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Plasmon tuning and local field enhancement maximization of the nanocrescent

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2008 Nanotechnology 19 275201

(http://iopscience.iop.org/0957-4484/19/27/275201)

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IOP PUBLISHING NANOTECHNOLOGY

Nanotechnology 19 (2008) 275201 (6pp) doi:10.1088/0957-4484/19/27/275201

Plasmon tuning and local fieldenhancement maximization ofthe nanocrescentBenjamin M Ross and Luke P Lee

Applied Science and Technology Graduate Group, Biomolecular Nanotechnology Center,Berkeley Sensor and Actuator Center, Department of Bioengineering, University ofCalifornia-Berkeley, Berkeley, CA 94720, USA

E-mail: benross@berkeley.edu and lplee@berkeley.edu

Received 1 April 2008, in final form 1 May 2008Published 27 May 2008Online at stacks.iop.org/Nano/19/275201

AbstractWe present a systematic numerical study of plasmon resonance of the nanocrescent. We showthat by varying the nanocrescent geometry, the plasmon resonance peak can be tuned into thenear-infrared and local field enhancement can be increased significantly, with maximumenhancement of the electric field amplitude of approximately 100 for realistic geometricparameters. Because of its wide tunability, high local field enhancement, and geometry whichutilizes both sharp features and intra-particle coupling, the nanocrescent is a structure wellsuited for in vivo cellular imaging as well as in vitro diagnostic applications.

1. Introduction

The theory of surface plasmon resonance (SPR) in sphericalmetallic nanoparticles has been known for over 100 years,following Drude’s model of the motion of free conductionelectrons in a metal [1–3] and Mie’s solution of Maxwell’sequations for the scattering of metal and dielectric spheres [4].Recently, SPR in metal colloids has seen a resurgence ofinterest, owing in part to a host of promising applications,including surface enhanced Raman spectroscopy (SERS),enhanced fluorescent emission, and plasmonic resonanceenergy transfer (PRET) [5].

For in vivo biological applications, an ideal plasmonicstructure must exhibit plasmon resonance in the near-infrared(NIR) regime [6], and must be mobile, robust, non-toxic,manufacturable, and produce high local field enhancementwithin a single probe. While nanospheres or nanoshells maymeet all but the last requirement, the local field enhancementof these structures can be orders of magnitude lower than forstructures which utilize plasmon coupling.

Inter-particle plasmon coupling has shown to be signif-icant between structures such as spheres [7], cylinders [8],rods [9], triangles [10], and squares [11]. However, such struc-tures strongly rely on a several nanometer distance (nanogap)between two or more particles, which is difficult to control,especially when particles are not affixed to a substrate. High

local field enhancement in single particles has been achievedprimarily by means of sharp features, such as triangles [12]and bar- or rice-shaped structures [13].

The nanocrescent is a structure utilizing both plasmoncoupling and sharp features. The structure has been shown toproduce high local field enhancement as well as some plasmonresonance tunability, and a basic physical understanding ofplasmon resonance of the nanocrescent as well as fabricationmethods have been described previously [14–17]. However,several important questions remain: what is the extent of theplasmon resonance tunability of the nanocrescent, and howdoes geometry affect plasmon resonance? In addition, whatare the critical features necessary to obtain high local fieldenhancement? We elucidate these issues in this paper.

2. Model

The geometry of the nanocrescent, shown in figure 1, isdefined by four parameters: an outer radius ro; an inner radiusri; the center-to-center distance between the circles (cavityoffset) d; and the fillet radius of the sharp tips s. Twodistinct geometries bear the title nanocrescent: the geometryresulting from extruding figure 1(b) out of the page, and thegeometry resulting from revolving the same figure about thevertical axis. The ‘revolved’ nanocrescent shown in figure 1(a)was fabricated by depositing a thin gold layer on polymer

0957-4484/08/275201+06$30.00 © 2008 IOP Publishing Ltd Printed in the UK1

Nanotechnology 19 (2008) 275201 B M Ross and L P Lee

(a) (b)

Figure 1. (a) TEM image of a 3D nanocrescent (scale bar represents 100 nm) and (b) diagram of the nanocrescent illustratingkey geometric parameters.

nanospheres at certain angles, followed by dissolution of thepolymer, as described elsewhere [14].

We consider a 2D gold nanocrescent present in freespace (vacuum) with a transverse magnetic (TM) plane waveincident at an angle θ measured from the vertical axis. Weassume the relative permeability of gold μr = 1 and thecomplex permittivity ε to be a function of wavelength [18].A finite element model was developed using the commercialsoftware COMSOL to solve over the domain of interestthe time-harmonic Maxwell equations, which reduce to theHelmholtz equation [19]. The domain consisted of the 2Dnanocrescent, a region of free space (greater than half thefree-space wavelength) surrounding the nanocrescent, anda perfectly matched layer (PML) to eliminate nonphysicalreflections at the domain boundaries [20]. Scattering boundaryconditions were used to further eliminate nonphysical results.An adaptive mesh was used, and the mesh was refined untilthe maximum electric field converged. We selected the finiteelement method primarily because of the ability to adaptivelymesh, and because it has been shown to be advantageous overthe finite difference time domain (FDTD) method for complexgeometries [21].

We briefly note that we have observed the local fielddistribution for 3D (i.e. ‘revolved’) nanocrescents to be similarto that of nanocrescents in 2D, with the high local fieldenhancement extending around the sharp edge in 3D. We havefound that the 3D nanocrescent follows trends similar to thosediscussed in this paper; however, a rigorous parametric study of3D nanocrescents is not feasible at this time using this method,due to the intense computation required.

3. Results and discussion

Unless otherwise noted, we have chosen a nanocrescent withthe parameters ro = 70 nm, ri = 50 nm, d = 40 nm, s = 1 nm,and θ = 0◦. In all cases we compute the maximum electricfield enhancement, defined as the ratio of the maximum valueof the electric field amplitude | �E |max to the amplitude of theincident field | �Ei|. The maximum field enhancement occurs atthe tips of the nanocrescent in all cases we have studied.

We first consider varying the outer radius ro of thenanocrescent and incident free-space wavelength λ0, whilekeeping the other parameter ratios fixed. Thus, all geometricparameters can be linearly scaled, resulting in a change inthe overall size of the nanocrescent while keeping its relativegeometry fixed. In this way, we observe how the plasmon bandof the nanocrescent varies with the nanocrescent size as shownin figure 2. The resonance peak of the nanocrescent is red-shifted as the nanocrescent size increases, and the relationshipis roughly linear. The red-shift is also accompanied by abroadening of the peak, and is consistent with the size-effectobserved in gold nanoparticles [22], and is also consistentwith recent experimental studies [23, 24]. Physically, the peakresonance is characterized by resonant coupling of the sharptips, inner cavity edge, and outer edge.

Significant plasmon band tuning can also be seen byvarying the cavity offset d , keeping the other parametersconstant. As shown in figure 3, by decreasing d , the plasmonresonance peak can be brought well into the NIR regime.Varying d affects the tip-to-tip distance of the nanocrescent,and as d is reduced, dipole-like coupling increases between thetips (figure 3(b)). This result is consistent with experimentalresults showing in increased resonance for decreasing tip-to-tip distance [24, 25]. We also note that varying d has theeffect of changing the thickness of the nanocrescent shell,and tuning in this manner might be thought of as analogousto plasmon resonance tuning in metallic nanoshells [26, 27].Since high enhancement can be achieved for fairly large tip-to-tip distances (e.g. 50 nm in figure 3(b)) and enhancement doesnot increase significantly as the distance is reduced, we deducethat it is tuning the shape to allow resonant coupling betweenthe inner and outer edges, as well as the tips, that dominatesthis phenomenon.

Varying the inner radius ri has comparatively little affecton the plasmon band, as shown in figure 4. However,decreasing ri reduces the tip-to-tip distance, increasingcoupling between the tips, and affecting the field distribution(figure 4(b)). Physically, one would expect the optimumwavelength for the dipole-like resonance between the tips todepend on their distance; specifically, a red-shift is expected

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Nanotechnology 19 (2008) 275201 B M Ross and L P Lee

(b)

(c)

(a)

Figure 2. (a) Maximum local field enhancement as a function ofouter radius ro and incident free-space wavelength λ0, (b) fielddistribution for ro = 200 nm, λ0 = 785 nm, and (c) field distributionfor ro = 100 nm, λ0 = 785 nm (ri = 50ro/70, d = 40ro/70,s = ro/70, θ = 0◦).

as the distance is reduced, as can be observed in figure 4.We consider even closer tip-to-dip distances in the followingdiscussion.

In experimental practice, it is difficult to fabricate nm andsub-nm sharp features such as the tips of the nanocrescent.For this reason, we considered the effect of varying the filletradius of the sharp tips, s. As shown in figure 5, varyingthe fillet radius does not significantly affect the plasmon band;thus, we expect the plasmon resonance of the nanocrescent isfairly robust with respect to the tip sharpness. The maximumfield enhancement, however, can be increased significantly as

(a)

(b)

(c)

Figure 3. (a) Maximum local field enhancement as a function ofcavity offset d and incident free-space wavelength λ0, (b) fielddistribution for d = 21 nm, λ0 = 785 nm, and (c) field distributionfor d = 46 nm, λ0 = 785 nm (ro = 70 nm, ri = 50 nm, s = 1 nm,θ = 0◦).

s decreases, especially below 1 nm. We have observed thephenomenological relationship | �E |max/| �Ei| = a + b s−1/2,where a and b are constants which depend on the wavelengthand geometry. As can be seen in figures 5(b) and (c), thefield enhancement remains highly localized near the sharptips. While increasing the sharpness of the tips increasesthe ‘lighting rod’ effect, thus increasing enhancement inclose proximity to the tips, it has little affect on the dipole-like coupling between the tips or cavity. We note that themultiple nodes for resonant coupling of the sharp tip notedpreviously [16] vanish for the more physical tip radii chosenhere.

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Nanotechnology 19 (2008) 275201 B M Ross and L P Lee

(a)

(b)

(c)

Figure 4. (a) Maximum local field enhancement as a function ofinner radius ri and incident free-space wavelength λ0, (b) fielddistribution for ri = 31 nm, λ0 = 785 nm, and (c) field distributionfor ri = 55 nm, λ0 = 785 nm (ro = 70 nm, d = 40 nm, s = 1 nm,θ = 0◦).

Figure 6 shows the result of varying the angle of incidenceθ of the incoming plane wave. A splitting of the plasmonresonance peak is prominent when θ is between 90◦ and135◦, agreeing with earlier results [16]. It is clear fromfigures 6(b) and (c) that non-normal incidence induces asignificant asymmetry in the local field distribution, causedby the asymmetry of the nanocrescent itself. Such angledependence is expected from the dipole-like nature of thecoupling modes. For example, for θ = 90◦, the driving field isperpendicular to the dipole coupling of the tips, so one wouldexpect a reduced enhancement near this regime, as is indeedseen in figure 6.

(a)

(b)

(c)

Figure 5. (a) Maximum local field enhancement as a function of filletradius s and incident free-space wavelength λ0, (b) field distributionfor s = 0.2 nm, λ0 = 785 nm, and (c) field distribution for s = 3 nm,λ0 = 785 nm (ro = 70 nm, ri = 50 nm, d = 40 nm, θ = 0◦).

Finally, we adapted our model to allow consideration ofsmaller tip-to-tip distances of the nanocrescent as follows: wefixed ro = 70 nm, ri = 50 nm, and d = 15 nm, which producesa small circle completely inside of a larger circle. We thenmade a rectangular cut (and rounded the edges with a radius of2 nm) such that the tip-to-tip distance t can be precisely chosen.We then observed the effect of varying t , as shown in figure 7.As t becomes less than 10 nm, strong coupling occurs betweenthe tips and high local field enhancement occurs, concentratedin a small region near the tips. Interestingly, high local fieldenhancement can also be achieved in the NIR for larger t ,and a physically larger region of enhancement occurs near

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Nanotechnology 19 (2008) 275201 B M Ross and L P Lee

(a)

(b)

(c)

Figure 6. (a) Maximum local field enhancement as a function ofincident plane wave angle θ and incident free-space wavelength λ0,(b) field distribution for θ = 45◦, λ0 = 785 nm and (c) fielddistribution for θ = 135◦, λ0 = 785 nm (ro = 70 nm, ri = 50 nm,d = 40 nm, s = 1 nm).

the nanocrescent. This high local field enhancement for twodifferent geometries can be explained by the multiple modesof resonance of the nanocrescent [17]: for close tip-to-tipdistances, the lightning rod effect and tip-to-tip coupling resultin large field enhancement that is highly localized, while forlarger tip-to-tip separations, tip, cavity, and surface couplingresult in a physically broader region of field enhancement. Thisresult emphasizes that while decreasing the tip-to-tip distancecan increase enhancement for a wide range of wavelengths,resonance at a particular wavelength can be achieved by tuning

(c)

(b)

(a)

Figure 7. (a) Maximum local field enhancement as a function oftip-to-tip distance and incident free-space wavelength λ0, (b) fielddistribution for t = 5 nm, λ0 = 1000 nm and (c) field distribution fort = 70 nm, λ0 = 1000 nm (ro = 70 nm, ri = 50 nm, d = 15 nm,θ = 0◦).

the remaining geometric parameters, due to the multiple modesof plasmon resonance that can occur in the structure.

4. Conclusion

In summary, we have observed that plasmon resonance ofthe nanocrescent is highly tunable: by varying the overallnanocrescent size or by varying the position of the cavity,the plasmon resonance can be brought into the NIR regime.Local field enhancement can be maximized by decreasing

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Nanotechnology 19 (2008) 275201 B M Ross and L P Lee

the inner radius, and by increasing the sharpness of the tips,and maximum enhancement | �E |max/| �Ei| ≈ 100 for realisticgeometric parameters. Varying the angle of incidence cancause splitting of the plasmon resonance peak, and also inducesan asymmetry in the local field distribution. Finally, small tip-to-tip distances result in highly localized field enhancement fora broad range of wavelengths, but comparable enhancement fora specific wavelength can also be achieved by tuning the overallstructure such that multiple mode resonance occurs.

Acknowledgments

BMR acknowledges support under a NSF graduate researchfellowship. LPL also acknowledges the support of DARPAfor the fundamental study of SERS. We thank two anonymousreviewers for their comments which improved this paper.

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