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The emerging frontier at the intersection of optics and electron microscopy

A comparison of electron-energy-loss measurements and optical spectroscopy shows that both are required to access the full dielectric surface-plasmon behavior of nanoparticles.
3 February 2009, SPIE Newsroom. DOI: 10.1117/2.1200901.1493

The extraordinary optical properties of noble-metal nanoparticles are attracting a great deal of interest due to their unusual behavior and because of promising applications. When light hits a metal nanoparticle (i.e., a species smaller than the illuminating wavelength), the associated electric field pushes the electrons back and forth along the particle. The collective natural oscillation frequency is known as the ‘plasma frequency’ and the corresponding electromagnetic mode is a ‘surface plasmon’ (SP). SP modes of metal nanoparticles generally fall in the optical (visible) and near-IR regime and can be tuned to a considerable degree by controlling the particles' shapes.

Among the first of the numerous SP-resonance applications were single-molecule surface-enhanced Raman scattering1,2 and enhancement of nonlinear light generation, e.g., of second-harmonic production at rough metal surfaces.3,4 More recently—with the development of nanofabrication techniques and advances in self-assembly based on wet chemistry—the range of applications has widened from highly integrated photonic structures5–7 to biological sensing and labeling (e.g., SP-resonance-based biosensors). The latter have become an established method to measure molecular interactions.8 SPs of noble-metal nanostructures are also the building blocks of metamaterial and negative-index structures, which offers new opportunities for realizing physical phenomena that—to date—have only been studied as theoretical exercises.9

Figure 1. Overview of the different sizes and shapes of the gold (Au) nanorods in the sample.

Optical-spectroscopy techniques such as near-field optical microscopy10 and dark-field illumination11 have been the primary methods to investigate the optical (and near-IR) properties of nanoparticle samples. However, although this approach is useful to isolate the optical spectra of single nanoparticles, the techniques are limited in their ability to resolve the nanoscale spatial variation of the SP modes within a single nanoparticle. These significant limitations can now be addressed with electron-energy-loss spectroscopy (EELS) using a scanning-transmission-electron microscope. This method has been routinely used for many years to study the bulk plasmon loss in thin metallic films12 and clusters13 for energies up to many electron volts. With the recent advent of monochromatic electron beams and improved energy detection, EELS has produced examples of SP characterization in single nanostructures at spatial resolutions of a nanometer or better and energies as low as 1eV14,15 (i.e., in the optical).

EELS involves analyzing the energy of initially monoenergetic electrons after they have interacted with a specimen: the electric field associated with a fast electron flying by the conducting material affects the electrons on the conductor surface, leading to charge displacement. The surface charges undergo a collective oscillation at their natural plasma frequency while the fast electron loses energy equivalent to the plasmon energy. This interaction takes place within a few atomic layers. Hence, EELS provides a highly localized spectrum of the system's excitations. The electron beam is collected through a spectrometer to display its energy distribution following the interaction, thus providing information on the energy exchange.16

Figure 2. Electron-energy-loss spectrum of a single nanorod (in arbitrary units, a.u.) where both plasmon peaks are resolved, at 1.9 (longitudinal mode) and 2.4eV (transverse mode), respectively.

The goal of both optical spectroscopy and EELS is to determine the dielectric function, ∊(ω) (where ω is the frequency of the applied field), of a nanoparticle or particle system, which provides a complete characterization of the interaction of a material with the electromagnetic field. Optical absorption generally measures the imaginary part, Im[∊(ω)]. The energy-loss function characterizing energy transfer to the electron gas of bulk plasmon modes is given by Im[1/∊(ω)].17

We compare the spectra obtained by optical absorption and EELS to determine their relative merits for plasmon spectroscopy. We use state-of-the-art EELS14,15 to resolve the plasmon peaks of gold (Au) nanorods.18 These nanoparticles have two visible/near-IR plasmon resonances, a transverse plasmon caused by electron oscillation along the short axis of the nanostructures with energy around 2.4eV (approximately coincident with that of a spherical Au nanoparticle) and a longitudinal resonance oriented electron oscillation along the long axis. The latter is redshifted with respect to the transverse mode and strongly dependent on the particle aspect ratio (the ratio of length to width).

Figure 3. Transmission-electron-microscope image of a single gold rod (70nm long and 28nm wide). The electron-beam position is indicated by the small red circle at the particle's tip.

The EELS data were obtained using a modified FEI Titan 80–300 microscope equipped with a special high-brightness Schottky-field emission-electron source, a gun monochromator, a high-resolution GIF Tridiem energy filter, and two Corrected Electron Optical Systems hexapole-type spherical-aberration correctors. This system has sufficient energy resolution to easily resolve both SP modes without the need for data processing. In addition, by using the nanoscale dimension of the focused electron beam, we can excite the nanoparticles at precise locations and thus probe the spatial and size dependence of the relative excitation efficiencies of both plasmon modes.15

Figure 4. Ensemble optical-absorption spectrum. The peak at 520nm (2.4eV) corresponds to the main surface-plasmon absorption while the second peak represents the longitudinal absorption of the Au nanorods. The significant spectral broadening is due to the sample's polydispersity.

Figure 2 shows the EELS spectrum of a 70×28nm Au nanorod (see Figure 3). The electron beam is placed at the edge of the particle to induce particle displacement along both axes. The resolved peaks at 1.9 and 2.4eV correspond to longitudinal and transverse plasmon resonance, respectively. For comparison, Figure 4 shows the corresponding optical-absorption spectrum of the solution, where the peak at 2.5eV is caused by transverse plasmon absorption. The broad peak at lower energy implies a highly polydisperse sample containing nanostructures with a wide range of lengths, shapes, and aspect ratios (see Figure 1).

We consider the nanorods to be reasonably approximated as prolate spheroids of varying aspect ratios. Then, we take the energy-loss spectra calculated from both Im[1/∊(ω)] and the analytical energy-loss probability calculated for prolate spheroids and relate these to optical-absorption spectra.15 The EELS and optical measurements are sensitive to the same modes (see Figure 5). Each clearly resolves the longitudinal and transverse modes. In addition, the redshift of the longitudinal plasmon peak (with increasing aspect ratio) is manifested in all three samples, although important differences are apparent. The spectral-peak position of the optical absorption, Im(∊p), the loss function, (), and the loss probability, Γloss, do not coincide exactly. The longitudinal loss function and the loss-probability peaks are blueshifted relative to the longitudinal peak of the optical absorption. Their transverse peaks also show less dependence on the aspect ratio than the transverse optical-absorption peak. The energy-loss expressions Γloss(ω) and for a prolate spheroid with aspect ratio ρ=4 show longitudinal peaks at 1.6 and 1.76eV, respectively, and transverse peaks between 2.4 and 2.5eV.

Figure 5. Comparison among analytical representations of the energy-loss peak for three prolate Au spheroids. For all expressions we set ∊m=1 and γ=1.06 for the host-dielectric medium and the damping coefficient for the Drude model, respectively. The aspect ratio ρis varied to show its effect on plasmon-peak absorption. Im(∊p): Optical absorption, (): Loss function, Γloss: Loss probability, ω: Frequency of the applied field.

Thus, the dielectric function for a single metallic nanostructure can be deduced from EELS experiments. Most importantly, we have shown that optics and EELS are in many ways complementary: optical measurements are good for high spectral but limited in spatial resolution, even using near-field techniques. Transmission-electron microscopy/EELS is good for nanometer-scale imaging and thus for detailed mapping of plasmon modes in nanostructures. Although EELS can distinguish different plasmon modes, it cannot yet produce meaningful measurements of spectral-line widths or shapes. Optical-frequency modes are accessible through both techniques and thus give us access to the full dielectric behavior of nanoparticles. However, a complete description still requires both. We expect that the intersection of optics and EELS will soon become a remarkably fruitful area of plasmonics research.

Moussa N'Gom
Applied Physics Program
Center for Ultrafast Optical Sciences
University of Michigan
Ann Arbor, MI
Theodore B. Norris
Department of Electrical Engineering
Computer Science and Center for Ultrafast Optical Sciences
University of Michigan
Ann Arbor, MI