Size Dependence of the Plasmonic Near-Field Measured via Single

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Size-Dependence of the Plasmonic Near-Field Measured via Single-Nanoparticle Photoimaging Claire Deeb, Xuan Zhou, Jerome Plain, Gary P. Wiederrecht, Renaud Bachelot, Milo J. Russell, and Prashant K. Jain J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp4020564 • Publication Date (Web): 01 May 2013 Downloaded from http://pubs.acs.org on May 5, 2013

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The Journal of Physical Chemistry

Size-Dependence of the Plasmonic Near-Field Measured via Single-Nanoparticle Photoimaging Claire Deeb,1,† Xuan Zhou,1 Jérôme Plain,1 Gary P. Wiederrecht,2 Renaud Bachelot1,* 1Laboratoire

de Nanotechnologie et d'Instrumentation Optique LNIO-CNRS UMR 6279, Université de Technologie de Troyes, Troyes, France

2Center

for Nanoscale Materials, Argonne National Laboratory, Argonne IL 60439 United States

Milo Russell,3 Prashant K. Jain,3,4,* 3Department

of Chemistry, University of Illinois Urbana Champaign, Urbana IL 61801 United States

4Department

of Physics, University of Illinois- Urbana Champaign, Urbana IL 61801 United States

1 ACS Paragon Plus Environment


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Abstract

Plasmonic nanostructures are being exploited for optical and photovoltaic applications, particularly where field enhancement of optical processes is desirable. Extensive work has focused on the optimization of plasmonic near-fields by geometric tuning and inter-particle coupling, but the size tunability of near-fields has received less attention. We used single-nanoparticle photochemical imaging to characterize the near-field intensity around a plasmonic nanoparticle as a function of size. The measured near-field intensity increases with nanoparticle size, reaching a maximum at a size of 50 nm, followed by a decrease at larger sizes. An electrodynamic model explains both the measured size-dependence and the optimum size for field enhancement. Whereas intrinsic damping is size-independent, the smallest nanoparticles exhibit weak fields due to surface damping of electrons. On the other end, larger nanoparticles show low field enhancement due to strong radiative scattering. The measured volcano trend, however, most closely mirrors the sizedependence of electromagnetic retardation. Above 50-nm size, retardation causes damping, but below a size of 50 nm, it surprisingly reduces non-radiative dissipation, a previously unknown effect. The size-dependence of plasmonic field intensity described here can guide design of plasmonic nanostructures for applications in spectroscopy, photovoltaics, photocatalysis, and lithography.

Keywords: surface plasmon resonance, nanostructure, surface damping, radiative scattering, retardation, near-field photopolymerization


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Introduction Plasmonic fields supported by noble metal nanoparticles are a topic of extensive investigation, especially the potential of employing these fields to amplify various forms of lightmatter interactions.1 Surface enhanced Raman scattering (SERS) is a classic example of such amplification, where enhancement factors of 104-108 have been found to result from strong electromagnetic near-fields.2-5 Further examples include efforts to employ plasmon resonances for enhancing otherwise weak non-linear optical, chiro-optical, and magneto-optical transitions.6-11 Plasmonic nanostructures are also being explored for improving light trapping in silicon photovoltaics. Plasmonic field-enhancement of the band-gap absorption of silicon may allow thinner films of silicon to be used in these devices.12,13 In addition, plasmon excitations are being exploited to drive photocatalytic reactions, both with and without semiconducting oxides.14 The mechanisms for plasmon-enhanced photocatalytic effects are as yet unclear, however strong field enhancements have been suggested to have a primary role.15 Optical and photovoltaic enhancements are expected, in principle, to depend directly on the intensity of the plasmonic near-field |Enf|2. It is therefore desirable that the nanoparticle support the most intense field. There has been extensive work on identifying nanoparticle geometries, such as sharp tips or nanoparticle junctions that exhibit the strongest possible field enhancements.16-20 Surprisingly, the size tunability of near-fields has not been characterized in as much detail, despite a few works on the topic of plasmon resonance lifetime and damping.21-25 In this paper, we elucidate the fundamental nanoparticle size-dependence of the plasmonic near-field. Prior knowledge about such size dependence was available either from electrodynamic models23,24 or indirect deductions from far-field measurements,21,22,25 but there has been no direct measurement of this important size dependence. Here, we present an experimental measurement of the near-field around a nanoparticle as a function of size. With the aid of our single-nanoparticle



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near-field measurements and electrodynamic theory, we characterize the size-dependence of nanoplasmonic near-fields and provide a physical model that can guide future nanostructure design. A dipolar quasi-static picture of plasmon resonances suggests size-independence of field enhancement, but our experiments show that near-field enhancement at the nanoparticle surface initially increases with nanoparticle size, reaching a maximum around 50 nm, followed by a reduction at sizes larger than 50 nm. We show using an electrodynamic model that this trend arises from the competitive interplay of non-radiative damping vis á vis radiative damping of the excited near-field. At small sizes, the near-field decay is dominated by non-radiative intrinsic and surface damping. At large sizes, radiative scattering dominates. A third factor, dynamic depolarization or electromagnetic retardation, plays a dual role: retardation causes damping of fields at large nanoparticle sizes (> 50 nm) as well known, but it reduces dissipation below 50-nm size, a surprising effect.21,23 As a result of the interplay of these three effects, intermediate-size nanoparticles, exhibit the most enhanced fields, with an optimal size of 50 nm for Au.

Methods Experimental In order to characterize the size-dependence of the near-field enhancement, we performed measurements of the near-field intensity around individual plasmonic nanoparticles by means of a quantitative nanometer-resolution photoimaging technique. In this technique, we exploit the localized near-field enhancement around the nanoparticle to structure a photopolymer,26-35 which results in a nanometer-scale imprint of the near-field around the nanoparticle. The field enhancement can be estimated from such an imprint.36-40 Our past polarization, orientation, and


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distance-dependence studies have confirmed that the photopolymerization results primarily from a plasmonic field enhancement,18, 36, 37 rather than due to effects such as heating or hot electron ejection, further confirmed by a control experiment (supporting information Fig. S1). Polarization dependence and the control experiment also eliminate the possibility of nanoparticle elongation resulting from their asymmetric melting rather than due to photopolymerization. We chose Au as a model system for this investigation. Au nanoparticles were synthesized using a seeded method from Murphy and coworkers.41 Starting from a seed solution of 12-nm diameter nanoparticles, the nanoparticles were grown to yield nine different sizes. The near-field photopolymerization imaging was carried out by means of AFM as described in previous studies.36,42 For the purpose of near-field imaging, the nanoparticles were dispersed onto aminefunctionalized glass substrates and precisely characterized using atomic force microscopy (AFM) before photopolymerization. The height of a nanoparticle measured in AFM was used as a measure of its diameter. AFM was also performed following photopolymerization in order to image the formed photopolymer. The formulation for the photopolymerization imaging was made up of three components: a sensitizer dye, a co-synergist amine, and a multifunctional acrylate monomer, pentaerythritol triacrylate (PETIA), which forms the backbone of the polymer network. PETIA was used as received from the supplier. The co-synergist amine was methyldiethanolamine (MDEA), and the Eosin-Y (2’,4’,5’,7’-tetrabromofluorescein disodium salt) was used as the sensitizer dye. This system has high sensitivity in the 450-550-nm spectral region. In the current study, we employed a mixture containing 0.5 wt % of Eosin-Y and 4 wt % of MDEA.



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Discrete Dipole Approximation Simulations The Discrete Dipole Approximation (DDA) method43 was used to simulate near-fields around resonantly excited nanoparticles. Briefly, DDA is a discretization procedure for solving the Maxwell’s equations for arbitrary shaped particles, which takes into account both electromagnetic retardation effects and multipolar modes.44 We employed the DDSCAT 7.1.0 code developed by Draine and Flatau. The Au nanoparticle was approximated as a sphere, represented by a cubic array of virtual point dipoles with an inter-dipole spacing of 1 nm. The radius of the sphere was varied as reff = 6, 12.5, 20, 25, 30, 35, 37.5, 40, and 42.5 nm. We employed the bulk experimental dielectric function for Au from Johnson and Christy49 and then size-corrected it to account for surface scattering of electrons as:45

(1)

where ωp is the bulk plasmon frequency taken as 1.36 x 1016 rad.s-1, γbulk is the electron collision frequency in bulk gold with a value of 1.1 x 1014 s-1, and is the size-corrected collision frequency calculated as:

(2)

υf is the Fermi velocity of gold electrons, i.e., 1.4 x 106 ms-1 and A is a theory-dependent parameter used to describe electron-surface scattering and may take values from 0 for no scattering to 1 for isotropic scattering.46 A value of 0.375 was considered for our calculations. The medium refractive index nm was set as 1.485 corresponding to the polymer/dye solution and the photopolymer. The imaginary part due to the dye absorption did not influence the calculated field enhancements and therefore was not included. Simulations were performed for a linearly polarized excitation of 532


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nm propagating along the x-direction and polarized along the y-direction with incident field amplitude Eo = 1. The DDFIELD routine was employed to obtain values of field amplitudes (Ex, Ey, Ez) and therefore the field intensity (E = Ex2+Ey2+Ez2) at various points in the y-direction along an axis passing through the center of the nanoparticle. The plot of the simulated field intensity as a function of distance from the center of the nanoparticle is shown for Au nanoparticles of different size in the supporting information (Fig. S2).

Results and Discussion Measurement of near-fields on single plasmonic nanoparticles Fig. 1A depicts an AFM image that shows individual Au nanoparticles before photopolymerization. Fig. 1B shows the AFM image of the same region after it was subject to irradiation with a linearly polarized 532-nm laser beam in the presence of a photopolymerizable solution. The excitation power was selected to be ¾th of Dth, a threshold light dose below which no polymerization occurs. If we assume that field enhancement alone (rather than other chemical or physical effects) dictates photopolymerization, then only those regions around the nanoparticle that experience a field enhancement of 4/3 or greater are above the polymerization threshold and can undergo polymerization. A differential image (after - before) clearly shows these photopolymerized regions (Fig. 1C). The latter represents a spatial map of the near-field excited around the nanoparticle. The differential procedure yields a noise and drift-free image.36 A line profile through the center of the nanoparticle in Fig. 1C reveals two peaks corresponding to the polymer lobes around the Au nanoparticle (Fig. 1D). The full-width of the peak (calculated as an average of both peaks) is a measure of the polymer thickness (t), which in turn is a measure of the field enhancement.



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Figure 1. Measurement of near-field intensity via photopolymerization-based imaging. (A) AFM image showing individual Au nanoparticles before photopolymerization. (B) AFM image of the same region after photopolymerization. The double arrow shows the polarization direction of the incident excitation beam. The Z-scale of the AFM images is shown on the left of the image. (C) Differential (after-before) AFM image showing photopolymer regions formed around the nanoparticle by means of near-field excitation. This polymer region constitutes a spatial map of the near-field excited around the nanoparticle. (D) Line profile through the center of the nanoparticle in panel (C) showing two peaks corresponding to the polymer lobes around the Au nanoparticle. The full width of the peak is a measure of the polymer thickness, from which the near-field intensity can be deduced. Scale bar in (A) and (B) is 70 nm.

Near-fields decay rapidly, i.e., near-exponentially, with distance away from the surface of a nanoparticle.40

The higher the field enhancement

| |

at the surface of the nanoparticle, the

greater is the “depth” of the photopolymerization away from the nanoparticle surface. The polymer


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thickness t is essentially the distance from the surface of the nanoparticle at which the field enhancement is equal to 4/3.

Size-Dependence of Measured Near-Field Enhancement Taking advantage of our single-particle photoimaging technique,18,36,37 we measured the photopolymer thickness t for individual nanoparticles of different size. Individual nanoparticles with diameters ranging from 12-86 nm were tested under the same conditions of 532-nm linearly polarized excitation at a fluence of ¾th the polymerization threshold. Fig. 2A shows the measured photopolymer thickness t as a function of the nanoparticle diameter. Each data point is a mean of measurements for up to three individual Au nanoparticles with a diameter similar to within 2% (see supporting information). Only nanoparticles exhibiting a high degree of circularity in the AFM images were selected so as to minimize effects resulting from differences in particle shape. The photopolymer thickness t, which is an experimental measure of the field enhancement, increases with increasing nanoparticle size, until it reaches a maximum at a size of 50 nm, beyond which it decreases. We refer to this trend in the following discussion as the volcano trend, owing to its inverted-V shape. Such a volcano size trend has been observed for plasmon lifetimes measured in sodium clusters.21 Note that at the smallest nanoparticle size of 12 nm, t is 0, implying that photopolymer thickness is smaller than the resolution limit of our technique, which we have established in a past study to be < 2 nm.37



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Confirmation of Size-Trend by Electrodynamic Simulations As further confirmation of our experimentally observed trend, we estimated the polymer thickness t from electrodynamic simulations of the near-field (see supporting information Fig. S2). The simulated polymer thickness values (Fig. 2B) are in the same range as those measured experimentally. Secondly, the simulated polymer thickness follows a similar volcano plot, with a maximum at a diameter of 50 nm.

Figure 2. Size-dependence of near-field enhancement. (A) Thickness of formed photopolymer, t as a function of nanoparticle diameter d. Each data point is a mean value deduced from measurements of up to three individual Au nanoparticles. Vertical error bars represent the standard deviation in the thickness measurement and horizontal error bars represent the worstcase precision (±2 nm) in measuring the diameter. The photopolymer thickness, which is an experimental measure of the near-field intensity around the nanoparticle, shows a volcano trend with respect to diameter, with a maximum around a diameter of 50 nm. (B) Polymer thickness simulated by electrodynamics shows a volcano-type size-dependence, similar to the experimentally observed trend. The excitation wavelength was 532 nm for all diameters, both in experiments and simulations. Both experiment and simulations indicate a maximum in polymer thickness at a size of 50 nm.


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Apart from field enhancement, several other chemical and physical effects are expected to influence photopolymerization in the vicinity of the excited nanoparticle, including perturbation of the chemical and electronic structure of the dye via chemical adsorption, non-radiative quenching of the dye excited state by the metal surface, Purcell enhancement of radiative decay of excited state, and polymer shrinkage during development. It is possible that some of the aforementioned effects are size-dependent and therefore contribute to the observed trend. Probably the quantitative differences between the experimentally measured polymer thickness in Fig. 2a and simulated values in Fig. 2b result from the importance of aforementioned effects, in particular Purcell enhancement, quenching, and strong optical coupling between dye and nanoparticle, which are all expected to be size-dependent, but disregarded in our simple analysis based on a classical electrodynamic field picture. Nevertheless, good qualitative agreement of the measured size-trend with that obtained from electrodynamic simulations suggests that the plasmonic field enhancement effect dominates the observed size dependence. Also, it is important to note that the photopolymer thickness depends not only on the surface field enhancement but also on the distance the near-field extends out from the nanoparticle surface. As the diameter increases, the near-field penetrates a longer distance (in proportion to the diameter) away from the surface of the nanoparticle.40 The observed size-trend of the photopolymer thickness thus involves a convolution of the latter effect with the true sizedependence of the surface near-field enhancement. Whereas, our experiment cannot provide a direct measure of the near-field intensity at the surface, simulations of the surface near-field enhancement F as a function of size are shown in Fig. 3. Due to the longer field penetration distance for larger diameters, the surface field enhancement peaks at a somewhat smaller size as compared to photopolymer thickness (Fig. 3). Nevertheless the volcano size-trend persists.



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Figure 3. Near-field enhancement at the nanoparticle surface. The simulated near-field enhancement at the surface of the nanoparticle |!"# |/|!% |& plotted as a function of nanoparticle diameter. A volcano trend is seen with a maximum at a somewhat smaller size (i.e. 40 nm) compared to the optimal nanoparticle size for measured photopolymer thickness.

Theoretical model for size-dependence of the plasmonic field We provide a theoretical model that explains the experimentally measured size-dependence of the near-field enhancement. The excitation of plasmon resonances in a metal nanosphere is described by its dipolar polarizability: 47 *+*

' ( ) *&*,

,

(3)

where is the dielectric function of the metal, - is the medium dielectric constant, and R is the radius of the particle. The near-field amplitude at the surface of the nanoparticle resulting from plasmon excitation is therefore: !"# !% |1 /|

(4)

where


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0

*+*

/ 1 *&*,

(5)

,

Thus, in the dipolar quasi-static model of plasmon resonances, the near-field amplitude at the nanoparticle surface is independent of nanoparticle size, expressed as: )*

!"# 3*&*, 4 !%

(6)

,

However, some realistic finite-size effects are absent in this simple description.

Finite-size effects Plasmon oscillations excited in a metal nanoparticle and the resulting near-field get damped via different mechanisms. The first one involves non-radiative damping of the field. This is mainly via excitation of inter-band and intra-band transitions, constituting light absorption by the plasmonic nanoparticle. Non-radiative damping is included in the dielectric function of the metal via the electron collision rate :

5

(7)

where 5 and 6 are the high-frequency dielectric constant and bulk plasma frequency of the metal, respectively. Intrinsic damping (interband or intraband) has no size dependence. However, for small nanoparticles, in addition to these intrinsic damping mechanisms, collisions of electrons with the nanoparticle surface also leads to significant non-radiative damping. The total damping rate in small nanoparticles, where the surface/volume ratio is non-negligible, is therefore given as:48

(8)



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where is the inter-band damping rate, 7# is the Fermi velocity of electrons, and A is a phenomenological constant with a value between 0 and 1 describing the nature of scattering. As the nanoparticle size R becomes smaller, the total non-radiative damping rate reflected by increases as a result of the increase in the surface damping contribution. Two additional size-dependent effects also play a role in the decay of the near-field. One is the far-field radiation of light by the oscillating field, which constitutes plasmonic light scattering.25,49 The rate of radiative damping is known to increase with increasing nanoparticle size as 8. () where 8

:

is the wave-vector of the incident light. Another is the dynamic

depolarization effect exhibited by finite-sized nanoparticles, resulting from the phase retardation of the exciting field with respect to the nanoparticle.24 A realistic description for plasmonic near-fields around a metal nanosphere ought to include all three finite-size effects described above: surface scattering, dynamic depolarization, and radiative decay. While surface scattering is included via eq. (8), dynamic depolarization and radiative decay result in an additional radiation field,23

!;

& 1 ?@ )

(9)

which modifies the near-field. Here, ?@ is the induced dipole moment on the nanoparticle: ?@ '!% !;

Size Dependence of the Plasmonic Near-Field Measured via Single

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