Improved performance of the surface plasmon resonance biosensor based on graphene or MoS2 using silicon

Optics Communications 359 (2016) 426–434

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Improved performance of the surface plasmon resonance biosensor based on graphene or MoS2 using silicon J.B. Maurya a, Y.K. Prajapati a,n, V. Singh b, J.P. Saini c, Rajeev Tripathi a a

Department of Electronics and Communication Engineering, Motilal Nehru National Institute of Technology, Allahabad 211004, Uttar Pradesh, India Department of Physics, B.H.U., Varanasi 221005, Uttar Pradesh, India c Department of Electronics and Communication Engineering, Bundelkhand Institute of Engineering and Technology, Jhansi 284128, Uttar Pradesh, India b

art ic l e i nf o

a b s t r a c t

Article history: Received 6 July 2015 Received in revised form 17 August 2015 Accepted 2 October 2015

In this paper a biosensor based on surface plasmon resonance is presented. This sensor is based on Kretschmann configuration. First of all, the thickness of gold and silicon layers is optimized under the consideration of sensitivity, full width at half maximum, and minimum reflectance. After that, at the optimized thicknesses of gold and silicon layers, the performance of the sensor in terms of sensitivity, detection accuracy and quality factor is analyzed. The effect of increasing the number of layers of the graphene and MoS2 on the performance is also analyzed. It is observed that all the performance parameters are enhanced if a silicon layer is deposited between the gold and graphene layer. It is also observed that if graphene is replaced with MoS2, the detection accuracy and the quality factor improve with great extent while maintaining the sensitivity. & 2015 Elsevier B.V. All rights reserved.

Keywords: Surface plasmon resonance Graphene MoS2 Sensitivity Detection accuracy Quality factor

1. Introduction A number of optical methods have been used for the purpose of chemical and biomolecule sensing since last four decades e.g. ellipsometry [1], spectroscopy [2], interferometry [3], spectroscopy of guided modes in optical waveguide structures [4], and surface plasmon resonance (SPR) [5]. With the help of these sensors, a desired quantity is determined by measuring the change in refractive index, absorbance and fluorescence properties of analyte molecules [6,7]. The strong capability of SPR to characterize the thin films attracts the researchers to opt SPR based sensor as the best optical method for sensing biomolecules and chemicals in eighties. In 1982, the application of SPR was done for the first time to detect the gas and biomolecules by Nylander and Liedberg [8]. Since then a large number of research on the basis of SPR have continued, as the new thin materials are discovered. In order to excite the surface plasmon, the wave vector of the incident light and surface plasmon must be matched [5]. Initially for the excitation of surface plasmon, SPR based on Otto's configuration [9] was applied in 1968, but this suffers from the problem of maintaining a very thin air gap between prism and metal. To overcome n

Corresponding author. E-mail addresses: [email protected] (J.B. Maurya), [email protected] (Y.K. Prajapati), [email protected] (V. Singh), [email protected] (J.P. Saini), [email protected] (R. Tripathi). http://dx.doi.org/10.1016/j.optcom.2015.10.010 0030-4018/& 2015 Elsevier B.V. All rights reserved.

the problem of Otto's configuration, SPR based on Kretschmann's configuration [10] was applied. The conventional SPR based on Kretschmann's configuration was limited to the laboratory because of the bulky prism which was required to excite surface plasmon polariton (SPP). Hence the scaled-down structure, suited for the realization of integrated photonics, was proposed with the help of resonant coupling between surface plasmon polariton (SPP) and the evanescent mode of the optical waveguide [11]. SPP is an electromagnetic wave which is continued to propagate along the interfacing boundary of metal–dielectric and decreases exponentially into both media [5]. In the conventional SPR based sensors, gold is chosen as the SPR active metal (others are silver, copper, aluminium, sodium, and indium) because of its most practical nature, stable and superior performance, and good resistance to oxidation and corrosion [12]. High intensity of surface plasmon wave (SPW), concentrated in the sensing layer (dielectric), signifies that the nature of the propagation constant of the SPW is very sensitive for any change in the refractive index of the sensing layer. Hence a biomolecular recognition element (BRE) is added, on the surface of the metal, which absorbs the analyte (biomolecules) present in the liquid sensing layer e.g. water, and this is the basic principle behind the affinity SPR biosensor [5]. Boundless research has been going on in the field of two-dimensional (2D) materials by the nanotechnology research group throughout the world, out of which graphene has attracted the most since it is discovered by Novoselov et al. in 2004 [13].

J.B. Maurya et al. / Optics Communications 359 (2016) 426–434

Graphene includes a plenty of properties out of which some needful for our sensor are mentioned here e.g. thinnest – which miniaturize the sensor, large surface to volume ratio – for better contact with the analyte, able to selectively detect the aromatic compound through π-stacking bonds, highly absorptive, strongest with high breaking strength for the easy deposition [14]. When graphene layer is deposited on the metallic thin film, strong coupling is induced at the metal–graphene interface because of the effective charge transfer due to high charge carrier mobility of graphene [15]. Hence many researchers throughout the world has chosen graphene as an enhanced SPR substrate for biosensing application [14,16–18]. Molybdenum disulphide (MoS2), also known as ‘beyond graphene’ nano crystal, belongs to transition-metal dichalcogenide (TMDC) semiconductor group, is discovered most recently in the vast field of 2D nano-materials [19–21]. Single layer of MoS2 is an ultra-thin 2D crystal layer composed of two layers stacked in the vertical direction via van der Walls force, hence they are widely used as solid lubricants. Bulk MoS2 has an indirect bandgap of 1.2 eV, whereas the single layer MoS2 has a direct bandgap of 1.8 eV due to quantum confinement effect [19]. Such a change in the electronic and optical property of single layer MoS2 attracts it to use similar to graphene. Monolayer MoS2 possesses a high optical absorption efficiency which can be utilized in the fabrication of ultrasensitive photodetectors having a higher responsivity [22] and can replace the graphene in the optical sensor also. The field intensity of the excited light at the dielectric–analyte interface can be enhanced by depositing a dielectric layer having high refractive index e.g. silicon over SPR active metal e.g Gold [23]. This concept to increase the sensitivity is used by Bhatia et al. [24] and Verma et al. [17]. Verma et al. have used gold–silicon– graphene structure and showed the variation of performance parameters namely reflectivity and change in resonance angle, with respect to the number of layers of graphene for different thicknesses of gold and silicon at three different wavelengths 600 nm, 633 nm, and 660 nm. Here in the present work, we have taken gold–silicon–MoS2 structure for sensing the ssDNA biomolecule as an analyte. The thickness of the gold and silicon layer is optimized first with respect to sensitivity, full width at half maximum (FWHM), and minimum reflectance at 633 nm wavelength. Thereafter the variation of performance parameters namely sensitivity, detection accuracy, quality factor, and minimum reflectance are shown with respect to the number of MoS2 layers as well as the regular change in the refractive index of the sensing layer is done. On comparing the proposed structure with simple gold–graphene structure and gold–silicon–graphene structure, it is

427

observed that the detection accuracy and quality factor of the proposed structure is far higher for the first three layers of the MoS2 with a very low penalty of decreasing the sensitivity. The sensitivity of the proposed structure is still far higher than the gold–graphene structure. The paper is organized as follows: an introduction to the SPR based sensor and its constituent materials are given in Section 1. Theoretical modelling with mathematical expression is presented in Section 2. Section 3 is composed of result and discussion. In the last of this paper the conclusion and necessary references are given.

2. Theoretical model and design consideration In this paper three structures for SPR biosensor are considered: (I) only graphene, (II) silicon/graphene, and (III) silicon/MoS2 (proposed structure). These three structures are combinedly given in Fig. 1. These SPR biosensors are based on Kretschmann's configuration in which a thin gold layer is deposited on the base of the SF10 prism. In the first structure, the graphene is directly deposited on the gold layer. In the second structure, a silicon layer is deposited on the gold layer and then graphene is deposited on the silicon layer. In the third structure, MoS2 is deposited instead of graphene in the second structure. In all of the three above-defined structures, an affinity layer is deposited above nanomaterial layer (graphene or MoS2). And then liquid sensing layer containing biomolecule as analyte make in contact with the affinity layer. These SPR biosensors are excited with a p-polarized (TM-polarized) light, having a wavelength of 633 nm, from one lateral face of the prism. The incident light is reached to the base of the prism and totally reflected out from the opposite lateral face. The reflected light is collected by lens and analyzed by photodetector with the help of other digital means. 2.1. Refractive index and thickness of various layers In all of the defined structures, the first layer is SF10 prism. The refractive index (n1) of prism is calculated from the following dispersion relation [25]:

⎛ 1.62153902 λ2 0.256287842 λ2 + 2 n1 = ⎜ 1 + 2 ⎝ λ − 0.0122241457 λ − 0.0595736775 1/2 1.64447552 λ2 ⎞ + 2 ⎟ λ − 147.468793 ⎠

Fig. 1. Schematic diagram of three structures of SPR biosensor combinedly: (I) only graphene, (II) silicon/graphene, and (III) silicon/MoS2.

(1)

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where λ is the wavelength of incident light in μm. Eq. (1) is valid for the 0.38–2.50 μm range of wavelength. Second layer of all defined structures is gold. The complex refractive index (n2) of gold at 633 nm is calculated from the data given by Palik [26]. The optimization of gold layer thickness is done later in this paper. The refractive index of gold layer for the optimized thickness of 50 nm is 0.1726þ i3.4218. Third layer of II and III structures is silicon layer. The refractive index (n1) of silicon is calculated from the following dispersion relation [17]:

n3 = A + A1e−λ / t1 + A2 e−λ / t 2

(2)

where A¼ 3.44904, A1 = 2271.88813, A2 = 3.39538, t1 = 0.058304 , and t2 = 0.30384 ; λ is the wavelength in μm. The optimization of silicon layer is also performed, as like the gold layer and discussed later in the paper. The optimized thickness of silicon layer is 50 nm. Fourth layer of II structure is monolayer graphene. The complex refractive index (n4) of graphene in the visible spectrum is given by Baruna and Borini [27]:

n4 = 3.0 + i

c1 λ 3

(3)

where the constant c1 ≈ 5.446 and λ is the wavelength of incident light beam in μm. The thickness of graphene is L  0.34 nm, where L is the number of graphene layers. In III structure the fourth layer is monolayer MoS2. The complex refractive index (n4) of MoS2 is 6.1 − 2.8i [21]. The thickness of MoS2 is M  0.67 nm, where M is the number of MoS2 layers. The fourth layer of structure I and the fifth layer of both the structures II and III are the affinity layer of ssDNA. The refractive index and thickness of affinity layer is 1.462 and 100 nm respectively [28]. The fifth layer of structure I and the sixth layer of both the structures II and III are the sensing layer. The sensing layer is liquid. In this paper the water is taken as the sensing layer, whose refractive index is 1.33.

μm−1

2.2. Mathematical modelling of reflectivity For better understanding of the change in the reflectivity of SPR sensors defined by structures I, II and III, the transfer matrix method (TMM) is employed [29]. The TMM is based on N-layer model which deduces the expression relating the tangential components of the electric and magnetic fields at first layer to the last layer. These N-layers are parallelly stacked. The z-axis considered here is perpendicular to the thickness (dk) of these layers. The dielectric constant of each layer is defined as square of corresponding refractive index (ϵk = nk2). It is considered that all layers are optically isotropic and non-magnetic. The boundary condition for the tangential components of electric and magnetic fields at the first boundary that is the interfacing plane of the first and the second layer can be expressed as Z = Z1 = 0. Now the tangential components of the fields at the first layer in terms of the tangential fields at the last layer can be given as [29]

⎡ U1 ⎤ ⎡ UN − 1 ⎤ ⎢ ⎥=P⎢ ⎥ ⎣ V1 ⎦ ⎣ VN − 1 ⎦

(4)

where U1and V1 are the tangential component at the first layer respectively for electric and magnetic field, and those at the last layer are UN − 1 and VN − 1. The reflection coefficient is dependent on the elements of this matrix (P). The matrix P can be obtained for p-polarized light beam as follows:

N−1

P=

∏ k=2

⎡ P11 P12 ⎤ Pk = ⎢ ⎥ ⎣ P21 P22 ⎦

(5)

where

⎡ cos β k Pk = ⎢ ⎢⎣ − i qk sin βk

(

− i sin βk )/qk ⎤ ⎥ ⎥⎦ cos βk

(6)

with

(

ϵk − n12 sin2 βk ⎛ μ ⎞1/2 qk = ⎜ k ⎟ cos θ k = ⎝ ϵk ⎠ ϵk

)1/2 (7)

and

βk =

2π 2π dk nk cos θ k (Zk − zk − 1) = (ϵk − n12 sin2 θ1)1/2 λ λ

(8)

in which, θ1 and λ are respectively the incident angle and the wavelength of the incident light beam. The total reflection coefficient (rp) for the p-polarized light can be obtained as

rp =

(M11 + M12 qN ) q1 − (M21 + M22 qN ) (M11 + M12 qN ) q1 + (M21 + M22 qN )

(9)

And finally the reflectivity (Rp) can be given as

Rp = rp

2

(10)

2.3. The attachment phenomena of ssDNA on the MoS2 Stacking a molybdenum plane (positively charged) between two sulfur planes (negatively charged), a single layer MoS2 can be consider of S–Mo–S sandwich structure. Each Mo atom is arranged in a trigonal prismatic geometry to six sulfur atoms. As the theoretical and experimental studies of physical adsorption of aromatic and conjugated compounds on the basal plane of MoS2 have been reported, and moreover most transition-metal ions possess intrinsic fluorescence quenching properties, one can expect that MoS2 could adsorb dye-labeled ssDNA probe via the van der Waals force between nucleobases and the basal plane of MoS2 and then quench the fluorescence of the dye. On the basis of microscopic and genetic studies, biofilm formation can be divided into four stages: attachment, aggregation, maturation, and dispersal. The attachment of bacteria surfaces can be divided into two stages: first stage is a fast initial adsorption phase, governed by physical forces such as electrostatic charges, Brownian motion, and van der Waals forces. It is likely that bacterial swimming, which requires flagella, is required for initial attachment to allow the bacteria to overcome these physical forces and come into close proximity to the surface. In the second stage the attachment is a slower cellular phase whereby bacteria tightly adhere to the surface via pili, proteins, polysaccharides, and fimbriae. For more detail one can follow the paper presented by Jenkins et al. [30]. 2.4. Performance parameters The performance of the SPR based sensors can be decided on the basis of three basic parameters: sensitivity, detection accuracy, and quality factor. These parameters are calculated with the help of reflectance curve; the curve of incident angle versus reflectivity. The incident angle corresponding to the minimum reflectivity is known as the resonance angle (θres). The sensitivity is defined as the ability of sensing the change in the refractive index of the sensing medium due to the absorption of the biomolecule. Mathematically, sensitivity (S) is defined as the ratio of the change

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in the resonance angle (∇θres ) to the change in refractive index (∇n ) i.e.

S = ∇θres/∇n

(11)

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known that for the generation of SPW the light must be absorbed into the gold layer. And as the thickness of gold layer is increased from some lower value (24 nm) to some higher value (48 nm) the absorption of incident light increases. But after some particular

Resolution, the minimum change in measured parameter that can be resolved, is one of the parameters that determines the performance of the sensor, depends upon the degree of accuracy of determination of resonance feature, and is limited by the system noise. To enhance the resolution of SPR sensor, it is necessary to decrease the FWHM [5]. The detection accuracy is defined as the ability of sensing the minimum change in the refractive index of the sensing medium. It depends on FWHM which is defined as the width of the reflectance curve at half of the maximum reflectivity. Mathematically, detection accuracy (D.A.) is defined as the ratio of the change in the resonance angle ( ∇θres ) to the FWHM

D. A. = ∇θres/FWHM

(12)

As the reflectance curve becomes sharper the FWHM will be small and because of which detection accuracy will increase i.e. a slight change in the refractive index can be detected by the sensor. The quality of the sensor can be judged with help of quality factor. Mathematically, the quality factor (Q.F.) of the sensor is defined as the ratio of the sensitivity (S) to the FWHM

Q . F . = S/FWHM

(13)

For a good SPR based biosensor all of the three above-defined performance parameters should be as high as possible. But this is very typical to have all the parameters high. Hence we have to optimize these parameters with respect to each other.

3. Result discussion and analysis Optimization of the thickness of constituting layers is the crucial point in deciding the performance of the SPR based sensor after defining the refractive index. In this paper the optimization of the thicknesses is done in two step. First, the thickness of gold layer and silicon layer is optimized for single layer of graphene and MoS2. Thereafter the number of layers of graphene (L) and MoS2 (M) are optimized for the optimized value of the gold and silicon layer. After optimizing the thicknesses of all layers, the shift in the resonance angle is observed from the reflectance curve, for sensing layer refractive index change of 0.07, for all the three structures. Thereafter the variation of the sensitivity, FWHM and minimum reflectance (Rmin) are analyzed with respect to the change in sensing layer refractive index. Finally, the behavior of transverse magnetic (TM) field intensity with respect to distance normal to the layer interface is done for structures II and III. 3.1. The optimization of the thicknesses of different layers Thickness of gold and silicon layers are optimized with respect to the sensitivity, FWHM and Rmin. For the optimization of gold layer thickness, the thickness of silicon layer is considered to be 50 nm, and as mentioned earlier the single layer of graphene and MoS2 is considered. It can be easily visualize from Fig. 2(a), the sensitivity curve is plotted for gold layer thickness (black, bottom x-axis, left y-axis) and for silicon layer thickness (blue, top x-axis, right y-axis). The sensitivity is represented by circle ( ○), square (□), and asterisk (n) respectively for the structure I (only graphene), structure II (Si/graphene), and structure III (Si/MoS2). It can be easily observed that the sensitivity for all the three structures increases for the thickness range of 24–48 nm, and then become constant for the thickness greater than 48 nm. Because, it is well

Fig. 2. Variation of (a) sensitivity, (b) FWHM, and (c) minimum reflectance with respect to gold layer thickness (black) with sensor structure having only graphene {circle (○)}, Si/graphene {square (□)}, Si/MoS2 {asterisk (n)}, and with respect to silicon layer thickness (blue) with sensor structure having Si/graphene {triangle (Δ)}, Si/MoS2 {plus ( þ)}. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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high thickness of gold layer (above 48 nm) the absorption of light becomes saturate. Hence as the absorption of light increases with the thickness from 24 nm to 48 nm, the generation of surface plasmons increases as a result of which the sensitivity increases, and when the absorption of light becomes saturate above 48 nm the generation of surface plasmons becomes constant and due to which the sensitivity also becomes constant. The similar effect is shown by Skivesen et al. [31] in 2005, Pechprasarn and Somekh [32] in 2012. Hence it can be said that the sensitivity is highest simultaneously for all the three structures for the thickness range of 48–100 nm of gold. For the optimization of silicon layer thickness, the gold layer thickness is assumed to be 50 nm. From Fig. 2 (a) it can also be observed that the sensitivity is highest for 50 nm silicon layer for both, structures II and III. In Fig. 2(b) the FWHM, at 1.33 sensing layer refractive index, is plotted with respect to the thickness of gold and silicon layer. Here, the FWHM having value less than 1 is considered. The FWHM having non-zero and less than 0.2 are considered to be good FWHM, as it is always required that the FWHM should be as low as possible. By keeping the sensitivity in mind, at the 50 nm gold layer, the FWHM values are 6.62 (not shown in figure), 0.2446, and 0.0006 respectively for the structures I, II, and III. Hence for the 50 nm gold thickness, the FWHM for the proposed sensor is very low, and due to which its detection accuracy and quality factor should be very high while maintaining the sensitivity approximately equal to the structure II and far greater than structure I, which will be discussed later in this paper. Similarly, for 50 nm silicon thickness, the FWHM values are 0.2446 and 0.0005 respectively for the structures II and III. Hence, again for 50 nm silicon thickness, the FWHM for the proposed sensor is very low while maintaining the sensitivity. In Fig. 2(c) the minimum reflectance (Rmin) is plotted with respect to gold and silicon layer thickness. It can be clearly observed that the minimum value of Rmin is found at 50 nm of gold as well as silicon layer thickness for all the structures. For 50 nm gold layer, the minimum reflectance values are 0.026, 0.006, and 0.016 respectively for structures I, II, and III. And for 50 nm silicon layer, the minimum reflectance values are 0.006 and 0.016 respectively for structures II and III. Low value of minimum reflectance signifies that the reflected light at the opposite plane of incidence of prism is very low. This low intensity reception signifies that the maximum light intensity is used in the excitation of the surface plasmons and because of which other performance parameters are improved. Hence on observing Fig. 2(a)–(c) combinedly, all the performance parameters are improved for the proposed biosensor at 50 nm thickness of gold as well as silicon. After optimizing the thickness of gold and silicon layer, now the variation of sensitivity, detection accuracy, quality factor, and minimum reflectance are done with respect to number of nanolayers (graphene and MoS2) for structures II and III, which are shown in Fig. 3(a)–(d). Plots in these figures are plotted for 1–10 number of nano-layers. Since the thickness of the MoS2 (0.67 nm) is approximately double of the graphene (0.34 nm), hence according to Eqs. (4) and (6) of the research paper presented by Pockarand [33], the damping of surface plasmons in the case of MoS2 (structure III) is more than that of the graphene (structure II). And it is well known from the peer reviewed research papers [34– 36] that the sensitivity decreases as the number of nano-layers increases because the nonzero imaginary dielectric constant of graphene and MoS2 induces the damping of plasmons. Hence the sensitivity in the case of graphene is greater than that of the MoS2, this can be clearly observed from Fig. 3(a) and Table 2. Moreover, it can also be observed from this figure and table that the sensitivity decreases with the number of nano-layers either in the case of graphene or MoS2 because the damping increases as the number of nano-layers increases. The gap of amount of damping between the

Fig. 3. Variation of (a) sensitivity, (b) detection accuracy, (c) quality factor, and (d) minimum reflectance with respect to the number of nano-layers (grpahene and MoS2).

case of graphene and MoS2 increases as the number of nano-layers increases because the gap of thickness increases with the number of nano-layers. Hence, it can easily be observed from Fig. 3(a) that at monolayer of graphene and MoS2, the difference of sensitivity is minimum whereas it is maximum at 10 layers of graphene and

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Table 1 Arrangement of values of minimum reflectance (Rmin) and FWHM at 1.33 refractive index (RI), and change in resonance angle (∇θres) corresponding to 0.07 change in RI, for number of graphene or MoS2 layers changing from 1 to 10.

1 2 3 4 5 6 7 8 9 10

Rmin at 1.33 RI

Extent values of θ at half reflectance at 1.33 RI

FWHM at 1.33

∇θres at 0.07 RI change

Graphene

Graphene

Graphene

MoS2

Graphene

MoS2

0.24 0.26 0.28 0.29 0.30 0.32 0.33 0.35 0.37 0.38

0.20 0.17 0.12 – – – – – – –

3.49 3.47 3.44 3.42 3.39 3.37 3.35 3.32 3.29 3.27

3.45 3.39 3.32 3.17 3.00 2.82 3.02 2.97 2.92 2.87

0.006 0.012 0.019 0.028 0.037 0.047 0.057 0.067 0.077 0.087

MoS2

0.016 0.109 0.310 0.539 0.662 0.715 0.742 0.757 0.767 0.775

MoS2

θhigh

θlow

θhigh

θlow

51.00 51.04 51.07 51.10 51.13 51.17 51.20 51.24 51.28 51.31

50.76 50.78 50.79 50.81 50.83 50.85 50.87 50.89 50.91 50.93

51.02 51.07 51.12 – – – – – – –

50.82 50.90 51.00 – – – – – – –

MoS2. Now, in the context of Fig. 3(b), since the imaginary part of the refractive index of graphene is positive whereas that of the MoS2 is negative, hence according to Eqs. (4) and (6) of the research paper presented by Pockrand [33], the damping of surface plasmons in the case of graphene (structure II) is more than that of the MoS2 (structure III). Also, the full width at half maxima (FWHM) is directly proportional to the damping [33]. Hence, the FWHM in the case of MoS2 is less than that of the graphene. But at the same time on increasing the number of nano-layers the shift in resonance angle increases for the graphene whereas it decreases for the MoS2, as discussed earlier. The FWHM and the shift in resonance angle are arranged in Table 1 for varying number of nano-layers. Now, on the basis of Eq. (12), the detection accuracy is directly proportional to the shift in resonance angle and inversely proportional to the FWHM. The detection accuracy, the ratio of the shift in resonance angle to the FWHM, is calculated for varying number of nano-layers and arranged in Table 2. From Fig. 3(a) and Table 2, it is observed that the detection accuracy decreases as the number of graphene layers increases in the structure II, whereas it increases as the number of MoS2 layers increases in the structure III. But this increment is very fast, so beyond three layers of MoS2 the detection accuracy is absent. The FWHM for the structure having more than three MoS2 layers is not considered because minimum reflectance is greater than 0.5 as shown in Fig. 3 (d) which is very high, hence according to Eq. (12) the detection accuracy is not considered. Behavior similar to detection accuracy can be observed in the case of quality factor which is shown in Fig. 3(c) and can be justified with the help of Fig. 3(d) and Eq. (13). Table 2 Arrangement of values of sensitivity, detection accuracy (D. A.) and quality factor (Q. F.), for number of graphene or MoS2 layers changing from 1 to 10. Number of graphene or MoS2 layers

From Fig. 3(d) it can be observed that the minimum reflectance increases as the number of nano-layers increases. This behavior for graphene is also shown by Verma et al. [16] and Wu et al. [37]. The broader and shallower reflectance curves due to dramatic variation of surface plasmons result in higher value of minimum reflectance and which are unavoidable. The inner damping is caused by energy absorption due to nonvanishing imaginary part of the dielectric functions of the layer system [33]. The thin film, MoS2 and graphene, is an absorbing material i.e. it has complex dielectric constant, hence Eq. (4) of the research paper presented by Pockrand [33] becomes a complex quantity, which indicates the rapid increase of the surface plasmon oscillation (SPO) damping with increasing the number of nano-layers due to absorption in the nano-layers. As a consequence, the inner damping increases more rapidly than the radiation damping, at this instant the ratio of the two damping processes and therefore the excitation strength of SPO change with the number of nano-layers leading to a strong dependence of the minimum reflectance on the number of nano-layers. And according to Figs. 2(c) and 6(c) of the same

1 0.9 0.8

Reflectance

Number of graphene or MoS2 layers

0.7 0.2

0.4

0.1

0.2

0.6 0.5 0.4

0.2

Sensitivity

D.A.

Q.F.

Graphene MoS2

Graphene MoS2 Graphene MoS2

49.86 49.57 49.14 48.86 48.43 48.14 47.86 47.43 47.00 46.71

14.54 13.35 12.29 11.79 11.30 10.53 10.15 9.49 8.89 8.61

0.1 49.29 48.43 47.43 45.29 42.86 40.29 43.14 42.43 41.71 41.00

17.25 19.94 27.67 – – – – – – –

207.75 190.65 175.5 168.48 161.43 150.44 145.03 135.51 127.03 122.92

246.45 284.88 395.25 – – – – – – –

51 54.3 54.35 54.4

50.9

Only Graphene at 1.33 Only Graphene at 1.40 Si/Graphene at 1.33 Si/Graphene at 1.40 Si/MoS2 at 1.33

0.3

0 1 2 3 4 5 6 7 8 9 10

0 50.8

Si/MoS2 at 1.40 0

10

20

50 30 40 Incidence angle

60

70

80

Fig. 4. Variation of reflectance with respect to the angle of incidence for sensing layer refractive index 1.33 and 1.40. The sensor structure having only graphene is plotted as black solid lines with black hollow circle (○) for 1.33 and black solid circle (●) for 1.40. The sensor structure having Si/graphene is plotted as red solid line for 1.33 and red dashed line for 1.40. The sensor structure having Si/MoS2 is plotted as blue dashdotted line for 1.33 and blue dotted line for 1.40. (For interpretation of the reference to color in this figure legend, the reader is referred to the web version of this article.)

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research paper, the minimum reflectance increases on increasing the number of nano-layers. This concept of increasing the minimum reflectance also correlates with the sensitivity which degrades on increasing the number of nano-layers as discussed earlier. But this increment for graphene is regular and less than the MoS2 while that is for MoS2 it increases at very fast rate up to five layers and then becomes consistent as it is cleared also from Table 1. The numerical value of minimum reflectance, FWHM and change in resonance angle is given in Table 1 and corresponding to these values the sensitivity, detection accuracy, and quality factor are calculated (as shown in Table 2) using Eqs. (11)–(13) respectively, for the number of graphene layers in structure II or the number of MoS2 layers in structure III increasing from 1 to 10. 3.2. Shift in resonance angle In Fig. 4 the variation of reflectance with respect to incidence angle is plotted. This figure depicts the shift in the resonance angle and change in minimum reflectance corresponding to the change of sensing layer refractive index from 1.33 to 1.40 ( ∇n = 0.07) for predefined structures I, II, and III. Here the black, red and blue curves represent the reflectance of the structures I, II, and III respectively. Along with these colors, the solid and dashed lines represent the reflectance at sensing layer refractive index 1.33 and 1.40 respectively. It can be observed from Fig. 4 that the reflectance curves for structure II and structure III are approximately the same, with slight difference in resonance angle and minimum reflectance, at 1.33 as well as 1.40 sensing layer refractive index. The shift in the resonance angle for structure II is slight greater than the structure III. The resonance angle for the structure I is at higher angle but it does not matter that the resonance angle is at higher value or at lower value, instead of this the shift in resonance angle matters. The change in resonance angle for structure I is less than both the structures II and III which can be clearly observed from the concerning figure. The resonance angle values for structures I, II, and III at 1.33 are 66.04, 50.85, and 50.89 and those at 1.40 are 67.95, 54.34, and 54.34. Hence the shift in resonance angle (∇θres ) values are 1.91, 3.49, and 3.45 respectively for structures I, II, and III. The minimum reflectance values for structures I, II, and III at 1.33 are 0.026, 0.006, and 0.016 and those at 1.40 are 0.031, 0.220, and 0.075. For structures I, II, and III respectively the sensitivities are 27.29, 49.86, and 49.29, the detection accuracies are 4.16, 14.54, and 17.25, and quality factors are 4.12, 207.75, and 246.45. Hence it can be said on the basis of above data that the proposed sensor has very high detection accuracy and quality factor while maintaining the sensitivity approximately equal to the structure II.

Fig. 5. Variation of (a) sensitivity, (b) FWHM, and (c) minimum reflectance with respect to sensing layer refractive index ranging from 1.33 to 1.40.

3.3. Sensing layer refractive index vs. performance parameters In Fig. 5(a)–(c) the sensitivity, FWHM, and minimum reflectance are plotted with respect to the variation of sensing layer refractive index. From Fig. 5(a), it can be observed that the sensitivity for all structures I, II, and III increases with increasing the sensing layer refractive index. It can also be observed that the sensitivity for structure II is higher than the structure III, which is much higher than the structure I. From Fig. 5(b), it can be observed that FWHM has not any particular pattern of increasing or decreasing instead the FWHM varied randomly at different refractive indexes of sensing medium. But it is worth noting that the FWHM is less than 0.25 for all the structures defined in this paper. From Fig. 5(c) it can be observed that the minimum reflectance for structure II is less than structure III, which is less than the structure I. This order is followed by all structures up to 1.39 sensing medium refractive index but beyond this the order is disturbed

and the value of minimum reflectance increases randomly because if the refractive index of sensing medium increases beyond a certain limit, i.e. the presence biomolecule is very high, then the sensing layer will behave like a separate layer of particular finite thickness and which will change the reflectance property of the sensor. 3.4. Transverse magnetic (TM) field intensity Fig. 6(a) and (b) depicts the behavior of transverse magnetic (TM) field intensity respectively for the structures II and III. It is well known from the literature that as the reflectivity approaches to the minimum value, the intensity of magnetic field approaches to its maximum value. At the instant of strongest intensity of the field, the maximum excitation of surface plasmon takes place and due to which the intensity of reflected light is minimum. It can be

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et al. [17] but the detection accuracy and the quality factor are far higher. Hence it is believed that it could reveal a new another possibility to detect the presence of ssDNA with very high detection accuracy and quality.

Acknowledgment The present work is partially supported by the Department of Science and Technology (DST), New Delhi, India, under the Fast Track Young Scientist Scheme no. SB/FTP/ETA-0478/2012.

References

Fig. 6. Transverse magnetic (TM) field intensity as a function of distance normal to the interface for silicon (a) Si/Graphene and (b) Si/MoS2 structures.

easily seen from Fig. 6(a) and (b) that the gold layer increases the field and shows a peak at the gold–silicon interface which represents the excitation of SPs at this interface. But the silicon layer increases the field intensity which is again enhanced by graphene layer of structure II (see Fig. 6(a)) and MoS2 layer of structure III (see Fig. 6(b)). This represents the enhancement of the excitation of SPs. The enhanced intensity of field by nano-layers again increases in the affinity layer. The field intensity falls suddenly at the affinity-sensing layer interface and continued to flow at approximately constant rate and deeper in the sensing medium.

4. Conclusion The sensitivity, detection accuracy, quality factor, and minimum reflectance are analyzed with respect to the number of graphene and MoS2 layers, and also with respect to the refractive index of sensing layer after the optimization of gold and silicon layer thickness. It is observed that the sensitivity of the proposed structure is approximately equal to the structure given by Verma

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