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Plasmonic Horizon in Gold Nanosponges Cynthia Vidal, Dmitry Sivun, Johannes Ziegler, Dong Wang, Peter Schaaf, Calin Hrelescu, and Thomas A Klar Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b04875 • Publication Date (Web): 16 Jan 2018 Downloaded from http://pubs.acs.org on January 16, 2018
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Nano Letters
Plasmonic Horizon in Gold Nanosponges Cynthia Vidal,† Dmitry Sivun,† Johannes Ziegler,† Dong Wang,‡ Peter Schaaf,‡ Calin Hrelescu,† and Thomas A. Klar†,*
† Institute of Applied Physics, Johannes Kepler University Linz, 4040 Linz, Austria ‡ Institute of Materials Engineering and Institute of Micro- and Nanotechnologies MacroNano, Technische Universität Ilmenau, 98693 Ilmenau, Germany
*
[email protected] ABSTRACT: An electromagnetic wave impinging on a gold nanosponge coherently excites many electromagnetic hot-spots inside the nanosponge, yielding a polarization dependent scattering spectrum. In contrast, a hole, recombining with an electron, can locally excite plasmonic hotspots only within a horizon given by the lifetime of localized plasmons and the speed carrying the information that a plasmon has been created. This horizon is about 57 nm, decreasing with increasing size of the nanosponge. Consequently, photoluminescence from large gold nanosponges appears unpolarized.
KEYWORDS: Plasmonics, nanosponges, event horizon, single particle spectroscopy, dark field scattering, fluorescence.
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Randomly percolated metal-dielectric thin films have been studied in detail within the last fifteen years as they are easily fabricated and allow for localizing electromagnetic energy to hot-spots substantially below the diffraction limit in free space.1 Applications include surface enhanced Raman scattering, fluorescence manipulation, sensing, and nonlinear photonics.2, 3 It has been thoroughly investigated to what extent these hot-spots are individual, localized entities or whether they are coherently linked together and hence form extended modes of hotspots.4, 5 So far, most work has been concentrated on two dimensional (2D) percolation. Only recently, three dimensionally (3D) percolated nanoparticles, so called gold (Au) nanosponges, with Au and air filaments below 20 nm in diameter, became available.6 Figure 1(a) shows an SEM image and Figure 1(b) a FIB cross cut of a gold nanosponge, proving that 3D percolation occurs throughout the whole nanosponge and the inside porosity is similar to the surface porosity. It was found that scattering from individual Au nanosponges shows a decisive dependence on polarization, despite a circular circumference,7 which means that an isotropic effective dielectric permittivity as suggested for nanoporous gold8 cannot be used for Au nanosponges. Numerical simulations showed that the three dimensional percolation pattern needs to be respected to determine the polarization sensitive scattering response and that hotspots exist throughout the interior of the Au nanosponges.7 Therefore, Au nanosponges pave the way to extend the research on 2D metallic percolation films into the third dimension. In this Letter, we address the differences in exciting hot-spots inside the Au nanosponges either from outside via a plane wave or from inside via a point-like dipole source. Both considerations are most relevant for applications of hot-spots: For instance in case of Raman enhancement, a plane wave excites a hot-spot which transiently excites a nearby molecule. After an inelastic scattering process, the molecule acts as a local source, again using the hot-spot as an amplifier for the outgoing wave. The same holds for plasmonically enhanced nonlinear processes where light from outside excites hot-spots which promote frequency conversion.2,
3
Subsequently,
frequency converted light out of the hot-spots couples to a propagating wave. One might argue, that (i) an incoming plane wave creating a local hot-spot or (ii) a locally excited hot-spot coupling to an outgoing wave are reciprocal or both are time-reverted problems.9,
10
Unfortunately, plasmons are lossy in the visible spectral range and hence these two situations are not equivalent. As we will show, local emitters cannot coherently excite the whole entity of hot-spots throughout a Au nanosponge larger than approximately 120 nm in diameter. The 2 ACS Paragon Plus Environment
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Figure 1. (a) SEM and (b) FIB cross cut of a gold nanosponge showing similar surface porosity and inside percolation patterns. (c) Unpolarized PL spectrum from another gold nanosponge. information of the local creation of a hot-spot can only propagate with a finite speed. Consequently, this information cannot reach the other end of the Au nanosponge within the limited lifetime of a plasmon if the Au nanosponge is too large, and the ensemble of hot-spots cannot be excited as a whole. In this sense, the finite distance over which the information of the local creation of a hot-spot is transmitted, resembles a plasmonic horizon. For this reason, photoluminescence (PL) originating from dipoles mutually outside of each other’s plasmonic horizons adds up to unpolarized PL, even for elongated nanosponges. In the case of 2D percolated films, hot-spots are readily accessible via a range of experimental techniques such as near field microscopy,11-14 localization microscopy,15 or photoemission electron microscopy.16 In the case of 3D percolated nanostructures, one may “look into” the structure using numerical simulations, but experimental access is intrinsically difficult. Nevertheless, one kind of nanolocal “light bulb” exists: The excitation of a localized plasmon via the recombination of a hole in the d-band with an electron in the sp-band.17-20 Boyd et. al. 21 and others
22-25
showed that, compared to bulk gold, the quantum efficiency is enhanced by
many orders of magnitude due to localized plasmons on rough surfaces or on nanoparticles. For excitation energies less than required for a d-band excitation, intraband excitation24 or possibly an electron excited to a virtual state and subsequently recombining with an sp-hole26 lead to PL. In any case, electron-hole recombinations are practically localized to one unit cell of the gold crystal, and resemble the most local way of exciting a plasmonic hot-spot inside a Au nanosponge. The hot-spot will subsequently decay radiatively with a finite quantum yield. Naturally, this PL signal will give only indirect information on the spatial pattern of hot-spots created inside a Au nanosponge, however, the degree of its polarization is an important experimental evidence. 3 ACS Paragon Plus Environment
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Figure 2. (a)-(c) SEM images (scale bars 100 nm) and polarization dependent scattering spectra of Au nanosponges, two almost spherical with diameters of 115, and 155 nm (a,b, respectively) and one with lateral dimensions of 410 and 195 nm (c). (d)-(f) Corresponding PL spectra. The legend in (d) gives the color coding of the polarization, valid for all panels. Further experimental data is shown in the Supporting Information. Here, we study the PL of Au nanosponges, fabricated via solid state de-wetting of metallic bilayers and dealloying.6 The Au nanosponges were transferred onto an indium tin oxide (ITO) covered glass slide. This allows taking scanning electron microscope (SEM) images, as well as scattering and PL spectra from one and the same individual Au nanosponge in a dark-filed / fluorescence confocal setup (details are shown in the Supporting Information). The scattering spectra were corrected for background, instrument response function, and the excitation source spectrum. Alternatively, the same Au nanosponge was excited by a linearly polarized, continuous wave 405 nm laser and the PL spectrum was recorded. For polarization sensitive measurements, a polarizer in the detection beam path was stepped by 20° from 0◦ to 160◦. We normalized the PL spectra to their spectral integral, in order to account for any residual polarization from the excitation, as observed in the PL from spherical Au nanoparticles, where the d-band holes were excited with linearly polarized light.27, 28 An example of PL from a Au nanosponge, recorded without a polarizer, is shown in Figure 1(c). As the major spectral weight
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of PL is in the range between 500 and 800 nm, we concentrate on this spectral range (for scattering spectra up to the IR, see Vidal et al.7). Figure 2(a-c) shows the polarized scattering spectra and the respective SEM images of three individual Au nanosponges, two with a rather spherical outer envelope and diameters of 115 and 155 nm, and one nanosponge with an elongated profile with a long axis of 410 nm and a short axis of 195 nm. Strong polarization dependence is observed in the scattering spectra, even for the spherical Au nanosponges, due to their highly inhomogeneous internal structure.7 Figure 2(d-f) shows the corresponding polarization dependent PL spectra. In case of the smallest Au nanosponge, the polarization dependence of the PL spectra (Figure 2(d)) is clearly influenced by the polarization dependence of the scattering spectra (Figure 2(a)), apart from a well-known overall blue shift.24, 28, 29 In stark contrast, the PL of the larger, 155 nm sized Au nanosponge (Figure 2(e)) shows much less polarization dependence, while its scattering spectra (Figure 2(b)) show quite strong polarization dependence. Even more so, the large non-spherical Au nanosponge shows, as expected, polarization dependent scattering spectra (Figure 2(c)), but an almost unpolarized PL (Figure 2(f)). This observation is quite surprising because the polarization dependence of the PL from solid Au nanorods usually follows the polarization dependence of their scattering spectra.29-32 In order to quantify the degree of polarization of the scattering and the PL spectra of each Au nanosponge further, the integrated polarization anisotropy ( x +150) nm
2 I (80°) − I (0°) ) d λ ( ( x −150) nm
A=∫
(1)
was calculated. λ is the wavelength and I(θ) are the polarization dependent PL or scattering spectra at the polarization angle θ. Integration was carried out over a window of 300 nm around a central wavelength of x nm of the respective PL and scattering spectra so that the major spectral emission was covered in each case. The PL and scattering spectra were normalized to their integral before calculating eq.(1). As reference, the experimental PL anisotropy of a smooth Au film (c.f. Supporting Information) yielded A = 1.3×10−6, representing the error of measurement. From the SEM images, we picked 14 Au nanosponges with similar porosity. The average sizes
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Figure 3. Polarization anisotropy for scattering and PL of individual Au nanosponges determined according to eq. 1. The average nanosponge size refers to the diameter averaged over the lateral principle axes of the nanosponges. ranged from 115 to 300 nm. The polarization anisotropies for PL and scattering are shown in Figure 3. The magenta shaded corridor encompasses all scattering anisotropies (Ascat), the blue shaded corridor those of the PL (APL). In case of the largest Au nanosponges, the scattering anisotropy ceases as expected. With increasing size, the strong influence of the unique inner percolation starts to vanish and nanosponges could be considered as a homogeneous effective medium (note that an effective medium not only requires that the sub-structure of the components is small compared to the wavelength, but also that the dimension of the medium itself is at least on the scale of the wavelength). However, the PL anisotropy ceases much faster with increasing size. For most of the Au nanosponges larger than 120 nm, the polarization anisotropy of the scattering spectra is larger than the polarization anisotropy of the PL. In addition, the particle-to-particle variations are much larger for the scattering than for the PL as reflected by the widths of the magenta and the blue corridors, respectively. (These are real particle-to-particle variations as the error of measurement for A is 1.3×10-6.) Only Au nanosponges smaller than 120 nm in diameter show large PL polarization anisotropy. In particular, APL is up to 10 times stronger for small Au nanosponges than for large ones. The polarization dependence of light scattering from Au nanosponges has been assigned to their individual interior percolation, which yields a unique pattern of hot-spots throughout the Au nanosponge.7 Conversely, the PL from gold has been found to be decisively related to localized plasmons.21 If now both the scattering and the PL from one and the same Au nanosponge show such differences as shown in and discussed for Figs. 2 and 3, we conclude that the localized plasmons, excited by a plane wave from outside or by an inside nanolocal 6 ACS Paragon Plus Environment
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Figure 4. Numerically calculated distribution of the E fields through a cross-section (red plane) inside Au nanosponges, excited by an external plane wave (scheme a, left column) or by an inside dipole (scheme b, right column). The diameters are 90 (c.d), 115 (e.f) and 195 nm (g,h). (c,e,g) Plane wave excitation, and (d,f,h) inside point dipole excitation. The dipole positions are indicated by small white circles. More examples are shown in the Supporting Information. dipole must be decisively different. In order to investigate the implications of different modes of excitation, simulations were performed using the finite difference time domain solver Lumerical Solution. Similar as in Ref. 7
, Au nanosponges were emulated on an ITO substrate as Au half-spheres, perforated by
randomly distributed air spheres, allowed to overlap by 20% in all directions. This permits the formation of intertwined air filaments and hence adequately imitates the 3D Au-air percolation of the nanosponges. White light excitation was modeled by an external incoming plane wave (blue arrow in Figure 4(a)), while a electron-hole recombination was modeled by an internal electric dipole source (blue double arrow in Figure 4(b)). In both cases, a temporally defined 7 ACS Paragon Plus Environment
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excitation with a Gaussian envelope of 3.3 fs full width half maximum was applied. A dielectric permittivity according to Johnson and Christy33 was used (more details can be found in the Supporting Information). The absolute value of the total electric fields within three Au nanosponges of 90, 115 and 195 nm diameter is shown for external plane wave illumination (left column, Figure 4 (c,e,g)) and for excitation by an internal dipole (right column, Figure 4(d,f,h)). The fields were evaluated in the planes where the dipole was located (red planes in Figure 4(a,b)). Assuming coordinate systems with the origin of the vertical (z) axis at the nanosponge/ITO interface and the lateral origin in the center of the half-spheres, the dipoles were located at the positions (given in nm): (-7,-0.5,20); (-7,-0.5,20); (-1,21,34) in case of the 90, 115, and 195 nm sized nanosponges, respectively. In all cases, the polarization was in the x-direction (for other locations and polarizations see the Supporting Information). All images are taken 10 fs after the peak of the excitation, which is three times longer than the full width at half maximum of the pulsed excitation. This ensures that only the scattered fields are shown (without the incident field) and it avoids divergences at the dipole locations in case of the PL simulations.34 Figs. 4 (c) and (d) show the distribution of the excited plasmonic hot-spots inside the small (90 nm) nanosponge for plane wave and for internal excitation, respectively. In both cases, hotspots throughout the whole volume of the nanosponge are excited in a similar way. The situation becomes markedly different in the case of the 115 nm nanosponge. While the plane wave from outside again excites a pattern of hot-spots throughout the nanosponge (Figure 4(e)), the local dipole emitter cannot excite all the hot-spots anymore (Figure 4(f)). In case of the largest nanosponge, the failure to excite hot-spots with a local dipole throughout the Au nanosponge is even more pronounced, see Figure 4(g,h). Apparently, and in contrast to plane wave excitation, a plasmonic horizon of about 57 nm is formed via local excitation from inside the nanosponge. We would like to note that the dimension of the plasmonic horizon is similar to the coherence length of around 50 nm, typically found in simulations of 2D percolated metallic films at the percolation threshold.5 It is beyond the scope of this Letter to discuss whether this is by chance of whether there is a physical reason. Twice the plasmonic horizon also fits the nanosponge size up to which a significant PL anisotropy is experimentally observed (Figure 3). This can now be explained with the results 8 ACS Paragon Plus Environment
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from simulations. For small nanosponges, there is only a limited number of anisotropic modes, extending over the whole nanosponge. Both a plane wave from outside or a local inside dipole excite similar modes (Figure 4(c,d)) and hence scattering7 and PL anisotropies are high. For large nanosponges, there are many more anisotropic modes that do not span the whole nanosponge when excited from a local, inside dipole (Figure 4 (f,h)). The PL, stemming from the modes of restricted volume will certainly show decisive polarization dependence, the same way as PL from a small Au nanosponge is polarized. However, modes localized elsewhere in a large Au nanosponge, excited by a subsequent electron-hole recombination outside the coherence volume of the previous event, will show a different polarization pattern. Each single event is polarized, but the total PL signal is made up from photons stemming from uncorrelated volumes and the PL appears unpolarized. In contrast, in the case of the scattering experiments, excitation from outside is apt to coherently excite the whole pattern of hot-spots throughout the nanosponge (Figure 4g) and hence the scattering is polarized7 (see also additional simulations in the Supporting Information). In most previous reports, where a polarization dependent PL was measured, e.g. from solid Au nanorods, the dimensions were below 120 nm,29-31 a size range where also Au nanosponges show polarized PL. In case of larger solid Au bipyramids,32 polarized PL was found as well. This does not contradict our findings shown in Figure 3 because solid Au bipyramids possess only three orthogonally polarized radiating dipolar modes. Local excitation will couple to those delocalized modes with different quantum efficiency depending on where the local emitter is located,20 but PL will be polarized. Instead, percolated metal shows a multitude of more or less dipole active hot-spot modes,4 which will add up incoherently in larger nanosponges. In previous theoretical work on Au bipyramids,35 reporting on plane wave versus local (yet external) plasmon excitation, results were evaluated in frequency domain such that a plasmonic horizon due to the limited plasmon lifetime remained elusive. This holds as well for the work by Zhou et al.36 who simulated local excitation of rods. Nevertheless they found that breaking of the rod symmetry influences the emission spectrum. Time domain simulations include implications by the finite plasmon lifetime due to radiative and nonradiative losses. Our simulations reveal plasmon ring-down times which decrease with increasing size of the nanosponges, specifically we get 7.9, 6.7, and 5.3±0.2 fs, for the 90, 115 and 195 nm Au nanosponges, respectively (c.f. Supporting Information). This decrease in ring9 ACS Paragon Plus Environment
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down time can be explained either by an increased radiation damping due to the increasing sizes of Au nanosponges37 or by increased nonradiative damping as the increased amount of gold around of the hot-spots may quench luminescence.38 Alternatively, a plasmon lifetime of 5.8±0.5 fs can be experimentally deduced for a nanosponge of 115 nm by fitting multiple Lorentzians to the experimental spectra and converting the widths to time.37, 39, 40 The central implication of this time-domain consideration is the following: The information, that a localized plasmon has been created by a local electron-hole recombination event, can propagate to coherently excite neighboring hot-spots only within the lifetime of the plasmon. This limited lifetime, together with a finite speed with which the information can travel, results in a plasmonic horizon. Taking an average lifetime of 6.3 fs (for 115 nm Au nanosponges) and an event horizon of 57 nm, one ends up with a speed of information propagation of v = 9.0 × 106 m/s. This velocity is about 6 times larger than the Fermi velocity of sp-electrons in bulk Au (vF = 1.4 × 106 m/s). It is reasonable that both velocities are on the same order of magnitude, because inside the gold it is the electrons that carry the information that a localized plasmon has been created. It is also reasonable that v > vF because the information inside a Au nanosponge travels only partially in metal, and partially in air, transported by 100 times faster electromagnetic waves. Further, comparing the panels (d), (f) and (h) in Figure 4, one notices that the volume, within which a local dipole is apt to excite hot-spots, decreases with increasing diameter of the nanosponge, which means that the plasmonic horizon shrinks, consistently with decreasing ring-down times. In summary, we have shown that the PL from large Au nanosponges is almost unpolarized while the scattering spectra are polarized. Only in the case of small Au nanosponges with radii 60 nm or less, the PL spectra are polarized, as well. PL from gold is a stepwise process where first an electron-hole recombination locally excites plasmonic hot-spots which then decay radiatively. Within the typical lifetime of localized plasmons in gold, it is impossible to couple all hot-spots throughout a large Au nanosponge coherently. Several d-hole recombination events from different places throughout a Au nanosponge form independent, local patterns of hot-spots, each of the size of a plasmonic horizon of less than 60 nm, which, in the end, yields unpolarized PL spectra. Our results on the distribution of hot-spots are relevant for all fields of applications of hot10 ACS Paragon Plus Environment
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spots, such as Raman scattering,41, 42 infrared absorption, bio-sensing and nonlinear optics,2, 3 specifically because the holes percolate throughout the Au nanosponges and hence organic molecules may access the hot-spots easily. Our findings may also affect fundamental considerations such as plasmonically enhanced coherence of thermal radiation,43 or plasmonic focusing beyond the diffraction limit using time reversal.9 Recently, complimentary experiments using photo-electron emission from single nanosponges have been reported on large nanosponges with optical response in the near IR.44
ASSOCIATED CONTENT Supporting Information Available: More details on the experimental setup; additional examples of polarization dependent scattering and PL spectra; details on the numerical simulations; ringdown times of plasmon resonances and additional examples of field distributions. This material is available free of charge via the Internet at http://pubs.acs.org.
ACKNOWLEDGMENT The authors would like to thank Heidi Piglmayer-Brezina and Günter Hesser for technical support on SEM and FIB. This work was financially supported by the European Research Council (ERC Starting Grant 257158 “Active NP”) and Deutsche Forschungsgemeinschaft (DFG, Grant SCHA 632/24).
AUTHOR INFORMATION Corresponding author *
[email protected] NOTES The authors declare no competing interest. 11 ACS Paragon Plus Environment
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