Evidence of Spatially Inhomogeneous Electron Temperature in a

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C: Plasmonics; Optical, Magnetic, and Hybrid Materials

Evidence of Spatially Inhomogeneous Electron Temperature in a Resonantly-Excited Array of Bow-Tie Nanoantennas Martin Lehr, Karina Bley, Nicolas Vogel, Bärbel Rethfeld, Gerd Schönhense, and Hans-Joachim Elmers J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b03722 • Publication Date (Web): 25 Apr 2019 Downloaded from http://pubs.acs.org on April 25, 2019

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The Journal of Physical Chemistry

Evidence of Spatially Inhomogeneous Electron Temperature in a Resonantly-Excited Array of Bow-Tie Nanoantennas M. Lehr,† K. Bley,‡ N. Vogel,‡ B. Rethfeld,¶ G. Schönhense,† and H.J. Elmers∗,† †Institut f¨ ur Physik, Johannes Gutenberg-Universität, Staudingerweg 7, D-55099 Mainz, Germany ‡Institute of Particle Technology, Friedrich-Alexander University Erlangen-N¨ urnberg, D-91058 Erlangen, Germany ¶Department of Physics and OPTIMAS Research Center, Technische Universität Kaiserslautern, Erwin-Schroedinger-Str. 46, D-67663 Kaiserslautern, Germany E-mail: [email protected]

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Abstract We studied the excitation of large-area Au bow-tie nanoantenna arrays, which we have fabricated on indium-tin-oxide (ITO) coated glass substrates using colloidal lithography with nanoscale polystyrene colloidal particles. Ultrashort (100 fs, 800 nm) laser pulses of a Ti-Sapphire laser resonantly excite electron emission from few tens of nanometer wide gap regions of the array. We investigated the near field enhanced photoemission using time-of-flight momentum microscopy. The variation of the electron emission intensity as a function of kinetic energy, parallel momentum, power density and polarization of the laser beam reveals two distinct emission mechanisms: a coherent multiphoton photoemission process from the optically heated electron gas and a fieldemission process resulting from the optical near-field enhancement at the nanoantenna tips. The analysis of the momentum-resolved kinetic energy spectra indicates a spatially inhomogeneous distribution of the electron gas temperature within the bow-tie resonators.

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Introduction

Plasmonic nanoparticles harvest energy from electromagnetic radiation in the microwave, 1 infrared 2 or even visible 3 wavelength range. In this context they act similar as radiofrequency antennas. 4 Individual metal nanoparticles, 5 ensembles of a few nanoparticles, 6 and nanoparticle arrays 7 have been shown to concentrate radiation energy into sub-wavelength sized volumes, thus enhancing the electric field 8,9 by several orders of magnitude. In particular optical nanoantennas 10–13 show full polarization control, 14,15 a tunable resonance 16 and a high efficiency. 17 Optical antenna arrays are interesting for applications in surface enhanced Raman spectroscopy, 18 vapor generation 19 high resolution lithography 20 and microscopy, 21 bio-chemical sensing, 22,23 spontaneous emission control 24 and enhancement, 25,26 non-linear optics 27,28 and solar energy conversion. 29 While nanolithography offers an arbitrary nanoantenna design, 30 allowing for tailoring 2


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the plasmon resonances, 31–33 excitation of multipolar surface plasmon modes 34,35 and magnetic polarizability, 36 bottom-up nanostructuring processes such as colloidal lithography enjoys great scientific interest because it can produce large amounts of nanoantennas using inexpensive equipment. 37–39 Localized surface plasmons strongly enhance the intensity of photoelectrons, for example at hot spots. 40,41 This effect has been widely used to characterize the near-field enhancement properties of nanoantennas. The high power density of ultrafast laser pulses allows the observation of multiphoton photoemission processes. 42–49 Studies of the emission properties of individual particles reveal large spatial variations 50–56 originating from the high sensitivity of the plasmon resonance on the particle morphology in combination with the strong non-linearity. The near-field enhancement has been further investigated quantitatively by photoemission microscopy and spectroscopy. 50,57–59 Optical field emission has been proposed as an additional emission mechanism. 60 Recently, an analysis of the electron momentum enabled a discrimination of optical field emission from multiphoton photoemission for individual Au nanorods. 61 Comprehensive discussions of various emission processes have been given in Refs. 62,63 Thermodynamically non-equilibrium states of matter excited by ultra-short laser pulses provide an important method to investigate energy, momentum and spin transfer processes from the optically excited electrons to the substrate sink. 49 On an ultra-short time scale below a few hundred femtoseconds the harvested light energy remains in the system of conduction electrons, thus creating a strong non-equilibrium state between electron gas and lattice. 64 For sufficiently high excitation strengths, the ultra-fast electron-electron interaction leads to a thermalization of the excited electrons in much shorter times than the time of energy transfer to the lattice, thus resulting in a hot electron gas. 65,66 The transition from photoemission to thermal emission provides insights on the non-equilibrium dynamics of the excited electrons. 67,68 In view of many potential applications of nanoantenna arrays, detailed information on the non-equilibrium state is required.

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In this article, we apply photoemission electron and momentum microscopy to analyze the energy and momentum distribution of electrons emitted from high-finesse bow-tie nanoresonators. We reveal that the transient hot electron gas develops a significant spatial inhomogeneity, focusing the thermal energy of the electron gas close to the nanogap area of the bow-tie antennas. The local heating of the electron gas potentially varies the dielectric constants and hence the resonator properties. Moreover, electron emission from the tips of the bow-tie antennas opens an undesired energy-dissipation channel. Providing quantitative information on this process, the present results are important for future light harvesting arrays.

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Experimental

The Au nanoantenna array is fabricated by colloidal lithography 69,70 on a conducting indium tin oxide layer, which in turn has been deposited on a glass substrate via spin-coating [see Fig. 1(a) and (b)]. The size of the polymer particles is adjusted such that the ensemble average of the resonance wavelength of the localized plasmon polariton is 800 nm, where also the dielectric constant of the substrate influences the system. 71 In brief, a colloidal monolayer is preassembled at the air/water interface and manually transferred to the solid substrate. 72 Subsequently, Au is thermally evaporated through this colloidal monolayer mask to form triangular structures in the interstitial sites. 34 After dissolution of the colloidal spheres in dichloromethane assisted by ultrasound an array of triangular structures remains. The nanotriangles have an edge length of 258 nm and a thickness of 30 nm Au on a 2 nm thick Ti adhesion layer. A pair of tip-to-tip nanotriangles form a coupled antenna structure, named according to their shape, bow-tie antenna. The sample was irradiated with laser pulses of varying power densities from the back side at normal incidence through the transparent substrate. The wavelength 800 nm was chosen

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as the resonance wavelength of the individual plasmonic nanostructures, the polarization of the electric field vector was linear and rotatable. The pulse duration was 100 fs. For the analysis of photoemitted electrons we use a photoemission electron microscope equipped with an electron optical immersion lens and three additional electrostatic lenses combined with a time-of-flight drift tube. The lens system allows to switch from real space (PEEM) to momentum (k) mode. We image the parallel electron momentum from the back focal plane of the immersion lens and measure the kinetic energy via the time-of-flight of the electrons within the drift tube as recorded by a time- and position- resolving detector. 73 Using a field aperture at the location of a real space intermediate image, we select sample areas without defects of the nanoantenna array. The spectral density of the photoemission intensity I(kx , ky , Ekin ) is detected as a function of momentum parallel to the surface, here the x-y plane, and kinetic energy simultaneously. 74

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Results

The equilateral nanotriangle exhibits three equivalent modes of excitation selected by the directing of the electrical field vector parallel to one of the three bisecting lines. 70 Illuminating the sample with appropriately adjusted linearly polarized light leads to electron emission from one of the three tips of each triangle. Hence, a close-packed structure of bright spots show up in the PEEM image [Fig. 1(c)]. Please note that the separation of two tip-to-tip triangles is too small to be spatially resolved and thus they appear as a single spot. Deviations from the perfect array result from dislocations within the original colloidal sphere lattice. Figs. 1(d-f) show three images of the same area illuminated with three linear polarization angles separated by 60◦ . The sum image, Fig. 1(g), reveals the positions of all pairs of triangle corners. The detailed analysis of the polarization dependence reveals an additional uniaxial anisotropy of the intensity, which we attribute to a small sample misalignment during the Au layer de-

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Figure 1: (a) Atomic force microscopy image of the nanoantenna array. (b) Scanning electron emission microscopy image of nanoantenna array. The area shown here is the same area used for the momentum resolved photoemission measurements.(c) PEEM image acquired with 800 nm femtosecond (100 fs) laser pulses illuminating the sample at normal incidence through the transparent substrate. The light polarization is horizontal. (d-f) PEEM images measured with different linear polarization orientations (red arrows denote the electric field vector). (g) Sum image of images (d), (e), and (f). The yellow dotted lines indicate the positions of the nanotriangles forming the nanoantenna array.

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position. The double-logarithmic plot (Fig. 2) of the integrated photoemission intensity I emitted from the sample area defined in Fig. 1(c) as a function of the illuminating peak power density P reveals a linear increase with a slope of 3.98(7). This is in agreement with a 4-photon

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Figure 2: Electron emission intensity I of the nanoantenna array as a function of peak intensity of the laser beam (black dots). The double-logarithmic plot (base 10) of the peak intensity reveals a slope of 3.98(7) (red line). The inset shows I as a function of the exciting wavelength. I0 corresponds to an intensity of 1000 counts per second on the detector and P0 = 1 MW/cm2 . Fig. 3 depicts the logarithmic plot of the differential photoelectron emission intensity as a function of the kinetic energy of the emitted electrons. Zero kinetic energy is defined by the momentum distribution of emitted electrons. The parabolic photoemission horizon defined 7



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by k⊥ = 0 has been fitted to the observed momentum distribution, where Ekin then results from the position of the bottom of the parabola at vanishing parallel momentum, thereby defining an absolute energy scale. The experimental error is smaller than 0.2 eV. Independent on the power density the maximum emission intensity occurs at a kinetic energy of 0.5 eV. For a 4PPE process we expect the signature of the Fermi edge and thus a large emission intensity up to a kinetic energy of Ekin,F = 4hν − φ(Au) = 0.7 eV with φ(Au) = 5.5 eV denoting the work function of a Au(111) surface. Indeed, the curves measured for low peak power densities of the laser beam show a significant drop at 0.7 eV. However, we observe a considerable number of electrons with larger kinetic energy. In the case of high power density, the logarithmic plot shows an almost linear, smooth decrease of the photoemission intensity with increasing kinetic energy above Ekin,F . A linear decrease represents an exponential drop of the electron distribution, which is expected for the high-energy tail of a Fermi distribution. Its slope increases for decreasing temperature. However, for small power densities, thus low excitation, a kink of the slope occurs at about Ekin = 1.0 eV. The kink becomes increasingly pronounced with decreasing power density. The kink could be an indication of a nonthermal electron distribution, which is excited by the laser in the conduction band of gold. Such nonequilibrium distribution thermalizes on timescales below our pulse duration, however, thermalization is slower for weaker excitations. 66 The kink can also be a signature of higher-order photoemission processes or optical field emission, as will be discussed below in detail. We determine the order n of the photoemission process as a function of the kinetic energy from the differential photoemission intensity dI(Ekin ) averaged over an interval of 100 meV versus the peak power density P [Fig. 4(a)]. The slope n = d log(dI/dI0 )/d log(P/P0 ) defines an effective value for n as shown in Fig. 4(b). A transition from n = 4 to n = 5 occurs close to Ekin = 1.0 eV indicating a transition from a 4PPE to a 5PPE photoemission or optical field emission process. In order to visualize the spectral density I(kx , ky , Ekin ) we show cuts through the three-

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dimensional data array for constant parallel momenta, kx = 0 and ky = 0, as well as for constant kinetic energy values in Fig. 5. The linear polarization of the laser light has been adjusted parallel to the x-axis. Please note that for the chosen polarization direction electrons are excited exclusively from triangle pairs, where the bisecting lines run parallel to the x-axis. For the constant momentum cuts we observe a pronounced difference for parallel momentum along kx and ky . For the cut along kx , Figure 5 (a), we observe that the intensity shows a pronounced rise with increasing parallel momentum, towards the photoemission horizon. Thus, for higher kinetic energy the electron emission intensity is shifted towards the photoemission horizon, indicating that electrons with the highest kinetic energy are emitted parallel to the sample surface, along the electric field vector of the photon beam. In case of the cut perpendicular to the light polarization along ky , Figure 5(b), the highest intensity instead appears more close to ky = 0 independent on the kinetic energy. An apparent shift of the photoemission horizon to lower kinetic energy by 0.25 eV in the case of the cut along kx manifests the second pronounced difference. This shift also shows up as an elliptical circumference in the constant energy cuts, cf. Figures 5(d-f). The elliptical shape vanishes for lower power density. The shift of the photoemission horizon can be explained by an effective decrease of the work function caused by a field emission process. By field emission the electrons tunnel through the work function barrier and thus have a lower kinetic energy compared to electrons that are emitted by normal photoemission. We observe a pronounced decrease of the electron emission intensity close to Ekin = 0. We will discuss this effect in Sec. 4. In order to emphasize the difference for emission parallel and perpendicular to the light polarization we plot in Fig. 5(c) the difference of the two constant momentum cuts along kx and ky .The additional intensity for parallel momentum along kx appears for Ekin > 0.2 eV and for parallel momentum close to the photoemission horizon. The integrated additional intensity amounts to 10 % of the total photoemission intensity.

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Figure 5: (a,b) Constant momentum cuts through the emission intensity array I(kx , ky , Ekin ) for constant ky and kx , respectively. The color bar at the bottom right refers to the intensity normalized to the maximum value. Dashed parabolas indicate the positions of the effective photoemission horizons. Horizontal dashed lines denote the positions of the constant energy slices. (c) Difference of the photoemission intensities parallel (along kx ) and perpendicular (along ky ) to the polarization direction. The intensity difference has been normalized to the maximum value. (d - f) Constant energy slices at energies indicated in (a). The electric vector of the photon beam points along the kx direction. The photoemission intensities are measured for a power density of 24 MW/cm2 . 12


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Discussion

A strong dependence of the electron emission yield in dependence on the azimuthal angle of linear polarization has already been discussed in Ref. 75 for a tip geometry. Here, we discuss the dependence on the parallel momentum (see also Ref. 56 ) for a particular nanostructure with translational symmetry exhibiting a resonant near-field enhancement. While the near field enhancement of individual particles such as nanorods can assume a factor of 60, 54 the enhancement factor can be considerably larger for coupled particles. This is the case for the bow-tie antennas discussed here, where two nanotriangles are arranged in a tip-totip configuration. Because the corresponding plasmon mode within one nanotriangle has a strong dipolar character, the mode couples to the adjacent triangle. The coupling and hence the near field enhancement strongly depends on the gap size. Enhancement factors of a few thousand have been reported for bow-tie antenna structures with small gap sizes. 47 The tip-to-tip geometry has been investigated by simulation using finite-difference time domain calculations and experimentally by extinction spectroscopy, 76 reporting a field enhancement factor of 1000 for a gap size of 80 nm. These statements are not without opposition. Wang et al. 77 estimates an enhancement factor of only 38 for a gap size of 20 nm. A combined experimental and theoretical study 78 reports enhancement factors of 50 for a similar gap size. Racz et al. 78 demonstrated a direct determination of the field enhancement factor from the maximum electron energy. The maximum kinetic energy in our case is 3.4 eV for a power density of 33 MW/cm2 [see Fig. 6]. These values result in a maximum local field of (2.0 ± 0.5) × 109 V/m and hence to an enhancement factor of 200 ± 50. The corresponding Keldysh parameter is 9, 60,63 suggesting that coherent multiphoton photoemission from an optically heated electron gas is the dominant emission process. This is consistent with the power dependence of the integrated photoemission intensity measured in our experiment. However, for a multiphoton emission process one expects an isotropic emission of electrons. In general, a multiphoton emission process could comprise anisotropic components. 13



This is for example the case for the phenomenon of linear dichroism in photoemission. Linear dichroism, however, requires p-polarized light in contrast to our geometry, where we excite electrons with s-polarized light. The initial state (band structure) of the sample may also cause an anisotropic emission yield. In our case, however, we assume a patterned polycrystalline Au film that would average over azimuthal orientations. Furthermore, a spatial dependence could generate non-isotropic emission. A tip, for example, will emit electrons only along the half sphere pointing away from the tip. In our case, the emission occurs at two oppositely arranged tips, thus restoring the azimuthal isotropy. Although we observe an isotropic emission for the majority of photoelectrons, the momentum resolved spectra clearly reveal a directional emission parallel to the electric field vector of the incident radiation. The non-isotropic intensity contribution occurs at higher kinetic energies and increases with increasing power density suggesting an emission contribution induced by the electrical field. Optical field emission is an obvious possibility that can explain a non-isotropic emission from a polycrystalline Au surface. Ref. 56 proposes nanocrevices as a possible origin of directed emission, which in that case, however, promote emission perpendicular to the polarization direction. The observed shift of the photoemission horizon for higher power density further supports the model of optical field emission for the small contribution to the totally observed intensity. The shift of the photoemission horizon results from an apparent decrease of the work function caused by a field emission process. By field emission the electrons tunnel through the work function barrier and thus have a lower kinetic energy compared to electrons that are emitted by normal photoemission. In order to quantitatively estimate the field emission contribution, we determine the fraction of the multiphoton process from the momentum distribution along ky [Fig. 5(b)], assuming that the momentum distribution of this process is isotropic, i.e. independent on the direction of the parallel momentum. Then we subtract this symmetrized spectral density from the total spectral density comprising the superposition of both processes. The

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resulting difference reveals the contribution from the purely anisotropic component, which we tentatively attributed to a field emission process. Integration in energy and momentum space results in a relative contribution of 0.06 of the field emission process for the highest power density. We further observe a pronounced decrease of the electron emission intensity close to Ekin = 0. Tentatively, this shortcoming of low energy electrons may be explained by a ponderomotive electron acceleration. 58 The ponderomotive forces act predominantly on zero kinetic energy electrons lingering longer above the surface and thus are longer exposed to high field gradients. Please note that the post-emission acceleration discussed here for the case of field emission also occurs in the perturbative regime discussed as laser-assisted photoemission 59 and may also alter the momentum distribution at very large near-field intensity. The question is how the small contribution of a field emission component can occur in view of the comparatively weak power density of the incident radiation. We tentatively suggest that the tip morphology of the nanotriangles may locally exhibit regions with a strongly decreased surface radius, representing local sharp tips that in turn promote optical field emission. We would also like to mention that Ref. 61 discusses similar emission processes as observed here in the case of single Au nanorods. Studies with considerably enhanced power densities would further elucidate the origin of the optical field emission process. Because the anisotropic part of the photoemission intensity is very small, we neglect this part in the following and only discuss multiphoton photoemission. Please note that the main purpose of this article is to discuss local heating of the electron gas. We have focused on lower power densities at high repetition rates in order to avoid detector saturation and space charge acceleration impeding the determination of kinetic energy. For further analysis, we analyze the differential intensity shown in Fig. 3 in an energy interval 0.4 eV< Ekin

Evidence of Spatially Inhomogeneous Electron Temperature in a

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