Design of Novel Sensitive Terahertz Biosensors Based on Graphene-Plasmonic Nanostructures

In this paper, four different configurations of sensitive biosensors based on graphene-plasmonic combinations are designed and proposed. The nanostructures are made of graphene, SiO 2 , aluminum and gold layers on a silicon substrate. Graphene-ring shaped structures with diagonal strips in vertical and horizontal directions are considered in the structures which greatly affect the absorption characteristics (absorption peak value and wavelength). Aluminum layer is used in the structure to prevent the transmission of light throughout some layers and improving the absorption factor. To promote the functionality of the structures, effects of the structural parameters ( R 1 and R 2 ) and chemical potentials ( E f1 , E f2, E f3 and E f4 ) on the absorption peak-wavelength and its value, are also studied. The four individual configurations with different layers and strip directions demonstrate distinct and different wavelength ranges; structure-1: 45-60 µm, structure-2: 50-70 µm, structure-3: 70-85 µm, and structure-4: 80-100 µm . Thus, they can be utilized for wide categories of applications.


Introduction
In recent decade, photonic biosensors have achieved specific and popular attentions by researchers.Different optical methods are proposed for bio-sensing structures, in which surface plasmon resonance (SPR) is supposed to be the preferable one due to its efficient functionalities, flexible designing, compact size, remote sensing and other important characteristics [1].Indeed, SPR-refractive index (SPR-RI) biosensors have attracted extreme attentions [2].Biosensors can be utilized as diagnosis instruments, clinical and lab detection devices [3,4], and also for sensing various bio-molecules such as proteins [5], DNA [6] and other vital tissues.SPR based sensors have interesting and appropriated specifications that make them good candidates for bio-sensing applications.Actually SPR refers to the interaction of oscillatory electrons and electromagnetic (EM) waves at the interface of metal and dielectric layers, which causes the confinement and increment of the optical fields at sub-wavelength dimensions [7].Graphene-plasmonic nanostructures can be scaled down to nano-meter dimensions as they can conquer the diffraction limits of light [8].Terahertz (THz) radiations with frequencies between 0.1 THz to 10 THz have also gained much interest [9].THz technology spans the operating regions from millimeter to infrared spectrum which covers many different applications.Graphene-plasmonic devices indicate better sub-wavelength confinement, lower losses, and EM tunability and thus are appropriate options for operating in THz spectrum [9,10].Different kinds of SPR-based biosensors had been proposed based on various dielectric media, metal types and different layers of graphene.Recently, an SPR biosensor was suggested for sensing glucose concentration in blood and gas with different RIs [1].This biosensor indicated acceptable sensitivities of 275.15˚/RIU and 92.1˚/RIU for glucose and gaseous analyte.In another research, an infrared biosensor for nano-fluidic analysis based on graphene plasmonics, which detected the change of RI by the wavelength shift of resonant dips, was reported [11].The sensitivity amount of 1920 nm/RIU was obtained for this biosensor.A graphene based biosensor for obtaining plasmonic induced transparency (PIT) with appropriate functionalities in mid-IR region, was suggested [12].By using periodic graphene nano-ribbons, biosensors for detecting vibrational fingerprints could be realized for bio-analytical and pharmaceutical applications [13].A graphene plasmonic biosensor for detection of colorless biomaterial was proposed and developed with sensitivity and figure of merit (FOM) of 333.3nm/RIU and 16.665 RIU, respectively [14].Also, in another work [15], a chalcogenide fiber optic sensor with graphene layer was proposed for detection of hemoglobin in human blood.In general, nowadays graphene-based biosensors are of great interest to scientists and researchers.As a result, four different structures based on graphene-plasmonic combinations are proposed for bio-sensing applications.

Structure description and theory
Consider a simple structure as shown in Fig. 1, which is consisted of a graphene pattern on the top, a silicon dioxide layer (SiO2), an aluminum (Al) layer and a silicon (Si) substrate.The relation between the transmission, absorption and reflection fields can be considered based on the simple relation of [16,17]: (1) in which, , where the scattering parameters S11() and S21() are the reflection and transmission coefficients.
The Al-layer is used in order to prevent the passage of the incident light through the first two layers [17].For blocking the transmission of the incident light, the thickness of Al is chosen to be greater than the penetration depth of light in the IR-region To achieve the perfect absorber (for sensing applications), the reflection parameter R(ω) must be equal to zero so that, A(ω) becomes 1 and hence the incident light would be completely absorbed.Considering the optimized parameters for the structure can lead to the complete absorption.As depicted in Fig. 1(c), the absorption peak values of 98 and 99.1 occur at 41µm and 54µm, respectively.
Special optical properties of graphene can lead to the production of great opacity in vacuum with absorption of about 2.3% of light.The light absorption can be increased for different designs of graphene and surrounding layers.The surface conductivity of a graphene layer can be calculated from the Kubo formula which is a function of different parameters such as wavelength, temperature and chemical potential [18]: where , f,  a n d T indicate the operation frequency, the chemical potential, the phenomenological scattering rate (   2 / 1  ,  is the scattering time) and the absolute temperature, respectively.The intra-band and inter-band electro-photon scattering parameters can be described as [18]: where kB and e are the Boltzmann constant and the electron charge.The dielectric function of the metals can also be described by the Drude model [18][19][20]: where ε ∞ = 3.7 (dielectric constant at infinite frequency), γ = 0.018eV (collision plasma angular frequency) and ωp = 9.1eV (bulk plasma angular frequency) [18][19][20].In the following section, different configurations with their results are presented.

Results and discussions
In this section, 4 different structures (models) based on of graphene-plasmonic nanostructures and their functionalities as biosensors are considered.It is important to note that the strips situated in the middle of the rings can greatly affect the characteristics of the structures.They can steer the direction of light to improve field distribution at specific wavelengths [17].Therefore, its effects on the absorption spectrum will be discussed.

A. First Structure
The first proposed structure with its side view (unit cell) is presented in Fig. 2  As shown in this figure, it is consisted of a periodic graphene pattern.The geometrical parameters of Fig. 2 are tabulated in Table .I. Simulation results reported in Fig . 2 (c), was obtained by the finite difference time domain (FDTD) method.Field distribution for this structure in different wavelengths can be seen in Fig. 3.As can be seen from Fig. 4(a), by considering R1=0.1µm, increasing R2 would lead to the blue shift of the absorption peak-wavelength and would decrease the absorption peak.The best result is obtained for R2=0.1µm with the absorption peak of 99.7%.In Fig. 4(b), by considering R2=0.1µm and R1=0.1µm, the absorption peak wavelength would experience the blue shift with the absorption peak of 99.9%.As a result, for obtaining the perfect absorber with nearly perfect absorption peaks, R1 and R2 should equal to 0.1µm.The variations of R1 and R2 can be explained by a simple LC resonant circuit.In the LC circuit, the upper and lower parts of the graphene make the two capacitors and the surface current is excited between the graphene and Al layers which would limit the incident light and lead to the perfect absorption [17,21].Another important parameter is the chemical potential, Ef1.Effects of various chemical potentials on the absorption spectrum are reported in Fig. 5.As can be seen from this figure, the absorption peak wavelength would have a blue shift, as Ef1 is increased.Again, this phenomenon can be explained by the circuit theory.In this theory, graphene can be described as a shunt admittance which can be varied by the geometrical parameters (R1, R2) and chemical potential (Ef1) [22,23].Therefore, changing Ef1 can alter the absorption peak wavelength according to the following equation [17,24]: where c, L and C are speed of the light in vacuum, capacitance and inductance, respectively.Enhancing Ef1 would diminish the inductance value L [25], which would decrease the absorption peak wavelength according to (6).Considering Ef1=0.9ev, the short wavelength ranges of 30-45µm with 97% absorption peak and long wavelength ranges of 45-60µm with 94% peak, would be achieved.So, in the following parts Ef1=0.9eV is selected.The proposed structure of Fig. 2 can be used as a biosensor with acceptable sensitivity.The absorption spectrum for materials with different refractive indices (2.32, 2.38, 2.44 and 2.5) can be seen in Fig. 6.As indicated in figure, increasing RI would increase the absorption peak wavelength [9,26] and the sensitivity factor   n   /  of 1500 nm/RIU can be obtained.

B. Second Structure
By considering 4 gold triangles at the corners and one square in the center of Fig. 2, second proposed arrangement of the biosensor would be presented.This shape is depicted in Fig. 7.The field distribution in the second structure at different wavelengths (resonant and nonresonant wavelengths) can be seen in Fig. 8.As can be seen, the strips affect the field distribution for different wavelengths.
Effects of chemical potential (Ef2) variations on the absorption spectrum are studied and the simulation results are plotted in Fig. 9.As stated for Ef1, by increasing Ef2 from 0.55 eV to 0.8 eV, the absorption peak wavelength would be blue shifted, which can be described by the circuit theory.Considering Ef2=0.8 eV, the short wavelength ranges of 38-50µm with 96% absorption peak and long wavelength ranges of 50-70µm with 98.5% peak are achieved.For the following simulations, Ef2=0.8 eV is selected.
By considering the second structure as the biosensor, the absorption spectrum for materials with different refractive indices (2.059, 2.106, 2.153 and 2.2) can be depicted in Fig. 10.From Fig. 10, it can be seen that, increasing RI would shift the absorption peak wavelength to higher values (materials with higher refractive indices can confine the light waves stronger than lower ones) [9,26].For the second structure, the sensitivity value of 2250nm/RIU can be achieved.

C. Third Structure
In the third proposal, by adding half circles of gold to the second structure, another configuration of the biosensor would be presented.This third suggested structure, with half circles of gold blocks, is depicted in Fig. 11.The parameters F=0.35µm, h3=0.5µm and e=0.35µm are considered for this configuration.For better understanding of the functionality of the third structure, effects of chemical potential (Ef3) on the absorption spectrum were studied.Simulation results are shown in Fig. 13.

Fig. 13. Schematic of the absorption spectrum versus wavelength for different values of Ef3
As can be seen in Fig. 13, by enhancing Ef3 from 0.4 eV to 1.2 eV, the absorption peak wavelength would be blue shifted, and it may also be explained by the circuit theory [17,24].Considering Ef3=1 eV, the short wavelength ranges of 60-75µm with 97% absorption peak and long wavelength ranges of 70-85µm with 99% peak are achieved.For the following simulations, Ef3=1 eV is used.
To consider the third structure as the biosensor, the absorption spectrum for materials with different refractive indices (1.335, 1.357, 1.379 and 1.405) are shown in Fig. 14 (these refractive indices are related to different hemoglobin concentrations) [15].The variation of absorption peak wavelength for the third proposal is the same as the first and second structures; increasing RI shift the wavelength to higher values [9,26].For the present case, the sensitivity value of 3750nm/RIU can be achieved.

D. Fourth Structure
In this section, by changing the strip direction of third structure (two vertical directed strips instead of horizontal stripes), another configuration of the biosensor would be presented which contains one absorption peak in the wavelength range of 80-100µm.The suggested structure is shown in Fig. 15.For studying the characteristics of this case, effects of its chemical potential (Ef4) on the absorption spectrum are also considered.Simulation results are shown in Fig. 17.As can be seen, by enhancing Ef4 from 0.6 eV to 1.2 eV, the absorption peak wavelength would have a blue shift (like the three other structures) [15].Considering Ef4=0.9 eV, the wavelength ranges of 80-100µm with 99.9% absorption peak is achieved.For the following simulations, Ef4=0.9 eV would be considered.
To consider this structure as the biosensor, the absorption spectrum for materials with different refractive indices (1.375, 1.365, 1.352 and 1.338) are plotted in Fig. 18 (these refractive indices are related to different glucose concentrations in blood samples; n=1.375 for 100mg/dl, n=1.365 for 75mg/dl, n=1.352 for 50mg/dl, n=1.338 for 25mg/dl) [1].It can be seen from Fig. 18, that enhancing RI has led to the increment of the absorption peak wavelength (as increasing the refractive index would lead to higher confinement of the lightwave) [9,26].For this case, the sensitivity value of 4850nm/RIU can be obtained.

Conclusion
Four different structures based on graphene-plasmonic nanostructures were proposed for biosensing applications.The proposed systems were consisted of graphene, SiO2, Al and gold layers on the silicon background.

Fig. 1
Fig. 1 Schematic of a simple absorber structure . The figure indicates the absorption, transmission and reflection spectrum.

Fig. 2 a
Fig. 2 a) Schematic of the first proposed structure, b) side view of the proposed structure, c) absorption, reflection and transmission spectrum.

Fig. 3 )Fig. 4 )
Fig. 3) Field distribution for the first proposed structure, Ef1=0.7eV and a)λ=50µm, b)λ=52µm, c)λ=54µm, d)λ=56µm.To improve the functionality of the proposed structure, effects of different geometrical parameters such as R1 (ring width), R2 (strip width, refer to Fig.2 b), chemical potential (Ef) on the wavelength and value of the absorption spectrum are investigated.Fig.4shows simulation results for different values of R1 and R2, while other parameters are kept constant.

Fig. 5 .
Fig. 5. Schematic of the absorption spectrum versus wavelength for different values of Ef1.

Fig. 7 a
Fig. 7 a) Schematic of the second proposed structure, b) side view of the proposed structure.

Fig. 9 .
Fig. 9. Schematic of the absorption spectrum versus wavelength for different values of Ef2 in the second proposed structure

Fig. 10 .
Fig. 10.Absorption spectrum versus wavelength for different materials for the second structure

Fig. 11 aFig. 12 )
Fig. 11 a) Schematic of the third proposed structure, b) side view of the proposed structure.

Fig. 14 .
Fig. 14.Absorption spectrum versus wavelength for different materials for third structure

Fig. 15 aFig. 16 )
Fig. 15 a) Schematic of the fourth proposed structure, b) side view of the proposed structure

Fig. 17 .
Fig. 17.Schematic of the absorption spectrum versus wavelength for different values of Ef4.

Fig. 18 .
Fig. 18.Absorption spectrum versus wavelength for different materials for the fourth structure

Figures
Figures

Figure 1 Schematic of a simple absorber structure Figure 2 a
Figure 1

Figure 3 Field
Figure 3

Figure 7 a
Figure 7

Figure 8 Field
Figure 8

Figure 11 a
Figure 11

Figure 12 Field
Figure 12

Figure
Figure

Table I : Parameter values for Fig 2.
Combinations of ring-shaped graphene layers with different strip directions resulted in various absorption specifications (affect the absorption peak value and wavelength).For conducting better investigation on the characteristics of the proposed structures, effects of geometrical and chemical potential on the absorption spectrum were also considered.The first, second, third and fourth suggested structures indicated sensing functionalities at 45-60 µm, 50-70 µm, 70-85 µm and 80-100 µm ranges, with the sensitivity factors of 1500nm/RIU, 2250/RIU, 3750nm/RIU and 4850nm/RIU, respectively.As a result, by introducing the four proposed structures, tunable biosensors appropriate for various applications like sensing different hemoglobin and glucose concentrations in blood samples were obtained.