Electric field enhancement in bimetallic gold and silver nanoshells

Electric field enhancement in bimetallic gold and silver nanoshells

Solid State Communications 148 (2008) 163–167 Contents lists available at ScienceDirect Solid State Communications journal homepage: www.elsevier.co...

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Solid State Communications 148 (2008) 163–167

Contents lists available at ScienceDirect

Solid State Communications journal homepage: www.elsevier.com/locate/ssc

Electric field enhancement in bimetallic gold and silver nanoshells DaJian Wu a,b , XiaoDong Xu a , XiaoJun Liu a,∗ a

Department of Electronic Science and Engineering, Key Laboratory of Modern Acoustics of MOE, Nanjing University, Nanjing 210093, China

b

Faculty of Science, Jiangsu University, Zhenjiang 212013, China

article

info

Article history: Received 15 February 2008 Received in revised form 16 May 2008 Accepted 17 July 2008 by D.D. Sarma Available online 23 July 2008 PACS: 78.67.Bf 73.22.Lp 78.40.Kc

a b s t r a c t The electric field enhancements in Au/Ag and Ag/Au core/shell nanoparticles have been investigated by means of quasi-static theory. The maximum enhancements of outside fields for Au/Ag and Ag/Au nanoshells occur along the incident polarization at plasmon resonance wavelength. It is surprised that the largest field enhancement in the shell of Ag/Au nanoshell occurs along the polarization direction, while that for Au/Ag nanoshell is perpendicular to the incident polarization. At off-resonance wavelength 1000 nm, the general shape of the field pattern is similar to that in resonance case except for much weaker amplitude. Furthermore, for the seamless nanoshells, the maximum enhancements of the electric field increase by increasing the shell thickness. As the shell thickness is small, the hot spots play an important role in the enhancement of the local electric field. © 2008 Elsevier Ltd. All rights reserved.

Keywords: A. Nanostructures D. Optical properties

The optical properties of bimetallic nanoparticles have attracted extensive interest due to their potential applications in catalysis, electronics, and optics [1–4]. Au and Ag colloids have been widely used to fabricate the bimetallic nanoparticles due to their almost identical lattice constants and extraordinary absorption properties. The identical lattice constant leads to a strong tendency toward the Au/Ag alloy structures. Shi et al. [5] and Mallin et al. [6] synthesized the Au/Ag alloy nanoparticles and found that the optical absorption peak of nanoparticles shifts from ∼400 nm to ∼530 nm with increasing Au content. Recently, the bimetallic gold and silver nanoshell, a particularly interesting structure consisting of an Au (Ag) core coated with an Ag (Au) layer, has received much attention. [3,7–13] Such core–shell nanoparticles possess the monodispersity of Au with a large extinction coefficient of the surface plasmon band [3]. The optical properties of bimetallic gold and silver nanoshells are dominated by the surface plasmon resonance (SPR) defined as collective motions of the conduction electrons induced by an interacting electromagnetic field, and thus remarkably sensitive to the parameters such as core/shell radius ratio, chemical composition, dielectric environment and size [7,8]. These effects may lead to applications such as resonant photo-oxidation inhibitors [9], optical data storage [10], and surface-enhanced Raman spectroscopy (SERS) materials [11–13].



Corresponding author. Tel.: +86 25 83593617; fax: +86 25 83315557. E-mail address: [email protected] (X. Liu).

0038-1098/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2008.07.030

The far-field properties of bimetallic nanoshells have been well studied theoretically and experimentally [14–16]. Among them, Yang et al. [14] prepared Au–Ag and Ag–Au nanoshells and investigated the optical properties. The dependence of nonlinear optical response properties as a function of relative composition is investigated in the bimetallic core/shell structure nanoparticles [15]. Bruzzone et al. [7] have investigated the linear optical response properties in Au/Ag nanoshells with various compositions, and found that the SPR shows a red-shift with increasing Au content. Moskovits et al. [16] also reported an approach for extracting the optical constants of bimetallic Ag–Au nanoparticles in terms of surface-plasmon extinction spectra. On the other hand, the bimetallic gold and silver nanoshells can be well used as an effective SERS substrate. Kumar et al. [4] have synthesized Ag–Au nanoshells and performed the SERS experiments on one of the therapeutically important human transcriptional coactivator p300. Ji et al. [12] have applied the Au–Ag nanoshells in the gene analysis and antibody or antigen detection in vitro. The Ag–Au nanoshells with good biocompatibility have been used as the SERS enhancing substrate for immunoassay [13]. It is well known that an important contribution to the SERS enhancement comes from the electromagnetic enhancement mechanism, in which plasmon excitation in the particle creates an enhanced electric field near the particle and hence the enhanced Raman excitation and emission [17]. Meanwhile, the electric field inside the particle also increases by several orders of magnitude, which plays an important role for many nonlinear phenomena [18]. However, little work has been

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carried out to clarify the enhancements of near and internal electric fields for bimetallic gold and silver nanoshells, especially for the difference between Au/Ag and Ag/Au nanoshells [19,20]. In this paper, we have investigated the electric field enhancements in Au/Ag and Ag/Au core/shell nanoparticles. The imag*

inary of electric field enhancements | E |2 /|E0 |2 (E0 means the incident field strength) in Au/Ag and Ag/Au nanoshells are provided with quasi-static theory. The electric field enhancements in Au/Ag and Ag/Au nanoshells are calculated at the resonance and off-resonance wavelengths, respectively. Furthermore, we have investigated the influence of shell thickness on the electric field enhancements of Ag/Au and Au/Ag nanoshells. The composite model consists of a spherical core of radius r1 coated by a shell of thickness (r2 − r1 ). The dielectric functions of the core, shell, and embedding medium are ε1 , ε2 and ε3 , respectively. In the bimetallic gold and silver nanoshell, ε1 and ε2 have real and imaginary frequency-dependent components and should be affected by the scattering of the conduction electrons in the particle surface. Thus, ε1 and ε2 are usually accounted by replacing the ideal Drude part in the dielectric functions with a size dependent one, and can be expressed as [21]

ε1 (ω) = 1 − ε2 (ω) = 1 −

ωp2 ω2 + iωγ1 ω

2 p

ω + iωγ2 2

+ χ1 ∞ ,

(1)

+ χ2 ∞ ,

(2)

Fig. 1. The energy diagram illustrating the plasmon hybridization in a metallic nanoshell.

where the background susceptibilities χ1∞ and χ2∞ arise from the electron polarizability and interband transition. ωp is the bulk plasma frequency. The modified collision frequencies γ1 and γ2 can be expressed as [21]

γ1 = γf +

Vf

γ2 = γf +

Vf

a1 a2

,

(3)

,

(4)

where γf is the bulk collision frequency, Vf is the Fermi velocity, and the reduced electron mean free paths a1 = 2r1 and a2 = r2 − r1 [18,21]. In our analysis, the particle diameter is much smaller than the wavelength of the incident field. Thus, the incident field is timedependent, and does not vary spatially over the diameter of the nanoparticle. Then the particle is subjected to an almost uniform field. In this case, the optical properties of the nanoshells can be calculated based on the quasi-static functions [21], which are derived by solution of Laplace’s equation for the potential. The electric fields in the core, shell and embedding medium can be expressed as [21] 9ε2 ε3 E0 (cos θ rˆ − sin θ θˆ ), (5) ε2 εa + 2ε3 εb   r 3  * 3ε3 1 E0 (ε1 + 2ε2 ) + 2 (ε1 − ε2 ) × E2 = ε2 εa + 2ε3 εb r    r 3  1 × cos θ rˆ − (ε1 + 2ε2 ) − (ε1 − ε2 ) × E0 sin θ θˆ , (6) *

E1 =

r

ε2 εa − ε ε + 1 E0 cos θ rˆ ε  2 εa + 2ε ε 3 ε2 εa − ε3 εb r2 − 1 E0 sin θ θˆ , (7) + ε2 εa + 2ε3 εb r 3 where r and θ are the radial distance and the polar angle of the nanoshell, respectively, and εa = ε1 (3 − 2P ) + 2ε2 P, εb = ε1 P +  3 ε2 (3 − P ), P = 1 − rr21 . *

E3 =



2

3 3 b r2 3 3 b r



We now discuss the optical response of metal nanoparticles due to the plasmon resonance, which is defined as collective motions of the conduction electrons with the restoring force provided by the induced surface charges. The intrinsic feature of the SPR in a nanoshell can be described by the plasmon hybridization model [22–24]. Fig. 1 illustrates the plasmon hybridization in a metallic nanoshell. In this model [23], the higher energy mode ω+ corresponds to an antisymmetric coupling between the surface plasmon on the surface of a solid sphere with energy ωS and dipolar cavity plasmon on the inner surface with energy ωC . The antisymmetric mode ω+ gets its dominant contribution from the plasmon on the inner surface. On the other hand, the lower energy mode ω− corresponds to a symmetric coupling, which is dominated by the contribution from the plasmon resonance on the outer surface. The strength of the interaction between the sphere and cavity plasmons is controlled by the thickness of the metal shell layer. Fig. 2(a) shows the calculated extinction spectra of Ag/Au and Au/Ag nanoshells suspended in water (ε3 = 1.7689) based on quasi-static theory. Here, the inner and outer shell radii r1 and r2 are fixed at 10 nm and 15 nm, respectively. The solid and dashed curves represent the extinction spectra of Au/Ag and Ag/Au nanoshells, respectively. For Au/Ag nanoshells, the peak at 447 nm has been ascribed to the SPR. Xu et al. [11] have reported that the SPR of Au/Ag nanoshells shows a blue-shift and an enhanced intensity with increasing the thickness of Ag shell. In Ag/Au nanoshells, there are two peaks appeared in the extinction spectrum. The peak appeared at 507 nm has been ascribed to the SPR of Ag/Au nanoshells, while the other peak appeared at 406 nm have been ascribed to silver surface plasmon band [16,25]. When the thickness of gold shell is thin (<1 nm), the surface plasmon extinction spectrum of Ag/Au nanoshells is very similar to that of silver (∼400 nm). With increase in the thickness of gold shell, the characteristic silver surface plasmon band decreases in intensity and broadens, as shown in Fig. 2(b). Meanwhile, the SPR peak near gold surface plasmon band (∼520 nm) shows a red-shift and progressively gets more intense. The behavior is in agreement with the previous experimental investigations for Ag/Au nanoshells [16, 25]. Fig. 3(a) shows the contour plot of electric field density for Au/Ag nanoshell suspended in water with r1 = 10 nm and

D. Wu et al. / Solid State Communications 148 (2008) 163–167

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Fig. 2. (a) Extinction spectra for Au/Ag (solid line) and Ag/Au (dashed line) nanoshells suspended in water (ε3 = 1.7689) with r1 = 10 nm and r2 = 15 nm. (b) Extinction spectra for Ag/Au nanoshells suspended in water (ε3 = 1.7689) with r1 = 10 nm and r2 = 11 (solid line), r2 = 12 (dashed line), r2 = 13 (dotted line), r2 = 14 (dash-dot line), r2 = 15 (dash-asterisk line), r2 = 18 nm (dash-circle line).

r2 = 15 nm. The wavelength at 447 nm corresponds to the plasmon resonance in Au/Ag nanoshell. The large field enhancements can be observed both inside and outside of the nanoshell. The field strength in the core keeps as a constant, which is consistent with the expectation of quasi-static principle. It is found that the maximum enhancement of outside electrical field occurs along the incident polarization and only locates within a few nm of the shell surface, which can be well interpreted by the dipole plasmon resonance [26]. We note that the largest field enhancement in the shell occurs perpendicularly to the incident polarization (not along the incident polarization). According to plasmon hybridization, the lower-energy resonance corresponds to a symmetric coupling, which results in the same kind of charges signed on both inner and outer surfaces of the nanoshell along the incident polarization. In general, number of the charges on the outer surface is much more than that on the inner surface [19,20]. Thus, the field lines inside the shell repel each other in the poles along the incident polarization and bunch at the poles, which are perpendicular to the polarization direction, as shown in Fig. 3(b). The contour plot of the electric field enhancement for Ag/Au nanoshell in water with r1 = 10 nm and r2 = 15 nm at the plasmon resonance wavelength 507 nm is displayed in Fig. 4(a). The maximum enhancement of outside field occurs along the polarization direction due to the well-known excitation of dipole mode [26]. However, it is found that the fields in the shell are concentrated in the poles along the incident polarization, which is

*

Fig. 3. (a) Contour plot of electric field enhancement | E |2 /|E0 |2 for Au/Ag nanoshells suspended in water (ε3 = 1.7689) at plasmon resonance wavelength 447 nm with r1 = 10 nm and r2 = 15 nm. (b) Schematic picture for distribution of electric field lines.

different from that discussed by Schelm et al. [20]. It is well known that silver colloid has a stronger and sharper plasmon resonance than that of gold [27]. This fact indicates that induced charges in silver colloid are much more than that in gold. Thus, the charges on the inner surface of Ag/Au nanoshells are much more than that on the outer surface. In this case, the electric field lines in the shell are strongly repelled each other and high compressed in the poles along the polarization direction, as shown in Fig. 4(b). In addition, the electric field enhancements in Au/Ag and Ag/Au nanoshells at off-resonance wavelength 1000 nm are also investigated. The general shape of the field pattern is same as that in resonance case, but much weaker than that at resonance (not shown). Fig. 5 shows the influence of shell thickness on the electric field enhancements of (a) Au/Ag and (b) Ag/Au nanoshells. Here, the solid and dashed curves represent the maximum enhancements of the electric field on outer and inner surfaces, respectively. For Au/Ag nanoshell, the increase of shell thickness leads to the increase of the maximum enhancements on the outer and inner surfaces, as shown in Fig. 5(a). As the particle size is small, the influence of the phase retardation on the SPR is weak. In this case,

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D. Wu et al. / Solid State Communications 148 (2008) 163–167

Fig. 5. The shell thickness dependence of the maximum enhancements on outer and inner surfaces for (a) Au/Ag and (b) Ag/Au nanoshells.

*

Fig. 4. (a) Contour plot of electric field enhancement | E | /|E0 | for Ag/Au nanoshells suspended in water (ε3 = 1.7689) at plasmon resonance wavelength 507 nm with r1 = 10 nm and r2 = 15 nm. (b) Schematic picture for distribution of electric field lines. 2

2

the increase of the shell thickness should lead to the increase of conduction electrons, which enhances the SPR in the particles and hence the enhanced local electric field [28]. Fig. 5(b) shows the variation of the maximum enhancements on the outer and inner surfaces of Ag/Au nanoshells with shell thickness. With increase in the shell thickness, the maximum enhancements on the outer and inner surfaces of Ag/Au nanoshells increase, which is also due to the increase of conduction electrons. We observe that the maximum enhancement of the electric field on the inner surface is larger than that on the outer surface when the shell thickness is less than 7.8 nm, which is mainly due to the stronger plasmon resonance of Ag core. With increasing the shell thickness, the contribution of Ag core should be reduced and SPR of the particles is enhanced. As the shell thickness is larger than 7.8 nm, the induced electrons on the outer surface is larger than that on the inner surface and hence the larger enhancement of electric field on the outer surface. However, the calculation results are different from the experimental results [11,13]. Cui et al.. [13] have reported that, with increase in the shell thickness, the SERS intensity of probe molecules (PM) adsorbed on the Ag/Au nanoshells enhanced first and then weakened. The similar result has also been found

in Au/PM/Ag sandwich structure [11]. The difference between the calculation and experimental results is mainly due to the presence of the pinholes on core/shell nanoparticles. Hao et al. have reported that the pinholes provide hot spots for electromagnetic field enhancement and the electric field can be 3–4 times larger or even 10 times larger than that of the seamless nanoshells [19]. Thus, as the shell thickness is small, the hot spots in nanoshells play an important role for the great enhancement of the local electric field. In summary, electric field enhancements in Au/Ag and Ag/Au nanoshells have been calculated based on the quasi-static theory. It is found that the maximum enhancements of outside electrical field for Ag/Au and Au/Ag nanoshells occur along the incident polarization due to the dipole plasmon resonance, which is similar to many metal nanoparticles. The maximum enhancements of the electric fields for Au/Ag and Ag/Au nanoshells are 181 and 58 times larger than the incident field, respectively. It is surprising that the largest field enhancement in the shell of Ag/Au nanoshell occurs along the incident polarization, while that of Au/Ag nanoshell is perpendicular to the incident polarization. We have further investigated the influence of shell thickness on the electric field enhancements for Ag/Au and Au/Ag nanoshells. For the seamless nanoshells, the maximum enhancements on the inner and outer surfaces of Ag/Au and Au/Ag nanoshells increase with shell thickness. However, as the shell thickness is small, the hot spots in nanoshells are more relevant for the local electric field.

D. Wu et al. / Solid State Communications 148 (2008) 163–167

Acknowledgments This work was supported by the National Natural Science Foundation of China under grant No.10574071 and 10374041, the Key Project of Chinese Ministry of Education under grant No.107051, and the program for New Century Excellent Talents in Chinese University under grant No. NECT-04-045. References [1] A.F. Lee, C.J. Baddeley, C. Hardacre, R.M. Ormerod, R.M. Lambert, J. Phys. Chem. 99 (1995) 6096. [2] H.Z. Shi, L.D. Zhang, W.P. Cai, J. Appl. Phys. 87 (2000) 1572. [3] L.L. Lu, H.S. Wang, Y.H. Zhou, S.Q. Xi, H.J. Zhang, J.W. Hu, B. Zhao, Chem. Commun. 2 (2002) 144. [4] G.V. Pavan Kumar, S. Shruthi, B. Vibha, B.A. Ashok Reddy, T.K. Kundu, C. Narayana, J. Phys. Chem. C 111 (2007) 4388. [5] H.Z. Shi, L.D. Zhang, W.P. Cai, J. Appl. Phys. 87 (2000) 1572. [6] M.P. Mallin, C.J. Murphy, Nano Lett. 2 (2002) 1235. [7] S. Bruzzone, G.P. Arrighini, C. Guidotti, Mater. Sci. Eng. C 23 (2003) 965. [8] H.M. Chen, R.S. Liu, L.Y. Jang, J.F. Lee, S.F. Hu, Chem. Phys. Lett. 421 (2006) 118. [9] G.D. Hale, J.B. Jackson, O.E. Shmakova, T.R. Lee, N.J. Halas, Appl. Phys. Lett. 78 (2001) 1502.

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