Dependence of Plasmonic Properties on Electron Densities for

Article pubs.acs.org/JPCC

Dependence of Plasmonic Properties on Electron Densities for Various Coupled Au Nanostructures Chihao Liow, Fanben Meng, Xiaodong Chen, and Shuzhou Li* School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore S Supporting Information *

ABSTRACT: Noble metallic nanostructures have great potential in optical sensing application in visible and near-infrared frequencies. Their plasmonic properties can be manipulated by in situ controlling their electron densities for isolated nanostructures. However, the effect of charging remains underexplored for coupled systems. In this work, we theoretically investigated the dependence of their far-field and near-field properties on their electron densities for various coupled gold structures. With increasing electron densities, their enhancement factors increase while their plasmonic resonance peaks are blue-shifted. The resonance peak position of ellipsoidellipsoid dimers shows the highest sensitivity in response to the charging effects with the slope of −2.87. The surface-averaged electric field of ellipsoid monomer shows largest enhancement ratio of 1.13 with 16% excess electrons. These results can be well explained by an effective dipole moment model. In addition, we also studied the sphere-on-substrate nanostructure which can be precisely fabricated. This system shows low sensitivity to the charging effect with the slope of −1.46 but remarkable enhancement ratio of 1.13 on near field response with 16% excess electrons.

■

dependent constant of an isolated nanostructure.17 This relationship has been proved in several isolated nanostructures such as nanorods,17,25 nanodisks,25 and nanoprisms.26 In general, increasing the free electron density of an isolated nanostructure will lead to a blue shift, while decreasing the free electron density will lead to a red shift. Furthermore, charging of an isolated metallic nanostructure will also alter its electromagnetic enhancement.27 Monitoring the enhancement alteration is crucial especially to obtain the dynamic information on a single molecule in optical spectroscopy measurement.23 Several reports have demonstrated the near field properties of a charged standalone nanostructure.27−29 Using a Gersten−Nitzan model, the electromagnetic enhancement of an isolated nanostructure can be numerically calculated.27,29 On the basis of their studies, charging (excess of electrons) will results in larger polarizability of the metallic nanostructure, which is analogy to the “lightning rod effect” of a sharp edge22 thus leads to a higher enhancement than its neutral counterpart.22,27 All previous studies have focused on isolated nanostructures. For coupled nanostructures, such as dimers, the effects of charging on their plasmonic properties have not been explored. In this paper, we employed a numerical method (discrete dipole approximation (DDA)) and the analytical method under quasistatic limit to study the charging effect of coupled

INTRODUCTION Because strong electromagnetic fields can be confined at a nanostructure surface under surface plasmon resonance (SPR), SPR has attracted a lot of attentions in biosensing,1,2 optoelectronic,3,4 and photothermal cancer therapy.5−7 These unique properties of SPR can be artificially tuned over visible and infrared regions to fit various requirements. The tuning of SPR positions can be either statically or dynamically. There are intensive studies about static tuning which involves tailoring the size,8−10 geometry,11,12 and dielectric environment.13,14 While the dynamic tuning is underexplored which involves altering the internal electron density of a metallic nanostructure.15−17 Recently, highly doped semiconductors have been reported to support surface plasmons in mid-infrared region, such as graphene,18,19 copper sulfide (Cu2S),20 tin telluride (SnTe),21 and germanium telluride (GeTe).21 Their plasmonic properties depends on their charge carrier densities directly. It is crucial to evaluate the dependence of plasmonic properties on charges carrier densities as this dependence directly reflects the sensing quality of a nanostructure.22,23 Here, we focus on the charging effect on metallic nanostructures, which can be easily extended to semiconductor nanostructures. Previous studies have demonstrated that SPR frequency of an isolated nanostructure can be dynamically tuned via electrochemical potential.15,17,24 Applying negative or positive potential to a metallic nanostructure injects electrons into or withdraws electrons from it. Using this method, Mulvaney and his co-workers have generalized a linear relationship between the magnitude of plasmon frequency shift with the shape © 2014 American Chemical Society

Received: October 3, 2014 Revised: November 1, 2014 Published: November 6, 2014 27531

dx.doi.org/10.1021/jp5099975 | J. Phys. Chem. C 2014, 118, 27531−27538

The Journal of Physical Chemistry C

Article

from neighboring induced dipole, Eneigh,i, which is shown at eq 3:

nanostructures, such as sphere dimer, ellipsoid−sphere dimer, and ellipsoid−ellipsoid dimer. We found that an ellipsoid− ellipsoid dimer exhibits the largest SPR shift in response to the charging effect because of its high shape dependent constant. However, its enhancement ratio is lowest because of its strongly distorted charge distribution, which is only 1.08 with 16% excess charge while the ellipsoid monomer has an enhancement ratio of 1.13 with the same amount of excess electrons. For a sphere-on-substrate nanostructure, its SPR position also shows blue-shifted with increasing charges. Although it only has a low value of electromagnetic enhancement, a sphere-on-substrate nanostructure exhibits a remarkable enhancement ratio of 1.13, which is comparable to that of the ellipsoid monomer.

Eloc , i = Einc , i + Eneigh , i = Eoeik . ri −

i≠j

Aij Pj =

ω 2 + ωγi

−

Cext =

−

(1)

EF =

N

∑ Im(Einc ,i·Pi ) i=1

(5)

|Eloc|2 |Einc|2

(6)

The behavior of EF increment in response to the charging effect is characterized by the enhancement ratio, given by eq 7. enhancement ratio =

EF(ΔN /N ) EF(ΔN /N = 0)

(7)

With the same amount of excess electrons, a large enhancement ratio means the near fields of a nanostructure has high sensitivity to the charging and vice versa. C. Analytical Solution under Quasistatic Limit. Analytical solution can provide more physical insight for plasmon position shifts than numerical solution. The validity of the quasistatic theory falls to small particles that only exhibit dipolar behavior in response to the incident electromagnetic wave.38 Using this method, the far field properties of an ellipsoid monomer can be calculated by eq 8:39

ωp 2(1 + ΔN /N ) ω 2 + ωγi

ΔεΩL 2(1 + ΔN /N ) ω 2 − ΩL 2(1 + ΔN /N ) + ω ΓLi

4πk |Einc|2

Extinction efficiency equals extinction cross section of a nanostructure divided by its geometric cross section. The electromagnetic enhancement is represented by the average enhancement factor (EF) over the whole nanostructure surface and is described in eq 6.37

where ε∞, ωp, and γ denote frequency independent dielectric constant, plasma frequency, and damping constant, respectively. In the Lorentz term, Δε, ΩL, and ΓL are the Lorentz weighting factor, the Lorentz oscillator strength, and the damping constant of the Lorentz oscillator, respectively. In eq 1, γ and ΓL are independent of the free electron density of materials.25 ωp2 is proportional to the free electron density N by ωp2 = Ne2/ meεo, where e, me, and ε0 denote electron charge, effective mass of electrons, and vacuum permittivity, respectively. The term of ΩL2 is linearly dependent to plasma frequency by ΩL2 = foωp2, where fo is a constant.32 The charging effect can be taking care of by adding excess electron (ΔN/N) to ωp2 term and ΩL2 term, which is eq 2. ε(ω) = ε∞ −

(4)

where k = ω/c = 2π/λ (ω is angular frequency and c is speed of light); rij is the magnitude of vector dipole i to dipole j. After determining Pi, the extinction cross section (Cext) can be calculated from eq 5

ΔεΩL 2 ω 2 − ΩL 2 + ω ΓLi

⎧ 1 − ikrj eikrij ⎪ 2 ×⎨ k r × ( r × P ) + × (rij 2Pj ij ij j 3 2 ⎪ rij r ⎩ ij

⎫ ⎪ − 3rij(rij·Pj)⎬ ⎪ ⎭

THEORETICAL METHODS During charging, the electron density of a metallic nanostructure varies with the applied electrochemical potential and the double layer capacitance.17,25 To take this variation into account, we investigated a wider range (0−16%) of the amount of excess electrons ΔN/N in this study.25 A. Modified Drude−Lorentz Model With Excess Electrons. Au was selected in this study because of its excellent thermal stability and chemical inactivity.30,31 For gold (Au) in visible region, a Drude−Lorentz model is needed to describe its dielectric constants where Lorentz term can catch the interband transition feature, which is in eq 1 ωp 2

(3)

where Pi is the dipole moment at location ri. Each Aij element with i ≠ j (j = 1, 2, 3, ..., N) is a 3 × 3 matrix interaction, such that

■

ε(ω) = ε∞ −

∑ AijPj

(2)

where ε∞ = 5.9673, ωp = 8.7411 eV, γ = 0.0658 eV, Δε = 1.090, ΓL = 0.4337 eV, and ΩL = 2.6885 eV.33 When ΔN/N = 0, this set of parameters can perfectly reproduce the SPR position of an ellipsoid monomer, which shown in Figure S1 (Supporting Information). B. Numerical Method by Discrete Dipole Approximation (DDA). DDA is a numerical method (package DDSCAT version 7.0)34−36 to solve the Maxwell equation. In this method, a nanostructure is discretized into N polarizable point dipoles localized at position i, i = 1, 2, ..., N. Each dipole has polarization Pi = αiEi, where αi is polarizability, and Ei is the electric field at location i. The local field of each dipole, Eloc,i is the sum of incident radiation field, Einc,i and the radiation field

Cext =

2πVεe 3/2 λL2

ε″ (λ ) (ε′ + κεe)2 + ε″ 2

(8)

where V, εe, L, ε′, and ε″ are the volume of particle, the dielectric constant of environment, the shape dependent constant, the real part, and the imaginary part of Au dielectric constants. The geometrical depolarization factor, κ, is defined: κ=

1 −1 L

(9)

The SPR shift, Δλ from its neutral state to a charged state can be determined analytically under quasistatic limit for monomer.17,40 27532


The Journal of Physical Chemistry C Δλ =

Article

⎛1 ⎞ −ΔN λp ε∞ + ⎜ − 1⎟εe ⎝ ⎠ 2N L

are available in Supporting Information. The resonance condition from eq 11 is given by20,46

(10)

(

ε′ = [(2 + Zκ2 + Zκ1)

On the other hand, the Δλ for a dimer can be derived as the following, where the average polarizability, ⟨α⟩ of a dimer is given by41−44 ⎧ α α α 1 + g 23 + α2 1 + g 13 εod εod 1⎪ 1 ⟨α⟩ = ⎨ αα 2⎪ 1 − g 2 12 26 εo d ⎩

(

)

(

±

) ⎫⎪⎬

)

/[2(1 − Z)] εe 6

⎪ ⎭

(11)

⎛ (2 + Zκ + Zκ ) ± ΔN 2 1 λp ε∞ − ⎜⎜ 2N ⎝

(2 + Z(κ1 + κ2))2 − 4(1 − Z)(1 − Zκ1κ2) ⎞⎟ ⎟εe 2(1 − Z) ⎠

2

(13)

When the electron density increases, such as ΔN/N = 16%, the real part becomes smaller than its neutral state counterpart. The imaginary part, it is smaller from 450 to 650 nm while no significant change from 650 to 800 nm. These results agreed well with previous findings,25 and the Au dielectric constants with 4% charges increments are available in Figure S2. We first studied the monomers nanostructures, which are depicted in Scheme 1. For the ellipsoid monomer with an

Here κ1 and κ2 are geometrical depolarization factor for first and second nanostructure that defined in eq 9. For near field properties, the average electromagnetic enhancement of an ellipsoid monomer can be determined from eq 14.47 ⎡ ⎤ 2Re(1 − ξ)ξ* |ξ|2 ⎥ + EF = ⎢|1 − ξ|2 + ⎢⎣ Q 1(ξo) Q 1(ξo)(ξo 2 − 1) ⎥⎦ ⎡ ⎤ − (ξo 2 − 1) + ξo 2 sin−1(1/ξo) ⎥ ⎢ × ⎢ (ξ 2 − 1) + ξ 2 sin−1(1/ξ ) ⎥ ⎣ o o o ⎦

2

(12)

where Z = (d )/(g C1C2); C1 and C2 are 4πba /3L1 and 4πba2/ 3L2; a and b are the semimajor and semiminor axis of ellipsoid nanostructure, note that a and b are the same for sphere nanostructure; L1 and L2 are shape dependent constants of first and second nanostructure. Plugging eq 12 into real part of the Drude model, we obtained that the Δλ of dimer is as follows:

where α1 and α2 are the polarizabilities of first and second particle; g is a constant which in this case equal to 1/2π;45 d is center to center distance of two particles. The derivation details

Δλ = −

(2 + Z(κ1 + κ2))2 − 4(1 − Z)(1 − Zκ1κ2) ]

Scheme 1. (a) Ellipsoid with a = 17.5 nm and Its Aspect Ratio a/b = 2 and (b) Sphere Monomer with Radius, r = 11 nma

(14)

where ξ = (ε − εo)/(ε + κεo), ξo = 1/(1 − (a )/(b )) ; Q1(ξo) = 1/2 ξo, ln((ξo + 1)/(ξo − 1)) − 1, and ε is the dielectric constant of the material. 2

2

1/2

■

RESULTS AND DISCUSSION The dielectric constants of Au are shown in Figure 1. The square symbols (solid and hollow) indicating real and

a

Note: the ellipsoid monomer and sphere monomer have equal volumes.

aspect ratio equal to 2, its semimajor axis is 17.5 nm, so that the biological optical windows (600 nm ∼1300 nm) can be covered.49 The polarization of incident light is along its major axis. The sphere monomer with radius of 11 nm has same volume as the ellipsoid monomer. The grid size was 0.5 nm grid and the surrounding medium was water for all simulations. The extinction spectra of the ellipsoid monomers are plotted in Figure 2. The DDA results in Figure 2a clearly show that the ellipsoid SPR positions are blue-shifted with increasing amount of electrons, which is from 594 nm for ΔN/N = 0 to 533 nm for ΔN/N = 16%. Figure 2b shows a direct comparison of extinction spectra calculated numerically (solid lines) and analytically (dash lines). They are not exactly same because the phase retardation effect is neglected in quasistatic limit treatment.50 Nevertheless, the deviation of SPR peak position between two methods are less than 1%, which can be defined from (|λDDA − λquasistatic|)/(λDDA + λquasistatic).51 It proves an excellent agreement between two independent calculation methods. For a sphere with same volume as an ellipsoid, the SPR position only shift from 526 nm at ΔN/N = 0 to 489 nm at ΔN/N = 16%, which is shown in Figure S3a. The smaller shift in the sphere monomer is because the SPR shifting is

Figure 1. (a) Real part and (b) imaginary part of Au dielectric constants. Note: Experimental data from Johnson and Christy (J&C, symbols)48 and the fitted Drude−Lorentz model at neutral (0, red curves) and 16% charged state (16, blue curves).

imaginary parts of Au obtained experimentally (Johnson and Christy),48 where the solid lines and the dash lines indicate real and imaginary parts of Au calculated from eq 2. It is seen that the dielectric constants obtained by Drude−Lorentz model are in excellent agreement with those experimental measurements for wavelength larger than 500 nm at neutral state (ΔN/N = 0). 27533



Article

Figure 2. (a) Extinction spectra of ellipsoid monomer calculated by DDA method. (b) Comparison of the extinction spectra from DDA method (solid lines) and analytical solutions under quasistatic limit (dash lines).

linearly related to the shape dependent constant of nanostructures. The ellipsoid has a larger shape dependent constant than the sphere, hence exhibiting larger shift. The correlation between SPR positions and the amount of excess electrons was investigated for dimers with a gap of 2 nm, where the particles in dimers have same size as their corresponding monomers. The extinction spectra from DDA method are plotted in Figure S3b−d for sphere dimer, ellipsoid−ellipsoid dimer, and ellipsoid−sphere dimer. Figure 3 summarizes their resonance peak positions with excess

Figure 4. Magnitude of the plasmon peak shift in response to charging effects for ellipsoid−ellipsoid dimer (squares), ellipsoid−sphere dimer (circles), ellipsoid monomer (triangles), sphere dimer (inverted triangles), and sphere monomer (diamonds). (a) Calculated from extinction spectra simulated by DDA method. (b) Calculated from analytical methods. The solid lines are representing best fit.

Table 1. Slope of the Surface Plasmon Resonance Position Shift Calculated from Figure 4

Figure 3. Response of plasmon peak positions to varied charged state of different nanostructure geometries simulated using DDA method. Nanostructure geometries include ellipsoid−ellipsoid dimer (squares), ellipsoid−sphere dimer (circles), ellipsoid monomer (triangles), sphere dimer (inverted triangles), and sphere monomer (diamonds). Note: the gap in dimers is 2 nm. The solid lines are representing best fit.

geometries

numerical

analytical

ellipsoid−ellipsoid ellipsoid−sphere ellipsoid sphere dimer sphere

−2.87 −2.78 −2.61 −2.46 −2.36

−2.80 −2.72 −2.69 −2.33 −2.19

The influence of the charging effect on the near field properties of the nanostructures was also investigated systematically. Figure 5a shows the numerical average EF of an ellipsoid monomer over visible region at different value of ΔN/ N. The EF spectra also shows blue shift from its neutral state with increased ΔN/N, where the results from the DDA method are quantitatively agreed with the results from analytical solutions, eq 14 (Figure S4). The electromagnetic fields are strongly confined at the end of the nanostructure along with the polarization direction, which is shown in Figure 5b. The EFs from DDA calculations are also obtained for various coupled nanostructures. Figure 6a summarizes EF of different geometries at their resonance peak, where the EF spectra and their electric field distribution are available in Figure S5. The EFs also increase monotonically with excess electrons for different geometries. Among all the systems that we studied, the ellipsoid-ellipsoid dimer shows the highest EF in the range of 485 to 521, which is 7.4% increase from its neutral state to 16% excess electrons state. On the other end, the sphere monomer has the lowest EF (in the range 13.04−14.15), which still have a 7.7% increase. Surprisingly, despite the absolute magnitude of EF exhibited by every nanostructure, ellipsoid-ellipsoid dimer has lowest relative EF increment comparing to other geometries. To quantify the charging effects to the enhancement properties with respect to their neutral state, the enhancement

electrons up to 16%. For comparison, Figure 3 also includes the results from sphere monomer and ellipsoid monomer. The SPR of all dimers show blue shifts with excess electrons, notwithstanding the coupling effects in their close proximity. The sensitivity of different geometries in response to excess electrons can be determined from the magnitude of slope of Δλ against varied ΔN/N. Figure 4a shows the Δλ from DDA method. The values of Δλ obtained from DDA method are qualitatively agreed with those from eq 10 and eq 13 (Figure 4b) for all studied nanostructures. Since the Δλ only depends on shape dependent constant under quasistatic limit, only the Drude model is used in eq 10 and eq 13 for simplicity. The slopes for different geometries are listed in Table 1. Δλ from DDA calculations showed that ellipsoid-ellipsoid dimer has the highest slope of −2.87 while the sphere monomer has the slope of −2.36. In a similar fashion, quasistatic limit results showed an ellipsoid dimer with a slope of −2.80 and a sphere monomer with a slope of −2.19. 27534



Article

corresponding to the shape.52 Charging of nanostructure can enhance the lightning rod effect, thus the higher intensity of enhancement is obtained for all geometries.22 Because of this effect is more pronounce with the present of protrusion surface, ellipsoid monomer (first row in Scheme 2) exhibiting higher enhancement ratio than sphere monomer. When a coupled nanostructure is charged, significant amount of charges are localized at edge near the gap (Scheme 2, second and third row). At the same time, the counter charges are much closer to the gap region, resulting in that the charge separation distances at charged state (Lee16 and Les16, where es = ellipsoid−sphere dimer, and ee = ellipsoid−ellipsoid dimer) are significantly shorter than their neutral state (Lee0 and Les0). The dipole moment is determined by the total amount of charges and the charges separation. Even more charges are near the edge of dimers in coupled nanostructure, the significant smaller charges separation distance leads to smaller dipole moment. Hence, the enhancement ratios in ellipsoid−sphere dimers and ellipsoid− ellipsoid dimers are smaller than those in ellipsoid monomers (last two rows in Scheme 2).52 This effect is more pronounce in ellipsoid than sphere, hence the distortion of charges distribution in ellipsoid-sphere dimer was lower than ellipsoid-ellipsoid dimer. The order of the charges separation distance is Le0 ∼ Le16 > Les0 > Les16 > Lee0 > Lee16 (e = ellipsoid monomer). A spiky nanoparticle dimer may be able to keep a large charge separation distance in the presence of extra charges.53 We have presented the charging response in SPR and EF for nanostructures with homogeneous dielectric environment. However, in most of the realistic studies, the nanostructures are deposited on a supporting substrate. A sphere-on-substrate system is also investigated here in order to investigate the optical properties of a nanostructure in the presence of a substrate. In this system, the same sphere monomer with a radius of r was used; the gap between sphere and substrate is restricted to 2 nm. In these simulations, a finite Au cylinder with diameter of 3r and height of 2r was used to represent the substrate.54,55 The electric field polarization is perpendicular to the gap between sphere and substrate. We used 0.5 nm grid size to discretize the sphere-on-substrate nanostructure and embedded it in water environment. Assuming Au sphere and Au substrate having equal percentage excess electrons, Figure 7a shows the extinction spectra of Au sphere-on-substrate at varied ΔN/N. In the presence of substrate, the SPR peak showed slightly red-shifted comparing to sphere monomer, which is 7 nm from 527 nm (sphere monomer) to 534 nm (sphere-on-substrate) at ΔN/N = 0%. Similar to the standalone systems, charging results in extinction spectra blue shifts (Figure 7a) where the SPR position is 534 nm for ΔN/N = 0% and 508.5 nm for ΔN/N = 16%. The dependence of SPR wavelength and the SPR position shift on charging effect is plotted in Figure 7b. Because of the SPR band broadening, the sensitivity of sphere-on-substrate SPR shift on charging effect is reduced, which gives the slope of −1.46 that is even lower than sphere monomer (Table 1). On the other hand, the EF spectra of sphere-on-substrate systems with excess charges are expressed in Figure 8. Similar to previous systems, the EF spectra are blue-shifted (Figure 8a) and the maximum EF values increase in response to increasing charges (black star symbols depicted in Figure 8b). Judging from the value of enhancement ratio (red star symbols depicted in Figure 8b), the sphere-on-substrate nanostructure showed an effective response toward the excess electrons and reaching

Figure 5. Near field properties of ellipsoid monomer calculated by DDA method. (a) Spectra of enhancement factors. (b) Electric field distributions at its resonance wavelength when ΔN/N = 0, the scale bar is 15 nm.

Figure 6. (a) Maximum enhancement factor from DDA calculations for various Au nanostructures. (b) Enhancement ratio from charged nanostructures relative to that of their neutral counterpart. The geometries includes ellipsoid−ellipsoid dimer (squares), ellipsoid− sphere dimer (circles), ellipsoid monomer (triangles), sphere dimer (inverted triangles), and sphere monomer (diamonds) with varied charging states. The solid lines are representing best fit.

ratio is plotted in Figure 6b. The enhancement ratio from highest to lowest at ΔN/N = 16% is ellipsoid monomer, sphere dimer, ellipsoid−sphere dimer, sphere monomer, and ellipsoid−ellipsoid dimer. The dependence of EF on electron densities can be explained by an effective dipole moment model in Scheme 2. Upon excitation, the charges with opposite sign will localize at the end of ellipsoids or spheres along the polarization direction, forming a dipole with the charge separation distance of LxN, where N is represents the percentage of excess electrons and subscript x is 27535



Article

Scheme 2. Effective Dipole Moment Models for Ellipsoid Monomer, Ellipsoid−Sphere, and Ellipsoid Dimera

a

LxN is the charge separation distance for an ellipsoid, with subscript x corresponding the shape (e = ellipsoid monomer, es = ellipsoid−sphere dimer, and ee = ellipsoid−ellipsoid dimer) and N corresponding the percentage of excess electrons. g is the gap between two nanostructures. Estimated charge separation distance in descending order: Le0 ∼ Le16 > Les0 > Les16 > Lee0 > Lee16. Note: charges distribution of sphere experience insignificant distortion.52.

Figure 8. Near field properties of a sphere-on-substrate at various charged states. (a) The spectra of enhancement factors. (b) The maximum enhancement factor (black stars) and the enhancement ratio (red stars). The solid and dash lines are representing best fit for plasmon peak position and peak shift, respectively.

Figure 7. Far field properties of a sphere-on-substrate nanostructure at various charged states. (a) Extinction spectra and (b) the plasmon peak positions (black stars) and the peak shifting (red stars) in response to varied charged states. The solid and dash lines are representing best fit for plasmon peak position and peak shift, respectively.

positions for all geometries exhibiting a significant blue shift with the increasing ΔN/N from 0 to 16%. The magnitude of Δλ varied corresponding to individual geometries, where ellipsoid−ellipsoid dimer shows the largest Δλ due to its highest depolarization factor among all geometries in this study. The ellipsoid−ellipsoid dimer exhibiting lowest enhancement ratio due to its highly distorted charges distribution. To mimicking a realistic system, we introduced the charging effect to a sphere-on-substrate nanostructure. Its SPR shifts showed less sensitivity than the standalone nanostructures because the presence of a substrate leads to a broader SPR band. Although the sphere-on-substrate system has a low EF value, it has a comparable enhancement ratio as the ellipsoid monomer. The physical insight for manipulating of the far fields and the near fields behavior in charges induced plasmonic systems can provide a guide for nanostructure design especially for semiconductor plasmonic sensors.

enhancement ratio of 1.13 at ΔN/N = 16%, at which the near field response has higher sensitivity than both the sphere monomer and dimer. Adapting the image charges theory to the proposed model in Scheme 2,56−58 a dipole from a sphere would be screened by the opposite-polarized image dipole in the metal substrate when the sphere is close to a substrate. Taking account of the sphere’s dipole and the image dipole in sphere-on-substrate, the average polarizability is larger than that of standalone sphere;59 hence, more effective in near field response to the charging effect. Figure S6 shows the evidence of strong coupling between sphere monomer and substrate, which leads to a strong electric field concentrated in the gap.

■

CONCLUSIONS We theoretically studied the influence of charging effect on various Au nanostructures. In general, we showed that SPR 27536



■

Article

(13) Grady, N. K.; Halas, N. J.; Nordlander, P. Influence of Dielectric Function Properties on the Optical Response of Plasmon Resonant Metallic Nanoparticles. Chem. Phys. Lett. 2004, 399, 167−171. (14) Tam, F.; Moran, C.; Halas, N. Geometrical Parameters Controlling Sensitivity of Nanoshell Plasmon Resonances to Changes in Dielectric Environment. J. Phys. Chem. B 2004, 108, 17290−17294. (15) Chapman, R.; Mulvaney, P. Electro-Optical Shifts in Silver Nanoparticle Films. Chem. Phys. Lett. 2001, 349, 358−362. (16) Funston, A. M.; Novo, C.; Davis, T. J.; Mulvaney, P. Plasmon Coupling of Gold Nanorods at Short Distances and in Different Geometries. Nano Lett. 2009, 9, 1651−1658. (17) Mulvaney, P.; Pérez-Juste, J.; Giersig, M.; Liz-Marzán, L. M.; Pecharromán, C. Drastic Surface Plasmon Mode Shifts in Gold Nanorods Due to Electron Charging. Plasmonics 2006, 1, 61−66. (18) Manjavacas, A.; de Abajo, F. J. G. Tunable Plasmons in Atomically Thin Gold Nanodisks. Nat. Commun. 2014, 5. (19) Xu, W. G.; Mao, N. N.; Zhang, J. Graphene: A Platform for Surface-Enhanced Raman Spectroscopy. Small 2013, 9, 1206−1224. (20) Luther, J. M.; Jain, P. K.; Ewers, T.; Alivisatos, A. P. Localized Surface Plasmon Resonances Arising from Free Carriers in Doped Quantum Dots. Nat. Mater. 2011, 10, 361−366. (21) Tsu, R.; Howard, W. E.; Esaki, L. Optical and Electrical Properties and Band Structure of Gete and Snte. Phys. Rev. 1968, 172, 779−788. (22) Wu, D. Y.; Li, J. F.; Ren, B.; Tian, Z. Q. Electrochemical SurfaceEnhanced Raman Spectroscopy of Nanostructures. Chem. Soc. Rev. 2008, 37, 1025−1041. (23) Dos Santos, D. P.; Andrade, G. F. S.; Temperini, M. L. A.; Brolo, A. G. Electrochemical Control of the Time-Dependent Intensity Fluctuations in Surface-Enhanced Raman Scattering (SERS). J. Phys. Chem. C 2009, 113, 17737−17744. (24) Ung, T.; Giersig, M.; Dunstan, D.; Mulvaney, P. Spectroelectrochemistry of Colloidal Silver. Langmuir 1997, 13, 1773−1782. (25) Juluri, B. K.; Zheng, Y. B.; Ahmed, D.; Jensen, L.; Huang, T. J. Effects of Geometry and Composition on Charge-Induced Plasmonic Shifts in Gold Nanoparticles. J. Phys. Chem. C 2008, 112, 7309−7317. (26) Salvador, M.; MacLeod, B. A.; Hess, A.; Kulkarni, A. P.; Munechika, K.; Chen, J. I. L.; Ginger, D. S. Electron Accumulation on Metal Nanoparticles in Plasmon-Enhanced Organic Solar Cells. ACS Nano 2012, 6, 10024−10032. (27) Chung, H. Y.; Leung, P. T.; Tsai, D. P. Effects of Extraneous Surface Charges on the Enhanced Raman Scattering from Metallic Nanoparticles. J. Chem. Phys. 2013, 138, 224101−224106. (28) Kocifaj, M.; Klačka, J. Scattering of Electromagnetic Waves by Charged Spheres: Near-Field External Intensity Distribution. Opt. Lett. 2012, 37, 265−267. (29) Gersten, J.; Nitzan, A. Electromagnetic Theory of Enhanced Raman Scattering by Molecules Adsorbed on Rough Surfaces. J. Chem. Phys. 1980, 73, 3023−3027. (30) Kneipp, K.; Kneipp, H.; Manoharan, R.; Hanlon, E. B.; Itzkan, I.; Dasari, R. R.; Feld, M. S. Extremely Large Enhancement Factors in Surface-Enhanced Raman Scattering for Molecules on Colloidal Gold Clusters. Appl. Spectrosc. 1998, 52, 1493−1497. (31) Qian, L. H.; Yan, X. Q.; Fujita, T.; Inoue, A.; Chen, M. W. Surface Enhanced Raman Scattering of Nanoporous Gold: Smaller Pore Sizes Stronger Enhancements. Appl. Phys. Lett. 2007, 90. (32) Rakić, A. D.; Djurišić, A. B.; Elazar, J. M.; Majewski, M. L. Optical Properties of Metallic Films for Vertical-Cavity Optoelectronic Devices. Appl. Opt. 1998, 37, 5271−5283. (33) Vial, A.; Grimault, A. S.; Macías, D.; Barchiesi, D.; de la Chapelle, M. L. Improved Analytical Fit of Gold Dispersion:Application to the Modeling of Extinction Spectra with a Finite-Difference Time-Domain Method. Phys. Rev. B 2005, 71, 085416. (34) Draine, B. T.; Goodman, J. Beyond Clausius-Mossotti: Wave Propagation on a Polarizable Point Lattice and the Discrete Dipole Approximation. Astrophys. J., Lett. 1993, 405, 685−697. (35) Draine, B. T.; Flatau, P. J. Discrete-Dipole Approximation for Scattering Calculations. J. Opt. Soc. Am. A 1994, 11, 1491−1499.

ASSOCIATED CONTENT

S Supporting Information *

Charged Au dielectric constant, SPR of ellipsoid monomer is based on dielectric constant from Drude−Lorentz and experimental models, extinction spectra of ellipsoid monomer calculated by analytical methods, extinction spectra of different geometries calculated by DDA methods, field enhancement of ellipsoid monomer calculated by analytical methods, field enhancement and electric field distribution of various geometries calculated using DDA methods, field distribution of sphere-on-substrate calculated using DDA methods, and detailed deviations of SPR peak shift for a dimer. This material is available free of charge via the Internet at http://pubs.acs.org

■

AUTHOR INFORMATION

Corresponding Author

*(S.L.) Telephone: +65 6790 4380. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS

■

REFERENCES

We thank the support by MOE Tier 2 (ACR12/12), MOE Tier 1 (RG43/10), and NTU Start-up funding.

(1) Haes, A. J.; Van Duyne, R. P. A Nanoscale Optical Biosensor: Sensitivity and Selectivity of an Approach Based on the Localized Surface Plasmon Resonance Spectroscopy of Triangular Silver Nanoparticles. J. Am. Chem. Soc. 2002, 124, 10596−10604. (2) Phillips, K. S.; Cheng, Q. Recent Advances in Surface Plasmon Resonance Based Techniques for Bioanalysis. Anal. Bioanal. Chem. 2007, 387, 1831−1840. (3) Heo, M.; Cho, H.; Jung, J. W.; Jeong, J. R.; Park, S.; Kim, J. Y. High-Performance Organic Optoelectronic Devices Enhanced by Surface Plasmon Resonance. Adv. Mater. 2011, 23, 5689−5693. (4) Choi, H.; Ko, S. J.; Choi, Y.; Joo, P.; Kim, T.; Lee, B. R.; Jung, J. W.; Choi, H. J.; Cha, M.; Jeong, J. R.; Hwang, I. W.; Song, M. H.; Kim, B. S.; Kim, J. Y. Versatile Surface Plasmon Resonance of Carbon-DotSupported Silver Nanoparticles in Polymer Optoelectronic Devices. Nat. Photonics. 2013, 7, 732−738. (5) Lal, S.; Clare, S. E.; Halas, N. J. Nanoshell-Enabled Photothermal Cancer Therapy: Impending Clinical Impact. Acc. Chem. Res. 2008, 41, 1842−1851. (6) Jain, P. K.; Huang, X.; El-Sayed, I. H.; El-Sayed, M. A. Noble Metals on the Nanoscale: Optical and Photothermal Properties and Some Applications in Imaging, Sensing, Biology, and Medicine. Acc. Chem. Res. 2008, 41, 1578−1586. (7) Huang, X.; Jain, P. K.; El-Sayed, I. H.; El-Sayed, M. A. Plasmonic Photothermal Therapy (Pptt) Using Gold Nanoparticles. Laser. Med. Sci. 2008, 23, 217−228. (8) Jain, P. K.; Lee, K. S.; El-Sayed, I. H.; El-Sayed, M. A. Calculated Absorption and Scattering Properties of Gold Nanoparticles of Different Size, Shape, and Composition: Applications in Biological Imaging and Biomedicine. J. Phys. Chem. B 2006, 110, 7238−7248. (9) Haynes, C. L.; Van Duyne, R. P. Nanosphere Lithography: A Versatile Nanofabrication Tool for Studies of Size-Dependent Nanoparticle Optics. J. Phys. Chem. B 2001, 105, 5599−5611. (10) Ozbay, E. Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions. Science 2006, 311, 189−193. (11) Halas, N. Playing with Plasmons: Tuning the Optical Resonant Properties of Metallic Nanoshells. MRS Bull. 2005, 30, 362−367. (12) Xia, Y.; Li, W.; Cobley, C. M.; Chen, J.; Xia, X.; Zhang, Q.; Yang, M.; Cho, E. C.; Brown, P. K. Gold Nanocages: From Synthesis to Theranostic Applications. Acc. Chem. Res. 2011, 44, 914−924. 27537



Article

(36) Draine, B. T.; Flatau, P. J. Diserete-Dipole Approximation for Periodic Targets: Theory and Tests. J. Opt. Soc. Am. A 2008, 25, 2693−2703. (37) Yang, W.-H.; Schatz, G. C.; Van Duyne, R. P. Discrete Dipole Approximation for Calculating Extinction and Raman Intensities for Small Particles with Arbitrary Shapes. J. Chem. Phys. 1995, 103, 869− 875. (38) Gulen, D. Optical Response of Lorentzian Nanospheres in the Quasistatic Limit. J. Lumin. 2012, 132, 795−800. (39) Baida, H.; Billaud, P.; Marhaba, S.; Christofilos, D.; Cottancin, E.; Crut, A.; Lermé, J.; Maioli, P.; Pellarin, M.; Broyer, M.; Del Fatti, N.; Vallée, F.; Sánchez-Iglesias, A.; Pastoriza-Santos, I.; Liz-Marzán, L. M. Quantitative Determination of the Size Dependence of Surface Plasmon Resonance Damping in Single Ag@Sio2 Nanoparticles. Nano Lett. 2009, 9, 3463−3469. (40) Novo, C.; Mulvaney, P. Charge-Induced Rayleigh Instabilities in Small Gold Rods. Nano Lett. 2007, 7, 520−524. (41) Sandrock, M. L.; Foss, C. A., Jr Synthesis and Linear Optical Properties of Nanoscopic Gold Particle Pair Structures. J. Phys. Chem. B 1999, 103, 11398−11406. (42) Gluodenis, M.; Foss, C. A., Jr The Effect of Mutual Orientation on the Spectra of Metal Nanoparticle Rod-Rod and Rod-Sphere Pairs. J. Phys. Chem. B 2002, 106, 9484−9489. (43) El-Kouedi, M.; Foss, C. A., Jr Optical Properties of Gold-Silver Iodide Nanoparticle Pair Structures. J. Phys. Chem. B 2000, 104, 4031− 4037. (44) Schmitt, J.; Mächtle, P.; Eck, D.; Möhwald, H.; Helm, C. A. Preparation and Optical Properties of Colloidal Gold Monolayers. Langmuir 1999, 15, 3256−3266. (45) Gluodenis, M.; Foss, C. A. The Effect of Mutual Orientation on the Spectra of Metal Nanoparticle Rod-Rod and Rod-Sphere Pairs. J. Phys. Chem. B 2002, 106, 9484−9489. (46) Bohren, F. C.; Huffman, R. D. Absorption and Scattering of Light by Small Particles; John Wiley & Sons Ltd.: New York, 1998. (47) Schatz, G. C. Theoretical Studies of Surface Enhanced Raman Scattering. Acc. Chem. Res. 1984, 17, 370−376. (48) Johnson, P. B.; Christy, R. W. Optical Constants of the Noble Metals. Phys. Rev. B 1972, 6, 4370−4379. (49) Anderson, R. R.; Parrish, J. A. The Optics of Human Skin. J. Invest. Dermatol. 1981, 77, 13−19. (50) Zeman, E. J.; Schatz, G. C. An Accurate Electromagnetic Theory Study of Surface Enhancement Factors for Ag, Au, Cu, Li, Na, Al, Ga, in Zn, and Cd. J. Phys. Chem. 1987, 91, 634−643. (51) Zhang, J.; Cao, C.; Xu, X.; Liow, C.; Li, S.; Tan, P.; Xiong, Q. Tailoring Alphabetical Metamaterials in Optical Frequency: Plasmonic Coupling, Dispersion, and Sensing. ACS Nano 2014, 8, 3796−3806. (52) Aizpurua, J.; Bryant, G. W.; Richter, L. J.; García De Abajo, F. J.; Kelley, B. K.; Mallouk, T. Optical Properties of Coupled Metallic Nanorods for Field-Enhanced Spectroscopy. Phys. Rev. B 2005, 71. (53) Li, A.; Li, S. Large-Volume Hot Spots in Gold Spiky Nanoparticle Dimers for High-Performance Surface-Enhanced Spectroscopy. Nanoscale 2014, 6, 12921−12928. (54) Dodson, S.; Haggui, M.; Bachelot, R.; Plain, J.; Li, S. Z.; Xiong, Q. H. Optimizing Electromagnetic Hotspots in Plasmonic Bowtie Nanoantennae. J. Phys. Chem. Lett. 2013, 4, 496−501. (55) Malinsky, M. D.; Kelly, K. L.; Schatz, G. C.; Van Duyne, R. P. Nanosphere Lithography: Effect of Substrate on the Localized Surface Plasmon Resonance Spectrum of Silver Nanoparticles. J. Phys. Chem. B 2001, 105, 2343−2350. (56) Wu, Y. P.; Nordlander, P. Finite-Difference Time-Domain Modeling of the Optical Properties of Nanoparticles near Dielectric Substrates. J. Phys. Chem. C 2010, 114, 7302−7307. (57) Noguez, C. Surface Plasmons on Metal Nanoparticles: The Influence of Shape and Physical Environment. J. Phys. Chem. C 2007, 111, 3806−3819. (58) Hu, M.; Ghoshal, A.; Marquez, M.; Kik, P. G. Single Particle Spectroscopy Study of Metal-Film-Induced Tuning of Silver Nanoparticle Plasmon Resonances. J. Phys. Chem. C 2010, 114, 7509−7514.

(59) Okamoto, T.; Yamaguchi, I. Optical Absorption Study of the Surface Plasmon Resonance in Gold Nanoparticles Immobilized onto a Gold Substrate by Self-Assembly Technique. J. Phys. Chem. B 2003, 107, 10321−10324.

27538


Dependence of Plasmonic Properties on Electron Densities for

Recommend Documents