Incoherent versus coherent emission

Figure 2a shows a CL spectrum taken from a bulk gallium arsenide crystal measured using our CL setup showing the characteristic band-edge emission at λ₀ = 870 nm.^{Reference Brenny, Coenen and Polman11} The measured azimuthally-averaged angular emission distribution around λ₀ = 870 nm is shown in Figure 2b. A Lambertian angular profile is found, consistent with an isotropic emission distribution within the GaAs crystal (see inset in Figure 2a). The emission observed here is the “classical” incoherent CL observed in many systems before. Angular measurements of incoherent CL can find applications in characterization of optoelectronic devices such as light-emitting diodes (LEDs) and solar cells.

Figure 2.

(a) Measured cathodoluminescence (CL) spectrum from a bulk GaAs single crystal taken at 30 keV electron energy. The inset schematically shows the isotropic radiation process inside GaAs. Only the light within the critical angle (θ_c) can escape. (b) Measured emission pattern (blue solid line) for GaAs as a function of zenithal angle θ (azimuthally averaged) for λ₀ = 850 nm. The black dashed line shows a theoretical Lambertian (Lamb.) pattern. The gray solid lines indicate the angular range corresponding to the hole in the mirror where no light is collected. (c) Measured CL spectrum from a bulk Al single crystal, which is dominated by transition radiation (TR). The inset schematically indicates this process where the electron creates an image charge, giving rise to a vertical dipole at the surface, emitting with a toroidal angular pattern. (d) Measured emission pattern (red solid line) for Al as a function of zenithal angle θ (azimuthally averaged) for λ₀ = 400 nm. The black dashed line shows the theoretical TR pattern. Reproduced with permission from Reference 10. © 2014 American Institute of Physics.

We studied the coherent emission that occurs when the incident electron beam passes through the vacuum/material interface. Figure 2c shows this transition radiation (TR) spectrum for a polished surface of an aluminum single crystal.^{Reference Yamamoto, Ohtani and García de Abajo10} A broad featureless spectrum is observed over the entire spectral range collected by the detector (λ₀ = 400–900 nm). This TR spectrum can be explained to first order by a simple electrodynamic model, in which the electron approaching the interface induces an image charge in the metal, thus inducing an effective vertical dipole moment that is oriented upward. This transient dipole then decays into the far field with a characteristic doughnut emission pattern. The observed CL spectrum reflects the inherent broad spectral nature of the electron-beam-induced excitation process as discussed above. The vertical scales in Figure 2a and c indicate the absolute emission rates per incident photon, per unit bandwidth. When integrated over the spectral range shown in Figure 2c, the TR emission rate is about 2 × 10^–4 photons per incident electron.

The measured angular emission pattern at λ₀ = 400 nm is shown in Figure 2d together with a calculation of the TR radiation pattern;^{Reference García de Abajo5} very good agreement between the two distributions is observed. The spectrum and angular profile of TR are only determined by the electron-beam energy and the optical constants of the substrate. Note that aluminum, like most metals, does not exhibit efficient intraband optical transitions and hence the spectrum in Figure 2c–d is dominated by TR. We note that a TR band is also present in the spectrum for GaAs in Figure 2a. However, it is overshadowed by the ∼5000 times stronger incoherent band gap emission. As TR is a well-characterized phenomenon, and metals show only weak incoherent emission, we use the combination of TR measurements and calculations for either single-crystal Al or Ag to calibrate the CL system, so that absolute CL measurements can be performed on other samples.

Excitation of plasmonic nanoparticles

We investigated the electron-beam-induced generation of nanoscale optical resonators next. The left inset in Figure 3a shows a SEM image of a single Au nanodisk on a Si substrate, made using electron-beam lithography and liftoff techniques. The Au nanoparticle is 100 nm in diameter and has a height of 80 nm. Figure 3a shows a CL spectrum obtained by spatially averaging the CL emission collected from a raster scan over the particle with 5 nm resolution. A clear resonant spectrum is observed, which reflects the radiation of a vertically-oriented dipolar plasmon resonance in the Au nanoparticle, peaking at λ₀ = 560 nm. Plasmons are elementary excitations of free electrons in metals. They can be efficiently excited as the electric field of the electron beam passing through the nanoparticle can couple to the unbound charges. The linewidth of the resonant peak in the spectrum is determined by radiative and Ohmic damping. A spatial map of CL emission in Figure 3a shows the nanoparticle plasmon is excited for all beam positions, but most efficiently in the center, where the electron beam direction aligns with the plasmonic eigenmode’s vertical dipole moment. Plasmonic metal nanoparticles and particle networks can find applications as antennas; for example, to enhance spontaneous emission,^{Reference Mertens, Biteen, Atwater and Polman12} form building blocks in subwavelength optical integrated circuits,^{Reference Huang, Seo, Sarmiento, Huo, Harris and Brongersma13} create optical hot spots for sensing,^{Reference Novotny and van Hulst14} enhance light absorption in photodetectors^{Reference Stuart and Hall15} and thin-film solar cells,^{Reference Catchpole and Polman16} as well as applications in photothermal therapy^{Reference Ayala-Orozco, Urban, Knight, Urban, Neumann, Bishnoi, Mukherjee, Goodman, Charron, Mitchell, Shea, Roy, Nanda, Schiff, Halas and Joshi17} and transparent conducting nanowire meshes.^{Reference van de Groep, Spinelli and Polman18,Reference Garnett, Cai, Cha, Mahmood, Connor, Cristoforo, Cui, McGehee and Brongersma19}

Figure 3.

(a) Normalized cathodoluminescence (CL) spectrum for an Au nanodisk on Si with a diameter of 100 nm and a height of 80 nm. A scanning electron microscope (SEM) image is shown as an inset (bottom left, scale bar: 50 nm). The spectrum is taken by averaging the CL spectrum over the particle. A 2D CL excitation map taken at the peak wavelength λ = 560 nm is shown as an inset (top right). The dashed line indicates the edge of the structure taken from the SEM image. (b) Normalized CL intensity as a function of azimuthal (ϕ) and zenithal (θ) angles taken at λ₀ = 600 nm for excitation on the left side of the structure. The geometry is indicated by the cartoon at the right. Reproduced with permission from Reference 20. © 2014 Nature Publishing Group.

The angular distribution of the radiation emitted by the single Au nanoparticle is shown in Figure 3b, in which the electron beam was placed on the left edge of the nanoparticle (see cartoon on the right in Figure 3b).^{Reference Coenen, Vesseur, Polman and Koenderink20} The CL emission intensity is shown as a function of zenithal angle θ and azimuthal angle ϕ. The black region around ϕ = 0°, where no light is observed, corresponds to the opening in the paraboloid mirror (see Figure 1b–c). While the nanoparticle excited at its center (data not shown) shows a symmetric angular profile reflecting the doughnut-type emission from an upward-pointing dipole, in this case the measured angular distribution shows a clear left-right asymmetry. CL emission is more intense toward the right side of the angular pattern (around ϕ = 90°) than toward the left side (around ϕ = 270°). This asymmetry arises from the fact that off-center excitation with the electron beam leads to the simultaneous excitation of in-plane and out-of-plane dipole components which interfere in the far-field.^{Reference Coenen, Vesseur, Polman and Koenderink20} This nanoscale beaming effect co-rotates with the electron-beam excitation position (data not shown). A more detailed analysis of the far-field interference of dipolar electric and magnetic dipole modes as well as quadrupolar modes is given in References Reference Coenen, Bernal Arango, Koenderink and Polman21 and Reference Coenen and Polman22.

Excitation of surface plasmon polaritons

Because the electron-beam-induced excitation is localized, it represents a large range of optical wave vectors. This, together with the inherently broad excitation spectrum, allows direct excitation of surface plasmon polaritons (SPPs). These guided surface waves have in-plane momenta larger than that of free-space light at the same frequency and cannot be directly excited with light. SPPs are transverse-magnetic waves, with their electric field pointing in the normal direction, and thus, couple well with the incident electron beam. In a simple model, the point dipole composed of the incident electron and its image charge in the metal decays, according to Fermi’s Golden Rule, to the available modes, in this case both the far field (TR) and SPPs.

Figure 4a shows an SEM image of a 400-nm-deep elliptical cavity, which is sculpted into the surface of a single-crystal gold substrate using focused ion beam milling.^{Reference Schoen, Coenen, García de Abajo, Brongersma and Polman23} These structures serve as cavities for SPPs that propagate at the Au surface and are confined within the cavity walls. The SPP cavity modes are excited with the electron beam, and CL emission is observed due to scattering of SPPs at the cavity walls into the far field. Figure 4b shows a 2D spatial excitation map taken at an emission wavelength of λ₀ = 720 nm. Two hotspots are observed resulting from the interference of SPPs within the cavity. This modal pattern strongly depends on the size of the SPP wave compared to the cavity size. If the cavity is large compared to the wavelength, higher-order modes are supported and the interference patterns become more complex.^{Reference Vesseur, Coenen, Caglayan, Engheta and Polman24} An angular emission pattern of the elliptical cavity, which is excited in one of the emission maxima, shows clear directional beaming of light at a wavelength of λ = 600 nm (Figure 4c).

Figure 4.

(a) Scanning electron microscope (SEM) image of a 400-nm-deep elliptical plasmon cavity with major/minor axes of 1000/600 nm milled into a single-crystal gold substrate using a focused ion beam. (b) 2D cathodoluminescence (CL) excitation map for the elliptical cavity at peak wavelength λ₀ = 720 nm, showing a surface plasmon polariton (SPP) resonant mode distribution. (c) Angular CL pattern measured on an elliptical cavity with major/minor axes of 1500/900 nm at λ₀ = 600 nm, with excitation in the left focal spot of the ellipse. (d) SEM image of a 2-μm-long plasmonic waveguide with a SiO₂ core and Ag cladding. The outside of the waveguide is coated with 10 nm of Cr to suppress SPP modes on the top and bottom interfaces. (e) CL line scan, measured along the center of the waveguide as indicated by the white arrow in (d). The structure has a 400-nm-wide core. (f) Angular CL pattern for a waveguide with a 210-nm-wide core, measured at λ₀ = 700 nm for central excitation. For this measurement, the waveguide was oriented from top to bottom. Reproduced with permission from Reference 22. © 2013 American Chemical Society; Reference 23. © 2013 American Physical Society.

Figure 4d shows an SEM image of a linear SPP waveguide composed of a dielectric silica core surrounded by Ag.^{Reference Coenen, Vesseur and Polman25} In such coaxial waveguides, strong coupling occurs between SPPs that propagate at the internal silica/Ag interfaces, and a hybrid SPP mode forms of which the dispersion (the relation between wave vector and frequency) strongly depends on the core dimensions. The silica/Ag waveguide has a length of 2 μm; therefore, standing SPP waves will form due to reflection of SPPs at the waveguide outer facets. CL spectra were taken by scanning the electron beam along the central axis of the waveguide (dashed line in Figure 4d).

Figure 4e shows these standing waves, taken at a broad range of emission wavelengths in the range λ₀ = 500–1000 nm. At each optical frequency, or vacuum wave length, a characteristic standing wave pattern is observed, the period of which is determined by the SPP wavelength at that frequency. SPPs have short wavelengths at frequencies corresponding to a free space wavelength of λ₀ = 500 nm and long wavelengths for frequencies corresponding to a wavelength of λ₀ = 1000 nm. In this way, the SPP dispersion diagram can be fully reconstructed. In this experiment, light is mostly collected from the two output facets. As the SPPs are coherently excited, there is a well-defined phase relation between these radiating point sources, which leads to a fringe interference pattern in the angular radiation patterns, as can be seen in Figure 4f.^{Reference Coenen, Vesseur and Polman25} Nanostructures supporting SPPs find applications in, for example, subwavelength optical components,^{Reference Verhagen, Spasenović, Polman and Kuipers26} lasers,^{Reference Oulton, Sorger, Zentgraf, Ma, Gladden, Dai, Bartal and Zhang27} LEDs,^{Reference Okamoto, Niki, Shvartser, Narukawa, Mukai and Scherer28} solar cells,^{Reference Atwater and Polman29} and sensors.^{Reference Wu, Khanikaev, Adato, Arju, Yanik, Altug and Shvets30}

Excitation of dielectric nanostructures

Imaging and angle-resolved CL is a powerful tool for studying localized and propagating plasmon resonances in metallic nanostructures; however, the concept of coherent electron-beam excitation is generally applicable to any polarizable medium including semiconductors and dielectrics. Figure 5a shows an electron micrograph of a silicon disk fabricated by electron-beam lithography in combination with reactive ion etching into the top layer of a silicon-on-insulator substrate.^{Reference Coenen, van de Groep and Polman31} The silicon disk shown in the image has a diameter of 200 nm and a height of 100 nm and is placed on a 300-nm-thick SiO₂ layer with a thick silicon substrate underneath. These dielectric nanocavities possess Mie-type resonant modes in which the local fields are mostly confined within the Si disk. Figure 5b shows a 2D excitation map for a 320-nm-diameter disk at a wavelength of λ₀ = 475 nm. A radially symmetric excitation distribution is observed, which reflects the resonant field distribution in the cavity. For this particular example, a minimum is observed in the center, and several subsequent maxima and minima are observed as the electron beam is moved outward. The angular emission pattern of such a structure shows an upward beaming of light within a relatively narrow cone (Figure 5c). Dielectric nanostructures can find applications in microcavity lasers,^{Reference Armani, Kippenberg, Spillane and Vahala32} integrated optical components, and light scattering layers in photovoltaics,^{Reference Spinelli, Verschuuren and Polman33} among others.

Figure 5.

(a) Scanning electron microscope (SEM) image of a silicon nanodisk (diameter 200 nm, height 100 nm) on a 300-nm-thick SiO₂ layer. (b) Two-dimensional (2D) cathodoluminescence (CL) excitation map of a 320-nm-diameter silicon disk at peak wavelength λ₀ = 475 nm. (c) Angular CL pattern for a 300-nm-diameter disk collected at λ₀ = 500 nm for excitation in the center. (d) SEM image of a photonic crystal cavity etched in a 200-nm-thick Si₃N₄ membrane. (e) 2D CL excitation map of the cavity (area shown by the white square in Figure 5d) for λ₀ = 650 nm. (f) Angular CL pattern for the photonic crystal, taken from a regular 2D hexagonal photonic crystal, measured at λ₀ = 700 nm. Reproduced with permission from Reference 30. © 2013 American Chemical Society; Reference 33. © 2012 Nature Publishing Group.

Excitation of photonic crystals

The power of the angle-resolved detection capability becomes clear further in CL studies of photonic crystals. Figure 5d shows an electron micrograph of a 200-nm-thick Si₃N₄ membrane in which a hexagonal photonic crystal is made using a combination of electron-beam lithography and reactive ion etching.^{Reference Sapienza, Coenen, Renger, Kuttge, van Hulst and Polman34} In this particular example, a point defect cavity is created by removing a hole in the center. The photonic crystal is designed such that light propagation in the plane of the crystal is forbidden for a certain wavelength band (the photonic bandgap). In the cavity, however, an optical mode can exist and its field distribution can be directly probed with CL. Figure 5e shows the spatial excitation distribution of the cavity collected at the cavity resonance wavelength of λ₀ = 650 nm. A complex field distribution pattern is observed inside the cavity and reveals features at a deep-subwavelength scale. Finally, Figure 5f shows an angular emission pattern from a regular hexagonal photonic crystal (without defect cavity). The hexagonal symmetry of the photonic crystal is clearly reflected in the azimuthal emission distribution. An emission band at a particular zenithal angle is directly related to the wave vector of the mode within the photonic crystal at the corresponding frequency and therefore, such measurements can be used to derive the photonic bandstructure of the photonic crystal in great detail. This analysis can even be performed in a spatially resolved manner, so that the 2D mode profile of each photonic band can be separately mapped. Photonic crystals find applications in, for example, miniature lasers,^{Reference Painter, Lee, Scherer, Yariv, O’Brien, Dapkus and Kim35} LEDs,^{Reference Wierer, David and Megens36} on-chip optical networks and memory,^{Reference Kuramochi, Nozaki, Shinya, Takeda, Sato, Matsuo, Taniyama, Sumikura and Notomi37} and sensors.^{Reference Chow, Grot, Mirkarimi, Sigalas and Girolami38}

CL imaging resolution

To first order, the resolution of the coherent CL imaging technique is limited by the spot size of the electron beam, which is typically in the range 1–10 nm, depending on SEM instrument, beam current, and acceleration voltage. The extent of the evanescent electric field about the electron trajectory will determine the spatial range over which a polarizable nanostructure is excited. By carrying out measurements of CL intensity across a square hole made into a thin silicon membrane, we have determined the spatial resolution for 30 keV electron-beam excitation to be 30–40 nm.^{Reference Sapienza, Coenen, Renger, Kuttge, van Hulst and Polman34} The field extent can be reduced by lowering the electron energy.