Rhodium Tripod Stars for UV Plasmonics - ACS Publications

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Rhodium Tripod Stars for UV Plasmonics R. Alcaraz de la Osa,† J. M. Sanz,† A. I. Barreda,† J. M. Saiz,† F. González,† H. O. Everitt,‡,§ and F. Moreno*,† †

Group of Optics, Department of Applied Physics, University of Cantabria, Avda de Los Castros, s/n 39005 Santander, Spain Department of Physics, Duke University, Durham, North Carolina 27708, United States § U.S. Army Aviation and Missile RD&E Center, Redstone Arsenal, Alabama 35898, United States ‡

ABSTRACT: Local field enhancements produced by metal nanoparticles have been widely investigated in the visible range for common metals like gold and silver, but recent interest in ultraviolet plasmonics has required consideration of alternate metals. Aluminum and gallium are particularly attractive, but the native oxide that forms on them consumes the metal in the smallest nanoparticles and limits the usefulness of larger nanoparticles for applications that require contact with a bare metal surface. The widely used catalyst rhodium is a noble metal that forms no native oxide under normal atmospheric conditions and has recently been shown to exhibit UV plasmonic behavior. Here we analyze the plasmonic properties of the most easily synthesized rhodium nanoparticle shapes and sizes and compare them to other UV plasmonic metals. Of particular interest is the tripod star monomer and dimer, for which we show the dependence of the absorption cross-section and the local electric field intensity on the constituent size and shape of tripod arms, and the gap distance in dimers, in representative dielectric hosts. It is shown that rhodium nanoparticles are particularly compelling for UV plasmonic applications requiring nanoparticles smaller than 20 nm.

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INTRODUCTION In the growing field of nanoplasmonics, metal nanoparticles (NPs) are routinely used to alter the electromagnetic field from an external irradiation to produce strong local field effects through their localized surface plasmon resonances (LSPRs).1,2 Nanoplasmonics has traditionally used the noble metals gold (Au) and silver (Ag), as well as copper (Cu), limiting their operation to the visible (Vis) or near-infrared (NIR) spectral regions.3,4 Interest in extending nanoplasmonics into the ultraviolet (UV) spectral region is growing.5−7 Because Au, Ag, and Cu cannot operate in this region, the search is on for new metals.8−11 Much recent work has focused on aluminum (Al) and gallium (Ga), both of which are compelling because of their low cost, wide availability, high conductivity, lack of UV interband transitions, and compatibility with complementary metal-oxide semiconductor (CMOS) processing.5−7,9,12 However, Al suffers from the formation of a native oxide shell several nanometers thick,13 as do other promising UV plasmonic metals including chromium (Cr), indium, lead, magnesium, thallium, tin, and titanium.8,10 For small NPs, this oxide dramatically reduces the volume of metal. For an oxide of thickness T, the volume fractions of metal in a spherical NP of radius R and in a cubical NP of side S are fs = ((R − T)/R)3 and fc = ((S − 2T)/S)3, respectively. For Al NPs with R = S = 10 nm and T = 3 nm, fs is 34% and fc is only 6.4%. Indeed, it is unlikely that Al NPs smaller than this retain any metal as the © 2015 American Chemical Society

aggressive oxide rapidly converts the remaining metallic Al to aluminum oxide Al2O3. Ga and Cr are more attractive UV plasmonic metals because their native oxide is only a few monolayers thick, so fs = 73% and fc = 51% for R = S = 10 nm and T = 1 nm. However, Cr UV absorption efficiency is low,10 while Ga exhibits a solid−liquid phase transition near room temperature that benefits from the protective thin oxide coating14,15 but requires new approaches to fabrication.16 Oxide-free noble metals (or their alloys17) with good UV plasmonic performance would be even more compelling, especially for applications that require contact with a bare metal surface. A recent study developed a simple chemical method to fabricate sub-10 nm tripod-shaped stars of rhodium (Rh), which forms no native oxide,18 and demonstrated surface enhanced Raman spectroscopy (SERS) of 4-mercaptopyridine.19 More recently, the UV plasmonic properties of similar Rh tripod stars have been experimentally examined by means of SERS, surface enhanced fluorescence, and photoinduced degradation of p-aminothiophenol.20 These demonstrations indicate a need for a comprehensive theoretical investigation of Rh NPs to guide future experiments. Here we report a detailed numerical investigation of the plasmonic properties of Rh spheres, cubes, tripod monomers, Received: January 30, 2015 Revised: May 4, 2015 Published: May 4, 2015 12572

DOI: 10.1021/acs.jpcc.5b00983 J. Phys. Chem. C 2015, 119, 12572−12580

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The Journal of Physical Chemistry C

When necessary, the discrete dipole approximation (DDA) has also been employed, by means of the publicly available code DDSCAT 7.3.29 In order to calculate light absorption from exactly the same system as with the finite-element simulations, the target generation tool DDSCAT Convert30 allowed us to take a triangular mesh surface of the system and convert it to a volume-based dipole set that can be used by DDSCAT. System Description. We have performed finite-element simulations of several Rh nanostructures and have compared these with identical nanostructures composed of Ag or Al.10 All nanostructures have been illuminated with a monochromatic plane wave, with k contained either in the xz-plane (either P plane or plane of incidence) or in the yz-plane (S plane), under an AOI θ with respect to the z-direction, and with either P (E lying in the plane of incidence) or S (E perpendicular to the plane of incidence) polarizations. This geometry is illustrated in Figure 1 for a tripod dimer with aligned points separated by a

and tripod dimers smaller than 20 nm. Sharply pointed tripods are particularly suitable for sensing adsorbed molecules through SERS,21,22 especially in the strong interaction (hot spot) region between metallic NP dimers where single molecules have been detected in other metals.23,24 This investigation explores the dependence of UV LSPRs and dimer hot spots25,26 on the geometry, shape, dielectric environment, angle of incidence (AOI), and polarization of the incident radiation.

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THEORETICAL METHODS The electromagnetic interaction of light with the Rh NPs has been modeled by means of finite-element simulations. For easy implementation and reliability of the solution, we have chosen COMSOL Multiphysics 4.4.27 In particular, we used the RF Module that allows us to formulate and solve the differential form of Maxwell’s equations (in the frequency domain) together with the initial and boundary conditions. The equations are solved using the finite element method with numerically stable edge element discretization in combination with state-of-the-art algorithms for preconditioning and solution of the resulting sparse equation systems. A spherical region of embedding medium around the NP is also modeled, whose radius is larger than a wavelength. A perfectly matched layer (PML) domain is outside of the embedding medium domain and acts as an absorber of the scattered field. The mesh was fine enough as to allow convergence of the results: the maximum mesh size was at most λ/6. In order to evaluate the NPs up to the accuracy level of the skin depth, the maximum element size inside the NP was set around a tenth of the minimum skin depth over the spectral range, computed via28 δ=

1 k 0ℜ{ −ε }

(1) Figure 1. Diagram of a tripod star dimer. The arms of the stars have length l, width w, and height h. The dimer is illuminated by a monochromatic plane wave, with k contained either in the xz-plane (either P plane or plane of incidence) or in the yz-plane (S plane), under an AOI θ with respect to the z-direction, for either P (E lying in the plane of incidence) or S (E perpendicular to the plane of incidence) polarization.

where k0 is the free space wavenumber, ℜ denotes the complex real part, and ε= εr + iεi is the complex-valued relative permittivity. The incident power density S is defined as S=

|E(r )|2 2Zsm

(2)

where E(r,t) is the local electric field, and Zsm is the impedance of the embedding medium, calculated via

Zsm

Z = 0 nsm

variable gap distance no smaller than 1 nm to avoid corrections due to quantum mechanical tunneling.31 (The electron tunneling transmission vanishes when the gap is larger than ≈8 Å, see, e.g., Figure 2 in ref 32.) The tripods, whose arms are separated by 120°, have height h and a wedge-shaped cross section of length l and width w. Unless stated otherwise, the embedding medium is air and the plane of incidence is the P plane, with parallel incident polarization (PP incidence). The dielectric functions have been obtained from two sources in the literature: ref 33 for rhodium and aluminum (as well as for aluminum oxide Al2O3), and ref 34 for silver. Figure 2 plots the complex relative permittivity of these metals, and the inset plots the skin depth δ calculated from eq 1. Note that Ag and Rh are lossier than Al in the UV and have larger skin depths, but Rh exhibits UV plasmonic behavior while Ag does not because of its interband transition near 4 eV.35 Although metallic Al exhibits superior UV plasmonic properties, its native oxide has a deleterious effect,9,10 especially in NPs with 2R, L < 20 nm which contain very little metal. All calculations presented here include the Al native oxide (using a widely

(3)

Here Z0 = μ0c is the impedance of free space (with μ0 being the vacuum permeability and c the speed of light in free space), and nsm is the refractive index of the embedding medium. The absorption cross-section Cabs can be calculated as the integral of resistive losses over the NP’s volume, normalized to the incident power density S. The scattering cross-section Csca is derived by integrating the Poynting vector over an imaginary sphere around the NP, normalizing again to the incident power density S. The absorption and scattering efficiencies, Qabs and Qsca respectively, are defined through the expressions Q abs =

Cabs , G

Q sca =

Csca G

(4)

where G is the NP cross-sectional area projected onto a plane perpendicular to the incident beam (e.g., G = πR2 for a sphere of radius R). 12573


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contributions of shape and dielectric function for these metals, calculations are also presented for spheres and cubes with the same volume as the tripod (sphere radius R = 5.0335 nm, cube side L = 8.1139 nm). To reflect experimental conditions, calculations are performed for NPs embedded in air and in water (nsm = 1.33). Figure 3 shows the spectral electric field intensity averaged over the NP’s closed surface ⟨|E|2⟩ (left column) and the absorption cross-section Cabs (right column) for equivalent tripod stars, spheres, and cubes using the dielectric function of Rh (first row), Ag (second row) and Al + Al2O3 (third row). It is immediately obvious that the different metals have very different behaviors: Rh has broad UV response, Ag has a sharp response between 3−4 eV, and Al has almost no response at all because the oxide has consumed most of the metal. The sphere and cube generally have LSPRs at higher energies than the tripod stars, and the peaks red-shift up to 0.5 eV when the NPs are in water instead of air. Embedding in another dielectric host, such as ethanol, also produces a red-shift of similar magnitude.20 Starting with Rh (first row in Figure 3), its main feature is the existence of a single broad peak for all shapes, located in an interesting region between 3 and 7 eV. In this region, Rh keeps its metallic character with a sufficiently large negative real part of the relative permittivity ε. The broadband response is mainly due to the large imaginary part of ε, as shown in Figure 2. The LSPR of the equivalent sphere is deep in the UV, near 6.5 eV,

Figure 2. Real (solid lines) and imaginary (dashed lines) parts of the complex relative permittivity ε for Rh, Ag, and Al as a function of the incident energy. The inset shows the skin depth δ for all three metals in this spectral region, according to eq 1.

accepted surface oxide thickness of 3 nm9) to provide a realistic comparison, sometimes with dramatic consequences.

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RESULTS AND DISCUSSION Comparison of Rh, Ag, and Al in Simple Geometries. As a first step, we consider tripod monomers of Rh, Ag, and Al (including its 3 nm thick native oxide), illuminated with a plane wave under normal incidence (θ = 0°) with its electric field aligned along one of the arms of the star (PP incidence). The dimensions of the star match the experimentally realizable l = 10 nm, w = 5 nm, and h = 5 nm.19,20 To explore the relative

Figure 3. Spectral electric field intensity averaged over the NP’s closed surface ⟨ |E|2 ⟩ (left column) and absorption cross-section Cabs (right column) for equivalent tripod stars (l = 10 nm; w = h = 5 nm), spheres (R = 5.0335 nm), and cubes (L = 8.1139 nm) composed of Rh (first row), Ag (second row), and Al + Al2O3 (third row), illuminated under normal incidence and embedded either in air (solid lines) or water (dashed lines). 12574


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The Journal of Physical Chemistry C in agreement with the Fröhlich frequency36 of Rh (see eq 7). The cube LSPR occurs between the tripod star and the sphere, indicating that even though this is the dipolar regime, the shape of the NP is critical, as if the NP could be described by a shapedependent electric polarizability. Given that the three NPs have the same volume, these variations with shape occur because of the differing effective lengths over which the charges move. Notice that the spectra for all shapes converge at high energies (E → 10 eV) where the variation of the optical constants becomes less pronounced (see Figure 2). For Ag (second row in Figure 3), all activity happens below 4 eV because of its UV interband transition35 and the correspondingly larger εi above 4 eV, as shown in Figure 2. Indeed, the low absorption together with a strong negative εr cause Ag to be extremely sensitive to the shape below 4 eV. This becomes evident especially in the case of the Ag cube, where the corners induce higher multipolar charge distributions, even in the quasistatic limit.37,38 The equivalent sphere behaves like a point dipole, with an LSPR falling as expected near the Fröhlich frequency of Ag (around 3.5 eV). The tripod star shows mainly a dipolar mode, although higher modes also contribute in spite of the small size. For Al + Al2O3 (third row in Figure 3), only the equivalent sphere shows an actual plasmonic response, below 6 eV, redshifted with respect to the Fröhlich frequency of Al (close to 9 eV). This is the result of the competition between the effect of the native oxide shell and the concomitant shrinkage of the metallic core.39 The metal fractions in the sphere, cube, and tripod star are 6.6%, 1.8%, and 0%, respectively. Indeed, the tripod star case clearly shows that Al2O3 is purely responsible for the increasing absorption above 6 eV. Tripod Star Monomer. Geometry Study. Given the strong dependence of the optical response on the geometry of the NP, we now consider in more detail the dimensional dependence of the LSPR for an isolated tripod star monomer in order to provide physical insight and identify optimal geometries for experimentalists.19,20 Specifically, we vary the length (from 5 to 15 nm), width (from 1 to 10 nm) and height (from 1 to 10 nm) of the arms of the star, illuminated with a plane wave under normal incidence (θ = 0°) with its electric field aligned with one of the arms of the star (PP incidence). Figure 4 shows both near field intensity |E|2 maps and absorption efficiency Qabs spectra (eq 4) for tripod stars of several lengths (w = h = 5 nm). In Figure 4a, |E|2 is shown at the HeCd laser energy E = 3.82 eV (λ = 325 nm), where the LSPR is resonant for l = 10 nm. As the lengths of the arms are varied, the variation of the near field can be observed in two different planes (xy and xz). Figure 4b shows the absorption efficiency spectrum, and the resonant behavior found in Figure 4a for l = 10 nm at E = 3.82 eV is confirmed. The inset shows both the value (Qmax abs ; red circles, left axis) and the spectral position (Emax; blue squares, right axis) of the maximum of Qabs as a function of the length of the arm. The peak value of Qabs increases with increasing l until leveling off for large l as the absorption begins to grow linearly with NP cross-sectional area (maximum absorption efficiency for l = 13 nm). An analogous study was performed varying the width (l = 10 nm, h = 5 nm) and the height (l = 10 nm, w = 5 nm) of the arms of the star. This is shown in Figures 5 and 6 respectively. The absorption efficiency is fairly insensitive to width variations, reaching a maximum absorption efficiency for w = 3 nm but never changing much from Qabs = 1. By contrast, Qabs monotonically increases with increasing h, a natural conse-

Figure 4. (a) Logarithmic scale |E|2 images at E = 3.82 eV (λ = 325 nm) for tripod stars of three different arm lengths. (b) Spectral absorption efficiency Qabs for tripod stars of arm lengths varying from l = 5−15 nm (w = h = 5 nm). The inset shows both the value (Qmax abs ; red circles, left axis) and the spectral position (Emax; blue squares, right axis) of the maximum of Qabs as a function of the length of the arm.

Figure 5. (a) Logarithmic scale |E|2 images at E = 3.82 eV (λ = 325 nm) for tripod stars of three different arm widths. (b) Spectral absorption efficiency Qabs for tripod stars of several arm widths varying from w = 1−10 nm (l = 10 nm, h = 5 nm). The inset shows both the value (Qmax abs ; red circles, left axis) and the spectral position (Emax; blue squares, right axis) of the maximum of Qabs as a function of the width of the arm.

quence of the increasing absorption cross section with constant geometrical cross section for normal incidence illumination. In order to explain the spectral shifts observed when varying the different geometric parameters of the tripod star, consider surface modes in nonspherical NPs.36 As can be seen in Figures 4a, 5a, and 6a, electric fields are strongest at the sharp tips of the star: the lightning-rod effect.40 If the tip of the star may be approximated by a small, homogeneous ellipsoid of volume v, with the incident electric field parallel to one of the arms of the 12575


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Figure 7. Spectral position (Emax) of the maximum of Qabs as a function of the length (upper blue axis), width, and height (lower red axis) of the arm, taken from the insets of Figures 4b, 5b, and 6b, as well as calculated from the ellipsoidal approximation described in eq 7

proportional to the restoring force experienced by the displaced electrons on one side of the NP caused by the background of exposed positive ions on the other side.42 Consider the case in which the incident polarization drives electrons along the length of the arm. In that configuration, increasing the width or height of the arms increases the amount of charge driven by the incident electric field, but since their separation remains unchanged, the displaced electron gas experiences a larger restoring force and the resonance blue shifts to higher energy. A similar argument may be applied to polarization along the other dimensions of an arm. Orientational Averaging Study. In order to evaluate how the incident polarization affects the optical response of the tripod stars, consider first the response of a representative star with dimensions l = 10 nm, w = 5 nm, and h = 5 nm, averaged over all planar orientations. This represents two different but concomitant situations in which the NP plane is perpendicular to the incident radiation: either unpolarized incident light or randomly oriented stars with respect to the incident polarized electric field. In this analysis, the NP is illuminated with a plane wave under normal incidence (θ = 0°) in the P plane, the polarization angle is varied from 0° to 360° in the xy-plane, and all the responses are arithmetically averaged. Figure 8 shows the near field intensity |E|2 maps and spectra of both the electric field intensity, averaged over the NP’s closed surface ⟨|E|2⟩, and the absorption efficiency Qabs for P-, S-, and planar-averaged polarizations. The averaged near field intensity map clearly shows how all three arms of the star are excited by the incident plane wave. Despite the remarkable differences found in the near field intensity maps shown in Figure 8a, both ⟨|E|2⟩ and Qabs spectra are virtually insensitive to polarization, as seen in Figure 8b. The characteristic spectral red-shift of the near field with respect to the far field is clearly observed as well.43 Next, to mimic the common experimental configuration of NPs on a dielectric substrate, Figure 9a shows spectra of the absorption cross-section Cabs for tripod stars (l = 10 nm; w = h = 5 nm) on substrates of various refractive indices (1.5 and 2.0). These results clearly show how the substrate produces a red-shift and a weakening of the LSPR.10,44,45 Finally, consider NPs suspended within a liquid dielectric host like water or ethanol,20 in which case the orientational averaging should be performed over all three dimensions so that out-of-plane components must also be considered. These calculations employed the discrete dipole approximation (DDA) using the publicly available code DDSCAT 7.3.29 The total number of dipoles was N = 13455, and we used the same

Figure 6. (a) Logarithmic scale |E|2 images at E = 3.82 eV (λ = 325 nm) for tripod stars of three different arm heights. (b) Spectral absorption efficiency Qabs for tripod stars of arm heights varying from h = 1−10 nm (l = 10 nm, w = 5 nm). The inset shows both the value (Qmax abs ; red circles, left axis) and the spectral position (Emax; blue squares, right axis) of the maximum of Qabs as a function of the height of the arm.

star (as it is the case in Figures 4-6), then section 12.2 in ref 36 shows its polarizability may be written as ε − εsm α=v Lε + (1 − L)εsm (5) where ε is the relative electric permittivity of the NP, εsm is the relative electric permittivity of the surrounding medium, and L is a geometrical factor which may take any value from 0 to 1, given by (see, e.g., section 5.3 in ref 36) L=

lwh 2

∫0

∞

dq 2

(l + q)f (q)

(6)

with f(q) =((q + l2)(q + w2)(q + h2))1/2. There will be a resonance as a surface mode is excited at the frequency where the denominator of α vanishes: ⎛ 1⎞ ε* = εsm⎜1 − ⎟ ⎝ L⎠

(7)

For a sphere, L = /3, and ε* = −2εsm gives the Fröhlich frequency for which eq 7 is satisfied. Therefore, eq 7 is a guide to the whereabouts of peaks in absorption spectra of small ellipsoidal NPs. Figure 7 shows the spectral position (Emax) of the maximum of Qabs as a function of the length (upper blue axis) and width and height (lower red axis) of the arm, taken from the insets of Figures 4b, 5b, and 6b as well as calculated from the ellipsoidal approximation described in eq 7. The differences between the calculated Emax and the estimates from eq 7 plotted in Figure 7 may be explained in part through the latter assumption of ellipsoidal NPs when the tripod stars are modeled as wedge-shaped. Nevertheless, both predict a red shift of the absorption efficiency as the length of the arms is increased and a blue-shift as the width or the height of the arms is increased.41 A simple interpretation can also be constructed using a harmonic oscillator model of localized plasmonic excitations, where the resonance frequency is 1

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Figure 10. (a) Logarithmic scale |E|2 images at E = 3.82 eV (λ = 325 nm) for a wedge-shaped “extruded” and ellipsoidal-shaped tripod star (l = 10 nm, w = 5 nm and h = 5 nm), illuminated under normal incidence with P polarization in the P plane. (b) Spectral electric field intensity averaged over the NP’s closed surface ⟨|E|2⟩ (solid lines, left axis) and volume-normalized absorption cross-section Cabs/V (dotted lines, right axis) for both cases.

Figure 8. (a) Logarithmic scale |E|2 images at E = 3.82 eV (λ = 325 nm) for a tripod star (l = 10 nm, w = 5 nm, and h = 5 nm), illuminated under normal incidence in the P plane with either P, S, or planar averaged polarization. (b) Spectral electric field intensity averaged over the NP’s closed surface ⟨|E|2⟩ (solid lines, left axis) and absorption efficiency Qabs (dotted lines, right axis) for all cases.

Figure 11. (a) Logarithmic scale |E|2 images at E = 3.82 eV (λ = 325 nm) and (b) spectral absorption cross-section Cabs for tripod star dimers of several gaps, varying from 1 to 10 nm, illuminated under normal incidence with P polarization in the P plane (PP incidence). The inset of part b shows both the ratio of the peak value (red circles, left axis) and the spectral shift (blue squares, right axis) of Cabs with respect to that of the isolated case, as a function of the gap size.

Figure 9. (a) Spectral absorption cross-section Cabs for tripod stars (l = 10 nm; w = h = 5 nm) on substrates of various refractive indices. (b) Spectral absorption cross-section Cabs for an identical tripod star embedded in a dielectric host (nsm = 1.5), illuminated in the P plane with either P (PP) or S (PS) polarizations. Planar and volume averages are also plotted (calculated with DDSCAT 7.3). The spectrum for the PP polarization case obtained by COMSOL is also shown (dashed black line).

dielectric function of Rh.33 Because the geometrical crosssection of the tripod star varies when changing its orientation with respect to the incident radiation, the absorption crosssection was calculated for this analysis, not the absorption efficiency. Figure 9b plots the absorption cross-section spectra for a tripod star embedded in a dielectric host with nsm = 1.5, illuminated in the P plane with either P (PP) or S (PS)

polarizations. Planar and volume averages are also plotted. The results for PP, PS, and planar averaged polarizations follow the same polarization insensitive trend as in Figure 8b, although the peak for PS polarization is slightly weaker and blue-shifted (around 0.04 eV, or 5 nm) with respect to the PP polarization. The planar averaged polarization lies between them. A COMSOL calculation of the spectrum for PP polarization agrees well with the equivalent calculation using DDSCAT. 12577


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Figure 12. Spectral electric field intensity at the center of the gap |E|2 (solid lines, left axis) and absorption cross-section Cabs (dotted lines, right axis) for (a) P-polarized light in the P plane (PP), (b) S-polarized light in the P plane (PS), (c) P-polarized light in the S plane (SP), and (d) S-polarized light in the S plane (SS), for AOI θ = {0°, 30°, 60°, 90°}.

shape of an actual tripod star probably lies somewhere in between. Tripod Star Dimer. Varying the Gap. We now consider the tripod star dimer as shown in Figure 1. Figure 11 plots near field intensity |E|2 maps and absorption cross-section Cabs spectra as a function of gap spacing for tripod star dimers under normal incidence illumination and P polarization in the P plane (PP incidence). For this analysis, tripod parameters are chosen as l = 10 nm, w = 5 nm, and h = 5 nm, with the gap varying from 1 to 10 nm. As can be seen in Figure 11a, |E|2 is predictably concentrated at the center of the gap, increasing in strength and redshifting with decreasing gap size as shown in Figure 11b.46 Conversely, as the gap increases, Cabs tends to a value that is twice that of a single tripod monomer and matches its spectral position, as it should for two noninteracting monomers. Varying the Incidence. In order to analyze the influence of the AOI on the optical response of the dimer, we fixed the gap to 5 nm and sequentially varied the plane of incidence (P and S), the incident polarization (P and S), and the AOI θ, keeping all other parameters constant. Figure 12 shows spectra of the electric field intensity at the center of the gap |E|2 and the absorption cross-section Cabs for tripod star dimers (l = 10 nm, w = 5 nm, and h = 5 nm) of gap = 5 nm, illuminated under several incidence configurations. For the case of P-polarized light in the P plane (Figure 12a), the component of the field along the line connecting the tips decreases as the AOI increases, so both |E|2 at the center of the gap and Cabs decrease as θ increases. Interestingly, as the AOI approaches 90°, a new and stronger resonance appears deep in the UV (E > 6 eV), due to the charge oscillation along the shorter height dimension of the tripod star. By contrast, center gap |E|2 and Cabs do not depend on AOI for S-polarized light in the P plane (Figure 12b). Indeed, this polarization produces

However, the volume averaged polarization deviates from the planar behavior in two distinct ways. First, the primary absorption cross-section near 3.6 eV is smaller, indicating that the out-of-plane contributions to the absorption are smaller. However, the out-of-plane geometrical cross section is also smaller, and the ≈1.4 ratio of the planar and perpendicular geometrical cross sections is quite similar to the ratio of the averaged absorption cross sections seen in Figure 9b. Second, the broad peak deeper in the UV strengthens because of the increased contribution from charge oscillation along the height of the tripod star. As can be expected, this broad peak sensitively depends on the height of the tripod star, blue-shifted because h < l but red-shifting as h increases, just as it red-shifted for increasing l in Figure 4b. Boundary Shape Influence. In the previous section, variations in the critical dimensions of the tripod star were analyzed, especially their influence on the LSPR. Here, we assess the influence of the sharpness of the arms of the star by comparing wedge-shaped “extruded” arms with ellipsoidalshaped arms. Figure 10a shows near field intensity |E|2 maps of both stars. The ellipsoidal arms have more intense hot spots than the extruded arms because the tips of the ellipsoidal star are sharper. Figure 10b plots the spectra of the electric field intensity, averaged over the NP’s closed surface ⟨|E|2⟩, and the volumenormalized absorption cross-section Cabs/V for both stars. Regarding the latter, since both stars have the same geometrical cross-section, the volume of the tripod star with ellipsoidal arms is therefore smaller than for the extruded arms. Consequently, in Figure 10b the absorption cross-section spectra are normalized by star volume, not by star area, and the resulting Cabs/V spectra are almost identical. The sharper tips of the ellipsoidal star are also the reason for the larger ⟨|E|2⟩ as compared to the wedge-shaped extruded star, but the arm 12578


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The Journal of Physical Chemistry C much weaker resonances in the gap since |E|2 is concentrated near the rear tips instead of the gap tips. This concentration also causes Cabs to blue-shift with respect to PP incidence, as the charge distributions of both NPs act cooperatively to enhance the repulsive action in both NPs, thus increasing the resonance frequency.47 Concerning incidence in the S plane, P-polarized light again produces much weaker resonances in center gap |E|2, although the variation of Cabs with θ is similar to that of PP incidence with the corresponding blue-shift due to NP-NP interaction. Spolarized light in the S plane shows, as expected, no AOIdependent variation in center gap |E|2 and Cabs. The characteristic spectral red-shift of the near field with respect to the far field is clearly observed.43 Varying the Material. Finally, we compare the UV performance of Rh, Ag, and Al tripod star dimers with l = 10 nm, w = 5 nm, h = 5 nm, and a 5 nm gap, illuminated at normal incidence with P polarization in the P plane (PP incidence). Figure 13 plots both near field intensity |E|2 maps and center gap spectra of the electric field intensity |E|2 and the absorption cross-section Cabs. As can be seen in Figure 13, Ag cannot operate in the UV range due to its interband transition, and neither can Al because its aggressive native oxide converts all Al metal to Al2O3 at these dimensions. This, plus the fact that only Rh is known to form branched nanocrystals useful for enhanced gap hot spots,19 make Rh the most compelling metal for UV plasmonics with NPs smaller than 20 nm.

that shape and native oxides play a significant role, especially for sizes

Rhodium Tripod Stars for UV Plasmonics - ACS Publications

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