Plasmon Control driven by Spatial Carrier Density Modulation in

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Plasmon Control driven by Spatial Carrier Density Modulation in Graphene Makoto Takamura, Norio Kumada, Shengnan Wang, Kazuhide Kumakura, and Yoshitaka Taniyasu ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b01623 • Publication Date (Web): 19 Mar 2019 Downloaded from http://pubs.acs.org on March 24, 2019

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Plasmon Control driven by Spatial Carrier Density Modulation in Graphene Makoto Takamura,∗ Norio Kumada, Shengnan Wang, Kazuhide Kumakura, and Yoshitaka Taniyasu NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan E-mail: [email protected] Phone: +81 46 240 3485. Fax: +81 46 240 4718

Abstract Self-assembled monolayers of organosilane formed at the interfaces between graphene and SiO2 /Si substrates were used for selective-area modulation of the charge carrier density in graphene. The interfaces between regions with different charge carrier densities were found to act as gate-tunable plasmonic reflectors, and this therefore allowed for spatial control of the plasmons. We numerically calculated the influence of the charge carrier concentration on the plasmon dispersion in graphene and found that the reflection coefficient may be tuned between 0 and 1.

Keywords graphene, plasmons, plasmon reflection, near-field microscopy, s-SNOM ∗

To whom correspondence should be addressed

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Plasmons are electromagnetic excitations of quasi-particles in matter. The low charge carrier concentration of graphene dictates that the plasmonic excitations occur at terahertz to mid-infrared frequencies. 1,2 Moreover, such low charge carrier concentrations allow for field-effect as well as chemically induced carrier concentrations. Finite element analysis simulations using electromagnetic properties specific to graphene pointed novel design concepts for waveguides and optical splitters. 3 Plasmonic refraction has been demonstrated by utilizing intrinsic charge density modulations at the interfaces between bi- and monolayer graphene, which are induced by the specific growth process of the chemical vapor deposition (CVD). 4 Plasmonic control has also been demonstrated at graphene/SiO2 , 5,6 graphene/moir´ e-patterned graphene, 7 and graphene/carbon-nanotube interfaces. 8 However, artificially designed interfaces have not yet been subject to plasmonic investigation. Such artificial interfaces can be induced in graphene via chemical doping using selfassembled monolayers (SAM) of organosilane. In particular, 3-amino-propyltriethoxysilane (NH2 -silane) is known to be effective at inducing electron charge carriers. 9–11 The SAM patterns are deposited on SiO2 by physical vapor deposition (PVD) and shaped by photolithography. The carrier concentration is modulated by electrostatic induction when the surfaces of a material are exposed to other materials of different polarizations. Therefore, exposing graphene to SAM or SiO2 results in it having different charge carrier concentrations due to their different dielectric constants. The interface that emerges between graphene surfaces exposed to different dielectric polarizations is known to be of the order of several unit cells of graphene in width, 11 and this width is significantly shorter than the expected wavelength of the plasmons (λp ). In this study, we investigated the plasmonic reflection behavior at such artificially designed interfaces.

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1

Experimental Section

We grew graphene via CVD on commercially available Cu foils (HA1, JX Nippon Mining & Metals); the details have been published elsewhere. 12 The number of layers was confirmed by the shape of Raman 2D peak. 13 SiO2 (285 nm) /Si (380 µm) substrates were treated by oxygen reactive-ion etching (O2 -RIE) to terminate their surfaces with silanol. 14 A SAM of NH2 -silane was formed on the substrates via PVD at room temperature. 15 3 µm × 1 cm stripes of NH2 -silane were patterned by photolithography. Subsequently, monolayer graphene domains were transferred to the SiO2 /Si substrates with the striped SAM by using the polymer-assisted method 16 (Figure 1a). Figure 1b shows an optical microscopy image and the associated Raman spectra taken at graphene/SAM and graphene/SiO2 . To independently estimate the charge carrier concentration, Raman spectra were taken by micro-Raman spectroscopy (Renishaw, Invia) at an excitation wavelength of 532 nm. The relaxation time of the charge carrirers was measured with the van der Pauw method. We measured the interference patterns of the plasmons by using a scattering-type scanning near-field optical microscope 17–19 (s-SNOM) (Neaspec), which is based on a tapping mode atomic force microscope (AFM), where the induced plasmons can be monitored via the coupling of light and plasmons. Plasmon excitations were induced in the graphene by illuminating a PtIr5 -coated AFM tip with a focused infrared beam from a quantum cascade laser (10.0 < λ0 < 11.0 µm) with a wavelength of λ0 = 10.7 µm. To suppress the background signal, the optical near-field intensity signal was demodulated at the third harmonic of the tapping frequency. 20 The launched and reflected plasmons interfered and generated an interference pattern. 5,6,21,22 In all of the s-SNOM images, the near-field amplitude was normalized to an interference pattern free zone of graphene/SAM. An electric field (E ≤ 2.1× 105 V /m) was generated between the graphene and Si by applying a gate voltage (Figure 1b). All experiments were performed at room temperature.

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Results and Discussion

We used the peak position of the Raman G and 2D bands (Pos(G) and Pos(2D)) to estimate the charge carrier concentrations. 23 (Pos(G), Pos(2D)) = (1589, 2686 cm−1 ) on graphene/SAM and (Pos(G), Pos(2D)) = (1596, 2684 cm−1 ) on graphene/SiO2 were obtained (upper-right in Figure 1b), which correspond to the charge carrier concentrations of about 4×1012 cm−2 for graphene/SAM and about 1.2×1013 cm−2 for graphene/SiO2 . 24 A map of the peak position of the Raman G band is presented in Figure 1b (bottom-right). The map shows lower wavenumber for graphene on SAM compared with graphene on SiO2 , thereby indicating selective area doping. 25 These results indicate that the charge carrier densities were spatially modulated in the graphene layer. Figures 1c and 1d plot topographic and near-field amplitude (s) information recorded by s-SNOM, respectively. It is pertinent to the near-field amplitude analysis procedure to ensure a flat surface without any potential scatterers. In fact, the only discernible scattering object in Figure 1c is the SAM layer beneath the graphene. The absence of scattering objects is furthermore apparent in the near-field amplitude image (Figure 1d). Hence, the near-field amplitude image highlights the higher charge carrier concentration in the graphene without the SAM layer beneath. In addition, due to the higher charge carrier concentrations along the grain boundaries of graphene (GB1 and GB2 in Figure 1d), which are invisible in the topographic image, the near-field amplitude image shows a brighter response than that of undistorted (apparently defect-less) graphene. 21 The spatial modulation of the near-field amplitude that arises at the grain boundary is due to constructive interference of plasmons at interfaces with widths smaller than λp . The distance between the constructive interference approximately corresponds to half the plasmon wavelength (λp /2). 21 Indeed, this is what is shown in Figure 2a. To see the influence of the charge carrier concentration on λp , we also measured the near-field amplitude along GB2, where the carrier concentration was altered by the SAM (Figure 2a). Noteworthy, λp is reduced in the graphene on the SAM. In particular, the near-field amplitude profiles taken perpendicular to GB1 and GB2 indicate λp /2 ∼130 4


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nm without the SAM and λp /2 ∼90 nm with the SAM. To relate the carrier concentration and the plasmon wavelength, it is prudent to make two assumptions. For one, we assume that the dielectric tensor to be constant between the SAM and SiO2 . This is justified by the fact that the influence of the 2-nm-thick SAM on the effective dielectric function of graphene environment can be estimated to be about only 3 % at λ0 = 10.7 µm. 28–30 The other is that the conductivity of graphene can be approximated by the Drude formula that is valid in the long-wavelength and low-frequency limit. Under these assumptions, the plasmon dispersion of graphene at the interface between vacuum and a substrate, λp is given by 21 λp ≈

√ e2 νF πnλ20 0) 2πhc2 ε0 Re( 1+ε(λ ) 2

,

(1)

where e is the elementary charge, n is the carrier density, νF is the Fermi velocity, and ε is the dielectric function of the substrate. The measured λ0 dependence of λp shows two distinct trends for graphene/SAM and graphene/SiO2 (Figure 2b). A fitting using equation (1) with ε(λ0 ) of SiO2 (ε = 4 at λ0 = 10.7 µm 31 ) results in the carrier concentration of 6.6×1012 cm−2 for graphene/SAM and 1.8×1013 cm−2 for graphene/SiO2 , which are similar to the values deduced via Raman scattering. This indicates that the change in λp is due to the change in charge carrier concentrations. Note that the difference in the carrier concentrations deduced via Raman scattering and λp is due to molecular adsorption in the air. 32 Plasmons are likely to be reflected at the interfaces between regions with different charge carrier concentrations, which results in a spatial modulation of the near-field amplitude. In fact, the near-field amplitude image shows a spatial modulation of the amplitude across the interface between graphene/SiO2 and graphene/SAM (line R in Figure 1d). Figure 2c plots the near-field amplitude as a function of position across the interface between graphene/SiO2 and graphene/SAM, where the amplitude shows a maximum and a minimum in intensity. The asymmetric near-field amplitude profile is due to the step-like profile of charge carrier concentrations. The reflection phase should differ by π depending on whether the plasmon wavelength of the injection medium is larger or smaller than that the medium reflecting 5


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plasmons. 33 This phase difference leads to the asymmetric near-field amplitude profile. The reflection coefficient (rp ) can be estimated from the near-field amplitude profile. 26 In particular, we estimated it from the ratio of the amplitude in the graphene/SAM area of the plasmon reflection at the interface (∆sB ) to that at the graphene edge (∆sE ), where the plasmon is completely reflected. For the line profile shown in Figure 2c, ∆sB /∆sE is about 0.2. Moreover, rp can be analytically calculated by modeling the interface as a step-like discontinuity in the plasmon wavelength: rp ≈ (λp1 − λp2 )/(λp1 + λp2 ) when (λp1 − λp2 ) ≪ λp2 , 7 and λp1 and λp2 are the plasmon wavelengths of graphene on the SiO2 and on the SAM, respectively. λp1 = 260 nm and λp2 = 180 nm estimated from Figure 2a give rp = 0.18, which is close to 0.2, the value obtained from the near-field amplitude. Consequently, we conclude that the plasmon reflection at the interface between graphene/SiO2 and graphene/SAM originates from the difference in the charge-carrier concentrations. To gain a better understanding of plasmon reflections at the interfaces, we performed a numerical calculation of the near-field amplitude profiles across the interface by using the finite element method. We approximated the tip of the s-SNOM system as a vertically oriented point dipole. 34 A schematic diagram of the calculation model is shown in Figure 3a. The point dipole was placed at a height d above the substrate. The substrate was modeled with ε = 4 at λ0 = 10.7 µm. Graphene was modeled as a conducting layer with the following surface conductivity 35–37 based on the Kubo formula: 38 [

(

EF e 2 kB T ln exp − σ = −i 2 −1 kB T π¯h (ω − iτ )

)

(

EF + exp kB T

)

]

+2 .

(2)

Here, kB is Boltzmann’s constant, T is temperature, h ¯ is the reduced Planck’s constant, ω √ is the frequency of the laser, EF = h ¯ νF πn is the Fermi energy with νF the Fermi velocity, and τ is the carrier relaxation time in graphene. Here, we only consider the intraband contribution, because the photon energy in this experiment (∼110-120 meV) is smaller than √ 2EF (∼200-800 meV). We used n and τ (= µEF /eνF2 = µ¯h πn/eνF with µ being the

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carrier mobility) as the simulation parameters. Assuming that n changes abruptly over a width shorter than λp , it would have a step-like change at the interface (Figure 2d). We simulated near-field amplitude profiles by calculating the vertical component of the electric field just below the dipole (at a height of z) as a function of its position (|Ez (x)|) since the scattering rate of the vertical dipole is proportional to |Ez |. Figure 2c shows the results for (n1 , τ1 ) = (1.8×1013 cm−2 , 0.05 ps) for graphene/SiO2 and (n2 , τ2 ) = (6.6×1012 cm−2 , 0.05 ps) for graphene/SAM (see Figure 2d); n1,2 and τ1,2 correspond to µ1 ∼1000 cm2 V−1 s−1 and µ2 ∼1700 cm2 V−1 s−1 , respectively. These values were independently confirmed from the van der Pauw measurements, where µ1 = 1000 ± 50 cm2 V−1 s−1 and µ2 = 1900 ± 250 cm2 V−1 s−1 . Within the error bars, the calculated amplitude dependence reproduces the near-field amplitude profile. Supposing that the transition width of the charge carrier concentration profile is 200 nm, the plasmon reflection is suppressed (Figure 2c). From these results, we can conclude that plasmon reflections at the interface are caused by the difference in n (∆n) and that an abrupt change in n is required for reflections to occur. In our sample, graphene is doped by the electrostatic potential produced by the SAM just below graphene, 11 results in an abrupt change in n. To demonstrate tunability of the plasmonic reflection coefficient in graphene, we examined the near-field amplitude profiles across the interface between regions with different charge carrier concentrations by using a back gate to vary n . We estimated n from λp with equation (1), where λp was obtained from the distance between the interference pattern across the grain boundary. Figure 3b summarizes the near-field amplitude profiles across the interface between graphene with and without the SAM for several values of gate voltages (Vg ). In these gate-voltage dependent measurements, the largest ∆n (= | n1 −n2 | = 1.4×1013 cm−2 ) is at Vg = 0 V. Under such conditions, the near-field amplitude clearly show maxima and minima. The reflection amplitude decreases with decreasing ∆n for both the graphene/SAM and graphene/SiO2 sides, and it vanishes for ∆n = 3.6×1012 cm−2 at Vg = 20 V. This indicates that the reflection coefficient increases with increasing ∆n. We quantitatively estimated

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the reflection coefficient for the graphene/SAM side from ∆sB /∆sE at each Vg . Figure 3c summarizes it the reflection coefficient as a function of ∆n. To reproduce the ∆n dependency of rp , we numerically calculated the reflection coefficient estimated by ∆sB /∆sE for several values of n2 and n1 = 2×1013 cm−2 . Here, τ1 = τ2 = 0.05 ps as τ ∝ µEF does not vary with n1,2 . 39,40 The calculation results are plotted in Figure 3c. To reach rp =1, ∆n would be 1.9×1013 cm−2 with n2 = 0.8×1012 cm−2 . Since plasmons would no longer be induced in graphene at such low charge carrier densities (n2 = 0.8×1012 cm−2 ) with λ0 = 10.7 µm, those propagating in the graphene with n1 = 2×1013 cm−2 would be completely reflected at the interface. On the other hand, graphene would become completely transparent (rp = 0) at ∆n = 1×1012 cm−2 (n2 = 1.9×1013 cm−2 ).

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Conclusions

We experimentally demonstrated spatial control of surface plasmons in monolayer graphene by selective-area chemical doping. The s-SNOM images indicated that spatial modification is possible as plasmons with shorter wavelengths were observed in graphene with low carrier density. We evaluated the carrier concentrations with Raman spectroscopy and s-SNOM and found that the plasmon reflection mechanism was driven by the difference in the charge carrier concentrations in the graphene. The reflection coefficient could be tuned by electrical gating. Our results reveal the possibility of realizing tunable plasmon reflectors and other optical elements for graphene-based plasmonic circuits through spatial control of the charge carrier concentration.

Acknowledgement The authors thank Dr. Masaaki Ono for his help with the COMSOL calculation and Dr. Yoshiharu Krockenberger for his valuable discussion.

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Note The authors declare no competing financial interest.

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(39) Zhu, W.; Perebeinos, V.; Freitag, M.; Avouris, P. Carrier scattering, mobilities, and electrostatic potential in monolayer, bilayer, and trilayer graphene. Phys. Rev. B 2009, 80, 235402. (40) Tanabe, S.; Sekine, Y.; Kageshima, H.; Nagase, M.; Hibino, H. Carrier transport mechanism in graphene on SiC(0001). Phys. Rev. B 2011, 84, 115458.

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For Table of Contents Use Only Manuscript title: Plasmon Control driven by Spatial Carrier Density Modulation in Graphene Names of authors: Makoto Takamura, Norio Kumada, Shengnan Wang, Kazuhide Kumakura, and Yoshitaka Taniyasu

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Figure 1: (a) Sketch of the sample structure for the investigation of plasmon reflections. n1 and n2 are the charge carrier concentrations in each area. (b) Optical image of the graphene on SAM and on SiO2 /Si (left), Raman spectra measured in areas of the graphene/SAM and graphene/SiO2 without gating (top-right), and a map of the peak position of Raman G band, Pos(G) (bottom-right). An Au electrode was used to apply voltages between the graphene and Si. The s-SNOM tip and the graphene were grounded. (c) Topography and (d) near-field amplitude (s) images. The solid white line in the topography image is the height profile. The 2-nm step stems from the underlying SAM. R is the scan direction for the near-field amplitude profiles shown in Figures 2 and 3. GB1 and GB2 are the scan directions across the grain boundary in graphene/SiO2 and in graphene/SAM, respectively. Note that, the 2-nm step does not induce plasmon reflections. 26,27

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Figure 2: (a) Near-field amplitude (s) as a function of position across the grain boundary (dashed lines of GB1 and GB2 in Figure 1d). (b) Dependence of plasmon wavelength (λp ) on incident beam wavelength (λ0 = 10.0, 10.7, and 10.9 µm). The dashed lines were calculated using different charge carrier densities. The length of error bars originates from the errors of the determination of the distance between interference patterns across the grain boundary and effects of the reflection phase shift. 21 (c) Near-field amplitude as a function of position across the interface between regions with different carrier densities (line R in Figure 1d). The red and blue dashed lines were obtained from numerical calculations with the parameters shown in (d), where the charge carrier density (| n |) profiles are step-like (red line) and monotonically varying over 200 nm (blue dashed line).

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Figure 3: (a) Schematic diagram of the model used in the numerical calculations. Graphene was modeled as a conducting layer with spatially different charge carrier concentrations (n1 and n2 ). A point dipole was placed at a height d above graphene. For the calculation of |Ez (x)|, d and z were kept constant at 125 and 16 nm, respectively. (b) Near-field amplitude (s) profiles measured by s-SNOM as a function of position across the interface between graphene with and without SAM at various gate voltages (Vg = 0, 20, 40, 60, and 80 V). n1 and n2 are the carrier densities of graphene on SiO2 and on SAM, respectively. The carrier concentrations were estimated from λp . Red and blue arrows indicate the amplitude of the plasmon reflection. (c) Reflection coefficient (rp ) as a function of the difference in carrier concentration between graphene with and without the SAM (∆n = | n1 − n2 |). The red and black dots indicate measured and numerically calculated values, respectively. n1 was 2×1013 cm−2 .

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Plasmon Control driven by Spatial Carrier Density Modulation in

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