Table Of ContentSurfaceplasmonpolaritonmodesinasingle-crystalAunanoresonatorfabricatedusing
focused-ion-beammilling
E. J. R. Vesseur,∗ R. de Waele, and A. Polman
CenterforNanophotonics,FOMInstituteforAtomicandMolecularPhysics(AMOLF),Kruislaan407,1098SJAmsterdam,TheNetherlands
H. J. Lezec† and H. A. Atwater
ThomasJ.WatsonLaboratoriesofAppliedPhysics,CaliforniaInstituteofTechnology,MS128-95,Pasadena,California91125
F. J. Garc´ıa de Abajo
Instituto de O´ptica - CSIC, Serrano 121, 28006, Madrid, Spain
Weusefocused-ion-beammillingofasingle-crystalAusurfacetofabricatea590-nm-longlinearridgethat
actsasasurfaceplasmonnanoresonator.Cathodoluminescenceimagingspectroscopyisthenusedtoexciteand
8
imagesurfaceplasmonsontheridge. Principalcomponentanalysisrevealsdistinctplasmonicmodes, which
0
0 provesconfinementofsurface-plasmonoscillationstotheridge. Boundary-element-methodcalculationscon-
2 firmthatalinearridgeisabletosupporthighly-localizedsurface-plasmonmodes(modediameter<100nm).
Theresultsdemonstratethatfocused-ion-beammillingcanbeusedinrapidprototypingofnanoscalesingle-
n
crystalplasmoniccomponents.
a
J
8 Surface plasmon polaritons (SPPs) are electromagnetic
waves confined to a metal-dielectric interface. As shown
]
s in recent experiments, SPPs can be manipulated using
c waveguides1,2 and resonators3,4. Surface plasmon polari-
i
t tons hold promise for application in sensing, photovoltaics,
p
telecommunications, and opto-electronic circuit integration,
o
due to their ability to concentrate and guide electromagnetic
.
s
energyatthenanoscale.
c
i FabricationofcomponentsthatguideandconfineSPPsin-
s
y volves structuring of metals, typically using methods such
h aselectronbeamlithography, nano-imprintlithography, self-
p assemblyortemplatingtechniques. Thesemethodsofferhigh
[ spatialresolution,butrequirecomplexmulti-stepprocessing.
200 nm
Moreover, the metal films, most often obtained by thermal
1
v evaporation, typicallyhaveapolycrystallinestructure. Grain
7 boundariesandsurfaceroughnessinpolycrystallinefilmsare
6 knowntocauseundesiredscatteringofSPPs. FIG.1:Scanningelectronmicrographofa590-nm-longlinearridge
2
Asingle-stepmethodtostructuremetalsforplasmonicap- fabricated in a single-crystal Au substrate using focused-ion-beam
1
plications,thatisgainingwidespreadacceptance,isfocused- milling. The ridge is approximately 95 nm high and 80 nm wide.
.
1 ion-beam(FIB)milling5,6. InatypicalFIBsystem,Ga+ ions Theleftinsetshowstheridgefromadifferentangle.Theinsetonthe
0 rightshowsthelightemissionfromtheridgeat585nmwavelength
are extracted from a liquid-metal ion source, accelerated to
8 uponirradiationwitha30kVelectronbeam,asfunctionofelectron
30keV,andfocusedbyanelectrostaticlenssystemtoaspot
0 beamposition.Allscalebarsare200nm.
sizewithdiameterassmallas5to10nm.
:
v
InthisLetterweshowhowFIBmillingofasingle-crystal
i
X Au substrate can be used for highly-reproducible, maskless
fabrication of a smooth plasmonic resonator, with minimum Ga beam from an FEI Nova 600 dual-beam workstation was
r
a lateral dimensions of 50 nm, and surface roughness on the rasteredin40passesovera4×5µmarea,usinga1000pixel
scale of only a few nm. We use cathodoluminescence (CL) ×1250pixelgridusingavariabledwelltimeperpixel. Sub-
imagingspectroscopytogenerateSPPs7,8andimageresonant tractivemillingleftbehindalinearridge,approximately590-
modeswithinthemetalnanostructures. Thedatademonstrate nmlong,95-nmhighand80-nmwide. Fabricationofsucha
thatFIBisanidealtoolforfabricationofnanoscaleplasmonic ridgetakesroughlyoneminuteandisveryreproducible. Re-
components,inparticularwhensingle-crystalmetalsubstrates sultingridgeroughnessisontheorderofafewnm,whichis
are employed. Our conclusions are supported by boundary- approcimately 10 times smoother than what can be achieved
element-method(BEM)calculationsofthelocalfieldsatthe usingpolycrystallinemetalsubstrates.
metalnanostructures9,10. Figure 1 shows scanning-electron-microscope (SEM) im-
Nano-plasmonic device fabrication consisted of focused- agesoftheridge,takenatlargeazimuthalanglewithrespect
ion-beam milling a polished <111> single-crystal Au sub- to the normal. Views of the structure at two different po-
strate,grownusingtheCzochralskiprocess. A10pA,30keV laranglesarepresented,respectivelyalong(mainpanel),and
5
(a)
0.6 5
4
4
m) 0.4 )
µ u.
n ( 300 b. 3
positio 0.2 unts sity (ar 2 32
m 0.0 o n
(b) c e
ea D nt
b 0.6 C I 1
n C
o 1
r
ct 0.4 0
e 0
El 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.2 Position (μm)
)
u. 0.0 FIG.3:LineprofilesobtainedbyafitofthedatainFig.2(a)usingthe
b. 1.0 (c) 5 4 3 2 1 modelingfactor-analysismethodofFig.2. Eachconsecutiveprofile
r
a
( isshiftedby1intensityunitforclarity.Numberslabelingeachprofile
nsity 0.0 creosrorensapnotnmdotdoesreosfptehcetirviedgsepewcittrhaoonfeFaingd.2tw(co).anPtrionfioldees3oanntdhe4rsihdogwe,
e 400 500 600 700 800
nt respectively.
I Wavelength (nm)
FIG.2: (a)Cathodoluminescenceemissionfromasingle-crystalAu tegration over 3 pixels (total distance: 21 nm) in the lateral
ridge as function of electron beam position and wavelength, mea-
direction of the ridge; the ridge position is indicated at the
suredalongthemajoraxisoftheridge(seerightinsetofFig.1).The
right-hand side of the figure. The data clearly show that a
ridgepositionisindicatedbythebartotherightoftheplot.Abroad
broadspectrumisemittedwhentheelectronbeamdwellson
spectrumisemittedwhentheelectronbeamdwellsontheridgeends,
the ends of the ridge, while the emission from the center of
whilethesignalfromtheridgecenterismoresharplywavelengthde-
pendent. (b)Reconstructionofthedatafromafitusingamodeling the ridge is more sharply wavelength dependent. As we will
factor-analysismethodwithaLorentzianshapeimposedonfivein- show next, these features are related to resonant geometrical
dependentspectra,labeled1to5andplottedin(c). Thecalculated modesofthelinearridgenanoresonator.
datasetin(b)closelymatchestheexperimentaldatain(a) Aspreviouslyshown,11,12,13,14,spatialCLimagesareadi-
rect probe of resonant modes of plasmonic nanostructures.
The measured CL spectrum at any position is assumed to be
several degrees off (inset) the ridge axis. The images reveal alinearsuperpositionofmultipleprincipal-modespectra. We
rounded features at the top of the ridge and at the base. We extract the principal modes from the data in Fig. 2(a) using
attributethisroundingtoredepositionofAuduringmillingas a factor analysis method15,16: a two-dimensional data matrix
wellasthefinitediameteroftheionbeam(∼10nm).Thefea- D isdefined,withonespectralandonespatialdimension,
(x,λ)
turesvisibleinthemilledareaaroundtheridgeareattributed corresponding to the dimensions of Fig. 2, respectively, as a
to roughness that was initially present on the substrate, and product of two matrices D = R C , one having
(x,λ) (x,n) (n,λ)
enhancedunderionmilling. n spatial profiles as columns and the other having the corre-
CL measurements were done using a FEI XL30 SEM spondingnspectraasrows.Wefindthatfiveprincipalcompo-
equipped with a parabolic mirror that collects (with a solid nentsformagoodrepresentationofthedata,sothatmatrices
angleof1.4π sr)lightgeneratedwhentheelectronbeamim- RandC withn=5canbeusedtoconstructthefulldataset.
pingesonthesample.ThemirrordirectstheCLemissioninto We then impose on the mode spectra a Lorentzian shape,
a spectrometer that is equipped with a CCD array detector. parametrizedbyapeakwavelengthandacharacteristicwidth
Spectraldataarecorrectedforsystemresponse. Theelectron for every spectrum; an initial matrix C is composed of five
beam is scanned across the sample and for every position of spectra. The profile matrix R can then be computed by the
theelectronbeamaspectrumiscollected. pseudoinverse16 of C: R = DC+, for which a data set
TherightinsetofFig.1showsaCLimageoftheridge,ac- Dˆ = RC is then calculated. The parameters for the spec-
quiredatacenterwavelengthof585nmandaspectralband- tramatrixC arethenoptimizedusingaleast-squaresmethod
widthof10nm. Theemissionfromtheridgeisstronglyde- byminimizingthedifferencebetweentheoriginaldatasetD
pendent on position: clear maxima are observed at the ends andthegeneratedDˆ. Figure2(b)showstheobtainedDˆ. The
andcenteroftheridge. Figure2(a)showsspectrallinetraces resultisinexcellentagreementwiththedata,reproducingthe
(wavelengthrange: 350–850nm),alongthemajoraxisofthe spectralshapeandintensityatallpositionsontheridge. The
ridge (see dashed line in the inset of Fig. 1) obtained by in- resultingfivespectrafromCareplottedinFig.2(c).Thepeak
2
250 1 spatialfrequenciesk alongtheridge.
(cid:107)
|E|2 2.13 eV For example, at an energy of 2.13 eV (corresponding to a
free space wavelength of 582 nm, and peak 3 in Fig. 2(c)),
200
wefindanLDOSmaximumfork = 1.14ω/c. Thisissig-
(cid:107)
m) nificantlylargerthanthecorrespondingvaluek(cid:107) = 1.07ω/c
n 150 calculated for SPPs on a planar Au surface (using identical
(
on optical constants), consistent with strong mode confinement
siti 100 totheridge. Weinvestigatethelateralfielddistributionofthe
o
P ridgemodebycalculatingthenearfieldaroundtheridgeex-
citedwithadipoleplacedabovetheridge(alsoattheposition
50
of the cross in Fig. 4). By subtracting the dipole field, we
air
calculate the induced field in the plane normal to the major
0 Au axis.
0
-150 -100 -50 0 50 100 150 Figure 4 shows the calculated values of |E|2 around the
Position (nm) ridge. Indeed,thefigureshowsthattheintensityisverymuch
confinedtothetopoftheridge,withatypicallateralconfine-
FIG.4: Boundary-element-methodcalculationofthefieldintensity mentinxandydirectionwellbelow100nm. FromtheBEM
|E|2 nearaninfinitelylongbell-shapedAuridge. Thiscalculation, calculationtheplasmonpropagationlengthalonganinfinitely
performedataphotonenergy2.13eVandk = 1.14ω/c, shows longridgeis4µm(Q = 43). Thisimpliesthatthemeasured
(cid:107)
thatpropagatingsurfaceplasmonsatthisenergyarewellconfinedto valueQ=5.3,isduetothecombinedeffectofOhmiclosses
thetopoftheridgeanddonotcoupletotheplanar-surfaceplasmons, (possiblyenhancedbythepresenceofimplantedGafromthe
forwhichk(cid:107) =1.07ω/c. FIBprocess)andradiationlossesfromtheridgeends.
In summary, we have shown that using focused-ion-beam
milling, a smooth linear ridge that supports surface plasmon
wavelengthsinFig.2(c)rangefrom425–797nm. Thecavity
resonancescanbefabricatedonasingle-crystalAusubstrate.
Qfactor,obtainedfromthewidthofspectrum3isQ=5.3.
Spatially-resolved cathodoluminescence spectroscopy shows
Fig.3displaysthespatialprofilesofthefivespectraalong
that surface plasmons generated on this ridge are well con-
the ridge, as given by R. Spatial profiles for spectra 3 and 4
fined to the ridge and form distinct geometrical modes. The
arecharacteristicofresonantmodes,withoneandtwoantin-
dataareconfirmedbyboundary-element-methodcalculations
odesontheridge,respectively. Thespatialprofilesforspectra
oftheplasmonfielddistributionontheridge,whichshowthat
1 and 2, at longer wavelengths, show antinodes on the ridge
a propagating surface plasmon is confined to the top of the
ends. The spatial profile for spectrum 5 shows a relatively
ridge, with a mode diameter <100 nm. These results show
constant intensity along the ridge; it may be associated to a
thatFIBmillingofasingle-crystalnoblemetalsurfacecanbe
higherordermodeofwhichthespatialprofilecannotbere-
usedinrapidprototypingofnanoscalesurfaceplasmoncom-
solved,ortransitionradiation17 thatdoesnothavespatialde-
ponents.
pendence. Notethatspectra2and3,whichareclosetogether
spectrally,haveverydistinctspatialprofiles.
This analysis demonstrates the existence of geometrical
plasmonmodesalongthesingle-crystalAuridgethatarepref- Acknowledgments
erentiallyexcitedatantinodesinthemodalelectricfieldinten-
sity. Aboundary-element-method(BEM)wasusedtocalcu- This work is part of the research program ’Microscopy
lateplasmonmodesofageometrysimilartothatoftheexper- andmodificationofnanostructureswithfocusedelectronand
imental structure. Starting from a shape profile as input, the ionbeams’(MMN)ofthe’StichtingvoorFundamenteelOn-
electricfieldisexpressedintermsofchargeandcurrentdistri- derzoek der Materie’ (FOM), which is financially supported
bution on the ridge, which are calculated self-consistently to by the ’Nederlandse organisatie voor Wetenschappelijk On-
fulfillthefieldboundaryconditions. Wechooseabell-shaped derzoek’ (NWO). The MMN program is co-financed by FEI
linear ridge of infinite length characterized by two different Company. This work is also funded by NANONED, a nan-
radiiofcurvature, asshownbythegreycurveinFig.4. The otechnology program of the Dutch Ministry of Economic
shapeissimilartothatoftheridgeimagedinFig.1. Wefirst Affairs. Work at Caltech is financially supported by the
calculatedthephotoniclocaldensityofstates(LDOS)inthe Air Force Office of Scientific Research under MURI Grant
dielectric just above the top of the ridge (indicated in Fig. 4 FA9550-04-1-0434. FJGA wants to thank Prof. Polman and
by the black cross). This was done for a range of energies, hisgroupfortheirkindhospitalityandsupport,andacknowl-
separatingtheLDOSintocontributionsarisingfromdifferent edgesfundingfromtheEU(STRP-016881-SPANS).
∗ Electronicaddress:[email protected] NIST,Gaithersburg,MD,USA
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