Momentum Distribution of Electrons Emitted from Resonantly Excited

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Momentum distribution of electrons emitted from resonantly excited individual gold nanorods Martin Lehr, Benjamin Foerster, Mathias Schmitt, Katja Krüger, Carsten Sönnichsen, Gerd Schönhense, and Hans-Joachim Elmers Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b02434 • Publication Date (Web): 20 Oct 2017 Downloaded from http://pubs.acs.org on October 21, 2017

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Momentum distribution of electrons emitted from resonantly excited individual gold nanorods Martin Lehr* †, Benjamin Foerster‡§, Mathias Schmitt‡, Katja Krüger‡, Carsten Sönnichsen‡, Gerd Schönhense †, Hans-Joachim Elmers† †Institut für Physik, Johannes Gutenberg-Universität, Staudinger Weg 7, D-55128 Mainz, Germany

‡Institut für physikalische Chemie, Johannes Gutenberg-Universität, Duesbergweg 10-14, D-55128 Mainz, Germany

§Graduate School for Excellence Materials Science in Mainz, Johannes Gutenberg University Mainz, Staudingerweg 9, D-55128 Mainz, Germany.

Corresponding Author Email: [email protected], fax number 0049 6131/39-23807

ABSTRACT:

Electron emission by femtosecond laser pulses from individual Au nanorods is studied by a

time-of-flight momentum resolving photoemission electron microscope (ToF k-PEEM). The Au nanorods adhere to a transparent indium-tin-oxide substrate allowing for illumination from the rear side at normal incidence. Localized plasmon polaritons are resonantly excited at 800 nm with 100 fs long pulses. The momentum distribution of emitted electrons reveals two distinct emission mechanisms: A coherent multiphoton photoemission process from the optically heated electron gas leads to an isotropic emission distribution. In contrast, an additional emission process resulting from the optical field enhancement at both ends of the nanorod leads to a strongly directional emission parallel to the

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nanorod’s long axis. The relative intensity of both contributions can be controlled by the peak intensity of the incident light.

KEYWORDS: Hot electrons, localized surface plasmon resonance, momentum microscopy, nanorods, photoemission electron microscopy, single particle spectroscopy Plasmonic nanoparticles are known to enhance the electromagnetic field of incoming radiation1, which is useful for a number of applications such as sensors2, photovoltaics3–5, steam generation6–8, ultrafast electron sources9–11 and Raman spectroscopy12. Furthermore, Plasmon-induced electron emission from nano structures13,14 may serve as electron source for time-resolved low-energy electron microscopy. Of particular interest is their application for ultrafast photoemitters in next generation Xray free electron lasers because nanoparticle emitters provide orders of magnitude higher conversion efficiency relative to conventional planar photocathodes15. For the latter application the control of the emission direction in addition to the distribution of kinetic energies is crucial because the momentum distribution determines the brilliance of the emitter. In addition, the hitherto neglected analysis of the electron momentum distribution allows disentangling previously discussed plasmon-enhanced electron emission mechanisms. Synthetic routes have been developed for the fabrication of particles with well-defined sizes and shapes, such that the resonant excitation of localized plasmon polaritons can be tuned throughout the visible spectral range16–20. As has been found in early studies of electron emission from particles, localized surface plasmons strongly influence the electron emission. One-photon photoemission spectra of metals are often dominated by strong plasmon-induced electron emission from small surface areas (hot spots)21,22. The high power density of ultrafast laser pulses allows the observation of multiphoton photoemission processes from metal nanoparticles23–26 and metallic nanostructures27,28.


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Ensemble-averaged measurements often underestimate the non-linear photoemission properties due to the strong size dependence of these effects. This is particularly important for the analysis of plasmonic properties of nanoparticles for applications as electron source with large brightness and low emittance of ultrashort electron pulses9,29, THz radiation30, high-harmonic generation31 and coherent control32. Therefore, recent studies focus on electron emission from individual particles, revealing large variations of the emission properties although the particles are intended to be identical11,33–38. The large efficiency variations originate from the high sensitivity of the plasmon resonance on the particle morphology in combination with the strong non-linearity. The question how energy and momentum of the plasmonic excitation within the nanoparticle is transferred to the emitted electron remains of considerable interest and debate.

Figure 1. a,b) Real-space PEEM images of the Au finding structure illuminated by a mercury arc lamp a) and illuminated by the laser b). The white spots in b) represent individual resonantly excited Au nanorods. Please note that the intensity in this picture is shown on a logarithmic scale. c) SEM image of 3 ACS Paragon Plus Environment

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the single Au nanorod indicated in b), with length 70 nm and width 20 nm. d) Representative scattering spectrum of a single gold nanorod. The spectrum (black) is fitted with a Lorentzian function (red) to extract the linewidth Γ =41 nm (80 meV). The Au nanorods were immersed in water supported on a glass slide inside a darkfield microscope. e) Photoelectron emission intensity of a single Au nanorod as a function of peak intensity (black dots). The double logarithmic plot (base 10) of the peak intensity reveals a slope of 3.06(12) (red line). f) Polar plot of the polarization dependence. Normalized emission intensity (black dots) is fitted with cos6 (red) and cos2 (blue) function following eq. (1).

For flat metal surfaces the coherent multiphoton photoelectron emission facilitates photoemission at photon energies below the work function9,39–44. The multiphoton photoemission process involves the coherent absorption of multiple photons in order to lift an electron above the work function. This mechanism is also considered to be responsible for photoemission from nanoparticles, whereupon the exciting photon intensity may be considerably increased by resonant plasmonic field enhancement as concluded from photoemission microscopy and spectroscopy studies35,36,45. Direct correlation of results from dark field microscopy and scanning photoionization microscopy strongly support coherent multiphoton photoemisson being the dominating emission process in resonantly excited nanorods33,36. On the other hand optical field emission has been discussed as an alternative emission mechanism. In this case the strongly enhanced transient near-field facilitates electron emission by quantum tunneling through the surface barrier analogously to field emission in static fields. Field emission requires the near-field to be directed perpendicular to the surface and it is expected to cause a strongly directional electron emission. Keldysh46 proposed a transition from photoemission to optical field emission with increasing field strength. Because experimental conditions often represent a borderline situation it is hard to distinguish the actual emission mechanism.


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In this work, we discuss the momentum of the emitted electrons, which is hidden in spatially resolved but angular averaging microscopy methods, e.g. PEEM, one of the commonly used techniques to quantify the extent of plasmonic near field enhancement of individual particles36,47. We use a modified PEEM setup to measure with angular and energy resolution revealing the photoelectron momentum distribution from individual Au nanorods. The momentum and energy distribution confirms the picture of a plasmon assisted emission process and implies the occurrence of a hot electron gas during the excitation pulse of 100 fs leading to a considerable amount of electrons emitted isotropically in all directions from the nanorod. An additional emission process caused by the near field enhancement at both nanorods’s tips leads to directed emission parallel to the axis of the nanorod. The directed plasmon assisted electron emission at the tip might become a key element for advanced optical elements utilizing plasmon assisted electron emission as a brilliant pulsed electron source. For the present investigations 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 samples are illuminated from the rear side at normal incidence. We image the parallel electron momentum from the back focal plane of the immersion lens and measure the kinetic energy via the flight time of the electrons within the drift tube as recorded by a time- and position- resolving detector48,49. Using a field aperture at the location of a real space intermediate image we select individual Au nanorod emitters. The spectral density ρ(kx,ky,Ekin) is measured as a function of parallel momentum and kinetic energy, simultaneously50. Further information about the experimental setup can be found in the supporting information. The 19±2 nm by 67±2 nm Au nanorods are deposited on a conducting indium tin oxide layer on a glass substrate via spin coating. The size of the particles is adjusted such that the ensemble average of the resonance wavelength of the localized plasmon polariton is 800 nm considering the dielectric constant of the substrate51. More details on the Au nanorods can be found in the supporting information. 5 ACS Paragon Plus Environment

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Using 800 nm linearly polarized laser illumination, the statistically distributed Au nanorods show up as bright spots in the PEEM image, if the polarization is parallel to the long axis of the nanorod33. To detect all Au nanorods independent of their orientation we rotated the laser polarization in steps of two degrees and summed up all images (Fig. 1b). We selected several isolated bright spots for further investigation. Please note that the spots appear much larger (1 µm) than their geometrical size due to the chromatic aberration in PEEM mode. Variation of the laser wavelength between 750 nm and 850 nm reveals a maximum photoemission intensity at 800 nm for the single Au nanorods. The full width at half maximum of < 50 nm for the resonance curve of a single Au nanorod (see Fig. 1d)) is considerably narrower compared to ensemble measurements of Au nanorods (133 nm, see supporting information) and indicates a small damping with a decay time T2 of an excited localized

plasmon polariton Δ = > 10 fs. The lifetime of the plasmon excitation thus exceeds typical values for lithographically fabricated nanostructures52. The double logarithmic plot of the integrated photoemission intensity I emitted by a single spot as a function of the peak intensity P on the sample surface Fig. 1e) reveals a linear increase with a slope of 3.06(12). This is in agreement with the expected 3 photon photoemission process (3PPE)33. The polarization dependence precisely follows the functional form expected for a 3PPE process:

∝ ( − ),

(1)

with azimuthal angle of laser light polarization (Au nanorod) ( ), respectively (see Fig. 1f). The vanishing intensity perpendicular to the nanorod axis proves that only the electric field vector component parallel to the long axis of the rod contributes to the plasmon excitation. The correlation of polarization angle and particle orientation was confirmed by recording high resolution SEM (scanning electron microscope) images of the same particle (Fig. 1c). For the experimental determination of zero kinetic energy the photoemission horizon defined by = 0 has been compared to a parabola assuming =

for the final photoemission state outside 6

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of the material. As a result we obtain the energetic position of Ekin = 0, i.e. the minimum of the momentum paraboloid, thereby defining an absolute energy scale. The experimental error is smaller than 0.2 eV. For all three curves the maximum occurs at an initial kinetic energy of 0.8 eV. For a 3PPE process we expect a maximum kinetic energy Ekin,max = 3hv -

!" =

1.25 eV with

!"

= 3.4 eV denoting

the measured workfunction of the Au nanorod. The low work function is due to the utilized substrate. The In-Sn oxide surface without Au nanorods shows a clear 3PPE process and a Fermi edge at Ekin = 1.25 eV (Fig.2), resulting in the work function

#

%$= 3.4 eV. Since the bottom of the photoemission

horizon of the Au nanorods is not significantly shifted compared to the In-Sn oxide surface the work function of the Au nanorods adjusts itself to the substrate as proposed by Cinchetti et al.53. Similar effects have been reported by Nesbitt et al. even resulting in a different order of photoemission depending on the substrate, in particular 3PPE on ITO and 4PPE on Pt34. Electrons with high kinetic energies larger than 3 eV originate from a 4PPE or field emission. The missing Fermi edge provides strong evidence of an alternative emission or acceleration process. Since plasmonic resonance effects in nanoparticles lead to an enhanced light absorption it is important to consider potential heating of the particle as well as of the electron gas. Taking into account heating of the lattice the temperature of the Au nanorod increases by &' =

&( *+ , = ≈ 200 1, ) - .

(2)

with pulse length *+ = 100 fs, peak intensity I = 664 MW/cm2, effective cross section , =

1.5 45 cm , and density - (specific heat capacity c) of Au 19.32 g/cm2 (128 J/kg K). Please note that the effective cross section in the plasmonic resonance is larger than the geometric footprint54. Since no electrons are emitted at this temperature, the rise of lattice temperature can be neglected. However, the electron gas within the nanoparticles can attain much higher temperatures than the lattice55. In case of a hot electron gas one expects a strong broadening of the Fermi edge combined with an exponential decrease of the intensity with increasing kinetic energy, as observed in our experiment. 7 ACS Paragon Plus Environment

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The linear decrease near the Fermi energy between 1.3 eV and 1.6 eV of the logarithmic plot (Fig. 2) is fitted using a high temperature approximation for the Fermi distribution function 8 9( $≫ ) ∝ −

& . ; '

(3)

The fit reveals electron gas temperatures of 1500-3900 K for power densities of 166-664 MW/cm2. Using a Sommerfeld model for the heat capacity of the electron gas33 and assuming that the energy of a laser pulse in the area of the nanoparticle is completely transformed into thermal energy, we calculate the temperature of the electron gas by: '= = >' ?

2 , *+ '@ . A B= .CD ;

(4)

' /'@ denotes the initial temperature and Fermi temperature of Au (6.4 ⋅ 10I K) respectively, Ne is the

conduction electron density (5.9 ⋅ 10 cm4L ) and VNP the volume of the nanoparticle. All cooling to the lattice or substrate is neglected. The deposited energy of a single pulse results in an electron gas temperature of 2100 K – 4200 K for the range of power densities applied here. A comparison of the calculated temperature following eq.(4) and the fitted values is shown in (Supporting information Fig. S10). The good agreement of the calculated temperature confirms the observed remarkable increase of the electron temperature.

Figure 2. Logarithmic plot of electron emission intensity of a single Au nanorod as a function of kinetic energy normalized to the maximum value. Fits to Eq. 3 are shown as straight lines. 8 ACS Paragon Plus Environment

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The high electron temperature in turn enables a modified multiphoton emission process. Here the electrons are emitted by a coherent 3PPE process from the hot electron gas. This process explains the high-energy tail and the exponential drop of the electron energy distribution. We base our identification of the emission process as a coherent process, as opposed to a step-wise process, on the work of Grubisic et al.33, who investigated a nearly identical system (Au nanorods; 63 nm * 20 nm on ITO, fsLaser). Grubisisc et al. compared his experimental results with predictions of a coherent multiphoton photoemission model proposed by Yalunin et al.56. The agreement of Grubisic’s experimental data with the theory proposed by Yalunin et al. supports coherent multiphoton photoemission as the predominant emission process. The 3PPE from a transient hot electron gas results in an isotropic distribution of emission directions as the electrons have changed their initial momenta by numerous scattering processes. Please note that the thermal energy of the electron gas dissipates to the substrate on a ps time scale57 and therefore the excitation is a repetitive process. The Keldysh parameter that is decisive for optical field emission versus normal photoemission is calculated as: 2 N= O P M = > , Q

(5)

with electron mass me frequency of light O, work function Φ, electron charge e and electric field E

consisting of the field of the laser light and the near field. The calculated values for M are between 1.55 and 2.75, depending on the peak intensity, if we assume a field enhancement factor of 60 at the tip of the Au nanrod as reportet by Nesbitt et. al for a similar system33. As reported in Ref. [15] the transition to optical field emission occours for 1 < M < 2. Therefore, we expect optical field emission for peak power densities between 332 MW/cm2 and 664 MW/cm2, equivalent to a laser pulse fluence of 33-66 µJ/cm2 with Keldysh parameters of 1.84 and 1.55, respectively. The optical field emission is restricted to the tip of the Au nanorod where the plasmonic excitation results in a strongly enhanced near field perpendicular to the surface of the Au nanorod and therefore parallel to the substrate. 9 ACS Paragon Plus Environment

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To verify the suggested optical field emission we analyze the spectral density function ρ(kx,ky,Ekin) of photoelectrons from a single Au nanorod. A schematic illustration of the experiment is shown in Fig. 3, the resulting spectral density function at peak intensity 498 MW/cm2 is shown in Fig. 4. The kx axis has been adapted to the direction of the long axis of the nanorod and to the electric field vector. The slight asymmetry of the plot in ky direction (Fig. 4 b) is attributed to a remaining misalignment of the electron optics and not related to the emission process. Constant-energy slices (Fig. 4 d-f) reveal an intensity maximum for emitted electrons with momentum parallel to the polarization/long axis of the Au nanorod, representing a strong hint to field emitted electrons. This feature only appears for peak intensities of 332 MW/cm2 or higher, as can be seen in the associated content.

Figure 3. Schematic illustration of the experiment. An individual au nanorod is resonantly excited by linear polarized, pulsed laser light. Illumination from the rear side at normal incidence allows true polarization dependence measurements. The emitted electrons result in a 3D spectral density function ρ(kx,ky,Ekin) shown on the right.

In order to isolate the field emission contribution, we subtract the spectral density along ky that exclusively originates from the isotropic 3PPE process (Fig. 4 b) from the spectral density in kx direction (Fig. 4 a) comprising the superposition of both processes. The resulting spectral density of the field emission process is shown in Fig. 5 c. The field emission contribution appears for kinetic energies Ekin > 0.6 eV. The lack of additional electrons below this energy may result from a post-emission acceleration by ponderomotive forces that predominantly acts on zero kinetic energy electrons lingering


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longer above the surface. For sufficiently large optical near fields a ponderomotive electron acceleration causes a large kinetic energy of emitted electrons58. Please note that the post-emission acceleration discussed here for the case of field emission also occurs in the perturbative regime discussed as laserassisted photoemission59 and may also alter the momentum distribution at very large near-field intensity.

Figure 4. a,b) Constant momentum cuts through the background corrected spectral density for constant ky and kx, respectively. c) Subtraction of b) and a), symmetrized. d-f) Constant energy slices along the dashed lines in a) for kinetic energies of 1.3 eV, 0.8 eV and 0.3 eV. The laser polarization points along the kx-direction. We calculate the ratio 0.29 of field emission and total emission in x-direction by dividing the integrated intensity of Fig. 4 c) by the value for Fig. 4 a). As the emission in x-direction is about 20 % of the total emission, a fraction of 5.8 % of the total emission stems from the optical field emission process. This small fraction confirms the assumption that the emission spectra are dominated by the coherent multiphoton photoemission process from the optically heated electron gas and also explains the linear increase with n=3 in Fig. 1 e). Deviations from the power law due to the additional field emission process60 at these low peak power densities are negligible. This is in agreement with Ref. [15], where 11 ACS Paragon Plus Environment

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the power dependency of similar Au nanorods is examined and the deviation can only be identified at pulse fluences higher 27 nJ, corresponding to peak intensities larger than 12.1 GW/cm2. Following the procedure described above we determined the field emission fraction of the total emission versus peak intensity as shown in Fig. 5. Constant energy and momentum maps dependent on the peak intensity are shown in the supporting information. The fraction of field emitted electrons clearly increases with increasing peak intensity. Similar measurements were carried out for 6 Au nanorods with different orientations. While the peak intensity of different rods varies, the qualitative characteristics are in excellent agreement (see supporting information Figs. S7-S9).

Figure 5. Fraction of field emitted electrons with respect to total emission yield as function of peak intensity. In summary, the momentum distribution of all photoelectrons emitted from single Au nanorods as function of peak intensity and orientation of the electric vector with respect to the long axis of the rod has been measured. The main contribution of the electron yield results from coherent multiphoton photoemission from an optically heated electron gas. This process leads to an isotropic electron emission. For peak power densities larger than 332 MW/cm2 the spectral density features maximum intensity for electrons with momentum parallel to the polarization and kinetic energies of 0.8 eV. We ascribe this effect to an emission process via optical field emission parallel to the polarization direction at the tip of the Au nanorod due to the strongly enhanced near field. This directed emission process is 12 ACS Paragon Plus Environment

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favorable for photo emitting devices exploiting the high brilliance. The peak brilliance amounts to B = 1019 e/(s mm2 mrad2), the calculation of this value is shown in the supporting information. This value is comparable to conventional field emitters (of Schottky-type) but is far below the requirements for free electron lasers, so beamlets from 103 to 104 nanorods have to be combined to reach suitable values61. Our findings reveal important constraints for the development of pulsed electron sources based on nanoparticles because the thermally-assisted multiphoton emission process results in undesired isotropic emission. On the other hand we show that with increasing peak intensity the contribution of directed optical field emission increases on the expense of thermally-assisted photoemission.

Supporting Information (S1) Synthesis, (S2) characterization and optical properties of Au nanorods, (S3) experimental setup of time-of-flight k-PEEM, (S4) background correction of momentum measurements, (S5) temperature dependence on peak intensity, (S6) energy distribution dependence on peak intensity, (S7) Comparative calculation of peak brilliance of the electron emission, (S8) constant momentum and energy maps for different peak intensities. This material is available free of charge via the Internet at http://pubs.acs.org AUTHOR INFORMATION Corresponding Author Email: [email protected], fax number 0049 6131/39-23807

Author Contributions M.L. performed the main experiments and data evaluation. B.F., K.K.,M.S. and C.S. synthesized and characterized the Au nanorods. G.S. and H.J.E. initiated and coordinated the project. Data interpretation was discussed among all authors. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. The authors declare no competing financial interest.


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Acknowledgements Financial support from Deutsche Forschungsgemeinschaft through SPP 1391 (EL 172/ 16-1 within SPP 1391) and SFB/TR 173 (Spin+X) is gratefully acknowledged. ABBREVIATIONS ToF k-PEEM, Time-of-flight momentum-resolved photoemission electron microscope; 3PPE, 3 photon photoemission; DLD, delayline detector; ROI, region of interest; SEM, secondary electron microscope REFERENCES (1)

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