IR SURFACE PLASMON SPECTROSCOPY

(1)

HAL Id: jpa-00223451

https://hal.archives-ouvertes.fr/jpa-00223451

Submitted on 1 Jan 1983

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

IR SURFACE PLASMON SPECTROSCOPY

A. Sievers, Z. Schlesinger

To cite this version:

A. Sievers, Z. Schlesinger. IR SURFACE PLASMON SPECTROSCOPY. Journal de Physique Collo-

ques, 1983, 44 (C10), pp.C10-13-C10-22. �10.1051/jphyscol:19831002�. �jpa-00223451�

(2)

J O U R N A L DE PHYSIQUE

Colloque CIO, suppl6ment a u n012, Tome 44, d k e m b r e 1983 page ClO- 13

I R SURFACE PLASMON SPECTROSCOPY A.J. Sievers and 2 . ~ c h l e s i n ~ e r *

luboratory of Atomic & ScZid S t a t e I'kysics and :dateriaZs Science Center, C ~ r n e l Z !lniuersiLy, ILkrrcu, IVY 748.5.3, U.S.A.

Resume

-

On passe en revue l e s avantages e t l e s p i c g e s de l a s p e c t r o s c o p i e G l a s m o n s de s u r f a c e dans 1 ' i n f r a - r o u g e .

A b s t r a c t

-

The p r a c t i c a l i t y and p i t f a l l s o f IR s u r f a c e plasmon s p e c t r o s c o p y a r e reviewed.

I

-

INTRODUCTION

Because i n f r a r e d s u r f a c e plasmons ( S P ' s ) pag gate f o r many wavelengths on metal surfaces, a g r e a t deal o f e f f o r t has gone 50 c h a r a c t e r i z i n g t h e p r o p e r t i e s o f t h i s unusual s u r f a c e probe /1,2/. A d i r e c t analogy w i t h p l a n e wave spectroscopy does n o t e x i s t . Developing e f f i c i e n t SP c o u p l e r s f o r t h e i n f r a r e d has been p a r t i c - u l a r l y c h a l l e n g i n g s i n c e n e i t h e r t h e SP a t t e n u a t i o n c o e f f i e c i e n t n o r t h e wave h e i g h t s c a l e s w i t h frequency. Couplers n o t o n l y e x c i t e t h e SP mode b u t a l s o e x c i t e some o f t h e p l a n e wave modes which occur a t t h e same frequency. Such " s u r f a c e skimming" waves have been p a r t i c u l a r l y h a r d t o e l i m i n a t e i n t h e f a r i n f r a r e d spec- t r a l r e g i o n .

I f t h e s e e x p e r i m e n t a l problems can be overcome t h e n a new k i n d o f measurement w i l l be p o s s i b l e . Because t h e SP a t t e n u a t i o n c o e f f i c i e n t i s d i r e c t l y p r o p o r t i o n a l t o t h e m e t a l reactance, a measurement o f t h i s a t t e n u a t i o n l e n g t h t o g e t h e r w i t h an i n f r a r e d r e f l e c t a n c e measurement a t t h e same f r e q u e n c y determine b o t h p a r t s o f t h e complex d i e l e c t r i c f u n c t i o n o f t h e m e t a l w i t h equal p r e c i s i o n . T h i s c o m b i n a t i o n o f t e c h n i q u e s may p r o v i d e t h e f i r s t independent measurement o f t h e i n f r a r e d e l e c t r o n mass o f m e t a l s .

Some p r o g r e s s has been made toward t h i s g o a l . SP's have been generated b o t h w i t h s i n g l e f r e q u e n c y 1 asers and a1 so w i t h broadband c o n t i n u o u s sources /3,4/. Measure- ments have been made o f t h e t r a n s m i s s i o n o f IR s u r f a c e plasmons across a v a r i e t y o f metal s u r f a c e s . For t h e b a r e metal agreement i s o b t a i n e d w i t h Drude model p r e d i c - t i o n s w h i l e f o r d i e l e c t r i c coated m e t a l s some d i s c r e p a n c i e s remain. By making use o f a novel i n t e r f e r e n c e phenomenon which i s unique t o inhomogenously p r o p a g a t i n g waves, i t has been p o s s i b l e t o measure t h e SP index o f r e f r a c t i o n f o r coated m e t a l s .

I 1

-

SURFACE PLASMONS ON BARE METAL SURFACES A

-

Model C a l c u l a t i o n s

To emphasize t h e unusual f e a t u r e s o f SP p r o p a g a t i o n on a metal a t a g i v e n i n f r a r e d frequency, i t i s u s e f u l t o compare t h e r e s u l t s w i t h t h o s e o b t a i n e d f o r p l a n e waves r e f l e c t e d f r o m a metal s u r f a c e . The IR a b s o r p t i o n b y a metal a t room t e m p e r a t u r e can be d e s c r i b e d by t h e c l a s s i c a l s k i n e f f e c t s i n c e t h e mean f r e e path, v ~ z i s much s m a l l e r t h a n t h e s k i n d e p t h 6. The Drude f o r m u l a f o r t h e c o n d u c t i v i t y

* c u r r e n t address: Be1 1 Telephone Labs, 600 Mountain Avenue, Murray Hi 11, New Jersey 07974.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19831002

(3)

JOURNAL DE PHYSIQUE

c o r r e c t l y d e s c r i b e s t h e e n t i r e regime: when WT

<<

1 t h e c o n d u c t i v i t y i s l i m i t e d b y

V F T and when ^WT

>>

1 t h e a c c e l e r a t i n g f i e l d r e v e r s e s s i g n b e f o r e a s c a t t e r i n g process occurs. Because much o f t h e work d e s c r i b e d below i s f o r good c o n d u c t o r s i n t h e 10 wavelength r e g i o n , t h e ^UYT

>>

1 l i m i t w i l l be emphasized.

The m e t a l i s t a k e n t o b e i n t h e ( - ) x h a l f space w i t h i t s boundary i n t h e (y,z) plane. The s u r f a c e impedance f o r a normal l y i n c i d e n t p l a n e wave p o l a r i z e d i n t h e z d i r e c t i o n i s

where ^E= i 471 a / w . L e t qo = w/c, t h e f r e e space wavevector, t h e n t h e wavevector i n t h e m e t a l i s

and t h e p e n e t r a t i o n d e p t h o f t h e f i e l d a m p l i t u d e i s

6 = [Re

.

For t h e IR

<<

wp and t h e a b s o r p t i v i t y

In t h e r e l a x a t i o n r e g i o n where ^WT

>>

1

Since x

<

0 t h e s u r f a c e r e a c t a n c e i s i n d u c t i v e . E q u a t i o n ( 4 ) becomes

and Eq. ( 5 ) s i m p l i f i e s t o

Now l e t ' s f i n d s i m i l a r r e l a t i o n s f o r a SP bound t o t h e a i r - m e t a l i n t e r f a c e . To t a k e i n t o account t h a t t h i s TM mode i s l o c a l i z e d a t t h e s u r f a c e and propagates i n t h e z d i r e c t i o n , t h e H f i e l d i s assumed t o have an inhomogenous wave form, namely

Combining t h i s f i e l d w i t h M a x w e l l ' s e q u a t i o n s one f i n d s t h a t

(4)

The s u r f a c e impedance f o r t h e s u r f a c e plasmon mode i s s l i g h t l y l a r g e r t h a n t h e impedance f o r p l a n e waves. I n o r d e r t o compare t h e SP and t h e p l a n e wave r e s u l t s , we d e s c r i b e t h e SP p r o p e r t i e s i n terms o f t h e p l a n e wave s u r f a c e impedance values.

I n t h e same l i m i t as t h e p l a n e wave problem t h e SP wavevectors s i m p l i f y t o

A

where

c

i s determined from Eq. 6. I n most o f t h e i n f r a r e d r e g i o n t h e b e h a v i o r of t h e SP f i e l d s i s dominated b y t h e r e a l p a r t s o f t h e wavevectors. These q u a n t i t i e s a r e p l o t t e d f o r Drude s i l v e r as a f u n c t i o n o f frequency i n Fig. 1.

F i g . 1

-

SP wavevectors f o r a metal

-

a i r i n t e r f a c e . The r e a l p a r t o f t h e p a r a l l e l SP wavevector i s q and t h e r e a l decay r a t e s o f t h e SP f i e l d s i n t h e a i r and metal r e s p e c t i v e l y , a r e

d,a

and

a,,,.

The l i g h t l i n e i s r e p r e s e n t e d b y qo. Note t h a t i n t h e i n f r a r e d . q l v e r y n e a r l y f o l l o w s t h e l i g h t l i n e , pl i s r o u g h l y c o n s t a n t and

Ql,a

g r o w s ' q u a d r a t i c a l l y w i t h f r e q u e n c y . From Eq. 14 t h e SP f i e l d s become i n c r e a s i n g l y c o n f i n e d t o t h e neighborhood o f t h e metal s u r f a c e w i t h i n c r e a s i n g frequency.

Frequency (cm-')

Note t h a t t h e h e i g h t which t h e f i e l d amplitude extends i n t o t h e a i r

depends o n l y on t h e s u r f a c e r e a c t a n c e w h i l e t h e depth which t h e f i e l d a m p l i t u d e p e n e t r a t e s i n t o t h e metal i s t h e same as Eq. 4, namely

The SP a t t e n u a t i o n c o e f f i c i e n t i s

(5)

JOURNAL DE PHYSIQUE

A comparison o f Eq. 15 and Eq. 5 demonstrates t h a t SP a t t e n u a t i o n and IR absorp- t i v i t y probe d i f f e r e n t p r o p e r t i e s o f t h e m e t a l . T h i s d i f f e r e n c e a l s o shows up i n another way. By E q u a t i o n 11, ql

+

^q, and p l a n e waves cannot d i r e c t l y c o u p l e t o SP's. Prism, edge and g r a t i n g c o u p l e r s a r e used t o overcome t h i s wavevector d i f - f e r e n c e between p l a n e waves and t h e bound mode 15-91.

B

-

Measured SP A t t e n u a t i o n C o e f f i c i e n t s

A v a r i e t y o f SP a t t e n u a t i o n c o e f f i c i e n t s have been r e p o r t e d f o r D r u d e - l i k e m e t a l s i n t h e f R /9-151. I n t h e f a r i n f r a r e d i n v e s t i g a t o r s have r e p o r t e d anomalously l a r g e a t t e n u a t i o n c o e f f i c i e n t s f o r a number o f s u r f a c e s 1161. However two r e c e n t s t u d i e s have concluded t h a t t h e p r e s e n t evanescent wave c o u p l i n g t e c h n i q u e s are t o o i n e f f i c i e n t f o r c o u p l i n g SP's a t 84 cm-'and t h e SP mode i s obscured b y a t r a n s - m i t t e d b u l k wave packet 117.181. It i s t h e s p r e a d i n g o f t h i s packet which accounts f o r t h e anomalously 1 arge a t t e n u a t i o n c o e f f i c i e n t s which have been r e p o r t e d . The reason t h e evanescent f i e l d c o u p l i n g t e c h n i q u e can be used s u c c e s s f u l l y i n t h e IR r e g i o n b u t n o t i n t h e F I R . i s t h a t t h e SP f i e l d p r o f i l e h e i g h t does n o t s c a l e w i t h wavelength whereas t h e evanescent f i e l d h e i g h t which i s t h e d r i v i n g source does.

The evanescent f i e l d c o u p l e r has been used w i t h somewhat more success i n t h e 1000 cm-I r e g i o n b u t even t h e r e t h e measured a t t e n u a t i o n c o e f f i c i e n t o f Au ranges over a f a c t o r t h r e e /10,11,14,15/. O n e ' p o s s i b i l i t y i s t h a t t h e i n t e g r i t y o f t h e t h i n f i l m s u r f a c e s v a r y w i d e l y . A measurement o f t h e d.c. r e s i s t i v i t y o f f i l m s would p r o v i d e some degree o f n o r m a l i z a t i o n a g a i n s t t h i s f a b r i c a t i o n problem b u t n o t a l l i n v e s t i - g a t o r s have r e p o r t e d r e s i s t i v i t i e s . Another p o s s i b i l i t y i s t h a t one has r u n i n t o t h e same fundamental problem which was observed i n t h e f a r i n f r a r e d , namely a mismatch between t h e SP p r o f i l e h e i g h t and t h e evanescent f i e l d p r o f i l e h e i g h t . The end r e s u l t o f a mismatch i s t h a t a t any d i e l e c t r i c i n t e r f a c e o r edge d i s c o u n t i n u - i t y , c o l i n e a r r a d i a t i v e and SP waves a r e generated. There i s now some evidence t h a t d i s t i n g u i s h i n g between t h e s e two s i g n a l channels w i t h t h e two p r i s m c o u p l e r i n t h e 10 p wavelength r e g i o n may be a more s u b t l e problem t h a n p r e v i o u s l y r e c o g - nized. Remeasurement o f t h e SP a t t e n u a t i o n c o e f f i c i e n t s o f Ag and Au i n t h e 10 ^p wavelength r e g i o n w i t h a d i f f e r e n t c o u p l i n g geometry t h a n e a r l i e r i n v e s t i g a t o r s have g i v e n much s m a l l e r values 1191. Good agreement between experiment and t h e Drude model i s o b t a i n e d when t h e IR r e l a x a t i o n t i m e i n c l u d e s b o t h t h e d.c. c o n t r i - b u t i o n and d i f f u s e s c a t t e r i n g o f t h e e l e c t r o n s a t t h e m e t a l s u r f a c e .

111

-

SP'S ON DIELECTRIC COATED METALS A

-

Model C a l c u l a t i o n s

The c a l c u l a t i o n o f t h e SP a t t e n u a t i o n c o e f f i c i e n t and i n d e x o f r e f r a c t i o n i s a s t r a i g h t f o r w a r d e x t e n s i o n o f t h e b a r e m e t a l case except now t h e r e s u l t s must b e determined n u m e r i c a l l y 1201. For t h e t h i n f i l m l i m i t approximate a n a l y t i c expres- s i o n s can be o b t a i n e d and we c o n s i d e r t h a t case 1211.

The m e t a l i s separated from t h e a i r b y a d i e l e c t r i c c o a t i n g o f t h i c k n e s s d and d i e l e c t r i c constan!

y.

I n t h e i n f r a r e d 5

<<

n and f o r t h i n f i l m s where d

<<

dc = h / 4 ( n - l )

,

t h e complex wavev

1

^c

l

o r can be w r i t t e n as

where Y = qo d.

(6)

For a Drude metal t h e a t t e n u a t i o n c o e f f i c i e n t i s

where a ( 0 ) i s g i v e n b y bq. J35) and 6 = c / t h e London p e n e t r a t i o n depth, when

WT

>>

1 and 6 = c / ( 2 w y , T ) ~

,

t h e

classic^'

^{s k i n}^' depth, when WT

<<

1.

Equation (19) c o n s i s t s o f f o u r terms. The f i r s t term i s t h e b a r e metal SP a t t e n u a t i o n c o e f f i c i e n t w h i l e t h e n e x t t h r e e terms r e p r e s e n t t h e i n c r e a s e i n SP l o s s i n t h e metal as induced b y t h e c o a t i n g . I n Ref. (17) i t

i s

shown t h a t i f l a t t i c e a b s o r p t i o n occurs i n t h e d i e l e c t r i c c o a t i n g so t h a t Im

n

f 0 t h e n f o u r a d d i t i o n a l terms appear i n t h e a t t e n u a t i o n c o e f f i c i e n t . The r a t i o o f t h e l a r g e s t o f t h e s e new terms t o t h e l a r g e s t t e r m i n Eq. ( 1 9 ) f o r t h e nonabsorbing c o a t i n g i s

Absorbing f i l m = 2WT

-

Im tl

(,I

d

.

Nonabsorbing f i l m 2

11

I f t h e t h i c k n e s s o f t h e absorbing d i e l e c t r i c f i l m i s l e s s t h a n o r comparable t o t h e metal s k i n depth, then t h e nonabsorbing f i l m l i m i t g i v e n b y Eq. (19) a p p l i e s t o b o t h cases.

Experiments w i l l be d e s c r i b e d below which measure t h e index o f r e f r a c t i o n o f t h e SP i n t h e r e l a x a t i o n r e g i o n . From Eq. (18) we f i n d

For SP's i n t h e 1000 cm-' r e g i o n and f i l m t h i c k n e s s d = 500 A t h e two terms a r e comparable i n s i z e . For t h i c k e r f i l m s Eq. (21) i s independent o f t h e p r o p e r t i e s of t h e metal i t s e l f .

6

-

I n f r a r e d Measurements 1

-

A t t e n u a t i o n

The e x p e r i m e n t a l /18/ f a r i n f r a r e d a t t e n u a t i o n c o e f f i c i e n t s a ( d ) as a f u n c t i o n o f Ge o v e r l a y e r t h i c k n e s s , d, are shown f o r Au and Pb i n Fig. 2. F i g u r e 2a shows t h e r e s u l t s o f measurements on t h r e e d i f f e r e n t Au f i l m s . The e r r o r b a r s i n d i c a t e t h e u n c e r t a i n t y i n t h e d e t e r m i n a t i o n o f a ( d ) from t h e t r a n s m i s s i o n measurements made on a p a r t i c u l a r f i l m . The somewhat l a r g e r s c a t t e r i n t h e d a t a may be due t o e f f e c t s a s s o c i a t e d w i t h roughness which may d i f f e r from f i l m t o f i l m .

The t h e o r e t i c a l SP a t t e n u a t i o n c o e f f i c i e n t i s g i v e n b y Equation 15 and i n t h e Drude l i m i t a ( 0 ) i s p r o p o r t i o n a l t o t h e d.c. r e s i s t i v i t y , p, so t h a t

Equations 19 and 22 have been used t o c a l c u l a t e t h e v a l u e o f t h e s u r f a c e wave a t t e n u a t i o n c o e f f i c i e n t f o r b o t h t h e Au and Pb f i l m s . The s o l i d curves i n F i g . 2a and b correspond t o t h e measured f i l m d.c. r e s i s t i v i t i e s p(Au) = 8 pi2 cm, c u r v e 2, and p(Pb) = 32 pQ cm. The d i s c r e p a n c y between t h e s e (Drude) t h e o r y 1 i n e s and experiment f o r l a r g e d i s o f undetermined o r i g i n ( i t may be due t o d dependent roughness). However, f o r t h e purposes o f t h i s r e v i e w we w i l l focus s o l e l y on t h e much l a r g e r d i s c r e p a n c y i n t h e small d r e g i o n . These i n v e s t i g a t o r s p o i n t o u t t h a t t h e n e g a t i v e s l o p e of t h e e x p e r i m e n t a l a ( d ) ( i n F i g . 2a and 2b f o r d

<

0.5 p) makes i t u n l i k e l y t h a t t h e SP a t t e n u a t i o n c o e f f i c i e n t i s a c t u a l l y b e i n g measured i n

(7)

JOURNAL DE PHYSIQUE

t h i s regime o f o v e r l a y e r thickness. I t i s concluded /18/ t h a t t h e SP mode i s obscured by a t r a n s m i t t e d b u l k wave packet i n t h e t h i n f i l m r e g i o n . It i s t h e spreading o f t h i s packet which accounts f o r t h e anomalously l a r g e a t t e n u a t i o n c o e f f i c i e n t s r e p o r t e d e a r l i e r /16/.

F i g . 2

-

Experimental FIR attenua- t i o n c o e f f i c i e n t s and t h e o r e t i c a l SP a t t e n u a t i o n c o e f f i c i e n t s f o r Ge coated metal surfaces versus c o a t i n g thickness. ( a ) Au: measured a t t e n - u a t i o n c o e f f i c i e n t s f o r t h r e e d i f - ferent f i l m s ( a . 0 , ~ ) are shown.

Theory curves ( s o l i d l i n e s ) are f o r (1) p = 4 @cm and (2) t h e measured value p = 8 p 8 cm. (b) Pb: measured

a t t e n u a t i o n c o e f f i c i e n t s f o r two f l l m s (0.0). Theory curve i s f o r t h e measured p = 32 pQ cm o f t h i s f i l m . A f t e r Ref. 18. Somewhat b e t t e r agreement between t h e o r y and experiment has been claimed by Ref.

22 b u t they d i d not use t h e measured t h i n f i l m values o f p i n t h e i r c a l c u l a t i o n s .

I n Fig. 3 some measured values o f t h e SP a t t e n u a t i o n c o e f f i c i e n t s as a f u n c t i o n o f f i l m t h i c k n e s s are shown f o r CuO on Cu /12/ and Ge on Ag /21/ i n t h e 10 wave- l e n g t h region. Both o f these d i e l e c t r i c s are thought t o be nonabsorbing i n t h i s wavelength r e g i o n b u t n e i t h e r set o f data agrees w i t h theory. The dependence o f t h e SP a t t e n u a t i o n c o e f f i c i e n t s f o r Ge coated Ag f i l m s have been analyzed i n some d e t a i l /21/ and we review these r e s u l t s here.

Fig. 3

-

SP absorption c o e f f i c i e n t f o r d i e l e c t r i c coated metals i n t h e 10 pm wavelength region. The measured values are s h o w as a f u n c t i o n o f the normalized c o a t i n g thickness. The n o r m a l i z a t i o n f a c t o r i s dc = ~ / 4 ( ~

-

1)1/2.

The Cu-CuO d a t a i s from Ref. 12.

The Ag-Ge data and t h e theory curve 6

-i

-

' 4 -

- g

c

.- 4l

u are from Ref. 21.

I I I /

Cu-cuo

/*

-

exp.

/ -

Ag-Ge /

C

exp. o o o

/'

-

theory-

(8)

The values o f a(0) measured f o r t h e Ag f i l m s agree w i t h those expected from t h e measured d.c. r e s i s t i v i t i e s . Given a ( 0 ) and

u,,

t h e n e a r l y s t r a i g h t l i n e i n F i g u r e 3 labeled theory r e s u l t s from ?q. (19). The c a l c u l a t e d slope i s

s u b s t a n t i a l l y less than t h a t measured. The i n v e s t i g a t o r s were n o t able t o improve t h e agreement between t h e o r y and experiment by i n t r o d u c i n g absorption i n t h e Ge

, Q , ,

Another s u r p r i s i n g aspect o f t h e thickness dependence data i s t h a t the s t r a i g h t dashed l i n e through t h e d a t a e x t r a p o l a t e s back t o t h e bare metal SP value. I f t h e mean f r e e path o f the e l e c t r o n s w i t h i n a s k i n depth o f t h e surface was reduced by t h e presence o f t h e Ge i n or on the metal, i f t h e surface roughness was enhanced by the c o a t i n g o r i f the i n t e r f a c e s t a t e s i n t h e Ge were important, t h e s t r a i g h t l i n e should e x t r a p o l a t e back t o a valve somewhat l a r g e r than the bare SP value. T h i s conclusion f o l l o w s since t h e slope and t h e i n t e r c e p t o f Equation 19 are not independent parameters as long as up i s f i x e d .

2

-

Index o f R e f r a c t i o n

The SP index o f r e f r a c t i o n has been measured by making use o f a novel i n t e r f e r e n c e phenomenon which i s unique t o inhomogeneous propagating waves 1201. The propaga- t i o n o f r a d i a t i o n across a step d i s c o n t i n u i t y i n t h e o v e r l a y e r t h i c k n e s s can be viewed i n terms o f the c o u p l i n g o f the normal modes on one s i d e t o t h e normal modes on t h e other. I n p a r t i c u l a r , consider a SP on t h e bare metal, t r a v e l i n g toward t h e step d i s c o n t i n u i t y produced by a t h i n d i e l e c t r i c coating. Since t h e d i s c o n t i n u i t y i s small, r e f l e c t i o n and r e f r a c t i o n are small. One might expect t h e i n c i d e n t SP t o couple predominantly t o t h e SP o f t h e coated r e g i o n s i n c e b o t h are bound modes;

however. Maxwell's equations r e q u i r e t h a t t h e t a n g e n t i a l E and H f i e l d s be c o n t i n u - ous across t h e step at a l l h e i g h t s above t h e surface. Even f o r f a i r l y t h i n over- l a y e r s d

-

0.02 dc t h e range o f t h e SP above t h e coated metal surface i s much l e s s than t h a t o f the SP above t h e bare metal 1211. The boundary c o n d i t i o n s at the c o a t i n g edge can be s a t i s f i e d o n l y i f t h e i n c i d e n t SP produces unbound b u l k r a d i a - t i o n i n a d d i t i o n t o t h e t r a n s m i t t e d SP. For t h i c k e r o v e r l a y e r s d

>

dc 112 t h e coated-metal SP i s so compressed t h a t t h e i n c i d e n t bare-metal SP cannot couple t o i t and almost a l l o f t h e i n c i d e n t i n t e n s i t y i s converted t o b u l k r a d i a t i o n . For thicknesses such t h a t 0.02

<

d/dC

<

112 t h e i n c i d e n t SP launches both b u l k and SP r a d i a t i o n . This b u l k r a d i a t i o n i s produced i n t h e form o f a packet t r a v e l i n g i n the forward d i r e c t i o n and spreading s l o w l y i n width. The SP t r a v e l s along t h e coated surface w i t h a phase v e l o c i t y c / n

.

w h i l e t h e phase v e l o c i t y o f t h e b u l k wave packet which t r a v e l s above t h e overlayer i s c. At the f a r edge o f t h e over- l a y e r , o f l e n g t h R, the SP and bulk wave packet both c o n t r i b u t e t o t h e t r a n s m i s s i o n o f a bare-metal SP, however, these two c o n t r i b u t i o n s w i l l i n general no longer be i n phase. The t o t a l i n t e n s i t y o f t h e r e s u l t a n t SP launched a t t h e t r a i l i n g edge o f t h e c o a t i n g can be w r i t t e n

where ISp(R) and I B ( I ) are t h e component i n t e n s i t i e s . A bulk wave packet i s also launched a t t h e t r a i l i n g edge w i t h an i n t e r f e r e n c e term complementary t o t h a t o f t h e SP. The f i r s t two terms i n Equation 23 decrease m o n o t o n i c a l l y w i t h i n c r e a s - i n g o v e r l a y e r l e n g t h I:

From t h e t h i r d term i n Equation 23, t h e s p a t i a l p e r i o d o f t h e i n t e r f e r e n c e i s

(9)

JOURNAL DE _PHYSIQUE

The d i f f e r e n c e i n i n d e x o f r e f r a c t i o n o f t h e SP wave and t h e b u l k wave can be e s t i - mated from Equation 21. Because n,

-

1 i s s m a l l , l a r g e i n t e r f e r e n c e p e r i o d s w i l l b e produced by r e 1 a t i v e l y s h o r t wavelength r a d i a t io n .

To t e s t t h e s e c o n c l u s i o n s t h e i n v e s t i g a t o r s I 2 0 1 evaporated Ag and Au f i l m s on KC1 c o u p l e r s . Over p a r t o f t h e s e r e c t a n g u l a r l y shaped f i l m s t h i n Ge o v e r l a y e r s o f a t r i a n g u l a r shape were t h e n d e p o s i t e d .

The SP was launched f r o m a C02 l a s e r beam a t one edge o f t h e metal f i l m by means o f t h e edge c o u p l i n g t e c h n i q u e /17/. At t h e c o r r e s p o n d i n g p o i n t on t h e o p p o s i t e edge o f t h e m e t a l t h e SP produced a t t h e t r a i l i n g edge o f t h e c o a t i n g c o u p l e d i n t o t h e d i e l e c t r i c s u b s t r a t e and was d e t e c t e d . The l e n g t h 1 o f t h e o v e r l a y e r r e g i o n probed b y t h e beam was c o n t i n u o u s l y v a r i e d b y t r a n s l a t i n g t h e f i l m assembly i n t h e p l a n e o f t h e s u r f a c e b u t p e r p e n d i c u l a r t o t h e beam d i r e c t i o n . The t r a n s m i s s i o n was measured as a f u n c t i o n o f L f o r f i x e d o v e r l a y e r t h i c k n e s s d and C02 l a s e r f r e q u e n c y U.

An example o f t h e observed t r a n s m i s s i o n vs 1 showing i n t e r f e r e n c e between a SP and b u l k r a d i a t i o n i s p r e s e n t e d i n F i g . 4 ( a ) a l o n g w i t h t h e F o u r i e r t r a n s f o r m o f t h e i n t e r f e r o g r a m i n F i g . 4 ( b ) . Values o f t h e i n t e r f e r e n c e p e r i o d AL a r e o b t a i n e d e i t h e r f r o m t h e s e p a r a t i o n o f t h e l o c a l maxima o f t h e i n t e r f e r o g r a m [ F i g . 4 ( a ) ] o r f r o m t h e p o s i t i o n o f t h e peak i n i t s F o u r i e r t r a n s f o r m [Fig. 4(b)].

independent o f t h e p r o p e r t i e s o f t h e metal i t s e l f .

7

I V

-

CONCLUSIONS

F i g . 4

-

SP i n d e x o f r e f r a c t i o n measurement o f a d i e l e c t r i c c o a t e d m e t a l . ( a ) SP t r a n s - m i s s i o n across a Ge-coated Ag f i l m vs o p t i - c a l p a t h . The Ge c o a t i n g i s d = 0.2 pm

Of fundamental importance i s t h e way t h e parameters which d e s c r i b e t h e e l e c t r o dynamics o f t h e m e t a l e n t e r t h e SP mode. It i s d i f f e r e n t t h a n f o r p l a n e wave spectroscopy. The appearance o f t h e p r o d u c t o f t h e s u r f a c e r e s i s t a n c e and s u r f a c e r e a c t a n c e i n Eq. 15 i s an i m p o r t a n t r e s u l t and r e q u i r e s some e x p l a n a t i o n . I n t h e

IR most o f t h e f i e l d i n t e n s i t y o f t h e SP mode i s i n t h e a i r above t h e m e t a l . The a m p l i t u d e o f t h e magnetic f i e l d a t t h e s u r f a c e i s i n v e r s e l y r e l a t e d t o t h e h e i g h t

% OU- t h i c k (d/dq = 0.3) and t h e l a s e r f r e q u e n c y

-

s i s 975 cm-

.

( b ) F o u r i e r t r a n s f o r m o f t h e

Z I i n t e r f e r o g r a m i n ( a ) . Measurements l i k e

t h e s e have been used t o s t u d y t h e s p a t i a l p e r i o d o f i n t e r f e r e n c e vs l a s e r frequency.

Because o f t h e r e l a t i v e l y l a r g e v a l u e of d/dc t h e approximate e x p r e s s i o n g i v e n b y Eq. 2 1 produces a 20 % e r r o r . I n c r e a s e d p r e c i s i o n was o b t a i n e d b y n u m e r i c a l c a l c u - l a t i o n . Good agreement was found between

(b) t h e o r y and experiment. A f t e r Ref. 17. It

s h o u l d be n o t e d t h a t f o r t h e s e r e l a t i v e l y t h i c k d i e l e c t r i c c o a t i n a s . t h e SP index i s

(10)

o f t h e mode above t h e s u r f a c e . Since t h e a t t e n u a t i o n c o e f f i c i e n t depends on t h e amplitude o f t h e f i e l d a t t h e s u r f a c e t h e n by Eq. 14 i t must be p r o p o r t i o n a l t o t h e s u r f a c e reactance. A measurement o f b o t h a and A f o r t h e same metal s u r f a c e would enable one t o s e p a r a t e l y determine up and r . Although i t has been known f o r many y e a r s t h a t t h e I R dependencies o f t h e s e two parameters should p r o v i d e a g r e a t deal o f i n f o r m a t i o n about t h e dynamics o f t h e electron-phonon i n t e r a c t i o n 1231 such a d e t e r m i n a t i o n w i t h p l a n e wave measurements has proven t o be e l u s i v e .

The same reason which makes t h e SP a t t e n u a t i o n measurement a t t r a c t i v e as a

fundamental probe makes it d i f f i c u l t t o use e x p e r i m e n t a l l y . To o b t a i n e f f i c i e n t SP g e n e r a t i o n t h e evanescent f i e l d d i s t r i b u t i o n generated a t a c o u p l e r by t h e spectrum o f p l a n e waves must match t h e s p a t i a l d i s t r i b u t i o n o f t h e f i e l d s associated w i t h t h e bound mode. Antennae f o r p l a n e waves s c a l e as a-' b u t t h e h e i g h t o f t h e SP v a r i e s as The c o n c l u s i o n i s t h a t a c o u p l e r designed t o work e f f i c i e n t l y i n one frequency r e g i o n cannot be s i m p l y s c a l e d t o g i v e t h e same performance i n

another f r e q u e n c y range. I f i t i s matched t o produce SP's i n one frequency r e g i o n t h e n i t i s l i k e l y t h a t i n t h e second, a wave packet o f s u r f a c e skiming p l a n e waves c o u l d be t h e dominant s i g n a l . The e x p e r i m e n t a l i d e n t i f i c a t i o n o f these two compo- n e n t s i s n o t simple. The p l a n e wave packet d i f f r a c t s as i t r o v e s across t h e s u r - f a c e so an "apparent" a t t e n u a t i o n c o e f f i c i e n t can be measured f o r t h i s component as w e l l .

From t h i s d i s c u s s i o n i t i s c l e a r t h a t t h e key parameter f o r u n d e r s t a n d i n g t h e i n f r a r e d p r o p e r t i e s o f SP's i s t h e h e i g h t t o which t h e SP f i e l d s extend above t h e s u b s t r a t e . The i n t e r f e r e n c e between SP's and p l a n e waves observed w i t h t h e SP i n t e r f e r o m e t e r i s one demonstration o f t h e importance o f t h i s parameter. The sub- s t a n t i a l c o u p l i n g o f t h e bound SP t o t h e unbound r a d i a t i o n , which can occur when- ever t h e n a t u r e o f t h e i n t e r f a c e s u p p o r t i n g t h e SP changes a b r u p t l y , i s p r o v i n g t o be one o f t h e more s u b t l e f e a t u r e s o f SP spectroscopy.

The authors acknowledge v a l u a b l e c o n v e r s a t i o n s w i t h Y. J. Chabal

.

T h i s work was supported by t h e N a t i o n a l Science Foundation under g r a n t no. DMR-81-06097 and by t h e A i r Force under g r a n t no. AFOSR-81-01218.

V

-

REFERENCES

AGRANOVICH V.M. and MILLS D.L., e d i t o r s , Surface P o l a r i t o n s ( N o r t h - H o l l a n d , Amsterdam, 1982).

BDARDMAN A.D., e d i t o r , E l e c t r o m a g n e t i c Surface Modes, (John W i l e y and Sons, New York

,

1982).

SCHLESINGER Z. and SIEVERS A. J., S u r f . S c i . 102 (1981) L29; 107 (1981) 639.

ZHIZHIN G.N., MOSKALOVA M.A., SIGAREV A.A. aXYAKOVLEV ~.A.,ptics Commun.

43 (1982) 31.

m T O A., Z. Physi k 216 (1968) 398; KRETSCHMANN E., Z. Physik 227 (1969) 412.

CHABAL Y.J. and S I E m S A.J., Appl. Phys. L e t t e r s 32 (1978) 9 c

RITCHIE R.H., ARAKAWA E.T., COWAN J.J. and HAMM R . r , Phys. Rev. L e t t e r s

2

(1968) 1530.

SEYMOUR R.J., KOTELES E.S. and STEGEMAN G.I., Appl. Phys. L e t t e r s

41

⁽¹⁹⁸²⁾

1013.

SCHOENWALD J.. BURSTEIN E. and ELSON J.M.. S o l i d S t a t e Commun. 12 (1973) 185.

SCHOENWALD J. .and BURSTEIN E., Proc. ~ a o r m i n a Conference on ~ o l % i t o n s , ' E . B u r s t e i n , e d i t o r (Pergamon Press, New York, 19/41 139.

MCMULLEN J.D., S o l i d S t a t e Commun. 17 (1975) 331.

BRYAN D.A., BEGLEY D.L., BHASIN K. ,TLEXANDER R.W., BELL R. J. and GERSON R..

Surface Sciences 57 (1976) 53.

ZHIZHIN G.N., MOSmLEVA M.A., SHOMINA E.V. and YAKOVLEV V.A., S o v i e t Physics S o l i d S t a t e 21 (1979) 1630.

ZHIZHIN G.N.,MOSKALEVA, M.A. SHOMINA E.V. and YAKDVLEV V.A., F i z Met. i. Met.

50 ( 1980) N3.

-

(11)

C 10-22 JOURNAL DE PHYSIQUE

15. ZHIZHIN G.N., MOSKALEVA M.A., SHOMINA E.V. and YAKOVLEV V.A. i n Ref. 1.

16. BEGLEY D.L., ALEXANDER R.W., WARD C.A., MILLER R. and BELL R.J., Surf. Sci.

81

(1979) 245.

17. KOTELES E.S. and MCNEIL W.H., I n t . J. o f I n f r a r e d and M i 1 li m e t e r Waves

2

(1981) 361.

18. SCHLESINGER Z., WEBB B.C. and SIEVERS A.J., S o l i d S t a t e Commun.

2

(1981) 1035.

19. SCHLESINGER Z. and SIEVERS A.J., S o l i d S t a t e commun. 43 (1982) 671.

20. SCHLESINGER Z. and.SIEVERS A.J., Appl. Phys. L e t t e r s (1980) 409.

21. SCHLESINGER Z. and SIEVERS A.J., Phys. Rev. B

26

( 1 9 8 T 6444.

22. STEGEMAN G. I. and SEYMOUR R.J., S o l i d S t a t e Conunun.

44

(1982) 1357.

23. ALLEN P.B., Phys. Rev. B

-

11 (1975) 2693.