and Hot-Electron Emission from Plasmonic Nanoantennas

Transcription

1 Supporting Information: Mapping Photoemission and Hot-Electron Emission from Plasmonic Nanoantennas Richard G. Hobbs 1,2,3, William P. Putnam 1,4,5, Arya Fallahi 6, Yujia Yang 1, Franz X. Kärtner 1,4,6 and Karl K. Berggren 1 1 Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, U.S.A. 2 Centre for Research on Adaptive Nanostructures and Nanodevices (CRANN) & Advanced Materials Bio-Engineering Research Centre (AMBER), Trinity College Dublin, Dublin 2, Ireland 3 School of Chemistry, Trinity College Dublin, Dublin 2, Ireland 4 Department of Physics and Center for Ultrafast Imaging, University of Hamburg, Hamburg, Germany. 5 Northrop Grumman Corporation, NG Next, Redondo Beach, CA, USA 6 Center for Free-Electron Laser Science, Deutsches Elektronen-Synchrotron, Hamburg, Germany 1

2 These authors contributed equally to this work. *To whom correspondence should be addressed: Tel: ; hobbsr@tcd.ie Supporting Information Experimental We fabricated arrays of nm wide, 20 nm thick, nm long, Au nanorods by highresolution electron beam lithography on indium tin oxide (ITO) coated sapphire substrates using a similar process to that reported previously. 1 Following the electron beam lithography, we then etched the ITO using dilute hydrochloric acid to form electrodes facilitating the application of a DC field to the emitter arrays on-chip as reported previously. 2 The nanorod arrays were then coated with either a 20-nm-thick layer of PMMA (Microchem Corp.) with a molecular weight of 950k, or hydrogen silsesquioxane (XR-1541, Dow Corning Corp.), which acts as the imaging layer for electron emission from the Au nanorod array. Electron emission from the Au nanorods was driven using an Er:fiber-seeded supercontinuum (SC) femtosecond laser source. The source produces pulses 2.5-cycle ( 10 fs) in duration with a central wavelength of 1.2 µm (SC spectrum ranges from µm) and a repetition rate of 78.4 MHz. The laser is linearly polarized such that the optical field is aligned to the long-axis of the Au nanorods and is focused to a spot with a 1/e 2 diameter of 5.2 µm on the nanorod array. The resulting peak laser intensity is ~ 150 GW/cm 2. Typical exposure doses expected at the poles of the Au nanorods are expected to be on the order of 10 9 electrons/pole for 10 s exposure times. Figure 1 shows SEM images of an Au nanorod array exposed as described above, developed in 3:1 IPA:MIBK at 0 C for 30 s, and dried in a stream of flowing N 2. Nanorod arrays coated with HSQ were developed by 2

3 immersion in salty developer (1 wt. % NaOH, 4 wt. % NaCl in water) for 2 mins at room temperature followed by rinsing in flowing de-ionized water for 90 s and 2-propanol for 30 s. Scanning electron microscopy SEM images were acquired with a FEI Helios Dual Beam SEM-FIB tool using a highresolution magnetic immersion lens allowing sub-nm resolution. We typically used an electronbeam energy of 10 kev, a beam current of 86 pa, and a working distance of 4 mm. Samples were imaged without a metal coating to allow direct inspection of the resist layer. Figure S1. Low-magnification SEM micrograph of a square array (520 nm pitch) of PMMAcoated 130-nm-long Au nanorods following exposure to the femtosecond laser source and development of exposed PMMA. 3

4 Figure S2. Higher magnification SEM micrographs of Au nanorods similar to those shown in figure S1. Figure S3. SEM micrographs of Au nanoantennas exhibiting crosslinked (negative-tone) PMMA at their apices. 4

5 Figure S1 shows a low-magnification SEM micrograph of an array of Au nanoantennas after exposure and development of exposed PMMA. Inspection of low-magnification micrographs suggests that a threshold laser intensity of ~ 0.1 GW/cm 2 (~ 5 µm from center of laser spot) is required to produce positive-tone exposure of PMMA in this work. Figure S3 shows a selection of SEM micrographs where negative-tone PMMA can be observed at the poles of nanorod antennas. Inspection of SEM micrographs revealed that laser intensities of ~ 50 GW/cm 2 are required to produce negative-tone exposure of PMMA. Figure S4. SEM micrograph of a PMMA-coated 130-nm-long Au nanorod following exposure to the femtosecond laser source and development of exposed PMMA. Regions where PMMA has been exposed and removed can be seen at the poles of the nanorod. 5

6 Figure S5. SEM micrograph of PMMA-coated 130-nm-long Au nanorods following exposure to the femtosecond laser source and development of exposed PMMA. Nanorods on the left are on a conductive ITO film, nanorods on the right-hand side of the micrograph are on the insulating sapphire substrate, while the two nanorods in the center straddle the conducting and insulating regions of the substrate. Estimation of electron dose at nanorod poles based on emission measurements The calculated electron doses at the poles of Au nanorods fabricated and tested in this work are consistent with the doses required to expose PMMA with low-energy electrons by a scanning probe technique. 3 In this work and our previous work we have measured emission currents of ~ 20 na from Au nanorod arrays driven by our Er:fiber-seeded supercontinuum (SC) femtosecond laser source. 2 At its 1/e 2 diameter, the laser spot typically illuminates nanorods (dependent on the areal density of the nanorod array). If we assume that the 20 na is emitted primarily from these nanorods, then we can expect an average emission current per nanorod of na. Considering our laser repetition rate of ~ pulses/s then each nanorod emits 1-10 electrons per pulse. If we assume that each pole of each nanorod emits ~ 1 electron per pulse, we can estimate that we produce ~ 10 9 electrons per pole per 10 s exposure 6

7 (assuming approximately 10 9 pulses), or equivalently ~ 0.1 nc per pole. Assuming an exposed area of ~ 10 4 nm 2, we can estimate an area dose of 10 fc/nm 2 ( electron/nm 2 ) or 1 C/cm 2. This dose is consistent with that required to expose PMMA by scanning probe lithography using low-energy electrons. Measurement of exposed volume of PMMA at nanorod poles As stated in the main text the volume (V) of developed PMMA at the poles of nanorod antennas was measured at a distance of µm from the center of the laser spot by manual inspection with SEM after development. Each value of PMMA volume used in the plot in figure 3 is the average of 5-10 inspected nanorod poles. The exposed regions at the poles were approximated as circular regions and the volume was calculated from the radius of the circle and the thickness of the resist measured by ellipsometry on a Si substrate. For comparison, image analysis was also performed using Image J image processing software. Figure S6 shows an example of this image analysis for an array of exposed 140-nm-long nanorods. Figure S6 (i) shows a cropped SEM micrograph including a linear array of nanorods spanning the width of the laser spot. Contrast thresholding was used to demarcate the regions of exposed PMMA as shown in the binary image in figure S6 (ii). Finally, the analyze particle function in Image J was used to determine the area of the black region in figure S6 (ii) as indicated by the boundaries shown in figure S6 (iii) (voids representing the metallic nanorods are subtracted from the total area). Figure S7 shows a log-log plot of exposed volume of PMMA (V) against local incident laser intensity (I). The plot shows the values of V measured for the nanorods shown in figure S6 using both the manual inspection method and the automated Image J method. The difference between two measurement methods is negligible. The dashed line in the plot in figure S7 represents a power-law fit to the measured data with V I

8 Figure S6. Image analysis process using Image J. (i) raw SEM micrograph cropped from larger image. (ii) Binary image after contrast thresholding. (iii) Outlines of regions of exposed PMMA used to calculate area of exposed PMMA. Figure S7. Plot of volume of exposed PMMA at nanorod apex against local incident intensity for 140-nm-long nanorods. Triangles represent values measured using automated Image J method while shaded squares represent values measured by manual inspection. Electromagnetic simulations The finite element method (FEM) software package COMSOL Multiphysics was used to perform electromagnetic simulations in this work. Using an FEM-based solver enables adaptive and highly non-uniform meshing to efficiently solve problems with large differences in length scale, such as the interaction of infrared light (1200 nm wavelength) with sub-wavelength nanostructures that support near-fields with decay lengths of tens of nanometers and that are 8

9 composed of metals with skin-depths of only a few nanometers. Moreover, FEM methods provide solutions to electromagnetic problems in the frequency domain. Considering the frequency-dependent optical properties of materials, especially metals, for which the permittivity exhibits a strong frequency dependence, such a frequency-domain method is a natural and accurate approach. The calculation domain used was a cuboid of size L y /2 L z /2 2λ (y z x) where L y and L z are the pitches in y- and z-directions respectively, and λ is the excitation wavelength (note that the coordinate system used here is different from that in figure 1 of the main text). The cuboid is one quarter of a unit cell of a square array of nanorods, and exploiting the symmetry of this regular square array, we use Perfect Electric Conductor (PEC) and Perfect Magnetic Conductor (PMC) boundary conditions at the sides of the cuboid. The cuboid consists of a stacked structure along the x-axis: a perfectly-matched-layer (PML), an air layer, a layer of resist with one quarter (exploiting symmetry) of an embedded nanorod, a substrate layer, and a final PML. The stacked structure is illustrated in figure S8. The PMLs at the top and bottom of the stack served as absorbing layers for the incident and reflected electromagnetic waves. The Au nanorod had a rectangular transverse cross section with curved corners and two hemispherical end-caps. Sharp edges were rounded with a 7.5 nm curvature to avoid singularities in the calculation as well as to better mimic the fabricated structure. The nanorod length, width, and thickness were varied. We should also mention that in the simulation the substrate layer was composed of PMMA; in the spectral range of interest (λ ~ µm), the refractive indices of PMMA, ITO, and sapphire are sufficiently similar to make this a reasonable approximation. (For the optical properties of the gold, data were taken from Johnson & Christy, 4 and for the PMMA, a Sellmeier fit 5 was used.) 9

10 PMMA substrate PML air PML y z x Au nanorod Figure S8. Geometry of model used to simulate the optical extinction of Au nanorod arrays. Linearly polarized light (polarized in the z-direction) is incident on the nanorod along the x-axis from the right-hand side of the schematic. The PMLs (perfectly-matched layers), substrate, and air layer are all half the excitation wavelength in thickness. FEM simulations were also used to estimate the absorption and scattering cross-sections of Au nanorods with different geometries as shown in figure S9. The decrease in resistive loss with increasing L for 60-nm-wide nanorods seen in figure 4d in the main text was likely due to a drop in the absorption cross-section for longer nanorods as shown in figure S9 (a) below. Figure S9. Simulated absorption and scattering cross-sections of Au nanorods. (a) Plot of absorption cross-section (σ abs ) against wavelength of LSPR (λ LSPR ) for nanorods having widths of 10

11 25 nm, 35 nm and 60 nm. (b) Plot of scattering cross-section (σ scat ) against λ LSPR for nanorods having widths of 25 nm, 35 nm and 60 nm. Dashed lines represent linear fits to the range of x- data covered by the dashed lines in both plots. Electron emission simulations For the simulation of emission process from the Au nanorods, two problems are treated and solved synergistically. First, the FEM simulation results are used to evaluate the normal electric field at the nanorod surface. The Fowler-Nordheim model (equation S1) is then used to obtain the emission current (J) at the surface. e 3 E 2 J= 16π 2 hwt 2 (y) e 4 2m e v( y)w 3/2 3he E (S1) Here, e is the charge of the electron, m e is the mass of the electron, W is the metal work-function, E is the magnitude of the electric field (static and optical) and y, ν(y) and t(y) are given in equations S2-4. y=1 e3 E 4πε 0 (S2) t(y)= 2π 4 ( y y y y2 1 8 y+1) (S3) v(y)= 3 2π ( y y y2 + y) (S4) 11

12 The simulated emission current was found to best agree with the experimentally observed charge-yield when the work-function of Au was set to 4.9 ev. Because of the discretization in time and space the emitted charge in a time step from a surface element may be less than the unit charge (e). Therefore, the obtained charge profile represents a probability distribution for the position and momentum of the emitted electrons. Second, the emitted electrons should be accelerated inside the electromagnetic fields. We developed a fast search algorithm to find the four closest discretization nodes to the charge position. Linear interpolation between the field values at these nodes returns the electromagnetic fields at the charge point. To consider the space-charge effect on the bunch variations, point-to-point approximation is used. For modeling the recombination with the substrate or emitter surface, the charge points are reflected with a probability of 30% after they hit the surfaces. Measurements of I th for HSQ exposures Following HSQ exposure and development, nanorod arrays were inspected by SEM to determine the area of the array that exhibited nanorods with w c > w p. Approximating the laser spot as a circle, we then determined the threshold radius within which nanorods exhibited HSQ exposure with w c > w p. The threshold radius was then used to calculate a threshold intensity I th based on a Gaussian intensity distribution for the laser spot. As an extension of this measurement, the error in the measured values of I th was taken as the change in intensity calculated for a change in the threshold radius of ± 0.5 lattice parameter of the unit cell of the nanorod array i.e. ± 2L where L is the designed length of the nanorod. References (1) Hobbs, R. G.; Yang, Y.; Fallahi, A.; Keathley, P. D.; De Leo, E.; Graves, W. S.; Berggren, K. K. ACS Nano 2014, 8,

13 (2) Putnam, W. P.; Hobbs, R. G.; Keathley, P. D.; Berggren, K. K.; Kärtner, F. X. Nat. Phys. 2017, 13, (3) McCord, M. A.; Pease, R. F. W. J. Vac. Sci. Technol. B 1988, 6, (4) Johnson, P. B.; Christy, R. W. Phys. Rev. B 1972, 6, (5) Szczurowski, M. Optical Constants of PMMA (accessed Sep 11, 2017). 13