Ultra-high-sensitive biosensor based on SrTiO<sub>3</sub> and two-dimensional materials: ellipsometric concepts

Mohammad Javad Haji Najafi Chemerkouh; Mohammad Javad Haji Najafi Chemerkouh; Seyedeh Bita Saadatmand; Seyedeh Bita Saadatmand; Seyedeh Mehri Hamidi

doi:10.1364/OME.457983

1. Introduction

During the past years, surface plasmon resonance (SPR) based sensors, a type of optical sensor, have been investigated intensely due to their wide variety of applications like gas detection [1], biomolecules detection like DNA and RNA [2–4], bacterial [5,6], etc. SPR based biosensors bring us excellent features like high sensitivity, being label-free, versatile, and providing real-time detection [7]. Because these surface waves cannot be excited by a 3D beam directly, utilizing different techniques like Kretschmann configuration (prism-based excitation), grating coupling, fiber coupling, and near field excitation can help us excite these types of helpful surface waves [8]. Among them, Kretschmann configuration-based SPR biosensors are mainly used ones in which a prism coated by a noble metal like gold or silver can be used to create evanescent waves (Fig. 1) [5,9]. These waves can penetrate the sensing medium in which they can interact with the analytes. Any changes in the sensing medium, here the refractive index (RI) of the sensing medium, can change the excitation's propagation constant, which in turn can be sensed by using the reflectance of the TM polarized (R_p) incident beam. The reflected light has a dip in the angle or wavelength of the resonance. As the RI of the sensing medium changes, the dip in the reflectance spectrum changes.

Fig. 1. Schematic diagram of our Proposed SPR biosensor.

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As discussed, SPR based sensors are so sensitive to any change in the sensing medium; however, many efforts have been made to increase the efficiency and sensitivity of these sensors and eliminate some problems in the sensor’s structure [10–25]. Ag can be oxidized if it is exposed to the air, but Au has more stable chemical stability. Nevertheless, Au has a poor absorption to biomolecules if the SPR sensors are intended to be used in sensing biomolecules. Using graphene and graphene oxide can mitigate this problem and it can help increase both the efficiency and sensitivity of the SPR based biosensors [15,16]. Graphene can provide better absorption of biomolecules than bare Au due to its π-π interaction with biomolecules. So, graphene can improve the sensor’s efficiency, and its physical properties can increase the sensitivity of the SPR sensor [15]. Also, using graphene with conventional SPR sensors can increase the charge carriers on the sensor’s surface, leading to enhancing the electric field, which can increase the sensor's sensitivity [17]. It has been shown that using graphene can improve the sensitivity of the conventional SPR sensor (prism/Au structure) by about 25% [15]. In a more recent work, N-FK51A/Ag/Graphene (N-FK51A is a prism with refractive index of 1.48 at 633 nm) structure have been used for detecting the waterborne bacteria. This SPR-based sensor yielded the sensitivity of about 221.63 °/RIU and 178.12 °/RIU for Escherichia coli and Vibrio cholera bacteria, respectively [26].

Besides, MX₂ Materials- like MoS₂, WS₂, MoSe_2, and WSe₂- have outstanding features -like large bandgap, large work functions, and high optical absorption- that make them suitable for electronics, photonics, and even biomedical applications [18–25]. For example, MoS₂ has been used in the nano-transistor to achieve a high switching ratio [18]. Studies showed that WS₂ showed better performance than MoS₂ when intended to be used in the nano-transistor’s channel because WS₂ provide better carrier mobility since WS₂ has lower electron effective mass than MoS₂ [20]. Moreover, MX₂ materials can also increase the sensitivity of the conventional SPR-based biosensors both as an interlayer and as a biomolecule recognition element (BRE) [20–25]. Monolayers MoS₂ and WS₂ with the RI of 5.0805 + 1.1723i and 4.8937 + 0.3124i, respectively, used as an interlayer- with structure of SF10/Gold/MoS₂/Graphene and SF10/Gold/WS₂/Graphene- and they improved the sensitivity of the SF10/Gold/Graphene from 80.70 °/RIU to 87.80 °/RIU and 95.71 °/RIU, respectively. This is due to the fact that MoS₂ and WS₂ have larger band gap than graphene and they can provide higher carrier concentration; therefore, the successful electric charge transfer will further enhance electric field in sensor’s surface which in turn it cases improvement in sensor’s sensitivity to target biomolecule. In other word, lower concentration of biomolecule can create better perturbation as compared to Ag/Graphene structure. Based on the results, WS₂ provide better sensitivity than MoS₂ when it comes to enhancing the SPR sensor sensitivity [25]. The reason for this issue will be discussed later in this manuscript.

Using 2D materials as an interlayer can be helpful if the metal coated on the hypotenuse is gold because it can be transferred on the Au surface after deposition in a different medium. In order to use Ag as noble metal on the prism’s hypotenuse, practically, a thin film is needed to be deposited in a sputtering or PVD chamber after deposition of Ag, without breaking the vacuum. Therefore, using a suitable thin-film material on the top of the prism/Ag not only can be an interlayer which in turn can increase the sensitivity, but it also can act as an Ag protector [27]. Many materials have been used as an interlayer to enhance the sensitivity of the biosensors [21,24,25,28–30]. ZnO sandwiched between prim and Au thin film showed it could improve the sensitivity of the conventional SPR sensor up to 187 °/RIU [28]. Barium titanate or BaTiO₃ is another material that has been used not only to enhance the sensitivity of the SPR biosensor but also can act as an Ag protector [29]. Using BaTiO₃ yielded a sensitivity of about 257 °/RIU, which is much higher than the conventional SPR biosensors [29]. Also, silicon can be used as an interlayer in order to enhance the sensitivity of SPR based sensors for detecting the Chikungunya Virus [31]. In this work by using the N-FK51A/Ag/Graphene the sensitivity of about 393 and 160 for detection of platelets and plasma cells have been achieved, respectively [31]. However, there is a need to enhance the SPR biosensors’ overall performance by utilizing more suitable interlayers and finding an approach to improve FWHM.

Oxide of the strontium and titanium, strontium titanate or SrTiO3 (STO), has a perovskite structure at room temperature, which has been used for many applications like improving the performance of the photocatalysis process [32]. STO would be a good candidate for being an interlayer due to its suitable RI since it does not have the imaginary in its refractive index. A higher extinction coefficient means higher loss and a broader spectrum of the SPR. As a result, a higher imaginary part impairs the quality factor of the SPR sensor, which in turn decreases the overall performance of the sensor. Due to the above-mentioned reasons, STO would be a good candidate since the imaginary part of its refractive index is zero. Furthermore, using STO as an interlayer increases the electric field at the sensor surface. This means further enhancement in electric field which turn lead higher sensitivity to targets molecule. SPR sensors based on STO have not been investigated combined with graphene and MX₂ materials yet.

By adding 2D materials, the reflectance spectrum will be broadened due to the excess extinction coefficient of these materials. As a result, the FWHM of the reflectance curve increases, so the SPR biosensors’ performance will decrease because of a decrease in quality factor. To solve this problem, we can use the Ψ, which can be calculated using the ellipsometry approach, a powerful tool for the morphological study of a sample and characterizing thin films [33–36]. Ellipsometry is an optical measurement technique that can characterize light reflection (or transmission) by measuring the change in the polarization state of the incident light. If a linearly polarized light, of a known orientation, is reflected from a sample, the reflected light would be elliptically polarized. The shape and orientation of the ellipse depend on the reflection properties of the surface, the direction of the incident polarized light, and the angle of incidence [35]. Therefore, using the information provided by the reflection, Ψ (ratio of the p-polarized and s-polarized reflection lights) and Δ (phase difference between p-polarized and s-polarized light) can be calculated from ellipsometry measurement (Theoretical information is provided in Materials and Method, section 2). As a result, by having the Ψ and Δ, the refractive index of the materials can be achieved. In SPR based sensors applications, using the Ψ instead p-polarized reflectance not only shows a better quality factor but is also an identifier of the reflectance the of incident TM-polarized beam [33]. Furthermore, using Δ combined with SPR biosensors can bring us ultra-high sensitivity because Δ, calculated from ellipsometry, is very sensitive to any change in the sensor's surface.

In this work, we represent a Kretschmann configuration-based SPR biosensor combined with STO-as an interlayer-, Graphene, MoS₂, WS₂, MoSe_2, and WSe₂. The performance of the Prism/Ag/STO/2D materials structures has been evaluated. Results show that using STO as an interlayer improves the sensitivity of the conventional SPR sensors. The highest sensitivity is 409 °/RIU for 40nm thickness of Ag and 14 nm thickness of STO, which is 250% more than the conventional SPR based sensors. However, in biosensors application, graphene is needed to enhance the adsorption of biomolecules to the sensor's surface. Using STO/Graphene yielded 333.2 °/RIU sensitivity, 187% more than the conventional Ag-based SPR biosensor and higher than the same class of proposed structures. Furthermore, we further improved the quality factor and especially the sensitivity of the proposed SPR biosensor by using ellipsometry parameters.

2. Materials and methods

The proposed sensor is based on the Kretschmann configuration shown in Fig. 1. We use the angle interrogation method in a constant incident wavelength. We can sweep the angle to find the resonance angle, which can be detected as a dip in the reflectance spectrum. To obtain the reflectance (R_p), the Transfer Matrix Method (TMM) for the N-layer system has been used [33,37]. Since TMM does not use any approximation, this method is efficient. By using TMM we can calculate the response of a N-layer structure to an incident wave which is a perfect and common approach for calculating the reflectance in prism-based SPR sensors. The tangential fields in the final boundary region are related to the first boundary fields by $\left[ {\frac{{{U_1}}}{{{V_1}}}} \right] = {M_{ij}}\left[ {\frac{{{U_{N - 1}}}}{{{V_{N - 1}}}}} \right]$; where U₁ and V₁ are tangential components of electric and magnetic fields in the first boundary and U_N-1 and V_N-1 are the electric and magnetic fields in the Nth layer. M is the characterization matrix of the whole structure. The reflectance (R_p) can be determined as [37]:

(1)$$R = {\left|{\frac{{({M_{11}} + {M_{12}}{q_N}){q_1} - ({M_{21}} + {M_{22}}{q_N})}}{{({M_{11}} + {M_{12}}{q_N}){q_1} + ({M_{21}} + {M_{22}}{q_N})}}} \right|^2}$$

in which

(2)$${M_{ij}} = {\left( {\prod\limits_{k = 2}^{N - 1} {{M_k}} } \right)_{ij}}{,^{{{^{}}_{}}_{}^{}}}i,j = 1,2,\ldots $$

where

(3)$${M_k} = \left[ {\begin{array}{cc} {\cos {\beta_k}}&{ - i\sin {\beta_k}/{q_k}}\\ { - i{q_k}\sin {\beta_k}}&{\cos {\beta_k}} \end{array}} \right],$$

(4)$${\beta _k} = {d_k}\left( {\frac{{2\pi }}{\lambda }} \right){({\varepsilon _k} - n_1^2{\sin ^2}\theta )^{{1 / 2}}}$$

(5)$${q_k} = \frac{{{{({\varepsilon _k} - n_1^2{{\sin }^2}\theta )}^2}}}{{{\varepsilon _k}}}$$

where θ is the incident angle, λ is the incident wavelength which is 633nm. The reason for choosing the 633 nm is to enhance the sensitivity with minimal Kerr effect [24]. The thickness and RI of the kth layer have been shown by n_k and d_k, respectively, and k = 2 to N-1. The first layer is the prism, BK7, and the last layer (kth) is the sensing medium. The RI of the BK7 can be calculated using Eq. (6) [12]:

(6)$${n^2} - 1 = \frac{{\textrm{1}\textrm{.03961212}{\lambda ^2}}}{{{\lambda ^2} - \textrm{0}\textrm{.00600069867}}} + \frac{{\textrm{0}\textrm{.231792344}{\lambda ^2}}}{{{\lambda ^2} - \textrm{0}\textrm{.0200179144}}} + \frac{{\textrm{1}\textrm{.01046945}{\lambda ^2}}}{{{\lambda ^2} - \textrm{103}\textrm{.560653}}}$$

where λ is in µm. At 633 nm, the RI of the BK7 is 1.5151 and the RI of the sensing medium will change from 1.33 for deionized water (DI water) to 1.335 when the bioreceptors and target analytes are introduced into the sensing medium.

The RI of the Au or Ag can be calculated using the Drude-Lorentz model [12]:

(7)$${n_m} = {\left[ {1 - \frac{{{\lambda^2}{\lambda_c}}}{{\lambda_p^2({\lambda_c} + i\lambda )}}} \right]^{0.5}}$$

where λ is the incident wavelength, λ_c and λ_p are the collision and plasma wavelengths which are 1.4541×10⁻⁷m and 1.7614×10⁻⁵ m for Ag, 8.9342×10⁻⁶m and 1.6826×10⁻⁶ for Au, respectively [12].

At 633nm, the RI of the STO, MoS₂, WS₂, MoSe₂ and WSe₂ are 2.38, 5.0805 + 1.1723i, 4.8937 + 0.3124i, 4.6226 + 1.0063i, and 4.5501 + 0.4332i, respectively [12].

The Thickness for MoS₂, WS₂, MoSe₂ and WSe₂ are 0.65 nm, 0.8 nm, 0.7 nm, and 0.7 nm, respectively [12].

Single layer graphene has a thickness of 0.34 nm, and its RI can be calculated using the equation [15]:

(8)$${n_g} = 3 + i\frac{{{C_1}}}{3}\lambda$$

where C₁= 5.446 um^-1 and is a constant. λ is the incident wavelength in um. Using Eq. (8), at 633 nm, n_g= 3 + 1.1487i.

Equations (1–(5) are for calculation of R_p; however, they remain the same for calculation R_TE (or R_s) but Eq. (5) changes to [37]:

(9)$${q_k} = {({\varepsilon _k} - n_1^2{\sin ^2}\theta )^{1/2}}$$

For evaluating the performance of the SPR based sensors, the most critical parameters are sensitivity (S) and quality factor (QF).

Sensitivity is equal to the ratio of the change in resonance angle $\Delta \theta$, before and after introducing the biomolecules, to change in the RI of the sensing medium $\Delta n$. So the unit of S would be °/RIU and it is equal to:

(10)$$S = \frac{{\Delta \theta }}{{\Delta n}}$$

Quality factor can be defined as:

(11)$$QF = \frac{S}{{FWHM}}$$

As a powerful and non-destructive optical tool, ellipsometry can determine materials characteristics by yielding the real and imaginary part of the refractive index. It is based on the measurement of change in polarization of the incident light. The outputs are Psi (Ψ), the ratio of the Fresnel’s reflection coefficients of the TM polarized wave (r_p) to TE polarized wave (r_s), and Delta (Δ), which is the differential phase change of the TM and TE polarized light [34]. Therefore, Ψ can be calculated as follows:

(12)$$\tan \Psi = \frac{{|{{r_P}} |}}{{|{{r_S}} |}}$$

where r_s,p are the Fresnel reflection coefficient. The reflectance of TM and TE polarized waves (R_p,s) can be defined as ${R_{p,s}} = |{{r_{p,s}}.r_{p,s}^\ast } |$; so ${r_{p,s}} = \sqrt {{R_{p,s}}}$. So Ψ can be calculated using the reflectance form TMM method with the following equation:

(13)$$\tan \Psi = \frac{{|{{R_p}} |}}{{|{{R_s}} |}} \to \Psi = {\tan ^{ - 1}}\left[ {\sqrt {\frac{{{R_p}}}{{{R_s}}}} } \right]$$

In order to calculate Δ, we need to apply the frequency-dependent of our parameters in all equations. Where we have:

(14)$${r_{p,s}}(\omega ) = |{{r_{p,s}}(\omega )} |= \sqrt {{R_{p,s}}} {e^{i{\theta _{p,s}}(\omega )}}$$

We should linearize the above equation to use Kramers–Kronig equation:

(15)$$Ln[{{r_{p,s}}(\omega )} ]= Ln\left[ {\sqrt {{R_{p,s}}(\omega )} } \right] + i\theta (\omega )$$

So by using the Kramers-Kronig relation, we have:

(16)$${\mathrm{\theta }_{\textrm{p,s}}}\mathrm{(\omega )\ =\ -\ }\frac{{\mathrm{2\omega }}}{\mathrm{\pi }}\mathrm{\Phi }\int\limits_\textrm{0}^\infty {\frac{{\textrm{Ln}\left[ {\sqrt {{\textrm{R}_{\textrm{p,s}}}\mathrm{(\omega^{\prime})}} } \right]}}{{{{\mathrm{\omega ^{\prime}}}^\textrm{2}}\textrm{ - }{\mathrm{\omega }^\textrm{2}}}}} \mathrm{d\omega ^{\prime}\ +\ }{\mathrm{\theta }_{_0}}$$

in which θ_p and θ_s are the TM and TE polarized light phases, respectively.

Finally, Δ can be calculated:

(17)$$\begin{aligned} \Delta &= {\theta _p}(\omega ) - {\theta _s}(\omega ) = \\ &- \frac{{2\omega }}{\pi }\Phi \int\limits_0^\infty {\left[ {\frac{{Ln\left[ {\sqrt {\frac{{{R_p}(\omega^{\prime})}}{{{R_s}(\omega^{\prime})}}} } \right]}}{{{{\omega^{\prime}}^2} - {\omega^2}}}} \right]} d\omega ^{\prime} \end{aligned}$$

Using the Ψ and Δ parameters calculated from numerical modeling of ellipsometry can be used in order to enhance the SPR sensors-based performance [33]. Integrated ellipsometry with SPR will increase the sensor sensitivity since the Delta parameter is very sensitive to any change in the sensor's surface. Furthermore, TE polarized light remains unchanged if it’s illuminated to the sensor. Therefore, it can be used as a reference signal to remove the environmental noise, which improves the stability and accuracy of SPR based sensors [17]. So, by using ellipsometry, not only can we improve the SPR based performance, but also we can increase the signal to noise ration (SNR).

3. Results and discussion

A combination of Ag with STO and 2D materials as an SPR sensor is investigated. The thickness of noble metals and STO are optimized to find the best sensitivity. In all structures, a single layer of 2D materials is used to avoid any excess loss, which causes broadening of the reflectance spectrum and degrading the QF [29]. Figure 2 shows the reflectance of the prism/Au or Ag/STO/graphene before and after injecting the biomolecules. After injecting biomolecules, the resonance angles will shift to higher degrees due to the higher RI of the sensing medium. The reason can be found in the propagation constant (${k_{sp}}$) formula, which is:

(18)$${k_{sp}} = {n_p}\frac{{2\pi }}{\lambda }\sin \theta = {\textrm{Re}} \left[ {{k_0}{{\left( {\frac{{n_m^2n_s^2}}{{n_m^2 + n_s^2}}} \right)}^{{1 / 2}}}} \right]$$

where λ is the incident wavelength, ${n_p}$ is the prim’s RI, ${k_0}$ is the propagation constant of the free space, ${n_m}$ is the RI of the metal/interlayer/graphene, and ${n_s}$ is the sensing medium’s RI. Therefore, in each structure, as the ${n_s}$ increases, the resonance angle increases too. From Fig. 2, it is evident that using the STO as an interlayer increase the sensitivity of the conventional SPR biosensor.

Fig. 2. Reflectance (TM polarized) of proposed structures.

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Figure 3(a) shows that using STO integrated with graphene remarkably improves the sensitivity of the conventional SPR biosensor. This is because of the high RI of the STO and enhancement of the electric field in the sensing medium, which in turn increase the sensor's sensitivity. To investigate the most optimized structure, different values for the thickness of the Ag and STO are assessed. So with a fixed thickness of Ag, the sensitivity for different values of STO have been extracted. Then by changing the thickness of the Ag the STO thickness have been swept for obtaining the best sensitivity and optimal structure. Fig.3b shows the sensitivity of structures with varying thicknesses of the metals and STO. As can be seen, with increasing the STO thickness, at the specific value, the sensitivity reaches a maximum value. After that value, since the resonance angle impinges the 90 degrees, it impairs the sensitivity calculation, so there is a limitation here, and analysis stop beyond that thickness. The highest sensitivity is 409 °/RIU for the 40 nm Ag, 14 nm STO without any graphene layer. However, as discussed, a single layer graphene is needed for biosensing applications. In order to find the highest sensitivity of the Ag/STO/SLG structure, thicknesses around the 45 nm Ag have been swept (Fig.3c) since the highest sensitivity in Fig.3b is around 45 nm of Ag. The best sensitivity by using graphene is 333.2 °/RIU for 44 nm Ag, 13 nm STO, and a single layer graphene structure. To our knowledge, these values are the highest sensitivity that has been reported for the conventional Kretschmann-based SPR biosensors. Also, the Au/STO/SLG graphene has been investigated, and the best sensitivity is 264.8 °/RIU for 40nm Au/9nm STO/SLG structure. The Ag-based sensor generally has better sensitivity for the proposed structure due to its higher extinction coefficient and lower real part of the refractive index. So we just bring the results of the Ag-based structures. Table 1 shows the sensitivities for some structures of the Ag-based SPR sensor (Results of the Au based structures are available in the Supplement 1 Table. S2)

Fig. 3. Sensitivity of different Ag/STO based SPR biosensor structures. (a) Ag/STO/SLG sensors sensitivity (b) Just Ag/STO sensor without any 2D materials (c) Optimized sensitivity for Ag/STO/SLG based biosensor (d) the enlarged shape of a part shown by the solid red circle in Fig. 3(c).

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MX₂ materials also can be used in SPR biosensors as a BRE [21]. Table 2 shows the best sensitivity for MoS₂, WS₂, MoSe_2, and WSe₂ based SPR sensors when used as a biomolecule recognition element in our structure (More results are provided in Supplement 1 Tbales. S3 to S6). The highest sensitivity for the proposed structures between MX₂ materials as BRE was 331 °/RIU which is for 45 nm Ag, 11 nm STO and a single layer of WS₂. This is due to the fact that WS₂ has a lower real part in the dielectric constant than MoS₂, so MoS₂ has higher energy absorption as compared to WS₂. However, just a little amount of this energy can be transferred to enhance the evanescent field due to the energy loss since MoS₂ has higher extinction coefficient than WS₂ [20]. Furthermore, since the real part of dielectric constant of the WS₂ is lower than MoS₂, penetration depth of evanescent field in Ag/STO/WS₂ chip is more than Ag/STO/MoS₂ which is a another reason that makes WS₂ a better candidate to enhance the sensitivity [20]. The same explanation can be applied to refer the higher sensitivity of WSe₂ as compared to MoSe₂. The small difference between sensitivity of WS₂ and WSe₂ stem from higher extinction coefficient of WSe₂. It is true that WSe₂ has lower real part of dielectric than WS₂ but it has higher extinction coefficient which indicates that the energy transmission to the sensor’s surface is not efficient as using WS₂ [20].

Sensitivity is the most important parameter in the SPR based biosensors; however, quality factor (QF) also needs to be calculated to investigate the overall performance of the SPR biosensors. The higher quantity of QF, the better performance of the SPR biosensor. Tables 1 and 2 show the FWHM of different proposed structures. QF has been calculated using equations Eq. (11). So, the less FWHM, the better QF. This is rational since a broader reflectance spectrum can hardly identify the exact resonance angle. As mentioned, the highest yielded sensitivity is for the 40 nm Ag and 14 nm of STO without any graphene layer. This structure has the highest QF between other calculated chips, so this structure is the best structure for sensing with angle interrogation using our proposed structure. For biosensing applications (structures that have 2D materials), however, there is a tradeoff between proposed structures when it comes to considering both the sensitivity and QF. Therefore, depending on the application, one can use arbitrary structure. Nevertheless, there is a slight difference between some sensitivity and quality factors. The structures in the Tables 1 and 2 are the most efficient ones.

Table 1. Performance of some of the proposed SPR biosensors using SLG as a BRE.

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Table 2. Performance of some of the proposed SPR biosensors using MX2 materials as a BRE.

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Adding the 2D materials decreases the QF amount because of the extinction coefficient of the 2D materials, which increases the energy loss. To improve the FWHM and QF, the Ψ parameter from the ellipsometry calculation can be helpful. The ratio of the R_p to R_s has a narrower spectrum than the R_p itself while representing the resonance angle, so Ψ can be used instead of R_p (Fig. 4). As can be seen in Fig. 4, the resonance angle or the turning point is the same in Ψ and R_p.

Fig. 4. Rp and Rs and ellipsometry parameters Ψ and Δ related to 44 nm Ag/13 nm STO/SLG structure.

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Table 3 shows the FWHM and QF of the Ψ for some structures in Tables 1 and 2. Using the Ψ can improve the quality factor of the SPR based biosensor. For the proposed design, using Ψ enhance the quality factor by about 53% for 44 nm Ag/13 nm STO/SLG, the structure with the highest sensitivity using the angle interrogation method.

Table 3. Quality factor of some structures in Tables 1 and 2 enhanced by using the Ψ.

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The Delta (Δ) calculated in the ellipsometry approach is very sensitive to any slight change in surface of the proposed sensor such as biomolecules concentration. Figure 4 shows a sharp change in Δ in the resonance angle or turning point of the Ψ, which is the inflection point of the Delta spectrum. This abrupt change can be useful in biosensors when it comes to sensing a very small change in the RI of the sensing medium because we can use the differential phase. It means, in our work, to use ellipsometry as a potential phase sensitivity enhancer, we subtract the Δ spectrums of injecting biomolecules (Δ_b) from water’s Δ spectrum (Δ_w), which is the reference medium (Δ_d=Δ_b-Δ_w). This subtraction will yield a peak. Using the maximum of the Δ_d, we can measure the maximum phase difference after injecting analytes in the sensing medium (Fig 5). By using the ratio of the maximum value of the Δ_d to the change in RI of the sensing medium (Δn_s), we define Δn_s= 1.335. We can determine the phase sensitivity (S_Δ) as follows:

(19)$${S_\Delta } = \frac{{\max ({\Delta _d})}}{{\Delta {n_s}}}$$

Figure 5 shows the Δ_d for the 44 nm Ag/13 nm STO/SLG structure with different refractive indexes. For this structure, changing the RI of the sensing medium from 1.33 to 1.3301 will yield a 0.033° phase change with the angle interrogation method; however, by using Δ_d, the phase change is 2.4050. Therefore, the sensitivity increases more than 72-fold. Moreover, this structure is not the optimized structure for phase measurement (in numerical modeling of ellipsometry). Table 4 shows the phase change of some optimized and efficient structures using the ellipsometry method (more data is available in the Supplement 1 in Tables S7 to S9). For instance, for Ag-based biosensors, one of the most sensitive structures is 47 nm Ag/7 nm STO/SLG with 152.13° phase change, yielding 30426 °/RIU sensitivity for 0.005 change in RI of the sensing medium. This is more than 91-fold sensitivity enhancement as compared to the sensitivity that yielded with our proposed structure using the angle interrogation method which is about 9000% of enhancement. Compared with conventional Ag-based SPR biosensors, this enhancement is about 262-fold which is significant. Another important point from Table 4 is enhancing phase sensitivity by using graphene and other 2D materials. For the 47 nm Ag/7 nm STO/SLG structure, using SLG improves the phase change from 79.45° to 152.13°, which is about 91.48% of enhancement. This enhancement varies depending on the structure since Δ is so sensitive to the physical properties of the sensor.

Fig. 5. Differential phase (Δd) of 44 nm Ag/13 nm STO/SLG structure.

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Table 4. Phase change and sensitivity using Δ calculated from numerical modeling of ellipsometry.

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Therefore, using ellipsometry not only can enhance the QF of the SPR biosensors, but it only can increase the phase sensitivity of these types of biosensors. Optimizing structures produced the 32140 °/RIU sensitivity with 42 nm of Ag/6 nm of STO/a single layer of MoS₂ system, which is 96 times more than the 333.2 °/RIU sensitivity, obtained by the angle interrogation method, which is tremendous enhancement. Moreover, 32140 °/RIU is about 277-fold of the conventional Ag-based SPR biosensor sensitivity.

Comparing to other related research can shed light on the importance of our proposed method. Table 5 shows the results of other works in the same class of our presented structure. In the angle interrogation method, we improved the sensitivity as compared to other works. This enhancement of sensitivity is more obvious and dramatic by using the integrated ellipsometry and SPR biosensor method.

Table 5. Comparison of the sensitivity of SPR based sensors with the proposed work

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4. Conclusion

A high-sensitive SPR biosensor is investigated based on 2D materials with the angle interrogation method and integrated ellipsometry SPR approach. It is shown that using STO as an interlayer can protect the Ag from being oxidized and significantly increase the conventional SPR sensor and biosensor sensitivity. The high sensitivity of 333.2 °/RIU, utilizing Ag/STO/SLG structure, and 409 °/RIU, for Ag/STO, optimizing the thickness of silver and STO have been yielded, which are 187% and 252% more than the sensitivity of the conventional SPR biosensor, respectively. The quality factor of the proposed SPR biosensor is improved with Ψ, which can be calculated with numerical modeling of ellipsometry. Furthermore, ultra-sensitive ellipsometry integrated with SPR biosensor showed that with using Δ, the sensitivity of more than 32000 °/RIU can be yielded, which is 270-fold more than the conventional Ag-based biosensor. As a result, Ag-based SPR biosensor performance has been enhanced dramatically. Our ultra-high-sensitive approach can be used to measure a very slight change in biomolecules samples and has a wide variety of biomedical applications like DNA and RNA (or any other analytes) detection, biomolecules interaction analysis, environmental monitoring, and food safety.

Disclosures

The authors declare no conflicts of interest.

Data availability

No data were generated or analyzed in the presented research.

Supplemental document

See Supplement 1 for supporting content.

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Thickness of Ag (nm)	Thickness of STO (nm)	Number of SLG layers	FWHM(°)	S (°/RIU)	QF (1/RIU)
35	13	1	8.48	263.6	31.10
35	14	1	8.22	326.8	39.76
40	13	1	7.63	316.6	41.50
40	14	0	6.82	409	59.97
44	13	1	7.18	333.2	46.41
45	11	1	5.99	237.8	39.70
45	13	1	7.09	330.2	46.57
50	12	1	6.25	310.6	49.70
50	13	1	6.74	277.4	41.16

Thickness of Ag (nm)	Thickness of STO (nm)	Single layer of MX₂	FWHM (°)	S (°/RIU)	QF (1/RIU)
45	11	WS₂	7.17	331	46.16
45	11	MoS₂	8.39	261.6	31.18
50	11	WSe₂	6.69	329.4	49.23
45	11	MoSe₂	8.09	274.2	33.89

Thickness of Ag (nm)	Thickness of STO (nm)	Single layer of 2D material	FWHM of Ψ (°)	S (°/RIU)	QF (1/RIU)
44	13	Graphene	4.69	333.2	71.04
45	11	WS₂	4.84	331	68.39
45	11	MoS₂	6.78	261.6	38.58
50	11	WSe₂	4.94	329.4	66.68
45	11	MoSe₂	6.13	274.2	44.73
40	14	0	4.57	409	89.50

Wavelength (nm)	Structure	Sensitivity (°/RIU)	Ref.
633	BK7/Ag/PtSe₂	162	[11]
633	BK7/Au/ MoS₂/Au/Graphene	182	[22]
632.8	BK7/ZnO/Au/Graphene	187.43	[28]
633	BK7/Au/MXene/Au/WS₂	198	[12]
633	BK7/Ag/BaTiO₃/SLG	257	[29]
633	BK7/Ag (Conventional)	116	Calculated
633	BK7/Ag/ STO/SLG	333.2	This Work
633	BK7/Ag/STO/MoS₂ (with ellipsometry)	32140	This Work

Thickness of Ag (nm)	Thickness of STO (nm)	Number of SLG layers	FWHM(°)	S (°/RIU)	QF (1/RIU)
35	13	1	8.48	263.6	31.10
35	14	1	8.22	326.8	39.76
40	13	1	7.63	316.6	41.50
40	14	0	6.82	409	59.97
44	13	1	7.18	333.2	46.41
45	11	1	5.99	237.8	39.70
45	13	1	7.09	330.2	46.57
50	12	1	6.25	310.6	49.70
50	13	1	6.74	277.4	41.16

Ultra-high-sensitive biosensor based on SrTiO₃ and two-dimensional materials: ellipsometric concepts

Abstract

1. Introduction

2. Materials and methods

3. Results and discussion

4. Conclusion

Disclosures

Data availability

Supplemental document

References

Supplementary Material (1)

Data availability

Cited By

Figures (5)

Tables (5)

Equations (19)

Optical Materials Express

Thickness of Ag (nm)	Thickness of STO (nm)	Single layer of 2D material	Max Δ_d (°)	S_Δ (°/RIU)
47	7	Graphene	152.13	30426
47	7	0	79.45	15890
46	8	WS₂	151.48	30296
46	8	0	68	13600
42	6	MoS₂	160.70	32140
42	6	0	31.94	6388