Compact simulation guides subnanometer, femtosecond measures of energy transfer between quasiparticles and hot carriers at interfaces between metals and two dimensional materials D. Keith Ropera,c*, Gregory T. Forcherioa, Drew DeJarnetteb, a MicroElectronics-Photonics Program, University of Arkansas, Fayetteville, AR, USA 72701; b Department of Mechanical Engineering, University of Tulsa, Tulsa, OK 74104; cRalph E. Martin Department of Chemical Engineering, University of Arkansas, Fayetteville, AR, USA 72701 ABSTRACT Compact computational structure-function relations are needed to examine energy transfer between confined fields and carrier dynamics at heterostructure interfaces. This work used discrete dipole approximations to analyze quasiparticle excitation and dephasing at interfaces between metals and van der Waals materials. Simulations were compared with scanning transmission electron microscopy (STEM) for energy electron loss spectroscopy (EELS) at sub-nanometer resolution and femtosecond timescale. Artifacts like direct electron-hole pair generation were avoided. Comparing simulation with experiment distinguished quasiparticle energy transfer to hot carriers at the interface, and supported development of structure-function relations between interface morphology and emergent discrete and hybrid modes. Keywords: plasmons, nanoparticles,van der Waals materials, DDA, EELS, hot electrons
1. INTRODUCTION Improved descriptions for intense, local electron fields on subwavelength nanoarchitectures induced by resonant photon and electron sources support progress in light filtration,1,2 photodetection,3,4,5,6,7 sensing,8,9,10 spectroscopy,11 imaging,12 and theranostics.13 Collective behavior of resonating electrons in a metal, metal oxide, semiconducting, and/or dielectric nanoarchitecture of arbitrary complexity may be described by decomposing it into an ensemble of polarizable dipole(s). The polarizability measures harmonic charge separation in such collective modal distributions. One such computational electrodynamic14,15,16,17,18 approach, the discrete dipole approximation (DDA) to Maxwell’s equations, offers a compact alternative to numerical solution of differential (finite difference time domain) and integral (boundary element method) equations.19 Resonant irradiation of subwavelength metallic nanostructures can excite surface electron oscillations known as plasmons. Plasmons dissipate energy via pathways that include photon scattering, phononic absorption, and transfer of hot electrons. Enhanced light absorption in graphene via hot electron transfer from plasmons supported on adjacent metal nanostructures has been reported using photocurrent/voltage20,21,22,23 or photoluminescence6 measurements. It is possible to avoid electron-hole pair generation in graphene by optical sources which confounds attribution of hot electron transfer to plasmons using electron energy loss spectroscopy (EELS). EELS positions a sub-nanometer probe and electron source on or near nanostructures to excite light and dark plasmon modes and directly characterize their dissipation. 24,25,26 This work4,27,28 compared DDA simulation with EELS and transmission UV-vis spectra to distinguish transfer of hot electrons from quasiparticles derived from plasmon excitation at interfaces between metals and two-dimensional (2D) materials. Hot electrons contribute to an increase in the 2D material charge carrier distribution adjacent to plasmonic particles, with a lifetime reported to be shorter than acoustic phonons. This necessitates ultrafast detection, e.g., using EELS. Compact DDA description validated by EELS supports plasmonic electron transfer into molecules for surface enhanced Raman spectroscopy (SERS),29,30,31,32 into water for splitting,33 into TiO2 for photo induced current, 34 and implementation in terahertz modulation.35,36 *
[email protected]; phone 1 801 891 8921; https://nbphotonics.uark.edu/
Physical Chemistry of Interfaces and Nanomaterials XV, edited by Artem A. Bakulin, Robert Lovrincic, Natalie Banerji, Proc. of SPIE Vol. 9923, 992312 · © 2016 SPIE · CCC code: 0277-786X/16/$18 · doi: 10.1117/12.2238102
Proc. of SPIE Vol. 9923 992312-1 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 05/09/2017 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx
2. MET THODOLO OGY 2.1 Experim mental Briefly,4,27,28 gold (Au) elliipses were evaaporated to a thickness t of 155 nm atop 50 nm-thick bare silicon nitridee (Si3N4, abbreviated SiN) S membran ne transmissionn electron micrroscope (TEM) grid via nanoolithography using an electroon resist. An interlayerr of 0.4-nm cheemical vapor deposition d (CV VD) graphene was w introduced between somee Au ellipses annd SiN. Optical anallysis used a spectrometer-c s oupled (Sham mrock 202; Anndor Technoloogy, Belfast, UK) U light miccroscope (Eclipse LV1100; Nikon Insstruments, Melville, NY USA A). Acqusitionn of transmissiion UV-vis exttinction spectrra used a circularly poolarized 230 µm m diameter proobe. EELS waas performed using u a scanninng transmissioon electron miccroscope (Tecnai F-200; FEI, Hillsborro, OR USA) at a 120 (graphenne) or 200 (MooS2) keV with 50 meV binniing by a GATA AN postcolumn imagging filter (GIF F Quantum 9633; GATAN, Plleasanton, CA USA). The zeero-loss peak was w extracted using u the built-in poweer law approxim mation. 2.2 Numerical Briefly,4,27,28 light-excitattion package DDSCAT D (v7.3) 37,38 and electron-excitat e tion packages eDDA (v1.2) 39 and DDEELS (vv2.0) were used in conjunctioon with a targeet generation code c hosted onn nanoHUB40 to t simulate opttical and electron enerrgy loss spectraa, respectively.. A complex diielectric functioon was employyed for gold (A Au).41
3. RESULTS An incident beam of fast electrons corrresponds to a time-varying electric field that induces collective moddal field ELS provides a subnanometerr measure of thhe transmitted electrons e that have h lost distributions in an underlyiing sample. EE e to the saample. This coorresponds to the t local dielecctric function of o the sample and a the probability that a particular energy an optical evvent, e.g., a plaasmon, has occurred which reeflect the electrromagnetic (EM M) local densiity of states. Rastering R the beam acrross a selected d area maps thee local energyy loss which coorresponds to near n fields sim mulated using DDA. D In EELS maps, bright plasmo on modes that have a net noonzero dipole moment correespond well with DDA resullts using conventionall photon plane wave or electrron excitation; while dark moodes that have a net zero dipoole moment reqquire use of an electronn source. 39,42
Figure 1. DDA computed EELS spectra for 270x115 nm Au ellipse.
Proc. of SPIE Vol. 9923 992312-2 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 05/09/2017 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx
EELS maps have been compared with local fields computed by DDA for numerous nanoarchitectures: Ag spheres,43 discs,26 split ring resonators,44 cubes,45 nanorods,46 columns,47 triangular prisms,48 nanoholes drilled in Ag film,49 and Au cross shapes.50 The laboratory group that produced the present work was the first to report characterization of high surface-to-volume51 and arrayed nanostructures including target substrate52 and direct attribution of hot electron transfer to 2D materials4,27,28 using DDA and EELS. Comparing DDA simulation with EELS experiments supported development of structure-function relations connecting interface morphology to emergent discrete and hybrid modes.53 Figure 1 illustrates resonances simulated at 1.0 to 2.08 eV supported by Au ellipses impacted at center (blue), mid-major (red), mid-minor (green), and edge (brown) points. These energies were correlated with bright, dark, and hybrid modes in EELS maps in Figure 2. Center impact produced a 1.43 eV resonance and centrosymmetric map corresponding to a single dark mode with net zero dipole moment. Edge impact produced resonances at 1.0 and 1.2 eV corresponding to multiple bright modes with net non-zero dipole moment (horizontally). Mid major/minor impacts yielded multiple resonances corresponding to a mixture of dark and hybrid modes.
Figure 2. EELS maps distinguish light, dark, and hybrid plasmon modes. Interfacing Au ellipses with silicon nitride convoluted and blue-shifted resonance energies. Addition of an unbiased graphene interlayer between the Au ellipse and SiN TEM grid shifted and dephased dark (filled blue circles) and edge (open and filled red circles) modes, as illustrated in Figure 3. Redshift of high energy modes was attributed to hybridization, rather than the conductivity of the underlying 2D material or its waveguiding effects. Bandwidth expanded significantly only for the low-energy bright (edge) mode, corresponding to measured increases in plasmon decay times. Contributions from radiative (Γ ; photon scattering), non-radiative (Γ ; quasistatic intraband phonon scattering and interfacial effects) were estimated using semi-analytical dipole polarizability, empirical, and numerical DDA approaches. Additional damping was directly attributable to carrier transport into adjacent media (Γ ). Graphene is good electron receiver with comparable Fermi levels and high electron mobility. Direct electron transfer is possible by a quantum mechanism via hot electrons created through Landau damping of LSPRs. From increased damping, a plasmon dephasing time for hot electron transfer of 9.2 femtoseconds (fs) was measured. The value was between a measurement of 160 fs for Au nanorods on graphene by dark field scattering and values between 2.5 and 18 fs for total damping measured for Au NR on SiN. It was within a range of 1-100 fs reported for Landau dephasing.54 The ratio of carrier transport bandwidth to overall peak width yielded a quantum efficiency of 20%, similar to comparable reports.
Proc. of SPIE Vol. 9923 992312-3 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 05/09/2017 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx
Graphene No graphene
(a)
....................... Center
2
3
Energy Loss (eV)
4
Graphene No graphene
1
2
L'«,......._.
3 T ,..... l,. T\ 4
Figure 3. Carrier density affects electron energy loss on graphene. [2]
4. SUMMARY Estimates using discrete dipole approximation, Mie theory, and semi-analytical polarizability were compared with measurements using energy electron loss spectroscopy (EELS) to examine effects of geometry and material composition on energy transfer between confined fields and carrier dynamics at interfaces between metals and 2D materials. Electron excitation provided sub-nanometer resolution and femtosecond timescales to avoid artifacts like direct electron-hole pair generation. It allowed induction of dark zero net dipole moments as well as optical bright modes. Quantum efficiencies of 20% and dephasing times of 9.2 femtoseconds were estimated for energy transfer between bright quasiparticle modes and hot carriers at interfaces between Au and graphene. Compact computational structure-function relations validated by high-resolution optoelectronic mapping can accelerate design and integration of metal-van der Waals interfaces in applications emerging to advance health, sustainable energy, and information science.
REFERENCES [1] [2] [3] [4] [5] [6] [7] [8]
DeJarnette, D., Otanicar, T., Brekke, N., Hari, P., and Roberts, K., “Selective Spectral Filtration with Nanoparticles for Concentrating Solar Collectors,” J. Photonics Energy 5, 057008 (2015). Taylor, R., Otanicar, T. P., Herukerrupu, Y., Bremond, F., Rosengarten, G., Hawkes, E. R., Jiang, X., and Coulombe, S., “Feasibility of Nanofluid-Based Optical Filters,” Appl. Opt. 52, 1413–1422 (2013) Liu, Y., Cheng, R., Liao, L., Zhou, H., Bai, J., Liu, G., Liu, L., Huang, Y., and Duan, X., “Plasmon Resonance Enhanced Multicolour Photodetection by Graphene,” Nat. Commun. 2, 579 (2011). DeJarnette, D., and Roper, D. K., “Electron Energy Loss Spectroscopy of Gold Nanoparticles on Graphene,” J. Appl. Phys. 116, 054313 (2014). Fang, Z., Liu, Z., Wang, Y., Ajayan, P. M., Nordlander, P., and Halas, N. J., “Graphene-Antenna Sandwich Photodetector,” Nano Lett. 12, 3808–3813 (2012). Hoggard, A., L.-Y. Wang, L. Ma, Y. Fang, G. You, J. Olson, Z. Liu, W.-S. Chang, P.M. Ajayan, and S. Link, “Using the plasmon linewidth to calculate the time and efficiency of electron transfer between gold nanorods and graphene,” ACS Nano 7, 11209 (2013). Shi, S.-F., X. Xu, D.C. Ralph, and P.L. McEuen, “Plasmon resonance in individual nanogap electrodes studied using graphen nanoconstrictions as photodetectors,” Nano Lett. 11, 1814 (2011). Offermans, P., Schaafsma, M. C., Rodriguez, S. R. K., Zhang, Y., Crego-Calama, M., Brongersma, S. H., and Gómez Rivas, J., “Universal Scaling of the Figure of Merit of Plasmonic Sensors,” ACS Nano 5, 5151–5157 (2011).
Proc. of SPIE Vol. 9923 992312-4 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 05/09/2017 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx
[9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37]
Chon, J. W. M., and Iniewski, K., [Nanoplasmonics: Advanced Device Applications], “Plasmon Coupling Enhanced in Nanostructured Chem/bio Sensors,”, CRC Press: Baca Raton, FL, 183–219 (2013). DeJarnette, D., Norman, J., and Roper, D. K., “Attribution of Fano Resonant Features to Plasmonic Particle Size, Lattice Constant, and Dielectric Wavenumber in Square Nanoparticle Lattices,” Photonics Res. 2, 15–23 (2014). Demming, A., Festy, F., and Richards, D., “Plasmon Resonances on Metal Tips: Understanding Tip-Enhanced Raman Scattering,” J. Chem. Phys. 122, 184716 (2005) Fang, N., Lee, H., Sun, C., and Zhang, X., “Sub–diffraction-Limited Optical Imaging with a Silver Superlens,” Science 80, 308, 534–537 (2005). Lukianova-Hleb, E., Oginsky, A., Samaniego, A., Shenefelt, D., Wagner, D., Hafner, J. H., Farach-Carson, M., and Lapotko, D., “Tunable Plasmonic Nanoprobes for Theranostics of Prostate Cancer,” Theranostics 1, 3–17 (2011). Kelly, K. L., Coronado, E., Zhao, L., and Schatz, G. C., “The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment,” J. Phys. Chem. B. 107, 668–677 (2003). Wriedt, T., “A Review of Elastic Light Scattering Theories,” Part. Part. Syst. Charact. 15, 67–74 (1998). Wriedt, T., and Comberg, U. “Comparison of Computational Scattering Methods,” J. Quant. Spectrosc. Radiat. Transf. 60, 411–423 (1998). Yurkin, M., and Hoekstra, A., “The Discrete Dipole Approximation: An Overview and Recent Developments,” J. Quant. Spectrosc. Radiat. Transf. 106, 558–589 (2007). Schebarchov, D., Auguié, B., and Le Ru, E. C., “Simple Accurate Approximations for the Optical Properties of Metallic Nanospheres and Nanoshells,” Phys. Chem. Chem. Phys., 15, 4233–4242 (2013). Myroshnychenko, V., Rodríguez-Fernández, J., Pastoriza-Santos, I., Funston, A. M., Novo, C., Mulvaney, P., Liz-Marzán, L. M., and García de Abajo, F. J., “Modelling the Optical Response of Gold Nanoparticles,” Chem. Soc. Rev. 37, 1792– 1805 (2008). Fang, Z., Liu, Z., Wang, Y., Ajayan, P.M., Nordlander, P., and Halas, N.J., “A graphene-antenna sandwich photodetector,” Nano Lett. 12, 3808 (2012). Echtermeyer, T.J., L. Britnell, P.K. Jasnos, a Lombardo, R. V Gorbachev, a N. Grigorenko, a K. Geim, a C. Ferrari, and K.S. Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011). Liu, Y., R. Cheng, L. Liao, H. Zhou, J. Bai, G. Liu, L. Liu, Y. Huang, and X. Duan, “Plasmon resonance enhanced multicolour photodetection by graphene,” Nat. Commun. 2, 579 (2011). Sun, D. G. Aivazian, A.M. Jones, J.S. Ross, W. Yao, D. Cobden, and X. Xu, “Ultrafast hot-carrer-dominated photocurrent in graphene,” Nat. Nanotechnol. 7, 114 (2012). Eggeman, A.S., P.J. Dobson, and A.K. Petford-Long, “Optical spectroscopy and energy-filtered transmission electron microscopy of surface plasmons in core-shell nanoparticles,” J. Appl. Phys. 101, 024307 (2007). Hohenester, U., H. Ditlbacher, and J. Krenn, “Electron-energy-loss spectra of plasmonic nanoparticles,” Phys. Rev. Lett. 103, 106801 (2009). Schmidt, F.-P., H. Ditlbacher, U. Hohenester, A. Hohenau, F. Hofer, and J.R. Krenn, “Dark plasmonic breathing modes in silver nanodisks,” Nano Lett. 12, 5780 (2012). Forcherio, G. T., Roper, D. K., “Spectral characteristics of noble metal nanoparticle-molybdenum disulfide heterostructures,” Adv. Opt. Mater., (2016). Forcherio, G. T., Benamara, M., Roper, D. K., “Electron energy loss spectroscopy of hot electron transport between gold nanoantennas and molybdenum disulfide by plasmon excitation,” Submitted. Brus, L., “Noble metal nanocrystals: plasmon electron transfer photochemistry and single-molecule Raman spectroscopy,” Acc. Chem. Res. 41, 1742 (2008). Zhang, Z., F. Xu, W. Yang, M. Guo, X. Wang, B. Zhang, and J. Tang, “A facile one-pot method to high-quality Aggraphene composite nanosheets for efficient surface-enhanced Raman scattering,” Chem. Commun. (Camb). 47, 6440 (2011). Ling, X., and J. Zhang, “First-layer effect in graphene-enhanced Raman scattering,” Small 6, 2020 (2010). Zhu, X., L. Shi, M.S. Schmidt, A. Boisen, O. Hansen, J. Zi, S. Xiao, and N.A. Mortensen, “Enhanced light-matter interaction in graphene-covered gold nanovoid arrays,” Nano Lett. 13, 4690 (2013) Linic, S., P. Christopher, and D.B. Ingram, “Plasmonic-metal nanostructures for efficient conversion of solar to chemical energy,” Nat. Mater. 10, 911 (2011) Lee, Y.K., C.H. Jung, J. Park, H. Seo, G.A. Somorjai, and J.Y. Park, “Surface plasmon-driven hot electron flow probed with metal-semiconductor nanodiodes,” Nano Letters, 4251 (2011) Xia, F., T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4, 839 (2009). Satou, A., Y. Koseki, V. Ryzhii, V. Vyurkov, and T. Otsuji, “Damping mechanism of terahertz plasmons in graphene on heavily doped substrate,” J. Appl. Phys. 115, 104501 (2014). Draine, B. T., and Flatau, P. J., “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11(4), 1491– 1499 (1994).
Proc. of SPIE Vol. 9923 992312-5 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 05/09/2017 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx
[38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54]
Flatau, P. J.., and Draine, B. T., “Fast near field calculations in the discrete dipole approximation for rectangular rectilinear grids,” Opt. Express 20(2), 1247–1252 (2012). Bigelow, N. W., Vaschillo, A., Iberi, V., Camden, J. P., and Masiello, D. J., “Characterization of the electron- and photondriven plasmonic excitations of metal nanorods,” ACS Nano 6(8), 7497–7504 (2012). Seeram, M., Forcherio, G. T., Blake, P., and Roper, D. K., “Shape Generator for the Discrete Dipole Approximation,” nanoHUB, (2015) . Johnson, P. B.., and Christy, R. W., “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972). Henrard, L., and Lambin, Ph., “Calculation of the energy loss for an electron passing near giant fullerenes,” J. Phys. B: At. Mol. Opt. Phys. 29, 5127 (1996). Litz, J.P., Camden, J.P., and Masiello, D.J., “Spatial, spectral, and coherence mapping of single-molecule SERS active hot spots via the discrete-dipole approximation,” J. Phys. Chem. Lett. 2, 1695 (2011). Boudarham, G., Feth, N., Myroshnychenko, V., Linden, S., Garcia de Abajo, J., Wegener, M., and Kociak, M., “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105, 255501 (2010). Mazzucco, S., Geuguet, N., Ye, J., Stephan, O., Van Roy, W., Van Dorpe, P., Henrard, L., and Kociak, M., “Ultralocal modification of surface plasmons properties in silver nanocubes,” Nano Lett. 12, 1288 (2012). N’Gom, M., Li, S., Schatz, G., Erni, R., Agarwal, A., Kotov, N., and Norris, T.B., “Electron-beam mapping of plasmon resonances in electromagnetically interacting gold nanorods,” Phys. Rev. B 80, 113411 (2009). Marty, R., Arbouet, A., Girard, C., Margueritat, and J., Gonzalo, “Sculpting nanometer-sized light landscape with plasmonic nanocolumns,” J. Chem. Phys. 131, 224707 (2009). Chalker, P.R., Romani, S., Marshall, P.A., Rosseinsky, M.J., Rushworth, S., and Williams, P.A., “Liquid injection atomic layer deposition of silver nanoparticles,” Nanotechnol. 221, 405602 (2010). Sigle, W., Nelayah, J., Koch, C.T., Ogut, B., Gu, L., and van Aken, P.A., “EFTEM study of surface plasmon resonances in silver nanoholes,” Ultramicroscopy 110, 1094 (2010). Bosman, M., Ye, E., Tan, S.F., Jihjuis, C.A., Yang, J.K., Marty, R., Mlayah, A., Arbouet, A., Gierard, C., and Han, M.Y., “Surface plasmon damping quantified with an electron nanoprobe,” Sci. Rep. 3, 1312 (2013). Forcherio, G.T., Blake, P., DeJarnette, D., and Roper, D.K., “Nanoring structure, spacing, and local dielectric sensitivity for plasmonic resonances in Fano resonant square lattices,” Optics Express 22(15), 17791-17804 (2014). Forcherio, G.T., Blake, P., Seeram, M., DeJarnette, D., and Roper, D.K., “Coupled dipole plasmonics of nanoantennas in discontinuous, complex dielectric environments,” J. Quant. Spectr. Rad. Trans. 166, 93-101 (2015). Forcherio, G.T., DeJarnette, D., Benamara, M., and Roper, D.K., “Electron energy loss spectroscopy of surface plasmon resonances on aberrant gold nanostructures”, Submitted. Brongersma, M. L., Halas, N. J.., and Nordlander, P., “Plasmon-induced hot carrier science and technology,” Nat. Nanotechnol. 10(1), 25–34 (2015).
Proc. of SPIE Vol. 9923 992312-6 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 05/09/2017 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx
