Transient electron energy-loss spectroscopy of optically stimulated gold nanoparticles using picosecond pulsed electron beam

The optical properties of metallic nanoparticles (NPs) have enabled many applications based on surface plasmon resonance (SPR), which is affected by the shape, geometric arrangement, and the electronic state of the NPs.^1–3 Ultrafast relaxation processes, such as electron–electron and electron–phonon scattering processes, are also critical for optical switching devices and light energy conversion devices based on NPs.^4,5 Gold NPs, in particular, have high chemical and optical stability, large optical cross sections, and biocompatibility.^1,6–8

Electron energy-loss spectroscopy (EELS) in transmission electron microscopy (TEM) has facilitated real-spatial mappings of elements, bonding information, and plasmons with nanometer resolution that cannot be achieved by optical techniques, including x ray and other analysis techniques.^9–11 Furthermore, the energy resolution, which is associated with the energy width of the incident electron beam and the electrical stability of the measurement apparatus, has improved, which has allowed the energy-loss peaks of phonons to be detected.^12,13 The time resolution of EELS in TEM has also been improved using a pulsed electron beam to probe specimens, which is realized with a photoemission gun and a pulsed drive laser.^14–16 The EELS method can observe not only the localized surface plasmons (LSPs) but also bulk plasmons and other quadrupole modes and longitudinal waves in materials, whereas the optical methods can only excite LSPs and the matched mode of surface plasmons. Furthermore, high-resolution EELS (HREELS) measurements in reflection mode have allowed detailed investigations of surface plasmons in bulk crystals and thin films, which show a geometric effect in gold.¹⁷ HREELS enables precise observation of the dispersion of plasmonic modes on the surface and reveals the morphological effect of the gold film on the surface plasmons.^18,19 Therefore, EELS with pulsed electron beams can reveal the dynamics of an entire system of excitation in NPs.

A time-resolved transmission electron microscope (TR-TEM) has been newly developed using a semiconductor photocathode with a negative electron affinity (NEA) surface for the pulsed electron source. The column system of the TR-TEM is based on 120 kV TEM (HT7830, Hitachi High-Tech Corp.). The TR-TEM is operated under beam energies of up to 100 keV, which improves the transmittance in a specimen and provides high brightness compared to the previously developed 30 keV spin-polarized TEM.²⁰ In this study, a thin GaAs film attached on a glass plate was used as a backside-illumination-type photocathode, fabricated by Hamamatsu Photonics Inc., and surface treatments of the photocathode were conducted in the TR-TEM. Electron beam is extracted from the flat surface of the photocathode with a high electric field gradient of 8 MV/m at an acceleration voltage of 100 kV. The emission process has advantages of a narrow energy dispersion and small transverse momentum due to the small residual energy in the conduction band of the semiconductor and suppression of the space charge effect due to the high gradient of the acceleration field.^21,22 The TR-TEM has two main detectors, one for EELS measurement and one for TEM imaging, which are an energy spectrometer (Enfina, Gatan Inc.) and an electron imaging sensor (Orius SC200, Gatan Inc.), respectively. The experimental setup shown in Fig. 1 was constructed to realize time-resolved measurement using the pump-probe method in the TR-TEM, which consists of the TR-TEM, a pulsed laser to emit a pulsed electron beam to probe the specimen, and another pulsed laser to stimulate the specimen. The two pulsed lasers are synchronized with each other by splitting the seed laser of a mode-locked Ti:Sapphire laser with a frequency of 80 MHz and a pulse duration of 150 fs, and are temporally adjusted by control of the traveling distance of the pumping laser path using a variable delay line with an accuracy of 33 fs. The pumping laser was injected into the specimen position at a tilt angle of approximately 80° to the electron beam axis.

Ultrafast phenomena in NPs were observed using the transient EELS (TEELS) technique in the TR-TEM with the pump-probe system. Gold nanotriangles (AuNTs) were used as NPs, which were synthesized using the seed-mediated growth method.²³ The AuNTs were dispersed on a carbon support film (Quantifoil Micro Tools GmbH) for the TEELS experiment in the TR-TEM. The average power of the pumping laser was set to 200 mW with a wavelength of 780 nm and a diameter of 200 μm on the specimen position, which corresponds to an energy density of $8.0×10−2$ J m⁻². The pulse durations of the pumping laser for the specimen and the electron beam emission were 150 fs and 7.8 ps, respectively. The amount of charge in a pulse was approximately 1 fC to suppress the Boersch effect, which affects the energy width of the electron beam and reduces the energy resolution of the EELS measurement.^24,25 The specimen was tilted by15° from the electron beam axis to simultaneously irradiate both the electron beam and pumping laser. The TEELS measurement was conducted in the time range of −20 to 50 ps in steps of 1 ps. The acceleration voltage was set to 80 keV due to the lens parameters for the energy spectrometer. Each time step of the EEL spectrum was acquired with an exposure time of 120 s and a frequency of 80 MHz under a beam energy of 80 keV.

Figure 2 shows a color mapping of the TEELS measurement and the time dependence of the intensity for AuNTs with 80 keV incident electrons under irradiation with the 150-fs pulse laser at 0 s. The energy spectrometer acceptance diameter was about 150 nm. The color indicates the intensity of the EEL spectrum for each delay time. The experimental results indicated that the increment of the energy-loss intensity in the EEL spectrum was observed around 0 s, whereas the previous irradiation of the pulsed laser in a negative time has a lower peak that corresponds to the EEL spectrum without laser irradiation. The time evolution of the bulk plasmon peak under irradiation with the pulsed laser was observed successfully, which cannot be detected by optical-probe measurement. The inset in Fig. 2 shows TEEL spectra at −15, 5, and 35 ps, and the fitting curves are an asymmetric Gaussian function that is the product of a Gaussian function and a sigmoid function. The fitting around a loss energy of 24 eV was performed with a single fitting function, because the peaks around 15 and 31 eV are too small for the fitting analysis. The time dependence of the EEL intensity at the energy-loss peak of bulk plasmons is shown in Fig. 3, which is extracted from the TEELS data of Fig. 2. The time constant for bulk plasmons shows two relaxation times of 7.8 ± 0.5 ps and greater than 100 ps. The electron pulse duration is also estimated from the rising time constant to be 8.5 ± 0.9 ps. The energy width in the bulk and surface plasmon peaks, as shown in Fig. 4(a), also changed with root mean square broadening of 0.83 ± 0.07 and 0.74 ± 0.13 eV, respectively. The energy loss peak of bulk plasmons in Fig. 4(b) shifted slightly to lower energy, which is synchronized with the intensity change of Fig. 2 with the pumping laser; the energy shift is 0.81 ± 0.04 eV.

The excitation photon energy is 1.59 eV, and the intra-band transition occurs in the gold 6 sp band.⁴ After the intra-band transition, the initial excited state is thermalized by electron–electron interactions and becomes a hot-electron state within 200 fs.^4,26,27 Hot electrons are relaxed by electron–phonon interactions, and the lattice temperature increases as the electronic temperature decreases. The previous results of AuNTs using all-optical measurement via transient absorption show that the electron–phonon and phonon–phonon relaxation times have the same time scales as the time constant of EELS in the bulk plasmon peak.^28–30 

The EEL spectrum is proportional to $ℑ[−1/ε(ω)]$⁠, where $ε(ω)$ represents the dielectric permittivity of the medium.³¹ TEELS experiments with transmitted electrons were conducted with a small angle on the order of 1 mrad. Therefore, the differential probability of energy loss for plasmons P_s at absolute zero temperature is expressed as

where Ω and E represent the solid angle and energy loss, respectively; a₀, m_e, v, and ρ are the Bohr radius, free electron mass, the velocity of free electrons, and the number of atoms per unit volume of the medium, respectively; and θ and θ_E represent the detection and characteristic angles, respectively.³² The $ℑ[−1/ε(q,ω)]$ term is known as the energy-loss function, which provides a complete description of the response of the medium through which the fast electron travels.

Based on the Drude model, the energy-loss function of bulk plasmons is rewritten as

where ω_p represents the plasma frequency, $ωp=nρe2/meε0$⁠, which is dependent on $nρ$⁠. $ε∞$ is a high-frequency limit dielectric constant that results from core electron polarizability and interband transitions. Γ represents the inverse of the relaxation time, which is dependent on the electronic and lattice temperatures. The energy loss function has an FWHM of Γ and a peak of $ωp/Γε∞3/2$⁠.

The energy shift and energy-width changes of the spectrum affect the energy-loss function, including the material functions and optical responses. The relaxation time can be described as $Γ(t)=1/τ(t)=AeeTe(t)2+BepTl(t)$⁠, where $Te(t)$ and $Tl(t)$ are electronic and lattice temperatures, respectively. A_ee and B_ep are constant coefficients, which are reported as $1.7×107$ and $1.45×1011$ s⁻¹ K⁻¹, respectively.³³ Although the pumping laser excites coherent electrons and hot electrons through electron–electron interactions, the present TEELS measurement cannot detect the primary process because of the fast time constant. Therefore, the lattice temperature is estimated to be approximately $(1.2 ± 0.4)×103$ K based on the broadening of the EELS width and the initial lattice temperature of 300 K.

The time-evolution process can be described using a two-temperature model (TTM):^26,33–35

where $Ce(Te)=γTe$ and C_l are the electronic and lattice heat capacities, respectively. γ and C_l are 66 and $2.4×106$ J m⁻³ K⁻¹ for Au, respectively.³⁴ G represents the electron–phonon coupling constant, $3×1016$ W m⁻³ K⁻¹. The size of the AuNTs is smaller than the irradiation area of the pumping laser under the experimental conditions; therefore, the spatial thermal diffusion term in the TTM equations is neglected. The calculated temperatures T_e and T_l are shown in Fig. 5. The inset of Fig. 5 shows the inverse of the relaxation time evaluated from T_e and T_l. The electronic temperature before the electron–phonon interaction is estimated to be $(8.4 ± 0.8)×103$ K based on the measured relaxation time. The high intensity of the pumping laser induces a high electronic temperature that contributes to a long decay time, which enables the detection of the decay process in the EEL spectrum measured using the TR-TEM with a pulse duration of 8.5 ps. Furthermore, the lattice temperature was estimated to increase up to $(1.1 ± 0.1)×$ 10³ K at 100 ps after photo excitation, which corresponds to the temperature estimated from the energy-width broadening. The increase in the lattice temperature contributes to volume expansion, which reduces ρ. The electronic temperature contributes mainly to the reduction of relaxation time, which causes energy-width broadening.

The broadening of surface and bulk plasmons has the same feature. The peak energy of bulk plasmons shifts to the lower energy of 3% evaluated by the shift energy $δEbulk$ of −0.8 eV and the peak energy E_bulk of 24.2 eV. The energy shift due to the volume expansion is given by $δEbulk/Ebulk∼−12∫T0Tαv(T′)dT′$⁠, where $αv(T)$ is a volumetric thermal expansion coefficient. The coefficient is rewritten as $αv(T)=a0+a1T$⁠. Using the volumetric thermal expansion coefficient of gold, $a0=3.62×10−5$ K⁻¹, $a1=1.88×10−8$ K⁻², the temperature is roughly estimated to be $(1.2 ± 0.2)×103$ K; the result shows the same temperature evaluated from the energy broadening.^36,37

The surface plasmon peak shifts to higher energy, as shown in Fig. 4(b), which is the opposite direction of the bulk plasmon peak shift. The peak shift is consistent with previously reported results of transient absorption spectra of LSPs, which shows that the spectral peak of optically excited AuNTs also has a shorter wavelength.^28–30 Furthermore, the wavelength of the LSP peak is dependent on the size of the AuNTs, for which the wavelength decreases with an increase in the particle size.²³ In contrast, the experimental results for bulk plasmons show a reduction in electron density in the bulk region due to the volume expansion. The present TEELS result shows an increased electron density in the LSPs on the stimulated AuNTs, whereas the electron density of the bulk region is reduced. The balance between the reduction of electron density in the bulk properties and the size and geometric effects of the AuNTs results in the opposite energy shift. The time-dependent specifications, energy-width broadening due to the increase in relaxation time, and energy shift due to the electron density change show that the electron–phonon interaction was successfully measured using the TEELS method in the TR-TEM.

The typical formula in Eq. (1) for the differential probability of energy loss does not consider the electronic and lattice temperatures. The lattice temperature is partially considered through lattice expansion. However, the electronic temperature does not affect the probability of Eq. (1). Therefore, the experimental results indicate that a correction term for the effect of the electronic temperature must be added to Eq. (1), where atom motion is frozen at 0 K. The energy width and shift can be detected simultaneously; therefore, the time evolution of the peak intensity was determined to be influenced by both the electronic and lattice temperatures. There are different behaviors in the energy shift and increase in the EELS intensity, which indicates that the electron density and probability are different at localized and bulk plasmons because of their different energy shifts.

The optical approach shows only the SPR due to the detection wavelength. In contrast, TEELS can reveal the relation between the time evolutions in surface and bulk plasmons. The experimental results show that bulk and surface plasmons have the same time evolution, which indicates that excited electrons on the surface and bulk regions have the same relaxation process in both electron–phonon and phonon–phonon interactions. The relation between bulk and surface plasmons shows correspondence in the energy-width broadening and the difference in the intensity increase due to the energy-loss function and the contributing electron numbers. Furthermore, the results show that the electronic temperature contributed to the energy-loss probability, which has not been considered in the EEL process. This will allow a new analytical method of the ultrafast dynamics of electrons and lattice in materials, where the results show the decay time of electron–phonon interactions based on EEL spectra. Details of excited electrons in NPs investigated via plasmon energy loss will lead to improvement in the performance of devices for the energy-harvesting of photons in nanostructure-controlled materials. TEELS measurements in electron microscopy are also expected to reveal time-dependent specifications of plasmons and bonding states at the nanoscale.

The authors wish to thank Dr. I. Nagaoki, Dr. T. Kobayashi, and Dr. S. Kawai of Hitachi High-Tech, and Dr. N. Togashi, Dr. Y. Yoshida, Dr. W. Nagata, Dr. K. Nakakura, and Dr. M. Furui of Nagoya University for helpful support and encouragement. The authors also thank Dr. J. Sasabe, Dr. M. Suyama, Dr. A. Ujima, Dr. Y. Matsuoka, and Dr. Y. Okamoto of Hamamatsu Photonics for technical support with the semiconductor photocathode. This research was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Nos. 17H02737 and 21H04637 and by the Japan Science and Technology Agency (JST)-Mirai Program Grant No. JPMJMI18G2, Japan.