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Probing the in-Plane Near-Field Enhancement Limit in a Plasmonic Particle-on-Film Nanocavity with Surface-Enhanced Raman Spectroscopy of Graphene Danjun Liu,†,□ Tingting Wu,‡,□ Qiang Zhang,§,□ Ximiao Wang,∥,□ Xuyun Guo,† Yunkun Su,∥ Ye Zhu,† Minhua Shao,⊥ Huanjun Chen,∥ Yu Luo,‡ and Dangyuan Lei*,†,#,¶ †
Department of Applied Physics, The Hong Kong Polytechnic University, Hung Hom, 999077, Hong Kong, China School of Electrical & Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore § School of Materials Science and Engineering, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China ∥ State Key Laboratory of Optoelectronic Materials and Technologies, Guangdong Province Key Laboratory of Display Material and Technology, School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou 510275, China ⊥ Department of Chemical and Biological Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, 999077, Hong Kong, China # Shenzhen Research Institute, The Hong Kong Polytechnic University, Shenzhen 518057, China ¶ Department of Materials Science and Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, 999077, Hong Kong, China ‡
S Supporting Information *
ABSTRACT: When the geometric features of plasmonic nanostructures approach the subnanometric regime, nonlocal screening and charge spill-out of metallic electrons will strongly modify the optical responses of the structures. While quantum tunneling resulting from charge spill-out has been widely discussed in the literature, the near-field enhancement saturation caused by the nonlocal screening effect still lacks a direct experimental verification. In this work, we use surface-enhanced Raman spectroscopy (SERS) of graphene to probe the in-plane near-field enhancement limit in gold nanosphere-on-film nanocavities where different layers of graphene are sandwiched between a gold nanosphere and a gold film. Together with advanced transmission electron microscopy cross-sectional imaging and nonlocal hydrodynamic theoretical calculations, the cavity gap width correlated SERS and dark-field scattering measurements reveal that the intrinsic nonlocal dielectric response of gold limits the near-field enhancement factors and mitigates the plasmon resonance red-shift with decreasing the gap width to less than one nanometer. Our results not only verify previous theoretical predictions in both the near-field and far-field regime but also demonstrate the feasibility of controlling the near- and far-field optical response in such versatile plasmonic particle-graphene-on-film nanocavities, which can find great potential in applications of graphene-based photonic devices in the visible and near-infrared region. KEYWORDS: nonlocal screening, charge spill-out, surface-enhanced Raman spectroscopy, nanoparticle-on-film nanocavities, graphene mental properties of single plasmonic junctions.3−5 According to the classical electromagnetic theory, which is interpreted via a local model, decreasing gap distance in MPoFNs will lead to a continuous rise of near-field enhancements and red-shift of
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n the last few decades, there has been a growing interest in the study of light−matter interactions at the nanoscale. One of the important themes in this field is to investigate light confinement in plasmonic metal particle-on-film nanocavities (MPoFNs), which can squeeze light into the small gap region and thus generate several-order field enhancements.1,2 In particular, such highly concentrated light in the gap region allows strong light−matter interaction, thus revealing funda© XXXX American Chemical Society
Received: January 28, 2019 Accepted: June 19, 2019 Published: June 19, 2019 A
DOI: 10.1021/acsnano.9b00776 ACS Nano XXXX, XXX, XXX−XXX
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Figure 1. (a) Raman spectra of an SLG, a 2LG, a trilayer graphene (3LG), and a 4LG all deposited on a gold thin film. The spectra were taken under 633 nm laser excitation with a commercial confocal microscope. (b) Schematics of a graphene-sandwiched MPoFN under an oblique p-polarized incidence. (c) High-resolution TEM cross-sectional image of an SLG-sandwiched MPoFN. The white box encloses a local area around the gap, while the red and yellow lines represent the edges of the graphene layer and the metals, respectively. (d) Average count profile across the local area enclosed in the white box in (c). The vertical red and yellow lines mark the positions of the edges of the graphene layer and the metals, respectively.
plasmonic modes.6−8 However, as the gap distance enters the nanometer or even subnanometre scale, quantum effects such as nonlocal screening and electron tunneling gradually appear and alter the plasmonic far-field and near-field response.9,10 Previous studies show that the charge spill-out of conduction electrons results in quantum tunneling of plasmons at extremely small separations between metallic particles. Above the quantum tunneling regime, the nonlocal screening effect plays an important role in the optical responses of the metallic nanoparticles. As one of the quantum effects, spatial nonlocality can be described by the theory of surface screening.11−14 There are some models such as the nonretarded specular reflection model and retarded hydrodynamic model to explain the conduction electron motion at subnanometer gaps.15,16 In particular, due to its high accuracy and easy implantation with commercially available numerical codes, the most common method employed to describe nonlocal screening is the nonlocal hydrodynamic (NLHD) model.17−20 In this model, the motion of free electrons is not determined solely by the local field at a specific point, but by the integration of the field in the vicinity. This model can well predict the blue-shift of plasmonic modes compared to the classical local model and attributes the blue-shift to the influence of surface charge thickening.21,22 The quantum mechanical effects, such as spatial nonlocality and electron tunneling, on both far-field and near-field properties of plasmonic nanogap systems have recently been observed.22−26 In the far-field regime, single-particle dark-field scattering spectroscopy has been used to probe the nonlocal screening-induced red-shift saturation of plasmon resonance
with decreasing the molecular spacer thickness between a gold thin film and a gold nanosphere22 and also the electron tunneling-induced emergence of a charge transfer plasmon mode in a pair of gold-coated atomic force microscopy (AFM) tips with subnanometer gaps;23 in the meanwhile, electron energy-loss spectroscopy has been applied to observe quantum plasmon resonances in tiny silver nanoparticles with diameters down to 1.7 nm24 and also molecular tunnel junction controlled tunneling charge transfer plasmons.25 In the nearfield regime, nonlinear optical spectroscopy26 and surfaceenhanced Raman scattering (SERS)27−29 have been used as indirect means to quantify the influence of those quantum mechanical phenomena in the ultimate plasmonic near-field enhancement limit in various plasmonic systems. In particular, SERS of graphene and two-dimensional transition metal dichalcogenides have been employed respectively to study the spatial nonlocality effect in rough silver films28 and determine plasmonic near-field enhancement factors (EFs) in MPoFNs.29 Specifically, in ref 29, the SERS intensities of the out-of-plane and in-plane lattice vibrations of layered MoS2 sandwiched in an MPoFN are used to probe both vertical and horizontal field enhancements in the system: a pronounced quenching of the vertical local field enhancement, compared to the classical electromagnetic prediction, is observed as the number of MoS2 layers decreases to monolayer.29 Yet, the horizontal field enhancement extracted from their measured SERS EF is even larger than classical predictions, leaving an open question whether the opposite variation trends of the two field components originate from the gentle ripples in the MoS2 layer or the relatively large thickness of monolayer MoS2 (0.62 B
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numbers, Raman spectroscopy has also proven to be an effective mean to reveal distinctive changes in their electronic band structures and phonon−electron interactions. In general, a single-layer graphene (SLG) has a single, sharp 2D peak, while the 2D peak for a bilayer graphene (2LG) undergoes a splitting and blue-shift due to the splitting of its phonon branches and electronic bands.35−37 For a graphene sample with less than five layers, the layer number can be precisely determined by calculating the Raman intensity ratio of their 2D and G bands. When the layer number is above 5, however, the difference in the Raman response of the sample and that of bulk graphite becomes hardly distinguishable,38,39 making it difficult to determine the exact layer number with Raman spectroscopy. We have also measured the Raman spectrum of an SLG under varied laser power, and the results show a linear dependence of both G and 2D peak intensities, indicating that a spontaneous Raman scattering in graphene occurs in our measurements. By simply drop-casting gold nanospheres onto a graphenecoated gold thin film, graphene-sandwiched MPoFNs are constructed as schematically shown in Figure 1b (for the SLG case). In our experiment, high-resolution TEM cross-sectional imaging is carried out to precisely determine the sphere−film gap widths of these nanocavities. Figure 1c and d show the TEM cross-sectional image of an SLG-sandwiched MPoFN and the corresponding average count profile in a local area (enclosed in the white box in Figure 1c) across the gap, respectively. First, the average count profile in Figure 1d exhibits two predominant peaks, as marked by two vertical red lines, which correspond to the edges of the graphene layer (see horizontal red lines in Figure 1c). Then, the thickness of the SLG can be estimated to be 0.37 nm, very close to the theoretical value (0.34 nm). Second, a closer look into the profile in Figure 1d reveals that the major count peaks are not very sharp, implying the presence of transition regions between the SLG and the gold nanosphere or the gold film. Such transition regions stem from air gaps between the graphene layer and the metals (both gold nanosphere and gold film). Generation of the metal−graphene air gaps can be attributed to several factors such as the surface roughness of gold films (see TEM image in Figure 1c), the van der Waals force relaxed metal−graphene distances,40,41 and the wrinkle of the graphene layer. Here we emphasize that these air gaps are crucial for characterizing the plasmonic response of each MPoFN because both the resonance wavelength and near-field properties of the cavity are extremely sensitive to the particle− film gap size, especially considering the fact that possible quantum effects exist in such small gap regions. Therefore, we determine the graphene−particle air gap size from Figure 1d as the distance between the top edge of the graphene layer (the left vertical red line) and the bottom edge of the gold nanosphere (the left vertical yellow line). Similarly, the graphene−film air gap size is the distance between the bottom edge of the graphene layer (the right vertical red line) and the top edge of the gold film (the right vertical yellow line). Then, the total size of the air gap estimated from the TEM characterization is simply the summation of the sizes of these two air gaps. Following this approach, the total air gaps in the MPoFNs with SLG (Figure 1c and d), 2LG (Figure S1a and b), and 4LG (Figure S1c and d) are measured as 0.22, 0.19, and 0.25 nm, respectively. As the best resolution of the TEM imaging is about 0.1 nm, we assume the total size of the local air gap for all four MPoFNs is identical, i.e. 0.2 nm. However,
nm as determined in this work). In addition, the nanocavity structures with particle−film gap distances determined by high-resolution transmission electron microscope (TEM) cross-sectional imaging are not correlated with those used in the dark-field scattering and SERS measurements; no quantum mechanical calculations are performed to fully understand both the far-field and near-field responses of the MoS2-sandwiched MPoFNs. In fact, the horizontal near-field enhancement in such MPoFNs is equally important because many exotic optical phenomena such as plasmon−exciton couplings in monolayerTMDC-sandwiched MPoFNs are associated with the horizontal field component due to the horizontal orientation of bright exciton dipole moments in monolayer TMDCs.30,31 In addition, we have recently observed that the horizontal field components in such MPoFNs also determine the plasmoninduced hot-carrier generation efficiency at relatively large gap widths.32 Therefore, it is strongly desirable to investigate the horizontal near-field enhancement limit of such MPoFNs with a rationally designed methodology where the particle−film gap distance can be further reduced and TEM morphological characterizations and optical spectroscopic measurements can be exactly one-to-one correlated. Moreover, a comprehensive comparison between experimental results and classical/ quantum calculations for the same plasmonic systems can further deepen our understanding of the near-field enhancement limits in various plasmonic systems and their associated quantum mechanical origins. In this study, we use layered graphene as a spacer to isolate the metal nanoparticle and the underlying metal film in MPoFNs and in the meanwhile employ the SERS spectroscopy of graphene to indirectly probe the quantum mechanical limit of the in-plane near-field component enhancement in the subnanometer gap region. The SERS intensities of two pronounced Raman modes of graphene, i.e., the G peak and 2D peak, corresponding respectively to a primary in-plane vibration mode and a second-order overtone of another inplane vibration,33 are measured as a function of graphene layer number varied from one to four. Therefore, it is possible to explore the impact of quantum mechanical effects on horizontal local field enhancements by measuring the SERS EFs of these two in-plane vibrational modes as the gap distance enters the subnanometer scale regime. More importantly, we have carried out correlated TEM imaging and optical spectroscopic measurements exactly on the same MPoFNs. Combined with both classical local and quantum nonlocal calculations, we show that the SERS EFs of the in-plane phonon modes of graphene are markedly modified by the nonlocal screening effect, enabling further quantitative understanding of the light−graphene interaction in the visible to near-infrared frequencies.34
RESULTS AND DISCUSSION Determining Graphene Layer Numbers and Gap Widths of Graphene-Sandwiched MPoFNs. Before studying the optical responses of graphene-sandwiched MPoFNs, we need to determine the number of graphene layers by analyzing the Raman spectra of the graphene layers deposited on a gold thin film. Figure 1a shows the Raman spectra of CVD-grown graphene with layer number varied from 1 to 4, all transferred onto a 100 nm thick gold film. Two characteristic Raman peaks, i.e., the G band and 2D band, are clearly observed. As a nondestructive optical method for determining graphene layer C
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Figure 2. (a) Schematics of unpolarized dark-field excitation in a standard dark-field optical microscope. (b) Measured scattering spectra of graphene-coupled MPoFNs with the graphene varied from SLG to 4LG. (c) Schematic diagram of excitation configuration and nanocavity system used in simulations. (d) Calculated classical local and quantum nonlocal scattering spectra of the graphene-coupled MPoFNs.
interaction area between the particle and the film. In addition, the gold films prepared by thermal evaporation have a rootmean-square (RMS) surface roughness of about 0.9 nm, as characterized by AFM mapping (see Figure S2). Considering these two factors, we decided to set the average air gap size (dair) in the effective interaction area to be the summation of the local air gap size (0.2 nm) and an external thickness of 0.5RMS, i.e., dair = 0.2 nm + 0.5·0.9 nm = 0.65 nm. In this manner, the total effective gap distance (d) in each MPoFN is obtained by dGr + dair, where dGr = N0.34 nm denotes the thickness of N-layer graphene. As a result, the maximum and minimum effective gap distances in the MPoFNs are about 2.0 nm (for the 4LG-coupled cavity) and 1.0 nm (for the SLGcoupled cavity), respectively. It is expected that, at such a length scale (1 nm ≤ d ≤ 2 nm), the spatial nonlocality effect significantly modifies both the far-field and near-field optical properties of the structures. To verify this, we numerically calculate the scattering spectra for the four graphene-coupled MPoFNs by using both classical local and nonlocal models implemented in a commercially available numerical software, COMSOL Multiphysics. In our numerical simulations, a TMpolarized plane wave is incident on the system at an angle of 53°, as illustrated in Figure 2c. In principle, the NLHD model can be implemented by solving the coupled eqs 1 and 2 with an additional boundary conditions (ABC) n·J(r,ω) = 0 at the boundaries of the metal, where n is the normal vector of the metal surface,
we must keep in mind that this air gap is determined only for a local area. Far-Field Scattering Spectroscopy of GrapheneCoupled MPoFNs. To study the far-field optical responses of the graphene-MPoFNs, we use a standard dark-field optical microscope coupled with an unpolarized excitation source (see Figure 2a) to measure the scattering spectra of those nanocavity structures at the single-particle level. The unpolarized excitation beam is tightly focused to the sample plane by a 100× objective (NA = 0.8), which produces, in addition to the dominant in-plane field component, a significant amount of out-of-plane field components. As a result, both the transverse resonance mode and the vertical gap mode of the MPoFNs can be effectively excited. From the scattering spectra shown in Figure 2b, one can observe two predominant scattering peaks. The short-wavelength scattering peak appears at around 530−540 nm, which is the transverse plasmon resonance mode of the MPoFN and thus insensitive to the gap width variation. In contrast, the long-wavelength one can be attributed to the vertical gap mode with a much stronger scattering intensity, the resonance wavelength of which significantly blue-shifts with increasing the graphene layer number (i.e., as the gap distance increases), agreeing well with previous reports.5,42−45 Specifically, the resonance wavelength blue-shifts from about 670 nm to 600 nm when changing the spacer from SLG to 4LG. As discussed above, the air-gap size determined from the TEM imaging is for a local area much smaller than the effective D
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Figure 3. (a−d) Raman spectra taken on (black) and off (red) each of the four MPoFNs with graphene spacers from SLG to 4LG. The signal integration time for both spectra was 10 s. (e−h) Scattering spectra and dark-field images (insets) of the same structure as in (a)−(d) taken before and after Raman measurements.
measured permittivity of gold.47 However, direct solving of the coupled eqs 1 and 2 for a large-scale plasmonic system in COMSOL such as a metallic particle-on-film nanocavity usually requires the use of tremendous memory and is very time-consuming. To tackle this problem in a more effective way, we employed the dielectric-layer model,48,49 where the nonlocality is accounted for by an inward shift of the metal− dielectric boundary; that is, a thin layer of metal is replaced with a dielectric material with a properly calculated dielectric function. Figure 2d shows the calculated local and nonlocal scattering spectra for the four plasmonic nanocavities. We can see that the vertical gap mode for each graphene-coupled MPoFN is obviously blue-shifted by the spatial nonlocal screening effect. This blue-shift can be straightforwardly understood as a result
∇ × ∇ × E(r, ω) = k 0 2 εcore(ω)E(r, ω) + iωμ0J(r, ω) (1)
β2∇[∇·J(r, ω)] + ω(ω + iγ0)J(r, ω) = iε0ωω2p E(r, ω) (2)
Here k0 is the wave vector in a vacuum, ε0(μ0) the permittivity (permeability) of the vacuum, εcore(ω) the local permittivity of gold responsible for the bound ions and electrons, and β the nonlocal screening parameter; γ0 and ωp are the collision and plasmon frequency of the Drude model. β is related to the Fermi velocity of gold, νF = 1.39 × 106 m/s via β2 = 3νF2/5. εcore(ω) of gold is obtained by subtracting the Drude part from the empirical data, i.e., εcore(ω) = εm(ω) + ωp2/(ω2 + iγ0ω), where ℏγ0 = 0.71 eV, ℏωp = 9.02 eV,46 and εm(ω) is the E
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Figure 4. Fraction of horizontal SERS enhancement factor as a function of integral radius in the gap region of (a, c) SLG- and (b, d) 4LGcoupled MPoFNs by the nonlocal model. The insets in (a) and (b) show the effective horizontal electric field distribution (under 633 nm excitation and emission at 704 nm, corresponding to the G peak) for the SLG- and 4LG-sandwiched MPoFN, respectively. The insets in (c) and (d) show similar results to those in (a) and (b) (under 633 nm excitation and emission at 760 nm, corresponding to the 2D peak) for the same MPoFNs. In the simulations, a p-polarized plane wave excites the MPoFNs at an incident angle of 64°. The white dashed lines in the insets represent the boundaries of the gold spheres and the metal films.
of an increased effective gap size due to the centroid displacement of the conduction charge density inward toward the metal surface from the geometry boundary in the gap region where the gold nanosphere and the gold film have the most intense interaction. However, the increased effective gap size has no pronounced impact on the transverse mode because this mode is inherently insensitive to the gap size as mentioned above. Moreover, the blue-shift in the gap mode resonance compared to the classical local prediction decreases as the total effective gap size increases when inserting more layers of graphene in the MPoFN system, which has been theoretically predicted50 and experimentally verified51 in plasmonic nanoparticle dimers with similar gap widths. Near-Field SERS Spectroscopy of Graphene-Coupled MPoFNs. In addition to the pronounced influence in the farfield optical response, the spatial nonlocal effect also results in an ultimate limit to the near-field enhancement and confinement in the small gap region of the MPoFNs. As discussed above, SERS is a powerful near-field probe that has been recently utilized to study the quantum mechanical effects on the plasmonic near-field EFs of various metallic nanostructures. In our graphene-coupled MPoFNs, Raman scattering of the sandwiched graphene layers can be dramatically amplified by the strong local near-field intensity induced in the gap region. Experimentally, we have measured the SERS signals of both G and 2D bands for the four graphene-coupled MPoFNs under 633 nm continuous wave (CW) laser excitation. The linearly polarized laser beam is tightly focused onto the sample plane
through a 100× objective lens (NA = 0.9), and the incident laser power is set to be 0.3 mW to avoid possible photodamage to the nanocavities or unwanted nonlinear optical effects in the gap region. Note that here the graphene Raman spectra were collected under 3 mW power of the same laser and then scaled down by 10 times to compare with the SERS spectra. The reason for this treatment is that the Raman signals of pristine graphene layers under 0.3 mW illumination are too weak to detect in our experiment. This treatment has been justified by observing a linear relationship between laser power and Raman intensity of a pristine graphene (see Figure S3), although it leads to the disparity of the noise between the SERS and Raman spectra. Figure 3a−d show the SERS spectra (black line) of the graphene-coupled MPoFNs and the corresponding Raman spectra (red line) of the same graphene layers on the bare gold thin film. Clearly, both the G band and 2D band Raman peaks are significantly enhanced due to the presence of the MPoFNs. In addition, structure-correlated dark-field scattering imaging and spectroscopy are performed on the same structures before and after the SERS measurements. We observe from Figure 3e−h that the dark-field images as well as the scattering spectra before and after the SERS measurements are identical to each other, indicating no perceivable photodamage induced by the CW laser illumination. Such control experiments ensure the accuracy and consistence of our results. Local and Nonlocal Predictions of the Far- and NearField Response of Graphene-Coupled MPoFNs. We F
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coupled MPoFNs and the corresponding effective horizontal electric field distribution are summarized in Figure S4. The extracted values of R∥ are then used to determine the surfaceaveraged in-plane near-field enhancement factor of each system given by eq 5 in both the classical local and quantum nonlocal regimes. Comparison between Experimental Results and Theoretical Predictions. Figure 5a presents a comparison
further theoretically calculate the graphene layer dependence of SERS EFs in the four graphene-coupled MPoFNs. Here, we define the SERS enhancement factor as EF =
INP Aeff IGr ASERS
(3)
where INP is the SERS signal collected from the confocal area containing an MPoFN and IGr is the Raman signal collected from the graphene layer in close proximity of the MPoFN (to ensure the same graphene quality and therefore the same intrinsic Raman response). Aeff is the effective laser excitation area with a spot size of about 340 nm in radius for the 633 nm laser, which corresponds to a 0.36 μm2 spot area, and ASERS is the effective local field area of the nanocavity, which is defined by ASERS = πR
2
(4)
where R∥ is the effective radius of the in-plane near-field “hot spot” in each graphene-coupled MPoFN and is obtained from the calculated field distribution profile of each structure. Numerically, the SERS enhancement factor for each system can be approximately determined by the surface-averaged inplane near-field enhancement factor with the following equation: 1 EF = πR
2
∫A
E (λ in)
2
E (λout)
E 0(λ in)
2
E 0(λout)
da (5)
where |E (λ in, λout)| = |Ex|2 + |Ey|2 is the amplitude of the total in-plane near field at the incoming (outgoing) wavelength. |E 0(λ in, λout)| = |Ex 0|2 + |Ey0|2 is the amplitude of the corresponding background in-plane electric field. In the simulations, the near fields at the outgoing wavelengths were obtained just by setting the wavelengths of the excitation the same as the emission wavelengths of the corresponding Raman signals, i.e., 704 nm for the G peak and 760 nm for the 2D peak. To determine R∥, we have calculated the fraction of horizontal SERS enhancement factor with the following equation:
f (ρ) =
∫0
πρ2 E (λ in) − E 0(λ in)
2
E 0(λ in) ∞ E (λ in) − E 0(λ in)
∫0
E 0(λ in)
E (λ out) − E 0(λ out)
2
da
E 0(λ out) 2
E (λ out) − E 0(λ out) E 0(λ out)
Figure 5. Simulated and measured resonance wavelength of the (a) vertical gap mode and the horizontal SERS EFs (b, c) as a function of graphene layer number. The simulations were performed with both classical local and quantum nonlocal models. The SERS EFs for both G and 2D bands were calculated with eqs 3 and 5. The measured SERS EFs are scaled up 20 times, and the error bars can be seen in the zoomed-in views in the insets.
between the measured and calculated plasmon resonance wavelengths for the vertical gap mode. As expected, the resonance wavelength calculated by the quantum nonlocal model blue shifts compared to that by the classical local model for each graphene-coupled MPoFN. The error bars represent standard deviations of the measured resonance wavelengths for the four graphene-coupled MPoFNs. Unambiguously, Figure 5a shows that the resonance wavelengths of the vertical gap mode obtained from the nonlocal calculations agree much better with the experimental results than those obtained from the local calculations. The difference between the measurement and nonlocal results is understandable because it is unlikely to ensure that all the parameters used in the simulations are exactly the same as those of the real samples. First, the total gap size used in each simulation must have a certain amount of discrepancy from that for the corresponding actual MPoFN sample. This is because the surface roughness of gold films and the local morphologies of gold nanospheres result in different gap sizes at different areas. Second, the dimensions of the gold nanospheres have fluctuation around
2
da
(6)
Note that in the calculations we used 350 nm as an actual integral radius in the denominator of eq 6. Figure 4 shows the calculated fraction of horizontal SERS enhancement factor as a function of integral radius ρ at the middle plane of the SLG (a, c) and 4LG (b, d) using the nonlocal model. We can see that the fraction saturates rapidly with increasing integral radius. Here we determine R∥ when the fraction of horizontal SERS enhancement factor reaches 99%. The insets in Figure 4a and b (c and d) show the effective horizontal electric field distribution profiles for the two MPoFNs corresponding to the G peak (2D peak). As can be seen from the profiles, the electric near fields in the SLG-MPoFN gap region are more tightly confined compared to that in the gap regions containing graphene multilayers, leading to smaller R∥ when the gap distance decreases. The fractions of horizontal SERS enhancement factor as a function of integral radius for 2LG- and 3LGG
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graphene-coupled MPoFNs. In comparison with the classical local and quantum nonlocal simulation results, the experimental SERS results clearly reveal that the in-plane near-field enhancement is strongly mitigated by the nonlocal screening effect when the gap thickness approaches the subnanometer scale. Distinctively different from many previous studies, we have first carried out rigorously correlated morphological characterizations and optical spectroscopies exactly on the same MPoFNs in order to avoid ambiguities induced by possible geometric variation from structure to structure. Consistent with the nonlocal model predictions, both nearfield SERS enhancement factor and far-field plasmon resonance shift exhibit a quantum mechanical limit to the gap width of the MPoFNs. This work not only deepens our understanding of the plasmonic response of subnanometer metallic nanogap cavities but also provides possibilities for controlling plasmonic resonances in graphene-based nanophotonic devices.
40 nm, as confirmed by the TEM characterization of different samples (see Figure S5). Third, the present modeling of the anisotropic dielectric response of graphene (see eqs 7 and 8) may be too ideal to accurately describe the dielectric properties of graphene at optical frequency. As seen from eq 7 (see Methods), the in-plane dielectric constant of graphene highly depends on the surface conductivity, which in turn is determined by several intrinsic physical parameters of graphene as seen from eq 8, such as Fermi energy, Fermi velocity, carrier relaxation lifetime, and carrier mobility. However, after calculating the scattering spectra of the SLGcoupled MPoFN with varied carrier mobilities and/or Fermi energy of graphene (see Figure S6), we found that the scattering responses of the cavity are insensitive to the in-plane dielectric constant of graphene. On the contrary, the resonance wavelength of the vertical gap mode significantly red-shifts (see Figure S6) when the out-of-plane dielectric constant of graphene is increased from 1.0 to 2.5. Despite these factors, our quantum nonlocal calculations have captured the essential physics of nonlocal screening in affecting the far-field optical response of the graphene-sandwiched MPoFNs. More importantly, by calculating the corresponding R∥ values for the four graphene-coupled MPoFNs, the experimental and numerical SERS EFs can be determined with eqs 3 and 5, with results shown in Figure 5b and c. Here the experimental results represent statistic results of SERS EFs measured over dozens of similar structures for each graphenecoupled MPoFN (see Figure S7). The error bars obtained from the standard error in Gauss fitting of the statistic EFs can be seen in the zoomed-in views in the insets in Figure 5b and c. In addition, the experimentally measured SERS EFs shown in Figure 5b and c are scaled up 20 times to better visualize the comparison with the numerical results. This is because the experimentally measured SERS EFs are approximately 1 order smaller than the calculated values due to the relatively low collection efficiencies during the SERS measurement. Apparently, Figure 5b and c show that the variation of the experimentally measured SERS EFs for both the G and 2D bands as a function of the graphene layer number exhibits a similar variation trend to that of the nonlocal results. In sharp contrast, as the graphene layer number decreases, the calculated local SERS EFs for both Raman bands increase much faster than the experimental results. Particularly, the calculated local SERS EFs for both Raman bands in the SLGcoupled MPoFN show a sharp rise, which clearly deviates from the experimental trends. Therefore, we can conclude that the in-plane near-field enhancement factor of the MPoFN system is significantly attenuated by the nonlocal charge screening effect. Meanwhile, it is worthy of noticing that the field enhancement has not reached saturation yet even in the SLGcoupled MPoFN since the gap width is still too large. Further experimental improvement in the preparation of such graphene-coupled MPoFNs, for example by using ultrasmooth gold film, may be able to further decrease the gap width such that more pronounced quantum mechanical effects such as surface charge spill-out and, very probably, electron tunneling could be observed in both far-field scattering and near-field SERS spectroscopies.
METHODS Sample Preparation. Gold thin films of about 100 nm thickness were prepared by thermal evaporation on a silicon wafer at a deposition rate of ∼1 Å/s. Large-area graphene flakes with varied layer number were grown with a chemical vapor deposition method on a copper substrate and then spin-coated with a thin layer of poly(methyl methacrylate) (PMMA) at 3000 r/s. The PMMAcovered graphene flakes were then put in a 10% FeCl2 solution for 2 h. After the copper substrate was completely dissolved, the remaining PMMA/graphene film was transferred onto the gold thin film, and the whole sample was then kept in acetone for 2 h to totally dissolve the PMMA layer. Colloidal gold nanospheres of 80 nm diameter were obtained from NanoSeedz. They were stabilized in an aqueous solution of cetyltrimethylammonium bromide (CTAB). The gold nanospheres were washed twice by centrifugation and then redispersed in H2O before drop-casting onto the graphene/gold film sample and subsequently dried in air at room temperature to produce graphene-sandwiched MPoFNs. Thermal annealing of the as-prepared graphene-sandwiched MPoFNs was carried out at 120 °C for over 5 h in order to improve the contact between the graphene layers and the gold nanospheres and gold film. Finally, an Al2O3 layer of about 5 nm thickness was grown on the MPoFN sample by using atomic layer deposition at 80 °C in order to protect the structures from degradation and also improve the stability of the MPoFNs. Dark-Field Spectroscopy. Optical dark-field imaging and spectroscopy were performed on a customized Olympus BX51 microscope. A 100× dark-field objective (LMPlanFLN-BD, NA = 0.8) was used to focus an unpolarized white-light beam from an incandescent lamp onto the sample plane. Scattered light was collected through the same objective and analyzed with an imaging spectrometer (Acton SP2300, Princeton Instruments) equipped with a gray CCD camera (PIXIS: 400BR eXcelon, Princeton Instruments). Raman Measurement. Raman spectra and images were collected with a WITec alpha300 M+ confocal Raman microscope (WITec GmbH) equipped with a 633 nm He−Ne gas laser. The incident laser power was controlled to be 3 mW in the graphene Raman and 0.3 mW in the SERS measurements to avoid laser-induced thermal effects or photodamage. A diffraction-limited spot size of about 340 nm in radius was obtained for the incoming 633 nm laser beam through a 100× objective (NA = 0.90). Raman scattered light was dispersed by a high-resolution grating of 300 grooves/mm and then analyzed by a 600 mm focal length spectrometer (UHTS 600). TEM Cross-Sectional Imaging. The cross-sectional slices containing graphene-coupled MPoFNs were prepared by a multiBeam SEM-FIB system (JEOL model JIB-4501), operated under 30 keV Ga+, equipped with a platinum (Pt) deposition cartridge. To minimize
CONCLUSION In conclusion, we have combined comprehensive theoretical calculations and far-field and near-field optical spectroscopic measurements to probe the near-field enhancement limit in H
DOI: 10.1021/acsnano.9b00776 ACS Nano XXXX, XXX, XXX−XXX
Article
ACS Nano the ion beam damage, first, a 5 nm thick Al2O3 layer was coated on the surface of a graphene-coupled MPoFN sample, which is also helpful to enhance the profile contrast for better cross-sectional imaging. Then the area of interest, i.e., the gap region of each graphene-coupled MPoFN, was protected by a ∼300 nm platinum layer by using low-voltage (5 kV) electron beam deposition. After that, a several micrometer thick platinum layer was deposited using a gallium ion beam and then milled to
