# Design and Bulk Sensitivity Analysis of a Silicon Nitride Photonic Biosensor for Cancer Cell Detection

Authors: Prasanna Kumaar S.; Sivabramanian A.
Journal: International Journal of Optics
 (2022)

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## Abstract

Bulk sensitivity is an important parameter to validate the efficiency of the photonic waveguide sensor. Due to recent advancements in point-of-care silicon photonic biosensing, the focus is to identify the effective way to improve sensitivity. Integrating polydimethylsiloxane (PDMS) microfluidic channel in sensor architecture decreases the sensitivity due to leakage of molecules at edges. The silicon nitride (SiN4) Mach–Zehnder interferometer utilizes the refractive index of different cancer cells (1.39–1.401) to determine the bulk sensitivity. The proposed gradient step rib-slot structure of 970 nm wide and 400 nm thickness is designed to hold the liquid sample without any PDMS material. This novel waveguide exhibits high waveguide bulk sensitivitySw,bulk and device bulk sensitivity Sd compared with the gradient rib waveguide. We achieved a waveguide bulk sensitivity Sw,bulk of 2.0699 RIU/RIU and device sensitivity Sd of 568 nm/RIU through finite-difference time-domain (FDTD) analysis.


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## Body

## 1. Introduction

Virus has been a significant outbreak in recent times. Interest in label-free biosensors has increased due to the diagnosis techniques used in postpandemic [1]. Cancer is the most severe disease globally at present [2]. There are more than 100 different types of cancer group cells that will affect every organ in a body [3]. Early detection of cancer in postpandemic is most important in current diagnosis and medication techniques [4]. Due to its rapid detection and high sensitivity capability, low-cost label-free point-of-care biosensors are developed [5]. Many research findings were reported in the literature on detection of target molecules in biological and environmental applications [6, 7]. Biosensors can be classified based on transduction mechanisms such as electrochemical, electro-optical, optical, mechanical, acoustical, chemical-immunoassays, spectroscopy [8], and image processing algorithms [9, 10]. In an optical method, no-chemical reagents are added to the sample [11]. This will increase the sensitivity to quantify the biomolecule present in the sample [12]. In future, the point-of-care devices may be integrated with mobile phones [13]. By considering all these parameters, we chose a silicon photonic waveguide biosensor [14].This silicon-based photonic device can be easily fabricated using the available CMOS foundry. This platform offers a wide variety of optimization based on application. The optimization may be waveguide geometry, spectrum analyzer, CCD (charge coupled device) detector, light sources, etc. [15]. For cancer cell detection, the main challenges are absorption of a biomolecule into the waveguide [16]. Integrating polydimethylsiloxane (PDMS) microfluidic channel in sensor architecture decreases the sensitivity due to leakage of molecules at edges. Silicon nitride waveguides are preferred as they offer low waveguide loss and are flexible in fabrication compared with silicon-on-insulator (SOI) waveguides [17, 18]. Some recent reports on fabrication up to 900 nm thickness are done without any cracking stress on silicon nitride [19]. Mach–Zehnder interferometer (MZI) exhibits good response for the cancer blood cell as MZI sensing arm has long length interaction over the sample, and dynamic waveguide structures are integrated [20].In this article, we analyzed the silicon nitride MZI sensor architecture for cancer cell detection using gradient rib and gradient rib-slot waveguide, as shown in Figure1 [18, 21]. We use cancer cell blood samples as bulk solution for sensing. For bulk sensitivity, the interferometer-based sensor offers a high sensitivity in the range of 10-7 to 10-8 RIU [22]. By integrating the polydimethylsiloxane (PDMS) microfluidic channel in the sensor, architecture decreases the waveguide bulk sensitivity Sw,bulk and device sensitivity Sd due to leakage of molecules at edges [23]. As evanescent field decays linearly over the length of the waveguide and to avoid antibody diffusion on the surface, we propose gradient step for every 2 mm length. The response of the gradient rib waveguide over the normal cell and cancer cell in the transmission spectrum is minimal, and Sw,bulk is 0.2568 RIU/RIU.Figure 1
Silicon nitride biosensor setup with MZI and a grating coupler.Our objective of the design is to accommodate analytes in the photonic biosensor integrated to mobile phones, which would increase the detection rate and sensitivity; hence, we proposed the design of a novel gradient rib-slot waveguide of rib width 970 nm, slot width 790 nm, and thickness 400 nm. This optimized structure holds the analyte without any external PDMS material and allows the sensor to be integrated with mobile phones in future. This structure also enhances the analyte transportation more effective. This results in increased interaction of analytes with light and exhibits more number of peaks in the transmission spectrum compared with the gradient-rib waveguide. The waveguide bulk sensitivitySw,bulk and device sensitivity Sd were found to be 2.0699 RIU/RIU and 568 nm/RIU through finite-difference time-domain (FDTD) analysis. These results were obtained for cancer cells, and this approach may be extended to other generic biomolecules of different sizes and refractive indices.


## 2. Materials and Methods

In this section, basic components of the photonic waveguide biosensor and properties of MZI with two different types of waveguide geometry structures are presented.


### 2.1. Properties of the Proposed Silicon Nitride (Si3N4) Photonic Waveguide Biosensor

Silicon nitride offers broad biosensing applications for integrated point-of-care devices. The operating wavelength of silicon nitride ranges from 400 nm to 3.7μm [18], which provides scope for designing instant-sensing biophotonic chip that can be integrated to mobile phones in future. In the asymmetric Mach–Zehnder interferometer configuration, the rib and novel rib-slot waveguide are used as the sensing arm. The other waveguide sensing structures are strip [24, 25], slot [26], double-slot [27], and sub-wavelength grating [28, 29] for biosensing applications to detect various diseases. The interferometer sensor gives high sensitivity (10-7 to 10-8 RIU), and it can operate at a telecommunication wavelength. Optimization of MZI improves the sensitivity of the sensor based on the evanescent field absorption over the waveguide structure. The design of the waveguide structure is different depending on the concentration of the sample used [30]. To increase the interaction of the evanescent field over the sensing arm, the proposed design of the novel gradient rib-slot waveguide structure has a sensing window of length 8 mm with an analyte volume of 1.0476 × 10−6 mm3. In FDTD simulation, each gradient step length of 2 mm has different analyte thicknesses ranging from 400 nm to 90 nm. Our earlier study [31] showed that the sensitivity of the silicon nitride waveguide structure is better than the silicon waveguide structure. Better absorption in the transmission spectrum leads to detect a particular biomolecule present in the sample. The transmission loss in the waveguide depends on the absorption of photons by the sample in the cladding region. In most commonly used 450 nm width wire waveguide, the loss ranges from 2.5 dB to 3.5 dB. The roughness of the sidewalls can significantly influence the propagation loss. In addition, when the rib waveguide is immersed in water, the intrinsic loss will decrease. Thus, the confinement factor of the rib waveguide is smaller, but it is more tolerant to fabrication process errors due to waveguide width variation. Sidewall roughness in the wire waveguide is vital for evanescent sensing. Rib waveguides are preferred for evanescent sensing because sidewall roughness has less effect on them [16].


### 2.2. Analysis for Cancer Cell Detection

Every disease blood cell sample has a different range in refractive index, and the blood sample of a healthy person is 1.35 [32].The light propagation in MZI waveguide will be varied due to the refractive index of cancer cells with the analyte thickness of 400 nm, 250 nm, 150 nm, and 90 nm. In the waveguide simulation, the refractive index of the cancer cells is applied over the surface of the sensing arm of MZI [22], and the corresponding variation in the transmission spectrum of cancer cell and healthy blood sample at 1550 nm is observed by using Optical Spectrum Analyzer.


### 2.3. Sensor Performance Evaluation by Sensitivity

FDTD accurately simulates the physical activity of photonics and optoelectronic circuits and systems. Analysis of electromagnetic wave propagation in the photonic device was performed by the FDTD approach. Due to this, computational electromagnetics has become an important area of research in developing efficient sensing platforms. In the waveguide structure, the mode profile overlaps with analytes highly. The change in effective index (neff) and refractive index of analyte (nc) can be in measurable quantity as bulk sensitivity [33].The waveguide bulk sensitivity novel gradient strip-slot waveguide equation is as follows:(1)Sw,bulk=∂neff∂ncRIURIU.Architecture (MZI) bulk sensitivitySaMZI,bulk equation for the novel gradient strip-slot waveguide with λr shift in resonance wavelength is as follows:(2)SaMZI,bulk=∂λr∂neffnmRIU.The efficiency of this sensor is calculated by device sensitivitySd for novel gradient strip-slot waveguide:(3)Sd=∂λr∂ncnmRIU.We analyzed this waveguide sensor atλ0 = 1550 nm. To validate this sensor sensitivity with other different wavelengths, the following equation is used to calculate normalized sensitivity Sd″:(4)Sd″=Sdλ0RIU−1.


## 2.1. Properties of the Proposed Silicon Nitride (Si3N4) Photonic Waveguide Biosensor

Silicon nitride offers broad biosensing applications for integrated point-of-care devices. The operating wavelength of silicon nitride ranges from 400 nm to 3.7μm [18], which provides scope for designing instant-sensing biophotonic chip that can be integrated to mobile phones in future. In the asymmetric Mach–Zehnder interferometer configuration, the rib and novel rib-slot waveguide are used as the sensing arm. The other waveguide sensing structures are strip [24, 25], slot [26], double-slot [27], and sub-wavelength grating [28, 29] for biosensing applications to detect various diseases. The interferometer sensor gives high sensitivity (10-7 to 10-8 RIU), and it can operate at a telecommunication wavelength. Optimization of MZI improves the sensitivity of the sensor based on the evanescent field absorption over the waveguide structure. The design of the waveguide structure is different depending on the concentration of the sample used [30]. To increase the interaction of the evanescent field over the sensing arm, the proposed design of the novel gradient rib-slot waveguide structure has a sensing window of length 8 mm with an analyte volume of 1.0476 × 10−6 mm3. In FDTD simulation, each gradient step length of 2 mm has different analyte thicknesses ranging from 400 nm to 90 nm. Our earlier study [31] showed that the sensitivity of the silicon nitride waveguide structure is better than the silicon waveguide structure. Better absorption in the transmission spectrum leads to detect a particular biomolecule present in the sample. The transmission loss in the waveguide depends on the absorption of photons by the sample in the cladding region. In most commonly used 450 nm width wire waveguide, the loss ranges from 2.5 dB to 3.5 dB. The roughness of the sidewalls can significantly influence the propagation loss. In addition, when the rib waveguide is immersed in water, the intrinsic loss will decrease. Thus, the confinement factor of the rib waveguide is smaller, but it is more tolerant to fabrication process errors due to waveguide width variation. Sidewall roughness in the wire waveguide is vital for evanescent sensing. Rib waveguides are preferred for evanescent sensing because sidewall roughness has less effect on them [16].


## 2.2. Analysis for Cancer Cell Detection

Every disease blood cell sample has a different range in refractive index, and the blood sample of a healthy person is 1.35 [32].The light propagation in MZI waveguide will be varied due to the refractive index of cancer cells with the analyte thickness of 400 nm, 250 nm, 150 nm, and 90 nm. In the waveguide simulation, the refractive index of the cancer cells is applied over the surface of the sensing arm of MZI [22], and the corresponding variation in the transmission spectrum of cancer cell and healthy blood sample at 1550 nm is observed by using Optical Spectrum Analyzer.


## 2.3. Sensor Performance Evaluation by Sensitivity

FDTD accurately simulates the physical activity of photonics and optoelectronic circuits and systems. Analysis of electromagnetic wave propagation in the photonic device was performed by the FDTD approach. Due to this, computational electromagnetics has become an important area of research in developing efficient sensing platforms. In the waveguide structure, the mode profile overlaps with analytes highly. The change in effective index (neff) and refractive index of analyte (nc) can be in measurable quantity as bulk sensitivity [33].The waveguide bulk sensitivity novel gradient strip-slot waveguide equation is as follows:(1)Sw,bulk=∂neff∂ncRIURIU.Architecture (MZI) bulk sensitivitySaMZI,bulk equation for the novel gradient strip-slot waveguide with λr shift in resonance wavelength is as follows:(2)SaMZI,bulk=∂λr∂neffnmRIU.The efficiency of this sensor is calculated by device sensitivitySd for novel gradient strip-slot waveguide:(3)Sd=∂λr∂ncnmRIU.We analyzed this waveguide sensor atλ0 = 1550 nm. To validate this sensor sensitivity with other different wavelengths, the following equation is used to calculate normalized sensitivity Sd″:(4)Sd″=Sdλ0RIU−1.


## 3. Results and Discussion

In the silicon photonic waveguide biosensor, evanescent wave interacts with analytes surrounding the core. Transverse electric mode is irregular at sidewalls, so the intensity of light waves will be maximum at the top of the waveguide structure. In this proposed design, we analyzed rib and gradient step rib-slot waveguide to get more interaction with samples over the length of 8 mm [34, 35]. The rib waveguide structure is more suitable for biosensing applications. The transverse-electric (TE) polarization mode in the rib structure exhibits good performance over the waveguide for high index-contrast. TE mode exploits light vertically, so the analyte interaction with the waveguide has improved the bulk sensitivity. In the strip waveguide, the analyte interaction is only with the horizontal surface area. The field effect in the bottom layer comprising silicon oxide has no effect on sensitivity. At 1550 nm, the well-established CMOS foundry waveguide with a geometric width of 970 nm and height of 400 nm is used. In the proposed waveguide structure, transverse-electric field that exceeds 450 nm from the surface core provides higher sensitivity than TM [15]. This gradient-step waveguide structure helps to avoid antibody diffusion on the surface. By analysing such advantages, the proposed waveguide with 970 nm width is appropriately chosen. To obtain higher bulk sensitivity, the analyte thickness is optimized.


### 3.1. Analyte Transporting for Bulk Sensitivity

The biosensor uses biological analyte placed in sensing arm where the analyte interacts with the evanescent field, which is above the core. The analyte is a biomolecule that is minimal in its concentration, so the viscosity and density of the sample are not changed. Normally, the human C-reactive protein (CRP) molecule weight is 115 kilodalton. The analyte is placed in sensing arm to obtain bulk sensitivity of the photonic waveguide sensor. The concentration of the analyte at waveguide surface [A]surface involves the variations of thickness and reaction of TE mode, which exceeds the waveguide surface [A] (x, y, t).The temporal and spatial variations of the analyte in the sensing arm are described by the following diffusion equation:(5)∂A∂t+u∂A∂x+v∂A∂y=D∂2A∂x2+∂2A∂t2+G,where [A] is the analyte concentration in bulk, D is the diffusion coefficient of the analyte, and G denotes the reaction of the biomolecule in the waveguide surface [23]. The bulk sensitivity of the biosensor was analysed for four different analyte thicknesses, viz., 400 nm, 250 nm,150 nm, and 90 nm, in the waveguide. In the rib and rib-slot waveguide structure, the effective index of each analyte thickness of the different samples is analyzed through FDTD [23]. Based on the various analyte thickness, the rib and rib-slot waveguides for normal and cancer cell are measured at 1550 nm. Lumerical INTERCONNECT has foundry-specific PDK, which verifies the fabrication feasibility of this sensor. Figure 1 shows the silicon nitride biosensor setup. MZI rib waveguide sensor and novel gradient step rib-slot waveguide sensor are shown in Figures 2 and 3, respectively.Figure 2
Rib waveguide with analyte.Figure 3
Novel gradient step rib-slot waveguide with analyte.The optimized waveguide geometry of the rib structure is 400 nm thick, and 970 nm width is analyzed for sensitivity, applying bulk solution as analyte thickness. For bulk sensitivity calculation, the refractive index of the analyte normal cell is 1.35 and of the cancer cells varies from 1.39 to 1.401, as shown in Table1. In this process, the effective index of each thickness is calculated.Table 1
Refractive index of different cancer cells [32].
Name of the cellDiseaseRefractive indexNormal1.35JurkatLeukemia1.39HeLaCervical cancer1.392PC-12Brain1.395MDA-MB-231Breast cancer1.399MCF-7Breast cancer1.401FDTD analysis of the rib waveguide with analyte thickness of 400 nm, 250 nm, 150 nm, and 90 nm was carried out. Based on the effective index, using equations (1) and (3), the bulk sensitivity for different refractive indices was computed, and the results are provided in Table 2. In this physical environment, the sensor is analysed with integration of all analyte thickness in the MZI sensing arm with a total length of 8mm. The density and viscosity of the analyte are not constant in the sensor physically. Based on these environmental factors, to improve the sensor sensitivity, the analyte thickness ranging from 400 nm to 90 nm with each thickness of the sensing arm with a length of 2 mm is analyzed.Table 2
Analysis of rib waveguide bulk sensitivity with the analyte thickness of 400 nm to 90 nm.
RI400 nm waveguide bulk sensitivity250 nm waveguide bulk sensitivity150 nm waveguide bulk sensitivity90 nm waveguide bulk sensitivity1.35–1.4010.3117 RIU/RIU0.2501 RIU/RIU0.1882 RIU/RIU0.12764 RIU/RIUThe peak of the transmission spectrum of the rib waveguide, as shown in Figure4, for the sample refractive index of 1.35 (normal cells) and 1.401 (cancer cells) is observed at 1563 nm wavelength. This shift in the transmission spectrum makes the sensor detect Breast Cancer (MCF-7). However, this rib waveguide structure is insensitive at 1563 nm over the normal cells. Due to this, the sensor detects cancer cells with minor variations in the transmission spectrum.Figure 4
Transmission spectrum of normal cells with refractive index 1.35 vs Breast Cancer (MCF-7) cells with refractive index 1.401 of rib waveguide with integrated analyte thickness of 400 nm, 250 nm, 150 nm, and 90 nm.


### 3.2. Novel Gradient Step Rib-Slot Waveguide

This rib-slot waveguide with analyte is shown in Figure3, a sensitive and enhanced guiding structure that provides a better confinement factor. Integration of the sample holder to the sensor is complex in fabrication over the small region. This proposed gradient step rib-slot waveguide holds the sample effectively without any polydimethylsiloxane (PDMS) layer. Numerically, for different analyte thickness layers, the effective area was computed for 400 nm, 250 nm, 150 nm, and 90 nm; they are tabulated in Tables 3, 4, 5, and 6, respectively, with waveguide bulk sensitivity using equation (1) and sensor architecture sensitivity using equation (2). The theoretical analysis has been investigated considering the fabrication tolerance of the waveguide structure. The key task of waveguide optimization for bulk sensitivity is mode field distribution over the sensor surface. Analysis of the bulk sensitivity in the rib-slot waveguide, slot geometry of the 790 nm width, and 400 nm thickness with low index region that influences the analyte perfectly [36]. The gap region of the rib-slot guiding structure highly supports the TE mode, which gives evanescent waves to interact with the analyte in the highly effective area [31]. Thus, the waveguide guiding structure strongly influences the bulk sensitivity of this gradient step rib-slot biosensor. By integrating this in the Mach–Zehnder interferometer, the design of silicon photonics label-free biosensing for point-of-care devices will be more effective, and fabrication tolerance will be less compared to conventional waveguide structures like strip and slot waveguides.Table 3
Analysis of bulk sensitivity of the rib-slot waveguide with 400 nm analyte thickness.
RIEffective indexEffective area400 nm bulk sensitivity1.351.4691331.530030.2574 (RIU/RIU)1.391.4792981.472121.3921.4798321.469351.3951.4806361.465221.3991.4817171.459751.4011.4822611.45703Table 4
Analysis of bulk sensitivity of rib-slot waveguide with 250 nm analyte thickness.
RIEffective indexEffective area250 nm bulk sensitivity1.351.5155381.267470.2033 (RIU/RIU)1.391.5236361.247791.3921.524051.246831.3951.5246731.245381.3991.5255071.243461.4011.5259251.2425Table 5
Analysis of bulk sensitivity of rib-slot waveguide with 150 nm analyte thickness.
RIEffective indexEffective area150 nm bulk sensitivity1.351.5494381.161190.1333 (RIU/RIU)1.391.5551381.154241.3921.5554261.153881.3951.5558571.153341.3991.5564331.152611.4011.5567211.15225Table 6
Analysis of bulk sensitivity of rib-slot waveguide with 90 nm analyte thickness.
RIEffective indexEffective area90 nm bulk sensitivity1.351.5698331.114250.0960 (RIU/RIU)1.391.5737021.112481.3921.5738951.112361.3951.5741841.112191.3991.5745691.111951.4011.5747611.11182By increasing the effective surface area in the sensor, the sample interacts more efficiently to obtain high waveguide bulk sensitivity. This numerical analysis of 400 nm, 250 nm, 150 nm, and 90 nm thickness in FDTD has been carried out based on device operation in the physical environment. Integration of all analyte thicknesses in the MZI sensing arm with a total length of 8μm generates increased absorption at three different wavelengths in the transmission spectrum, as shown in Figure 5. This proposed rib-slot waveguide geometry optimization increases the detection rate of cancer cells compared with single analyte thickness of sensing arm length two μm waveguide.Figure 5
Gradient rib-slot waveguide structure with a width of 450 nm and height of 220 nm with integrated analyte thickness of 400 nm, 250 nm, 150 nm, and 90 nm.The transmission spectrum of the rib-slot waveguide in Figure6 shows the peaks at three different points of wavelength, 1563 nm, 1573 nm, and 1579 nm, of the sensor to detect Breast Cancer (MCF-7) cells. However, the rib-slot waveguide structure provides a good response and differentiates the cancer cells from the normal human cells. From the numerical analysis of different geometric, the proposed design of novel gradient rib-slot waveguide structure is in high bulk sensitivity. With 90 nm analyte thickness, in Table 7, the bulk sensitivity of breast cancer cells (MCF-7) is 1.1240 (RIU/RIU), which is higher than that in the rib waveguide. This structure makes the sensor efficient in detecting cancer cells. This design can be integrated in a point-of-care sensor system with a read-out.Figure 6
Silicon nitride rib-slot waveguide transmission spectrum of normal cells with refractive index 1.35 vs. Breast Cancer (MCF-7) cells with refractive index of 1.401 with integrated analyte thickness of 400 nm, 250 nm, 150 nm, and 90 nm.Table 7
Comparison of bulk sensitivity ofλ0 = 1550 nm with other silicon-based photonic sensors.
SensorArchitectureSw,bulk(RIU/RIU)Sdnm/RIUSd″RIU−1[38]Ring0.453830.247[39]Ring0.894900.316[28]Ring0.854400.284[40]Ring0.805800.374[41]PSBGn/a5790.374[42]Ring0.975750.371[43]Ring1.035450.352[33]Bragg0.935070.387[44]MZI0.79−599−0.386This workMZI2.06995680.366The performance of the sensor depends upon the TE polarization on waveguide mode, as this analyte thickness is more sensitive to refractive index changes in cladding. In this numerical analysis, two different waveguide geometry structures, rib and rib-slot, have been simulated and the dispersion characteristics are studied [37]. In convention, silicon nitride waveguides achieve sharp bending with low loss, as shown in Figure 7(b), dispersion due to modes that overlap with the analyte. Rib-slot waveguide is more dispersive than rib waveguide, as shown in Figure 7(a). However, the sensitivity of the rib-slot waveguide sensor is higher. Normalized sensitivity Sd″ will be calculated to compare (λ0) for different wavelengths using equation (4).Figure 7
Dispersion of RI 1.35 normal cells and 1.401 cancer cells: (a) rib waveguide and (b) rib-slot waveguide.
(a)(b)


## 3.1. Analyte Transporting for Bulk Sensitivity

The biosensor uses biological analyte placed in sensing arm where the analyte interacts with the evanescent field, which is above the core. The analyte is a biomolecule that is minimal in its concentration, so the viscosity and density of the sample are not changed. Normally, the human C-reactive protein (CRP) molecule weight is 115 kilodalton. The analyte is placed in sensing arm to obtain bulk sensitivity of the photonic waveguide sensor. The concentration of the analyte at waveguide surface [A]surface involves the variations of thickness and reaction of TE mode, which exceeds the waveguide surface [A] (x, y, t).The temporal and spatial variations of the analyte in the sensing arm are described by the following diffusion equation:(5)∂A∂t+u∂A∂x+v∂A∂y=D∂2A∂x2+∂2A∂t2+G,where [A] is the analyte concentration in bulk, D is the diffusion coefficient of the analyte, and G denotes the reaction of the biomolecule in the waveguide surface [23]. The bulk sensitivity of the biosensor was analysed for four different analyte thicknesses, viz., 400 nm, 250 nm,150 nm, and 90 nm, in the waveguide. In the rib and rib-slot waveguide structure, the effective index of each analyte thickness of the different samples is analyzed through FDTD [23]. Based on the various analyte thickness, the rib and rib-slot waveguides for normal and cancer cell are measured at 1550 nm. Lumerical INTERCONNECT has foundry-specific PDK, which verifies the fabrication feasibility of this sensor. Figure 1 shows the silicon nitride biosensor setup. MZI rib waveguide sensor and novel gradient step rib-slot waveguide sensor are shown in Figures 2 and 3, respectively.Figure 2
Rib waveguide with analyte.Figure 3
Novel gradient step rib-slot waveguide with analyte.The optimized waveguide geometry of the rib structure is 400 nm thick, and 970 nm width is analyzed for sensitivity, applying bulk solution as analyte thickness. For bulk sensitivity calculation, the refractive index of the analyte normal cell is 1.35 and of the cancer cells varies from 1.39 to 1.401, as shown in Table1. In this process, the effective index of each thickness is calculated.Table 1
Refractive index of different cancer cells [32].
Name of the cellDiseaseRefractive indexNormal1.35JurkatLeukemia1.39HeLaCervical cancer1.392PC-12Brain1.395MDA-MB-231Breast cancer1.399MCF-7Breast cancer1.401FDTD analysis of the rib waveguide with analyte thickness of 400 nm, 250 nm, 150 nm, and 90 nm was carried out. Based on the effective index, using equations (1) and (3), the bulk sensitivity for different refractive indices was computed, and the results are provided in Table 2. In this physical environment, the sensor is analysed with integration of all analyte thickness in the MZI sensing arm with a total length of 8mm. The density and viscosity of the analyte are not constant in the sensor physically. Based on these environmental factors, to improve the sensor sensitivity, the analyte thickness ranging from 400 nm to 90 nm with each thickness of the sensing arm with a length of 2 mm is analyzed.Table 2
Analysis of rib waveguide bulk sensitivity with the analyte thickness of 400 nm to 90 nm.
RI400 nm waveguide bulk sensitivity250 nm waveguide bulk sensitivity150 nm waveguide bulk sensitivity90 nm waveguide bulk sensitivity1.35–1.4010.3117 RIU/RIU0.2501 RIU/RIU0.1882 RIU/RIU0.12764 RIU/RIUThe peak of the transmission spectrum of the rib waveguide, as shown in Figure4, for the sample refractive index of 1.35 (normal cells) and 1.401 (cancer cells) is observed at 1563 nm wavelength. This shift in the transmission spectrum makes the sensor detect Breast Cancer (MCF-7). However, this rib waveguide structure is insensitive at 1563 nm over the normal cells. Due to this, the sensor detects cancer cells with minor variations in the transmission spectrum.Figure 4
Transmission spectrum of normal cells with refractive index 1.35 vs Breast Cancer (MCF-7) cells with refractive index 1.401 of rib waveguide with integrated analyte thickness of 400 nm, 250 nm, 150 nm, and 90 nm.


## 3.2. Novel Gradient Step Rib-Slot Waveguide

This rib-slot waveguide with analyte is shown in Figure3, a sensitive and enhanced guiding structure that provides a better confinement factor. Integration of the sample holder to the sensor is complex in fabrication over the small region. This proposed gradient step rib-slot waveguide holds the sample effectively without any polydimethylsiloxane (PDMS) layer. Numerically, for different analyte thickness layers, the effective area was computed for 400 nm, 250 nm, 150 nm, and 90 nm; they are tabulated in Tables 3, 4, 5, and 6, respectively, with waveguide bulk sensitivity using equation (1) and sensor architecture sensitivity using equation (2). The theoretical analysis has been investigated considering the fabrication tolerance of the waveguide structure. The key task of waveguide optimization for bulk sensitivity is mode field distribution over the sensor surface. Analysis of the bulk sensitivity in the rib-slot waveguide, slot geometry of the 790 nm width, and 400 nm thickness with low index region that influences the analyte perfectly [36]. The gap region of the rib-slot guiding structure highly supports the TE mode, which gives evanescent waves to interact with the analyte in the highly effective area [31]. Thus, the waveguide guiding structure strongly influences the bulk sensitivity of this gradient step rib-slot biosensor. By integrating this in the Mach–Zehnder interferometer, the design of silicon photonics label-free biosensing for point-of-care devices will be more effective, and fabrication tolerance will be less compared to conventional waveguide structures like strip and slot waveguides.Table 3
Analysis of bulk sensitivity of the rib-slot waveguide with 400 nm analyte thickness.
RIEffective indexEffective area400 nm bulk sensitivity1.351.4691331.530030.2574 (RIU/RIU)1.391.4792981.472121.3921.4798321.469351.3951.4806361.465221.3991.4817171.459751.4011.4822611.45703Table 4
Analysis of bulk sensitivity of rib-slot waveguide with 250 nm analyte thickness.
RIEffective indexEffective area250 nm bulk sensitivity1.351.5155381.267470.2033 (RIU/RIU)1.391.5236361.247791.3921.524051.246831.3951.5246731.245381.3991.5255071.243461.4011.5259251.2425Table 5
Analysis of bulk sensitivity of rib-slot waveguide with 150 nm analyte thickness.
RIEffective indexEffective area150 nm bulk sensitivity1.351.5494381.161190.1333 (RIU/RIU)1.391.5551381.154241.3921.5554261.153881.3951.5558571.153341.3991.5564331.152611.4011.5567211.15225Table 6
Analysis of bulk sensitivity of rib-slot waveguide with 90 nm analyte thickness.
RIEffective indexEffective area90 nm bulk sensitivity1.351.5698331.114250.0960 (RIU/RIU)1.391.5737021.112481.3921.5738951.112361.3951.5741841.112191.3991.5745691.111951.4011.5747611.11182By increasing the effective surface area in the sensor, the sample interacts more efficiently to obtain high waveguide bulk sensitivity. This numerical analysis of 400 nm, 250 nm, 150 nm, and 90 nm thickness in FDTD has been carried out based on device operation in the physical environment. Integration of all analyte thicknesses in the MZI sensing arm with a total length of 8μm generates increased absorption at three different wavelengths in the transmission spectrum, as shown in Figure 5. This proposed rib-slot waveguide geometry optimization increases the detection rate of cancer cells compared with single analyte thickness of sensing arm length two μm waveguide.Figure 5
Gradient rib-slot waveguide structure with a width of 450 nm and height of 220 nm with integrated analyte thickness of 400 nm, 250 nm, 150 nm, and 90 nm.The transmission spectrum of the rib-slot waveguide in Figure6 shows the peaks at three different points of wavelength, 1563 nm, 1573 nm, and 1579 nm, of the sensor to detect Breast Cancer (MCF-7) cells. However, the rib-slot waveguide structure provides a good response and differentiates the cancer cells from the normal human cells. From the numerical analysis of different geometric, the proposed design of novel gradient rib-slot waveguide structure is in high bulk sensitivity. With 90 nm analyte thickness, in Table 7, the bulk sensitivity of breast cancer cells (MCF-7) is 1.1240 (RIU/RIU), which is higher than that in the rib waveguide. This structure makes the sensor efficient in detecting cancer cells. This design can be integrated in a point-of-care sensor system with a read-out.Figure 6
Silicon nitride rib-slot waveguide transmission spectrum of normal cells with refractive index 1.35 vs. Breast Cancer (MCF-7) cells with refractive index of 1.401 with integrated analyte thickness of 400 nm, 250 nm, 150 nm, and 90 nm.Table 7
Comparison of bulk sensitivity ofλ0 = 1550 nm with other silicon-based photonic sensors.
SensorArchitectureSw,bulk(RIU/RIU)Sdnm/RIUSd″RIU−1[38]Ring0.453830.247[39]Ring0.894900.316[28]Ring0.854400.284[40]Ring0.805800.374[41]PSBGn/a5790.374[42]Ring0.975750.371[43]Ring1.035450.352[33]Bragg0.935070.387[44]MZI0.79−599−0.386This workMZI2.06995680.366The performance of the sensor depends upon the TE polarization on waveguide mode, as this analyte thickness is more sensitive to refractive index changes in cladding. In this numerical analysis, two different waveguide geometry structures, rib and rib-slot, have been simulated and the dispersion characteristics are studied [37]. In convention, silicon nitride waveguides achieve sharp bending with low loss, as shown in Figure 7(b), dispersion due to modes that overlap with the analyte. Rib-slot waveguide is more dispersive than rib waveguide, as shown in Figure 7(a). However, the sensitivity of the rib-slot waveguide sensor is higher. Normalized sensitivity Sd″ will be calculated to compare (λ0) for different wavelengths using equation (4).Figure 7
Dispersion of RI 1.35 normal cells and 1.401 cancer cells: (a) rib waveguide and (b) rib-slot waveguide.
(a)(b)


## 4. Conclusion

We proposed silicon nitride MZI sensor architecture as integrated biosensor for point-of-care device. This biosensor detects virus and biomolecules fast and is cost-effective. Our simulated analysis determines optimized waveguide geometry that maximizes the bulk sensitivity. MZI utilizes the refractive index of different cancer cells (1.39–1.401) to determine the waveguide bulk sensitivitySw,bulk. In addition, we compared gradient step rib waveguide with rib-slot waveguide. The results show that the gradient step rib-slot waveguide is efficient and can hold analytes without any PDMS material. Analyte transportation and leakage of molecules at the edge of the waveguide lead to decrease in the sensitivity of the sensor. Our proposed design exhibits a high Sw,bulk of 2.0699 RIU/RIU and a device sensitivity Sd of 568nm/RIU calculated based on analyte thickness. The absorption of cancer cells at three wavelengths 1563 nm, 1573 nm, and 1579 nm offers high detection rate compared with the standard rib waveguide. The silicon nitride-based waveguide biosensor may be fabricated using CMOS E-beam lithography, and its stability will be matched to the simulated results. The proposed biosensor can provide test results in a short time than the conventional biopsy, which takes two days to detect cancer cells.



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