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PHYSICAL REVIEW B 15 SEPTEMBER 1998-IVOLUME 58, NUMBER 11

Silver-filled carbon nanotubes used as spectroscopic enhancers

F. J. Garcı´a-VidalDepartamento de Fı´sica Teo´rica de la Materia Condensada, Facultad de Ciencias, Universidad Auto´noma de Madrid,

Madrid 28049, Spain

J. M. PitarkeMateria Kondentsatuaren Fisika Saila, Zientzi Fakultatea, Euskal Herriko Unibersitatea, 644 Posta kutxatila, 48080 Bilbo, Sp

J. B. PendryCondensed Matter Theory Group, The Blackett Laboratory, Imperial College, London SW7 2BZ, United Kingdom

~Received 11 February 1998!

We analyze from a theoretical point of view the optical properties of arrays of carbon nanotubes filled withsilver. Dependence of these properties on the different parameters involved is studied using a transfer matrixformalism able to work with tensorlike dielectric functions and including the full electromagnetic couplingbetween the nanotubes. We find that these structures exhibit very strong linear optical response and hencecould be used as spectroscopic enhancers or chemical sensors in the visible range. Very localized surfaceplasmons, created by the electromagnetic interaction between the capped silver cylinders, are responsible forthis enhancing ability. Enhancements of up to 106 in the Raman signal of molecules absorbed on these arrayscould be obtained.@S0163-1829~98!04032-6#

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The so-called coinage metals~Au, Ag, and Cu! exhibitvery strong linear and nonlinear optical response when tare structured on the nanometer scale. Their ability tohance optical fields has been widely used in the last tweyears to study spectra of several molecules, taking advanof the surface enhanced raman scattering~SERS! effect.1

This effect appears on suitably rough metal surfaces ofAg, or Cu and is connected with excitation of very localizsurface plasmons present in the vicinity of highly coupmetal features.2 However, controlled use of coinage metaas spectroscopic enhancers has proven to be very diffidue to the absence of well-defined, stable macroscopicterials made of them, and various approaches to preparaof ordered arrays of metal nanoparticles have been repoonly very recently.3 Basically, these techniques consistcapping the nanoparticles with organic molecules of differsizes in order to control the interparticle separation.

Carbon nanotube technology is another promising narea in materials science.4 Multishell nanotubes made ofnumber of concentric cylinders of planar graphite with diaeters ranging from 2 to 25 nm and lengths of up to sevemicrometers have now become available. One of the minteresting applications of these nanometer size tubelinked to their hollow character: carbon nanotubes couldused as nanoscale molds. Filled nanotubes can be sysized by capillary action5 or by using composite anodesthe arc discharge,6 resulting in formation of encapsulatecompounds or elongated nanostructures of different maals ~carbides, oxides, organic solvents, or even pure met!.Very recently it has been possible to fill carbon nanotuwith a coinage metal-like silver, using capillary forces.7 Onthe other hand, bulk alignment of nanotubes has beenreported using different techniques.8,9 In these ordered arraythe carbon nanotubes form very close-packed structures

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The aim of this paper is to propose a scenario that cobines both areas of materials science. We investigate thetical response of arrays of Ag-filled carbon nanotubes inder to see if the capacity of silver nanostructures to enhaoptical fields is retained when they are encapsulated incarbon nanotubes. If so, these well-defined structures chave important optical applications as, for example, specscopic enhancers or chemical sensors in the visible rang

Our model for an array of Ag-filled carbon nanotubesdisplayed in Fig. 1. The tubes are infinitely long in thezdirection and form a periodic structure in thex direction. Inaccordance with experimental evidence,7,9 the outer diameterof the nanotubes is chosen to bedout510 nm and the dis-tance between them,d, 10.3 nm~close-packed structure!. Ithas been reported that only tubes with inner diameters onm or more can be filled with silver using capillary forceand the distribution of inner diameters is broad varying fro4 to 9 nm.7 Bearing this in mind, the diameter of the enca

FIG. 1. Our model of an array of Ag-filled carbon nanotubethe cylinders of outer diameterdout510 nm are infinitely long in thez direction and are distributed periodically in thex direction with aseparation ofd510.3 nm. The inner core filled with silver will bevaried between 3 and 9.5 nm in our calculations. We studyelectromagnetic interaction of this structure with a normally indentp-polarized plane wave of momentumk and energyv.

6783 © 1998 The American Physical Society

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sulated silver tubules,din , will be varied in our calculationsbetween 3 and 9.5 nm, in order to study the dependencthe optical response of these arrays on the diameter ofinner core. Since the outer diameter of the tubes anddistance between them are fixed, varyingdin changes theseparation between metal nanoparticles.

We consider an electromagneticp-polarized plane waveof frequencyv and momentumk normally incident on thestructure, and we analyze its interaction with an arraycarbon nanotubes. For this polarization, the incidentE fieldis perpendicular to the axis of the tubes and surface plasmof the nanotubes can be excited. In particular, we calcuthe optical reflectance,R(k,v), of these structures and thpossible enhancement of the electric field at various ptions on the surface. For both quantities we first needcompute the reflection matrices,R̂(k,k8;v), defining scatter-ing of the incoming wave into outgoing waves of momenk8. When dealing with materials whose dielectric respondisperses strongly with frequency, such as graphite andver, on-shell methods like the one developed in our grou10

are ideally suited to calculate these matrices. First we fivand hencee~v! can be specified. By approximating the cotinuous fields by their values at a series of discrete pointscan construct the EM transfer matrix of our system. Ttransfer matrix, relating EM fields at one side of the structto those on the other side in they direction, allows us tocalculate transmission and reflection coefficients for ancoming plane wave.10 Once we have these matrices, theflectance of the surface can be easily calculated:

R~k,v!5(k8

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where the sum runs over only propagating outgoing wavIn order to calculate the electric field surrounding the c

bon nanotubes, we first construct the totalE field outside thesurface as a sum of the incident and reflected waves,

Etotal~r ,v!5eik–rEinc~k,v!1(k8

eik8•rR̂~k,k8;v!E~k8,v!,

~2!

whereEinc(k,v) is the electric field associated with an incoming plane wave andE(k8,v) is the electric field associated with the outgoing plane wavek8. In this case the sumruns over both propagating and evanescent waves. Theintegrate the EM fields in real space through the systemobtain a detailed picture of the electric field.

As we said above, multishell nanotubes are made of seral concentric cylinders of planar graphite. Graphitehighly anisotropic and it is necessary to distinguish two dferent components,e i(v) and e'(v), in its dielectric func-tion for the directions parallel and normal to the axis, resptively. When transferring these dielectric functionscylindrical geometry, for every point (x,y) inside the nano-tube and outside the inner core we can write down a lodielectric tensor,11,12

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wherer 5Ax21y2. For a point inside the inner core the locdielectric tensor is diagonal and equal to the dielectric fution of silver, eAg(v). For the calculations we show in thipaper we have used the dielectric functions of graph@e i(v) ande'(v)] and silver@eAg(v)#, as tabulated in Ref13.

Very recently, an extension of the transfer matrix formism described above has been developed,14 which is able tosolve Maxwell equations with tensorlike dielectric functiolike the one present in Eq.~3!. This method has been appliewith success12 to explain the reported optical data of alignecarbon nanotube films.9 Within this on-shell formalism it ispossible to compute the reflection matrices needed to calate the optical reflectance and the electric fields in rspace.

The linear optical response of silver and other coinametals is dominated by the surface plasmon resonance,vsp.For a nanometric particle,vsp depends on the plasma frequency of the metal, the dielectric surroundings and the pticular geometry of the nanostructure. For anisolatedmetalcylinder in vacuum, the location ofvsp is determined by theequatione~v!1150 and the surface plasmon has a dipocharacter. For the case of a silver cylindervsp53.6 eV.When nanoparticles are brought into close contact, elecmagnetic coupling between them provokes a shift ofvsp tolower energies and the dipolar surface plasmon convertsa localized one, trapped in the region betweennanostructures.2 An incident plane wave of appropriate frequency can excite this surface plasmon, creating a hugEfield at this location and leading to large reductions in optireflectance at this frequency.

In Fig. 2 we show the optical reflectance for frequencranging from 1 to 4 eV, calculated for an array of clos

FIG. 2. Calculated optical reflectance of the structure shownFig. 1 for a normally incident photon of frequency ranging fromto 4 eV, and different values of the inner core filled with silver,din .

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FIG. 3. A detailed picture of the totalE field gener-ated by a normally incident plane wave impinging othe array of Ag-filled carbon nanotubes of Fig. 1 widin58 nm. TheE field is evaluated atv52.5 eV, thefrequency at which the optical reflectance is minimufor this case. The totalE field is shown for two unitcells of the array.

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packed carbon nanotubes filled with silver~see Fig. 1!. Thediameter of the inner core,din , is varied between 3 and 9.nm. As shown in the figure, fordin>5 nm there is a dip inthe frequency dependence of the optical reflectance. Thisclear signal that for these values ofdin , the incident photonis exciting surface plasmons associated with the silver cyders filling the nanotubes. Plasmons of carbon are locatehigher energies, 5.2 and 6.2 eV, and cannot be excitethese frequencies.12 Moreover, the shift to lower energies ovsp as din is increased indicates that encapsulated silnanostructures are electromagnetically coupled, their carshells serving as the medium for this interaction. We nthat the silver surface plasmon is absent whendin is less than4 nm, just the minimum value ofdin at which a carbonnanotube can be filled with silver using capillary force7

Another interesting conclusion that can be drawn from loing at this figure is that the shift to lower energies ofvsp isaccompanied by a narrowing of the plasmon linewidth.narrow linewidth indicates that radiative coupling to tvacuum of the plasmon is weak, and therefore a hugehancement of the optical fields is expected for the largvalues ofdin .

It can be shown that for small values ofdin ~5 or 6 nm! thedip in the frequency dependence of the optical reflectancassociated with excitation of a dipolar surface plasmon, silar to the one present inisolatedsilver cylinders. However,as the distance between the silver cylinders is reduced,surface plasmon excited becomes more localized. In Figwe show a detailed picture of theE field generated by theincident photon fordin58 nm. We have evaluated the fieldat v52.5 eV, the frequency of minimum reflectance for thcase~see Fig. 2!. Clearly the incident radiation is excitingvery localized surface plasmon and the intensity of theEfield is strongly enhanced with respect to the incident oThe electric field within the carbon shell is also large becaat this range of frequencies carbon behaves effectivelylossy dielectric. It is also worth mentioning that the induccharge~just the divergence of theE field shown in Fig. 3! islocated not only on the surface of the silver cylinders balso within the carbon shell. This is due to the tensorlcharacter of the optical response of graphite that allowsfulfill the condition ¹•( «̂E)50 with ¹•E different fromzero not only at the interfaces but also inside the nanotu

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This bulk induced charge reinforces the intensity of theEfield created by excitation of the silver surface plasmon.

These results demonstrate that the ability to enhancetical fields, inherent to silver nanostructures, is still preswhen they are encapsulated inside carbon nanotubes. Hever, as the surface plasmon strength depends on the deter of the silver inner core, this capability is expected tovery sensitive to this diameter. In order to evaluate thishancing property quantitatively, and investigate the possiity of using these surfaces as SERS active substrateshave calculated the local enhancement of the Raman siof a molecule absorbed in the region between the nanotuTo a first approximation, this Raman signal depends onfourth power of the total electric field at the molecule potion @E(rm ,v)#, and hence its enhancement due to the prence of the surface is simply

r~rm ,v!5UE~rm ,v!

Einc~v!U4

, ~4!

where rm represents the location of the molecule, aEinc(v) is the electric field associated with the incident plawave.

In Fig. 4 this enhancement is shown, as a function ofincoming photon energy and for different values ofdin ,ranging from 5 to 9.5 nm. As expected from dependencethe excited surface plasmon linewidth ondin , enhancementgrows rapidly from 104 for din55 nm to 106 for din59.5 nm.As din is increased, the induced charge is becoming mlocalized and, therefore, theE field in the region between thenanotubes is larger. This behavior had previously been fowhen studying the optical response of silver nanoparticdeposited on a silver surface.2 For comparison, we showin the same figure the expected enhancement of the Rasignal for an array of bare silver cylinders with diameters9.5 nm, their axis being separated by a distance of 10.3Due to the lossy characteristics of carbon at this rangefrequencies, encapsulated silver nanostructures havweaker enhancing capacity with respect to the bare onesthe other hand, in the case of encapsulated tubes the dedence of the enhancement on the energy of the incomphoton has a less pronounced resonant behavior, anvalue is large and practically constant at all frequenc

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within the visible range. This distinctive property of Agfilled carbon nanotubes might be expected to be usefupractical applications.

In conclusion, we have investigated the optical respo

FIG. 4. The local enhancement of the Raman signal evaluatethe region between the nanotubes, for different values ofdin and asa function of the energy of the incoming photon. The same quanas evaluated for bare Ag cylinders of diameter 9.5 nm and separby 10.3 nm, is also shown.

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of carbon nanotubes filled with silver. We have shown howsilver nanostructure’s ability to enhance optical fields istained when it is encapsulated inside these tubes. Forlargest values of inner core radius, the enhancement of thEfield intensity can be as large as 103. The experimental vi-ability of building up ordered structures made of these silvfilled carbon tubes could open the possibility of using thesystems as spectroscopic enhancers in the visible rangeoptical properties of these structures could be tuned by ving the diameter of the inner core, carbon shells playingrole of molds that avoid aggregation between the metal naparticles and fix their mutual separation. Standard SERactive surfaces are well known to be difficult to use incontrolled way, and encapsulated nanostructures canvide, therefore, a novel technique for the preparation of wdefined SERS-active substrates. Moreover, the capabilitthese systems to enhance optical fields can be used notfor spectroscopic purposes: if we shine a laser beam ofpropriate frequency into a solution of Ag-filled carbon nantubes, van der Waals attraction between the tubes cangreatly photoenhanced and binding into 3D structures of Afilled carbon nanotubes can be facilitated.

One of us~J.M.P.! acknowledges financial support by thBasque Hezkuntza, Unibertsitate eta Ikerketa Saila, andSpanish Ministerio de Educacio´n y Cultura.

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