Scientia Iranica F (2017) 24(6), 3531{3535

Sharif University of TechnologyScientia Iranica

Transactions F: Nanotechnologywww.scientiairanica.com

Graphene-based nano bio-sensor: Sensitivityimprovement

M. Majdi and D. Fathi�

School of Electrical and Computer Engineering, Tarbiat Modares University (TMU), Tehran, P.O. Box 14115-194, Iran.

Received 8 August 2016; received in revised form 7 October 2016; accepted 4 March 2017

KEYWORDSBiosensor;Sensitivityenhancement;S-parameter;Surface plasmonresonance;Graphene.

Abstract. In this paper, we attempt to present a multilayer-structure biosensor. Agraphene-based Surface Plasmon Resonance (SPR) biosensor is considered as a structure,which o�ers enhancement of sensitivity in comparison with the conventional biosensors.The sensitivity improvement caused by the presence of graphene is discussed throughmonitoring of the biomolecular interactions and following that the Refractive Index (RI)changes. For this purpose, an RI change, which increases during the course of biomolecularinteraction, is considered from 1.462 to 1.52. Our numerical results show that the proposedSPR biosensor with a graphene layer can provide a better sensitivity due to the �elddistribution at the binding region. This paper investigates the Sensitivity EnhancementFactor (SEF) according to the S-parameters and the e�ects of design parameters such asthicknesses of the gold and graphene layers and the refractive index change during thecourse of DNA hybridization in this biosensor.© 2017 Sharif University of Technology. All rights reserved.

1. Introduction

Surface Plasmon Resonance (SPR) is an opticalmethod based on the excitation of collective free elec-trons oscillations at the metal-dielectric interface [1].The SPR biosensors are supported by the Surface Plas-mon Polaritron (SPP) waves in order to investigate anddetect the biomolecular interactions. In this method,a certain incidence light angle (resonance angle) canbe applied to obtain the required SPR condition [1].Under this condition, momentum matching betweenthe incident photon and the surface plasmon is attainedand the Attenuated Total Re ection (ATR) occurs [1].The resonance angle as a function of the refractiveindex of sensing medium can be measured as the

*. Corresponding author. Tel.: +98 21 82884973;Fax: +98 21 82884325E-mail address: d.fathi@modares.ac.ir (D. Fathi)

doi: 10.24200/sci.2017.4430

biosensor response to the biomolecular interactionssurrounding it. During the sensing operation, theadsorption of biomolecules to the receptor moleculeswill produce a local change in the refractive index atthe metal-dielectric interface and enables us to detectthese biomolecules by measuring the shift of resonanceangle [2].

In this paper, the sensitivity enhancement hasbeen investigated by designing a multilayer structurein which a graphene layer has been applied. Theproposed multilayer biosensor has been modelled andsimulated using the Finite Element Method (FEM)and the Finite Di�erence Frequency Domain (FDFD)method using CST MICROWAVE STUDIO [3]. Theaim of this simulation is the investigation of sensitivityenhancement with the measurement of scattering pa-rameters (S-parameters) with respect to the refractiveindex occurring during the biomolecular interactionsand the thicknesses of gold and graphene layers. Theincorporation of graphene layer in the conventionalSPR biosensor can enhance the sensitivity. The lack

3532 M. Majdi and D. Fathi/Scientia Iranica, Transactions F: Nanotechnology 24 (2017) 3531{3535

of band gap in graphene turns it to a semi-metaldi�erent from other semiconductor materials. Theseunique properties of graphene can be used in futureelectronic and optoelectronic devices [4]. In this paper,di�erent properties of graphene have been used inorder to improve sensitivity of the proposed biosen-sor [4].

One of the disadvantages of conventional SPRbiosensors is the lower limit of detection and their sensi-tivity is faced with small ligands and low-concentrationanalytes [1]. To overcome this limitation, severalapproaches have been proposed. In this paper, in orderto resolve this issue, a graphene-based biosensor hasbeen introduced. The improved sensitivity due to theinterpolation of a graphene layer into the conventionalSPR biosensor comes from the increased adsorption ofbiomolecules [5]. Moreover, applying a graphene layermodi�es the propagation constant of SPP, which willbe followed by changing the sensitivity to the refractiveindex variation [5].

2. Materials and method

The schematic of the proposed SPR biosensor is shownin Figure 1. To excite the surface plasmon, the lightis coupled through the int glass prism with a speci�cincidence angle.

The base of the prism is covered by a thin gold�lm with the thickness of 50 nm and a graphenelayer on top of the gold layer with the thicknessesof 2 nm. Binding analytes (biotin-streptavidin; DNAhybridization reaction) are considered as a layer withan initial refractive index of 1.462 [6] in an aqueousmedium of phosphate bu�er solution, the refractiveindex of which is 1.33 [7].

Figure 1. 3-D model of the proposed graphene basedbiosensor.

In order to �nd out the best coupling and producethe necessary resonance condition, a TM-polarizedplane wave light with the �xed wavelength of 632.8 nmand di�erent incidence angles is coupled into the prism.The optical constants, " = (n; k), of glass prismand gold layer are set to (1.75, 0) and (0.178, 3.07),respectively, at � = 632:8 nm [8].

It has been shown that graphene has a broadand constant absorption range in the visible spectralregion [4]. In this method, a model has been developedfor the in-plane optical conductivity of graphene in thevisible range. In order to calculate the permittivity,the transmittance, and the re ectance of graphenein the visible range, perturbation Hamiltonian isconsidered as [4]:

H 0(t) = ��"(t); "(t) = Re�"xe�i!tx̂

�; (1)

where � is the electric dipole moment.By applying the suitable approximation and the

simpli�cation of equation, conductivity can be obtainedas [4]:

�(!) = � ie2

!A

Xk

�2x

(��� � �cc)Ec;k � E�;k � ~(! + i�)

; (2)

where A is the cross-section area and �x is the velocityoperator along x-direction that can be related to theposition operator x by the equation of motion.

As we know, the �rst Brillouin zone of grapheneis a hexagon with a unit cell of two atoms. Theconduction and valence bands touch each other at thecorners of hexagon, which are called the Dirac points.For an intrinsic or lightly doped graphene, the Fermienergy level is around the Dirac points, where thecharge carriers experience only a linear dispersion [9].This linear dispersion is called the Dirac cone sinceit is described by the relativistic Dirac equation [9].To calculate the optical properties of graphene in thevisible range, one can consider only the Dirac cone ifthe photon frequency is low compared to the resonancefrequency and the Fermi energy is near the Diracpoints [4,9].

The direct result of the linear electronic dispersionof Dirac cone is the e�ective massless fermions, suchthat the related energy dispersion can be writtenas [10]:

E = �~�f j~kj; (3)

where ~ is the reduced Plank's constant, �f is the Fermivelocity in graphene, and ~k is the wave vector. Inorder to obtain an analytical form of conductivity, wecan apply the Dirac cone approximation wherein weassume that conductivity contributes only through thecarriers to the Dirac cone. Thus, permittivity, ", and

M. Majdi and D. Fathi/Scientia Iranica, Transactions F: Nanotechnology 24 (2017) 3531{3535 3533

the optical conductivity of graphene, �0, in the visiblerange are related by [4]:

"(!) = 5:5"0 + i�0

!d; (4)

where "0 is the permittivity of vacuum and d is thethickness of graphene. Therefore, the refractive indexof graphene in the visible range can obtained [4]:

n(�) = 3 + i5:446

3�0; (5)

where �0 is the vacuum wavelength.

3. Results and discussion

Our numerical model is based on the biomolecular in-teraction of DNA (DNA hybridization). As mentionedin the previous section, it is de�ned as a layer withthe refractive index of 1.462. The initial value of1.462 corresponds to an ssDNA layer with a densityof 0.028 g/cm3, obtained from the ellipsometry mea-surements. After the hybridization events, the dsDNAlayer with a density of 0.061 g/cm3 corresponding tothe refractive index of 1.52 will be obtained [11].

The optical characteristics (e.g., S-parameters) ofthe biosensor are a�ected by the biomolecular interac-tions between ssDNA and cDNA. Measuring the shiftof S-parameters is the base of our investigation in thispaper.

For achieving the coupling between the plasmonresonance and incident photons, the following conditionmust be maintained to excite the SPs on the metal-dielectric interface [12]:

Ksp = Kev =!c

r"M"D"M + "D

=!cp"p sin �res; (6)

where Ksp and Kev are the wave vectors of the surfaceplasmon and the evanescent wave, respectively, c is thespeed of light, "M and "D are the dielectric constants ofmetal and dielectric layer, respectively, and �res is theresonance angle [12]. The S-parameters are complex-valued wavelength-dependent matrices expressing thedevice characteristics (e.g., the transmission and re- ection of electromagnetic energy) using the amountof absorption or transmission. For a two-port device,the S-parameters are de�ned as [13]:

S =�S11 S12S21 S22

�; (7)

where the matrix elements S11, S12, S21, and S22are known as the scattering parameters or the S-parameters. In the meantime, S11 and S22 represent re- ection coe�cients, whereas S12 and S21 are de�ned asthe transmission coe�cients. In addition, we have [13]:

S11 =r

Power re ected from 1Power incident on 1

;

S21 =r

Power delivered to 2Power incident on 1

: (8)

The magnitude of S11 (jS11j) gives the normalizedre ectance. The normalized re ectance for thismultilayer SPR is calculated using [1]:

S11 =����M11

M12

����2 exp(i'11); (9)

where '11 contains the phase information of S11.The total M -matrix of the whole structure canbe expressed as the product of interface and layermatrices that describe the e�ects of the individualinterfaces and layers of the entire strati�ed structure,taken in proper order, as:

M =�M11 M12M21 M22

�= I01L1I12L2I23L3I34L4:::Ij�L�;

(10)

with:

Jj� =1tjk

�1 rj�rj� 1

�; rjk =

�Kzj"j � Kzk

"k

�Kzj"j + Kzk

"k

;(11)

where tjk and rjk are the Fresnel complex transmissionand re ection coe�cients, respectively. Also, the layermatrix (phase matrix) describing the propagationthrough layer j is de�ned as:

Lj =�eeidzKzj 00 e�idzKzj

�; (12)

with:

Kzj =r�!

c

�2 �"j � "0 sin2 �

�; (13)

where "j and dj are the dielectric constant and thethickness of the jth layer, respectively.

For the detection of biomolecules, variations ofS-parameters along with their phase characteristics re-sulting from biomolecular interactions with the sensingsurface are studied in this paper. Thus, in order toinvestigate the sensor performance, we have studiedthe change of S-parameters for detection and sensitivityenhancement. In our proposed design, the resonancesbefore and after binding occur at the incidence anglesof 47.052 and 47.506 degrees, respectively. As shownin Figure 2, before the resonance with the angle of45 degrees, the intensity plasmonic wave is re ectedback whereas at the resonance condition with the angleof 47.506 degrees, the oscillation of plasmonic wave ismaximum.

3534 M. Majdi and D. Fathi/Scientia Iranica, Transactions F: Nanotechnology 24 (2017) 3531{3535

Figure 2. Absolute electric �eld: (a) Before and (b) at resonance condition.

Figure 3. The peak values of SPR sensitivity as afunction of the gold thickness changing from 10 to 90 nm.

Figure 4. Vertical �eld along the z axis, Ez, when theSPR structure processes the gold layer with thethicknesses of 45, 60, 75, and 90 nm.

Figure 3 shows the peak values of sensitivity as afunction of gold thickness in the range of 10 to 90 nm.It is clearly observed in this �gure that the maximumsensitivity has been obtained as high as 3.82 at anoptimal thickness of 60 nm. This is because the thickergold layer leads to a resonance excitation of surfaceplasmons in a higher momentum.

The vertical �eld along the z axis (Ez) for thegold layer thicknesses of 45, 60, 75, and 90 nm isshown in Figure 4. According to this �gure, as thegold layer thickness increases from 10 to 90 nm, thesensitivity increases at the initial stage with increasein grating thickness. However, when it exceeds 60 nm,the sensitivity begins to decrease (see [14] for moreinformation).

Figure 5. Changes of di�erent S-parameters versus theincidence angle.

Figure 6. Phase variation of S11 (arg S11) versus theincidence angle before and after the biomolecularinteraction.

Figure 5 shows the changes of S-parameters versusthe incidence angle for the proposed SPR biosensor. Itis outlined that the maximum values of changes in S-parameters, �jS11j, �jS12j, �jS22j, and �jS21j, appearat their resonance angles and the greatest change isrelated to the S11 parameter.

In Figure 6, the phase plot of S11 versus theincidence angle before and after the biomolecular in-teraction is shown. It is observed that there is a rapidtransition in the phase of S11 at the resonance angle of47.052 degrees before binding.

M. Majdi and D. Fathi/Scientia Iranica, Transactions F: Nanotechnology 24 (2017) 3531{3535 3535

Figure 7. Various graphs demonstrating the e�ects dueto the thickness of target biomolecules on the jS11jparameter.

Figure 7 shows the investigation of jS11j param-eter changes versus the incident angle for di�erentthicknesses of graphene layer. As can be observed inthis �gure, with increase in the thickness of graphenelayer, the magnitude of S11 begins to decrease.

4. Conclusions

In this paper, we presented the design and analysis ofa multilayer SPR biosensor using the FDFD method.The ssDNA was used as a receptor molecule, which wasmobilized on the sensor surface to speci�cally adsorbits complementary counterpart (cDNA) immersed ina phosphate bu�er solution. With employing the S-parameters-based detection, it was demonstrated thatthe proposed structure would improve sensitivity andspeed of detection.

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Biographies

Mahdieh Majdi received the MSc degree in Opto-electronics from Tarbiat Modares University (TMU),Tehran, Iran, in 2015. Her research interests includegraphene plasmonics, plasmonic waveguides, plasmonicgates, and switches.

Davood Fathi received the BSc degree in ElectronicEngineering from Amirkabir University of Technology,Tehran, Iran, in 1990, and the MSc degree in Biomed-ical Engineering from Sharif University of Technology,Tehran, Iran, in 1994. After some years of working inindustry, he worked toward the PhD degree between2006-2009 in Nanoelectronics with the NanoelectronicCenter of Excellence, Thin Film and Photonics Re-search Laboratory, School of Electrical and ComputerEngineering, University of Tehran, Tehran, Iran. Dr.Fathi joined the School of Electrical and ComputerEngineering at Tarbiat Modares University (TMU),Tehran, Iran, in 2010, as a faculty member. His currentresearch interests include nanoelectronics, nanopho-tonics and optoelectronics, solar cells, and quantumtransport. He is also author or coauthor of more than50 journal and conference papers in various �elds ofnanoelectronics and nanophotonics.