1 Introduction

Malaria is a serious illness that affects people and is one of the main causes of death in endemic nations among both adults and children. The disease poses a risk to approximately 44 percent of people on the planet (Nureye and Assefa 2020). In order to treat and control the disease and avoid complications and mortality, it must be diagnosed quickly and accurately (Bilal et al. 2015). There are five different Plasmodium classes that can cause malaria: falciparum, ovale, malariae, vivax, and knowlesi. P. falciparum infections are the most common cause of malaria-related deaths. The parasite often infects people by the Anopheles mosquito bite (Molina-Franky et al. 2020). In the form of merozoites, the parasites arrive the bloodstream after the hepatocytes are damaged and assault the red blood cells (RBCs), then they start an intraerythrocytic cycle. Red blood cells undergo structural and metabolic changes as a result of this cycle. The phase of ring, which starts this cycle, is brought on by merozoites confronting the RBCs and is pass by mononuclear trophozoites. Further, trophozoites change into cells with many nuclei known as schizonts, that can be created when hemoglobin is broken down and hemozoin is produced (Liu et al. 2016). In the intraerythrocytic series, festering erythrocytes have a varied refractive index distribution across the cell's cytoplasm, whereas healthy erythrocytes exhibit a homogenous distribution (Akpa Marcel et al. 2019). Red blood cells with and without infection have a considerable change in refractive index, which can be used as a crucial criterion in the diagnosis of malaria (Bendib and Bendib 2018). The primary approach for determining whether a patient has malaria is based on an analysis of a blood smear under an optical microscope. This procedure needs a laboratory specialist who is proficient and experienced, and the results take a while to come back. Somewhat slowly (Ragavan et al. 2018). The polymerase chain reaction (PCR) and rapid diagnostic testing (RDT) are the other two ways to diagnose malaria. These methods are less effective due to several issues with their sensitivity and specificity. Also, they are more costly and require specialized workers (Krampa et al. 2020). As a result, a more accurate and quicker device is required to identify malaria.

Surface plasmon resonance (SPR) is a potent optical technology expended in the detection of enzymes and chemicals, medical diagnostics, and safety of food (Mudgal et al. 2020; Daher et al. 2022a; Almawgani et al. 2022a; Srivastava et al. 2016). This system has been commonly used to correctly and quickly identify a range of physical and biological indicators. The majority of SPR-based sensors employ the attenuated total reflection (ATR) process, in which p-polarized (TM) incoming light generates a surface plasmon wave together with the dielectric-metal interface. In ATR configurations, an optical coupling prism's base typically has a thin metallic coating placed on it. (Daher et al. 2022b). Silver, gold, copper, aluminum, sodium and indium are the active metals that are commonly used in SPR biosensors (Maurya and Prajapati 2016; Maharana et al. 2013; Jha and Sharma 2009). Many researches have put dielectric layers over the metal layer to enhance SPR performance and provide protection against oxidation for the metal film (Yupapin et al. 2022; Huang et al. 2011). Here, we have here proposed the bismuth ferrite (BiFeO3) as a novel dielectric layer. Due to its enormous potential, high electric field absorption, and tiny gap, the BiFeO3 is a hopeful material that has received a lot of attention. It exhibits outstanding characteristics, such as high index of refraction and small loss and has shown a significant shift in resonance angle within a minute variation in the analyte's refractive index (Papich 2016). Recently, 2D-nanomaterials have become a new possibility for progressing the sensitivity of various sorts of photodetectors. Owing to its commonly adjustable direct poor gap, exceptional electrical and optical belongings, and improved carrier mobility (Li et al. 2014; Qiao et al. 2014; Rodin et al. 2014; Wang et al. 2014), black phosphorus (BP) has gained attention as an encouraging 2D nanomaterial (Churchill and Jarilloherrero 2014). BP is an allotrope of phosphorus that consists of several layers with two-dimensional structures maintained by forces of van der Waals. Additionally, the BP possesses attractive chemical, mechanical, and physical anisotropic properties that make it an excellent choice for various applications with high efficiency (Mao et al. 2016). Srivastava et al. claim that coating the SPR sensors with BP can improve the sensitivity (Srivastava and Jha 2018). On the other hand, the amazing properties of graphene have recently been identified. For instance, its great charge carrier mobility leads to significant coupling at the graphene—metal contact (Srivastava and Jha 2018). According to Wu et al., employing graphene can increase the sensitivity of SPR sensors (Elias et al. 2011). MXene has unique properties that make it a viable 2D material for biomolecule sensing, including greater binding, high carrier confinement, a small work function, a layered structure, and a high surface area (Almawgani et al. 2022b). Changing the surface terminations of MXene can change its plasmonic characteristic (Bai et al. 2016). Wu et al. (2018) have proposed an SPR detector using some layers of MXene and various metals.

An SPR-based photodetector is suggested for the detection of infected red blood cells (IRBCs) with Plasmodium Falciparum. The nanostructure employs a layer of BiFeO3 to improve the efficiency of the proposed sensor. Three 2D-nanomaterials are examined: MXene, Graphene and Black Phosphor (BP). The study examines the number of 2D-nanomaterial sheets, the thickness of the silver and BiFeO3 materials.

2 Structure consideration and theoretical method

2.1 Structure consideration

A biosensor based on SPR is suggested for the detection of different IRBCs. The suggested structure of biosensor is comprised five layers: BK7 prism, Ag, BiFeO3, 2D-nanomaterials, and analyte. The thicknesses of Ag, BiFeO3, and 2D-nanomaterial layers will be denoted it as hAg, hBF and h2D with refractive indices nAg, nBF and n2D, respectively. A schematic illustration of the suggested SPR photodetector based on BiFeO3/2D-nanomaterial layers is presented in Fig. 1.

Fig. 1
figure 1

Schematic representation of an SPR photodetector based on BiFeO3/2D-nanomaterial layers

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The refractive index of BK7 glass prism can be estimated by the next equation (Lin et al. 2016)

$$ n\left( \lambda \right) = \sqrt {1 + \frac{{1.03961212{ }\lambda^{2} }}{{\lambda^{2} - 0.00600069867}} + \frac{{1.01046945{ }\lambda^{2} }}{{\lambda^{2} - 103.560653}} + \frac{{0.231792344{ }\lambda^{2} }}{{\lambda^{2} - 0.0200179144}}} $$
(1)

The dielectric constant of the metal medium is acquired by Drude-Lorentz model (Avsar et al. 2015)

$$ n\left( \lambda \right) = \left( {1 - \frac{{{ }\lambda^{2} \lambda_{cw} }}{{\lambda_{pc}^{2} \left( {\lambda_{cw} + i \lambda } \right)}} } \right)^{0.5} $$
(2)

where \({\lambda }_{cw}=1.7614\times {10}^{-5}\) m and \({\lambda }_{pw}=1.4541\times {10}^{-7}\) m are the collision wavelength and the plasma wavelength and of silver. The refractive index of BiFeO3 is 2.9680 at a wavelength of 632.8 nm (Vasimalla and Pradhan 2021).

2.2 Theoretical modeling

All L layers are package-like configuration along the z-axis. Mathematically, tangential field of the initial limit is at z = 0 and the tangential field of the last limit is at z = zL−1 are as:

$$ \user2{ }\left[ {\begin{array}{*{20}c} {S_{1} } \\ {D_{1} } \\ \end{array} } \right] = W\left[ {\begin{array}{*{20}c} {S_{{{\varvec{L}} - 1}} } \\ {D_{{{\varvec{L}} - 1}} } \\ \end{array} } \right] $$
(3)

where S1 and SL−1 are the tangential electric fields at initial layer limit and Lth layer limit respectively, D1 and DL−1 are the tangential magnetic fields at initial layer limit and Lth layer limit respectively. Now, distinguishing matrix (Fj) for L-layer system can be clarified as (Daher et al. 2022c, 2022d, 2022e; Panda et al. 2022)

$$ F_{j} = \left[ {\begin{array}{*{20}l} {\cos \left( {K_{j} } \right)} \hfill & {\quad - \frac{{i \sin \left( {K_{j} } \right)}}{{Y_{j} }}} \hfill \\ { - iY_{j} \sin \left( {K_{j} } \right)} \hfill & {\quad \cos \left( {K_{j} } \right)} \hfill \\ \end{array} } \right] $$
(4)

\({K}_{j}\) is the variation in phase experienced by the light wave as it travels through the jth layer.

$$ K_{j} = \frac{2\pi }{\lambda }h_{j} \left( {\varepsilon_{j} - (n_{1} \sin \theta_{1} )^{2} } \right)^{1/2} $$
(5)

where \({n}_{j}\) is the layer's refractive index and hj its thickness. \({n}_{1},{\lambda , \mathrm{and} \theta }_{1}\) are the refractive index of prism, the incident wave's wavelength and angle of incidence. Finally, \({\varepsilon }_{j}\) is the dielectric permittivity of the jth layer. For transverse magnetic (TM) wave \({Y}_{j}={({\varepsilon }_{j}-{{{(n}_{1}\mathrm{sin}\theta }_{1})}^{2})}^{1/2}/{\varepsilon }_{j}\). The full transfer matrix F of the structure can be expressed as

$$ F = F_{Ag} F_{BF} F_{2D} = \left[ {\begin{array}{*{20}c} {F_{11} } & {\quad F_{12} } \\ {F_{21} } & {\quad F_{22} } \\ \end{array} } \right] $$
(6)

Finally, reflectance (R) for hybrid L-layer system can be computed by:

$$ R = \left| {\frac{{\left( {F_{11} + F_{12} Y_{N} } \right)Y_{1} - \left( {F_{21} + F_{22} Y_{N} } \right)}}{{\left( {F_{11} + F_{12} Y_{N} } \right)Y_{1} + \left( {F_{21} + F_{22} Y_{N} } \right)}}} \right|^{2} $$
(7)

The sensitivity is dependent on both the resonance angle shift (Δθres) and change of RI in analytes, which is defined as (Vasimalla and Pradhan 2021)

$$ S = \frac{{\Delta\uptheta \,{\text{res}}}}{{\Delta {\text{n}}}} $$
(8)

3 Results and discussions

An SPR nanostructure based optical sensor is explored for the detection of IRBCs. The suggested structure of biosensor is comprised five layers: BK7 prism, silver, BiFeO3, 2D-nanomaterials, and analyte. According to Sect. 2, the indices of refraction of the materials are determined at λ = 632.8 nm. In the first, layers' thicknesses are chosen as hAg = 40 nm, hBF = 1 nm, and d2D (Graphene) = S \(\times \) 0.34 nm where S = 1. It is worth noting that the reflectance spectrum is not clear for hAg < 40 nm and hBF < 1 nm for the proposed structure. So we start with these values and then explore higher values in the following parts. The reflectance profiles of the suggested SPR nanostructure are studied using Mathematica software and transfer matrix approach. It is worth to mention that the least the thickness Fig. 2a, b shows the SPR reflectivity spectrums for both the normal and infected red blood cells as treated as a analytes. The suggested sensor's reflectance spectra with a 0 nm BiFeO3 layer are shown in Fig. 2a (without a BiFeO3 layer). On other hand, Fig. 2b gives the reflectivity spectra with 1 nm of BiFeO3 layer. The results indicate that as the refractive index of the analyte is decreased, the minimum reflectivity corresponding to the resonance dip gradually increases. Moreover, it is obvious that as the refractive index of the analyte decreases, the resonance angle shifts to a smaller angle. The resonance angles change from 78.16 to 73.23 and 79.67 to 74.34 for SPR sensor without the BiFeO3 layer and SPR photosensor with 1 nm of BiFeO3 layer, respectively. Figure 3 illustrates how the SPR angle varies when the analyte’s refractive index changes. The shift is fully linear across the entire range of refractive indices in linear regression analyses of the suggested SPR photosensor. As a result, for SPR photosensors based on BiFeO3, adding a 1 nm BiFeO3 layer enhances Δ\(\theta \) of SPR by at least 8% when compared to the SPR photosensor without this layer. This implies an increase in sensitivity of 8%. The sensitivity of the suggested photosensor and the photosensor without the BiFeO3 material is evaluated and then are explained in Table 1.

Fig. 2
figure 2

Reflectance spectra of the suggested SPR photosensors. a without BiFeO3 and b with BiFeO3 layer

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Fig. 3
figure 3

Resonant angle of the suggested SPR sensor versus refractive index of the sensing medium. a without BiFeO3 layer and b with BiFeO3 layer at hAg = 40 nm, hBF = 1 nm and h2D (Graphene) = S \(\times \) 0.34 nm where S = 1

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Table 1 The structures that were employed and their sensitivity at hAg = 40 nm, hBF = 1 nm and h2D (Graphene) = S \(\times \) 0.34 nm where S = 1
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To increase the SPR sensor’s sensing performance, 2D nanomaterials are frequently coated on the sensor’s surface since it has a very large specific surface area and high carrier mobility In this section, We will talk about how 2D materials affect SPR sensor performance. The performance of the photosensor is simulated when some 2D nanomaterials such that MXene, Graphene and Black Phosphor (BP) cover the surface of the nanostructure. The refractive indices of MXene, Graphene and Black Phosphor are 2.38 + 1.33i, 3 = 1.149i and 3.5 + 0.01i, respectively. Thickness of monolayer of these 2D materials are 0.993, 0.34 and 0.53 nm, respectively. Peng et al. (2016); Nurrohman and Chiu (2020); Almawgani et al. (2022c). The initial thickness of BiFeO3 is adjusted to 1 nm and that of Ag to 40 nm in order to streamline the research procedure when monolayers of various 2D nanomaterials are applied to the structure. The SPR reflectivity spectra for MXene, Graphene and Black Phosphor are shown in Fig. 4a–c, respectively as the sensing layer selected as normal and ring red blood cells (NRBC and RRBC). The first choice is as BK7 glass prism/silver/BiFeO3/MXene/analyte. The resonance angles are obtained at 80.45° and 78.92° for the NRBC and RRBC, respectively. The sensitivity is computed and recorded as 218.57 deg/RIU. Now, the second choice is selected as BK7 glass prism/silver/ BiFeO3/ Graphene /analyte and the angles of dip are located at 79.67° and 78.19° for the NRBC and RRBC, respectively. The computed sensitivity for this structure is realized as 211.43 deg/RIU. Finally, the third choice is selected as BK7 glass prism/silver/BiFeO3/BP/analyte. The angles of dip for the last structure are obtained at 80.24° and 78.67°. The sensitivity is evaluated and became as 224.28 deg/RIU. The results of these structures are tabulated in Table 2. It is obvious that the third system with BP as 2D material has higher sensitivity than other structures. Therefore, the last structure will be taken up for the upcoming investigations.

Fig. 4
figure 4

Reflectance curves of the suggested SPR sensors for some 2D nanomaterials. a MXene, b graphene and b black phosphor

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Table 2 The used 2D-nanomaterials and their sensitivity at hAg = 40 nm, hBF = 1 nm and monolayer of 2D-nanomaterial
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The influences of certain factors on the sensitivity of the SPR photosensor like metal\thickness, number of 2D nanomaterial layers and thickness of BiFeO3 material are inspected. The nanostructure of BK7 glass prism/silver/BiFeO3/BP/analyte is utilized. The silver layer is employed in a variety of thicknesses between 40 and 60 nm, with steps of 5 nm. The sensitivities are calculated and found as 224.28, 238.57, 251.42, 260 and 264.28 deg/RIU corresponding to silver layer thicknesses of 40, 45, 50, 55 and 60 nm, respectively. As shown from Fig. 5, the optimal thickness of the Ag layer is 60 nm which will consider in the next investigation. The calculations and results of all these thicknesses of Ag layer are clarified in Table 3. The resonant dip in the reflectance spectra is not seen for thicknesses greater than 60 nm.

Fig. 5
figure 5

Sensitivity versus the thickness of silver for the suggested SPR nanostructure at hBF = 1 nm and h2D (BP) = S × 0.53 nm where S = 1

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Table 3 Variation the sensitivity with different thicknesses of Ag at hBF = 1 nm and h2D (BP) = S × 0.53 nm where S = 1
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On other hand, when the 2D nanomaterial covers the surface of the nanostructure, the thickness of the BiFeO3 layer needs to be modified and adjusted since the 2D nanomaterial, like BiFeO3, has a high refractive index real portion. The BiFeO3 layer is employed in a variety of thicknesses between 1 and 2.5 nm, with steps of 0.5 nm. For each thickness of the BiFeO3 layer, the sensitivity is evaluated and determined. It found as 264.28, 304.28, 357.14 and 461.42 deg/RIU for dBF = 1, 1.5, 2 and 2.5 nm, respectively. For dBF > 2.5 nm, the resonant dip vanishes. Thus, thickness of BiFeO3 layer (dBF = 2.5 nm) is the optimum. Figure 6 exhibits variation the sensitivity with thickness of BiFeO3 layer as thickness of Ag has been fixed at 60 nm with monolayer of BP. The calculations of all these thicknesses of BaTiO3 layer are listed in Table 4.

Fig. 6
figure 6

Sensitivity versus the thickness of BiFeO3 for the suggested SPR structure at hAg = 60 nm and h2D (BP) = S \(\times \) 0.0.34 nm where S = 1

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Table 4 Variation the sensitivity with different thicknesses of BiFeO3 at hAg = 60 nm and h2D (BP) = S \(\times \) 0.0.34 nm where S = 1
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A Black Phosphor (BP) layer has a thickness of 0.53 nm. It is assumed that the BP material thickness is S × 0.34 nm, where S is the number of BP layers. The computed sensitivity is found as 461.42, 218.57 and 185.71 deg/RIU for S = 1, S = 2 and S = 3, respectively. This means sensitivity of the suggested detector shrinkages with growing the number of BP sheets as shown in Fig. 7. Therefore, monolayer is the preferred number of BP layers. The calculations of the resonant angle, shift of angle and sensitivity for all investigated values of number of BP layers are listed in Table 5.

Fig. 7
figure 7

Sensitivity versus number of BP for the proposed SPR structure at hAg = 60 nm and hBF = 2.5 nm

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Table 5 Variation the sensitivity with different number of BP layer at hAg = 60 nm and. hBF = 2.5 nm
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According the previous investigations, the optimal parameters are selected as hAg = 60 nm, hBF = 2.5 nm and dBP = S × 0.53 nm, S = 1. The resonant dips for different infected red blood cells are depicted in Fig. 8. When the NRBC is taken as an analyte, the resonant angle is set up at 86.35°. It is observed when infected red blood cells (IRBCs) are used as analytes, the resonant dip changes to smaller angles. The new resonant angles for the RRBC, TRBC, and SRBC are found to be 83.12°, 79.53°, and 77.26°, respectively. The sensitivities are found as 461.43, 358.95 and 313.45 deg/RIU for the RRBC, TRBC and SRBC, respectively as exhibited in Fig. 9. The calculations of sensitivity for those IRBCs are evaluated and presented in Table 6. The highest sensitivity of the suggested photosensor is 461.43 deg/RIU for RRBC, which is an ultra-high value as compared to recently performed publications in this field as shown in Table 7.

Fig. 8
figure 8

Reflectance curve of the suggested SPR sensors at hAg = 60 nm, hBF = 2.5 nm, and h2D (BP) = S \(\times \) 0.53 nm where S = 1

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Fig. 9
figure 9

Sensitivity versus index of refraction of analyte for the suggested SPR structure at hAg = 60 nm, hBF = 2.5 nm and h2D (BP) = S \(\times \) 0.53 nm where S = 1

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Table 6 Variation the sensitivity with concentration at hAg = 60 nm, hBF = 2.5 nm, and h2D (BP) = S \(\times \) 0.53 nm where S = 1
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Table 7 The sensitivity of this research compared to the most recent reported SPR biosensors
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4 Conclusion

An SPR nanostructure-based bio-photonic detector has been reported for the detection of infected red blood cells (IRBCs) with Plasmodium Falciparum. To examine the suggested structure, the TMM has been used. At first, the sensitivity are calculated without/with BiFeO3 layer. It is found the BiFeO3 layer improves the sensitivity. Three different 2D-nanomaterials have been examined which are Graphene, MXene and BP. The structure with BP as a 2D-nanomaterial has been obtained to correspond to the greatest performance Then, the sensitivity is analyzed with the thickness of Ag and BiFeO3 materials. As the thicknesses of the Ag and BiFeO3 layers are increased, the angular sensitivity grows. Also, it is deduced that the maximum sensitivity favors a lower number of BP layers. The best sensitivity is acquired at 60 nm (for Ag), 2.5 nm (for BiFeO3) and monolayer of black phosphor. The variation of angular sensitivity is then studied with infected red blood cells (IRBCs) at different stages. The greatest sensitivity is obtained as 461.43 deg/RIU corresponding to a ring phase of IRBC which is improved compared to lately published papers. As a result, we believe the suggested SPR nanostructure will provide a novel opportunity for highly efficient photodetectors.