Surface plasmon polariton modes in a single-crystal Au nanoresonator fabricated using focused-ion-beam milling
E. J. R. Vesseur, R. de Waele, A. Polman, H. J. Lezec, H. A. Atwater, F. J. García de Abajo
SSurface plasmon polariton modes in a single-crystal Au nanoresonator fabricated usingfocused-ion-beam milling
E. J. R. Vesseur, ∗ R. de Waele, and A. Polman
Center for Nanophotonics, FOM Institute for Atomic and Molecular Physics (AMOLF), Kruislaan 407, 1098 SJ Amsterdam, The Netherlands
H. J. Lezec † and H. A. Atwater Thomas J. Watson Laboratories of Applied Physics, California Institute of Technology, MS 128-95, Pasadena, California 91125
F. J. Garc´ıa de Abajo
Instituto de ´Optica - CSIC, Serrano 121, 28006, Madrid, Spain
We use focused-ion-beam milling of a single-crystal Au surface to fabricate a 590-nm-long linear ridge thatacts as a surface plasmon nanoresonator. Cathodoluminescence imaging spectroscopy is then used to excite andimage surface plasmons on the ridge. Principal component analysis reveals distinct plasmonic modes, whichproves confinement of surface-plasmon oscillations to the ridge. Boundary-element-method calculations con-firm that a linear ridge is able to support highly-localized surface-plasmon modes (mode diameter < nm).The results demonstrate that focused-ion-beam milling can be used in rapid prototyping of nanoscale single-crystal plasmonic components. Surface plasmon polaritons (SPPs) are electromagneticwaves confined to a metal-dielectric interface. As shownin recent experiments, SPPs can be manipulated usingwaveguides and resonators . Surface plasmon polari-tons hold promise for application in sensing, photovoltaics,telecommunications, and opto-electronic circuit integration,due to their ability to concentrate and guide electromagneticenergy at the nanoscale.Fabrication of components that guide and confine SPPs in-volves structuring of metals, typically using methods suchas electron beam lithography, nano-imprint lithography, self-assembly or templating techniques. These methods offer highspatial resolution, but require complex multi-step processing.Moreover, the metal films, most often obtained by thermalevaporation, typically have a polycrystalline structure. Grainboundaries and surface roughness in polycrystalline films areknown to cause undesired scattering of SPPs.A single-step method to structure metals for plasmonic ap-plications, that is gaining widespread acceptance, is focused-ion-beam (FIB) milling . In a typical FIB system, Ga + ionsare extracted from a liquid-metal ion source, accelerated to30 keV, and focused by an electrostatic lens system to a spotsize with diameter as small as 5 to 10 nm.In this Letter we show how FIB milling of a single-crystalAu substrate can be used for highly-reproducible, masklessfabrication of a smooth plasmonic resonator, with minimumlateral dimensions of 50 nm, and surface roughness on thescale of only a few nm. We use cathodoluminescence (CL)imaging spectroscopy to generate SPPs and image resonantmodes within the metal nanostructures. The data demonstratethat FIB is an ideal tool for fabrication of nanoscale plasmoniccomponents, in particular when single-crystal metal substratesare employed. Our conclusions are supported by boundary-element-method (BEM) calculations of the local fields at themetal nanostructures .Nano-plasmonic device fabrication consisted of focused-ion-beam milling a polished < > single-crystal Au sub-strate, grown using the Czochralski process. A 10 pA, 30 keV
200 nm
FIG. 1: Scanning electron micrograph of a 590-nm-long linear ridgefabricated in a single-crystal Au substrate using focused-ion-beammilling. The ridge is approximately 95 nm high and 80 nm wide.The left inset shows the ridge from a different angle. The inset on theright shows the light emission from the ridge at 585 nm wavelengthupon irradiation with a 30 kV electron beam, as function of electronbeam position. All scale bars are 200 nm.
Ga beam from an FEI Nova 600 dual-beam workstation wasrastered in 40 passes over a 4 × µ m area, using a 1000 pixel × a r X i v : . [ phy s i c s . op ti c s ] J a n l e c t r on bea m po s i t i on ( µ m ) CCD c oun t s
400 500 600 700 8000.01.0 I n t en s i t y ( a r b . u . ) Wavelength (nm)0.00.20.40.6 (a)(b)(c) 5 4 3 2 1
FIG. 2: (a) Cathodoluminescence emission from a single-crystal Auridge as function of electron beam position and wavelength, mea-sured along the major axis of the ridge (see right inset of Fig. 1). Theridge position is indicated by the bar to the right of the plot. A broadspectrum is emitted when the electron beam dwells on the ridge ends,while the signal from the ridge center is more sharply wavelength de-pendent. (b) Reconstruction of the data from a fit using a modelingfactor-analysis method with a Lorentzian shape imposed on five in-dependent spectra, labeled 1 to 5 and plotted in (c). The calculateddata set in (b) closely matches the experimental data in (a) several degrees off (inset) the ridge axis. The images revealrounded features at the top of the ridge and at the base. Weattribute this rounding to redeposition of Au during milling aswell as the finite diameter of the ion beam ( ∼
10 nm). The fea-tures visible in the milled area around the ridge are attributedto roughness that was initially present on the substrate, andenhanced under ion milling.CL measurements were done using a FEI XL30 SEMequipped with a parabolic mirror that collects (with a solidangle of 1.4 π sr) light generated when the electron beam im-pinges on the sample. The mirror directs the CL emission intoa spectrometer that is equipped with a CCD array detector.Spectral data are corrected for system response. The electronbeam is scanned across the sample and for every position ofthe electron beam a spectrum is collected.The right inset of Fig. 1 shows a CL image of the ridge, ac-quired at a center wavelength of 585 nm and a spectral band-width of 10 nm. The emission from the ridge is strongly de-pendent on position: clear maxima are observed at the endsand center of the ridge. Figure 2(a) shows spectral line traces(wavelength range: 350–850 nm), along the major axis of theridge (see dashed line in the inset of Fig. 1) obtained by in- I n t en s i t y ( a r b . u . ) Position (μm)54321
FIG. 3: Line profiles obtained by a fit of the data in Fig. 2(a) using themodeling factor-analysis method of Fig. 2. Each consecutive profileis shifted by 1 intensity unit for clarity. Numbers labeling each profilecorrespond to respective spectra of Fig. 2(c). Profile 3 and 4 showresonant modes of the ridge with one and two antinodes on the ridge,respectively. tegration over 3 pixels (total distance: 21 nm) in the lateraldirection of the ridge; the ridge position is indicated at theright-hand side of the figure. The data clearly show that abroad spectrum is emitted when the electron beam dwells onthe ends of the ridge, while the emission from the center ofthe ridge is more sharply wavelength dependent. As we willshow next, these features are related to resonant geometricalmodes of the linear ridge nanoresonator.As previously shown, , spatial CL images are a di-rect probe of resonant modes of plasmonic nanostructures.The measured CL spectrum at any position is assumed to bea linear superposition of multiple principal-mode spectra. Weextract the principal modes from the data in Fig. 2(a) usinga factor analysis method : a two-dimensional data matrix D ( x,λ ) is defined, with one spectral and one spatial dimension,corresponding to the dimensions of Fig. 2, respectively, as aproduct of two matrices D ( x,λ ) = R ( x,n ) C ( n,λ ) , one having n spatial profiles as columns and the other having the corre-sponding n spectra as rows. We find that five principal compo-nents form a good representation of the data, so that matrices R and C with n = 5 can be used to construct the full data set.We then impose on the mode spectra a Lorentzian shape,parametrized by a peak wavelength and a characteristic widthfor every spectrum; an initial matrix C is composed of fivespectra. The profile matrix R can then be computed by thepseudoinverse of C : R = DC + , for which a data set ˆ D = RC is then calculated. The parameters for the spec-tra matrix C are then optimized using a least-squares methodby minimizing the difference between the original data set D and the generated ˆ D . Figure 2(b) shows the obtained ˆ D . Theresult is in excellent agreement with the data, reproducing thespectral shape and intensity at all positions on the ridge. Theresulting five spectra from C are plotted in Fig. 2(c). The peak2 P o s i t i on ( n m ) FIG. 4: Boundary-element-method calculation of the field intensity | E | near an infinitely long bell-shaped Au ridge. This calculation,performed at a photon energy 2.13 eV and k (cid:107) = 1 . ω/c , showsthat propagating surface plasmons at this energy are well confined tothe top of the ridge and do not couple to the planar-surface plasmons,for which k (cid:107) = 1 . ω/c . wavelengths in Fig. 2(c) range from 425–797 nm. The cavity Q factor, obtained from the width of spectrum 3 is Q = 5 . .Fig. 3 displays the spatial profiles of the five spectra alongthe ridge, as given by R . Spatial profiles for spectra 3 and 4are characteristic of resonant modes, with one and two antin-odes on the ridge, respectively. The spatial profiles for spectra1 and 2, at longer wavelengths, show antinodes on the ridgeends. The spatial profile for spectrum 5 shows a relativelyconstant intensity along the ridge; it may be associated to ahigher order mode of which the spatial profile can not be re-solved, or transition radiation that does not have spatial de-pendence. Note that spectra 2 and 3, which are close togetherspectrally, have very distinct spatial profiles.This analysis demonstrates the existence of geometricalplasmon modes along the single-crystal Au ridge that are pref-erentially excited at antinodes in the modal electric field inten-sity. A boundary-element-method (BEM) was used to calcu-late plasmon modes of a geometry similar to that of the exper-imental structure. Starting from a shape profile as input, theelectric field is expressed in terms of charge and current distri-bution on the ridge, which are calculated self-consistently tofulfill the field boundary conditions. We choose a bell-shapedlinear ridge of infinite length characterized by two differentradii of curvature, as shown by the grey curve in Fig. 4. Theshape is similar to that of the ridge imaged in Fig. 1. We firstcalculated the photonic local density of states (LDOS) in thedielectric just above the top of the ridge (indicated in Fig. 4by the black cross). This was done for a range of energies,separating the LDOS into contributions arising from different spatial frequencies k (cid:107) along the ridge.For example, at an energy of 2.13 eV (corresponding to afree space wavelength of 582 nm, and peak 3 in Fig. 2(c)),we find an LDOS maximum for k (cid:107) = 1 . ω/c . This is sig-nificantly larger than the corresponding value k (cid:107) = 1 . ω/c calculated for SPPs on a planar Au surface (using identicaloptical constants), consistent with strong mode confinementto the ridge. We investigate the lateral field distribution of theridge mode by calculating the near field around the ridge ex-cited with a dipole placed above the ridge (also at the positionof the cross in Fig. 4). By subtracting the dipole field, wecalculate the induced field in the plane normal to the majoraxis.Figure 4 shows the calculated values of | E | around theridge. Indeed, the figure shows that the intensity is very muchconfined to the top of the ridge, with a typical lateral confine-ment in x and y direction well below 100 nm. From the BEMcalculation the plasmon propagation length along an infinitelylong ridge is 4 µ m ( Q = 43 ). This implies that the measuredvalue Q = 5 . , is due to the combined effect of Ohmic losses(possibly enhanced by the presence of implanted Ga from theFIB process) and radiation losses from the ridge ends.In summary, we have shown that using focused-ion-beammilling, a smooth linear ridge that supports surface plasmonresonances can be fabricated on a single-crystal Au substrate.Spatially-resolved cathodoluminescence spectroscopy showsthat surface plasmons generated on this ridge are well con-fined to the ridge and form distinct geometrical modes. Thedata are confirmed by boundary-element-method calculationsof the plasmon field distribution on the ridge, which show thata propagating surface plasmon is confined to the top of theridge, with a mode diameter <
100 nm. These results showthat FIB milling of a single-crystal noble metal surface can beused in rapid prototyping of nanoscale surface plasmon com-ponents.
Acknowledgments
This work is part of the research program ’Microscopyand modification of nanostructures with focused electron andion beams’ (MMN) of the ’Stichting voor Fundamenteel On-derzoek der Materie’ (FOM), which is financially supportedby the ’Nederlandse organisatie voor Wetenschappelijk On-derzoek’ (NWO). The MMN program is co-financed by FEICompany. This work is also funded by NANONED, a nan-otechnology program of the Dutch Ministry of EconomicAffairs. Work at Caltech is financially supported by theAir Force Office of Scientific Research under MURI GrantFA9550-04-1-0434. FJGA wants to thank Prof. Polman andhis group for their kind hospitality and support, and acknowl-edges funding from the EU (STRP-016881-SPANS). ∗ Electronic address: [email protected] † present address: Center for Nanoscale Science and Technology, NIST, Gaithersburg, MD, USA J. Krenn and J.-C. Weeber, Phil. Trans. R. Soc. Lond. A. , 739 W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature , 824(2003). H. T. Miyazaki and Y. Kurokawa, Phys. Rev. Lett. , 097401(2006). H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers,F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. ,257403 (2005). H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, Science , 820(2002). C. A. Volkert and A. M. Minor, MRS Bull. , 389 (2007). R. H. Ritchie, Phys. Rev. , 874 (1957). F. J. Garc´ıa de Abajo, unpublished (2007). F. J. Garc´ıa de Abajo and A. Howie, Phys. Rev. Lett. , 5180(1998). F. J. Garc´ıa de Abajo, Phys. Rev. B , 3095 (1999). N. Yamamoto, K. Araya, and F. J. Garc´ıa de Abajo, Phys. Rev. B , 205419 (2001). N. Yamamoto, M. Nakano, and T. Suzuki, Surf. Interface Anal. , 1725 (2006). E. J. R. Vesseur, R. de Waele, M. Kuttge, and A. Polman, NanoLett. , 2843 (2007). C. E. Hofmann, E. J. R. Vesseur, L. A. Sweatlock, H. J. Lezec,F. J. Garc´ıa de Abajo, A. Polman, and H. A. Atwater, Nano Lett. (2007). M. Bosman, M. Watanabe, D. Alexander, and V. Keast, Ultrami-croscopy , 1024 (2006). E. R. Malinowski,
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