a l d i f f e r e n c e o f l ess

than one v o l t .

E lectrodes and P o t e n t i a l s

Electrodes

I n t h i s d iscuss ion I w i l l consider t h e hypo the t i ca l e l e c t r o -

chemical c e l l c o n s i s t i n g of a l e f t e lec t rode (L) and a r i g h t e lec t rode

( R ) . The n o t a t i o n f o r t he c e l l w i l l be ( L ) / ( R ) . The e l e c t r i c po-

t e n t i a l d i f f e r e n c e (PD) across t h e c e l l i s . de f ined as t h e p o t e n t i a l

uf the r i g h t e l e c t ~ o d c minus t h e p o t e n t i a l of the l e f t e lectrode,

Two major ca tegor ies o f e lec t rodes e x i s t : 1) P o l a r i z a b l e e lec-

t rodes are those which can assume any p o t e n t i a l w i t h i n some a l lowab le

range wi thout t h e t rans fe r of charge across t h e in ter face. 2) Non-

p o l a r i z a b l e e lec t rodes mainta in a constant p o t e n t i a l regardless of

how much charge t r a n s f e r i s occu r r i ng a t t h e in ter face. Ne i ther of

these idea l cases e x i s t i n r e a l i t y bu t t he re are good approximations.

I n s tud ies o f e lec t rode processes i t i s d e s i r a b l e t o work w i t h a c e l l

t h a t cons is ts o f one p o l a r i z a b l e e lec t rode and one non-po lar izab le

e l e c t rode. When PD changes are imposed across t h e c e l l , t h e changes

are concentrated a t t h e p o l a r i z a b l e e lec t rode since, by d e f i n i t i o n ,

t h e o the r e lec t rode mainta ins a constant p o t e n t i a l . I n t h i s way one

can study t h e p o l a r i z a b l e e lec t rode alone. Th is avoids the. problem

i n e lec t rochemis t ry associated w i t h t h e inherent presence o f two

double layers, one a t each e lectrode, i n any c e l l .

E lec t rode p o t e n t i a l s

The re has recent 1 ygl been some controversy and hi sunderstandi ng

among e lec t rochemis ts over t h e c o r r e c t r e l a t i o n o f exper imenta l ly

measured PD's t o t h e actual me ta l / so lu t i on PD. I n t h i s d iscuss ion the

p o t e n t i a l o f an e lec t rode i n s o l u t i o n i s de f ined i n terms o f standard

e lectrochemical experimental technique.' Th is insures reproduci b i 1 i t y

and u n i f o r m i t y o f my r e s u l t s when compared t o t h e body o f e l e c t r o -

chemical l i t e r a t u r e .

An experimental c e l l cons is t s o f t h ree e lectrodes. The sample

e l e~L~ .ode , a re fercncc c lcct rode, and a counter electrode. The re fe r -

ence e lec t rode i s some conventional non-po lar izab le e lectrode. I t s

a b i l i t y t o main ta in a constant p o t e n t i a l depends on t h e ease w i t h which

i t can pass charge across t h e in ter face. Two commonly used reference

e lec t rodes a re t h e normal hydrogen e lec t rode (NHE), which achieves

+ charge t r a n s f e r through the reac t i on 2H + 2e' - H2, and t h e calomel

e lec t rode (most commonly saturated, SCE), which achieves charge

\ - t r a n s f e r by the reac t i on 2Hg + 2 ~ 1 - w Hg2C12 + 2e . To ensure t h a t

t h e cu r ren t capaci ty of t h e reference e lec t rode i s no t overloaded, an

e l e c t r o n i c b u f f e r i s included t o l i m i t t h e demand. The counter e lec-

t rode i s someine.rt ma te r ia l (Pt) which merely serves t o d e l i v e r cur -

r e n t t o t h e sample/solut ion in ter face.

The exper imental ly measured PD i s t h a t o f t h e c e l l , ( re ference

e lectrode) / (sample e lectrode). By standard e lectrochemical conven-

t ion , t h e po ten t ia l , 'NHE, o f a sample e lec t rode i s de f ined t o be the

experimental l y measured PD o f t h e c e l l , (NHE) /(sample). The NHE i s

a r b i t r a r i l y assigned a p o t e n t i a l o f zero. When o the r reference e l ec-

t rodes are used t h e e lec t rode p o t e n t i a l can be def ined w i t h respect

t o them. For instance, 'SCE

i s the PD o f t he c e l l (Sc~)/ (sample) . ' .. .

The saturated calomel e lec t rode i s more convenient t o use and was ' . . .

. employed ' i n t h i s experiment. All e lec t rode p o t e n t i a l s reported in

t h i s work are w i t h respect to t h e saturated calomel e lectrode. The . . ---- . .

expe;imentally measured PD o f t h e c e l l (NHE)/(sCE) i s roughly 0.24 V.

The r e l a t i o n between t h e PD'sof two c e l l s w i t h d i f f e r e n t references 1s

I t should be,remembered t h a t t h i s i s an exper imental ly defined,

a r b i t r a r y means o f reproducib ly c o n t r o l l i n g a p o l a r i z a b l e e lec t rode

p o t e n t i a l and not a numerical representa t ion o f t h e t r u e PD across

t h e me ta l / so lu t i on inter face.

D i f f e r e n t i a l Capacitance

The double layer, as a macroscopic d i p o l e layer, behaves e lec-

t r i c a l l y l i k e a capaci tor . Mic roscop ica l ly , t h e d i f f e r e n t i a l capaci-

tance, which r e l a t e s an increment i n e lec t rode p o t e n t i a l t o an in -

crement i n e lec t rode charge, r e f l e c t s t h e t o t a l e f f e c t o f t h e con-

f i g u r a t i o n and c o n s t i t u t i o n o f i n d i v i d u a l components o f t h e double

layer . As such, t h e d i f f e r e n t i a l capacitance, Cdl, i s very s e n s i t i v e

t o s t r u c t u r e and contaminat ion o f t h e i n t e r f a c e region. There i s a

wide v a r i a t i o n i n exper imental ly reported Cdl which t e s t i f i e s t o t h i s

s e n s i t i v i t y . Absolute p u r i t y o f t h e system as w e l l as a smooth sample

e lec t rode are p r e r e q u i s i t e s f o r r e p r o d u c i b i l i t y . The vas t m a j o r i t y

o f double l aye r s tud ies have been performed on Hg s ince i t represents

a smooth, renewable surface.

An equ iva lent c i r c u i t c o n s i s t i n g o f two impedances i n p a r a l l e l

serves as a use fu l approximation o f t h e double l aye r f o r ana lys i s o f

t h e e f f e c t o f rap id p o t e n t i a l changes. The c a p a c i t i v e impedance de-

creases w i t h d r i v i n g frequency, f. The fa rada ic impedance (see next

sect ion) , due t o chemical reac t ions a t t h e in ter face, i s q u i t e large.

A t h igher frequencies, t h e AC charge f l o w i s dominated by t h e capaci-

t i v e impedance. Under these cond i t i ons a simple r e l a t i o n e x i s t s

between t h e AC current , IAC, and t h e AC p o t e n t i a l , QAC.

I n t h i s equation, A i s t h e exposed e lec t rode area which i s micro-

s c o p i c a l l y a v a i l a b l e t o t h e charging process.

The Gouy-Chapman model of t h e e l e c t r o l y t e p r e d i c t s that , i n t h e

absence o f s p e c i f i c adsorpt ion, when the sum of anion and c a t i o n

charge i n t h e double l aye r i s zero C d l i s minimized. T h i . s w i l l occur

f o r a given system a t a c h a r a c t e r i s t i c e lec t rode p o t e n t i a l , t h e po-

t e n t i a l o f zero charge (PzC). The PD across t h e i n t e r f a c e i s - not

zero here due t o sur face c o n t r i b u t i o n s which a re not inc luded i n t h e

ana lys is of i o n i c d i s t r i b u t i o n s . Th is minimum behavior i s observed

i n experiments i n d i l u t e so lu t i ons where Gouy-Chapman ideas hold. The

f o l l o w i n g t a b l e l i s t s t h e PZC's determined by t h e minimum i n Cdl f o r

s i n g l e c r y s t a l nob le metals.

92' Table C2. P o t e n t i a l s o f zero charge f o r t he nob le metals

Mater i a1 C r y s t a l . face PZC ( v o l t s vs sCE)

Note how t h e PZC i s s h i f t e d t o more p o s i t i v e values as the packing

dens i ty on t h e c r y s t a l face increases. There i s a great deal o f con- ,

t roversy concerning these assignments bu t t h e reported values i n

Table C2 represent t h e most r e l i a b l e experimental information. An

extension - to concentrated so lu t i ons i s probably not s t r i c t l y v a l i d .

I t i s known t h a t the PZC s h i f t s t o more negat ive values i n t h e pres-

ence o f s p e c i f i c adsorpt ion

Charge Transfer 9 3

A p o l a r i z a b l e i n t e r f a c e ac ts l i k e a capac i to r i n t h a t i t pro-

h i b i t s the t r a n s f e r o f charge across the boundary. A f t e r charging

cond i t i ons have been es tab l ished the re i s no net cu r ren t f l o w through

a c e l l w i t h such a sample e lectrode. I f cu r ren t i s present a f t e r

charging i t r e f l e c t s charge motion w i t h adsorpt ion processes o r t h e

presence of a chemical reac t i on ( fa rada ic cu r ren t ) . I f e lec t rons are

suppl ied t o ' t h e s o l u t i o n from the ele,ctrode the re i s a ca thod ic . .

cur rent . When e lec t rons are suppl ied t o t h e e lec t rode from the solu-

t i o n an anodic c u r r e n t resu l t s . There i s an energy b a r r i e r . a t a . '

p o l a r i z a b l e e lec t rode t h a t p r o h i b i t s these mechanisms. The b a r r i e r

can be manipulated through changes i n t h e e lec t rode potent ' i a1 to:. i,n-

h . i b i t o r promote the tendency toward charge t rans fe r processes. When

t h e var ia t i ,on promotes a c t i v i t y , t h e t r a n s f e r proceeds a t a r a t e de-

termined by % and t h e concent ra t ion , o f reac,Lar~Ls. As the energy

b a r r i e r i s approached and surpassed i n a p o t e n t i a l scan, t h e cu r ren t

f i r s t increases. . W i t h reac tant dep le t i on near t h e e lec t rode t h e

cu r ren t eventual l y . decreases causing a peak i n t h e I(@) curve. With

fa rada ic reac t ions the same behavior i s observed i f reac t i on 'p roduc ts

b u i l d up, however i f a steady s t a t e can be achieved, t h e cu r ren t w i l l

l eve l o f f .

Charge t r a n s f e r cu r ren ts invar i .ably accompany t h e format ion o f

an adsorbed o r reac t i on product f i l m , contaminat ion o f t h e so lu t ion ,

o r dec6rnposition o f t he sample, I n doub le ' l aye r s tud ies such as ER

i t i s essen t ia l t o avoid t h e cond i t i ons which promote charge t rans -

f e r . By moni to r ing the I(@) behavior o f t h e e lectrode, voltammetry,

t h e p o l a r i z a b l e p o t e n t i a l range can be i d e n t i f i e d and e l e c t r o a c t i v e

i m p u r i t i e s detected.

I n t h e absence o f i m p u r i t i e s t h e i d e a l l y p o l a r i z a b l e region i s

l i m i t e d on t h e negat ive end by the beginning o f hydrogen e v o l u t i o n as

e l e c t r o l y s ' i s of water s t a r t s . The reac t ion r a t e depends on the con-

+ c e n t r a t i o n ' o f H i n s o l u t i o n which i s r e f l e c t e d i n t h e pH. Acids

+ + have.a h igh H concentrat ion, u s u a l l y , i n t h e form H 0 , and a low 3 pH w h i l e t h e reverse c o n d i t i o n app l ies t o bases. An approximate

r e l a t i o n f o r t h e hydrogen evo lu t i on reac t i on i s g iven.by t h e poten-

t i a l where t h e reac t i on r e s u l t s i n a c u r r e n t dens i t y o f about

~ h l s c i = - ($ I '+ 0.06 pH + 0.24) i n v o l t s

The so-ca l led hydrogen overpotent ia l , @I, i s d i f f e r e n t f o r each metal.

For s i l v e r i t i s 0.2 V w h i l e f o r go ld i t i s zero. Using C-5, mhIStE est imates i n 1 M H2S04 are -0.5 V f o r Ag and -0.3 V f o r Au, w h i l e i n

1 M KOH t h e r e s u l t s a re -1.3 V f o r Ag and - 1 . 1 V f o r Au.

On t h e p o s i t i v e end, t h e p o l a r i z a b l e l i m i t i s imposed by t h e

format ion o f sur face compounds i n v o l v i n g oxygen as t h e OH- i n s o l u t i o n

breaks down. The reac t i on r a t e i s h igher i n more bas ic so lu t i ons .

F i l m format ion may o r may no t be reve rs ib le .

S i l v e r i n bas ic so lu t i ons acqui res a f i l m o f ~ g ~ 0 ' w h i c h begins

' forming a t +O. 1 V (SCE). 94 There i s some evidenceg5 t h a t AgOH may

' f o r m f i r s t a t a p o t e n t i a l s l i g h t l y l ess p o s i t i v e than +0.1 V. The

o x i d e i s i n a weakly bound s'tate. I t can be reduced. by hydrogeng6 o r

decomposed by photochemical means. Gold i s harder t o o x i d i z e w i t h

. s t a b l e Au20g forming a t +l.l V (SCE).

E lec t ropo l i shing 97

A spec ia l k i n d o f f.aradaic reac t i on o f i n t e r e s t t o o p t i c a l s tud ies

i n general and ER i n p a r t i c u l a r i s t h e anodic d i s s o l u t i o n o f t he sample

so as t o leave the sur face smooth and shiny. The react i .on occurs 'under I

proper cond i t i ons when t h e c o n t r o l l i n g energy b a r r i e r f o r decomposit ion

i s surpassed. E l e c t r o p o l i s h i n g i s almost a b lack a r t i n many labora-

t o r i e s t h a t depend on i t f o r sample preparat ion. To t h e f i e l d o f ,elec-

t r o c h e m i s t r y ' i,t i s no d i f f e r e n t from any o the r charge t r a n s f e r process.

The important v a r i a b l e t o c o n t r o l i s t h e e lec t rode p o t e n t i a l . The c e l l

c u r r e n t w i l l f l o w i n response t o proper man ipu la t ion o f t h e energy

b a r r i e r . Fo r tuna te l y t h i s procedure, which requ i res s o p h i s i t i c a t e d

equipment, i s n o t requi red f o r t h e r o u t i n e e l e c t r o p o l i s h i n g o f many

common m a t e r i a l s ( i .e . Cu, AU). S u f f i c i e n t c o n t r o l can be mainta ined

w i thou t a non-po lar izab le reference e lec t rode simply by mon i to r i ng the

cu r ren t . I n more d e l i c a t e systems wuch as Ag, proper p o t e n t i a l c o n t r o l '

i s requi red.

In F igure C2 t h e behavior t y p i c a l t o many metals i s i l l u s t r a t e d .

No t i ce t h a t t h e p o t e n t i a l a x i s i s p l o t t e d w i t h i nc reas ing ly negat ive

values t o t h e r i g h t . This obscure t r a d i t i o n i s rooted i n e l e c t r o - . .

chemistry so I make no attempt t o reverse i t here. The zero o f t h e

graph i s i n t h e upper r i g h t hand corner. Increasing anod.ic cu r ren t

i s downward.

Curve ABCDE i s t h e normal ac t ive-pass ive behavior fo l lowed by

many metals and a l l oys . I n region AB, anodic d i s s o l u t i o n o f t h e metal

occurs, however atoms tend t o leave p r e f e r e n t i a l l y from d i s l o c a t i o n s

and k inks r e s u l t i n g i n an etched surface. As an ox ide o r o the r pas-

s iva . t ion layer i s formed, t h e metal i s covered and d i s s o l u t i o n stops,

region CD. A t s t i I 1 more p o s i t i v e po ten t ia l s , e l e c t r o l y s i s begins and

oxygen i s evolved, region DE.

Curve ABFGE i s c h a r a c t e r i s t i c o f an e l e c t r o p o l i s h i n g system.

or p o t e n t i a l s more p o s i t i v e than B, t h e metal cont inues t o d i sso lve

a t an appreciable r a t e due t o random, non-crystallographic,dissolu-

t i on . The cu r ren t i n region FG i s independent o f e lec t rode p o t e n t i a l .

A viscous laye r o f reac t i on products forms soon a f t e r B t h a t c o n t r o l s

d i s s o l u t i o n . This c o n d i t i o n i s d e s i r a b l e f o r maximum e f f i c i e n c y i n

producing a m ic roscop ica l l y smooth surface.

The viscous laye r may no t d i s s o l v e when t h e sample i.s r insed o f f .

Anod ica l ly pol ished- metals u s u a l l y c a r r y a compact s o l i d f i l m t h a t i s

o f t e n o f subs tan t ia l t f i ickness and p r o t e c t i v e value, a f a c t no t f u l l y

appreciated by many inves t i,gators. E lec t ron d i f f r a c t ion s tud ies o f

e l ec t ropo l i shed s i n g l e c r y s t a l s o f Ag42 d i sp lay a contaminat ion t h a t

F i g u r e C2. The e l e c t r o d e c u r r e n t versus p o t e n t i a l c h a r a c t e r i s t t c s o f an ac t i ve -pass i ve meta l and an e l e c t r o p o l i s h i n g metal ( do t t ed ) . The c h a r a c t e r i s t i c reg ions a r e ' d e s c r i b e d i n t h e t e x t . The o r i g i n o f t h i s cu rve i s t h e upper r igh t -hand corner .

5.

+Anode Potential

i s not present on chemically etched samples. E lect ropol ish ing re-

mains, however, t h e best way t o prepare s t r a i n f ree, microscopical ly

smooth surfaces provided s u i t a b l e e l i m i n a t i o n of t h e viscous l a y e r i s

accounted for .

APPENDIX D. LINEAR APPROXIMATION THEORY FOR STRATIFIED MEDIA

The re f l ec tance ( r a t i o o f r e f l e c t e d t o i n c i d e n t l i g h t i n t e n s i t y )

o f a mul t iphase assembly i s a complicated f u n c t i o n o f t h e o p t i c a l

p roper t i es of each phase. When cons ider ing modulat ion experiments

where t h e th ickness and/or t h e o p t i c a l parameters associated w i t h

one o r more phases i s changing, t h e ana lys i s can become q u i t e d i f f i-

c u l t . Under c e r t a i n s i m p l i f y i n g assumptions and employing a formal ism

o u t l i n e d by AspnesYg8 concise expressions are obtained. Th is w i l l be

c a l l e d t h e l i n e a r approximation theory (LA theory) .

The q u a n t i t y o f experimental i n t e r e s t i s t h e r e l a t i v e change i n

re f l ec tance due t o a change i n t h e modulat ion parameter. Th is i s ex-

pressed as AR/Ry where AR = R ' - R. Each separate phase, j, can be

o p t i c a l l y s p e c i f i e d by i t s thickness, d and i t s complex d i e l e c t r i c j '

funct ion, s o r complex index o f re f rac t i on , n = s j ' j j

. ~ o r m ~ l

incidence i s assumed here so t h e t e n s o r i a l p r o p e r t i e s o f t h e i n d i -

v idua l phases are decoupled (orthorhombic o r h igher symmetry). For

i s o t r o p i c media an uncomplicated extension can be made t o descr ibe

o b l ique inc iden t phenomena.99 F igu re D l i 1 l u s t r a t e s t h e cond i t i ons

o f d e f i n i t i o n f o r R ' and R i n th ree simple cases of i n t e r e s t t o ER.

I n each subf igure t h e ambient medium, from which t h e i nc iden t l i g h t

o r i g ina tes , i s on t h e r i g h t , and t h e subst ra te o r b u l k sample i s on

t h e l e f t .

Figure Dl. Schematic representa t ion o f s t r a t i f i e d media con f igu ra t i ons used i n t h e LA theory t o compute AR = R ' - R, t he change ' in r e f l e c t i v i t y . 1 ) th ickness modulation, 2) th ickness modula- t i o n w i t h an i n e r t over layer , 3) s p a t i a l l y va ry ing modulation. "af' i s t h e ambient, f fs l f i s the. substrate.

. .

Case 1 : Thickness Modulat ion

Th is i s t h e bas ic example upon which more e labora te treatments

expand. The modulated c o n d i t i o n involves an intermediate layer, d ,

o f th ickness d. The temporal v a r i a t i o n o f t h e photon f i e l d goes l i k e

e -iwt where hm i s t h e photon energy. With c as t h e speed o f 1 i g h t i n

vacuum, the LA theory appl i es i n t h i s case when 1 n*md/c 1 << 1. I t

should be app l i cab ie when t h e th ickness i s much less than t h e o p t i c a l

wavelength, h = 2nc/w.

I n D-1, t h e parameter D describes the e f f e c t o f over layers on top o f

t h e modulated stratum. In t h i s case the re are no over layers besides

t h e ambient, and D = Dl where, . .

For p a r t i a l coverage t h e th lckness assumes t h e va lue which i s t h e

th ickness o f a un i fo rm laye r w i t h an equ iva lent o p t i c a l e f f e c t t o t h e

ac tua l i nhomogeneous coverage.

The LA theory requ i res t h a t t h e o p t i c a l p r o p e r t i e s o f these very

t h i n layers be descr ibab le i n terms o f b u l k o p t i c a l funct ions. c l e a r l y '

t he severe non-un i fo rmi ty requ i res a non-local theory f o r a completely

r i gorou s t matmen t .

Case 2: Thickness Modulat ion With Overlayer

I f an unmodulated over layer o f th ickness d and d i e l e c t r i c 0

f u n c t i o n eo i s added t o case 1, t h e s i t u a t i o n i s o n l y moderately more

complicated. The r e s u l t i n Eq. (D-1) s t i l l holds, as i t does f o r any

number o f over layers, on l y now D = D2 where

The' LA theory i s v a l i d i n t h e case i f do/A << 1 and as long as t h e

c o r r e c t i o n t o Dl i s small.

Case 3: S p a t i a l l y va ry ing D i e l e c t r i c Funct ion

This case covers t h e s i t u a t i o n where t h e modulat ion i s manifested

b y ' t h e presence o f a non-unifo'rm intermediate l aye r which decays t o '

t h e bu lk substrate. Assume t h a t t h e d i e l e c t r i c f u n c t i o n o f t h e sub-

s t r a t e can be represented i n func t i ona l form as cS(z), w i t h the sur-

face a t z = 0. Provided t h e m a j o r i t y of t he pe r tu rba t ion from t h e

b u l k subst ra te value, eS = s (m), occurs w i t h i n a . d i s t a n c e d, Eq. (D-1) s

holds w i t h (s* - s ) replaced by where s

The LA theory app l i es when ee(z) e, and exp( ins(z)zw/c) P I. This a

should be good f o r d/h << 1.

I f cS(z) has an exponential d ropo f f w i t h z, then (asS) =

es(z=O) - € s'

Genera 1

Note t h a t f o r separate a d d i t i v e c o n t r i b u t i o n s t o t h e i n t e r -

mediate l aye r o p t i c a l p roper t i es ( i . e . € & = EL + €;), AR/R i s addi-

t i v e

Other cases must be t r e a t e d w i t h more complicated and less

easi l y understood formal i sm. Dignam -- e t a1. loo have presented expres-

s ions f o r t h e o p t i c a l e f f e c t o f a u n i a x i a l f i l m w i t h t h e o p t i c a x i s

o r i e n t e d perpendicular t o t h e surface. I l c ln ty re28 has reviewed t h e

usefu lness o f o p t i c a l probes o f t h e e lectrochemical in ter face, de-

noted by t h e general term electrochemical modulat ion spectr.oscopy.

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ACKNOWLEDGMENTS

My thanks are extended t o D r . D. W. Lynch who n o t o n l y prov ided

t h e best work atmosphere i n which I f e e l t he most comfortable, bu t a l so

spoke ou t on my beha l f many t imes du r ing my graduate t r a i n i n g .

I am indebted t o D r . D. C. Johnson who c h e e r f u l l y acted as my

counselor i n mat ters of e lec t rochemis t ry , and t o t h e members o f D r .

R. S. Hansen's surfac'e chemist ry group who supp l ied t h e h igh p u r i t y

water used i n t h i s experiment.

F i n a l l y , t o my w i f e Kay, who always empathized w i t h every problem

o r success and who supported me hi t h l ove and understanding a1 lowing me

t o accomplish t h i s goal, I o f f e r a spec ia l thanks.