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Photochemistry at Corrugated Thin Metal Films: A Phenomenological Approach

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P. T. Leung, Y. S. Kim and Thomas F. George

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Photochemistry in Thin FilmsEdited by Thomas F. GeorgeProceedings of the Society of Photo-Optical Instrumentation EngineersVoume 1056

Departments of Chemistry and PhysicsState University of New York at BuffaloBuffalo, New York 14260

December 1988

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Photochemistry at Corrugated Thin Metal Films: A Phenomenological Approach

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16. SUPPLEMENTARY NOTATION Prepared for publication in Photochemistry in Thin Films, Edited byThomas F. George, Proceedings of the Society of Photo-Optical Instrumentation Engineers,Volume 1056

17. COSATI CODES 18. SUBJECT TERMS (Continue on reverse if necessary and identify by block number)FIELD GROUP SUB-GROU P HOTOCHEMISTRY , SELECTIVE PHOTOABSORPTION

OP THIN META IM, MOLECULAR DIPOLE,CORRUGATED . SRFACE PLASMON

19. ABST (Contnu or'evee if neco y and identify by block number)

A phenomenological model is adopted to explore possible novel photochemicalphenomena for molecules in the vicinity of a corrugated thin metal film, withdetailed results worked out for the photoabsorption cross section for moleculesin the vicinity of a grating film. A mechanism is proposed by which enhancedselective photoabsorption may be achieved based on the different nature of thecoupling of the molecular dipole and the incident laser light to the surfaceplasmon modes of the thin films.

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Photochemistrv in Thin Films

Edited by Thomas F. George

Proceedings of the Society of Photo-Optical Instrumentation Engineers

Volume 1056 (1989)

Photochemistry at corrugated thin metal films: a phenomenological approach

P. T. Leung

Department of Physics, Portland State University

P. 0. Box 751, Portland, Oregon 97201

Young Sik Kim* and Thomas F. George

Departments of Chemistry and Physics & Astronomy

239 Fronczak Hall, State University of New York at BuffaloBuffalo, New York 14260

ABSTRACT

A phenomenological model is adopted to explore possible novel photochemical

phenomena for molecules in the vicinity of a corrugated thin metal film, with

detailed results worked out for the photoabsorption cross section for molecules in

the vicinity of a grating film. A mechanism is proposed by which enhanced

selective photoabsorption may be achieved based on the different nature of the

coupling of the molecular dipole and the incident laser light to the surface

plasmon modes of the thin films.

1. INTRODUCTION

The discovery of the dramatic surface-enhanced Raman scattering1 has opened

up the possibility of enhancing other photochemical processes by similar mechanisms

employing the resonance condition of the surface plasmon field. Upon realizing the

importance of surface roughness in these processes, intensive theoretical 2 ' 3 and

experimental4 '5 efforts have been devoted to the study of processes like

photoabsorption/dissociation (direct dissociation) of molecules in the presence of

both localized2 and extended3 surface structures. By now, it has become clear that

for such first-order processes, the surface-enhanced field and the induced decay

rate will play the role of two competing factors in determining the ultimate2-4

enhancement of the process.

In this work, we would like to explore the possibility of novel photochemical

phenomena for molecules located in the vicinity of a thin metal film. Roughly

speaking, when the thickness is thin enough, a thin-film system can be viewed as

two surfaces interferring with each other, and hence we would expect richer

proximity effects to arise. In the following, we shall study photoabsorption for3

these molecules by generalizing two of our previous works on photoabsorption and

decay rates6 for the case of a single roughened surface.

* Present address: Department of Chemistry, Princeton UniversityPrinceton, New Jersey 08544

2. PHOTOABSORPTION CROSS SECTION

The configuration of our problem is depicted in Fig. 1, where we consider a

two-level system (modeled by a dipole moment p) located at z - d above a thin

_I/ -" Accession Fjr

LASER '"TIS GRA&ID' IC TAB

6 Unannounced 01Justification-

\ iByDistribution/

Availability CodesA'V. r i -

2 Dist Special

Figure 1. Configuration of the photoabsorptionproblem at a corrugated thin film.

metal (taken as Ag) film bounded by two grating surfaces located at z - 0 and z - -

t, respectively. Thus the profile functions take the simple forms

iQlx iQ2xr 1 1 e r2 - o2e

respectively, where we shall assume small corrugations ( o.Qi << 1), so that

perturbation theory can be applied. For simplicity, we consider only replicatedfilms for which o1 - o2 - %o and Q " Q2 - Q0, although different combinations of7

i and 2 can also yield film systems of great interest. The optical properties

of the three media are described by their dielectric functions eI, C2 - e'(w) +

ic"(w) and e3' respectively. Consider p-polarized laser light of the form

i(k(O)z-wt) ik(O).-l

E -(E~ + E e )e z e 1 (2)in o x oz z

-#(0)i-z

;(° ) k(°) A r, - (x,y) , (3)

being incident on the system at an angle 0 with the normal direction. We want tocalculate the absorption cross section of the molecule. For simplicity, let us

assume that the dipole p is oriented perpendicular (p - g z) to the film.

According to the phenomenological model, 2'3 the absorption cross section forthe free-molecule case can be obtained in a Lorentzian form as

0

a(w) - AIEn sin 2 2 (4)0 in n2 )

where A is a proportionality constant, and w0 and 7 denote the natural frequency

and the width of the excited state for the free molecule, respectively. In thepresence of the substrate film, Eq. (4) then becomes

a(w) - AIE dr(d,w)l 2 ( w M 2 (5)z (W- M ) 2 + (7M/2) 2 '

where E (d,w) is now the total field driving the dipole, and w and IM denote thez

dressed values for the frequency and width, respectively, due to the presence ofthe film substrate. Since these are usually dependent on the driving frequency W,Eq. (3) is in general distorted from a Lorentzian shape. Moreover, it is knownthat the induced frequency shift can most of the time be neglected compared to the

8 oinduced decay rate, and hence in the following we shall assume wM - M and take

into account only the substrate-induced decay rate which can be obtained as

I 3qe1IS l + ImG(W) (6)o37 02k3

where

G(W)- E r (di) (7)

q is the quantum yield of the emitting state, k c ) is the emission wave

number, and Er(d,w) is the reflected field from the film upon incidence by thedipole emissions, acting back on the dipole. Our remaining job then is to

dr rcalculate the fields E and E

3. SURFACE ELECTROMAGNETIC FIELDS

In order to calculate the surface fields generated by the incident laser

field (E dr) in Eq. (5) and the dynamic reflected field at the dipole site in Eq.

(7), we resort to a pertubative approach formulated by Maradudin and Mills.9

According to their theory, the p-th theory component for the roughness contribution

(E R ) to the reflected field from first-order perturbation theory can be obtainedas

Ro k ~ 2 ikp.iI dkrz)(clztE ~) 16x 3 l z m 11w I z) (2e~' cl]S(z')E" dk e "+ ( _+ z (d0)

x M(1k-kl )) + [C3 e 2e(-z')16(z'+t)[ (k 11'ki )) + t1)

x E(O)(kO)wz') (8)

where 11 denotes any vector on the xy-plane, is the Fourier transform of theprofile function, 8 is the Heaviside step function, and d is the Fourier

transform of the two-dimensional "flat propagator" obtained in Ref. 9. E(0 ) in Eq.V

(8) denotes the total field for the homogeneous case of a perfectly flat film.Hence, to calculate Edr, one simply employs the expressions of E(0 ) for a flat film

10 rwhich are available in the literature. Similarly, for the calculation of E , the

problem of E( 0 ) has also been solved by Chance, Prock and Silbey in terms of the10

8Green dyadics. Furthermore, we remark that to evaluate the integral of 6(z') in

Eq. (8), where E( 0 ) may be discontinuous across the boundaries of the film, one

must adopt Agarwal's modifications and not just take the mean value of the

integrals at each side of the boundary. Using the various appropriate E(O) 's,

we finally obtain12

2ikld ikld

E r(d,w) - (1 + R e ) EnsinO + ER°(dw) e , (9)z i

where R is the Fresnel reflectance for a flat film,10 and E is given byz

E RO (d w ) "-" e 2 (0 ) +C4)

0)iald+ (e3-,2)[Cc 3E °)(W-t.) + CE(°)(Wj-t.)]) e 1 (10)

mm mmm m 3 2 1 3 -- 5m z

where k - w/c and E (0, E(0) and a are given in detail in Ref. 12. Similarly, we

have7

i 3 2hld E o

Er(dw) - dA 2 (f' 1) e 1 +zo (d,+) , (11)eJ h 1 z

where

E Ro(d;w) - -2 E 2 -o C1 1 + (C3-e2)12 ] (12)z 4 (

with the functions f and hl given in Ref. 7. In Eqs. (10) and (12), the

coefficients Ci and the integrals Ii are complicated functions of the film

parameters and are given in detail in Refs. 12 and 7. Hence, from Eqs. (6), (7),

(11) and (12), we then obtain the complete determination of 1 in terms of 7 .

Taking this value for 7M and together with Eq. (9) into Eq. (5), we can then

calculate the photoabsorption cross section at the grating film [a(w)] for a givenfree-molecule cross section ao()

4. POSSIBILITY OF ENHANCED SELECTIVE PHOTOABSORPTION

Instead of showing some straightforward model calculation based on Eqs. (4)and (5), here we shall pay attention to a very interesting feature of the problemwhich may lead to the realization of a mechanism for enhanced selective

7photoabsorption for adsorbed molecules. In a recent study, we have pointed outthat the coupling of the molecular fluorescence radiation to the two thin-filmsurface plasmons is governed by very different dispersion relations as compared tothose in the case of plane-wave light-scattering experiments. The differencearises from the dipole nature of the molecular emission which consists of asuperposition of all the plane-wave harmonics. Hence the resonance peaks due tothe cross-coupling of the plasmons on the two film surfaces into the long-(andshort-)range surface plasmons [L(S)RSP] in the decay-rate spectrum are in general

12at different DgOStions as compared to those in the light scattering spectrum.

Since these peak positions (in both spectra) are very sensitive to the geometrical(roughness, thickness.... ) and dielectric properties of the film, for a given level

W 0 one can then try to adjust these parameters so that the cross-coupling peak of

00

the scattered field lies close to Mand that of the induced decay rate stays away

from w . Upon optimal conditions, enhanced selective photoabsorption of this

particular level (N) may be achieved since the other levels close to it may now be

damped seriously due to the fact that they can possibly experience large values forthe induced decay rates.

As a numerical illustration, we consider a hypothetical molecular system with

30.0

15.0 Figure 2. Hypothetical3 molecular system

0 with two Lorentzianb absorption lines.

0.01 IL

0.5 2.8 5.0

W(eV)

10.0

Figure 3. D i s t o r t e d

photoabsorption3 cross section for

' 5.0 the molecularb system in Fig. 2 in

the presence of aAg grating film,whose parametersare described inthe text.

0.00.5 2.8 5.0

w(eV)

0

two Lorentzian absorption lines WM as shown in Fig. 2. Let this system be located

at d - 150 A from a supported grating film with e1 - 1.0, e3 - 3.6, t - 100 A and Q

- 1.5 x 10 3 A. From previous analyses,7,12 the peak due to cross-coupling intoLRSP is located at w - 1.1 eV, whereas that for the light-scattering spectrum is at

- 1.6 eV. Note that at this distance the coupled SRSP almost vanishes and does

not play a role in the photabsorption process. Hence for the system as shown in

Fig. 2, we expect that only the one with wm - 1.5 eV will be excited and the other

one will be suppressed due to the surface-induced damping. Indeed, these effectsare manifested in Fig. 3 where we show a plot of a(w), except that no enhancement

of the line at 1.5 eV is observed, due to the fact that the corrugation amplitude

used in this calculation ([o - 40 A) is not large enough. We have tried to

increase this to go beyond 100 A, where we do see enhancement, but then the resultgoes beyond the validity of our present perturbative approach. Nevertheless, the

present results d2 give very strong indications that such enhanced selective

photoabsorption may indeed be possible for deeper grating films, where a non-perturbative treatment must be used.

5. CONCLUSION

It is well known that due to its monochromaticity and tunability, the laser hasfound great applications in various selective photochemical processes.Nevertheless, to have the selective absorption enhanced, one requires a highly-intense laser source, which may then lead to multiphoton processes and henceweakens the selectivity in the photoprocess. In this present mechanism that we areproposing, however, we have made use of the fact that the induced decay rate andthe enhanced LRSP field have very different resonance structures, and henceexcitation of other levels may be SUporessed by the enhanced decay rates at theirnatural frequencies. Hence, we conclude that it is worth pursuing the problemfuther using a non-perturbative approach to allow large grating amplitudes for thefilm and to recalculate o(w) for such a system, so that a realistic enhancedselective photoabsorption may be exhibited.

6. ACKNOWLEDGMENTS

This research was supported by the Office of Naval Research, the NationalScience Foundation under Grant CHE-8620274 and the Air Force Office of ScientificResearch (AFSC), United States Air Force, under Contract F49620-86-C-0009. TheUnited States Government is authorized to reproduce and distribute reprints forgovernmental purposes notwithstanding any copyright notation hereon.

7. REFERENCES

1. M. Fleischmann, P. J. Handra and A. J. McQuillan, Chem. Phys. Lett. 26,163 (1974).

2. J. I. Gersten and A. Nitzan, Surf. Sci. 158, 165 (1985), and referencestherein.

3. P. T. Leung and T. F. George, J. Chem. Phys. 85, 4729 (1986).4. G. M. Goncher, C. A. Parsons and C. B. Harris, J. Phys. Chem. 88, 4200

(1984).5. R. A. Wolkow and M. Moskovits, J. Chem. Phys. 87, 5858 (1987).6. P. T. Leung and T. F. George, Phys. Rev. B 36, 4664 (1987).7. P. T. Leung, Y. S. Kim and T. F. George, Phys. Rev. B, submitted.8. R. R. Chance, A. Prock and R. Silbey, Adv. Chem. Phys. 37, 1 (1978).9. A. A. Maradudin and D. L. Mills, Phys. Rev. B 11, 1392 (1975); D. L.

Mills and A. A. Maradudin, Phys. Rev. B 12, 2943 ((

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