Introduction

Prostate cancer remains one of the most common cancers worldwide [1] and is usually diagnosed by testing serum levels of prostate-specific antigen (PSA). Despite the great importance and use of PSA, there are inherent limitations due to the limited specificity that lead to a significant rate of unnecessary biopsy [2]. In addition, PSA screening is unsatisfactory, and therefore, there is disagreement about the cancer benefits of prostate cancer screening with PSA. High-volume trials have shown a 20% reduction in prostate cancer mortality in patients undergoing PSA screening [3]. Accordingly, there is a great need to improve methods for assessing prostate cancer risk. The introduction of new imaging modalities, including multimeter MRI (mpMRI), has improved the diagnosis of prostate cancer [4,5,6]. However, mpMRI is expensive and not widely available, so optimal patient selection is crucial for diagnosis. Various strategies have been added to clinical practice to improve the sensitivity and risk classification of PSA-based prostate cancer. Such strategies include PSA-based kinetics (PSA velocity), utilization of total free PSA ratio, and PSA density (based on prostate volume). Especially those with PSA between 4.0 and 10 ng/ml [7, 8]. To provide specific binding of PSA, there are several methods like the immuno-PCR (IPCR), bio-barcode assay, surface-enhanced Raman scattering (SERS), and electrical detection of micro-cantilever bending [9,10,11,12]. IPCR is a technique where after PSA capture by anti-PSA antibodies on the surface of a biosensor, a DNA-labeled detection antibody binds. IPCR is a powerful method for detecting low quantities of protein antigens [9]. Bio-barcode assay is a rapid and ultrasensitive tool for detecting biological targets such as proteins and nucleic acids in the entire sample [10]. In SERS, binding of PSA to anti-PSA antibodies functionalized with Raman reporter molecules (RRMs) and immobilized onto gold microparticles leads to the altered spectroscopic output of the RRMs, which can be used to quantify the concentration of PSA [11]. In the electrical detection of the micro-cantilever bending technique, piezoresistive microcantilevers, functionalized with anti-PSA antibodies, bend owing to surface stress caused by PSA capture. Micro-cantilever bending is measured by electrical detection [12]. Surface plasmon biosensors are a sensor designed based on the surface plasmon resonance (SPR) phenomenon to detect biological substances. The basic principle is based on the specific binding of chemical molecules or biomolecules on the material’s surface, resulting in the change of the local refractive index of the environment and the change of the surface plasmon resonance frequency. In recent years, rapid and accurate point-of-care medical diagnosis and biological detection have attracted more and more attention, and surface plasmon biosensors have also become a hot topic in scientific research. Its label-free detection method has become one of the unique advantages of this type of material. In the surface plasmon polariton (SPP)-type biosensors, electromagnetic waves are emitted at the interface between metal and dielectric materials Many optical components, such as filters [13, 14], sensors [15], and amplifiers [16, 17], have been reported using SPP waves. Among the mentioned applications, refractive index sensors have many applications. They have been widely used in biomedical applications such as cancer diagnosis [18,19,20], blood component measurements [19,20,21], and health care programs [22]. Instruments that use surface plasmons are usually much smaller in area than conventional optical components, optical fibers, and photon crystal devices. This feature is an excellent reason to use them as bio-implantable sensors. In addition, it became higher sensitivities using SPPs than other methods such as photon crystals. Despite the different configurations of plasmonic sensors, MIM topologies can be a good choice for efficiently transmitting electrical and optical signals in an integrated circuit. Due to the unique optical properties that MIM configurations show, they have been highly regarded by researchers in the design of optical devices [23]. The MIM topology, due to the severe confinement of the electric field and the long propagation amplitude, maximizes the interaction length of the field with the sensing substance and has received considerable attention [24]. Early detection of cancer makes treatment more effective and cheaper, so by identifying a specific antigen, we can detect cancer earlier than it spreads. In this article, we use prostate-specific antigens for the early detection of prostate cancer. We propose a nanoring-shaped biosensor based on local surface plasmon resonance (LSPR) using the MIM topology. We use FDTD for validation and show that the proposed structure performs better than the disk structure and can be used to detect prostate-specific antigens. Because this is an optical detection method, the sensor is sensitive to changes in surface refractive index.

The Structure Design and Simulation Methodology

In this section, we present the proposed structure and governing equations for PSA detection. Figure 1a shows the proposed structure. As it is evident in this figure, the proposed structure consists of a base layer of metal, the second layer of insulation, and the last layer of metal. In the proposed structure, the base layer is a continuous plate and the second and third layers are alternate and ring-shaped. The cross-sections from the proposed structure are depicted in Fig. 1b. Also, for comparison of performance parameters, the disk-shaped biosensors are simulated. Figure 1c shows the layer arrangement of simulated disk biosensors. In each case, the first and third layers are from one type of metal. In this research, two types of metal, Au and Ag, are used, and SiO2 is used as an insulation section. The Au refractive indexes are extracted from the Johnson and Christy [25] data, and the Ag and SiO2 refractive indexes are extracted from Palik data [26].

Fig. 1
figure 1

a The proposed ring shape MIM-based biosensor. b The different cross-sections views of ring shape biosensor and c disk-shaped biosensors

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The refractive index of PSA is presented in Table 1, which is calculated from the results of [27] using the following equation:

Table 1 Refractive index for different concentrations of PSA \(\left({n}_{0}=1.33\right)\)
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$${\Delta \lambda }_{max}=S\Delta n$$
(1)

Here \(\Delta \lambda\) represents the wavelength changes with increasing refractive index, S represents the sensitivity to refractive index, and \(\Delta n\) represents the refractive index changes. PSA samples ranging from 50 (1.7 ng/mL) to 600 pM (20.4 ng/mL) [27]. According to [28], a PSA concentration above 4 ng/ml is important for diagnosing prostate cancer, so we used four cases of 100, 200, 300, and 400 pM.

In our simulations, a plane wave light source is irradiated on a biosensor from the top side in different wavelengths. The perfectly matched layer (PML) boundary conditions are applied in the direction of light radiation and periodic boundary conditions in the direction perpendicular to the light radiation. The sensor’s sensitivity for wavelength interrogation can be defined as [29].

$${s}_{\lambda }=\frac{\Delta \lambda }{{\Delta n}_{s}}$$
(2)

Here \({d}_{\lambda }\) is the differential change of the wavelength due to \({dn}_{s} \mathrm{and} {dn}_{s}\) is the refractive index change of the sensor layer. We define the figure of merit (FOM) of the sensor as Eq. (3) [30].

$$\mathrm{FOM}=\frac{{\mathrm{S}}_{\lambda }}{\mathrm{FWHM}}$$
(3)

where FWHM implies full width at half maximum.

Results and Discussions

In this section, we aim to select the optimal structures by analyzing the simulation results and comparing them. Due to the same path of determining the most optimal dimensions of the ring biosensor and preventing duplication using the two metals Ag and Au, we only bring the Au steps in this section. In Fig. 2a, the effect of the inner radius of the ring (\({r}_{\mathrm{in}}\)) is simulated. According to the figure, the spectral response of the designed biosensors with radii of 55 and 50 nm are very similar, but we chose the spectral response of 55 nm because of their proximity to the telecommunication window. In Fig. 2b, the effect of the ring thickness (\({T}_{\mathrm{ring}}\)) on the reflection spectrum is calculated in terms of depth or maximum reflection and FWHM. The ring with a thickness of 72 nm is selected. In Fig. 2c, the effect of the distance of the rings from each other is compared, and the distance of 130 nm is selected due to high reflection and low FWHM.

Fig. 2
figure 2

Reflection of Au ring shape NPs as a function of the wavelength for a different inner radii of the ring, b different thicknesses of the ring, and c different distances of adjacent ring

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In Fig. 3a, the effect of changing the height of the metal (\({h}_{\mathrm{Au}}\)) is presented; here, 30 nm is selected for the above-mentioned reason. Figure 3b shows the effect of SiO2 insulation height (\({h}_{\mathrm{SiO}2}\)) changes that we choose 25 nm for the maximum depth and lower FWHM. According to the results, d and \({T}_{\mathrm{ring}}\) have the most negligible effect, and as mentioned in [31], the high effect of insulation thickness (\({h}_{\mathrm{SiO}2}\)), has the highest effect.

Fig. 3
figure 3

Reflection of Au ring-shape NPs as a function of the wavelength for a effect of Au height and b effect of SiO2 heights

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The biological substances can be measured using proposed structures through spectral changes. For biosensors, a high figure of merit and high sensitivity is more desirable. So, here both of them are calculated and compared. In Fig. 4a and b, we show the sensitivity of a proposed structure for different \({T}_{\mathrm{ring}}\) for Au and Ag, respectively. According to the diagram, the highest sensitivity of 567.2 nm/RIU is related to Ag with \({T}_{\mathrm{ring}}\) = 70 nm. The highest sensitivity of Au at \({T}_{\mathrm{ring}}\) = 72 nm and \({T}_{\mathrm{ring}}\) = 73 nm is approximately equal to 527.4 nm/RIU. In Fig. 5a and b, we have examined the FOM for different \({T}_{\mathrm{ring}}\) for Au and Ag, respectively. Here also, Ag has better performance, and the maximum FOM at \({T}_{\mathrm{ring}}\) = 70 nm is 3.72.

Fig. 4
figure 4

Sensitivity as a function of refractive index a Au ring-shape nanoparticles and b Ag ring-shape nanoparticles

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Fig. 5
figure 5

FOM as a function of refractive index a Au ring-shape nanoparticles and b Ag ring-shape nanoparticles

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The sensitivity and FOM of the proposed structure by varying the environment refractive index depict that using an Ag ring has better performance. Here, the performance parameters of ring-shaped nanoarrays and disk shape one are compared. In Fig. 6a, we compare the reflection of ring-shaped and disk shape biosensors with Ag and Au nanoparticles, which shows the better performance of ring-shaped reflection. In Fig. 6b, we have compared the sensitivity with different shapes. This diagram clearly shows the superiority of the biosensor in the form of a ring, and also, the superiority of Ag over Au in both different shapes is visible.

Fig. 6
figure 6

a Comparison of the reflection of ring- and disk-shape Ag and Au NPs and b comparison of the sensitivity of ring and disk shape Ag and Au NPs

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Here, the excellent potential of the designed structure is used to examine them as a biosensor for the early diagnosis of prostate cancer. Identifying the amount of PSA can help us to be aware of prostate cancer. PSA is a protein produced by cancerous and noncancerous prostate tissue. Usually, a small amount of PSA enters the blood. Prostate cancer cells typically produce more pre-PSA than noncancerous cells, leading to higher levels of PSA in the blood. Our simulated results show that the ring shape based on MIM structure is a highly sensitive plasmonic biosensor in the communication window, and it is an appropriate candidate for PSA detection. The sensing strategy is based on the plasmonic effect and the shift of resonance peak due to refractive index changes of the surrounding medium of nanorings due to the existence of PSA. As mentioned, the refractive index is defined as n = n0 + Δn. Here, all the data are calculated concerning the water state (\({n}_{0}\) = 1.33). With increasing the concentration of PSA, changes in the refractive index are accompanied by a red-shift of surface plasmon resonance (see Fig. 7).

Fig. 7
figure 7

Reflection as a function of wavelength for different refractive indices (concentration) where a redshift occurs

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In Table 2, we have provided the information of biosensors with two shapes of ring and disk with different metal nanoparticles, Au and Ag. Benefiting from the excellent refractive index sensitivity designed systems, our results show sensitivity higher than 500 nm/RIU, which is more sensitive than previously reported sensitivity [27]. It is important to mention that in [27], the sensitivity of 116 nm/RIU has been reported for Au nanodisks array-based biosensor for detecting PSA. Here, this value is increased to higher than 500 nm/RIU using MIM structures in the form of nanorings. Some prostate cancers may not produce large amounts of PSA, and higher sensitive biosensors are the more appropriate choice for detecting such PSA levels. However, the findings of this work reveal that it is possible to detect different PSA concentrations with higher sensitivity.

Table 2 The performance parameters of proposed structures in different PSA concentrations in water (\({n}_{0}\) = 1.33)
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In the case of the fabrication process of our design biosensor, it is important to mention that such a structure can be fabricated using a combined protocol of electron beam lithography (EBL) and thermal evaporation [32,33,34,35]. Due to the use of silver nanoparticles (AgNPs) in our proposed structure, which are nontoxic, highly compatible with biomolecules, high catalytic activity, antibacterial activity towards microbes without the release of toxic biocides, and exceptional physical and chemical properties, that lead to the high stability of the biosensor [36, 37]. Also, our proposed structure has an absorbance near 100%, close to the information telecommunication window, as shown in Fig. 8. Because of such high absorption and tunability, this proposed configuration is highly recommended for many other optical applications like absorbers and imaging. The proposed plasmonic device can also be utilized in the hot electron-based plasmonic modulators and switches because of the narrow perfect absorption close to the information’s communication window.

Fig. 8
figure 8

Reflection and absorption of our designed structure as a function of wavelength

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Conclusion

Due to the fatality of cancer and the need for early detection, in this study, we tried to achieve a biosensor with high sensitivity and a high figure of merit (FOM). According to our simulated results, we recommend a ring-shaped Ag nanoparticle biosensor to detect PSA with a sensitivity of 567.23 nm/RIU and FOM of 3.72 that can detect PSA well. Due to its less complexity, it is easy to build and can be used in real biosensors technologies. The proposal is analyzed using an FDTD method. According to the results, we can reach high-sensitivity and easy-to-fabricate sensors with the MIM topology. It is important to mention that the sensitivity of 116 nm/RIU has previously been reported for Au nanodisks arrays-based biosensors for detecting PSA. Here, this value is increased to higher than 500 nm/RIU using MIM structures in the form of nanoring. The findings of this work reveal that it is possible to detect different PSA concentrations with higher sensitivity.