Numerically investigating the enhanced Ramanscattering performance of individual

Ag nanowire tips

ChaoLing Du,1,* ChaoJun Du,2,3 YuMeng You,4 Yan Zhu,1

SongLin Jin,1 CongJun He,1 and DaNing Shi1

1College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, China2Department of Chemical and Biochemical Engineering, Nanyang Institute of Technology Nanyang 473004, China

3Department of Chemical Engineering and Environment, Beijing Institute of Technology, Beijing 100081, China4Department of Chemistry, Yale University, 225 Prospect Street, Connecticut 06520, USA

*Corresponding author: cldu@nuaa.edu.cn

Received 25 April 2011; revised 9 July 2011; accepted 12 July 2011;posted 14 July 2011 (Doc. ID 146488); published 23 August 2011

The enhanced Raman scattering (ERS) performance of individual Ag nanowire (NW) tips with the shapeof a bulb, a crown, a pencil, and a nanoparticle randomly decorated crown was numerically investigatedby the finite elementmethod. Their polarized surface ERS is revealed to be either anisotropic or isotropic,which is affected by the incident light wavelength and polarization and the shape of the tips. In ourresults, the pencil tip presents strong ERS effects with optimized ERS enhancement and lateral spatialresolution of about 0:3 × 109 and 1:3nm, respectively. Effects of the pencil tip geometry (including theshape, angle, length, and size) on its tip ERS behavior are discussed as well. The present work alsoholds promise for individual Ag NW tip applications in microscope and spectroscope imaging andimprovement, etc. © 2011 Optical Society of AmericaOCIS codes: 240.6695, 300.6450, 260.3910.

1. Introduction

Individual Ag nanowires (NWs) have recently at-tracted growing interest in enhanced Raman scatter-ing (ERS), including surface ERS (SERS) and tipERS (TERS) [1–5], which are powerful techniqueswith the capability of even single molecule detection[6,7]. This is attributed to the large enhancement oftheir electrical near field, resulting from the reso-nant excitation of surface plasmons (SPs) and/orfrom lightning rod effects due to high curvatures andsharp edges.

The tips of individual Ag NWs have recently beenexperimentally reported as a good candidate forSERS substrates and TERS tips [3,5]. However,

experimental polarized SERS of individual Ag NWtips is reported to be either anisotropic or isotropic[1–3], which needs to be clarified. Meanwhile, it isalso noted that how to produce “hot” tips, i.e., thosethat are high performance and reproducible, is stillbothering TERS scientists [8], although different me-tallic tips have been fabricated by growing metallicNWs [5], etching metallic wires [8], coating a thinmetal layer on atomic force microscope tips [9], andother methods[10]. Numerical simulations, such asthe finite element method (FEM), make it easier toimplement and provide more feasible ways to opti-mize ERS experimental conditions (including thetip geometry, light polarization, etc.) to search for“hot” TERS tips and SERS substrates, compared toexperimental methods. Yet, earlier simulationsabout TERS in the literature focused on optimizingmetal coated dielectric tips [11] and metal SPM tips

0003-6935/11/254922-05$15.00/0© 2011 Optical Society of America

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[12–14]. Moreover, to the best of our knowledge,there were no simulation works on ERS that ad-dressed optimizing the parameters of metallic NWtips (such as the tip geometry and NW diameter) un-til now. Such work is significant to directly correlateERS performance with the detailed NW tip geome-tries and to reveal mechanisms of electromagnetic(EM) enhancement for ERS. It is also necessary tooptimize geometry parameters of the NW tips to im-prove their ERS performance and improve their ap-plication potential for sensing and detection.

In this paper, we have performed numerical simu-lations by FEM to investigate the near field opticalproperties of individual Ag NW tips with four typicalshapes. The aims of the present work are (i) to ex-plore the ERS performance of the NW tips, (ii) to ob-tain the polar behavior of the NW tips serving asSERS substrates, and (iii) to obtain the optimizedgeometric parameters of NW tips working as TERStips.

2. Simulation Structures, Results, and Discussion

Considering the Ag NW tips encountered in experi-ments [1–3], we chose four typical individual Ag NWtips with the shapes of a crown, a pencil, a bulb, and ananoparticle (NP) randomly decorated tip, respec-tively, for investigation as illustrated in Fig. 1(1).Their EM field properties were simulated usingthe three-dimensional harmonic propagation modelunder the radio frequency module built in the soft-ware of COMSOL Multiphysics. It is based onFEM and has been proved to be accurate and effi-cient [12–17]. It also has been widely employed tostudy the EM field properties of different nanostruc-tures [12–17]. Throughout the paper, Ag was mod-eled as lossy dielectric material using empirically

determined bulk dielectric values [18] with piecewisecubic interpolation, while the NWs were constructedas cylinders with one end capped by different shapedtips. Unless otherwise stated, the incident light wasset as a localized plane wave, for which the propagat-ing direction is perpendicular to the NW tips’ axis, tobetter mimic the localized excitation of samples inERS experiments under a backscattering configura-tion [2,3]. The excitation wavelength was chosen as532 and/or 514nm, which are two commonly usedwavelengths for Ag ERS in the visible light region.According to experiments [2,3], the excitation beamsize was taken to be 500nm.

In our simulations, the default element type of vec-tor quadratic was used. To avoid spurious reflectioneffects at the simulation zone boundaries, perfectlymatched layers (PML) had been applied, while at theinner side of PML, scattering boundary conditionswere adopted. Then, discretization of the simulationspace was conducted employing the built-in freemeshing algorithm in COMSOL, which partitionedthe simulation space into a collection of tetrahedralfinite elements. Large field enhancement, resultingfrom the lightning rod effect, required the applica-tion of mesh constraints to ensure convergence ofthe simulations. The surfaces of the tips were re-stricted to a maximum triangle mesh side lengthof 1:5nm with an element growth rate of 1.20, speci-fying that elements adjoining the tip surface could beno more than 1.2 times the size of surface elements.Typical NW tip meshes using the constraints listedhere resulted in 1 × 105 to 7 × 105 degrees of freedom.All the simulations herein were performed on a desk-top workstation using 64 bit eight-core processorsand 24GB of RAM. A single NW tip geometry re-quired several to tens of minutes using the GMRESsolver by setting the matrix symmetry as symmetric.We also refined the corresponding meshes to get sa-turated mesh densities until a further increase ineach would not affect the results.

In what follows, we will go into the details of inves-tigating the ERS performance of the four individualAg NW tips concerned.

Figures 1(21) and (22) show the electrical field (jEj)distributions around the four NW tips under two ty-pical incident light polarizations. For comparison,their NW diameter and tip length were adjusted tobe equal. Then we put the NW tip at the excitationbeam center. jEj was set to 1 for the incident light, sothe obtained jEj throughout the paper equals to jEjenhancement. As the dominant SERS enhancementmechanism is EM enhancement [1–3,19], larger loca-lized jEj (jElocj) will lead to larger SERS enhance-ment. Figure 1 shows that with the incident lightpolarized perpendicular to the NW long axis [θ ¼ 0∘,Fig. 1(21)(a) and (21)(b)], jElocj is much more en-hanced than that of parallel polarization [θ ¼ 90∘,Fig. 1(22)(a) and (22)(b)] for the bulb and crownNW tips. This predicts larger SERS enhancementat θ ¼ 0∘ than at θ ¼ 90∘ when the two tips serveas SERS substrates. Different from these two tips,

Fig. 1. (Color online) (1) Schematic geometries of the four individualAg NW tips and (21), (22) their electric field (jEj) distributions under532nmlight localizedexcitation. (1)(d) is thesideview(yzcrosssection)of the corresponding NW tip. (21) θ ¼ 0∘, (22) θ ¼ 90∘.

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larger SERS enhancement is expected at θ ¼ 90∘ forthe pencil NW tip as it achieves larger global jEjmaxat θ ¼ 90∘ than at θ ¼ 0∘. For the NP randomly deco-rated NW tip, its jEj distributions in Fig. 1 appearalmost polarization independent. The randomly dis-tributed NPs on the NW tip also account for the al-most isotropic SERS signals when the tip serves asan SERS substrate, which also explains the experi-mental results elsewhere [1]. Meanwhile, the com-parison among the four subfigures of Fig. 1(22)reveals that the shape of the NW tips significantlyaffects their jEj distributions: the sharper the tip,the higher jElocj enhancement around the tip apexat θ ¼ 90∘. This originates from their lightning rodeffect, which is sensitive to the tip geometry.Figures 1(21) and (22) also demonstrate that amongthe four NW tips concerned, the NP randomly deco-rated tip gets the maximum jElocj enhancement.Although the NP randomly decorated tip achievesmaximum SERS enhancement among the four tips,the poor reproducibility of the tip and its SERS en-hancement limits its future application. Hence, sucha tip will not be discussed in the following sections.The first three tips are noted to present strong jElocjenhancement, too, especially for the pencil NW tip,where a maximum enhancement of a factor of ∼10was obtained, originating from its sharp apex. More-over, such an enhancement can be improved by opti-mizing its geometry parameters, making it a goodcandidate for ERS, which will be discussed later.

To further explore the polarized SERS behavior ofthe bulb, crown, and pencil NW tips, we have simu-lated their jEj distributions at different θ. As pointedout in Ref. [20], SERS signals are proportional to thevalue of

R jEj4dS over the surface area of the corre-sponding SERS substrate. Then, their normalizedSERS signals (NSM) of

R jEj4dS=A were calculated,where A refers to the surface areas of the correspond-ing NW tips under localized excitations. Figure 2(1)demonstrates that the NSM from both the bulb andcrown NW tips follows a cos2 θ function, which agreeswell with the polarized SERS reports for individualAg crown NW tips [3]. It is also similar to the polar-ized SERS behavior for the body of individual AgNWs, which is attributed to the anisotropic excita-tion of its transverse SP mode and the enhancedjElocj. Meanwhile, the NSM from the pencil tip devi-ates from such a trend at 532nm. With incident lightshining on the three NW tips, the lightning rod effectof their tip leads to a higher jElocj, producing higherSERS enhancement at θ ¼ 90∘ than at θ ¼ 0∘, whichpredicts a totally different polarized SERS trendfrom that of the SP effect on their body part. Accord-ingly, considering only the lightning rod effect, thepolarization dependence of NSM should follow asin2 θ function, which is obviously different fromthe results shown in Fig. 2. However, it is clarifiedand understandable with a closer inspection of ourexcitation condition and the simulated jEj distribu-tions as mentioned in Fig. 1. First, besides the tipconcerned, part of the body of the NWwas also under

illumination due to the larger excitation beam sizethan the size of the tip. Second, Figs. 1(21) and (22)show that the maximum enhancement of jElocj doesnot always occur near the apex at θ ¼ 90∘ for thethree NW tips. Therefore, both the lightning rod ef-fect and the transverse SPs contribute to the ob-served jElocj enhancement and the different polarbehaviors in Fig. 2. In addition, Ag has a differentoptical constant at different wavelengths, which af-fects both their SP and lightning rod effects, andhence their jEj distributions. This accounts for theirobtained wavelength dependent NSM and polar be-haviors in Fig. 2. Figure 2(2) reveals that the NSMfrom the bulb NW tip can be fitted with a cos2 θ func-tion at 514nm, too, similar to its result at 532nm,indicating the dominant role played by the trans-verse SPs at these two excitation wavelengths. Com-paratively, the NSM from the pencil NW tip at514nm is demonstrated to follow a trend of sin2 θ, im-plying the dominant role played by its lightning rodeffect. Figure 2(2) also indicates that the calculatedNSM from the Ag crown NW tip at θ ¼ 0∘ and θ ¼ 90∘

gets almost the same intensity. It provides an expla-nation for the nearly same level SERS signals for asingle Ag crown NW tip at θ ¼ 0∘ and θ ¼ 90∘ under514nm localized light excitation [3].

In brief, SERS performance of individual Ag NWtips is sensitive to the shape of tip and the incidentlight polarization and wavelength, which can be elu-cidated well in terms of the jEj enhancement at dif-ferent wavelengths induced by the tip lightning rodeffect and the transverse SP mode of the NW body.Moreover, the aforementioned agreement betweenour results and available reported experiments [1–3]validates the corresponding simulation results.

Besides SERS applications, NW tips have also beenreported as TERS tips [3,5]. Therefore, it is necessaryfor us to study the TERS performance of the indivi-dual Ag NW tips. From their jEj distributions at dif-ferent θ and the aforementioned analysis, it isdemonstrated that among all the tips discussedpreviously, the Ag pencil NW tip (labeled as Tip1) pro-vides the best TERS tip candidate and achieves max-imum jElocj enhancement at θ ¼ 90∘. Accordingly, bykeeping θ ¼ 90∘, we will focus on optimizing the geo-metry parameters of the tip to improve its TERS per-formance, including TERS enhancement, i.e., jEj4max,which contributes to the signal enhancement, and the

Fig. 2. (Color online) Polar plot of the calculated NSM for the fourindividual AgNW tips with shapes of bulb (a), crown (b), and pencil(c) under (1) 532 and (2) 514nm localized light excitation.

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electrical field lateral confinement (C), which contri-butes to the spatial resolution. Here, jEjmax is themaximum jElocj achieved near the tip apex, while Crefers to the FWHM of the jEj4 enhancement on aplane z ¼ 0:5nm under the tip apex. The value of Caffects the TERS imaging resolution directly whenthe corresponding tipworksasaTERStip.The follow-ing discussions about the TERS enhancement of theAg pencil NW tip apply for its SERS enhancementas well.

In Fig. 3, we examine the effect of the tip curvaturerelated to the field enhancement and confinement,while the tip curvature is affected directly by theparameters of the tip angle and tip length. The insetof Fig. 3(1) schematically labels the different geome-try parameters of the pencil NW tip. We first variedthe tip angle φ while keeping D, L, and L0 fixed at100, 50, and 8nm, respectively, then simulated thecorresponding jEj distributions to obtain the func-tions of jEjmax and C versus φ. The results wereplotted as Fig. 3(1). They show that by decreasingthe angle φ, jEjmax decreases and C increases. Witha smaller φ, the transverse size of the tip apex D0 in-creases while the longitudinal size of the tip apex L0is fixed. This makes the tip apex blunt and leads to aless obvious lightning rod effect, which further de-creases jEjmax and loosens the field confinement bythe tip. Then, as φ decreases further, only severaltimes the jElocj enhancement near the apex is ob-tained, making jEjmax almost unchangeable, asshown in Fig. 3(1). Figure 3(1) also shows that thehighest jEjmax ∼ 100V=m along with C ∼ 1:8nm isachieved at φ ¼ 42∘ under 514nm localized light ex-citation. This is very promising for TERS imaging,for which higher jEjmax and smaller C are desired.Yet, at such an angle, the tip is noted to be more likean NP attached tip but not a pencil tip anymore,which is beyond the scope of the present work. How-ever, at φ ¼ 39∘, the tip kept a pencil shape well andachieved a high jEjmax enhancement of ∼12 and C of∼5nm, showing better TERS performance than thesmaller tip angles.

Then, the above tip with φ ¼ 39∘ (labeled as Tip2)was chosen as the starting point for our second stepof optimization. While keeping both the x- and y-direction scales unchanged, the longitudinal tip sizeLþ L0 was optimized. The obtained plots of jEjmaxand C versus Lþ L0 were shown in Fig. 3(2). The

lightning rod effect of the tip apex gets strengthenedwith Lþ L0 increasing and D0 being fixed, whichfurther makes the obtained jEjmax larger and the lat-eral field below the apex concentrate tighter. Hence,jEjmax and C are revealed to increase and decrease,respectively, as Lþ L0 increases. This implies thata larger Lþ L0 is expected to provide higher jEjmaxand smaller C for TERS. However, pencil tips witha large Lþ L0 are still difficult for the present fabri-cating techniques. According to Fig. 3(2), the highestjEjmax ∼ 90V=m along with C ∼ 2:3nm is achieved atLþ L0 ¼ 116nm (the corresponding tip is labeled asTip3), providing a high TERS enhancement of 6:6 ×107 and lateral spatial resolution of 2:3nm. In addi-tion, the small difference between the results of532nm and 514nm in Fig. 3 confirms that the light-ning rod effect can be perceived as a geometryeffect [13,21].

Third, by setting the scale size M of Tip3 to 1, wescaled M to finely optimize jEjmax and C further. Forconvenience, the incident light was set as a nonloca-lized plane wave. Figure 4 reveals that with Mincreasing, jEjmax shows fluctuation, while C is con-stantly increasing until M reaches 1.25. The furtherincrease of M will lead to the decay of C afterM > 1:5. These features are understandable basedon the analysis of Fig. 3. It has been demonstratedthat jEjmax decreases and C increases when D0 in-creases, and Lþ L0 is fixed. Meanwhile, Fig. 3 alsoreveals that jEjmax increases and C decreases whenL and L0 increase and D0 is unchanged. The wholetip size increases as M becomes larger, then bothD0 and L0 increase simultaneously, which contributesto the observed trend of jEjmax and C. According toFig. 4, the optimized TERS tip is achieved at M ¼0:5 with D0 and L0 being 8nm and 10nm, respec-tively. It provides an ERS enhancement up to0:3 × 109, high enough for many ERS detection, sen-sing, and spectroscopy applications. Meanwhile, abelow 10nm lateral spatial resolution of 1:3nm isachieved, which approximates to single-molecule re-solution and is comparable to previous reports [22].

Finally, it is noted that substrates supporting ERSsamples have not been taken into consideration inthe present work, which has the ability to increaseERS enhancement several orders more [13]. The

Fig. 3. (Color online) Functions of jEjmax and C versus (1) the tipangle φ and (2) the tip length Lþ L0 (solid and dashed lines for 532and 514nm light excitation, respectively). The inset of (1) schema-tically labels the different geometry parameters for the pencilNW tip.

Fig. 4. Functions of jEjmax and C versus the scale size M under532nm light excitation.

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optimization of such effect along with effects of thematerial and the wavelength, the angle, and polari-zation of the incident light is also important and de-serves to be investigated in our future work.

3. Conclusions

By FEM simulations, we have demonstrated that(i) the ERS performance of individual Ag NW tips de-pends on the tip geometry, and the wavelength andpolarization of the incident light, (ii) the polarizedSERS signals from the tips are isotropic or anisotro-pic, which can be elucidated well in terms of the tiplightning rod effect and the body SP effect, and(iii) the optimized pencil tip provides an ERS en-hancement as high as 0:3 × 109 and a lateral specialresolution of 1:3nm. It provides a spatial resolutionhigh enough for single-molecule and quantum dot in-vestigation in TERS. This originates from the stronglightning rod effect of the tip, which is sensitive to thetip geometry, including its shape, angle, length, andsize. Our predictions of ERS performance hereinopen up new methods for future designing and opti-mizing SERS/TERS experiments for their applica-tion in sensing and detection.

This work is financially supported by the NationalNatural Science Foundation of China (NSFC) (Nos.11004103 and 60808026), the Nanjing University ofAeronautics and Astronautics research funding(Nos.NS2010186andNS2010195), ChinaPostdoctor-al Science Foundation funded project (Nos.20100471332 and 20110491420), Natural ScienceFoundation of Jiangsu Province (No. BK2010499),and Jiangsu Planned Projects for PostdoctoralResearch Funds (Nos. 0902016C and 1001038C).

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