Study of Silicon Nitride Waveguide Platform for On- Chip Virus Detection: Prospects for COVID-19

This work presents a rigorous sensitivity analysis of silicon nitride on silicon dioxide strip waveguide for virus detection, focusing on COVID-19. In general, by functionalizing the waveguide surface with specific antibodies layer, we make the optical sensor sensitive only to a particular virus. Unlike conventional virus detection methods such as polymerase chain reaction (PCR), integrated refractive index (RI) optical sensors offer cheap and mass-scale fabrication of compact devices for fast and straightforward detection with high sensitivity and selectivity. Our analysis includes a wide range of wavelengths from visible to mid-infrared. We determined the strip waveguide's single-mode dimensions and the optimum dimensions that maximize the sensitivity to the virus layer attached to its surface at each wavelength. We also compared the strip waveguide to the widely used slot waveguide. Our study shows that silicon nitride strip waveguide working at lower wavelengths is the optimum choice for virus detection as it maximizes both the waveguide sensitivity (S wg ) and the figure of merit (FOM) of the sensor. Furthermore, the optimized waveguide can work for a range of viruses. Balanced Mach-Zehnder interferometer (MZI) sensors were designed at different wavelengths showing high FOM at λ = 450nm ranging from 500 RIU -1 up to 1231 RIU -1 with L MZI =500 µm. Different MZI configurations were also studied and compared. Finally, edge coupling from the fiber to the sensor was designed, showing insertion loss (IL) at λ = 450nm of 4.1 dB for the design with FOM = 500 RIU -1 . The obtained coupling efficiencies are higher than recently proposed fiber couplers.


Introduction
CORONA virus disease of 2019 (COVID-19) pandemic is currently an exceptional threat to human lives all over the world. Its expeditious spread has led to millions of cases and hundreds of thousands of deaths in a few months. Almost all countries worldwide are forced to lockdown for several months to limit the spread of the virus, leading to devastating social and economic effects. In general, many people across the globe lose their life due to viral infection diseases [1]. Hence, simple, fast, cheap, and accurate detection of viruses are of great importance. Polymerase chain reaction (PCR) is one of the well-known methods used for virus detection and it is the primary method used currently for COVID-19 detection [2].
Although this technique is highly sensitive and accurate, it is expensive, time-consuming and involves complex procedures and sample preparation.
Optical refractive index (RI) sensing is one of the main integrated optical techniques used for biodetection [3][4][5][6][7][8]. RI sensors offer fast, compact and cheap detection with high sensitivities. However, RI sensors are not selective as they only detect the change in the medium (clad) refractive index which can occur due to different substances. A widely used technique to solve this problem in bio-sensing is surface functionalization [9][10][11]. In surface functionalization, the surface of the sensing waveguide is coated with speci c molecules called binder or capture molecules and immobilized through a certain process. These immobilized molecules selectively capture the analyte molecules to be detected from the whole sample.
After sensor exposure to the sample, a washing step is needed to make sure that only the analyte of interest is present in the sensors' medium (clad) hence, the detected refractive index change is due to this analyte alone.
RI sensors' performance is determined mainly by the gure of merit (FOM) which is the ratio between the sensor sensitivity (S) and full width half maximum (FWHM) of the output spectrum, FOM=S/FWHM. RI sensors' sensitivity (S) can be divided into device sensitivity (S D ) and waveguide sensitivity (S wg ). Device sensitivity is de ned as the ratio between the change in the resonance wavelength and the change in the waveguide mode effective index, S D =dλ res /dn eff . S D is determined by the optical sensor con guration used and its dimensions such as Mach-Zhender interferometer and its arm's length [3][4][5] or ring resonators and its ring radius [6][7][8]. While waveguide sensitivity is de ned as the ratio between the change in the mode effective index and the change in the medium index, S wg =dn eff /dn med . S wg is determined by the sensing waveguide structure such as strip, rib or slot waveguides and its dimensions. The overall sensitivity of the optical sensor is the product of both parameters, S=S D ×S wg . Hence, to maximize any RI sensor performance waveguide sensitivity (S wg ) should be maximized.
Silicon nitride on insulator (SiNOI) waveguide platform, where insulator here is the silicon dioxide, offers numerous advantages for various applications [12][13][14][15]. Similar to SOI platform SiNOI is CMOS compatible allowing for mass-scale and low cost fabrication [14][15]. It also allows for monolithic integration with silicon devices and other electronic circuitry [12]. The lower refractive index contrast of the SiNOI waveguide compared to SOI reduce scattering loss due to surface roughness resulting in much lower propagation losses [12][13][14], while still maintaining device compactness. This lower index contrast also makes SiNOI devices more tolerant to fabrication errors [12][13]. In addition, Si 3 N 4 thermo-optical coe cient is one order of magnitude lower than Si [13], hence Si 3 N 4 based devices are less sensitive to temperature uctuations.
Moreover, SiNOI platform has wider transparency range, from visible to mid-infrared, compared to SOI platform [12][13][14][15]. This allows the realization of photonic applications outside the telecom bands, such as integrated optical phased arrays for LIDAR applications [16]. Finally, while silicon have large Kerr effect the two-photon absorption (TPA) prevents e cient nonlinear applications. Si 3 N 4 on the other hand, has adequate Kerr nonlinearity and almost zero TPA [14][15]. Thus, SiNOI platform allow for frequency comb as well as supercontinuum generation [17][18], which are essential for high data-rate telecommunications, high-resolution spectroscopy and frequency metrology [19].
In this work, we present a detailed sensitivity analysis of silicon nitride (Si 3 N 4 ) on silicon dioxide (SiO 2 ) strip waveguide for virus detection. The waveguide surface is assumed to be functionalized by the antibodies of the virus to be detected, using a process similar to that in [10], such that the medium index change is only due to this virus.
A Finite difference eigenmode solver (FDE) [20] is used to determine the waveguide dimensions that maximize the waveguide sensitivity (S wg ) to a virus layer attached to its surface. Both fundamental quasi-transverse electric (TE) and quasi-transverse magnetic (TM) mode are studied. Moreover, slot waveguide was also analyzed and compared to the strip waveguide. Different operating wavelengths were examined from the visible to the mid-infrared range. We found that S wg and FOM increase at lower wavelengths. This analysis is essential to construct a cheap, mass-scale fabrication of compact and highly sensitive RI optical sensor for fast virus detection . The optimized waveguides can be used in different integrated optical devices such as interferometers and resonators to construct the virus sensor.
MZI sensors utilizing the optimized waveguides were designed reaching FOM=1231 RIU -1 at λ=450 nm with 500 µm arms' length. We also designed a MZI sensor with waveguide widths above 1 µm that can be easily fabricated in simple and cheap facilities. Finally, ber edge coupling to the sensors chip was studied and optimized, showing higher coupling e ciencies than recently demonstrated ber couplers.
This analysis is generic for any biosensor that uses surface functionalization for selective sensing. One will only need to adjust the optimum waveguide dimensions according to the molecules' size and refractive index to be detected. on SiO 2 substrate and water clad. The waveguide surface is functionalized for selective detection such that only the virus of interest will adhere to the surface and form a layer. We model this layer by a thickness h vir equal to the virus diameter and a refractive index n layer , as shown in Fig.1

(a). For COVID-19
the virus diameter is around 80 nm [21][22] and hence we use h vir =80 nm. The refractive index n layer is given by (1). The value of n layer changes between the refractive index of the water n water and the refractive index of the virus n vir according to the virus coverage fraction r.
In this case, virus binding to the immobilized antibodies on the waveguide surface will change this layer refractive index which will accordingly change the waveguide mode effective index.
Different operating wavelengths are studied from visible range λ=450 nm (blue) and λ=650 nm (red), to near-infrared λ=980 nm and λ=1550 nm, and MIR λ=3600 nm. Material dispersion is considered where silicon nitride, silicon dioxide and water refractive index data along the wavelength are obtained from [23][24]. At each operating wavelength, we rstly de ne the single-mode dismensions by determining the maximum width at different thicknesses using FDE solver [20], as shown in Fig. 1(b-c). Then we calculate the waveguide sensitivity (S wg ) at different waveguide dimensions (w and h), for both fundamental quasi-TE and fundamental quasi-TM modes, which we will denote as TE and TM for simplicity. Note that, unlike most RI sensors designs, here we calculate the surface waveguide sensitivity, S wg =dn eff /dn layer , not the bulk sensitivity, S wg =dn eff /dn clad , which is more accurate for viral detection. S wg is calculated with n layer around the water index, which means that the waveguides are optimized to have maximum sensitivity at minimum virus coverage (r close to 0). Accordingly, the exact virus refractive index n vir doesn't affect the obtained results. show that for each waveguide thickness, there is an optimum width that maximizes the waveguide sensitivity. Such behavior is expected [25]. For large waveguide widths most of the mode eld is con ned inside the silicon nitride core, resulting in low sensitivity. As the width decreases, the mode becomes less con ned and the evanescent eld in the cladding increase, increasing the sensitivity. However, for small widths, near cut-off, more eld moves to the higher (than clad) refractive index substrate which again decreases the sensitivity [25]. Results also show that as the waveguide thickness increases, the optimum width (w opt ) decreases and optimum sensitivity increases, which is also expected [25]. Hence, waveguides with a higher aspect ratio (AR), AR=h/w opt , can achieve higher S wg reaching 0.513 for the TE mode with w=104 nm and h=300 nm (AR=2.88). This behavior is similar for all wavelengths. However, high AR waveguide sensors are more challenging to fabricate and expensive as they need a ne mask and complex lithography system to obtain the small waveguide widths needed.
Moreover, at high AR the waveguide sensitivity is very sensitive to width variations. For example, changing the width by only 20 nm for the TE mode with AR=2.88 will signi cantly reduce S wg to lower than 0.15, i.e. 3.4 times reduction. Also, this optimum width (w opt =104 nm) is close to the mode cut-off width (w cut-off =78 nm) and multimode width (w MM =110nm). Figure 2(c) shows that for high thicknesses with low optimum widths (high AR) TE mode can achieve higher S wg than TM mode while, for lower thicknesses (higher w opt and low AR) TM mode exhibit higher S wg than TE mode. This is because the TE/TM modes have eld discontinuity at the core edges in the x/y direction; hence, decreasing the width/thickness will increase the evanescent eld's amount and, hence, sensitivity. Hence, TM mode is optimum for cheap and easy to fabricate large feature size sensors. Figure 3 shows the optimum S wg and the optimum width (w opt ) dependence with the AR (or h) at different wavelengths for the TE and TM mode, respectively. We can see that both the operating wavelength and AR have a signi cant effect on the obtained S wg . In addition, the highest S wg is obtained at the lowest operating wavelength (λ=450 nm) and it decreases monotonically as the wavelength increases. It is important to note that, scaling the waveguide dimensions with the wavelength does not result in the same waveguide sensitivity. This is mainly due to the unchanged layer's thickness that changes its refractive index (representing virus attachment). Results also show that TE mode achieves the highest possible S wg at every wavelength.
We have also examined Si 3 N 4 slot waveguides (TE mode only). Slot waveguides sensitivity increase as slot width decrease. Here we used a slot width (w slot ) of 200nm as this is the smallest width that can still allow waveguide functionalization [5], [26]. Figure 4(a) shows the maximum slot waveguide sensitivities at λ=1.55µm and λ=3.6µm for the TE mode. At λ=1.55µm S wg =0.22 while at λ=3.6µm S wg =0.192. In order to obtain slot mode in the visible range, the slot width should be less than 200nm hence not suitable for virus detection (functionalization). Consequently, strip waveguides are more suitable for virus detection as they can achieve higher S wg at lower wavelengths leading to much higher FOM. In addition, the functionalization process in tiny a 200nm slot is challenging. Moreover, strip waveguide offers a simple sensor design as for example there is no need for a strip to slot mode converter.
We also tested the optimized waveguides for different virus diameters (i.e. different h vir ) from 60 nm to 200 nm. Figure 4(b) shows that the waveguide sensitivity increase as the virus size increase. It is important to note that, the optimum waveguide dimensions don't change signi cantly, from the one obtained for h vir =80nm, by changing the virus size. Hence, the same waveguide can be used for a range of viruses with different diameters.
While waveguide sensitivity is an important parameter, the RI optical sensors' overall performance is determined by the FOM. In both interferometers and resonators, the sensitivity (S) is proportional to S wg ×λ. However, the FOM is proportional to S wg /λ because the FWHM is proportional to λ 2 . Hence, operating the sensor at lower wavelengths will achieve the highest performance as S wg increase and λ decrease maximizing the FOM. Figure 5 shows tted curves of both S wg ×λ and S wg /λ terms versus wavelength for different AR. It can be seen that FOM increased around 8 times from NIR (λ=1.55 µm) to visible (λ=450 nm) wavelength for both TE and TM modes while the sensitivity decreased only 1.4 times. Moreover, working in the visible wavelength range have another advantage for biosensing as in this range, the losses due to water absorption are minimized. From more than 200 dB/cm mode loss at λ=3.6 µm to less than 3×10 -3 dB/cm in the visible range.

Sensors Design
Different MZI sensors have been designed to convert the change in the waveguide's effective index to a sensible quantity for COVID-19 detection. The Si 3 N 4 waveguide surface will be functionalized with the virus antibodies. In this case, the COVID virus in the sample will be selectively captured by the waveguide. COVID virus binding will change the refractive index of the 80 nm layer covering the waveguide core. Accordingly, a wavelength shift (Δλ) in the transmission spectrum of the MZI will occur, from which the virus concentration can then be determined.
For a MZI device with power evenly devided to its arms the transmission spectrum can be derived to be [27]: where Δφ the phase difference of the MZI arms; n eff,sens , n eff,ref and L sens , L ref are the waveguide mode effective index and length of the sensing and reference arms of the MZI sensor, respectively.
From which we can get the peak wavelengths as: Accordingly, the free spectral range (FSR), full-width half maximum (FWHM), sensitivity (S) and FOM of the MZI sensor can be derived as follows [27]: FOM is the main performance parameter of any RI sensor as it determines the minimum detectable refractive index change. Table 1 Table 1 also shows FOM at λ=450 nm for different AR, reaching a maximum of 1231 RIU -1 at AR=2.88. As mentioned before, at higher waveguide widths, TM mode was used as it can reach higher S wg than TE mode, see Fig. 2(c). Note that, MIR range was discarded due to its low S wg and high (water absorption) losses. Although small waveguide dimensions in the visible range exhibit high sensing performance, the fabrication of such waveguides require complex and expensive lithography systems like electron beam or deep UV lithography. Hence, we want to determine a sensor's performance with a feature size above 1µm, which will allow for easy and cheap fabrication. While lower wavelengths exhibit higher performance, the blue wavelength has almost zero sensitivity for small AR waveguides with w opt >1µm. Hence, we choose to compare two designs both with TM mode. The rst design is operating at low (red) wavelength λ=650 nm exhibiting S wg of 0.115, and the second is operating at a higher wavelength at λ=980 nm but demonstrating slightly higher S wg of 0.13. Table 2 shows the dimensions and the FOM of both MZI sensor designs. We can see that the rst design operating at lower (red) wavelength with AR=0.05 has a higher FOM of 158 RIU -1 even if it exhibits slightly lower S wg . The minimum detectable index change of the virus layer can be calculated from [29] as Δn min =1/FOM.
These values can then be converted to minimum detectable virus coverage r min using (1). Table 3 shows Δn min and r min for the MZI sensors designs at the blue wavelength with different AR and the design at red wavelength optimized for large dimensions (AR=0.05) with L MZI =500µm. Note that lower virus concentrations (coverage r) can be detected by increasing the FOM by increasing the MZI sensor length as given in (7).
It is important to note that, silicon nitride waveguides with lm thickness great than 300 nm suffer large stress, and different techniques are used to overcome this problem [30][31][32]. However, our analysis shows that thin silicon nitride waveguides, with h<300 nm, in the visible range are of better sensing performance. In this case, such stress is reduced and a homogeneous index and thickness can be obtained using lowpressure chemical vapor deposition (LP-CVD) [32]. Finally, different MZI con gurations were studied and compared for sensing, namely symmetric MZI (s-MZI), asymmetric MZI (a-MZI) and loop terminated MZI (LT-MZI) shown in Fig. 6. The simulated results of the different con gurations are summarized in Table 4 for the design of TM mode with w sens =270 nm, h=100 nm and w ref =300 nm at λ=450 nm and L sens =500 µm. While s-MZI (L sens =L ref ) sensitivity is determined only by its waveguide structures, i.e. Δn eff =n eff,sens -n eff,ref , a-MZI (L sens =L ref +ΔL) sensitivity can be engineered using ΔL=L sens -L ref , according to (6). However, both structures will exhibit almost the same FOM for the same L sens . On the other hand, LT-MZI is a recently proposed design [33] that consists of a conventional MZI with a loop connecting the output directional coupler arms, re ecting back the wave to the interferometer. For the same waveguide structure and L sens , LT-MZI will exhibit the same sensitivity with the conventional MZI while the FWHM will reduce to half resulting in twice the FOM. The LT-MZI directional couplers are also assumed to be ideal 3-dB couplers. The asymmetric LT-MZI can also be used to control the sensitivity using ΔL as in the a-MZI case.  [34][35][36], reaching a measured coupling e ciency as low as -1.75 dB [34], using bottom multilayer re ector and apodized grating coupler. However, few work have been pubished for coupling in the visible wavelength range [37][38][39].
In this section, we study the coupling from single-mode bers [40] in the visible region (blue and red) to the silicon nitride chip through edge coupling again using an FDE solver. We focus on the coupling to the TM mode sensors designs mentioned in the previous section, which can achieve high coupling e ciencies and high FOM with waveguide widths larger than 250nm, see Table 1 and Table 2. Design 1: w sens =550 nm, h=70 nm (AR=0.13) and Design 2: w sens =270 nm, h=100 nm (AR=0.37) both at λ=450 nm. While Design 3: w sens =1500 nm, h=80 nm (AR=0.05) at λ=650 nm for large feature size sensor (w>1 µm). Figure 7(a) shows the coupling e ciency at blue and red wavelengths to a waveguide with thickness h=20nm and h=40nm, respectively. A maximum coupling e ciency of 93% and 92.7% can be achieved from the ber to the waveguide TM mode at λ=450nm with w=600 nm and at λ=650nm with w=565 nm, respectively. Note that, waveguides with higher thicknesses exhibit signi cantly lower coupling for w>250nm. Hence, there is a mismatch between the waveguides' dimensions with optimum ber coupling (w cpl , h cpl ) and optimum sensing (w sens , h sens ), as shown in Fig. 7(b). Accordingly, the coupling between these two waveguides was studied and the insertion loss (IL) was determined for the different sensing waveguides. For each design we optimize the waveguide-waveguide coupling, w cpl ×h cpl → w out ×h sens , by changing the output waveguide width (w out ), which can then be converted to w sens with signi cantly low losses using a taper. Hence, for the blue wavelength the IL from the ber to the optimum coupling waveguide, w cpl =600 nm and h cpl =20 nm, is 0. These designs exhibit higher coupling e ciencies than most ber couplers proposed for the Si 3 N 4 platform at the same wavelength range [37][38][39]. This is mainly due to the different waveguide dimensions, as the optimum waveguides for sensing have small core thickness dimensions. Thus, exhibiting large mode size which leads to better matching with the ber mode. The recently proposed ber couplers and our proposed ones are summarized in Table 5.