Modeling and Proposal of a Black Phosphorus-based Nanostructure for Detection of Avian Inuenza Virus in THz Region

: In this paper, a multilayer/monolayer black phosphorus (BP)-based nanostructure is presented to detect the avian influenza virus. The nanostructur is a grating arrangement made of BP over SiO 2 or Al 2 O 3 substrate. To achieve the transmission spectrum, depend on the changes in the lateral length of BP, namely (L = 100, 150, 170 nm) as well as the complex refractive index of each of three viruses types (H1N1, H5N2, H9N2) in the THz range, the structure is numerically simulated by 3D Finite Difference Time Domain (3D-FDTD) method. The change in resonance frequency is greater for the H9N2 virus because the real part of its refractive index is relatively larger. Here, too, the rate of change is examined based on the different thicknesses of the H9N2 virus. Also, changes in the refractive index of the environment have been used to calculate important parameters in the sensors, such as sensitivity, FWHM, and figure of merit. Overall, this platform provides a promising platform for detecting influenza viruses.

situations where a high on-off current ratio and intense light-material reactions are needed [23][24][25][26]. In contrast, TMDs such as MoS2, MoSe2, and MoTe2 have a limited bandgap of 1 to 2 ev, they have a high on-off current ratio, however, the narrow range of the bandgap and their low mobility may prevent their use in many fields (Such as FETs and IR optoelectronics) [27]. One another 2D material is BP that shows a direct and adjustable bandgap that depends on the number of layers (For example, bulk 0.3 ev, two layers 1.88 ev, single layer 2 ev) [28]. Thus, single-layer BP as an option for bandwidth optical applications the infrared and terahertz spectra are considered [27]. Therefore, as a plasmonic platform, it enables atomic-scale thin BP to confine plasmons in a very small amplitude and increase lightmater reactions [29]. Due to the mobility carrier 1000 cm 2 V -1 s -1 and the bandgap of 0.3 ev, BP can be used as a suitable option for the design of absorbers [30]. 2D BP has strong anisotropic electrical and optical properties in the plane. Both single and multi-layer BP shapes make it an ideal semiconductor device for various applications, like efficient photo-electrical conversion and ultra-light emission, due to its adjustable direct bandgap. As the number of layers increases, the interactions within the layers are determined. Single-layer / multi-layer BP has a high bandgap value compared to its balk shape. The basic optical properties in anisotropic light absorption such as their narrowdirected bandgap, excitation effect, photoconductivity is usually determined by measuring their linear absorption, while under adjustable optical properties, the desired feature for their photonic devices and semiconductors are considered [31].
In this regard, researchers have proposed many structures based on BP. In 2018, Paul et al. proposed a BP-based biosensor to detect DNA hybridization that exhibits 125º/RIU sensitivity, 0.95 detection accuracy, and 13.62 RIU -1 quality factor [32]. In 2019, a gas sensor structure was proposed by Singh et al. to increase the surface plasmon resonance sensitivity [33]. In the same year, a BP-JL-RC-MOSFET biosensor was introduced by Kumar et al. for electrical detection of biomolecules of deadly diseases [34]. For the ultrasensitive detection of human neuron-specific enolase cancer biomarkers, the first BP-fiber-optic biosensor was proposed by Zhou et al. in 2019 [35]. Jia et al. presented a highly sensitive plasmon biosensor through vertically stacking halloysite nanotubes (HNTs). The HNTs-MoS2 composite layer dramatically increases the long-term stability of BP as well as the angular and phase-detection sensitivities due to its thickness of several hundred nanometers [36]. Recently BP-TMDC based SPR biosensor was investigated by Sarika et al. the sensitivity of the proposed biosensor with Si, BP with TMDCs is better than the results achieved for Si-graphene and Si-TMDCs based SPR biosensor [37].
Despite the excellent applications of BP in the above articles, but three types of Influenza viruses, H1N1, H5N2, and H9N2, have been less studied by research groups. One of the main pathogens between humans and other species that cause seasonal epidemics each year is the Influenza A Virus (IAV). H1N1 is one of the subtypes of IAV, the influenza virus H1N1, generally referred to as the "swine flu", in April 2009 spread rapidly around the world. Influenza virus infection occurs by inhaling particles that contain the virus or through contact with infected surfaces, and respiratory infection is characterized via acute symptoms like high fever, lethargy, and cough [38]. Influenza viruses of the H9N2 subset have appeared in various species of poultry in Eurasia and Africa, causing periodic infections in humans and mammals. China can be considered the main center of the H9N2 virus epidemic [39]. H5N2 Influenza virus activity sometimes has been seen in Taiwanese chickens in the last few years. The first outbreak of low-pathogenic avian influenza (LPAI) H5N2 viruses in late 2003 and the second outbreak of LPAI in 2008 was observed. Genetic analysis of the Taiwanese H5N2 viruses shows that their surface protein genes, hemagglutinin (HA) and neuraminidase (NA), were not taken from the source viruses of the Eurasian gene but were closely related during the 1994 outbreak to the H5N2 virus isolated from chicken in Mexico [40]. Therefore, the purpose of this paper is to introduce a biosensor based on the valuable properties of BP for the detection of H1N1, H5N2, and H9N2 viruses. Fig. 1(a) presents the BP nanostructure as a square array of BP as the main cell with a period of P = 200 nm to measure the transmission through a biosensor chip for viruses detection. The square BP array is covered on the SiO2 or Al2O3 substrate. Multilayer/monolayer BP nano-flake has dimensions L×L×d with L = 100, 150, 170 nm, and d = 2 nm, and the distance between the two layers of BP is 1 nm. The top cover viruses is a layer of air. According to the optical properties of BP, using the Drude model, the conductivity of few-layer BP can be defined as follows [41]:

THEORY AND ANALYTICAL TREATMENT
where j (= 1, 2) indicates the direction of x or y, and Dj is the weight of Drude model along the j-axis, equal to πe 2 nsj/mj. Also, ηe and ω represent the scattering rate and frequency of the incoming light, respectively. Finally, m1 and m2 are the electron effective masses near the Γ point which can be written as follows using the Hamilton model.
The electronic density of BP, ns, with thickness of d is calculated as [30]: where kB is the Boltzmann constant, T is temperature, and Ef -Ec is the relative Fermi energy level. Using a layer of phosphorene with volumetric anisotropic permittivity, 2D surface conductivity can be expressed as 3D surface conductivity through the relation of 2D 3D d     . This allows the relative permittivity diagonal tensor εD (ε11, ε22, ε33) to be defined for BP with thickness of d. The permittivity of a 2D-BP can be calculated by [42,30]: The value of the BP collision frequency, γbp of Drude model in the infrared range is approximately equal to ηe/ℏ, and the z component is ε33 = εr = 5.76, for 2D-BP. The real and imaginary parts of the relative permittivity components are shown in Fig. 1(b). According to it, the real part of the permittivity components at the wavelength of 5 µm has a greater value than at the wavelength of 15 µm. In the imaginary part, on the other hand, the components of the relative permittivity act inversely to the real part. The properties of BP surface plasmon in nanostructure BP can be expressed by the coupled-mode theory (CMT) method according to Fig. 1(c). Also, the incoming and outgoing light waves S±, in(out) are shown in Fig. 1(c). When the incoming light wave S+,in passes through the BP grating, according to the SPR effect the energy can be coupled to the BP grating. BP surface plasmon resonance modes are inspired by the BP grating region am (m = 1,2) due to the energy range, where am is the m th mode of the resonance modes with resonant frequency ωm. To calculate the absorption coefficient, we first need to calculate the transmission and reflection coefficients, t(ω, Ef) = S+,out/S+,in and r(ω, Ef) = S-,out/S+,in of BP gratings plasmonic, respectively, that can be obtained from the following equations [30]: As a result, the absorption efficiency in the light spectrum is defined as follows: 1/τωm and τωm show the decay rate and the lifetime, respectively, due to the energy coupling of each mode in the light field. Also, 1/τim and τim determine the decay rate and lifetime, respectively, due to inherent losses of m th mode in BP grating. The coupling coefficient between two resonance modes is μpq which can be considered as χ1 = iµ12 and χ2 = iµ21. On the other hand, χ1, χ2, τm, τim and ωm are used to describe the absorption coefficient of BP absorption equation, A(ω).
For identifying viruses, each of these three types of viruses has a complex refractive index of N = αn+iβκ, while α and β are the frequency-independent parameters in the range of 1-1.4 for n and 1-2 for κ and also identify the different types of viruses and protein concentrations. Finally, n and κ are the real and imaginary parts of the dielectric constant that can be extracted using the following relations [43].
where ωp and γ have a same value, equal to 4 THz.

RESULTS AND DISCUSION
The three-dimensional Finite Difference Time Domain (3D-FDTD) method is used in our simulations with the perfectly matched absorbing boundary conditions for the below and top of the computational space along the zdirection, and the periodic boundary conditions for the both x and y-directions. A single unit cell is considered in our 3D simulations. According to Table 1, the total protein concentration and complex refractive index of three Avian Influenza virus samples are measured by advanced biochemical measurements. The three Avian Influenza virus subtypes are H5N2, H1N1, and H9N2. When the light is coupled vertically to the nanostructure BP-based, a propagating wave is generated in the BP flake with an effective wavelength, corresponds to the grating period. If the wavelength of the incoming light is proportional to the grating period, the surface plasmon resonance can be stimulated. To investigate the optical properties of the square array of the BP flake, the light transmission and absorption spectrums for the proposed nanostructure with two different SiO2 and Al2O3 substrate, when the BP length, L, is equal to 150 nm are plotted in Fig. 2(a) and (b), which have been investigated by the 3D-FDTD simulation method. From these figures, it is clear that there are two resonance frequencies, in which the power transmission is decreased dramatically. In other words, in these two wavelengths, surface plasmons are created and incident power is absorbed by the surface plasmons. When the substrate layer is SiO2, the two surface plasmons are created at about 4.5 µm and 9 µm respectively. For the Al2O3 substrate, the surface plasmons are created at wavelengths of 5 µm and 15 µm. Any physical change in the proposed nanostructure, like variation in the BP length or environment refractive index, can change the wavelength of surface plasmons or intensity of the transmission spectra. Therefore, the proposed device works as a refractive index biosensor which can detect different Avian Influenza viruses (H5N2, H1N1, and H9N2). Using the L parameter of the proposed structure, the intensity, wavelengths, and amplitudes of the resonance peaks can be adjusted. Therefore, to further investigate the BP surface plasmon in nanostructured, transmission spectra of the two surface plasmon resonance modes with different lengths (L = 100, 150, 170 nm) over SiO2 substrate are simulated and presented in Fig. 3. Longer length leads to higher wavelength surface plasmon resonance and larger light absorption value. In the following section, light transmission spectra with three specific virus samples in the biosensor structure, when the length of BP equal to 150 nm with SiO2 and Al2O3 substrate versus wavelength range from 0.35 to 20 µm are examined. The thickness of the desired layer is considered to be 2 µm to calculate the transmission spectrum for each of the three virus samples. In this case, the first resonance peaks for SiO2 and Al2O3 is happened at frequencies of 64.86 THz and 61.538 THz, respectively. Fig. 4(a-b) shows the light transmission spectrum for the three H1N1, H5N2, H9N2 virus samples at L = 150 nm, and the SiO2 and Al2O3 substrate. As it is clear, the magnitude of transmission for viruses H1N1 and H5N2 is slightly higher than for virus H9N2 and the rate of variation in the resonance frequency for H9N2 virus is higher than that of the two other viruses, H1N1 and H5N2. This can be attributed to the fact that the real part of the H9N2 virus refractive index has a larger amount than the two other viruses. Also changing the analyte virus types changed the frequency of surface plasmon resonances. Al2O3 substrate.
In one study, Cheng et al. [43] examined that the size of viruses can be selected from 1 to 8 µm. Here, we express the volume of the virus by the amount of thickness on the surface of the sensor. In Fig. 5(a-b), for different thicknesses of the H9N2 virus samples from 1 to 4 µm, the transmission spectrum diagram is shown for L = 150 nm over SiO2 and Al2O3 substrates. As can be seen in the figures, increasing the analyte thickness, increase the amplitude of the transmitted light, so that higher transmission is achieved at higher thicknesses of AI. Refractive index measurement applications are one of the most important applications of BP-based nanostructures.
The proposed structure is able to detect the refractive index of its surroundings. This nano-biosensor is very sensitive to the refractive index of the environment. The sensitivity of a biosensor is the ratio of the frequency at resonance peak shift to the change of the refractive index of the environment and is described by the relation [43]: S n     (9) Other important parameters in nanosensors are full width at half maximum (FWHM) and figure of merit (FoM = S/ FWHM). Therefore, in the following section, a table related to the behavior of the proposed structure when L is equal to 150 nm in two cases of SiO2 and Al2O3 substrates, is presented to show the sensitivity, FWHM, and FoM of the different refractive indexes of the surrounding medium is examined. We first examined the structure using different refractive indexes of the environment. Fig. 6(a-b) show the transmission spectra of the proposed BP-based biosensor for different refractive indexes. It is clear that the surface plasmon resonance wavelength increases as the refractive index increased. According to these graphs, a table related to the sensitivity, FWHM, FOM values is created.   In the following, the results are achieved when the BP is monolayer. As can be seen in Fig. 7(a), the light transmission spectra for two different substrates, SiO2 and Al2O3, has only one surface plasmon resonance, at about 9 µm and 15 µm wavelengths, respectively. Also, when the environment refractive index, n, increased, the surface plasmon resonance has a red shift. According to Table. 3(a), for example, the maximum sensitivity, FWHM, and FoM for the case of SiO2 at n = 1.3 is equal to 1.06 THz/RIU and 6.355 THz, 0.166, respectively. Despite this, by increasing the value of n for the case of Al2O3 substrate, the frequency of resonance peak, increases and causes the creation of a negative sensitivity.

CONCLUSIONS
In this paper, we propose a BP-based nanostructure (monolayer/multilayer) as a suitable structure for the detection of avian influenza viruses (H1N1, H5N2, H9N2) that have different refractive index values. We observed that the resonance frequency of the nano-biosensor changes for different lengths of BP (L = 100, 150, 170 nm) and (SiO2 and Al2O3) substrates. By placing the avian influenza viruses, the resonance frequency changes, so we can detect them by considering the variation in the resonance frequency change. The change of the resonance frequency of H9N2 virus is greater, due to the greater amount of the real part of its complex refractive index than the other avian influenza virus subtypes. It can be concluded that the real part of the virus refractive index is related to the resonance frequency and the imaginary part is related to the rate of virus transmission in the spectrum responses. In addition, in the proposed nanostructure, we examined the rate of transmission based on the different thicknesses of H9N2 virus. As the thickness of H9N2 virus increases from 1 μm to 4 μm, the amount of transmission increases. We also examined important parameters of the sensors such as sensitivity, FWHM, and FOM. According to these parameters, we can also use of this sensor for refractive index sensing. Overall, introduced BP nanostructure-based THz sensing, can provide a quick solution for the detection of avian influenza viruses by a label-free manner.