sensors Article
Conformal Graphene-Decorated Nanofluidic Sensors Based on Surface Plasmons at Infrared Frequencies Wei Wei 1,2,3, *, Jinpeng Nong 1,2,3 , Linlong Tang 3,4 , Guiwen Zhang 2 , Jun Yang 3,4 and Wei Luo 2,3 1 2 3 4
*
Key Laboratory of Optoelectronic Technology & Systems, Ministry of Education of China, Chongqing University, Chongqing 400044, China;
[email protected] College of Optoelectronic Engineering, Chongqing University, Chongqing 400044, China;
[email protected] (G.Z.);
[email protected] (W.L.) Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing 401122, China;
[email protected] (L.T.);
[email protected] (J.Y.) Chongqing Engineering Research Center of Graphene Film Manufacturing, Chongqing 401329, China Correspondence:
[email protected]; Tel.: +86-23-6510-2511
Academic Editors: Fan-Gang Tseng and Tuhin Subhra Santra Received: 15 March 2016; Accepted: 26 May 2016; Published: 16 June 2016
Abstract: An all-in-one prism-free infrared sensor based on graphene surface plasmons is proposed for nanofluidic analysis. A conformal graphene-decorated nanofluidic sensor is employed to mimic the functions of a prism, sensing plate, and fluidic channel in the tradition setup. Simulation results show that the redshift of the resonant wavelength results in the improvement of sensitivity up to 4525 nm/RIU. To reshape the broadened spectral lines induced by the redshift of the resonant wavelength to be narrower and deeper, a reflection-type configuration is further introduced. By tuning the distance between the graphene and reflective layers, the figure of merit (FOM) of the device can be significantly improved and reaches a maximum value of 37.69 RIU´1 , which is 2.6 times that of the former transmission-type configuration. Furthermore, the optimized sensor exhibits superior angle-insensitive property. Such a conformal graphene-decorated nanofluidic sensor offers a novel approach for graphene-based on-chip fluidic biosensing. Keywords: sensor; surface plasmons; nanofluidic; conformal grapheme; infrared
1. Introduction Lab-on-chip systems combined with surface plasmon resonance (SPR) sensors provide a powerful technique to perform label-free biomolecular interaction measurements with high sensitivity [1–3]. A typical lab-on-chip system consists of a SPR excitation setup, a sensing plate, and a fluidic channel. In the traditional Kretschmann configuration [4], the prism used as the excitation setup is isolated from the sensing plate and the fluidic channel [5]. This means that the system needs to be attached and detached in each independent experiment, which largely decreases the efficiency and the usability. Furthermore, the prism needs to be angled appropriately to ensure the optimum output of incident light, hence making the system more complicated and less portable. To overcome these issues, a prism-free all-in-one setup is proposed, combining the SPR excitation item, sensing plate and flow channel in a single setup. For instance, Yang Hyun Joo et al. [6] demonstrated a long-range surface plasmon-polariton waveguide sensor employing an asymmetric double-electrode waveguide configuration. This consists of a microfluidic channel and a Bragg grating layer, which can effectively measure the refractive index of the inserted analyte. Ken-Ichi Nomura et al. [7] introduced a V-shaped trench-sensing system that minimizes the system and is unnecessary to adjust optical alignment, which contributes to the improvement of the detection efficiency. The above all-in-one setups extremely simplify the sensing system and reduce the sample volumes, promoting the development of the
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nanofluidic chip. However, these structures are based on the SPR in noble metals, of which the working wavelength is mainly located at the visible frequencies. While at mid-IR frequencies, these structures exhibit extremely large ohmic loss due to the low carrier mobility and increasingly large permittivity in magnitude [8]. Additionally, the metals cannot adsorb the biomolecules effectively because of the high surface inertness and intrinsic hydrophobicity [9]. Further extension of SPR sensors from visible and near-IR frequencies to mid-IR frequencies remains a significant challenge. In contrast to the metals, graphene [10] that emerged as a unique two-dimensional carbon atoms possesses a high surface-to-volume ratio and strong π-π stacking interaction with the carbon-based ring structures in biomolecules [11]. Thereby, it can effectively adsorb the biomolecules on its surface. Particularly, graphene supports propagating surface plasmons with smaller loss, stronger confinement, and gate-tunability at the mid- and far-infrared frequencies [12,13]. These superior features render graphene a promising candidate for engineering infrared SPR sensors. Up to now, graphene-based SPR sensors have mainly employed the localized plasmons in patterned graphene [14,15] or surface plasmons in continuous graphene [16,17]. In these devices, the sample solution (fluidic biomolecules or liquid chemical reagent) would be dropped on the sensor surface for detection. As a consequence, the thickness of the sample solution cannot be effectively controlled, which introduces uncertainties in the measurement results. To alleviate this problem, an extra flow channel is added to contain the sample solution in order to accurately control the sample volume, as reported in [9]. However, this makes the system more complicated and hence lacks stability. Recently, a new type of sensor that integrates nanofluidic channel with a flat graphene sheet is reported [18]. In such a configuration, the nanofluidic channel can not only contain the sample solution, but also directly excite graphene surface plasmons (GSPs) without the need of an extra optical component, which significantly reduces the complexity of the device. However, the sensitivity of the sensor is limited (1920 nm/RIU with an optimal device) due to the small contact area between the sample solution and graphene. Herein, we propose a novel infrared sensor based on graphene surface plasmons by decorating a conformal graphene [19–21] on a nanofluidic channel. Such a configuration allows for the detection of biological molecules in an aqueous environment. Besides, the conformal graphene can preserve the excellent electronic property of graphene and enlarge the contact area between graphene and biomolecules. A physical model was built employing the finite element method to improve the sensitivity of the sensor by optimizing the structure parameters of nanofluidic channels and Fermi level of graphene. Furthermore, a reflection-type configuration is proposed to improve the FOM while maintaining the high sensitivity. 2. Structure and Principles The structure of the proposed conformal graphene-decorated nanofluidic channel (CGDNC) infrared sensor is schematically illustrated in Figure 1a. A conformal graphene is decorated on an open nanofluidic channel array etched on a SiO2 substrate. In this case, the conformal graphene becomes hydrophilic due to the short-range chemical forces bonding between graphene and water [22]. Then, the sample fluidic can flow into the nanochannels for detection. The nanofluidic channels contain the following structural parameters: the period Λ, the width W, and the height H. A normally incident light with transverse magnetic polarization is used to excite the surface plasmon mode, and the transmitted light is detected as the signal of the change of the refractive index in the channels, as sketched in the cross section in Figure 1b. Since the proposed open nanofluidic channels are periodic arrays, it also can be regarded as an optical gating. When the light irradiates from the top of the channel arrays, it will be scattered into evanescent waves with various diffraction orders due to the introduced periodic modulation originating from different regions of the channel [23]. Once the wave vector of an evanescence wave matches the dispersion relation of a GSP mode, the incident photons couple with the electrons on the surface of graphene, and a GSP wave can be excited [24]. Then, the incident light is absorbed strongly due to the excitation of the GSP wave, and a resonant dip is observed in the transmission
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spectrum. This resonant dip is very sensitive to the refractive index change in the channel induced by Sensors 2016, 16, 899 3 of 10 the adsorption of biomolecules at the graphene interface. The change in refractive index, δnd , can be spectrum. This resonant dip is veryshift, sensitive to the refractive indexSchange in the channel measured by detecting the wavelength δλGSP . The sensitivity of a SPR sensor caninduced be defined as of biomolecules the graphene interface.index The change in refractive index, δnd, can the ratioby ofthe theadsorption wavelength shift to theatchange in refractive be measured by detecting the wavelength shift, δλGSP. The sensitivity S of a SPR sensor can be defined as the ratio of the wavelength shift to δλ the change S“ {δn in refractive index GSP
d
S GSP / nd
(1)
(1)
Equation (1) indicates that the sensitivity is decided by the resonant wavelength, and a large Equation (1) indicates that the sensitivity is decided by the resonant wavelength, and a large wavelength shift isshift highly desired, as itasallows a small refractive change. wavelength is highly desired, it allowsfor forthe the detection detection ofof a small refractive indexindex change.
Figure 1. (a) Schematic of the conformal graphene-decorated nanofluidic channel (CGDNC) infrared
Figure 1. (a) Schematic of the conformal graphene-decorated nanofluidic channel (CGDNC) infrared sensor. (b) The cross section of the CGDNC. (c) The mode profiles of graphene plasmonics. sensor. (b) The cross section of the CGDNC. (c) The mode profiles of graphene plasmonics. (d) Transmission spectra when the refractive index of sensing medium is 1.37, 1.41, 1.45, 1.46, and (d) Transmission spectra when the refractive sensing mediumare is 1.37, 1.41, 1.45,such 1.46, as and 1.53, 1.53, respectively (refractive indices of index some of typical molecules in this range, respectively (refractiveDNA indices double-stranded [9]). of some typical molecules are in this range, such as double-stranded DNA [9]). To obtain the resonant spectra of the sensor, a physical model is built based on the finite element method employing Comsol mutiphysics. In the model, the dielectric constant of the channel To obtain the Graphene resonant is spectra of the a physical model isof built onthe theconsider finite element is 2.1 [25]. modeled as asensor, monolayer with a thickness 0.34based nm. For method infrared employing Comsol mutiphysics. the model, constant the channel is 2.1 [25]. frequency region where theInphoton energythe ħωdielectric is much smaller thanof2E f, the interband absorption of graphene is Pauli blocked the surface conductivity of graphene be simply Graphene is modeled as a monolayer with a and thickness of 0.34 nm. For the considercan infrared frequency characterized by the energy Drude model only for intraband transition [26]: absorption of graphene region where the photon h¯ ω isaccounting much smaller than 2E , the interband f
is Pauli blocked and the surface conductivity of graphene e2 E f ican be simply characterized by the Drude (2) int ra model accounting only for intraband transition [26]: 2 i1 in graphene, τ is the relaxation time of charge where e is the elementary charge, Ef is the Fermi level e2 E fand ħ is i the reduced Planck’s constant. carriers, ω is the angular frequency of incident light, σintra pωq « (2) 2 ` iτ The excited GSP mode when Λ = 200 nm, Wπ=}100ωnm, H´ = 1100 nm, and Ef = 0.3 eV is presented in Figure 1c. It is seen that the excitation of GSP exhibits a strong ability to couple the incident-free where e space is thelight elementary charge, Efand is the Fermi level in graphene, is the relaxation into the GSP wave concentrate optical energy into τsub-wavelength spotstime withofa charge 6 carriers,near-field ω is the angular frequency of incident light, and h ¯ is the reduced Planck’s constant. |Ex| peak intensity of ~7.5 × 10 V/m on the graphene surface. In addition, the optical
The excited GSP mode when Λ = 200 nm, W = 100 nm, H = 100 nm, and Ef = 0.3 eV is presented in Figure 1c. It is seen that the excitation of GSP exhibits a strong ability to couple the incident-free space light into the GSP wave and concentrate optical energy into sub-wavelength spots with a near-field |Ex| peak intensity of ~7.5 ˆ 106 V/m on the graphene surface. In addition, the optical energy of GSP
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wave is dissipated while propagating along the graphene due to the ohmic loss. Then, a dip can be Sensors 2016, 16, 899 4 of 10 observed in the transmission spectra at the resonant wavelength, λGSP , as shown in Figure 1d. One can see that of theGSP resonant wavelength redshifts from 10.613 11.204 µm index energy wave is dissipated while propagating alongµm thetographene dueastothe therefractive ohmic loss. increases from 1.37 to 1.53, corresponding to a sensitivity of S = 3694 nm/RIU. To further improve Then, a dip can be observed in the transmission spectra at the resonant wavelength, λGSP, as shown the sensitivity, the 1d. structure parameters the channel and theredshifts property of graphene optimized in the in Figure One can see that theofresonant wavelength from 10.613 μmare to 11.204 μm as the refractive following context. index increases from 1.37 to 1.53, corresponding to a sensitivity of S = 3694 nm/RIU. To further improve the sensitivity, the structure parameters of the channel and the property of
3. Improvement the Sensitivity graphene are of optimized in the following context. 3.1. Effect of the Structure Parameters of CGDNC on the Sensitivity 3. Improvement of the Sensitivity Simulation showParameters that the spectral characteristics and the performance of the sensor can be 3.1. Effect of results the Structure of CGDNC on the Sensitivity modulated by tuning the period Λ and height H of the CGDNC. The transmission spectra with varying Simulation results show that the spectral characteristics and the performance of the sensor can Λ when H = W = 0.5Λ is illustrated in Figure 2a. One can see that the resonant wavelength redshifts be modulated by tuning the period Λ and height H of the CGDNC. The transmission spectra with from 7.535 µm to 12.935 µm as Λ increases from 100 nm to 300 nm. To evaluate the sensing performance varying Λ when H = W = 0.5Λ is illustrated in Figure 2a. One can see that the resonant wavelength of theredshifts sensor, from the resonant shift as a function of refractive index is plotted Figure 2b. 7.535 μm wavelength to 12.935 μm as Λ increases from 100 nm to 300 nm. To evaluate theinsensing The linear fitting results indicate that the sensitivity of the sensor is significantly improved by 63.3% performance of the sensor, the resonant wavelength shift as a function of refractive index is plotted from in 2668 nm/RIU to 4356 Figure 2c presents withisvarying H when Figure 2b. The linearnm/RIU. fitting results indicate that thetransmission sensitivity ofspectra the sensor significantly improved by W 63.3% from 2668 nm/RIUthat to 4356 2c presents transmission spectra Λ = 200 nm and = 100 nm. It shows the nm/RIU. resonantFigure wavelength redshifts from 8.134 µm to H whenfrom Λ = 200 nm to and Wnm. = 100 nm. It showsas that the resonant wavelength redshifts 10.773with µm varying as H increases 20 nm 100 Additionally, plotted in Figure 2d, the corresponding from 8.134 μm to 10.773 as nm/RIU H increasesto from 20 nm/RIU. nm to 100 nm. Additionally, as plotted Figure 2d, sensitivity improves from μm 3075 3693 This is attributed to theinredshift of the the corresponding sensitivity improves from 3075 nm/RIU to 3693 nm/RIU. This is attributed to the and resonant wavelength and, partly, the immense increase of the contact area between graphene redshift of the resonant wavelength and, partly, the immense increase of the contact area between biomolecules. Therefore, the sensitivity of the sensor can be improved by increasing the period and graphene and biomolecules. Therefore, the sensitivity of the sensor can be improved by increasing height of the CGDNC in the initial design. the period and height of the CGDNC in the initial design.
Figure (a) Transmission spectra with varyingΛ Λ when when H nm. (b) (b) TheThe calculated Figure 2. (a)2.Transmission spectra with varying H ==100 100nm nmand andWW= 100 = 100 nm. calculated sensitivity when Λ = 100 nm, 150 nm, 200 nm, 250 nm, and 300 nm, respectively. (c) Transmission sensitivity when Λ = 100 nm, 150 nm, 200 nm, 250 nm, and 300 nm, respectively. (c) Transmission spectra with varying H when Λ = 200 nm and W = 100 nm. (d) The calculated sensitivity when spectra with varying H when Λ = 200 nm and W = 100 nm. (d) The calculated sensitivity when H = 20 nm, 40 nm, 60 nm, 80 nm, and 100 nm, respectively. The lines in (b) and (d) are linear fittings H = 20 nm, 40 nm, 60 nm, 80 nm, and 100 nm, respectively. The lines in (b) and (d) are linear fittings to to the data. the data.
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Effect of of the the Coupling Coupling of GSP GSP Modes on the Sensitivity 3.2. Effect Further investigation investigation indicates indicatesthat thatthe theGSP GSPmodes modes propagating along inner sides of Further propagating along the the inner sides of the the channel strongly couple together width thechannel channeldecreases, decreases, resulting resulting in in the channel strongly couple together as as thethe width W Wofofthe significant improvement improvement of of the sensitivity. The The corresponding corresponding GSP GSP mode mode profiles profiles in in two periods significant 100 nm, nm, 60 60 nm nm and and 20 20 nm nm are are shown shown in in the the Figure Figure 3a,b,c, 3a,b,c, respectively. respectively. As expected, when when W == 100 thethe GSP modes propagating alongalong the inner sides of the channel are isolated W == 100 100nm nm(Figure (Figure3a), 3a), GSP modes propagating the inner sides of the channel are from each other. adjacent GSP modes in theinchannel couple withwith eacheach other when W isolated from each Then, other. the Then, the adjacent GSP modes the channel couple other when decreases to 60 (Figure 3b). As further decreases to 20 nm, thenm, GSPthe modes overlap W decreases to nm 60 nm (Figure 3b).WAs W further decreases to 20 GSP completely modes completely and couple forming aforming hybrid coupled at the bottom andbottom the ridge of theedges channel overlap andstrongly, couple strongly, a hybridmode coupled mode at the andedges the ridge of (Figure 3c). The strong of GSP modesofsignificantly the peak intensity the intensity localized the channel (Figure 3c).coupling The strong coupling GSP modesenhance significantly enhance the of peak electric field by 39.7% in field the channel andinresults in the redshift of theinresonant wavelength by 24.1% of the localized electric by 39.7% the channel and results the redshift of the resonant from 10.613 µm to 13.171 µm, as shown Figureμm, 3d. Such behavior extremely enhances the interaction wavelength by 24.1% from 10.613 μm toin13.171 as shown in Figure 3d. Such behavior extremely between the biomolecules the incident light andand makes it more sensitive the change in enhances thefluidic interaction between and the fluidic biomolecules the incident light andtomakes it more the refractive index, which contributes toindex, the improvement of sensitivity. indicated inof Figure 3e, the sensitive to the change in the refractive which contributes to the As improvement sensitivity. sensitivity increases by 3e, 63.1% 3695 nm/RIU 6025 nm/RIU as nm/RIU W decreases nm to As indicated in Figure thefrom sensitivity increasesupbyto63.1% from 3695 up tofrom 6025100 nm/RIU 20 W nm.decreases Thus, in order higher sensitivity the sensor, a narrower should be sensor, designed as from to 100gain nmato 20 nm. Thus, inoforder to gain a higher channel sensitivity of the a to ensure the strong coupling of GSP modes along the inner sides of the channel. Considering the narrower channel should be designed to ensure the strong coupling of GSP modes along the inner sides processing craftConsidering of the nanofluidic channelcraft and of thethe incorporation of the channel graphene,ofa of the channel. the processing nanofluidic channel and thewith incorporation width of 40 nm chosen for the following the channel withwas graphene, a width of 40 nm analyses. was chosen for the following analyses.
Figure Figure 3. 3. The The GSP GSP mode mode profiles profiles when when (a) (a) W W ==100 100nm, nm, (b) (b) 60 60 nm, nm, and and (c) (c) 20 20 nm nm in in two two periods. periods. (d) (d) Transmission Transmission spectra spectra with with decreasing decreasing W W from from 100 100 nm nm to to 20 20 nm nm when when Λ Λ == 200 200 nm nm and and H H ==100 100nm. nm. (e) The calculated sensitivity when W = 100 nm, 80 nm, 60 nm, 40 nm, and 20 nm, respectively. The (e) The calculated sensitivity when W = 100 nm, 80 nm, 60 nm, 40 nm, and 20 nm, respectively. The lines are linear fittings to the data.
3.3. Effect of the FERMI Level of Graphene on the Sensitivity Since the structure parameters of CGDNC can be only tuned during the fabrication, they cannot be dynamically controlled after the fabrication of the sensor. Therefore, we further considered actively improving the sensitivity by adjusting the Fermi level Ef of graphene. The
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3.3. Effect of the FERMI Level of Graphene on the Sensitivity Sensors 2016, the 16, 899 Since structure
6 of 10 parameters of CGDNC can be only tuned during the fabrication, they cannot be dynamically controlled after the fabrication of the sensor. Therefore, we further considered actively evolution of the transmission spectra with varying Ef is illustrated in Figure 4a. The figure indicates improving the sensitivity by adjusting the Fermi level Ef of graphene. The evolution of the transmission that the sensor can operate within a wide range of infrared wavebands by applying an external gate spectra with varying Ef is illustrated in Figure 4a. The figure indicates that the sensor can operate voltage. The resonant wavelength redshifts from 9.15 μm to 20.45 μm as Ef decreases from 0.5 eV to within a wide range of infrared wavebands by applying an external gate voltage. The resonant 0.1 eV. This results in the improvement of the sensitivity from 3495 nm/RIU to 8004 nm/RIU, as wavelength redshifts from 9.15 µm to 20.45 µm as Ef decreases from 0.5 eV to 0.1 eV. This results shown in Figure 4b. Consequently, the sensitivity of the sensor can be actively improved by in the improvement of the sensitivity from 3495 nm/RIU to 8004 nm/RIU, as shown in Figure 4b. gate-tuning the external voltage to decrease the Fermi energy level of graphene after the fabrication Consequently, the sensitivity of the sensor can be actively improved by gate-tuning the external voltage of the device. to decrease the Fermi energy level of graphene after the fabrication of the device.
Figure 4. (a) The transmission spectra with varying Ef when Λ = 200 nm, H = 100 nm, and W = 40 nm. Figure 4. (a) The transmission spectra with varying Ef when Λ = 200 nm, H = 100 nm, and W = 40 nm. (b) The calculated sensitivity when Ef = 0.5 eV, 0.4 eV, 0.3 eV, 0.2 eV, and 0.1 eV, respectively. The lines (b) The calculated sensitivity when Ef = 0.5 eV, 0.4 eV, 0.3 eV, 0.2 eV, and 0.1 eV, respectively. The are linear fittings to the data. lines are linear fittings to the data.
4. Improvement of of the the FOM FOM 4. Improvement The analysis brings bringsus ustotothe theconclusion conclusion that redshift of the resonant wavelength The above above analysis that thethe redshift of the resonant wavelength can can significantly improve the sensitivity of the sensor by optimizing the structural parameters significantly improve the sensitivity of the sensor by optimizing the structural parameters of of CGDNC CGDNC and and the the Fermi Fermi level level of of graphene. graphene. However, However, the the redshift redshift of of the the resonant resonant wavelength wavelength of of such such aa transmission-type transmission-type sensor sensor is is always always accompanied accompanied with with the the broadening broadening of of the the resonant resonant dip dip (shown (shown in Figure 2a,c, Figures 3d and 4a). This results in the decrease in detection accuracy (defined as the in Figures 2a,c, 3d and 4a). This results in the decrease in detection accuracy (defined as the reciprocal of the full width at half maximum (fwhm)). This means that a higher sensitivity is generally reciprocal of the full width at half maximum (fwhm)). This means that a higher sensitivity is at the cost at of athe lower accuracy andaccuracy that there is athat trade-off sensitivity andsensitivity detection generally cost detection of a lower detection and there between is a trade-off between accuracy. To effectively evaluate the overall performance of sensor, the figure ofofmerit (FOM) defined and detection accuracy. To effectively evaluate the overall performance sensor, the isfigure of as in [27,28]: merit (FOM) is defined as in [27,28]: ∆R FOM “ S (3) R f whm FOM S (3) fwhmSince the sensitivity is closely related to where ∆R is the resonance depth, and S is the sensitivity. the resonant thedepth, key toand improve thesensitivity. detection accuracy to reshapeisthe spectral line to where ΔR is wavelength, the resonance S is the Since theissensitivity closely related to have a large resonance depth and a small fwhm while keeping the resonant wavelength unchanged. the resonant wavelength, the key to improve the detection accuracy is to reshape the spectral line to To thisa end, further depth propose a reflection-type sensor with an Au layer atwavelength the bottom unchanged. of the SiO2 have largewe resonance and a small fwhm while keeping the resonant layer, sketched in Figure 5a. Aa 5-nm Ti layer issensor sandwiched the and To thisasend, we further propose reflection-type with anbetween Au layer at Au the layer bottom ofthe theSiO SiO22 layer in order to improve their adhesion. In such a configuration, an asymmetric Fabry–Perot (F–P) layer, as sketched in Figure 5a. A 5-nm Ti layer is sandwiched between the Au layer and the SiO2 cavity is order formed graphene andInreflective layers, whichan allows the incident light to make layer in tobetween improvethe their adhesion. such a configuration, asymmetric Fabry–Perot (F–P) two passes (forward and reflected) through the graphene sheet. The spectral line can be reshaped cavity is formed between the graphene and reflective layers, which allows the incident light to to modulate graphene–light by adjusting cavity length. parameters make twothe passes (forward interaction and reflected) throughthe theF–P graphene sheet. The Theoptimized spectral line can be Λ = 200 nm, = 100 nm, the W =graphene–light 40 nm, and Ef = interaction 0.3 eV (corresponding to Sthe = 4525 are usedThe in reshaped toHmodulate by adjusting F–Pnm/RIU) cavity length. the following analysis. optimized parameters Λ = 200 nm, H = 100 nm, W = 40 nm, and Ef = 0.3 eV (corresponding to
S = 4525 nm/RIU) are used in the following analysis. Simulation results indicate that the FOM of the sensor can be modulated periodically by tuning the F–P cavity length (spacer thickness T). The reflection spectra with several sets of spacer thickness T are presented in Figure 5b. As expected, the notch broadens and becomes deeper as T increases from 200 nm to 1000 nm. To quantitatively reveal the reshaping of the spectral line, the Ra
in the periodical variation of FOM with the same period of 4000 nm, as plotted in Figure 5d. The FOM obtains two maximum value of 37.69 RIU−1 in a period. According to the F–P physical model, the variation period of the FOM is determined by the resonant wavelength λ0 and refractive index n of the spacer through T0 = λ0/2n, which is coincident with the results in Figure 5d. Therefore, the FOM Sensors can 2016, achieve 16, 899 a maximum value periodically by fabricating a suitable F–P cavity length in 7 ofthe 10 initial design.
Figure 5. 5. (a) sensor; (b) spectra with with Figure (a) Schematic Schematic of of the the reflection-type reflection-type CGDNC CGDNC infrared infrared sensor; (b) The The reflection reflection spectra f = 0.3 eV; (c) The varying spacer thickness T when Λ = 200 nm, H = 100 nm, W = 40 nm, and E varying spacer thickness T when Λ = 200 nm, H = 100 nm, W = 40 nm, and Ef = 0.3 eV; (c) The extracted 0 and fwhm from the reflection spectra with varying spacer thickness; (d) The calculated extracted R R0 and fwhm from the reflection spectra with varying spacer thickness; (d) The calculated FOM with FOM with varying spacer thickness. varying spacer thickness.
To further quantitatively reveal the condition to obtain the maximum FOM, the sensor is Simulation results indicate that the FOM of the sensor can be modulated periodically by tuning modeled as a resonator with a resonant frequency of ω0 and an intrinsic loss rate of γ0, which couples the F–P cavity length (spacer thickness T). The reflection spectra with several sets of spacer thickness with the incident TM wave with a leakage rate of γ1 (Figure 5a). According to the temporal coupled T are presented in Figure 5b. As expected, the notch broadens and becomes deeper as T increases mode equations [15,29], the reflectance of the resonator at ω can be given by from 200 nm to 1000 nm. To quantitatively reveal the reshaping of the spectral line, the Ra and fwhm 2 2 are further extracted from the reflection spectra a wide range of T from 100 nm to 4100 nm and ( in 0 ) ( 0 1 ) R 2 2 plotted in Figure 5c. This suggests that R0 (and fwhm vary periodically with T, and this results (4) in 0 ) ( 0 1 ) the periodical variation of FOM with the same period of 4000 nm, as plotted in Figure 5d. The FOM Thistwo gives us twovalue essential parameters and fwhm) of thetospectral lines. Themodel, resonant obtains maximum of 37.69 RIU´1 in(R a 0period. According the F–P physical the reflectance R0 at of ω =the ω0FOM is represented as by the resonant wavelength λ0 and refractive index n of the variation period is determined spacer through T0 = λ0 /2n, which is coincident with in Figure 5d. Therefore, the FOM can ( the 1results )2 R0 0 a suitable (5) achieve a maximum value periodically by fabricating F–P cavity length in the initial design. 2 ( 0 1 ) To further quantitatively reveal the condition to obtain the maximum FOM, the sensor is modeled as resonator with a resonant anda the corresponding fwhm asfrequency of ω0 and an intrinsic loss rate of γ0 , which couples with the incident TM wave with a leakage rate of γ1 (Figure 5a). According to the temporal coupled mode fwhm 2( 0 1 ) (6) equations [15,29], the reflectance of the resonator at ω can be given by R“
pω ´ ω0 q2 ` pγ0 ´ γ1 q2 pω ´ ω0 q2 ` pγ0 ` γ1 q2
(4)
This gives us two essential parameters (R0 and fwhm) of the spectral lines. The resonant reflectance R0 at ω = ω0 is represented as pγ ´ γ1 q2 R0 “ 0 (5) pγ0 ` γ1 q2
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and the corresponding fwhm as
f whm “ 2pγ ` γ q (6) Equations (5) and (6) manifest that the intrinsic0 loss 1rate γ0 and the leakage rate γ1 are the key physical parameters the the shape of theloss spectral Here, the intrinsic 0 is Equations (5) andthat (6) dominate manifest that intrinsic rate γline. the leakage rate γloss the γkey 0 and 1 arerate the intrinsic property of graphene, which cannot be changed, while the leakage rate γ 1 is physical parameters that dominate the shape of the spectral line. Here, the intrinsic loss rate γ0 is the determined by the thickness Considering these two the equations, can be further intrinsic property of spacer graphene, which T. cannot be changed, while leakage the rate FOM γ1 is determined by written as the spacer thickness T. Considering these two equations, the FOM can be further written as
FOM 2S γ0 γ01 1 3 FOM “ 2S pγ0( `0 γ1q13)
(7) (7)
According to to the the first-order first-order derivative derivative of of Equation Equation (7), (7), there there is is aa solution solution for for obtaining obtaining the the According maximum FOM, i.e., γ 1 = 2γ0 for a fixed γ0. By substituting this solution into Equation (5), we learn maximum FOM, i.e., γ1 = 2γ0 for a fixed γ0 . By substituting this solution into Equation (5), we learn that the the FOM FOMachieves achievesthe themaximum maximumvalue valuewhen whenreflectance reflectanceRR0==1/9, 1/9, which which agrees agrees well well with with the the that 0 simulation results in Figure 5c,d. Hence, a maximum FOM can be achieved by adjusting the F–P simulation results in Figure 5c,d. Hence, a maximum FOM can be achieved by adjusting the F–P cavity cavity to length to the satisfy the condition R0 ≈in11% in the design. initial design. length satisfy condition of R0 «of 11% the initial Finally, itit isis found found that that the the proposed proposed sensor sensor can can work work in in aa wide wide angle angle range range of of incident incident light. light. Finally, The reflectance of the reflection-type sensor as a function of incident angles and wavelength when The reflectance of the reflection-type sensor as a function of incident angles and wavelength when 800 nm nm isis mapped mapped in inFigure Figure6a. 6a. One One noticeable noticeable feature feature is is that that the the narrow narrowbandwidth bandwidth and and large large TT== 800 resonance depth of the reflection spectrum are maintained until the incident angle is larger than resonance depth of the reflection spectrum are maintained until the incident angle is larger than ˝ 60°. This indicates that the proposed sensor possesses excellent angle-insensitive property, which is 60 . This indicates that the proposed sensor possesses excellent angle-insensitive property, which is attributedtotothethe deep sub-wavelength nature of graphene plasmons theof effects of Bragg attributed deep sub-wavelength nature of graphene plasmons and the and effects Bragg scattering scattering at the Brillouin zone center [16]. Such a feature contributes to the superior sensing at the Brillouin zone center [16]. Such a feature contributes to the superior sensing performance of performance of the device in a wide angle range, as plotted in Figure 6b. The FOM is maintained at the device in a wide angle range, as plotted in Figure 6b. The FOM is maintained at a high level −1 1 . Furthermore, a high level and reaches of 37.69 RIU . Furthermore, the FOMsensor of the and reaches a maximum valuea ofmaximum 37.69 RIU´value the FOM of the reflection-type is reflection-type sensor is compared with that of the transmission-type in Figure 6b. As expected, the compared with that of the transmission-type in Figure 6b. As expected, the former one is 2.6 times formerthan one the is 2.6 times larger than the latter one, signifying structure that the reflection-type structure larger latter one, signifying that the reflection-type gains an advantage overgains the an advantage over the transmission-type one from a practical point of view. transmission-type one from a practical point of view.
Figure (a) Reflectance of reflection-type sensor mapping Figure 6.6. (a) mapping with with varying varying incident incident angles angles and and wavelength = =100 nm, WW = 40 nm, and Ef =Ef0.3 eV;eV; (b) (b) TheThe calculated FOM of the wavelengthwhen whenΛ ==400 400nm, nm,HH 100 nm, = 40 nm, and = 0.3 calculated FOM of transmission-type (black(black hollow sphere) and reflection-type (red solid a function the transmission-type hollow sphere) and reflection-type (redsphere) solid sensors sphere) as sensors as a of θ. function of θ.
5. Conclusions 5. Conclusions Asaasummary, summary, a novel CGDCN sensor onis GSP is proposed. It is that observed that the As a novel CGDCN sensor basedbased on GSP proposed. It is observed the redshift of redshift of the resonant wavelength can significantly improve the to a high sensitivity of the resonant wavelength can significantly improve the sensitivity to asensitivity high sensitivity of 4525 nm/RIU 4525 nm/RIU by the structure parameters CGDNC and the Fermi level graphene. A by optimizing theoptimizing structure parameters of CGDNC andofthe Fermi level of graphene. A of reflection-type reflection-type is further proposed to improve FOM the sensor reshaping sensor is furthersensor proposed to improve the FOM of the the sensor by of reshaping theby spectral line. the A spectral line. A maximum FOM of 37.69 RIU−1 can be achieved by adjusting the F–P cavity length, which is 2.6 times larger than that of the transmission-type sensor. Moreover, the proposed sensor can work at a broad range of incident angles. Such a CGDNC sensor provides a green platform for
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maximum FOM of 37.69 RIU´1 can be achieved by adjusting the F–P cavity length, which is 2.6 times larger than that of the transmission-type sensor. Moreover, the proposed sensor can work at a broad range of incident angles. Such a CGDNC sensor provides a green platform for on-chip biochemical fluidic analysis and finds potential applications in fields such as pharmaceuticals, environmental monitoring, and food safety. Acknowledgments: This work is supported by the National High Technology Research and Development Program of China (2015AA034801), the National Natural Science Foundation of China (No. 61405021), the Specialized Research Fund for the Doctoral Program of Higher Education (20120191120021), the Natural Science Foundation of Chongqing, China (cstc2014jcyjA40045), and the Fundamental Research Funds for the Central Universities (CDJZR12120004, 106112013CDJZR120006). Author Contributions: W.W. provided the idea and wrote the paper; J.N. wrote the paper; L.T. built the models; G.Z. performed the computer simulations; J.Y. and W.L. analyzed the data. Conflicts of Interest: The authors declare no conflict of interest.
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