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Highly sensitive and tunable terahertz biosensor based on optical Tamm states in graphene-based Bragg reflector
Journal Pre-proofs Highly sensitive and tunable terahertz biosensor based on optical Tamm states in graphene-based Bragg reflector Yunyang Ye, Minzhu Xie, Jiao Tang, Jianxing Ouyang PII: DOI: Reference:
S2211-3797(19)32645-2 https://doi.org/10.1016/j.rinp.2019.102779 RINP 102779
To appear in:
Results in Physics
Received Date: Revised Date: Accepted Date:
18 September 2019 26 October 2019 26 October 2019
Please cite this article as: Ye, Y., Xie, M., Tang, J., Ouyang, J., Highly sensitive and tunable terahertz biosensor based on optical Tamm states in graphene-based Bragg reflector, Results in Physics (2019), doi: https://doi.org/ 10.1016/j.rinp.2019.102779
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier B.V.
Highly sensitive and tunable terahertz biosensor based on optical Tamm states in graphene-based Bragg reflector Yunyang Ye1, Minzhu Xie2, *, Jiao Tang1, Jianxing Ouyang2 1
School of Physics and Electronics, Hunan Normal University, Changsha 410081,
China. 2
College of Information Science and Engineering, Hunan Normal University,
Changsha 410081, China. Present/permanent address: *Corresponding author. E-mail address: [email protected]
Abstract: A highly sensitive and tunable biosensor at terahertz (THz) frequencies is proposed by using a composite structure of graphene and one-dimensional photonic crystal. The theoretical analysis and simulation results show that the sensitivity and figure-of-merit of the biosensor can reach
517.9 / RIU and 222.9RIU-1 ,
respectively. The high sensitivity of the biosensor originates from the excitation of optical Tamm states caused by graphene-based distributed Bragg reflector. By varying the voltage on graphene, we can electrically control the sensitivity and figure-of-merit of the biosensor. Furthermore, we have shown that the biosensor has a wide range (1.40~1.70) for measuring the refractive index of the sensing medium. We believe the biosensor has a good application prospect in the field of biological detection. .
1. Introduction A biosensor is a cunning combination of biological molecules and microelectronics in the measurement of biological elements [1]. Optical biosensors are a classic type of biosensors obtaining biological information by detecting changes in specific wavelengths of light. Owing to the advantages of non-contacting, non-destructive and non-interferential measuring, and remote sensing [2], optical biosensors have wide applications in food safety [3], environmental monitoring [4], biomedical application [5], drug testing [6] and biochemical testing [7]. In particular, micro/nano-optical biosensors in chip size play an important role in developing of integrated devices and systems for rapid and real-time analyses of biological ingredients [8]. In 2007, Levi et al. designed an integrated semiconductor biosensor, based on which a lab-on-a-chip had been developed [9]. In 2012, Xu et al. proposed an optical biosensor based on magnetic micro/nano particles [10], and Song et al. designed an aptamer optical biosensor using upconversion nanoparticles as donors [11]. Recently, many micro/nano-optical biosensors based on surface plasmon resonance (SPR) are reported [12, 13]. SPR biosensors apply special optical waves to detect the interactions between an analyte in solution and a biomolecular recognition element immobilized on the SPR sensor surface [14]. In 2011, Verma et al. designed a sensitive SPR biosensor with a high sensitivity 134.6°/RIU [15]. In 2019, Gan et al. proposed a SPR sensor with 2D franckeite nanosheets whose sensitivity achieved as high as 188°/RIU [16]. However, the design of dynamically controllable optical sensors with higher sensitivity and simpler structure based on SPR involves a lot of challenging work. The formation mechanisms of biosensors based on novel structures or new materials have now become a major research focus in the realm of optical sensing. Optical Tamm states (OTSs), a kind of surface wave confined to the interface between two different media, are lossless interface modes decaying exponentially in the surrounding media [17]. Compared to SPR, OTSs can be directly excited by TM-polarized or TE-polarized waves even at normal incidence. Therefore, OTSs have
attracted a great deal of attention from both theoretical and experimental realms [18, 19]. OTSs are usually excited in metal-distributed Bragg reflector (DBR) structures. Although extensive researches on metal-DBR structures have produced some meaningful findings, these structures still lack of adequate dynamic adjustability and can hardly stimulate OTSs in THz frequencies. Graphene, a two-dimensional and one-atom-thick carbon crystal, has attracted intensive interest due to its unique optical and electrical properties [20]. It is a zero band-gap material that can be used to realize electromagnetic response from ultraviolet to THz range [21]. In addition, graphene is very attractive because the carrier concentration can be controlled via external gate voltage or chemical doping [22]. This means the conductivity of graphene can be continuously tuned over a broad frequency range by shifting the Fermi energy. It is even more important that graphene is intrinsically a semimetal with specific metallic properties under certain conditions, such as the ability to excite OTSs [23]. Researches on exciting OTSs with graphene started to emerge [24, 25], and an interesting question is open: is it possible to design a nanoscale, tunable and highly-sensitive biosensor based on OTSs with graphene? To answer this question, we designed a new graphene-based one-dimensional photonic crystal (1D PC) biosensor and analyzed its performance in the THz band. The theoretical analysis and simulation results show that the sensitivity and figure-of-merit (FOM) of the biosensor can reach 517.9 / RIU and 222.9RIU-1 , respectively, and the sensitivity and FOM can be adjusted by varying the voltage on graphene. The performance of the biosensor is related with the relaxation time of the graphene, the number of the graphene layers, the number of 1DPC periods and the thickness of the sensing layer. As a highly-sensitive and tunable terahertz biosensor based on OTSs with graphene, the biosensor has a good application prospect in biological detection.
2. Theoretical Model and Method We used a graphene-based DBR structure to excite OTSs. It has been reported that the excitation of OTSs is rather sensitive to the spacer layer [24]. Therefore, the analyte in
Fig. 1. Schematic diagram of the proposed biosensor, which composed of the 1D PC (formed by alternately superposing dielectric layer A and B), the sensing medium(the spacer layer), the graphene and the substrate.
biological solution (the sensing medium) is placed in the spacer layer. As shown in Fig. 1, the sensing medium with thicknesses of d s is placed between the graphene layer and the 1D PC. The 1D PC is formed by alternately superposing dielectric layer A and B, where A is the TPX (4-methylpentene-1) with refractive index of na 1.46 and B is SiO2 with refractive index of nb 1.9 . The thicknesses of TPX and SiO2 are denoted d a by d a and d b , respectively. Assuming the center wavelength of the incident light is c ,
da c∕4na and db c∕4nb . Since the biosensor is designed for applications in the THz band, the center wavelength c is set as 300 m . As mentioned above, the excitation of OTSs is very sensitive to the structural parameters of the spacer layer. Since the biological analyte is always resolved in alcohol solution and the initial refractive index of the solution is 1.410, the refractive index of the sensing medium is set to 1.410 ns , where
ns 0 represents the increment of the sensing medium’s refractive index above 1.410. Besides, we choose germanium with a refractive index of 3.84 as the substrate. In order to calculate the sensitivity of the biosensor in Fig. 1, we use the classical transfer matrix method to calculate the reflectance of the whole structure, whose total
matrix can be represented by a 2 2 matrix [26]. In this paper, the incident light is assumed to be TM-polarized, the transmission matrix between the dielectric A and dielectric B can be written as Da b
1 1 ab 1 ab , 2 1 ab 1 ab
(1)
with parameters ab given by
ηab
ε a k ba
ε b k ab
，
(2)
where, kab k0 a 0 sin 2 , kba k0 b 0 sin 2 , and k0 / c ; is the incident angle of incident light and 0 is the permittivity in the vacuum; a and
b is the dielectric constant of the dielectric 1 and dielectric 2, respectively. Analogously, we can write Dba (the transmission matrix between the dielectric B and dielectric A), Doa (the transmission matrix between the air and dielectric A). It is well known that the conductivity of graphene is the sum of inter-conductivity and intra-conductivity. Since the inter-conductivity of graphene is far less than the intra-conductivity in the THz band, the conductivity of the few-layer graphene in THz range under approximate local random phase can be calculated as follows [27, 28]
G
ie2 E F
2
i
，
(3)
where e , and represent the elementary electric charge, the relaxation time of graphene and angular frequency, respectively. G is the number of the graphene layers.
E F is the Fermi energy of graphene. It is known that E F is closely related to the carrier density n2 D : E F F n2 D
(
is the reduced Planck constant and
F 106 m / s represents the Fermi velocity of electrons). Then the transmission matrix between the sensing medium and the substrate can be written as
Ds t
1 1 p p 1 p p , 2 1 p p 1 p p
(4)
with parameters p and p given by
ηp
εs k tz
ε t k sz
，ξ p
σk tz
ε 0ε t ω ,
(5)
where, ksz k0 s 0 sin 2 , ktz k0 t 0 sin 2 , s and t is the dielectric constant of the spacer layer and the substrate of the graphene, respectively. The propagation matrix P(d a ) ( d a is the thickness of the dielectric A) of the electromagnetic wave in the dielectric layer can be expressed by the following matrix eikaz da P(d a ) 0
0
,
eikaz da
(6)
where, kaz k0 a 0 sin 2 . Similarly, we can get P(db ) and P(d s ) . Therefore, the total matrix of the whole structure can be modified as
M Doa Pa da Dab Pb db Dba
N 1
Pa da Dab Pb db Dbs Ps d s Ds t , (7)
where N is the period of 1D PC. Thus the reflectance of the whole structure would be
rp
M 21
M11 ,
(8)
where M 11 and M 21 are the elements of the total transfer matrix M. The reflectance 2
of the structure can be expressed as R rp . When the OTSs excited by the graphene in the structure, the change in the refractive index ( ns ) of the sensing medium can lead to a change ( ) in the resonance angle of the reflectance curves. Then the sensitivity S of the biosensor would be
S
ns .
(9)
The FOM is defined as FOM S DA, where quality factor (DA) satisfies
DA= 1/FWHM , and FWHM is the full width at half maximum of the reflectance curves [29].
3. Results and Discussions It is well known that when OTSs are excited in the graphene-based DBR structure, the electric field energy is mainly located near the graphene [25]. Now we discuss the impact of graphene on the reflectance of TM-polarized wave in the proposed configuration. The parameters of the configurations are set as G 5, N 7,
EF 1.0eV , 12o , d s 313 m , ns 1.410 and f 1.015THz , if they are not specified. Fig. 2 shows the difference between the reflection spectrums of the configurations with graphene and without graphene. When there is no graphene in the structure, we can find that there exists optical band gap nearby 1.0 THz. When there is graphene in the structure, due to the OTSs excited by the graphene, the reflectance decreases to near zero at the resonance frequency. It means that the light wave near the resonance frequencies would penetrate the structure, while the wave at other frequencies would be reflected [30].
Fig. 2. Reflection spectrums of the configurations with graphene and without graphene.
To better illustrate the OTSs excited by graphene, we conduct a simulation analysis using the transmission matrix and display the electric field distribution along the z axis in the graphene-based DBR. For the sake of better comparison, the calculated electric field is normalized by the incident electric field, and the z-coordinate of the top surface of the 1D PC layer is set as 0. Fig. 3 shows the electric field distributions of the configurations with graphene and without graphene. Fig. 3 (a) shows the electric
field distribution in the multilayer configuration without graphene, where the electric field decays rapidly for z 0 without local field enhancement. However, the situation is changed significantly by introducing a graphene layer into the configuration as shown in Fig. 3(b). Fig. 3(b) shows that the electric field is strongly enhanced on the interface between the graphene and DBR. When OTSs are excited, a maximal electric field about 70 times of that in Fig. 3(a). Therefore, Fig. 3 shows that the graphene plays an important role in enhancing the local field, and contributes greatly to the improvements of highly-sensitive detection of the proposed biosensor. The above results can be obtained by using numerical simulation software such as FDTD Soltions [31, 32].
Fig. 3. The distributions of normalized electric field of the configurations (a) without graphene and (b) with graphene.
From Equation (3), we know that the key parameter controlling the conductivity of the graphene is Fermi level, which can be turned in a wide range (typically from 0 eV to 1 eV) by applying a transverse electric field via a DC biased gated structure, thus controlling the graphene conductivity [33]. It means the performance of the biosensor can be directly tuned by external voltage. Fig. 4(a) shows the curves of the graphene’s reflectance at different incident angles (from 6° to 14°) for EF 0.7eV,0.8eV,0.9eV and 1.0eV . With the Fermi energy increases, we find that the reflectance curve gradually shifts to the left (which means the decline in the resonance angle) and the
minimum reflectance gets smaller and smaller. According to Fig. 4 (b), the S and FOM of the biosensor are mounting as E F increases from 0.5eV to 1.0eV . These properties indicate that a higher E F of the graphene is highly effective in regulating the performance of the biosensor. Therefore, in order to improve the sensitivity of the biosensor, we should set the Fermi energy to a higher value.
Fig. 4. (a) Variations of the reflectance with respect to the incident angle for EF 0.7eV,0.8eV,0.9eV and 1.0 eV of graphene. (b) Changes of the S and FOM with respect to the E F of the graphene.
Fig. 5. (a) Changes of the S and FOM with respect to the relaxation time of graphene. (b) Variations of the reflectance with respect to the incident angle for 0.5ps and 1ps .
Next, we discuss the influence of relaxation time on the biosensor performance, as
shown in Fig. 5(a). With the increase of the , the FOM of the biosensor increases, while the S decreases. In Fig. 5(b), the S is 337.96°/RIU and FOM is 146.20RIU-1 at
0.5 ps ; the S changes to 335.98 / RIU and FOM to 93.56RIU-1 at 1ps . In order to ensure good performance of the sensor, the relaxation time of the graphene is set as 0.5 ps . It is noteworthy that although the relaxation time can easily influence the sensitivity of the sensor, this approach still lacks flexibility, because the relaxation time would no longer be effective in adjusting sensor’s sensitivity on completion of the graphene.
Fig. 6. (a) Variations of the reflectance with respect to the incident angle for G= 0, 1,2,3,4 and 5. (b) Changes of the S and FOM with respect to the layer number of graphene.
From Equation (1) we can see that the layer number of graphene (denoted by letter G) has a strong influence on the performance of optical biosensor due to the absorptive property of the graphene. As mentioned above, when the layer number of the few-layer graphene satisfies G 6 , there would be an approximate linear relationship between the conductivity and the layer number of graphene, from which we can easily evaluate the influence of G over the sensitivity of the sensor. The influence of the layer number of graphene on reflectance dip is illustrated in Fig. 6(a).
It is obvious that the reflectance dip is shifting toward a smaller incident with the increase of graphene layers, accompanied by a sharp decline of FWHM. This phenomenon can be applied to develop various OTSs based photoelectric devices. At the same time, with G increases from 0 to 5, the S and FOM of the biosensor gradually increase, as shown in Fig. 6(b). However, the electrical and optical properties of graphene would become very complicated if the number of graphene layers is large. Therefore, we only consider the effect of fewer graphene layers on the performance of the sensor.
Fig. 7. (a) Variations of the reflectance with respect to the incident angle for N=4, 5,6,7,8 and 9. (b) Changes of the S and FOM with respect to the numbers of 1D PC periods.
Furthermore, the number of 1D PC periods N also has an important effect on the spectral and sensitivity of the proposed biosensor, as shown in Fig. 7(a) and Fig. 7(b). With N increases from 4 to 9, the FWHM of the spectral reflectance curves gradually becomes narrower, and the reflectance dip of the composite configuration first decreases and then mounts up. Meanwhile, the increase of N would result in the increase of FOM and sensitivity decreases in Fig. 7(b). Obviously, “ N 6 ”, under current structure parameters, is the demarcation point for the performance of the biosensor. If Nis larger than seven, the reflectance increase would lead to the decrease of the monitoring resolution. Therefore, when N 6 , the biosensor has superior performance in measuring biological medium.
Fig. 8. Changes of S with respect to the thickness of the spacer layer, it particularly shows the variation of the reflectance with respect to the incident angle for
ns =1.410 and 1.415.
The characteristics of the spacer layer (also known as the sensing medium) in the configuration have a strong influence on the excitation of OTSs. Therefore, the integral sensitivity of the biosensor is highly susceptible to the thickness and refractive index of the sensing layer, as shown in Fig. 8 and 9, respectively. According to Fig. 8, as the thickness of the sensing layer increases from 312 m to 400 m , the sensitivity of the structure is decreasing. Specifically, when the thickness of the sensing layer goes below 312 m , the sensitivity of the biosensor sharply declines to near zero. When the thickness of the sensing medium satisfies d s 312.3 m , we can calculate the maximum difference of the resonance angle ( 2.5897 ) and the O
highest sensitivity (Smax= 517.9 / RIU ) of the biosensor. In the mean time, the FWHM of the reflectivity curve corresponding to ns 1.410 is 2.346, and we have
DA=1/FWHM=0.430 and FOM=S DA= 222.9RIU-1 . Therefore, in order to ensure the high S of the sensor, the thickness of the sensor layer should be set between 312 m and 318 m .
Fig. 9. Changes of S with respect to the refractive index of the spacer layer. It specifically shows the variations of the reflectance with respect to the incident angle for
ns =1.700 and 1.705.
Meanwhile, in order to determine the detection range of the refractive index for the biosensor, the variation of the S with respect to different refractive indexes of the sensing layer is discussed, as shown in Fig. 9. It is clearly shown that the S of the biosensor gradually decreases as the refractive index of the sensing medium increases from 1.410 to 1.700. In the refractive index range of 1.410 to 1.425, the S of the biosensor can reach more than
500 / RIU .When the refractive index of the
sensing medium is 1.700, the S is 67.19 / RIU . Simultaneously, it is found that the larger the refractive index of the sensing medium the greater the resonance angle corresponding to the dip (the reflectance curve shifts toward right). Therefore, it is verified that the sensor offers a wide range of refractive index measurements (1.40~1.70) for measuring the refractive index of the sensing medium.
4. Conclusions In summary, we proposed a novel THz optical biosensor using the graphene-based DBR structure to excite OTSs, and analyzed how the performance of the biosensor was affected by the Fermi energy, the dielectric relaxation time, the number of layers of graphene, the number of 1D PC periods, and the thickness of the spacer layer. We
can adjust the voltage on the graphene and the thickness of the spacer layer to obtain the highest sensitivity when using the biosensor to detect biological analyte with different refractive index. The simulation results showed that the sensitivity and FOM of the biosensor could reach as high as 517.9 / RIU and 222.9RIU-1 , respectively. The theoretical analysis of the electric field distribution in the proposed structure also verified the high sensitivity of the biosensor. Finally, the relationship between the performances (sensitivity and FOM) of the biosensor and the parameters (refractive index and thickness) of the sensing medium are discussed. We believe this novel optical biosensor has an excellent application prospect in optical detection, biological information detection and other related fields.
Acknowledgments This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 61772197) and the Hunan Provincial Natural Science Foundation of China (Grant Nos. 2019JJ70087).
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Highlights 1.
We propose a novel terahertz biosensor based on optical Tamm states in graphene-based
Bragg reflector.
2.
The sensitivity and figure-of-merit of the biosensor can reach more than 500°/RIU and 200
RIU-1 , respectively. 3.The sensitivity and figure-of-merit of the proposed biosensor can be improved by adjusting the applied voltage and other parameters of the biosensor. 4.The biosensor has a wide range of refractive index sensing range (1.40~1.70).
S2211-3797(19)32645-2 https://doi.org/10.1016/j.rinp.2019.102779 RINP 102779
To appear in:
Results in Physics
Received Date: Revised Date: Accepted Date:
18 September 2019 26 October 2019 26 October 2019
Please cite this article as: Ye, Y., Xie, M., Tang, J., Ouyang, J., Highly sensitive and tunable terahertz biosensor based on optical Tamm states in graphene-based Bragg reflector, Results in Physics (2019), doi: https://doi.org/ 10.1016/j.rinp.2019.102779
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier B.V.
Highly sensitive and tunable terahertz biosensor based on optical Tamm states in graphene-based Bragg reflector Yunyang Ye1, Minzhu Xie2, *, Jiao Tang1, Jianxing Ouyang2 1
School of Physics and Electronics, Hunan Normal University, Changsha 410081,
China. 2
College of Information Science and Engineering, Hunan Normal University,
Changsha 410081, China. Present/permanent address: *Corresponding author. E-mail address: [email protected]
Abstract: A highly sensitive and tunable biosensor at terahertz (THz) frequencies is proposed by using a composite structure of graphene and one-dimensional photonic crystal. The theoretical analysis and simulation results show that the sensitivity and figure-of-merit of the biosensor can reach
517.9 / RIU and 222.9RIU-1 ,
respectively. The high sensitivity of the biosensor originates from the excitation of optical Tamm states caused by graphene-based distributed Bragg reflector. By varying the voltage on graphene, we can electrically control the sensitivity and figure-of-merit of the biosensor. Furthermore, we have shown that the biosensor has a wide range (1.40~1.70) for measuring the refractive index of the sensing medium. We believe the biosensor has a good application prospect in the field of biological detection. .
1. Introduction A biosensor is a cunning combination of biological molecules and microelectronics in the measurement of biological elements [1]. Optical biosensors are a classic type of biosensors obtaining biological information by detecting changes in specific wavelengths of light. Owing to the advantages of non-contacting, non-destructive and non-interferential measuring, and remote sensing [2], optical biosensors have wide applications in food safety [3], environmental monitoring [4], biomedical application [5], drug testing [6] and biochemical testing [7]. In particular, micro/nano-optical biosensors in chip size play an important role in developing of integrated devices and systems for rapid and real-time analyses of biological ingredients [8]. In 2007, Levi et al. designed an integrated semiconductor biosensor, based on which a lab-on-a-chip had been developed [9]. In 2012, Xu et al. proposed an optical biosensor based on magnetic micro/nano particles [10], and Song et al. designed an aptamer optical biosensor using upconversion nanoparticles as donors [11]. Recently, many micro/nano-optical biosensors based on surface plasmon resonance (SPR) are reported [12, 13]. SPR biosensors apply special optical waves to detect the interactions between an analyte in solution and a biomolecular recognition element immobilized on the SPR sensor surface [14]. In 2011, Verma et al. designed a sensitive SPR biosensor with a high sensitivity 134.6°/RIU [15]. In 2019, Gan et al. proposed a SPR sensor with 2D franckeite nanosheets whose sensitivity achieved as high as 188°/RIU [16]. However, the design of dynamically controllable optical sensors with higher sensitivity and simpler structure based on SPR involves a lot of challenging work. The formation mechanisms of biosensors based on novel structures or new materials have now become a major research focus in the realm of optical sensing. Optical Tamm states (OTSs), a kind of surface wave confined to the interface between two different media, are lossless interface modes decaying exponentially in the surrounding media [17]. Compared to SPR, OTSs can be directly excited by TM-polarized or TE-polarized waves even at normal incidence. Therefore, OTSs have
attracted a great deal of attention from both theoretical and experimental realms [18, 19]. OTSs are usually excited in metal-distributed Bragg reflector (DBR) structures. Although extensive researches on metal-DBR structures have produced some meaningful findings, these structures still lack of adequate dynamic adjustability and can hardly stimulate OTSs in THz frequencies. Graphene, a two-dimensional and one-atom-thick carbon crystal, has attracted intensive interest due to its unique optical and electrical properties [20]. It is a zero band-gap material that can be used to realize electromagnetic response from ultraviolet to THz range [21]. In addition, graphene is very attractive because the carrier concentration can be controlled via external gate voltage or chemical doping [22]. This means the conductivity of graphene can be continuously tuned over a broad frequency range by shifting the Fermi energy. It is even more important that graphene is intrinsically a semimetal with specific metallic properties under certain conditions, such as the ability to excite OTSs [23]. Researches on exciting OTSs with graphene started to emerge [24, 25], and an interesting question is open: is it possible to design a nanoscale, tunable and highly-sensitive biosensor based on OTSs with graphene? To answer this question, we designed a new graphene-based one-dimensional photonic crystal (1D PC) biosensor and analyzed its performance in the THz band. The theoretical analysis and simulation results show that the sensitivity and figure-of-merit (FOM) of the biosensor can reach 517.9 / RIU and 222.9RIU-1 , respectively, and the sensitivity and FOM can be adjusted by varying the voltage on graphene. The performance of the biosensor is related with the relaxation time of the graphene, the number of the graphene layers, the number of 1DPC periods and the thickness of the sensing layer. As a highly-sensitive and tunable terahertz biosensor based on OTSs with graphene, the biosensor has a good application prospect in biological detection.
2. Theoretical Model and Method We used a graphene-based DBR structure to excite OTSs. It has been reported that the excitation of OTSs is rather sensitive to the spacer layer [24]. Therefore, the analyte in
Fig. 1. Schematic diagram of the proposed biosensor, which composed of the 1D PC (formed by alternately superposing dielectric layer A and B), the sensing medium(the spacer layer), the graphene and the substrate.
biological solution (the sensing medium) is placed in the spacer layer. As shown in Fig. 1, the sensing medium with thicknesses of d s is placed between the graphene layer and the 1D PC. The 1D PC is formed by alternately superposing dielectric layer A and B, where A is the TPX (4-methylpentene-1) with refractive index of na 1.46 and B is SiO2 with refractive index of nb 1.9 . The thicknesses of TPX and SiO2 are denoted d a by d a and d b , respectively. Assuming the center wavelength of the incident light is c ,
da c∕4na and db c∕4nb . Since the biosensor is designed for applications in the THz band, the center wavelength c is set as 300 m . As mentioned above, the excitation of OTSs is very sensitive to the structural parameters of the spacer layer. Since the biological analyte is always resolved in alcohol solution and the initial refractive index of the solution is 1.410, the refractive index of the sensing medium is set to 1.410 ns , where
ns 0 represents the increment of the sensing medium’s refractive index above 1.410. Besides, we choose germanium with a refractive index of 3.84 as the substrate. In order to calculate the sensitivity of the biosensor in Fig. 1, we use the classical transfer matrix method to calculate the reflectance of the whole structure, whose total
matrix can be represented by a 2 2 matrix [26]. In this paper, the incident light is assumed to be TM-polarized, the transmission matrix between the dielectric A and dielectric B can be written as Da b
1 1 ab 1 ab , 2 1 ab 1 ab
(1)
with parameters ab given by
ηab
ε a k ba
ε b k ab
，
(2)
where, kab k0 a 0 sin 2 , kba k0 b 0 sin 2 , and k0 / c ; is the incident angle of incident light and 0 is the permittivity in the vacuum; a and
b is the dielectric constant of the dielectric 1 and dielectric 2, respectively. Analogously, we can write Dba (the transmission matrix between the dielectric B and dielectric A), Doa (the transmission matrix between the air and dielectric A). It is well known that the conductivity of graphene is the sum of inter-conductivity and intra-conductivity. Since the inter-conductivity of graphene is far less than the intra-conductivity in the THz band, the conductivity of the few-layer graphene in THz range under approximate local random phase can be calculated as follows [27, 28]
G
ie2 E F
2
i
，
(3)
where e , and represent the elementary electric charge, the relaxation time of graphene and angular frequency, respectively. G is the number of the graphene layers.
E F is the Fermi energy of graphene. It is known that E F is closely related to the carrier density n2 D : E F F n2 D
(
is the reduced Planck constant and
F 106 m / s represents the Fermi velocity of electrons). Then the transmission matrix between the sensing medium and the substrate can be written as
Ds t
1 1 p p 1 p p , 2 1 p p 1 p p
(4)
with parameters p and p given by
ηp
εs k tz
ε t k sz
，ξ p
σk tz
ε 0ε t ω ,
(5)
where, ksz k0 s 0 sin 2 , ktz k0 t 0 sin 2 , s and t is the dielectric constant of the spacer layer and the substrate of the graphene, respectively. The propagation matrix P(d a ) ( d a is the thickness of the dielectric A) of the electromagnetic wave in the dielectric layer can be expressed by the following matrix eikaz da P(d a ) 0
0
,
eikaz da
(6)
where, kaz k0 a 0 sin 2 . Similarly, we can get P(db ) and P(d s ) . Therefore, the total matrix of the whole structure can be modified as
M Doa Pa da Dab Pb db Dba
N 1
Pa da Dab Pb db Dbs Ps d s Ds t , (7)
where N is the period of 1D PC. Thus the reflectance of the whole structure would be
rp
M 21
M11 ,
(8)
where M 11 and M 21 are the elements of the total transfer matrix M. The reflectance 2
of the structure can be expressed as R rp . When the OTSs excited by the graphene in the structure, the change in the refractive index ( ns ) of the sensing medium can lead to a change ( ) in the resonance angle of the reflectance curves. Then the sensitivity S of the biosensor would be
S
ns .
(9)
The FOM is defined as FOM S DA, where quality factor (DA) satisfies
DA= 1/FWHM , and FWHM is the full width at half maximum of the reflectance curves [29].
3. Results and Discussions It is well known that when OTSs are excited in the graphene-based DBR structure, the electric field energy is mainly located near the graphene [25]. Now we discuss the impact of graphene on the reflectance of TM-polarized wave in the proposed configuration. The parameters of the configurations are set as G 5, N 7,
EF 1.0eV , 12o , d s 313 m , ns 1.410 and f 1.015THz , if they are not specified. Fig. 2 shows the difference between the reflection spectrums of the configurations with graphene and without graphene. When there is no graphene in the structure, we can find that there exists optical band gap nearby 1.0 THz. When there is graphene in the structure, due to the OTSs excited by the graphene, the reflectance decreases to near zero at the resonance frequency. It means that the light wave near the resonance frequencies would penetrate the structure, while the wave at other frequencies would be reflected [30].
Fig. 2. Reflection spectrums of the configurations with graphene and without graphene.
To better illustrate the OTSs excited by graphene, we conduct a simulation analysis using the transmission matrix and display the electric field distribution along the z axis in the graphene-based DBR. For the sake of better comparison, the calculated electric field is normalized by the incident electric field, and the z-coordinate of the top surface of the 1D PC layer is set as 0. Fig. 3 shows the electric field distributions of the configurations with graphene and without graphene. Fig. 3 (a) shows the electric
field distribution in the multilayer configuration without graphene, where the electric field decays rapidly for z 0 without local field enhancement. However, the situation is changed significantly by introducing a graphene layer into the configuration as shown in Fig. 3(b). Fig. 3(b) shows that the electric field is strongly enhanced on the interface between the graphene and DBR. When OTSs are excited, a maximal electric field about 70 times of that in Fig. 3(a). Therefore, Fig. 3 shows that the graphene plays an important role in enhancing the local field, and contributes greatly to the improvements of highly-sensitive detection of the proposed biosensor. The above results can be obtained by using numerical simulation software such as FDTD Soltions [31, 32].
Fig. 3. The distributions of normalized electric field of the configurations (a) without graphene and (b) with graphene.
From Equation (3), we know that the key parameter controlling the conductivity of the graphene is Fermi level, which can be turned in a wide range (typically from 0 eV to 1 eV) by applying a transverse electric field via a DC biased gated structure, thus controlling the graphene conductivity [33]. It means the performance of the biosensor can be directly tuned by external voltage. Fig. 4(a) shows the curves of the graphene’s reflectance at different incident angles (from 6° to 14°) for EF 0.7eV,0.8eV,0.9eV and 1.0eV . With the Fermi energy increases, we find that the reflectance curve gradually shifts to the left (which means the decline in the resonance angle) and the
minimum reflectance gets smaller and smaller. According to Fig. 4 (b), the S and FOM of the biosensor are mounting as E F increases from 0.5eV to 1.0eV . These properties indicate that a higher E F of the graphene is highly effective in regulating the performance of the biosensor. Therefore, in order to improve the sensitivity of the biosensor, we should set the Fermi energy to a higher value.
Fig. 4. (a) Variations of the reflectance with respect to the incident angle for EF 0.7eV,0.8eV,0.9eV and 1.0 eV of graphene. (b) Changes of the S and FOM with respect to the E F of the graphene.
Fig. 5. (a) Changes of the S and FOM with respect to the relaxation time of graphene. (b) Variations of the reflectance with respect to the incident angle for 0.5ps and 1ps .
Next, we discuss the influence of relaxation time on the biosensor performance, as
shown in Fig. 5(a). With the increase of the , the FOM of the biosensor increases, while the S decreases. In Fig. 5(b), the S is 337.96°/RIU and FOM is 146.20RIU-1 at
0.5 ps ; the S changes to 335.98 / RIU and FOM to 93.56RIU-1 at 1ps . In order to ensure good performance of the sensor, the relaxation time of the graphene is set as 0.5 ps . It is noteworthy that although the relaxation time can easily influence the sensitivity of the sensor, this approach still lacks flexibility, because the relaxation time would no longer be effective in adjusting sensor’s sensitivity on completion of the graphene.
Fig. 6. (a) Variations of the reflectance with respect to the incident angle for G= 0, 1,2,3,4 and 5. (b) Changes of the S and FOM with respect to the layer number of graphene.
From Equation (1) we can see that the layer number of graphene (denoted by letter G) has a strong influence on the performance of optical biosensor due to the absorptive property of the graphene. As mentioned above, when the layer number of the few-layer graphene satisfies G 6 , there would be an approximate linear relationship between the conductivity and the layer number of graphene, from which we can easily evaluate the influence of G over the sensitivity of the sensor. The influence of the layer number of graphene on reflectance dip is illustrated in Fig. 6(a).
It is obvious that the reflectance dip is shifting toward a smaller incident with the increase of graphene layers, accompanied by a sharp decline of FWHM. This phenomenon can be applied to develop various OTSs based photoelectric devices. At the same time, with G increases from 0 to 5, the S and FOM of the biosensor gradually increase, as shown in Fig. 6(b). However, the electrical and optical properties of graphene would become very complicated if the number of graphene layers is large. Therefore, we only consider the effect of fewer graphene layers on the performance of the sensor.
Fig. 7. (a) Variations of the reflectance with respect to the incident angle for N=4, 5,6,7,8 and 9. (b) Changes of the S and FOM with respect to the numbers of 1D PC periods.
Furthermore, the number of 1D PC periods N also has an important effect on the spectral and sensitivity of the proposed biosensor, as shown in Fig. 7(a) and Fig. 7(b). With N increases from 4 to 9, the FWHM of the spectral reflectance curves gradually becomes narrower, and the reflectance dip of the composite configuration first decreases and then mounts up. Meanwhile, the increase of N would result in the increase of FOM and sensitivity decreases in Fig. 7(b). Obviously, “ N 6 ”, under current structure parameters, is the demarcation point for the performance of the biosensor. If Nis larger than seven, the reflectance increase would lead to the decrease of the monitoring resolution. Therefore, when N 6 , the biosensor has superior performance in measuring biological medium.
Fig. 8. Changes of S with respect to the thickness of the spacer layer, it particularly shows the variation of the reflectance with respect to the incident angle for
ns =1.410 and 1.415.
The characteristics of the spacer layer (also known as the sensing medium) in the configuration have a strong influence on the excitation of OTSs. Therefore, the integral sensitivity of the biosensor is highly susceptible to the thickness and refractive index of the sensing layer, as shown in Fig. 8 and 9, respectively. According to Fig. 8, as the thickness of the sensing layer increases from 312 m to 400 m , the sensitivity of the structure is decreasing. Specifically, when the thickness of the sensing layer goes below 312 m , the sensitivity of the biosensor sharply declines to near zero. When the thickness of the sensing medium satisfies d s 312.3 m , we can calculate the maximum difference of the resonance angle ( 2.5897 ) and the O
highest sensitivity (Smax= 517.9 / RIU ) of the biosensor. In the mean time, the FWHM of the reflectivity curve corresponding to ns 1.410 is 2.346, and we have
DA=1/FWHM=0.430 and FOM=S DA= 222.9RIU-1 . Therefore, in order to ensure the high S of the sensor, the thickness of the sensor layer should be set between 312 m and 318 m .
Fig. 9. Changes of S with respect to the refractive index of the spacer layer. It specifically shows the variations of the reflectance with respect to the incident angle for
ns =1.700 and 1.705.
Meanwhile, in order to determine the detection range of the refractive index for the biosensor, the variation of the S with respect to different refractive indexes of the sensing layer is discussed, as shown in Fig. 9. It is clearly shown that the S of the biosensor gradually decreases as the refractive index of the sensing medium increases from 1.410 to 1.700. In the refractive index range of 1.410 to 1.425, the S of the biosensor can reach more than
500 / RIU .When the refractive index of the
sensing medium is 1.700, the S is 67.19 / RIU . Simultaneously, it is found that the larger the refractive index of the sensing medium the greater the resonance angle corresponding to the dip (the reflectance curve shifts toward right). Therefore, it is verified that the sensor offers a wide range of refractive index measurements (1.40~1.70) for measuring the refractive index of the sensing medium.
4. Conclusions In summary, we proposed a novel THz optical biosensor using the graphene-based DBR structure to excite OTSs, and analyzed how the performance of the biosensor was affected by the Fermi energy, the dielectric relaxation time, the number of layers of graphene, the number of 1D PC periods, and the thickness of the spacer layer. We
can adjust the voltage on the graphene and the thickness of the spacer layer to obtain the highest sensitivity when using the biosensor to detect biological analyte with different refractive index. The simulation results showed that the sensitivity and FOM of the biosensor could reach as high as 517.9 / RIU and 222.9RIU-1 , respectively. The theoretical analysis of the electric field distribution in the proposed structure also verified the high sensitivity of the biosensor. Finally, the relationship between the performances (sensitivity and FOM) of the biosensor and the parameters (refractive index and thickness) of the sensing medium are discussed. We believe this novel optical biosensor has an excellent application prospect in optical detection, biological information detection and other related fields.
Acknowledgments This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 61772197) and the Hunan Provincial Natural Science Foundation of China (Grant Nos. 2019JJ70087).
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Highlights 1.
We propose a novel terahertz biosensor based on optical Tamm states in graphene-based
Bragg reflector.
2.
The sensitivity and figure-of-merit of the biosensor can reach more than 500°/RIU and 200
RIU-1 , respectively. 3.The sensitivity and figure-of-merit of the proposed biosensor can be improved by adjusting the applied voltage and other parameters of the biosensor. 4.The biosensor has a wide range of refractive index sensing range (1.40~1.70).