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Nano-Architecture Driven Plasmonic Field Enhancement in 3D Graphene Structures Kriti Agarwal, Chunhui Dai, Daeha Joung, and Jeong-Hyun Cho ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b08145 • Publication Date (Web): 27 Dec 2018 Downloaded from http://pubs.acs.org on January 1, 2019
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Nano-Architecture Driven Plasmonic Field Enhancement in 3D Graphene Structures Kriti Agarwal, Chunhui Dai, Daeha Joung, Jeong-Hyun Cho* Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA *E-mail:
[email protected] ABSTRACT The limited spatial coverage of the plasmon enhanced near-field in 2D graphene ribbons presents a major hurdle in practical applications. In this study, diverse self-assembled 3D graphene architectures are explored that induce hybridized plasmon modes by simultaneous in-plane and out-of-plane coupling to overcome the limited coverage in 2D ribbons. While 2D graphene can only demonstrate in-plane, bi-directional coupling through the edges, 3D architectures benefit from fully-symmetric 360° coupling at the apex of pyramidal graphene, orthogonal fourdirectional coupling in cubic graphene, and uniform cross-sectional radial coupling in tubular graphene. The 3D coupled vertices, edges, surfaces, and volume induce corresponding enhancement modes that are highly dependent on the shape and dimensions comprising the 3D geometries. The hybridized modes introduced through the 3D coupling amplify the limited plasmon response in 2D ribbons to deliver non-diffusion limited sensors, high efficiency fuel cells, and extreme propagation length optical interconnects.
KEYWORDS plasmons, 3d structures, self-assembly, graphene, near-field enhancement
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The extreme light confinement by two-dimensional (2D) graphene plasmons enhances the electric field around the graphene surface, making the near-field intensity several orders of magnitude higher than the incident wave. The long lifetime tunable plasmon resonance alongside superior mechanical properties in graphene have been utilized for a diverse range of applications such as reconfigurable metamaterials, and optoelectronic devices for photo-detection, vibrational spectroscopy techniques, solar cells, cell therapeutics, and light sources.1-5
However, the
exponential decay of the enhanced field a few nanometers from the surface severely degrades the performances of graphene-based devices such as lower propagation length in graphene waveguides and interconnects,6-8 diffusion-limited sensitivity of molecular sensors,9-12 and low efficiency and long response time of photodetectors.13-20 Attempts have been made to achieve stronger field enhancements with minimal spatial decay through arrays and stacks of graphene21,22 including circular and triangular shaped ribbons23-25 for large area hotspots of intensified electric (E) field.2627
Although, the 2D stacks and arrays exhibit highly tunable plasmon resonance through changes
in ribbon width or fermi levels,28 they can only produce non-homogeneous hotspots localized to edges or a point and cannot significantly change the exponential decay in the field away from ribbon surface. For sensing applications, the presence of molecules results in a shift in the plasmon resonance and additional absorption peaks proportional to the molecules optical properties.29 However, the targeted molecules need to be bound to the surface of the graphene due to the sharp decrease in the electric field even at a distance of 2 nm from the graphene surface,30,31 presenting a major disadvantage due to changes in the molecular structures and loss of intrinsic target molecule properties from binding to the surface.32,33 Furthermore, at lower concentrations of analytes, the detection is severely limited by the time required for diffusion of the molecules (over 24 hours for 10 molecules) to the graphene surface.34-37 Thus, a high spatial coverage of the
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plasmonic near-field (extreme volumetric enhancement, not limited to surface but extending into bulk space) is required to overcome surface and edge-limited efficiencies in current plasmonic devices, thereby, achieving longer propagation length optical devices, larger hot carrier generation, and non-diffusion limited high sensitive molecule sensors. To achieve non-spatially constrained near-field enhancement, a hybridized plasmon technique is introduced here that benefits simultaneously from two coupling modes (out-of-plane stacking and in-plane coupling) by adopting properties of hollow three-dimensional (3D) nanoarchitectures. Previous studies introduced that when patterned 2D graphene defined on a planar substrate (Fig. 1a) is transformed into multi-faced polyhedron(Fig. 1b), hybrid plasmons modes are caused by uniform multi-dimensional coupling in the graphene faces and edges over an extra spatial degree of freedom.38-40 Unlike solid 3D structures with graphene draped over them that can only achieve minimal 3D coupling through adjoining edges,41-43 the hollow polyhedral geometries allow a stronger out-of-plane coupling of the field within their volume and adjoining faces. Thus, giving rise to surface and volume enhancement modes that are also easily accessible due to their hollow architecture. As an advanced study, the effect of the diverse 3D architectures on the coupled plasmon modes have been explored here, including effects of shape, size, and ratio of dimensions comprising the structures. While 2D graphene offers limited edge and surface plasmon behavior (Fig. 1a,c), our results reveal that a much higher tunability of the plasmonic enhancement is afforded by 3D graphene for desired applications based on their nanoarchitecture (Fig, 1b,d). The 3D nanoarchitectures (pyramids, cubes, and tubes) provide an insight into geometry-dependent coupled plasmon modes inducing intensified single point enhancements (Ig), confined edge modes at the periphery (Pg), uniform total surface (Sg), and non-surface-limited volumetric (Vg) field enhancements (Fig. 1d). 3 ACS Paragon Plus Environment
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RESULTS 3D graphene nanoarchitectures (Fig. 2) can be realized by an origami-like self-assembly technique where the melting of a hinge is utilized to generate a surface tension force that folds 2D patterns into 3D structures.38,44,45 Diverse 2D graphene patterns were used to achieve three distinct types of hollow 3D graphene architectures namely, 5-faced square pyramids (Fig. 2d-f), 5- or 6-faced cubes (Fig. 2j-l,t), and cylindrical tubes (Fig. 2p-r) with heat energy supplied from hot plates, focused ion beams, and exothermic reactive ion etching. Raman spectroscopy of the samples before and after self-assembly was used to assess changes in the properties of graphene before (Fig. 2c,i,o) and after self-assembly (Fig. 2f,l,r). The mapped images of the G-band peaks in the Raman spectra (Fig. 2c,f,i,l,o,r) underwent same transformations in shape as the actual sample between the respective 2D patterned graphene and 3D graphene architectures. Thus, demonstrating that intrinsic graphene properties are preserved in the self-assembled 3D nanoarchitectures. The self-assembly approach for fabrication of 3D structures is a highly versatile process that can be easily scaled for diverse architectures ranging in size from 500 nm (Fig. 2a-r) to 200 µm (Fig. 2u) based on the 2D patterns that are folded or curved. Detailed fabrication procedures and Raman spectra can be found in the Methods section.
To assess the nanoarchitecture-based plasmonic enhancement in the fabricated 3D structures, the polyhedral prisms and tubes were simulated under an incident plane wave and the resulting near-field enhancements (Ig, Pg, Sg, and Bg) were computed as detailed in the Methods section. First, when 2D graphene patterns are self-assembled into square pyramids (Fig. 2a-f), the coupling of plasmons on adjoining graphene surfaces leads to distinct hybridized modes (Fig. 3). It is known that plasmons on the slant faces of pyramids propagate towards the apex under TM
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(transverse magnetic) polarization to constructively interfere at a single point (apex) delivering intense nano-focused fields.46 Modification of dimensions comprising the nanopyramids could achieve highly customized enhancement not limited to classical hybridized TM and TE (transverse electric) plasmon modes (see detailed mode analysis in Supporting Information). For the graphene pyramid, while maintaining equal length of base (L) and height (H), the height of pyramids was decreased from 50-500 nm. The near-field enhancement within pyramids increases as the size of pyramids is reduced (Fig. 3a,b). For the 500 nm pyramid, the maximum enhancement (Ig_max~4.4×104) exists at the apex, which is two orders of magnitude higher than at the base of the pyramid (Ig_min~100) (Fig. 3a). At reduced sizes, the shorter height of pyramids allows the field at the apex to couple strongly with the base; thereby, sustaining the point-based apex field over longer distances (even at reduced plasmon wavelength) within the spatial volume of the pyramid as observed by an increase in the Ig,min inside the pyramids (Fig. 3a, 250 nm and 50 nm). Hence, for 50 nm pyramids, the strong enhancement encompasses the entire pyramid structure (Fig. 3a, 50 nm). Moreover, changes in dimensions of the pyramids not only sustains the field at apex over the entire geometry, but also exponentially increases the maximum enhancement for the pyramids (Fig. 3b, yellow line) as a direct consequence of increased resonant frequency at smaller size of pyramids (Figure S2c). The smaller decay of the near-field enhancement inside the structures and the increase in the maximum enhancement gives an overall increasing total (volumetric) enhancement within the pyramids with decreasing size (Fig. 3b, blue line). The simultaneous scaling of the length (L) of the base and height (H) of the pyramid, proportionally changes the plasmon wavelength and consequently the near-field enhancement. However, depending upon the application it maybe imperative to control the enhancement while preserving the frequency range as in the case of molecular sensing for diminishing concentrations, where the operating frequency
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is determined by the vibrational frequency of the molecule to be analyzed. In 3D pyramidal graphene, for a constant height, the plasmon wavelength remains nearly constant; thus, by varying other dimensions in the pyramid (length of base) diverse hybrid modes can be obtained with a nearly constant operating frequency range (see detailed resonant frequencies in the Supporting Information). At low values of dimensionality parameter (αp=L/H), of 0.5 and 1.0, obtained by decreasing L, (Fig. 3c), the narrower slant surfaces of the pyramid structure result in an increased E-field at the slant edges that increases towards the apex. The uniform interference of the fields from the slant edges results in a strong volumetric enhancement and a constant surface enhancement at the base of the pyramid (Fig. 3c). Thus, even for decreased resonant frequency (at αp=2.0) that decreases the maximum enhancement, the 3D plasmon coupling exhibits an increased surface and volumetric enhancements between αp=0.5-2.0. However, at larger values of αp=4, 8 (Supporting Information Fig. S3), the interference from the edges of the pyramid and the field scattered from the apex is unable to sustain the extreme enhancement across the entire area of the enlarged base and volume of pyramid (Fig. 3c). The nearly constant field enhancement of ~2000 obtained at any point on the 3D coupled base for αp=1 square pyramids is reduced to ~9 for base of pyramids with αp=8. Thus, at αp=0.5, 3D couplings between the edges, apex, and base leads to a maximum enhancement (Ig_max~1.05×106) that is more than 3 orders of magnitude stronger than for a pyramid with αp=8 (Ig_max~353) (Fig. 3d). On the other hand, at small αp values (0.5-2), large areas of surface enhancement (Sg~900) are induced that couple with the apex to cause an increased volumetric field (Fig. 3d). In comparison, even at small widths classical 2D graphene nanoribbon (Supporting Information Fig. S1a, b), a strong (1/e) drop in the enhanced electric-field (Ig) is seen across the ribbon surface even few nanometers away from the edge (25 nm for a 50 nm width ribbon) (Supporting Information Fig. S1c,d).
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The extreme point enhancement at the apex of nanopyramids induces a strong volumetric enhancement, but only a small dimensionality range (αp
