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Abstract
We propose a novel type of waveguides, called the slot hybrid-core waveguides (HCWs), for temperature-independent integrated optical sensors. The HCWs are composed of different core materials having the opposite thermo-optic coefficients (TOCs) and, therefore, are immune to temperature variations. On this basis, slot HCWs are proposed for the microring resonator-based optical sensors, enabling the sensors to simultaneously present high sensitivities and temperature independence. The temperature-dependent wavelength shifts of the proposed sensors are calculated to be less than 1 pm/K while the sensitivities to the cladding refractive indices attain 468 nm/RIU and 536 nm/RIU, respectively, for the asymmetric and symmetric slot structures.
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1. Introduction
Integrated optical sensors are evolving as powerful tools for acquiring information of refractive indices [1,2], chemical compositions [3,4], protein concentrations [5,6], etc., exhibiting great potentials in material analysis. Among diverse waveguide structures for the integrated optical sensors, slot waveguides are of special interests predominantly due to their capabilities of enhancing the light-analyte interaction in a nano-scale slot and thus resulting in sensors with very high sensitivities [7–9]. Unfortunately, similar as sensors based on any other conventional on-chip waveguides, the sensors based on the slot waveguides have also been suffering from the thermal drift issue. For example, the temperature-dependent wavelength shifts (TDWS) of a silicon slot waveguide microring resonator (MRR) with air cladding were as high as 48 pm/K [10], since the thermo-optic coefficient (TOC) of the silicon is as large as 1.84 × 10−4/K. Even if a material like the silicon nitride (SiN) which possesses a much smaller TOC of ∼0.25 × 10−4/K was used, the TDWS were still moderately large, e.g., 6 pm/K and 5 pm/K for a SiN slot waveguide MRR [11] and a SiN slot waveguide Mach-Zehnder interferometer (MZI) [12], respectively.
The most straightforward way to address this thermal drift issue is to stabilize the temperature of the whole chip as much as possible, which, however, “straightforwardly” increases the power consumption and footprint. Same drawbacks exist in the approach of using the feedback temperature stabilizing systems with localized heaters off the chip or on the chip [13,14]. Sensor arrays including one or several reference sensors might help to remove the temperature influence during the data processing and a temperature-dependent wavelength shift (TDWS) of 0.3 pm/K was demonstrated for a SiN slot waveguide MRR sensor array [15]. Apparently, sensor arrays increase the device footprint and the reference sensor can’t accurately reflect the in-situ temperature variations of the working sensor. Cladding the slot waveguide MRRs with polymers having a negative TOC like the benzocyclobutene (BCB) [16] or Ormocomp [17] may dramatically lower down the temperature dependence (e.g., to 0.6 pm/K), but this is not suitable for sensing applications.
Here, we propose a novel sort of waveguides, called the slot hybrid-core waveguides (HCWs), to resolve the thermal drift issue of slot waveguide sensors. The concept of the HCW was first proposed and experimentally demonstrated in 2019 by Wang and Guan et al., where a Si/SiN HCW was fabricated to leverage the overall nonlinear properties of the Si and SiN materials by allowing light to fairly distribute in the two material cores [18]. Similar structure with 3-layered cores has also been used by He et al. to demonstrate the athermal waveguides [19]. But the waveguides in the two proposals are not suitable for the sensing purposes. In this work, two structures of slot HCWs for high-sensitivity and temperature-independent sensors are proposed. One is with the asymmetric structure where the two cores with TOCs having the opposite signs sit on the two sides of a vertical slot. The other is with the symmetric structure where the vertical slot is directly inscribed in the middle of an athermal HCW. Titanium dioxide (TiO2)/silicon-rich nitride (SRN) slot HCWs are designed as an example for the asymmetric case while the TiO2/Si slot HCWs are for the symmetric case. With optimization to the waveguide dimensions, both slot waveguides can be athermal and the TDWSs of these waveguide-based MRR sensors are calculated to be <1 pm/K while their sensitivities to the refractive indices (RIs) of the cladding analytes sustain high values around 500 nm/RIU.
2. Waveguide structure and design
2.1 Asymmetric slot HCWs with SRN and TiO2 cores
Figure 1(a) shows the 3D schematic of the MRR sensor based on the proposed asymmetric slot HCW, of which the cross-section view is illustrated in Fig. 1(b). The slot HCW consists of a TiO2 core and a SRN core, separated by a vertical slot, and their widths are defined as w1, w2, and g1, respectively. The two cores have the same heights of h1 and sit on a SiO2 insulator which can be deposited or oxidized on a silicon wafer or just a quartz wafer. For the sensor, an SRN bus waveguide is used to couple light with the slot HCW MRR having a radius of r1 and analytes are cladded on the sensor. Hereinafter, we consider water and sodium chloride (NaCl) solutions with different concentrations as the analytes.
Fig. 1. Performances of the MRR sensor based on the slot HCW with the asymmetric structure. (a) 3D schematic of the sensor. (b) Schematic of the slot HCW. (c) Calculated TDWS as a function of the core widths at g1 = 100 nm. (d) Mode profile (electric field) of the slot HCW with w1 = 350 nm and w2 = 420 nm. (e) TDWS and resonance wavelength shifts with respect to the concentrations/RIs of the NaCl solutions. Here, the wavelength is 1.55 μm.
The temperature dependence of the effective RI of the proposed HCW can be calculated by [20]
In order to greatly enhance the light-analyte interaction in the slot, the core materials should possess RIs as large as possible [21]. Among different materials having a negative TOC, TiO2 has the largest RI around 2.3 at the infrared wavelengths, to the best of our knowledge. On the other hand, SRN can exhibit different RIs, e.g., from 2.01 to 2.71 [22], by setting different ratios of the gaseous reactants during the film deposition. Therefore, we choose SRN and TiO2 as the positive-TOC and negative-TOC core materials, respectively. Literatures have reported different values for the RI and the TOC of TiO2 and here we use a RI of 2.35 and a TOC of -1 × 10−4/K in the calculations since these values have been experimentally verified in an athermal TiO2 cladded silicon waveguide [23]. The TOC of a material may vary at different wavelengths [24], but in this work we only consider the wavelength range around 1.55 µm. The RI of SRN is set to be 2.34, almost the same as that of TiO2, which can be achieved by tailoring the N:Si ratio in the deposited SRN film to be 0.98 [25]. At this film composition, the TOC was measured to be ∼4.6 × 10−5/K. As for the silica substrate, we use 1.428 for the RI and 0.95 × 10−5/K for the TOC at the wavelengths around 1.55 µm [26].
With the material parameters, we first calculate the mode properties and optimize the HCW structure using a finite-domain method (Mode Solutions, Ansys Inc.). Water with a RI of 1.33 at 1.55 µm is used for the cladding and its TOC of -2.77 × 10−6/K [27] at this wavelength range is also taken into account despite a small effect on the HCW’s temperature dependences. Figure 1(c) shows the TDWS of the MRR sensor based on the HCW with the asymmetric structure as a function of the widths of the two cores. Here, h1 = 300 nm, g1 = 100 nm and r1 = 50 µm are fixed. It can be clearly seen that, for a fixed width of the positive-TOC SRN core (w2), values of the TDWS decrease as the negative-TOC TiO2 core becomes wider, i.e., a larger w1. At some w2, the TDWS is first positive at a narrower w1 since most part of the light is confined in the SRN core, then approaches zero as w1 increases and finally becomes negatively large when light is predominantly confined in the relatively wide TiO2 core. This trend points out that the temperature dependences of the HCWs and the corresponding sensors can be dramatically mitigated and even eliminated at some waveguide dimensions. According to our calculations, at w1 = 350 nm and w2 = 420 nm, the TDWS is approximately zero (0.4 pm/K). Figure 1(d) shows the electric field distribution of the fundamental transverse-electric (TE0) mode in the waveguide and the field is found to be significantly enhanced in the slot, which will tremendously benefit the sensitivity. We have calculated the TDWSs of the sensor and its RI sensitivities with NaCl solutions having different concentrations and the results are shown in Fig. 1(e). The RI of the cladding NaCl solution increases by 0.0018 for an 1% increment of the concentration. A small change of the NaCl concentration can produce a pronounced shift of the resonance wavelength, resulting in a sensitivity of 468 nm/RIU. At the same time, the TDWS can be kept at a very low level, i.e., from 0.4 pm/K to -0.3 pm/K when the cladding changes from pure water to the saturated NaCl solution. These results concretely show the promises of the proposed slot HCW-based sensors to simultaneously achieve the high sensitivities and the low or even negligible temperature dependences.
Since the proposed slot HCW is composed of different materials, different bending radii may re-distribute the light especially for a sharp bend. Thus, we have checked the dependences of the TDWS of the slot HCW-based MRR on the bending radii, as shown in Fig. 2(a). When the bending is very sharp, light is inclined to be pushed outwards, i.e., more confined in the SRN core. Therefore, TDWS degrades and the value is much positive. Nevertheless, it can still keep <1 pm/K for r1 is about 50 µm allowing the temperature-independent slot HCW-based MRR sensors to exhibit compact footprints. Besides, light may also re-distribute at different wavelengths and thus change the temperature dependences of the slot HCW. Figure 2(b) shows the calculated wavelength dependences of the TDWS, from which the athermal bandwidth can be extracted as 100 nm showing large freedom for choosing the operating wavelength. Here, the bandwidth is defined as the wavelength range, in which the TDWS of the sensor at any resonance keeps within ±1 pm/K.
Fig. 2. Dependences of the TDWS of the proposed MRRs based on the slot HCW with the asymmetric structure on the bending radius (a), the wavelength (b), the RI of the SRN core (c) and the slot width (d), respectively. Here, pure water is used as the cladding. The wavelength used is 1.55 µm for (a), (c) and (d).
For the proposed waveguide with hybrid materials and asymmetric structures, several lithography and etching processes may be required and, what’s more, alignments should be involved as well. Thus, it is important to investigate the fabrication tolerances of the proposed slot HCWs and the corresponding MRR sensors. From Fig. 1(c), we find the TDWS can sustain a small value within ±1 pm/K when the variations of w1 and w2 are ±5 nm and ±7 nm, respectively. Despite being possible, the price for controlling the waveguide dimensions to such fabrication tolerances may be high. Fortunately, the TDWS can still sustain small values, e.g., within ±5 pm/K even for variations of ±30 nm and ±40 nm of w1 and w2, respectively. Though it is possible to precisely tune the RI of the deposited SRN film, it still makes sense to explore how the RI variation affect the performances of the proposed MRR sensor in case there is instability during the film deposition. Figure 2(c) shows the TDWS with respect to the RI of the SRN film and great tolerances can be found, i.e., a variation of ± 0.04 of the RI of the SRN film is allowable for a degradation of ± 1 pm/K of the TDWS. Besides, the SRN and TiO2 cores will be fabricated in different processes making the alignment errors unavoidable. Thus, it is necessary to assess the influences of the gap variation on the temperature dependence of the HCW, which is shown in Fig. 2(d). When the gap changes from 80 nm to 110 nm, e.g., with a variation of -20 nm to 10 nm, the TDWS can be kept within ±1 pm/K.
2.2 Symmetric slot HCWs with Si and TiO2 cores
The benefits of using silicon to transmit light for a sensor are obvious for the sake of integration with other mature silicon photonic devices for chip-scale sensing systems. Thus, in some cases, athermal waveguides including silicon medium may needed for the sensors. However, as the RIs of all negative-TOC materials including the polymers and the TiO2 and the RI of silicon have large discrepancies, it is hard to use the above investigated asymmetric structure for the silicon-included athermal slot HCW. In this section, we propose the MRR sensor which are composed of the athermal slot HCWs with a symmetric structure. The 3D schematic of the sensor is shown in Fig. 3(a) and the waveguide cross-section is illustrated in Fig. 3(b). The slot HCW is formed by inscribing a slot in a TiO2/Si wide waveguide where the TiO2 layer is sitting on top of a thin Si layer instead of being on the side. The thicknesses of the Si and TiO2 layers are denoted as h2 and h3, respectively, while w3/w4 and g2 separately represent the trail widths and the slot width. Here, we set w3 = w4 and, thus, the proposed HCW possesses a symmetric structure. The MRR sensor based on the slot HCW with the symmetric structure has a radius of r2 and is coupled with a HCW bus waveguide.
Fig. 3. MRR sensor based on the slot HCW with the symmetric structure. (a) 3D schematic of the sensor. (b) Schematic of the slot HCW. (c) Calculated TDWS of the sensor as a function of the core widths at g1 = 100 nm and w3 = w4 = 300 nm. (d) Mode profile (electric field) of the slot HCW with h2 = 60 nm and h3 = 210 nm. (e) TDWS and resonance wavelength shift with respect to the concentrations/RIs of the NaCl solutions. Here, the wavelength is 1.55 μm.
Different from optimizations for the sensor based on the asymmetric slot HCW, to reduce the temperature dependences of the sensor based on the symmetric slot HCW, one should first optimize the thicknesses of the negative-TOC TiO2 layer and the positive-TOC Si layer. The same simulation method of FDM is used and we use 3.478 for the RI and 1.85 × 10−4/K for the TOC of Si [28]. Figure 3(c) shows the TDWS of the MRR sensor based on the HCW with the symmetric structure as a function of the thicknesses of the TiO2 and Si layers. Here, w3 = w4 = 300 nm, g2 = 100 nm and r2 = 50 µm are fixed. Apparently, for a fixed thickness of the positive-TOC Si core (h2), values of the TDWS decrease as the negative-TOC TiO2 core becomes thicker, e.g., a larger h3. At some h2, the TDWS is first positive at a smaller h3 since most part of the light is confined in the Si core, then approaches zero as h3 continues to increase and finally becomes more and more negative when light is predominantly confined in the relatively thick TiO2 core. Based on this trend, one can dramatically eliminate the temperature dependences of the HCWs and the corresponding MRR sensor by optimizing the waveguide dimensions. Calculations show that when h2 is 60 nm and h3 is 210 nm, the TDWS is approximately zero (-0.1 pm/K). Figure 3(d) shows the electric field distribution of the TE0 mode in the waveguide and the field is enhanced in the slot. Figure 3(e) shows the calculated TDWSs of the sensor and its RI sensitivities to NaCl solutions exhibiting a sensitivity of 536 nm/RIU. The sensitivity is slightly higher than that of the sensors based on the asymmetric slot HCWs, which is probably due to the light being a bit more confined in the slot by the high-RI silicon waveguide trails. The TDWS can be kept very small from -0.1 pm/K to 1 pm/K when the cladding changes from pure water to the saturated NaCl solution, showing great potentials for temperature-independent high-sensitivity sensors.
Since the slot and the waveguide trails can be fabricated in one process (see the process flow in the Discussion section), we don’t consider the influences of the possible asymmetry of the two waveguide trails in the following fabrication-tolerance analysis. First, from Fig. 3(c), one can find the TDWS is kept at a small value within ±1 pm/K when the variations of h2 and h3 are ±2 nm and ±8 nm, respectively. Such delicate control of the film thicknesses may be achieved by oxidizing the SOI wafer and then wet etching the oxidized layer to reach the aimed Si layer thickness and by lowering down the sputtering power to enable a low deposition rate for the TiO2 film, respectively. Then, the dependences of the TDWS of the MRR sensor on the radius and the wavelength are analyzed and shown in Figs. 4(a) and 4(b), respectively. Since the effective RI of the mode is quite large (2.24), the waveguide can be sharply bent, e.g., to 8 µm and simultaneously sustain a small temperature dependence within ±1 pm/K. Moreover, the athermal bandwidth at TDWS of ±1 pm/K is found to be 180 nm. Finally, the dependence on the variation of the gap, which equals the variation of the waveguide trail widths (w3 and w4) but in the opposite way, is considered with the results shown in Fig. 4(c). The TDWS can be kept within ±1 pm/K when the g2 variations are within ±50 nm. Figure 4(c) also shows the sensitivity versus the g2 variation (red line) and the sensitivity keeps larger than 388 nm/RIU.
Fig. 4. Dependences of the TDWS of the proposed MRRs based on the slot HCW with the symmetric structure on the bending radius (a), the wavelength (b) and the slot width variation (c), respectively. In (c), the dependence of the sensitivity on the slot width variation is also given (red line). Here, pure water is used as the cladding and the wavelength used is 1.55 µm.
3. Discussion
Figures 5(a) and 5(b) illustrate the process flows for fabricating the proposed TiO2/SRN asymmetric slot HCW and the TiO2/Si symmetric slot HCW, respectively. For the asymmetric slot HCW, one can first deposit the SRN film on an oxidized silicon wafer or on the quartz wafer using plasma-enhanced chemical vapor deposition (PECVD) (a1) and then pattern the SRN waveguides with lithography and reactive ion etching (RIE) (a2). Next, resist is spun on the sample and reflowed to enable a smooth surface (a3). After the second lithography with alignment and development, the voids for TiO2 parts are formed, followed by a conformal TiO2 deposition using the atomic layer deposition (ALD) (a4). Then, the top TiO2 is etched and the etching stops at the top surface of the SRN waveguides (a5). After the resist stripping, the TiO2/SRN asymmetric slot HCW and the resonators are formed (a6). Processes for patterning the SiN parts have already been very productive while that for the TiO2 parts are expected to be efficient as well since they have been successfully used to achieve the metasurface based on the TiO2 subwavelength structures having dimensions as small as 40 nm [29]. For fabricating the TiO2/Si symmetric slot HCW, one can use a standard silicon-on-insulator (SOI) wafer (b1) and thin it down to 60 nm by oxidation and silica wet etching (b2). Then, the TiO2 film is deposited using ALD or sputtering (b3), followed by hard mask patterning (b4). The hard mask can be chromium (Cr) and can be patterned by lift-off or dry etching. Next, the TiO2 and Si layer stack is etched through using RIE (b5) and, after the hard mask stripping, one can obtain the TiO2/Si slot HCWs and the resonators (b6). The process flow should work since it has been used to realize TiO2 MRRs with quality factors (Qs) as large as 1.4 × 105 [30]. Meanwhile, the Si layer is very thin here and should not challenge the etching too much.
Fig. 5. Process flows for fabricating the proposed TiO2/SRN asymmetric slot HCW (a) and the TiO2/Si symmetric slot HCW (b).
In addition to the sensitivity, limit of detection (LOD) is another important figure of merit (FOM) to evaluate the performances of a sensor. Limited by the experimental conditions, we don’t fabricate and measure the proposed slot HCWs and the resonators. Here, we attempt to estimate the achievable LOD of the sensors based on the slot HCWs by referring to slot waveguide losses or Qs of the corresponding MRRs reported in the literatures. Many measurements on the Qs of the Si slot waveguide MRRs have been reported, showing great discrepancy, e.g., 800/1700 [10], 13200 [16], 30600 [31] and 27000 [32]. The work presented by Zhang et al. in 2015 [31] may represent one of the best achievements for Si slot waveguides, i.e., showing a waveguide loss as low as 1.32 ± 0.87 dB/cm at the wavelength 1550 nm. The contemporary processes for fabricating the SiN waveguides have been very mature as well. For example, Tyndall et al. reported in 2021 the SiN slot waveguides with a loss of 0.3 dB/cm [33]. However, to date, few reports on the TiO2 slot waveguides have been reported except the work presented by Hayrinen et al. in 2015 that a TiO2 slot waveguide MRR exhibited a Q of 3446 at the wavelength 1516 nm [34]. This corresponds to a waveguide loss of 61 dB/cm which is way larger than that of the Si slot waveguides and the SiN slot waveguides. Thus, we expect that, for both our proposed slot HCWs, the loss will mainly come from the TiO2 parts. Meanwhile, the Qs of the MRRs based on the proposed slot HCWs can be larger than 3446 and the loss can be smaller than 61 dB/cm, considering that the measured MRR in [34] had a very small radius of 6 μm. A Q of 3446 corresponds a resonance linewidth of ∼450 pm. Considering a minimal wavelength shift equivalent to 1/15 of the resonator linewidth can be easily detected [35], it is possible to achieve LODs smaller than 6.4 × 10−5 RIU and 5.6 × 10−5 RIU for the MRR sensors based on the TiO2/SRN slot HCW and TiO2/Si slot HCW, respectively.
Besides the sensitivity and the LOD, in practice, the insertion loss and the extinction ratio (ER) of the resonance mode of a MRR sensor also matter the overall measurement performances. For a MRR sensor with a large loss, the point coupling scheme may not be feasible since the MRR will be probably very under-coupling, giving a weak ER and imposing challenges on the measurements. Approaching the bus waveguide to the MRR may enhance the coupling but probably increases the scattering loss. This issue can be solved using a racetrack structure for the MRR or using a bend structure for the bus waveguide, both extending the coupling area while keeping an enough distance between the bus waveguide and the MRR. For examples, a racetrack structure was used to improve the ER of a metamaterial-based MRR from 23 dB to 30 dB [36] and a bent coupler was used to pump enough light to MRRs with the radius as small as ∼5 μm [37]. The MRR sensors based on the proposed slot HCWs may also take advantages of these coupling schemes to secure small insertion losses and large ERs.
Table 1 shows the comparison of the temperature-dependent property and other characters of some previously reported on-chip sensors and our proposed sensors based on the slot HCWs. Performances of a Si slot waveguide (WG)-based MRR sensor [38] without the capability of being temperature independent are also listed and one can find the TDWS is 1-2 orders larger than the others with the athermal capability. Mach-Zehnder interferometers (MZIs) with asymmetric arm waveguides [39,40] and cascaded MRRs [41] have ever been used for temperature-independent high-sensitivity sensors. However, the designs are very restricted. Though a SiN slot waveguide sensor [12] exhibited a high sensitivity of ∼772 nm/RIU (1720(2π)/RIU) and a small TDWS of 5 pm/K, such a sensor again had to use the design restricted asymmetric MZI structure since the SiN waveguide itself is temperature dependent. From the comparison, it is not doubt that our proposed sensors based on the asymmetric or symmetric slot HCWs can dramatically lower down the temperature dependence and simultaneously retain the high sensitivities. Meanwhile, the achievable LODs are foreseen to be at the same level as the sensors based on the Si or SiN slot waveguides. Furthermore, compared with other sensors, the proposed sensors can achieve unprecedentedly large bandwidth for the athermal capability, e.g., 180 nm.
Table 1. Comparison of the temperature-dependent properties and other characters of the on-chip sensors with various structures and waveguides (WGs).a
4. Conclusion
In conclusion, we have proposed novel slot hybrid-core waveguides for the temperature-independent sensors. Two waveguide structures, one with the TiO2/SRN asymmetric slot HCW and the other with the TiO2/Si symmetric slot HCW, are investigated and the MRR sensors based on the two slot HCWs are calculated. Calculations show that sensors based on the two sorts of waveguides can achieve low temperature dependences within ±1 pm/K in a large operating wavelength range of >100 nm. The two kinds of athermal waveguide structures have their own specific advantages and can be used for meeting different requirements. For example, the TiO2/SRN asymmetric slot HCW can be possibly used for visible wavelengths to avoid the water absorption at infrared wavelengths and avoid the high losses introduced by a Si slot. The TiO2/Si symmetric slot HCW may be very sharply bended to produce more compact MRR sensors. Nevertheless, the temperature-independent sensors based on the two proposed slot HCWs show high sensitivities of 468 nm/RIU and 536 nm/RIU. Meanwhile, both of them are expected to be very tolerant to the fabrication imperfections. With delicate manufacturing under the contemporary fabrication techniques, we believe the fabrication tolerance requirements can be met and thus the aimed TDWS of ±1 pm/K will be promisingly achieved. Furthermore, the temperature independent sensors are based on the athermal waveguides, implying that such slot waveguides don’t necessarily limit their applications to the sensing but pave new ways for temperature-independent on-chip devices for other applications like the optical interconnects or on-chip quantum information processing.
Funding
National Natural Science Foundation of China; Fundamental Research Funds for the Provincial Universities of Zhejiang (2020YW08).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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