Measurement and Reduction of Damping in Plasmonic Nanowires

Jan 23, 2012 - ABSTRACT: We report on a spectroscopic study of surface plasmon damping and group velocity in polycrystalline silver and gold nanowires...
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Measurement and Reduction of Damping in Plasmonic Nanowires Primoz Kusar,* Christian Gruber, Andreas Hohenau, and Joachim R. Krenn Institute of Physics, Karl-Franzens-University, Universitätsplatz 5, 8010 Graz, Austria S Supporting Information *

ABSTRACT: We report on a spectroscopic study of surface plasmon damping and group velocity in polycrystalline silver and gold nanowires. By comparing to single-crystalline wires and by using different substrates, we quantitatively deduce the relative damping contributions due to metal crystallinity and absorption in the substrate. Compared to absorbing substrates, we find strongly reduced plasmonic damping for polycrystalline nanowires on quartz substrates, enabling the application of such wires for plasmonic waveguide networks.

KEYWORDS: Nanowires, surface plasmons, plasmonics, plasmon damping, metal crystallinity, nanowire photonics

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smaller, as due to sufficiently small SP wavelengths, no leakage radiation occurs.5,13 SP scattering at metal roughness along the wire in the case of lithographed nanowires usually plays a minor role due to the small roughness dimensions on the order of 1− 2 nm. The rather weak impact of roughness on damping has been recently reported for the case of radiative SP modes in nanoparticles.14 In this Letter, we probe the SP modes in silver and gold nanowires by scattered light spectroscopy and deduce quantitatively the relative damping contributions due to, first, the metal crystallinity and, second, the type of the supporting substrate, optically absorbing or nonabsorbing. Therefore we investigate chemically synthesized and lithographically tailored nanowires of single- and polycrystalline morphology, respectively, supported by either quartz or indium−tin-oxide (ITO) covered glass substrates. By the analysis of the spectral signatures, we retrieve the spectrally dependent damping of the nanowire plasmons and reconstruct the SP dispersion. Furthermore, we show that despite their relatively strong damping lithographically fabricated polycrystalline nanowires can be applied for plasmonic waveguide networks, which considerably widens the range of potential nanowire applications. For the chemical synthesis of silver nanowires, we reduce AgNO3 with ethylene glycol in the presence of poly(vinyl pyrrolidone).15 The particular method we use is described in ref 16 and relies on FeCl3 to control the nanowire growth. The process yields (quasi) single-crystalline wires with diameters of 60−100 nm and lengths of up to 40 μm. For our experiments

etal nanostructures sustaining surface plasmon (SP) excitations are basic building blocks for nanophotonic systems and show promise for applications in, e.g., optical sensor devices, photovoltaics, and data storage. A geometry of particular interest is the nanowire, i.e., a metal structure with subwavelength cross-section extending over many wavelengths along the wire axis. The wavelengths of SP modes propagating along a nanowire scale with the cross-section dimension of the wire, thus showing no cutoff behavior (for the fundamental mode) as for a dielectric waveguide.1,2 The SP fields are highly confined, and the correspondingly high mode densities give rise to efficient coupling with photon emitters.3 Plasmonic nanowires have been thoroughly investigated in recent studies reporting on SP propagation,4,5 the coupling of SPs with light,6,7 and the interaction with single-photon emitters as quantum dots 3,8 or color centers in nanodiamonds. 9 Furthermore, plasmonic wires provide an appealing nanooptical platform for photonic logic circuits,10 detectors,11 and transistor functionality.12 As for any plasmonic system, damping limits the propagation of nanowire SPs. For minimizing loss or for introducing gain, it is first of paramount importance to understand the loss mechanisms in detail. Ohmic damping plays the central role, and it was reported in ref 5 that chemically synthesized (quasi) single-crystalline nanowires show significantly less damping than polycrystalline wires fabricated by the vacuum deposition of metal through lithographic masks. The nature of the surrounding medium or of a substrate supporting the nanowires has to be considered as well, as besides direct absorption by a nontransparent substrate, a higher refractive index material usually leads to a SP mode more confined to the metal and thus to increased loss. On the other hand, radiation damping along the wire for substrate-supported samples can be disregarded for nanowires with diameters around 100 nm or © 2012 American Chemical Society

Received: October 3, 2011 Revised: December 9, 2011 Published: January 23, 2012 661

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we chose wires with diameters of 90 ± 15 nm, as measured by scanning electron microscopy (SEM). The synthesized solution is cleaned through centrifugation in acetone and stored in ethanol. Samples are prepared by spin coating on quartz or ITO/glass substrates. For the lithographic fabrication of silver and gold nanowires, we use standard electron beam lithography (EBL) with poly(methyl metacrylate) (PMMA) resists17 on quartz or ITO/glass substrates. After exposure, chemical development, and plasma cleaning, the PMMA masks are transferred to a vacuum chamber (base pressure 5 × 10−6 mbar), and 75 nm of silver or gold is evaporated with the substrate at room temperature. The metal thickness is limited by the PMMA mask thickness (100 nm). SEM images of both nanowire types are shown in Figure 1a,b, highlighting the

quartz. Scattered light spectra acquired from the distal end of individual nanowires are shown in Figure 2a−c, for three

Figure 2. Scattered light spectra acquired from the distal ends of silver nanowires of lengths as indicated for (a) SCW on quartz, (b) PCW on quartz, and (c) PCW on ITO/glass.

different wire lengths L. We observe the typical line shape of low-quality Fabry−Perot resonances.5,13,20 The modulation contrast is strongest for the SCW on quartz, indicating the highest resonator quality factor due to relatively low damping for a single-crystal structure on a nonabsorbing substrate. For the PCW on quartz substrate, the broader oscillation peaks indicate higher SP damping, which is even more pronounced for the PCW on the ITO/glass substrate. In addition, the mode spacing Δω = vgrπ/L for the nanowires on ITO/glass (Figure 2c) is smaller than on the quartz substrate (Figure 2b), as the higher refractive index of ITO leads to a higher SP mode index and thus lower SP group velocity vgr. With increasing wire length, the modulation contrast in the spectra gets smaller due to increased damping and completely disappears on the highenergy side for the longest wires. In this case, due to high damping only a single pass SP transmission contributes to the detected signal, which explains the absence of any signal modulation. The clear visibility of the Fabry−Perot resonances from PCW in the data reported here is in apparent contrast to previous reports, e.g., our own study in ref 5. We note, however, that resonant modes in PCW up to about 1 μm long had been successfully investigated before by extinction spectroscopy21 and near field imaging.22 That plasmonic modes in longer PCW are now addressable at all by scattered light spectroscopy is mainly due to improved light detection equipment. For the quantitative analysis of SP damping, we apply an extension of the Fourier transform approach as discussed for plasmonic nanowires by Allione et al.,20 relying on work by Hofstetter and Thornton.23 The Fourier transform function of the spectrum acquired from the 5 μm long SCW (Figure 2a) is plotted in Figure 3a, showing a series of peaks as a function of time. The peaks mimic the resonator round-trip times describing the propagation of a short pulse in the cavity. We now apply a band-pass filter around these individual, wellseparated peaks (up to the third harmonic order) and arrive at the energy-dependent amplitudes, as plotted in Figure 3b with an inverse Fourier transform. In addition, we plot the unfiltered spectrum as the blue curve that oscillates around the background (zeroth) order level. For the details of this and the following steps of the calculation procedure see the Supporting Information. The higher order signals are successively falling below noise level on the high-energy side due to the stronger SP damping in this spectral region. As discussed in the Supporting Information, damping is expected

Figure 1. SEM images of (a) a chemically synthesized single-crystalline nanowire and (b) a lithographically fabricated polycrystalline nanowire. The scale bars measure 100 nm. (c) Sketch of the excitation and scattered light detection setup.

different morphologies of the synthesized single-crystalline and the EBL fabricated polycrystalline wires. As emphasized in recent studies,18,19 SP damping in polycrystalline samples is generally expected to be larger due to scattering at grain boundaries. The samples are illuminated with a slightly focused white light beam from a halogen lamp under total internal reflection through an optically coupled glass prism. This kind of a dark field technique suppresses direct detection of the excitation light and launches SPs from the input nanowire end, as defined in the sketch in Figure 1c. In this configuration direct SP excitation at the distal nanowire end is negligible.5 Light scattered from the distal nanowire end is collected by a microscope objective (100×, numerical aperture 0.95), dispersed by a spectrophotometer (Andor Shamrock SR303i), and detected by a camera (Andor Ixon). For all experiments, the excitation light is transverse magnetic polarized, i.e., in the plane of incidence which coincides with the long axis of the nanowires. Upon optical excitation a SP launched from the input end propagates to the distal end of the nanowire where it is partly reflected and partly scattered to light.5,13 Interference due to multiple SP reflection gives rise to Fabry−Perot type longitudinal cavity modes in the nanowire.5,6,20 Light emission due to SP scattering at the nanowire ends allows to probe these modes, in particular their spectral dependence. For highlighting the respective roles of crystallinity and substrate type on SP damping, we investigate three silver nanowire samples: chemically synthesized single-crystalline nanowires (SCW) on quartz, EBL fabricated polycrystalline nanowires (PCW) on quartz, and PCW on ITO/glass substrates. For comparison we also include a gold PCW on 662

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Figure 3. (a) Fourier transform amplitude of the spectrum acquired from the distal end of a 5 μm long SCW on quartz (Figure 2a). (b) Inverse Fourier transform function for band-pass filtering the individual peaks in (a), marked by the corresponding peak number. The curve oscillating around the background signal (zeroth peak) is the unfiltered inverse transform function and corresponds thus to the original spectrum. The square symbols along the envelope of the curve corresponding to the first peak mark the maxima and minima used to derive SP damping and end face reflectivity (see Supporting Information).

to give rise to equidistant harmonic amplitudes Ai on a logarithmic scale,23 as indeed observed in Figure 3b. The ratio of successive harmonic amplitudes ai yields the information about the SP damping parameter k″ and the end face reflectivity R of the plasmonic modes in a nanowire of length L according to ai(ω) = Ai+1(ω)/Ai(ω) = R(ω)e−2k″(ω)L (ref 23). We then extract R(ω) and k″(ω) by fitting this expression to the ai derived from the measurements of nanowires of different lengths with a least-squares minimization.5 Due to the effect of damping on the harmonic spectra, we use only a0 = A1/A0 for the analysis. The resulting SP damping for the nanowire discussed so far (SCW on quartz) is shown in units of SP propagation lengths in Figure 4a by the triangle symbols, ranging from about 10 to 4 μm for energies of 1.2 and 2.0 eV, respectively. The observed spectral dependence reflects the ohmic loss of silver, both in terms of material and plasmonic nanowire mode dispersions. Retrieved from the fitting procedure on 10 individual wires with diameters of 90 ± 15 nm, we plot the average damping values together with the according error margins. These are rather large due to strongly varying end face reflectivities, which we deduce as, for example, R = 40 ± 5% for an energy of 1.2 eV. In addition, we find for SCW that R significantly decreases with wavelength down to R = 15 ± 5% for an energy of 2.0 eV. We explain these observations by different end face geometries for chemically synthesized nanowires, as evidenced for our samples by high-resolution SEM imaging. This interpretation is corroborated by the findings reported in ref 7 on the important role of end face geometry on the coupling of light to nanowires, suggesting the same for the SP reflectivity, ultimately leading to a rather large spread in R. The impact of polycrystallinity on SP modes in nanowires becomes evident from the propagation length values of a PCW on quartz, plotted in Figure 4a by the full square symbols. We

Figure 4. (a) SP propagation lengths as obtained from the Fourier analysis of the scattered light spectra (Q, quartz substrate). The inset shows the values calculated from the analytical nanowire dispersion. Different substrates are modeled by effective permittivities of the surrounding medium (Q, quartz; ε′ ITO, assuming a real permittivity). (b) SP group velocity for silver and gold nanowires on quartz and ITO/glass substrates.

find a decrease in propagation length to about 7 and 1 μm for energies of 1.2 and 2.0 eV, respectively. Since virtually no scattered light (and thus radiation damping) is observed from the wires apart from the wire ends, we assign the propagation length decrease mainly to the higher ohmic loss of the polycrystalline silver. The SP reflectivity is fairly reproducible between individual PCW, in accordance with the observation of virtually identical end face geometries as tailored by EBL. For the PCW, the SP reflectivity R = 31% is also rather uniform, showing only a 7% variation over the measured wavelength range. In addition to the silver nanowires we investigated a gold PCW on quartz; the according propagation values are plotted by the open circles in Figure 4a. Interestingly, the damping is practically identical to the silver PCW, indicating similar permittivities which is plausible for the concerned spectral range. Again, the end face reflectivity of 27 ± 4% is reproducible and rather independent of wavelength. Illustrating the impact of an absorbing (and high refractive index) substrate, the open square symbols in Figure 4a show the SP propagation length for a PCW on ITO/glass. Compared to the quartz substrate, we find a significant reduction in propagation length. Exemplarily, the reduction factor is 2.5, 2.0, and 1.9 for energies of 1.2, 1.5 and 1.9 eV, respectively. With 35 ± 8%, the end face reflectivity for the silver PCW on ITO/glass substrates is within the same range as for the quartz substrate case. To better understand these observations, we include the analytical solutions for SP damping in a nanowire. The 663

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Plasmonic nanowires as submicroscopic waveguides are promising building blocks for highly integrated photonic circuitry capable of managing (single) photons and plasmons on the nanoscale. With the combination of individual nanowires, the routing of SP propagation10 and even logic networks25 were achieved. Therefore SCW was first dispersed on a substrate and then assembled manually, a technique that is clearly limiting the applicability of nanowire networks. Here we show that PCW can be used for such networks as well, thus adding the whole lithographic toolbox for nanowire fabrication. As a proof of principle, we have fabricated SP splitters by forking silver and gold PCW into two ends, as shown in the electron micrograph insets in Figure 5. We excite SPs at the

presence of a substrate is accounted for by an effective permittivity of the medium surrounding the wire, resulting from a weighted average of the dielectric constants of air and substrate (see Supporting Information). The material data of silver were taken from literature.24 For quartz we used a real permittivity of 2.105, and the ITO data was obtained by ellipsometry (see Supporting Information). First, we calculate the SP wavelengths and apply them to normalize the measured SP propagation lengths. The ratios of the resulting values for quartz and ITO/glass substrates (2.5, 1.7, and 1.8 for energies of 1.2, 1.5 and 1.9 eV, respectively) are comparable to those discussed above for the propagation lengths. This indicates that the short SP propagation length on the ITO substrate is mainly due to absorption of the ITO, whereas the higher permittivity of ITO (and thus the modified SP wavelength) plays a minor role for the damping. Second, the calculated SP propagation lengths are shown in the inset of Figure 4a. The curves corresponding to the quartz (full line) and ITO substrates (dashed line) agree fairly well with the measured values. In particular, the stronger damping induced by the ITO at lower energies is nicely reproduced. We illustrate again the important role of absorption, including a calculation on the fictitious assumption of the imaginary part of the ITO permittivity equal to zero (dotted line). In this case the calculated SP damping deviates only a little from the quartz case, illustrating the dominant role of absorption in the ITO/glass substrate for limiting the SP propagation. Besides the differences in crystallinity, there is as well some difference in the geometric cross-section between SCW (90 ± 15 nm) and PCW (100 × 75 nm) due to the different fabrication schemes. We tried to minimize the impact of geometry-induced differences on SP damping by choosing SCW with cross section variations overlapping the lithographically rather precisely controlled PCW cross-section. The damping and reflectivity values reported here agree quite well with previously reported values. The deviation from the SP propagation length on SCW reported in ref 5 of 10.1 μm at 1.58 eV can be explained by the larger nanowire diameter used there (110 ± 15 nm). We note that the standard deviations reported here are due to a fitting procedure including the whole analyzed spectral range and can thus be significantly larger than reported before for a single wavelength.5 We now turn to the SP group velocity which we derive as well from the measured spectra in Figure 2. Under the assumption of only weakly varying SP reflectivity and loss over the range of one oscillation period, the condition for a resonator transmission maximum (i.e., a local extremum in the measured scattered light spectra) is 2k′L + 2ψ = Nπ, k′ being the wavenumber, ψ the phase shift upon SP reflection at the nanowire end, and N a positive integer. The difference in wavenumber between subsequent extrema in the spectra is Δk′ = π/2L. Obtaining Δω from the measurement, we can thus deduce the SP group velocity vgr = Δω/Δk′ (ref 20), as plotted in Figure 4b for the different samples. For the nanowires on quartz, vgr varies from the low to the high end of the observed energy range from about 0.6 to 0.4 c, independent of the nanowire type and thus damping.20 All observed SP modes are truly bound modes, as no leakage into the quartz substrate can occur due to the short SP wavelengths. We note that leakage does occur for thicker nanowires than investigated here, as discussed in ref 13. For the silver PCW on ITO/glass, we observe a reduced vgr between 0.5 and 0.3 c due to the higher refractive index of ITO.

Figure 5. PCW splitters as simple lithographically tailored SP nanowire networks. The optical images show SP scattering to light at the distal ends of (a,b) silver and (c−e) gold nanowire SP splitters, as shown in the inset SEM images. The exciting laser spot (wavelength 780 nm, perpendicular incidence, polarization direction along the nanowire axis) is seen in the left part of the images. All optical and SEM images are shown at an identical magnification scale, as defined by the 5 μm long scale bar.

input end with a focused laser beam (wavelength 780 nm, perpendicular incidence, polarization direction along the nanowire axis) and observe SP splitting, as evidenced by the scattered light spots from both distal ends. Our examples include smooth symmetric and asymmetric silver splitters in Figure 5a,b, respectively, and sharp gold splitting transitions in Figure 5c−e. These examples clearly illustrate the feasibility of lithographically tailored nanowire networks, based on an accordingly chosen substrate. In summary, we have retrieved the spectrally resolved SP damping and end face reflectivities in single- and polycrystalline nanowires and have shown that damping can be reduced by using quartz instead of ITO/glass substrates. In future work our methods could be used to assess the role of, e.g., crystal grain size as modified by thermal annealing on plasmonic damping. Despite being stronger damped than their single-crystalline counterparts, lithographically tailored nanowires work as building blocks for subwavelength plasmonic networks, thereby significantly widening the perspectives for nanoscale plasmonic addressing and routing. 664

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(23) Hofstetter, D.; Thornton, R. L. Opt. Lett. 1997, 22, 1831−1833. (24) Palik, E. Handbook of Optical Constants of Solids; Academic Press, Inc.: Waltham, MA, 1985; Vol. 1. (25) Wei, H.; Li, Z.; Tian, X.; Wang, Z.; Cong, F.; Liu, N.; Zhang, S.; Nordlander, P.; Halas, N. J.; Xu, H. Nano Lett. 2011, 11, 471−475.

ASSOCIATED CONTENT

S Supporting Information *

Detailed analysis of the experimentally observed nanowire spectra, the spectral dependence of nanowire plasmon loss and reflectivity, and the modeling of the nanowire dispersion relation. This material is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

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ACKNOWLEDGMENTS Financial support is acknowledged from the European Union under project no. ICT-FET 243421 ARTIST and the Austrian Science Foundation (FWF) under grant no. P21235−N20. We thank Georg Jakopic for providing the ellipsometry data on the permittivity of our ITO/glass substrates.

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