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APPLICATION OF RAMAN SCATTERING
EXCITED IN CONDITION OF TOTAL REFLECTION (RSTR) TO THE STUDY OF SURFACE
PHENOMENA IN CRYSTALS
G. Mattei, B. Fornari, M. Pagannone, L. Mattioli
To cite this version:
G. Mattei, B. Fornari, M. Pagannone, L. Mattioli. APPLICATION OF RAMAN SCATTERING EXCITED IN CONDITION OF TOTAL REFLECTION (RSTR) TO THE STUDY OF SURFACE PHENOMENA IN CRYSTALS. Journal de Physique Colloques, 1984, 45 (C5), pp.C5-249-C5-253.
�10.1051/jphyscol:1984537�. �jpa-00224155�
A P P L I C A T I O N OF RAMAN SCATTERING EXCITED I N CONDITION OF TOTAL
REFLECTION (RSTR) TO THE STUDY OF SURFACE PHENOMENA IN CRYSTALS
G . Mattei, B. Fornari, M . Pagannone and L. M a t t i o l i
ConsigZio NazionaZe deZZe R i c e r e h e , Area deZZa Ricerca d i Roma, J s t . M.A.I.,
C . P . 10, 00016 Monterotcndo SeaZo (Roma), I t a l y
R6sumE
-
On discute l e s aspects gEnGraux de l a diffusion Raman excitEe en condition de rEflection totale(RSTR) avec une attention spsciale pour l e s t r a i t s particul i e r s d u RSTR (profondeur de pEnGtration, eff i c a c i t e Raman e t sa dGpendance angulaire, e t c . ) qui sont s i g n i f i c a t i f s dans llGtude des phEnomGnes qui interviennent aux interfaces. On donne aussi les r g s u l t a t s expErimentaux regardant I ' a p p l i c a t i o n du RSTR 2 llEtude de la dispersion des polaritons de surface 2 1'
interface e n t r e deux milieux transparents.Abstract - The general aspects of Raman Scattering excited in condition of Total Reflection (RSTR) are discussed with special emphasis on the peculiar features of t h e RSTR (penetration depth, Raman efficiency and i t s angular dependence, e t c . ) t h a t are relevant i n the study of phenomena occurring a t interfaces. Experimental r e s u l t s regarding the application of RSTR t o the study of surface polariton dispersion a t the interface between two transparent media are also reported.
I t i s well known t h a t when an electromagnetic (em) wave i s t o t a l l y reflected a t the interface between two transparent media an evanescent em wave i s present a t the interface in the lower r e f r a c t i v e medium. Since t h i s evanescent wave c a r r i e s only a real wavevector component parallel t o the interface (so t h a t i t t r a v e l s along the s u r f a c e ) , i t s wavevector component perpendicular t o the interface i s purely imaginary and i t s penetration depth can be controlled by varying the angle of incidence, i t seems t o be an ideal tool f o r exciting Raman scattering in a thin reg ion under the surf ace.
W discuss here, on the basis of our previous theoretical /1/ and experimental e / 2 / work, the main features of t h i s Raman Scattering excited in Total Reflection condition (RSTR) and we emphasize i t s application t o the study of interface phenomena.
Let us summarize t h e main r e s u l t of our theoretical treatment of RSTR, t h a t i s the expression of the RSTR efficiency
a
defined as t h e r a t i o between the power scattered and transmitted in medium 1 , see Fig. 1 , along the direction OF,, per unit surface area per unit solid angle, and the power of the exciting radiation striking t h e unit interface area along the direction F,O. In particular we considered t h e case of RSTR from bulk phonons and from surface phonon-polaritons, t o which the superscripts B and S r e f e r , respectively, in equation ( 1 ) . The subscripts ho and ev are used t o emphasize t h a t two l i g h t scattering mechanisms can contribute t o the RSTR: ho r e f e r s t o the emission of homogeneous t r a v e l l i n g em waves refracted from medium 2 into medium 1 , ev r e f e r s t o the emission ofArticle published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984537
C5-250 J O U R N A L DE PHYSIQUE
evanescent em waves, t h a t a r e n o r m a l l y n e g l e c t e d i n t h e Raman s c a t t e r i n g and become i n s t e a d v e r y i m p o r t a n t i n RSTR because o f t h e p r o x i m i t y o f t h e s c a t t e r i n g c e n t e r t o t h e i n t e r f a c e . These evanescent waves a r e r e f r a c t e d as t r a v e l l i n g waves i n medium 1
F i g . 1 - Scheme o f t h e employed RSTR g e o e e t r y . The l a s e r beam focused by t h e l e n s L1 i n F, i s c o l l i m a t e d i n t o t h e hemisphere along t h e d i r e c t i o n F,O w i t h angle o f i n c i d e n c e
Gi
> @, = s i n-'
( n,
/ n , ) ( n,
and n,
being t h e r e f r a c t i v e i n d i c e s o f t h e p r i s m and o f t h e c r y s t a l , r e s p e c t i v e l y . The s c a t t e r e d l i g h t under t h e i n t e r f a c e i n t h e c r y s t a l i s r e f r a c t e d along t h e d i r e c t i o n OF, ( d e f i n e d by8
and a ), focused i n F2 , c o l l e c t e d by t h e l e n s L 2 and t h e n focused o n t o t h e e n t r a n c e s l i t o f t h e monochromator.a t angles exceeding t h e c r i t i c a l angle. Another r e l e v a n t f e a t u r e i n t h e RSTR i s t h e f a c t t h a t momentum c o n s e r v a t i o n i s s t r i c t l y observed o n l y along t h e i n t e r f a c e . The f i n a l e x p r e s s i o n o b t a i n e d f o r t h e RSTR e f f i c i e n c y i s :
where k i s a c o n s t a n t c h a r a c t e r i s t i c f o r t h e two media, N( o , T ) i s t h e Bose-Einstein f a c t o r , s($~ ,@,a )
I , , , .
i s a t e r m depending on b o t h t h e angles and,
t h e sample t h r o u g h i t s Raman s u s c e p t i b i l i t y . The f a c t o r h
~ ~ ~ . ,
i s an " i n t e r a c t i o n t h i c k n e s s " which t a k e s d i f f e r e n t values f o r t h e case o f homogeneous and evanescent RSTR as w e l l as f o r t h e s u r f a c e and t h e b u l k modes. I n p a r t i c u l a r , we havewhere k T z , k s Z and q a r e t h e wavevector components p e r p e n d i c u l a r t o t h e i n t e r f a c e o f t h e i n c i d e n t t r a n s m i t t e d e x c i t i n g em wave, o f t h e s c a t t e r e d em wave and o f t h e s u r f a c e p o l a r i t o n , r e s p e c t i v e l y . Besides t h e Raman e f f i c i e n c y , an i m p o r t a n t q u a n t i t y i s t h e r a t i o @ = (equal t o h S /h ) t h a t g i v e s us an i n d i c a t i o n o f t h e degree o f d e t e c t a b i l i t y o f t h e s u r f a c e modes by means o f RSTR. If we p l o t c a l c u l a t e d values o f
a
andg
f o r a chosen r e a l i s t i c i n t e r f a c e as a f u n c t i o n o f t h e s c a t t e r i n g angles$,,@
and a we see f i r s t o f a l l t h a t a l l t h e f u n c t i o n s are s h a r p l y p i c k e d a t9,
and @ very c l o s e t o t h e c r i t i c a l anglefiC
(see Figs .2,3).Moreover, t h e r a t i o Q ( r a n g i n g f r o m 0.1 t o 0.5, see F i g . 5 ) t a k e s t h e most f a v o u r a b l e values i n t h e evanescent RSTR (@a @,). As a f u n c t i o n o f a , instead,
in t h e sapphire-NaBr03 system. The c r o s s e s represent our experimental r e s u l t s . b) Calculated and measured Raman e f f i c i e n c y as a function of
oi
f o r t h e same c a s e a s in Fig. 2.Fig. 3 - Calculated s u r f a c e RSTR e f f i c i e n c y 0 (dashed l i n e ) and s u r f a c e t o bulk RSTR e f f i c i e n c y r a t i o
g
( s o l id l i n e ) as a function of@
, in t h e c a s e of t r a n s v e r s e magnetic polarized incident l i g h t , a tei
= 60' and a = 5' , f o r t h e s u r f a c e p o l a r i t o n in t h e gap TO-LO a t 965-987 cm-' of the sapphire-NaC103 i n t e r f a c e .Fig. 4 - Calculated s u r f a c e RSTR e f f i c i e n c y 0 (dashed l i n e ) and surface t o bulk RSTR e f f i c i e n c y r a t i o
g
( s o l i d l i n e ) as a function of a a tG i = @ =
60° f o r t h e same case a s in Fig. 3.t h e s e q u a n t i t i e s have a smooth f l a t behaviour a t l e a s t from 0" t o 30°, see Fig.4.
We a r e then a b l e t o choose t h e best experimental c o n d i t i o n s f o r t h e d i f f e r e n t experiments we want t o perform. For i n s t a n c e , t h e s t r o n g e s t Raman signal can be
C5-252 J O U R N A L DE PHYSIQUE
obtained taking oiand @ g r e a t e r but very close t o @,and
a
about 0'. By changing@i
a t fixed @and
a
the RSTR signal a t varying distances from the interface can be monitored. This feature can be useful f o r studying d i f f e r e n t layers near t h eC I I ~ ~ A C P . The decay shown i n Fig. 2b i s due t o the decreasing of the penetration depth i n medium 2 of the exciting evanescent em wave as the incidence angle increases. To study the dispersion of surface polaritons t h e best condition i s t h a t of fixing @ i and
8
a 1 i t t l e greater t h a t 8,and then t o varya
in order t o s e l e c t the wavevector component parallel t o the interface of the surface polariton. In t h i s condition we have higher surface signal and higher surface t o bulk Raman signal r a t i o in a l l the explored range ofa .
Fig. 5
-
Results f o r the surface polariton in the gap TO-LO a t 965-987 cm-'in the sapphire-NaC102 interface. Experimental spectra f o r some values of the anglea
(
ai
= @ = 6 0 ) are shown in the i n s e r t , where the arrows indicate the surface polariton peak (on the bottom the frequency positions of the bulk phonons in NaC103 are indicated). The calculated dispersion curves with n , = 1.513 (curve a ) and n,
= 1.18 (curve b ) are compared w i t h the experimental values ( d o t s ) .Before discussing our experimental r e s u l t s we want t o recall t h a t the kind of Raman scattering we are talking about has been successfully applied by others t o the study of solid-liquid interfaces, see f o r instance /3-5/, and solid-solid interfaces 1 6 1 and t h a t our theoretical r e s u l t s , concerning the angular dependence of the RSTR efficiency, agree with those obtained by others / 7 / in the case of molecules in isotropic disordered systems.
c a l c u l a t e d c u r v e s . I n Fig.5 some e x p e r i m e n t a l s p e c t r a f o r t h e sapphire-sodium c h l o r e t e i n t e r f a c e a r e shown f o r d i f f e r e n t values o f t h e angle a .The s u r f a c e p o l a r i t o n mode i n t h e gap TO-LO 965-987 cm-' o f sodium c h l o r a t e i s i n d i c a t e d by t h e arrows. The e x p e r i m e n t a l d i s p e r s i o n c u r v e ( d o t s ) i s compared w i t h t h e o r e t i c a l curves c a l c u l a t e d f o r d i f f e r e n t values o f n 2 f o r t h e a c t i v e medium NaC103
.
The comparison between t h e o r y and experiment f o r t h e Raman s c a t t e r i n g by s u r f a c e p o l a r i t o n s i s s t i l l an open problem whose s o l u t i o n i s sought by t a k i n g i n t o c o n s i d e r a t i o n many i n f l u e n c i n g f a c t o r s ( g e o m e t r i c a l roughness, induced s t r a i n s , anharmonicity, e t c .)/8,9/.I n c o n c l u s i o n we have t r i e d t o b r i e f l y d i s c u s s some o f t h e i m p o r t a n t f e a t u r e s o f RSTR t o g e t h e r w i t h some e x p e r i m e n t a l r e s u l t s w i t h t h e aim o f showing t h a t t h i s t e c h n i q u e i s a u s e f u l one i n t h e study o f s u r f a c e and i n t e r f a c e phenomena.
References.
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/3/ UKESHOJI,T., ON0,Y. and MIZUNO,T., Appl. O p t i c s 12 (1973) 2236.
/4/ REDEL, K.,H., SPENKUCH,D. and WESSLER, G., R., O p t i c s and Spectrosc. 38 ( 1975) 649.
/5/ FUJIHIRA,M. and OSA,T., J. Am. Chem. Soc. 98 (1976) 7850.
/6/ BAPTIZMANSKII, V., V., NOVAK, I., I. and CHMEL,A., O p t i c s and Spectrosc. 43 ( 1977) 106.
/7/ DIHOOGE,L.,VIGOREUX,J.,M. and MENU,C., J. Chem. Phys 74 (1981) 3639.
/8/ USHIODA,S., AZIZA,A., VALDEZ, J.,B. and MATTEI,G., Phys. Rev. B19 (1979) 4012.
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