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aCAS Key Laboratory of Materials for Ener

Science and Engineering, University of Sc

230026, P. R. China. E-mail: zhuyanwu@usbSino-French Institute of Nuclear Engineerin

Zhuhai Campus, 519082, Guangdong, P. R.

Cite this: RSC Adv., 2014, 4, 26535

Received 16th April 2014Accepted 5th June 2014

DOI: 10.1039/c4ra03431g

www.rsc.org/advances

This journal is © The Royal Society of C

High Q-factor plasmonic resonators in continuousgraphene excited by insulator-covered silicongratings

Yuan Zhao,a Guanxiong Chen,a Zhuchen Tao,a Chunyu Zhangb and Yanwu Zhu*a

We propose a structure to excite plasmons in large-area continuous graphene films with insulator-covered

sub-wavelength silicon gratings (ICSWSG). By numerical simulations we have demonstrated that, after

adding a low-permittivity insulator underneath graphene, the graphene/gratings hybrid structure has a

high Q-factor (�66) and a sharp notch (with the full width at half maximum of �122 nm) in the

transmission spectra at mid-infrared resonant wavelength. Furthermore, the plasmonic properties, e.g.

the resonant wavelength, magnitude and Q-factor, can be tuned over a wide range via structure

modulation and/or gating of graphene. The transmission dip is achieved over a wide angle range. Finally

we demonstrate that such highly confined graphene plasmons could also be excited in graphene

sandwiched between silicon gratings and a SiO2 substrate.

1. Introduction

Graphene emerging as a novel two-dimensional (2D) materialhas attracted signicant attention due to its unique electronicand optical properties, which has inspired a plethora of fasci-nating applications in photonics and optoelectronics.1–5 Gra-phene has been found to support plasmons (collectiveoscillations of charged carriers) for a wide wavelength rangefrom mid-infrared to terahertz with interesting properties suchas sub-wavelength connement and prominent enhancementof electromagnetic eld near graphene surface.6,7 The conne-ment of plasmons in graphene is stronger than that on metallicsurface due to the 2D nature of graphene and extremely shortplasmonic wavelength compared to the excitation wavelength,which can create strong light–matter interactions and can bepotentially used to build optical detectors, modulators andnonlinear optical devices with high efficiency.8–11 Moreover, itwas shown that the plasmonic properties can be dynamicallytuned by doping or gating graphene.12,13 Furthermore, the highcarrier mobility in graphene at room temperature and at highcarrier concentrations leads to an effective propagation ofplasmonic waves in graphene with a spatial scale of severaltimes of the wavelength of graphene plasmons at mid-infraredfrequencies.10,14,15 Such large propagation range of grapheneplasmons (albeit at different frequencies) are substantiallymore favorable than those of conventional surface plasmons.

gy Conversion, Department of Materials

ience and Technology of China, Hefei

tc.edu.cn

g & Technology, Sun Yat-Sen University,

China

hemistry 2014

For example, the plasmonic propagation lengths are only0.1 times of the wavelength of surface plasmons at the Ag/Siinterface.14Due to the highmobility, the tuning response occursin a duration shorter than a nanosecond.1 Therefore graphenehas been recognized as a versatile and promising plasmonicmaterial.

For exciting plasmons in graphene, a key challenge is toefficiently couple to the plasmonic wave, as its wavevector ismuch larger than that of free-space waves.15,16 Experimentally,excitations of plasmons in graphene have been realized usingperiodically patterned graphene structures, e.g., one-dimen-sional (1D) nanoribbons13 or micro-ribbons6 and 2D nano-disks12 or micro-disks.17 Graphene/insulator stacking structureshave been investigated to enhance the tunability of the plas-monic resonance magnitude.18 These designs usually suffer arelatively low quality factor (Q-factor) (dened as the ratio ofresonant wavelength to the full width at half maximum) whichpossibly restricts the practical applications, e.g. in sensing. Onthe other hand, although extremely high carrier mobility, e.g.230 000 cm2 (V�1 s�1), has been demonstrated in high-qualityexfoliated graphene samples,19 the lithography process neces-sary for fabricating graphene nanostructure or microstructurearrays may severely deteriorate the mobility, thus leading to abig loss and much lower Q-factors.12,20 It will be valuable to haveoptimized Q-factors, especially in large-area continuous lms.

Plasmonic excitations in graphene with sub-wavelengthdielectric gratings to compensate wavevector have beenproposed to generate a resonance with a Q-factor of �40.15,16 Inthese structures, the dispersion of graphene plasmons splitsinto bands due to the different dispersions of plasmons ondifferent regions of gratings, which allows the excitation ofplasmons in graphene by external incident light.16 Utilizing

RSC Adv., 2014, 4, 26535–26542 | 26535

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these structures, plasmonic excitations may be realized withoutthe need of engineering graphene, which may benet tomaintain the excellent electronic property in graphene.21

Moreover, by tuning the period of gratings, the structure canwork in mid-infrared, far-infrared or terahertz wavelengths.15

For example, plasmons in a continuous monolayer graphenehave been detected in mid-infrared regions with the assistanceof sub-wavelength silicon gratings.21 However, the challengescould remain considering the proposed process of experimentalpreparations andmicrostructure inuences. When compared toat substrates, the rough gratings may increase the interfacescattering and deteriorate the mobility in graphene,12,22–24 thusleading to bigger losses and lower Q-factors in the practicaldevices.

In this work, a structure with insulator-covered sub-wave-length silicon gratings (ICSWSG) is proposed to excite plasmonsin a continuous graphene lm. The structure experiences a highQ-factor aer a low-permittivity insulator is added underneathgraphene. Finite element electromagnetic simulations revealthe strong electric eld connement around the graphene layerat the resonant wavelengths. We demonstrate that the plas-monic properties can be modulated by tuning the insulatorlayer thickness, grating period, Fermi energy level, carriermobility and the number of graphene layers. Moreover, thestrong resonance has been observed over a wide incident angleof the light. Similar plasmonic resonances and eld conne-ments can also be realized in a graphene layer sandwichedbetween silicon gratings and a SiO2 substrate. The excellentfeatures of our proposed structures would make high-perfor-mance graphene-based plasmonic sensors possible.

2. Structure and methods

The structure of ICSWSG is schematically illustrated in Fig. 1aand the 2D simulation conguration is depicted in Fig. 1b. Thesurface of a silicon wafer was patterned into a periodic array ofgratings with period p, width w (w¼ 0.5p) and thickness T1. Theslits between silicon gratings were lled with organic solution of

Fig. 1 (a) Schematic view of insulator-covered sub-wavelength silicongratings-assisted graphene plasmons. The gratings patterned onsilicon wafer surface have period p, width w (w ¼ 0.5p) and thicknessof T1. The slits between silicon gratings are filled with an insulator (e.g.NFC), and another thin insulating layer with thickness of T2 is coated onthe top of graphene films. The electrical field distributions in the yz-plane at the resonant wavelength are depicted in the inset at lowerright corner. (b) 2D configuration of graphene on NFC-covered silicongratings for simulation.

26536 | RSC Adv., 2014, 4, 26535–26542

an insulator such as NFC (NFC is a derivative of poly-hydroxystyrene that is conventionally used as a planarizingunderlayer in lithographic processes.18,22 It can be diluted inpropylene glycol monomethyl ether acetate, and spin-coatedonto the surface. The dilution and spin speed can be adjusted tocontrol the desired thickness and uniformity of the bufferlayer.22). Another thin layer of NFC with a thickness of T2 wasspin-coated on the top of silicon gratings and was used as bufferlayer, with an attempt to construct a relatively gentle contact forgraphene. Finally, a graphene lm was transferred onto the topof the buffer layer. To excite the resonance, a mid-infrared wavewas incident onto the device from the top with transversemagnetic (TM) polarization (the magnetic eld parallel to thesilicon grating stripe) and transmittance was recorded to exhibitthe electromagnetic response of the hybrid structure. Once theplasmonic resonance is excited, the electrical eld is connedaround the graphene layer as depicted in the inset of Fig. 1a.

For a continuous monolayer graphene, the dispersion rela-tionship of plasmonic wave is given by14,25

kp ¼ ið3r1 þ 3r2Þ30cs

k0 (1)

where, kp is the wavevector of plasmons in graphene, k0 is thefree-space wavevector, 3r1 and 3r2 are dielectric constants of thematerials above and under the graphene, 30 is the permittivity ofvacuum, c is the speed of light, and s is the conductivity ofgraphene.

The conductivity of graphene is modeled using Drude modelwith D (Drude weight) and G (scattering width) as two ttingparameters,26

sðuÞ ¼ iD

pðuþ iGÞ (2)

where u is the incident light frequency; D ¼ e2EF/ħ2 and G ¼ s�1

¼ enF2/mEF, where e is the elementary charge, ħ is the reduced

Planck's constant, EF is the Fermi energy level, m is the carriermobility, nF z 2.11/2 � 106 m s�1 is the Fermi velocity and s isthe intrinsic relaxation time (e.g., s ¼ 3.8 � 10�13 s for EF ¼ 0.8eV and m ¼ 10 000 cm2 (V�1 s�1)). Here, as the photon energy inthe simulated spectral range is always less than 2EF, interbandtransitions in graphene are forbidden by the Pauli exclusionprinciple.25–27 Thus the effect of the interband transition hasbeen neglected in the simulations.25

Combining eqn (1) and (2), the wavevector of grapheneplasmonic wave can be expressed as

kp ¼ pħ230ð3r1 þ 3r2Þe2EF

u�uþ is�1

�(3)

When graphene is placed on a uniform dielectric medium,its plasmonic modes can't be excited directly by mid-infraredlight, since the wavevector of graphene plasmonic waves is farlarger than that of light in vacuum, as shown in Fig. 2a.However, once the difference is overcomed, the plasmonic wavecan be excited in graphene and the electric eld is highlyconned due to the large differences in wavevector.13,15

Herein, the ICSWSG is used to compensate the wavevectormismatches caused by the difference in the dispersion of

This journal is © The Royal Society of Chemistry 2014

Fig. 2 (a) Dispersion curves of graphene plasmons (red lines) onuniform dielectricmedium (3r1¼ 3r2¼ 1) and light line (black lines) in air.(b) Real part of the conductivity of graphene as a function of wave-length. Here, graphene Fermi energy level EF ¼ 0.6 eV and carriermobility m ¼ 10 000 cm2 (V�1 s�1) were used.

Fig. 3 Simulated normal-incidence transmission spectra for grapheneon silicon gratings (a) with and (b) without a 10 nm-thick buffer layerbeneathwhen EF¼ 0.6 eV, m¼ 10000 cm2 (V�1 s�1), p¼ 200 nm and T1¼ 500 nm. The insets show the side-view electrical field distribution inone grating period at the corresponding resonant wavelength of (a)8.08 mm and (b) 11.19 mm, respectively.

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graphene plasmons on different regions of ICSWSG,16 whichenables the efficient coupling of the incident electromagneticeld and the plasmonic modes in graphene. Introducing a low-permittivity polymer buffer layer between silicon gratings andgraphene lms may allow a relatively gentle contact for gra-phene and decrease the resonant wavelength l0 (eqn (6)), whereQ-factors are further improved as decreased value of Re(s) (realpart of the graphene conductivity) in small wavelength rangecorresponds to low losses (Fig. 2b). Furthermore, it has beenclaimed that adding a polymer buffer layer underneath gra-phene may help to minimize the mobility degradation due tothe suppression of extrinsic surface phonons and reduction ofthe impurity concentration.18

For a grating period p, the resonant wavelength l0 is deter-mined by phase match equation15

Re�kp�� 2p

l0sin q ¼ 2p

hp(4)

where q is the incident angle, h is a dimensionless constantwhich is related to the dielectric constant and the thickness ofbuffer layer and can be deduced from our simulation results.

For a normal incidence wave, q ¼ 0, eqn (4) is simplied as

Re�kp

� ¼ 2p

hp(5)

From eqn (5), it can be seen that the plasmonic resonantwavelength lp ¼ 2p/Re(kp) is related to grating period p and h aslp ¼ hp.

Combining eqn (3) and (5), the resonant wavelength l0 isgiven by

l0 ¼ffiffiffi2

ppħce

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih30ð3r1 þ 3r2Þp

EF

s(6)

Since the optical energy dissipates due to the ohmic losswhile the plasmonic wave propagates in the continuous gra-phene layer, a notch can be observed around the resonantwavelength in the transmission spectrum.15 The simulationswere performed in frequency domain using Comsol Multi-physics (COMSOL 4.3a), which implements the nite elementmethod (FEM) to solve Maxwell's equations and is a widelyacceptedmethod for modeling optics.28,29 In the simulations, we

This journal is © The Royal Society of Chemistry 2014

set the perfectly matched layer (PML) in the vertical direction toachieve absorbing boundary conditions, while in the horizontaldirections we used periodic boundary conditions for simulatingan innite silicon grating array (Fig. 1b). The graphene lm wasmodeled as a thin layer with a thickness of 0.5 nm, as in ref. 11and 15 and dielectric constants of silicon, SiO2 and NFC weretaken from ref. 18, 22 and 30. The meshing was done with theprogram built-in algorithm, which creates a tetrahedral mesh.The mesh maximum element size (MES), which limits themaximum size of the edges of the tetrahedrons, was set to be 0.1nm in the domain representing the graphene, 1 nm for NFC and6 nm for all the elements in the air, silicon and SiO2 sub-domains. Direct PARDISO solver was used to solve the problem.

3. Results and discussion

Fig. 3 shows the simulated transmission spectra for a mono-layer graphene on silicon gratings with or without a 10 nm-thickpolymer buffer layer underneath graphene, respectively. Strongresonance with a transmission dip was seen at 8.08 mm or11.19 mm, for the case with or without buffer layer, respectively.The full width at half maximum (FWHM) of the resonancedecreases from 248.87 nm for graphene on silicon gratings to121.80 nm aer a polymer buffer layer is added, leading to animprovement of 47.55% in the Q-factor (from 44.96 to 66.34).The increase in the Q-factor at smaller resonant wavelength is aresult of decreased real part of the graphene conductivity(Fig. 2b), corresponding to lower losses.25 This merit is desiredin applications such as sensing as gure of merit (FOM) isproportional to Q-factor. The side-view prole of the electriceld in one grating period for graphene on the buffer layer(inset of Fig. 3a) conrms that the electric eld is tightlyconned around the graphene layer. In addition, the electriceld has a 2p phase shi with the sign of the electric eldipping at the edge of the silicon slits. Specially, the conne-ment of electric eld is strong at the corner of silicon gratings,further beneting the electric eld connement. It is worthnoting that the electric eld for graphene on silicon gratings(inset of Fig. 3b) is also conned within the graphene layer.Here, the higher-order modes have been neglected at the

RSC Adv., 2014, 4, 26535–26542 | 26537

Fig. 5 The simulated angular dispersions of the transmittance forTM configurations when EF ¼ 0.6 eV, m ¼ 10 000 cm2 (V�1 s�1), p ¼

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smaller resonant wavelength due to the shallow notch in thetransmission spectra.

The Q-factor of the plasmonic spectra is determined by theoptical loss in graphene and can be calculated from relaxationtime s of charge carriers in graphene at resonance wavelengthl0. Theoretically, the Q-factor is expressed as25

Q ¼ Re�kp�

Im�kp� ¼ 2pcs

l0¼

ffiffiffi2

pesħ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiEF

h30ð3r1 þ 3r2Þp

s(7)

where Re(kp) and Im(kp) are the real and imaginary part of thewavevector of the plasmonic wave in graphene. For a specicresonant wavelength l0, the only way to increase the Q-factor isimproving the quality of graphene, i.e., by increasing s or m (m ¼enF

2s/EF). The simulated transmission spectra with variouscarrier mobilities in graphene are shown in Fig. 4a. It can beclearly seen that the FWHM decreases and Q-factor increaseslinearly (inset of Fig. 4a) with increasing the carrier mobilitywhile the resonant wavelength (l0 ¼ 8.08 mm) maintainsunchanged. The curve of Re(s) versus mobility m at resonantwavelength l0 ¼ 8.08 mm (inset of Fig. 4a) suggests that Re(s) isinversely proportional to m, explaining the lower loss, smallerFWHM and higher Q-factor for a graphene with higher mobilityat a xed resonant wavelength. Recent developments in thelarge-area synthesis and transfer techniques of high-qualitygraphene lms grown on metal substrates make the fabricationof devices with improved performance possible.18,31,32

In the proposed structure, another factor affecting FWHMand Q-factor is the thickness of buffer layer, which inuencesthe effective dielectric constants of 3r2. Fig. 4b shows thesimulated transmission spectra with different thicknesses ofbuffer layers. It can be seen that the resonant wavelength blue-shis as increasing the thickness of buffer layer due to theadditional decrease in the effective permittivity 3r2. Thus FWHMdecreases and Q-factor increases due to the low loss at smallerresonant wavelength. However, if the thickness of buffer layer istoo large, the transmission notch is too shallow to ensureenough detection (it is 100 nm in our case); 10 nm was used inthe following discussions.

Fig. 4 (a) Simulated normal-incidence transmission spectra with variou500 nm and T2¼ 10 nm. The real part of graphene conductivity and Q-facare shown in the inset. The dots are simulated data and the lines are cathickness of 5, 10, 20, 30 or 50 nm, respectively when EF ¼ 0.6 eV, m ¼

26538 | RSC Adv., 2014, 4, 26535–26542

Furthermore, our simulations (Fig. 5) show that the deeptransmission dip can be realized over a wide angle range. Such aresult is explained by the existence of at graphene plasmonbands above the light line at mid-infrared regions, which isattributed to the deep sub-wavelength nature of grapheneplasmons and effects of Bragg scattering at the Brillouin zonecenter.16

The Q-factor can be tuned by the Fermi energy level EF ingraphene relative to the Dirac points via gate voltage or elec-trostatic doping and period p of silicon gratings. From thesimulation results shown in Fig. 6a, it can be seen that thetransmission spectra can be effectively tuned with varyingFermi energy level EF of graphene. The resonant wavelength andQ-factor with respect to the Fermi energy level EF agree well witheqn (6) or (7) (h ¼ 1.50), as shown in Fig. 6b. Recent studiessuggested that, adding a buffer layer before transferring addi-tional graphene layers could help to distribute carriers intomultiple graphene layers andmake the structure have a broadertunability.18 Fig. 6c shows the transmission spectra in themultilayer graphene/insulator structures. It can be seen thatthe resonant properties can be tuned in a broader range viachanging the number of multilayer structures. It is worth

s carrier mobilities of graphene when EF ¼ 0.6 eV, p ¼ 200 nm, T1 ¼tor with varying carrier mobilities at resonant wavelength l0¼ 8.08 mmlculated from eqn (2) or (7). (b) Transmission spectra with buffer layer10 000 cm2 (V�1 s�1), p ¼ 200 nm and T1 ¼ 500 nm.

200 nm, T1 ¼ 500 nm and T2 ¼ 10 nm.

This journal is © The Royal Society of Chemistry 2014

Fig. 6 (a) Simulated normal-incidence transmission spectra with different Fermi energy level EF in graphene when m¼ 10 000 cm2 (V�1 s�1), p¼200 nm, T1 ¼ 500 nm and T2 ¼ 10 nm. (b) Scaling rule of the resonant wavelength l0 and Q-factor with respect to EF. The dots are simulatedresults and the lines are calculated from eqn (6) or (7). (c) Transmission spectra with different number of graphene/insulator multilayer structurewhen EF ¼ 0.6 eV, m ¼ 10 000 cm2 (V�1 s�1), p ¼ 200 nm, T1 ¼ 500 nm and T2 ¼ 10 nm. (d) Scaling rule of the resonant wavelength l0 and Q-factor versus the number of multilayer structure. The dots are simulated results and the lines are calculated from eqn (6) or (7) when substitutingN1/2EF for EF. (e) Transmission spectra with different period p of silicon gratings when EF ¼ 0.6 eV, m ¼ 10 000 cm2 (V�1 s�1), w ¼ 0.5p, T1 ¼ 500nm and T2 ¼ 10 nm. (f) Scaling rule of the resonant wavelength l0 and Q-factor with respect to p. The dots are simulated results and the lines arecalculated from eqn (6) or (7).

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noticing that the contribution of the buffer layer to the totalconductivity has been ignored since the buffer layer is thin (10nm) and non-conducting.18 In the calculations of multilayergraphene, we considered each graphene layer has the sameFermi energy level, mobility and relaxation time. The totalconductivity still has the Drude form, stotal ¼ iDtotal/p(u + iG),where the sum of the Drude weights for N layer graphene Dtotal

¼ N1/2e2EF/ħ.18,26 The resonant wavelength and Q-factor withrespect to the number of graphene layers agree well with

This journal is © The Royal Society of Chemistry 2014

theoretical values (substituting N1/2EF for EF in eqn (6) or (7)), asshown in Fig. 6d. Thus, multilayer graphene lms (e.g. bysequentially transferring monolayer) could be used to furtherimprove the tunability of such devices.

The effects of the period of silicon gratings were studied byxing the ratio of grating width w and period p (w/p) to be 1/2. Itcan be seen from Fig. 6e that the transmission spectra arelargely tuned with varying periods. The resonant wavelengthand Q-factor with respect to the period agree well with eqn (6) or

RSC Adv., 2014, 4, 26535–26542 | 26539

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(7), as shown in Fig. 6f. Specially, when the period of silicongratings is reduced to 50 nm, the Q-factor can be as high as 155.For large period, the notches at the higher frequencies arecaused by higher order modes.

Finally, the dependence of the resonant wavelength to therefractive index (RI) of dielectric environment above graphene(n1 ¼ 3r1

1/2) has been considered for possible applications of thegraphene/ICSWSG hybrid structure as sensors since graphenehas strong bio-compatibility and adsorption to biomoleculesdue to the p-stacking interactions and the high surface tovolume ratio of graphene.31,33–37 Fig. 7 shows the transmissionspectra with a 20 nm-thick sensing medium on graphene lmsand corresponding sensitivity calculated (dened as the ratio ofthe shi of resonant wavelength dl0 to the change of RI of thesensing medium dn1, dl0/dn1), with or without buffer layer. Thesensitivity improves 45.13% and gure of merit (FOM, denedas the ratio of sensitivity to FWHM) increases �190% (from�3.84 to �11.38) aer a thin buffer layer is present underneaththe graphene. The increase in the sensitivity and in the FOM isdue to the decrease in the effective permittivity 3r2 and mini-mization of the loss at smaller resonant wavelength.25 Further-more, the sensitivity is related to the thickness of sensingmedium since the characteristic decay length of grapheneplasmons is as high as �100 nm.25 Fig. 8a shows the trans-mission spectra with sensing medium RI n1 ¼ 1.31 and thick-ness of 1, 2, 5, 10, 20, 50, 100 and 200 nm above graphene lms,

Fig. 7 Simulated normal-incidence transmission spectra (a) with and(c) without a 10 nm-thick polymer buffer layer beneathwhen changingthe RI n1 of 20 nm-thick sensing medium from 1 to 1.5, respectivelywhen EF ¼ 0.6 eV, m ¼ 10 000 cm2 (V�1 s�1), p ¼ 200 nm and T1 ¼ 500nm. The resonant wavelength l0 versus sensing medium RI curve andthe corresponding sensitivity (b) with and (d) without buffer layerunderneath. The solid dots are simulated results and the lines are linearfittings to the data.

26540 | RSC Adv., 2014, 4, 26535–26542

respectively when EF ¼ 0.6 eV, m¼ 10 000 cm2 (V�1 s�1), p ¼ 200nm, T1 ¼ 500 nm and T2 ¼ 10 nm. It can be seen that theresonant wavelength red-shis with increasing lm thickness,and saturation of the shi is observed when the thicknessexceeds 100 nm (Fig. 8b), where the sensing is close to the bulkRI sensitivity. For bulk medium, the RI sensitivity can be as highas 1923 nm per RIU, as can be deduced using eqn (6),

S ¼ dl0

dn1¼

ffiffiffi2

ppħce

ffiffiffiffiffiffiffiffiffih30p

EF

rn1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðn12 þ 3r2Þp (8)

From eqn (8), we can see that the bulk RI sensitivity is relatedto period, permittivity of material beneath graphene and Fermienergy of graphene. By decreasing the Fermi energy of grapheneto 0.2 eV, the bulk sensitivity can be up to 3328 nm per RIU(Fig. 8c and d).

To further demonstrate the exibility of the dielectric envi-ronment surrounding graphene in the hybrid structure, weshow that setting sub-wavelength silicon gratings above gra-phene lms can also be used for compensating wavevectordifferences and exciting graphene plasmons (Fig. 9). Similarly,adding a buffer layer underneath (and/or above) graphene isbenecial to decrease FWHM and to increase Q-factor in thetransmission spectra around the resonant wavelength. Fromthe simulated transmission spectra and the side-view electriceld proles, it can be seen that the transmission spectra varysimilarly to those for placing sub-wavelength silicon gratingsbeneath. Moreover, the fundamental mode and second-modeare detected simultaneously for the structure either with or

Fig. 8 Simulated normal-incidence transmission spectra with sensingmedium RI n1 ¼ 1.31 and thickness of 1, 2, 5, 10, 20, 50, 100 and200 nm when (a) EF ¼ 0.6 eV, m ¼ 10 000 cm2 (V�1 s�1), p ¼ 200 nm,T1 ¼ 500 nm and T2 ¼ 10 nm or (c) EF ¼ 0.2 eV, m ¼ 20 000 cm2 (V�1

s�1), p ¼ 200 nm, T1 ¼ 500 nm and T2 ¼ 10 nm, respectively. Theresonant wavelength l0 with respect to the thickness of sensingmedium (b) in (a), giving a bulk sensitivity of 1923 nm per RIU or (d) in(c), giving a bulk sensitivity of 3328 nm per RIU, respectively.

This journal is © The Royal Society of Chemistry 2014

Fig. 9 Simulated normal-incidence transmission spectra for sub-wavelength silicon gratings on the top of graphene (a) with and (b)without a 10 nm-thick polymer buffer layer beneath when EF ¼ 0.6 eV,m ¼ 10 000 cm2 (V�1 s�1), p ¼ 200 nm and T1 ¼ 500 nm. The insetsshow the side-view electrical field distribution of the fundamentalmode and second-order mode in one grating period at the corre-sponding resonant wavelength, respectively. (c) Transmission spectrafor sub-wavelength silicon gratings on the top with 10 nm-thickpolymer buffer layer both above and beneath graphene films andcorresponding electrical field distribution of the fundamental mode.

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without a buffer layer beneath graphene. When adding bufferlayers both on the top and beneath graphene lms, the resonantwavelength blue-shis and FWHM decreases due to the furtherdecrease in the effective permittivity 3r1 above graphene, and thesecond mode is too shallow to be detected. The structureprovides an alternative to excite plasmons in continuous gra-phene lms.

4. Conclusion

In conclusion, we have demonstrated that ICSWSG can be usedto excite highly conned plasmonic modes in large-area

This journal is © The Royal Society of Chemistry 2014

continuous graphene lms. By numerical simulations, wefound that graphene/silicon gratings hybrid structure exhibitsan improvement of 47.55% in the Q-factor and a decrease of50.91% in the FWHM aer a low-permittivity insulator beneathgraphene was added. The plasmonic properties including theresonant wavelength andmagnitude were tuned viamodulatingstructure and/or gating of graphene. When the hybrid platformwas employed in sensing, the sensitivity improved 45.13% andFOM increased �190% aer a thin buffer layer was presentunderneath the graphene. In addition, we demonstrated thatthe highly conned plasmonic modes in graphene could beachieved by embedding graphene between silicon gratings anda SiO2 substrate. The excellent features of the proposed struc-tures may have implications on the development of high-performance and active plasmonic devices for sensing.

Acknowledgements

Y. Zhao, G. Chen, Z. Tao and Y. Zhu appreciate the nancialsupport from China Government 1000 Plan Talent Program,China MOE NCET Program and Natural Science Foundation ofChina (51322204).

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