Enhanced absorption in graphene on periodic patterned SiO2 substrate George Jacob
Gargi Raina
Centre for Nanotechnology Research VIT University Vellore, India
[email protected]
School of Electronics Engineering VIT University Chennai, India
[email protected]
Abstract— The aim of this paper is to study graphene plasmonics for THz applications. The range of absorbance of electromagnetic waves on a graphene monolayer is investigated to understand the plasmonic behaviour of graphene on patterned SiO2 substrate. Simulation results show that absorption range and intensity gets altered according to the graphene doping level, periodicity of grating and dielectric media used on the patterned substrate. These results show the plasmonic effect on graphene has a tuneable behaviour, and it can be utilised for the future plasmonic sensors and optoelectronics devices in the midinfrared region.
(1) If kBTاȝc, the equation is simplified to (2)
Keywords— Graphene; tunable plasmonics; periodic patterned SiO2 substrate; absorption
(3) I. INTRODUCTION Plasmonics is a promising technology for the future electronics and photonics domains [1]. The excellent capability of plasmonic materials to concentrate light into deep-subwavelength volume and guiding through a diffraction limited nanostructure indicate their potential for nanophotonics applications [2]. Graphene, the exciting material, shows better confinement of light compared to other conventional plasmonic materials [3]. The tunable plasmonic behaviour of graphene provides a two-dimensional metamaterial in the THz range optoelectronics applications [4]. In this work, finite element analysis on atomically thin monolayer graphene placed on a SiO2 grating substrate is performed and the change in the absorption of light in midinfrared frequencies range is studied. Calculation of optical dynamic conductivity of graphene allows us to model the material for computation and measure the other optical parameters.
where σintra(ω), σinter(ω) and ‘μc’ are the intra, inter band conductivities and chemical potential for graphene, respectively at room temperature. The relaxation time ‘τ’ of , where μ is carrier electron is given by mobility and vF = 106 m/s is the Fermi velocity [7]. To obtain the plasmon excitation range, the permittivity of graphene ‘εg,eq (ω)’ is calculated as given by equation (4) (4) For the study of optical absorption in graphene, a monolayer graphene (MLG) (thickness ~ 0.4 nm) is placed on a SiO2diffraction grating substrate as shown in the Figure 1.
II. DESIGN AND SIMULATION CONSIDERATIONS The graphene material was defined by numerically calculating the complex conductivity with interband and intraband contributions [5]. For certain thickness ‘¨’ of the graphene sheet, the bulk conductivity can be defined as ıg(Ȧ)/ǻ, where the dynamic conductivity is derived from the Kubo formula (see equation 1) [6].
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Fig.1. Schematic of plasmons excitation on graphene monolayer placed on a SiO2 diffractive grating.
Initially, the effect of doping in graphene material is studied by varying ȝc from 0.2 eV to 1.2 eV in steps of 0.2 eV.
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The grating pattern of SiO2 substrate is defined as having width ‘w’ of 10 nm and height ‘h’ of 10 nm. The periodicity of the grating (p) is varied from 20 nm to 30 nm with a step of 5 nm. Finally, to study the effect of medium in between the substrate and graphene material, the refractive index of the medium (n) is varied from 1 to 2.5, by considering that the refractive medium fills in the gap between the grated patterns. In all cases, the total absorption of the TM-polarized electromagnetic wave in a graphene material is studied using Finite Element Method (FEM) with COMSOL Multiphysics.
generation of surface plasmon of graphene with different chemical potential ȝc and two frequency points which viz. lower and upper bound, which can be determined from this figure. Accordingly, lower crossover frequency (LCF) and higher crossover frequency (HCF) are defined as the lower and higer frequency points where |İg, real| = |İg, img| and zero crossover frequency (ZCF) is defined as the frequency at which the real part of permittivity crosses zero value. Figure 3 depicts the LCF and ZCF points for graphene with ȝc = 0.2 eV at 0.8 THz and 79.6 THz, respectively.
III. RESULTS AND DISCUSSIONS The relative complex permittivity of graphene was calculated and derived from Drude formula using Equation 4 and plotted in figure 2 as a function of input exciting frequency on differently doped graphene. The results show that there is a blue shift in the real part of permittivity according to the increase in chemical potential. This indicates that the plasmon effect on graphene has a tunable behaviour.
Fig. 4. Simulated spectra of absorption in graphene as a function of frequency at different chemical doping.
Fig. 2. Spectra of real and imaginary part of permittivity in 0.4 nm thick graphene.
Fig 5. Absorption of light in a graphene with different grating period.
Fig. 3. Spectra of the modulus of real and imaginary part of the permittivity to calculate the LCF and ZCF at ȝc = 0.2 eV.
The condition for the generation of surface plasmon for a metal dielectric interface is that the effective permittivity should be lesser than zero, and real part of metal permittivity should be greater than its imaginary part for the generation of surface plasmon [8]. Figure 3 shows the range of dominant
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Fig 6. Absorption spectra in graphene with different dielectrics
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The results of absorption of light on a differently doped graphene with the SiO2 diffraction grating is shown in figure 4. There is a shift of absorption peak of graphene towards the high energy side as well as an increase in intensity, with increase of chemical potential; showing that the number of electrons excited increases, by absorbing the energy from incident light. As the grating period of the patterned SiO2 substrate is varied from 20 nm to 30 nm, the simulated normal incident absorption peak shifts from 2.5 THz to 1.9 THz with slight decrease in intensity, as depicted in Figure 5.
grating period and dielectrics confirms this material is suitable to develop nanosensors.
The variation of light absorption in graphene on increasing refractive index media filled in the grating of SiO2 substrate shows a red shift in absorption peak with decrease in absorption intensity as shown in Fig. 6. This shows the sensitivity of graphene plasmonic structure to the refractive index of dielectric. This demonstrates that graphene on patterned SiO2 structure can be used as a tunable plasmonic sensor to detect the different biological materials with high sensitivity.
[4]
REFERENCES [1] [2]
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[5]
[6]
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IV. CONCLUSION The tunable behaviour of graphene plasmonics designates graphene as the best metamaterial for future application. The change in absorption of graphene at different chemical doping,
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