LETTER pubs.acs.org/NanoLett
Vertical Plasmonic Resonant Nanocavities Xinli Zhu, Jiasen Zhang,* Jun Xu, and Dapeng Yu* State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100871, People’s Republic of China
bS Supporting Information ABSTRACT: We demonstrate plasmonic modes in a vertical nanocavity with an air output window at the top surface and Ag reflectors. The resonances of surface plasmon polaritons are investigated using cathodoluminescence spectroscopy. The resonant modes are determined by comparing experiment and theoretical simulations. The plasmon dispersion relation in the vertical nanocavities shows a strong confinement to the electromagnetic field, and the smallest modal volume is only 0.0014 μm3. Our work provides insights into the development of nanoscale plasmonic vertical cavity surface-emitting lasers. KEYWORDS: Surface plasmon polaritons, vertical resonance, cathodoluminescence spectroscopy, nanocavities
V
ertical cavity surface-emitting lasers (VCSELs), which are promising ideal candidates for light sources, have attracted considerable research interest due to their fascinating properties, including light emission in the vertical direction, single mode emission, and array configurability.1-3 However, the dimensions of VCSELs can be as large as several hundred micrometers. Scaling optical devices down to the nanoscale level is required for future high-density integrated optical circuits. Surface plasmon polaritons (SPPs),4,5 which are electromagnetic waves coupled with the oscillation of collective electrons bound to a metal-dielectric interface, promise to be a promising route for downscaling photonic devices below the diffraction limit of light.6-8 Studies of plasmonic cavities with nanoscale dimensions are currently a popular research topic. A nanosheet plasmon cavity was proposed for squeezing visible light waves into nanometer-sized optical cavities.9 Hofmann et al.10 observed the plasmonic modes of annular resonators by cathodoluminescence (CL). Using two high metallic fins as cavity reflectors, quality factors (Q factors) up to 200 have been obtained at visible frequencies in plasmonic Fabry-Perot nanocavities.11 Previous studies12 have successfully resolved whispering gallery modes of plasmonic ring cavities with subwavelength ring radii. Recently, an ultrasmall cavity mode volume was achieved via nanoscale plasmonic metal-insulator-metal (MIM) disk resonators.13 All of the abovementioned resonators, however, are in-plane resonators. Using a plasmonic vertical cavity, it is possible to implement VCSELs with an ultrasmall mode volume at the nanoscale level. In this Letter, vertical plasmonic nanocavities are fabricated and demonstrated. Resonant wavelengths of nanocavities with cavity lengths in the range of 120-840 nm are obtained using CL spectroscopy. The dispersion relations for these nanocavities are determined and show that the effective SPP wavelength is much smaller than the free-space wavelength. Simulations using the finitedifference time-domain (FDTD) technique suit the experiment r 2011 American Chemical Society
Figure 1. Plasmonic vertical nanocavity. (a) Schematic of a single nanocavity and excitation of SPPs with backscattered electrons. (b) The 30°-tilted SEM image of a representative cavity with length, width, and height of 360, 120, and 500 nm, respectively.
well, allowing us to obtain the mode patterns with FDTD simulations. The plasmonic vertical nanocavity, which features strong optical confinement and flexibility of fabrication, demonstrates the possibility of achieving VCSELs at the nanoscale level. The schematic of a vertical plasmonic nanocavity is shown in Figure 1a. The nanocavity is a rectangular hexahedron with a Received: November 17, 2010 Revised: January 14, 2011 Published: January 31, 2011 1117
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Figure 2. Resonances and mode patterns of plasmonic nanocavities with 70 nm widths, 500 nm heights, and increasing lengths. (a) CL spectra of 16 nanocavities with cavity lengths increasing from 120 (bottom) to 770 nm (top). (b) Calculated spectra using the FDTD method. Spectra are offset vertically for clarity. The black arrow at 655 nm indicates that the spectra were collected twice at the same position due to the limited measuring range of the spectrophotometer. (c,d) Calculated mode field intensity patterns and electric field amplitude of a 260 nm long cavity at 635 nm in the y = -35 nm and x = 0 planes, respectively. (e,f) Calculated mode patterns in the y = -35 nm plane of 420 and 610 nm length cavities at 539 and 523 nm, respectively.
height H, length L, and width W. Besides the output window, which is an air reflector located on the surface of the structure, the five other faces of the hexahedron are walled by silver. Three faces that are perpendicular to the x-z plane act as Ag reflectors, where reflections can be near 100%. The origin of coordination is located at the center of the cavity. The plasmonic vertical nanocavities were fabricated via a template stripping method we previously proposed.14 In brief, PMMA with designed thickness is spun on silicon wafer and then patterned via EBL. A metal layer, which is thicker than the PMMA layer to ensure complete coverage, is then deposited on the patterns. After being glued to another silicon substrate, due to the weak adhesion of the PMMA the metal layer can be easily stripped off the first silicon substrate. After cleansing the residual PMMA with acetone, a metal layer that strictly inherits the morphology of the PMMA patterns is obtained. In the experiment, the height of the cavities was maintained at 500 nm, and the length and width were changed to tune the plasmon resonant wavelength and pattern. Figure 1b shows 30°-tilted scanning electron microscope (SEM) images of a representative nanocavity with a length of 360 nm and width of 120 nm. As an effective plasmonic source, a free-electron beam manifests its advantages with respect to exciting SPPs at a nanoscale spot.15-20 To assess the characteristics of the nanocavities, the resonant wavelengths of the nanocavities were measured using a CL detection spectrometer installed in the SEM. This technique has been used in previous studies to investigate plasmonics.15-17 A 30 keV highly localized electron beam with a beam diameter of ∼5 nm from a thermal field-emission gun was passed a 1 mm diameter hole in a parabolic reflector above the sample holder and then impinged upon the undersurface of the nanocavities with an exposure time of 16 s. Backscattered electrons with energy levels similar to that of the incident electron beam effectively excited SPPs at the side wall of the nanocavity. The parabolic reflector with an off-axis focus effectively collected the light emitted from the output window of the nanocavity. Light was coupled through a monochromator to a charge-coupled
device (CCD) array detector. The CL spectrum at every scanning point was recorded by the CCD detector. The emission spectra collected includes transition radiation emissions21,22 and light decoupled from the SPPs. For accuracy, the CL spectroscopic responses were corrected by subtracting the background emission spectra of unstructured Ag obtained far from the structured Ag sampling area. To understand the excitation of SPPs, we used Monte Carlo simulation program to calculate backscattered probability of 30 keV incident electrons on a plane silver surface. It shows that about 40% probabilities of backscattered electrons are produced by the incident electrons. The nature of the backscattered electrons is of the energy level similar to that of incident electrons and cos θ distribution (Supporting Information Figure S1) above the sample surface. Most of the backscattered electrons impinge upon the side walls of the nanocavity owing to the narrow nanocavity with relative high aspect ratio and then excite SPPs at the side wall (Figure 1a). Figure 2a shows the CL spectra of 16 different nanocavities with cavity lengths increasing from 120 to 770 nm and a constant width of 70 nm. All the CL spectra were obtained when the electron beam was positioned at the geometric center of the undersurface with 16 s collected time (Figure 1a). Generally the spatial maps of mode should be easy to obtain with the 5 nm resolution of the microscope when the electron beam scans over the undersurface. In the experiment, we have tried our best to map the plasmonic modes, but we cannot obtain spatial maps of the modes. We attribute it to the backscattered electron excitation of the vertical cavity modes. In the experiment, the incident electron impinged on the undersurface of the cavity and cannot excite vertical cavity modes directly. However, backscattered electrons were incident upon the side walls and excited SPPs (Figure 1a). Because of the large-range angular distribution of the backscattered electrons (Figure S1, Supporting Information), we cannot obtain spatially resolved vertical cavity mode patterns but the CL spectra only. The excitation efficiency of backscattered electrons at the side wall are slightly different when the incident 1118
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Figure 3. Calculated far-field angular distributions of the leakage radiation from the nanocavities (unit, degree). (a-c) Calculated angular distributions for the plasmonic mode (1, 1), (1, 2), and (1, 3), corresponding to Figure 2c,e,f, respectively.
electron beam is positioned at different points in the undersurface of the cavity. At the same time, there is no plasmonic resonant mode at the undersurface of the cavity due to the small cavity widths. All the cavities had more than one peak in the measurement range. Additionally, new resonant peaks appeared with every increase in cavity length. Most of the resonant wavelengths can be sorted into five series, indicated by two green dashed lines and three blue dashed lines. The resonant wavelengths in the same series shifted to longer wavelengths with increasing cavity lengths. We will illustrate the origin of these peaks below in combination with numerical simulations. To determine the plasmonic modes, the FDTD method was used to calculate the resonant modes of the cavities with the same geometric structure. Because the plasmonic modes of the vertical nanocavities do not depend on the excitation source, in the simulations we used a pulsed light wave to excite SPPs in the cavities. Then the free oscillation of the SPPs in the cavities formed plasmonic modes. Therefore, the location of the excitation light is of unimportance as long as the symmetry of the system does not prohibit the excitation of the modes. To excite the symmetrical mode of MIM structure, a plane wave was incident along the x axis in the simulations and the spectrum was taken at a selected point on the side wall, where the relative intensities at the resonant wavelengths are similar with the experimental results. The simulated resonant wavelengths, shown in Figure 2b, are sorted into six series, indicated by green and blue dashed lines. Comparing the numerical and experimental results, it can be seen that the resonant wavelengths agree well with each other, except for the first green line on the lefthand side of Figure 2b, which disappears in the experimental results. These resonant wavelengths overlapped with the adjacent resonant wavelengths due to the large full width at the halfmaximum (fwhm) of the experiment. The propagation loss originating from the surface roughness was not considered in the simulations, resulting in a smaller fwhm. First, we analyzed the resonant mode indicated by blue lines. Figure 2c shows the simulated intensity pattern of the out-of-plane component (ycomponent) of the electric field in the y = -35 nm plane at the resonant wavelength of 635 nm for the 260 nm long cavity. Generally speaking, the electron beam locally excites the out-ofplane electric field component of the SPPs when the electron beam impinges on the sample surface under normal incidence.23 In the experiment, the vertical cavity modes cannot be excited directly by the incident electron beam. However, backscattered electrons with oblique incidence instead of the incident electron beam excite the SPPs at the side wall. As a consequence, both in-plane and out-of-plane electric field components of SPPs are excited by the backscattered electrons with different mode patterns.23 The total intensity is dominated by the out-of-plane component. The plasmonic field distributions of the
out-of-plane component in the x- and z-directions are standing waves. Nodes appear near the three Ag reflectors, and an antinode appears near the air reflector on the top surface. This is attributed to the different reflection phase shifts of the Ag and air reflectors. Numerical results show that the reflection phase shifts of the Ag and air reflectors are ∼π and ∼0, respectively, for the out-of-plane component of the electric field. Here, we name the modes (m, n), where the integers m and n denote the numbers of intensity antinodes of the out-of-plane component in the z- and x-directions, respectively, except for the antinode at the boundary of the air reflector. The resonant modes can be identified from the intensity distribution of the out-of-plane component in the x-z plane calculated by FDTD. Therefore, the mode in Figure 2c is assigned to the (1, 1) mode. The cavity has an MIM plasmon structure19,24 with two possible plasmonic modes, a lower energy symmetric or a higher energy antisymmetric modes.25 Figure 2d shows the amplitude pattern of the out-of-plane component of the electric field in the x = 0 plane at the resonant wavelength of 635 nm for the 260 long cavity, indicating the symmetric mode of the MIM structure. No antisymmetric mode was observed in the experiment, which can be attributed to the high propagation loss of the antisymmetric mode. Two resonant modes of the out-of-plane components of the 420 and 610 nm long cavities at resonant wavelengths of 539 and 523 nm are also calculated and respectively shown in Figure 3e,f. From the results, we can determine the modes of the three series indicated by the blue dashed lines, which are (1, 1), (1, 2), and (1, 3) modes, respectively. Small deviations of the resonant wavelength between experiment observations and calculations, which are more obvious for shorter cavity lengths, are caused by the slightly irregular geometry of the fabricated nanocavities (Figure S2, Supporting Information). This issue is unavoidable in the fabrication process. The angular distribution of the emission resulting from radiation leakage is of importance for applications, such as nanolaser. Here, we calculated the angular distributions by projecting the near-field electromagnetic field in the plane 50 nm above the aperture to the far-field in the x-y plane, and the results are shown in Figure 3 for the modes in Figure 2c,e,f, respectively. For the (1, 1) mode, there is only one radiation lobe with high divergence angles, which is the fundamental transverse mode. For high-order modes, multiple radiation lobes along the x axis appear. The divergence angle and direction of the leakage radiation can be controlled by decorating the aperture of the cavities.26 Benefiting from the flexible fabrication method, the angular distributions can also be modulated by array of vertical nanocavities. We have demonstrated that the resonant modes indicated by green lines in Figure 2a,b are not modes of plasmonic vertical cavities but surface modes, which will be discussed in another 1119
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Figure 4. Experimental and calculated dispersions of plasmonic modes (1, 1), (1, 2), and (1, 3) in vertical nanocavities. The gray and black lines respectively represent the dispersions of light in a vacuum and SPPs on an infinite Ag film.
paper. While the electron beam impinges the undersurface of the nanocavities, the excitation efficiency of the surface modes is low. Some surface modes shown in Figure 2b disappear in the experimental results. In the experiment, the widths of the cavities are much smaller than the free-space wavelength of the detection range. As a result, there is no plasmonic resonant mode in the three faces perpendicular to the x-z plane. To gain insights into the nature of these plasmonic vertical nanocavities, a simple analytical model is used to investigate the experimental results based on geometry and the experimental results. Considering the standing wave mode in the cavity, when the penetration depths are ignored, the resonant condition of the nanocavity is given by 2 m 1 2 n þ 1 2 4 2 ¼ þ 2 ð1Þ H2 L λ2SPP where λSPP is the SPP resonant wavelength. The dispersion relation of the cavity is essential to the accurate design and evaluation of the confinement of the cavity. Using eq 1 and the data in Figure 2a,b, the dispersion relations of 16 different nanocavities for the (1, 1), (1, 2), and (1, 3) modes are obtained and shown in Figure 4. The dispersion of different plasmonic modes exhibits similar behaviors with respect to the cavity length, and the experimental SPP dispersion agrees well with the calculated results. The plasmonic modes supported by the vertical cavity possess a wave vector larger than the SPP wave vector for an infinite planar Ag surface. This means that the SPPs are tightly confined to the MIM structure vertical cavity with an enhancement factor for a small width. One can precisely design a plasmonic vertical cavity based on the dispersion of the cavity. To investigate how the cavity width impacts the SPP resonant wavelength, two vertical nanocavities with different widths were fabricated. Figure 5a,b show the measured CL spectra of plasmonic cavities with cavity widths of 40 and 120 nm, respectively, 500 nm cavity heights, and increasing cavity lengths. Plasmonic modes are indicated by blue lines. From Figure 5a, we can see that there is a peak at around 550 nm that does not depend on the cavity length. Compared to the resonant wavelengths of 70 nm
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Figure 5. Resonances of plasmonic nanocavities with 40 and 120 nm widths, 500 nm heights, and increasing lengths. (a) CL spectra of 14 nanocavities with 40 nm widths and cavity lengths increasing from 160 (bottom) to 730 nm (top). The black arrow at 625 nm indicates two measurements. (b) CL spectra of 17 nanocavities with 120 nm widths and cavity lengths increasing from 160 (bottom) to 840 nm (top). The black arrow at 640 nm indicates two measurements. The various plasmonic modes are indicated with blue dashed lines. Spectra are offset vertically for clarity.
wide cavities, the resonant wavelengths of 40 and 120 nm wide cavities, respectively, exhibit red and blue shifts for the same mode and the same cavity length. For example, for a 360 nm long cavity, the resonant wavelength of the (1, 1) mode red-shifts from 737 to 760 nm when the cavity width is deceased from 70 to 40 nm, and blue shifts from 737 to 690 nm when the cavity width is increased from 70 to 120 nm. This result reveals that the cavity width, as a tunable parameter, can effectively modulate the SPP dispersion relation and provides another degree of freedom with which to control the resonant wavelength. Using eq 1, the dispersion relations of the cavities with 40 and 120 nm cavity widths were obtained (Figure S3, Supporting Information). The results clearly illustrates that vertical cavities with smaller cavity widths present tighter confinement and stronger interactions, as most of the electromagnetic field energy is confined to the insulator layer of MIM structures.27 Thus, one can tune the SPP resonant wavelength and confinement by changing the size of the vertical cavity in three dimensions. For an optical cavity, a small mode volume is always desirable for concentrating electromagnetic energy to a small volume. The characteristics of a three-dimensional confinement cavity lead to a small mode volume. The plasmonic field distributions in the xand z-directions of the cavity are standing waves, and the distribution in the y-direction is a symmetric mode of MIM plasmon. For the (1, 1) mode, the nanocavity’s mode volume, V = (3Wλ2SPP)/32, is estimated according to eq 1 and the definition of the mode volume.28 For example, for a 120 nm long and 70 nm wide cavity, the resonant wavelength in a vacuum is 490 nm. Thus, we can obtain V = 0.014λ3SPP = 0.0014 μm3. This mode volume is much smaller than those of traditional photonic crystal cavities and microdisk cavities,29 indicating that strong confinement of electromagnetic energy in volumes much smaller 1120
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Nano Letters than the cube of the wavelength can be achieved by this type of nanocavity. It is expected that mode volumes can be further reduced by decreasing the size of the cavity. The quality factor (Q-factor) of the plasmonic vertical nanocavity depends on the reflectivity of the reflectors and the propagation loss. The reflectivity of the Ag reflector is near 100%. The reflectivity of the air reflector depends on its geometry and wavelength. A smaller size and a larger free-space wavelength result in higher reflectivity. In Figure 2, the experimental Q-factor is smaller than that expected from calculations. This is attributed to the surface roughness of the side walls (Figure 1b). According to the numbers of the Ag and air reflectors, there are two other types of plasmonic vertical nanocavities, which were fabricated and shown in Figure S4 (Supporting Information). These cavities have two or three air reflectors. Different boundary conditions will result in different mode patterns. Therefore, the resonant features of these two types of cavities are different from those of the above-mentioned cavity. We did not obtain the plasmonic resonant modes in these cavities under the same experiment conditions, although FDTD simulations show the existence of the modes of plasmonic vertical cavities. These are expected to arise from high propagation losses due to the surface roughness and increase in the number of air reflectors, whose reflectivities are smaller than those of the Ag reflectors. In conclusion, we demonstrated, for the first time controllable vertical plasmonic resonant nanocavities on Ag films with an air output window and Ag reflectors. The plasmonic resonances of cavities with different cavity lengths were derived using a CL microscope, while the modes were explained by a comparison between the experimental and FDTD simulation results. The dispersion can be easily tuned by changing the width of the cavities. The nanocavities were fabricated on a metal film, which allows connection with other plasmonic devices and two-dimensional arrays building. The three-dimensional subwavelength confinement and intrinsic output window at the top surface make the cavity very suitable for VCSELs at the nanoscale level. The plasmonic vertical nanocavities are also an ideal platform for studies of Purcell-enhanced spontaneous emissions due to their small mode volume. Different emitters can be placed in cavities through the open window. The plasmonic vertical cavities are promising for numerous nanoplasmonic applications, such in surface-enhanced Raman scattering,30 plasmonic nanoscale VCSELs, and cavity quantum electrodynamics. They may also be used as basic building blocks of integral nano-optical devices.
’ ASSOCIATED CONTENT
bS
Supporting Information. Angular distribution of backscattered electrons, top-view SEM images of plasmonic nanocavities, dispersion relations of the cavities with 40 and 120 nm cavity widths, and SEM images of two other kinds of cavities. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail: (J.Z.)
[email protected]; (D.Y.)
[email protected].
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’ ACKNOWLEDGMENT This work was supported by NSFC (Nos. 11023003 and 61036005) and the National 973 Program of China (No. 2009CB623703), MOST. 1121
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