1. Introduction and background

Silicon photonic sensors have been extensively investigated for use as biosensors in fields such as basic medical research and diagnosis [1], bioterror detection [2,3], and smart home healthcare [4] diagnostics. Their small size, immunity to electromagnetic interference, sensitivity to adsorbed biomolecular layers at their surface, and compatibility with established, high volume CMOS foundry processes make them an attractive technology for lab-on-chip applications [5–8]. With their diagnostic platform that leverages TE mode silicon photonic ring resonators, Genalyte has demonstrated significant progress towards realizing the first commercially available, highly multiplexed, silicon photonic biosensor for clinical and research use [1, 9–12]. There still exists many medical diagnostic applications where TE mode ring resonators cannot achieve the sensitivities required for a definitive clinical diagnosis without secondary amplification [9, 13]. With higher sensitivities resulting from an increased overlap of the electric field with the target analyte, TM mode based rings have been investigated as alternatives to their TE mode counterparts [8,14,15].

Researchers have investigated the optimum waveguide thicknesses needed to obtain maximum sensitivities for a slab waveguide sensor [14], but not for waveguide resonator sensors, which have different characteristics.

In the cases of resonators and interferometers, the sensitivities also depend on the group index of the waveguide (n_g), which accounts for the dispersion effects. In this paper, we have calculated, and experimentally validated, optimum thicknesses to achieve the highest sensitivities for resonator sensors. We fabricated TM resonators with the standard etch layer thicknesses offered by MPW foundries and verified our theoretical predictions with experimental observations. Until now, the highest experimental sensitivity reported for quasi-TM ring resonators was 135 nm/RIU [15]. Using the optimum waveguide thickness to maximize sensitivity, we demonstrate quasi-TM ring resonators with a bulk sensitivity of 270 nm/RIU. This value is within 90% of the maximum achievable sensitivity for a resonator sensor using strip waveguides.

2. Theory and simulation results

Employing fully-vectorial 2D eigenmode (using Lumerical MODE Solutions) calculations and analytical equations in MATLAB, we have determined our design parameters for a racetrack at, or close to, critical coupling [6,16]. These methods were also used to investigate the waveguide dimensions that result in maximum sensitivity for the fundamental quasi-TE mode and the fundamental quasi-TM mode (henceforth referred to as “TM”).

2.1. Waveguide sensitivity

There are two types of waveguide sensitivity: (1) bulk sensitivity and (2) surface sensitivity. The homogenous or bulk sensitivity of a waveguide is defined as the sensitivity to changes in the refractive index of the cladding, e.g., an aqueous solution, surrounding the waveguide. Assuming that the cladding is homogenous, the bulk sensitivity is given by $\frac{\delta n_{\text{eff}}}{\delta n_c}$, where n_eff is the effective index of the waveguide, and n_c is the refractive index of the cladding. The other type of sensitivity, commonly referred to as surface sensitivity, is defined as the sensitivity to an adsorbed biomolecular layer to the surface of the silicon core. Therefore, a waveguide’s surface sensitivity is defined as $\frac{\delta n_{\text{eff}}}{\delta t}$, where t denotes the thickness of the adsorbed layer. Diagnostic applications exist in which sensing the average concentration of the bulk cladding is more advantages (e.g., glucose monitoring) than sensing biomolecules adsorbed to the sensor’s surface (e.g., pathogen or biomarker presence). Both sensitivities were investigated for a simplified slab waveguide with a silicon core on a silicon dioxide substrate and an aqueous cladding in [14]. These results suggested that a maximum bulk sensitivity ( $\frac{\delta n_{\text{eff}}}{\delta n_c}$) would be obtained for the waveguide thickness of 190 nm and that a maximum surface sensitivity ( $\frac{\delta n_{\text{eff}}}{\delta t}$) would be obtained for a waveguide thickness of 210 nm. The molecular adlayer, used to determine the surface sensitivity, was assumed to be a protein adlayer with a refractive index of 1.48 [14,17]. We have verified these optimum thicknesses using analytical methods [18] for the bulk sensitivity and fully-vectorial 2D eigenmode calculations (Lumerical Solutions, Inc.) for both sensitivities. The optimum value for the surface sensitivity will depend on the distance of the newly adsorbed layer from the surface of the waveguide core.

2.2. Effect of dispersion on resonator sensitivity

For resonators, sensitivity is defined as the shift in resonant wavelength due to a refractive index change in the cladding. Such changes in the refractive index of the cladding can result from changes in the concentration of the analyte in the cladding or from biomolecular adsorption to the surface of the silicon waveguide. To include the effect of dispersion, the group index (n_g) is used since it relates to the effective index of the waveguide (n_eff) to changes in the resonant wavelength [16]:

Simulations of various waveguide core thicknesses were used to calculate n_g and, ultimately, determine the resonator sensitivity ( $\frac{\delta n_{\text{eff}}}{\delta n_c}$). Using the simulations results and Eq. (1) for a slab waveguide with a silicon core (n_co=3.47), a silicon dioxide substrate (n_sub=1.48), and an aqueous cladding (n_cl=1.31), values for n_g as a function of the slab thickness is shown in Fig. 1. It can be observed that the group index (n_g) of a TM propagating mode varies significantly as slab thicknesses vary between 100 nm to 300 nm (Fig. 1).

 

Fig. 1 Group indices of slab waveguides as functions of slab thicknesses.

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The next two subsections discuss the fully-vectorial 2D eigenmode calculations (simulations) and compare them with the observed, experimental results for both kinds of sensitivity (bulk and surface).

2.3. Resonator bulk sensitivity: theory and design

The bulk sensitivity of a resonator is defined as the shift in the resonant peak that is caused by a change in the refractive index of the cladding ( $\frac{\mathrm{\Delta }{\lambda }_{\mathit{res}}}{\mathrm{\Delta }{n}_c}$) [6].

To calculate the sensitivities of resonators based on slab waveguides, Eq. (2), the above simulated n_g results, and the simulated waveguide sensitivities ( $\frac{\delta n_{\text{eff}}}{\delta n_c}$) are used (Fig. 2(a), dashed lines with hollow markers). For these calculations, we have considered a perturbation of 0.01 RIU for the refractive index of the cladding, assuming that $\frac{\delta n_{\text{eff}}}{\delta n_c}$ is nearly constant over small ranges. These results indicate that the maximum sensitivity for a TM mode happens when the silicon core thickness is around 155 nm. Conditions for maximum sensitivity for a waveguide resonator and for a waveguide alone differ because of the effect of n_g on the sensitivity of the resonator.

 

Fig. 2 (a) Calculated resonator’s sensitivities, based on simulations, as functions of silicon core thicknesses. The hallowed markers are the simulated sensitivities for the case of a slab waveguide, the black filled markers are the simulated sensitivities for the case of rectangular waveguides with waveguide widths of 750 nm and 900 nm, and the red markers are averages of our experimental results for TM ring resonators with 150 nm and 220 nm thick silicon cores. (b) Contour plot of sensitivity in nm/RIU as functions of waveguide widths and thicknesses. The cross-section corresponding to the dashed line representing the slab is plotted in Fig. 2(a), and the other two cross-sections representing the thicknesses of 150 nm and 220 nm are plotted in Fig. 3(d). The red markers show the fabricated TM mode resonator devices (Star: Width = 900 nm and Thickness = 150 nm, Triangle: Width = 750 nm and Thickness = 220 nm).

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As can be seen in Fig. 2(a), the optimal thickness is close to 150 nm waveguide thickness offered by a standard MPW process after etching.

To further improve our model, we simulated the sensitivity of a TM mode propagating in a rectangular waveguide as a function of the waveguide width and thickness. These results are illustrated in Fig. 2(b) as contour plots. The simulation area was fixed to 4 μm×4 μm and only structures with less than 2% error in their sensitivities (based on the error calculated using the convergence test described in [19]) were considered. These results indicate that a maximum bulk sensitivity of 363 nm/RIU is achieved at a waveguide thickness of 165 nm. The closest thickness offered by MPW foundries to this optimum thickness is 150 nm. The two vertical dashed lines in Fig. 2(b) represent the cross-sections for the thicknesses offered by MPW foundries (150 nm and 220 nm).

2.4. Resonator surface sensitivity: theory and design

The surface sensitivity of the resonator is defined as the resonant wavelength shift as a function of the thickness of the adlayer ( $\frac{\delta {\lambda }_{\mathit{res}}}{\delta t}$, where t denotes the thickness of the adsorbed biomolecule). Surface sensitivity is approximately linear for small adlayer thicknesses (<30 nm). We approximate the simulated surface sensitivity of our fabricated devices based on a 10 nm protein-like adlayer with a refractive index of 1.48 [20]. Using our simulation/analytical model for a slab waveguide, the maximum surface sensitivity of a TM resonator sensor is calculated to be at a thickness of about 185 nm, with simulated sensitivities of over 700 pm/nm. The surface sensitivity for TM resonator sensors with the waveguide dimensions of 750 nm×220 nm and 900 nm×150 nm of our fabricated devices are simulated to be 300 pm/nm and 245 pm/nm, respectively, for a protein-like adlayer with a refractive index of 1.48; and 600 pm/nm and 460 pm/nm, respectively, when the adlayer has a refractive index of 1.68, as is the case for polymers.

2.5. Simulated sensitivity: summary of results

Using our simulation/analytical model for slab waveguide resonator sensors, the maximum bulk sensitivity of a TM resonator is calculated to occur at a thickness of around 155 nm, and a maximum surface sensitivity is calculated to occur at the thickness of around 185 nm, with simulated sensitivities of over 270 nm/RIU and 700 pm/nm, respectively. The surface sensitivities for TM resonator sensors with waveguide dimensions of 750 nm×220 nm and 900 nm×150 nm (our fabricated devices) are simulated to be 300 pm/nm and 245 pm/nm, respectively, for a protein-like adlayer with a refractive index of 1.48.

3. Experiments and results

In this section, we discuss and compare the measured and simulated results for bulk and surface sensitivities. TM resonators with 150 nm thick silicon cores, close to the thickness with maximum sensitivity, and 220 nm thick resonators, as conventional references for comparison purposes, were fabricated at The Institute of Microelectronics (IME) foundry in Singapore.

3.1. Designed devices

Racetrack resonator sensors were designed for critical coupling to achieve a maximum Extinction Ratio (ER). We have designed racetrack resonator sensors with a radius of 40 μm and calculated the bend losses as well as material absorption losses using fully-vectorial 2D Eigenmode (Lumerical MODE Solutions) calculations. We assumed the scattering losses of ∼ 2 dB/cm based on our group’s previously acquired data [16]. Then, we calculated the coupling length to achieve critical coupling. Our calculated and therefore fabricated coupling lengths for these devices were 13.15 μm, and 3 μm for 150 nm and 220 nm thick TM resonator sensors, with a coupling gap of 200 nm.

Increasing the waveguide width reduces scattering loss as the mode is more confined, however, the sensitivity decreases as well. For our experiments, waveguide dimensions to support single mode operation were chosen.

3.2. Experimental setup

Fabricated devices were characterized using a custom test platform developed by our lab to sequence solutions over the sensor [5, 21, 22]. Briefly, the test platform consists of a 1.55 μm tunable laser source and accompanying optical power meters, a temperature controller to thermally tune the stage, optical and fluidic stage controllers, and a pump to sequence reagents across the sensor. Using the tunable laser, we investigated the wavelength range of 1515 nm to 1570 nm, however, a single peak in this range has been tracked to determine the sensitivity. An array of four polarization-maintaining fibers facilitate coupling of TM mode light into and out of the chip via on-chip vertical grating TM mode couplers [23, 24]. To deliver reagents to the sensor, a 500 nm thick laser-cut silicone gasket (Grace BioLabs, Bend, Oregon) defined 300 nm wide channels over the optical sensors and mated with a custom, PTFE (Teflon®) flow cell to connect the Tygon tubing. The pump was operated in withdraw-mode, pulling reagents from the well plates using negative pressure. All the instruments are controlled via a custom MATLAB application hosted on a Windows PC.

3.3. Bulk sensitivity

For bulk sensitivity measurements, a set of NaCl refractive index (RI) titrations ranging from 62.5 mM to 1 M were subjected to the sensors to measure their responses and determine the resonant shift [22]. Since the chips lacked reference sensors, the experimental setup was thermally tuned to 25 °C to limit the impact of thermal noise and drift on the measurements.

The bulk sensitivities of the fabricated resonator sensors were obtained experimentally using these refractive index standards. Figures 3(a) and 3(b) show one set of spectra for each of the TM resonator sensors with 220 nm and 150 nm thick waveguide cores, respectively. Each of these sensors has been exposed to sodium chloride (NaCl) solutions with different refractive indices. It can be observed how the resonant wavelength shifts as a function of the change in RI (the concentration of aqueous solution in the cladding medium). Plotting these resonant wavelengths as a function of the change in RI, the slope of the best fit line through the different resonant wavelengths at each concentration provides the bulk sensitivity [nm/RIU]. Figure 3(c) shows one set of measurements for a thin TM sensor (150 nm thick) and one for a regular TM sensor (220 nm thick). Each sensor was measured multiple times, and the experimental results are compared with the simulation results, as shown in Fig. 2(a) and Fig. 3(d). To better understand and compare the simulation results with the experimental results, we included simulated sensitivities for rectangular waveguides and interpolated the experimental results (Fig. 2(a)). The sensitivities are plotted for a device with a waveguide core thickness of 220 nm and a width of 750 nm, and for a device with a waveguide thickness of 150 nm and a width of 900 nm. The sensitivities for the two thicknesses (150 nm and 220 nm) that are offered by MPW foundries (represented as the two vertical dashed lines in Fig. 2(b)), are plotted as functions of the waveguide width in Fig. 3(d), where hollow markers indicate simulation results and filled markers indicate experimental results. The slight variations between the experimental and simulation results partly come from the imprecision in the concentrations of the salt solutions (measurement error) and any thermal noise in tuning the stage and can partly be explained with the non-uniformities that exist on SOI chips [25]. Using deionized water at flow rates suitable for biosensing assays, we observed 1-3 pm RMS jitter in the resonant wavelength of the resonator sensors [26]. We hypothesize that this results from gas in the fluid (micro bubbles), thermal fluctuations caused by evaporating fluid in the well tray, and coupling fluctuations between on-chip gratings and a fiber array. We suspect that any laser noise (wavelength jitter, wavelength accuracy and repeatability, wavelength drift) or power meter noise (dark current) is negligible when compared to these other sources. Regardless, all these noise sources ultimately impact the limit of detection.

 

Fig. 3 (a, b) Spectra showing that the resonant wavelength shifts as the refractive index of the aqueous cladding medium changes, for the TM resonator sensors with (a) 220 nm thick waveguide cores, and (b) 150 nm thick waveguide cores. (c) Sensitivities of TM waveguide resonators to the aqueous cladding. (d) Sensitivities of TM waveguide resonators to the aqueous cladding, for the optimum silicon core thickness of 150 nm and for the conventional thickness of 220 nm, as functions of the waveguide width. The filled markers show corresponding experimental results. The labels “TM1 is mode 2” and “TM1 is mode 3”, means the first guided TM mode is the second and third guided mode in the waveguide, respectively. The first guided mode is the fundamental TE mode. For the strip waveguides wider than ∼ 650 nm, the first two TE modes are guided before the first TM mode.

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3.4. Surface sensitivity (characterized using electrostatic polymers)

To investigate the sensitivity where most molecules and proteins bind (within 10–50 nm of the waveguide surface), we employed electrostatically charged polymers, similar to the approach developed by Luchansky et al., to characterize the evanescent field profile [27]. We used our conventional 220 nm TM resonator sensors for this experiment. The sensors were cleaned with a Piranha solution (1:1 H2SO4:H2O2 (30%)) for 30 minutes, rinsed with deionized water, and dried with air prior to functionalization. To initiate adhesion of the electrostatic bilayer polymers, the sensors were first exposed to a solution of positively charged polyethylene imine (PEI; 5 mg/ml) followed by a rinse using Tris buffer (0.5 mM, 100 mM NaCl, pH 7.1). Next, solutions of negatively charged polystyrene sulfonate (PSS, 5 mg/ml) and positively charged polyallylamine hydrochloride (PAH, 5 mg/ml) were alternated at 20 uL/min to create the electrostatic bilayers. The introduction of each polymer was followed by a Tris buffer rinse to avoid polymer precipitation and clogging of the fluidic tubing. After an initiating layer, alternating cationic and anionic polymers were used to create a step-wise layering (∼ 2.4 nm per iteration) on the waveguide surface for at least 10 bilayers. The layering was monitored in real-time and was assumed to have a refractive index of 1.68. The thicknesses of the bilayers were determined in two ways. First, we used simulations to determine adlayer thicknesses (and subsequent effective indices) that resulted in the observed resonance shifts. Second, a glass slide with no bilayers, 10 bilayers, and 20 bilayers was manually prepared using the same electrostatic polymers and the resulting thicknesses were measured using ellipsometry.

Figure 4 shows experimental results for the first 10 bilayers, which is representative of the total thickness of most biological capture assays involving immobilized immunoglobulins and their conjugate analytes (20–30 nm). The thicknesses of the bilayer formations were measured using ellipsometry and found to be approximately 2.4 nm thick, which is close to the reported value of 3 nm [27]. Figure 4 shows a wavelength shift of 1050 pm for one bilayer with the thickness of approximately 2.4 nm. This is equivalent to a sensitivity of approximately 437.5 pm/nm.

 

Fig. 4 Experimental results includes the measurement of the wavelength shift over time as the various layers of electrostatically charged polymers were introduced to the surface of our conventional TM resonator sensor. Polymers corresponding to the labels A–D are: A = Tris Buffer (0.5 mM, 100 mM NaCl, pH 7.1); B = PEI (solution of positively charged polyethylene imine, 5 mg/ml); C = PSS (solution of negatively charged polystyrene sulfonate, 5 mg/ml); D = PAH (solution of positively charged polyallylamine hydrochloride, 5 mg/ml).

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Using a refractive index of 1.68 [27] for the electrostatic polymers, simulations were performed using an eigenmode solver to predict and compare the surface sensitivity with the observed result. The simulations predict a 460 pm shift in resonance wavelength for each 1 nm adlayer. This simulated value is well compares well to the observed results of a 437.5 pm shift in resonance wavelength per 1 nm adlayer.

3.5. Demonstration of TM sensors for biosensing

For surface sensitivity measurements, standard sandwich assays, involving well characterized molecules, were used to demonstrate the sensor’s ability to detect biological interactions as described in [22], which is briefly mentioned here. Protein-A (MW ∼42kDa) was obtained from ThermoFisher (Chicago, IL). Anti-streptavidin (antiSA) (MW ∼150kDa) and Streptavidin (SA) (MW ∼57kDa) were obtained from Vector Labs (Burlingame, CA). A kit from Bangs Labs (San Diego, CA) was used to conjugate biotin to BSA (MW ∼66kDa) for the final amplification step. A PBS buffer, with a pH of 7.39 and n = 1.35, was used to create an initial baseline and as a rinse after the introduction of each reagent. Figure 5(a) is schematic representation of our biological assay material.

 

Fig. 5 (a) Schematic representation of model biological sandwich bioassay. Reagent sequencing corresponding to regions [A–E] include: Region A= Protein A adsorption, B= anti-streptavidin (Anti-SA) functionalization, C= Bovine Serum Albumin (BSA) challenge and block, D= streptavidin (SA) target analyte binding, E= Biotin-BSA amplification step. Introduction of each reagent was followed by a PBS wash. (b) Experimental results of biosensing assay following the physisorption of Protein A offline (Region A not shown). The blue-dashed vertical line shortly before Region C denotes the unintended introduction of an air bubble. While the air bubble desorbs some of the immobilized antibody, it does not impact the viability of the subsequent binding steps.

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A sandwich assay representing a model biological system was performed to demonstrate the biosensing capability and surface sensitivity of our TM mode ring resonator. Similar reagents and protocols were used as described previously [22]. Figure 5(b) shows the result of the biological sandwich assay used to demonstrate the sensor’s capability to detect molecular binding at its surface. The experimental results show subsequent binding steps after the physisorption of Protein A to the sensor’s surface.

After achieving a baseline reading in PBS buffer at 37 °C, a series of the above mentioned biomolecules were sequenced through the channel. The introduction of each reagent was followed by a 20 minute rinse using PBS buffer to remove any unbound species in the channel (shown by the short, black dashed lines in Fig. 5(b)). Signal baseline was achieved after Protein-A (1 mg/ml) adsorption to the sensor’s native oxide surface and prior to Region B. This process has been shown to facilitate the immobilization and orientation of the capture antibodies [28,29]. Region B shows the robust immobilization of the IgG capture antibody, anti-streptavidin (10 μg/ml), which was introduced and bound to the Protein-A adlayer (Region B).

The unintended introduction of an air bubble mid-way through the antiSA rinse cycle (Region B), indicated by the blue-dashed vertical line, does not impact the viability of the subsequent biological species or their functionality. To show that subsequent molecular binding interactions are specific, and to prevent unwanted, non-specific adsorption to the sensor, BSA (20 μg/ml) was introduced next (Region C) to block any exposed surfaces remaining on the sensor (Region C). The slight negative shift in resonant wavelength after the BSA block and challenge (Region C) suggests that a small portion of the antibody adlayer lifts off but that the original sensor coverage (Region B) was robust. Next, the functionalized and blocked sensor was subjected to 10 μg/ml of SA, the model analyte captured by the antibody (Region D). The resulting shift in the sensor’s resonant wavelength after the buffer rinse suggests specific and irreversible binding interaction, as expected. To further demonstrate the sensor’s capability, to detect molecular binding, biotin conjugated with BSA was introduced as a final amplification step. Biotin and SA have one of the highest non-covalent binding interactions known [30] resulting in another, permanent resonant shift (Region E).

Protein A (with a diameter of approximately 3 nm [31,32] and refractive index of 1.48 [20]) can form a thin layer of approximately 1–3 nm thick [21,33]. Based on simulations that mimic our experimental results, a 1 nm thick protein layer would have covered around 50% of our sensor’s surface to result in the observed shift. Subsequently, if a 3 nm layer was formed, about 16% surface coverage results in the observed shift. These results are within the range of surface coverage that was determined by other researchers [33].

4. Conclusion

We have investigated the optimum thickness of the waveguide core that results in the highest sensitivity for a strip waveguide resonator sensor. The results indicate that guided TM modes have higher sensitivities to the changes in refractive indices of the cladding media, since larger evanescent field component is traveling above the waveguide, where the target molecules exist. In addition, for the case of the resonators, n_g also affects the sensitivity of the device. Our investigations determined that the optimum thickness for TM resonator sensors is around 165 nm, which is close to one of the thicknesses offered by MPW foundries (150 nm). The compatibility of these resonators with the standard CMOS processes and MPW foundries, in terms of their minimum feature size requirements as well as offered thicknesses, make them a cost-effective candidate for a sensor.

The measured Q values, from the spectra of these resonators in water solutions, are 10,100 and 4,500 for 220 nm thick and 150 nm thick resonator sensors, respectively. These give intrinsic limits of detection (iLoD) of approximately 7.5 × 10⁻⁴ RIU and 1.2 × 10⁻³ RIU for 220 nm thick and 150 nm thick resonator sensors, respectively (an increase by a factor of 1.6). The extinction ratios for both of these devices were measured to be around 30 dB. The higher iLoD values indicate that although the sensitivity has improved significantly, the Q factor is degraded. Therefore, the choice of using these sensors will depend highly on specific requirements of the end-application. The sizes of the target molecules, the distance of these molecules from the surface, and the expected concentrations of the analyte are examples of factors that must be considered for an optimal sensor design. For example, a TM resonator sensor provides larger penetration depths. Our thin TM resonator sensor has a calculated evanescent field (EF) penetration depth of about 350 nm, which is more than twice of comparable TE mode resonator sensors [6]. Larger penetration depths may allow for sensing of molecules attached to long-branched chemistries further from the surface of the sensor. An example is a glycoprotein receptor molecule that plays an important role in initiating cellular binding and communication. These membrane-bound proteins, which can be immobilized on a silicon photonic biosensor, often bind small ligands (10–15 nm in size) or in the case of bacteria, the adhesins at the end of their long fimbria. Since fimbria are often 100’s nm long, a sensor capable of detecting a bound mass several 100’s nm from the sensor’s surface is needed, especially for bacterial adhesion and other cellular diagnostic applications. Therefore, silicon photonic biosensors with a TM guided mode, which naturally extends their sensing field 100’s of nm from the sensor’s surface, are ideally suited for these kinds of biosensing applications.

The lower Q value associated with 150 nm thickness, compared to the conventional 220 nm thick silicon core, is partly due to lower group index associated with this thickness, and partly due to higher intrinsic losses (bend loss, mode-mismatch loss, substrate leakage loss). Assuming that these resonators are close to critical coupling, their Q values translate to distributed losses of 34 dB/cm and 48 dB/cm for the resonators with 220 nm and 150 nm thick silicon core respectively. Based on fully-vectorial 2D Eigenmode calculations using Lumerical’s MODE Solutions, we found that material absorption losses, including water absorption, are responsible for approximately 23 dB/cm and 19 dB/cm of these losses in the resonators with 220 nm and 150 nm thick silicon cores, respectively. The estimated losses based on measurements of these devices in a dry environment are 14 dB/cm and 28 dB/cm for the resonators with 220 nm and 150 nm thick silicon cores, respectively. These approximate values exclude losses due to water absorption, which suggest material absorption losses close to 20 dB/cm. Since scattering losses typically result from interaction of the propagating mode with the sidewall roughness [6,34–36], TM modes experience less scattering loss due to sidewall roughness when compared to TE modes since the majority of the mode’s electric field travels above and below the waveguide. A propagation loss of ∼ 3 dB/cm for TE guided mode in a strip waveguide, dominated by sidewall scattering, is demonstrated experimentally and analytically [16,34–36]. It has also been shown that thinner waveguides, fabricated in CMOS-compatible processes, exhibited lower scattering losses, in the order of 2 dB/cm [37]. Therefore, we estimate the scattering losses for TM modes to be less than 3 dB/cm. The remaining losses (∼ 9 dB/cm and 26 dB/cm for the resonators with 220 nm and 150 nm thick silicon core respectively) result from bend losses (radiation loss, and mode mismatch loss), substrate leakage, and coupling loss. Propagation losses, including the scattering loss and substrate leakage, as well as bend losses, can be improved by using wider waveguides [19]. The loss due to substrate leakage can be improved using SOI wafers with thicker silicon oxide substrates (e.g. SOI wafers with 3 μm thick silicon oxide substrate). These improvements should ultimately improve the iLoD and therefore the overall performance of the biosensor.

Simulations supported by experimental results in this paper demonstrate achievement of higher sensitivity devices within the constraints of MPW foundries, which has numerous advantages such as possibility of mass fabrication and integration with CMOS circuitry for potential system-on-chip implementations.