1. Introduction

The past decades have seen promising developments in silicon-based photonic integrated circuits (PICs) which offer a scalable, low-cost and high-throughput platform [1,2]. Silicon nitride (Si$_{3}$N$_{4}$) is an emerging platform for photonic circuits with advantageous properties such as ultra-low loss [3], a broad transparency window [4], strong optical nonlinearity [5] and compatibility with the low-cost complementary metal-oxide-semiconductor (CMOS) fabrication standards. Active devices such as amplifiers [6], modulators [7] and high-speed detectors [8] have been integrated on the Si$_{3}$N$_{4}$ photonic platform, showcasing the potential of this technology in data transmission, sensing and signal processing. Also, large-scale production of Si$_{3}$N$_{4}$-based chips has been realized in foundries [9,10]. However, an inevitable challenge (as with all PIC production) is the processing variation which results in a distribution of device properties such as the resonance wavelengths in an optical filter [11–15]. A particularly important example is the need for control of the resonance wavelength of an optical Micro-Ring Resonator (MRR). Such control is most often achieved through the integration of micro-heaters, used to locally tune the resonance by the thermo-optic effect [16–20]. However, this type of tuning consumes considerable power, which scales with the complexity of the PIC. Moreover, the associated control circuits similarly scale in complexity.

An alternative approach is to permanently trim the device to a resonance at a desired wavelength, usually achieved by changing the effective index of the optical waveguide, often the cladding which is accessible post-fabrication. Prominent examples of modification of an SiO$_{2}$ cladding include the work of Spector et al. [21] who employed integrated micro-heaters formed within the silicon waveguide slab region of a silicon photonic circuit to anneal low-temperature deposited SiO$_{2}$; Schrauwen et al. [22] who used electron beam irradiation to induce SiO$_{2}$ compaction, straining a silicon waveguide core causing a shift of 4.91 nm in an MRR; Biryukova et al. [23] who showed a shift of 1.1 nm in a silicon MRR clad in hydrogen silsesquioxane (HSQ) using visible irradiation solicited through a commercial micro-Raman spectrometer; and Hagan et al. [24] in which a 4-channel silicon filter was trimmed via ion implantation and integrated annealing of lattice defects. Other trimming methods have also been reported, including changing the index of a photosensitive cladding polymer by UV irradiation [25,26], visible irradiation of a chalcogenide cladding on a silicon waveguide [27]; local oxidation of Si waveguides [28]; deposition of thin films followed by partial etching [29]; UV laser annealing [30]; application of an electric field to a polymerizable liquid crystal [31]; and direct UV irradiation of the core of a Si$_{3}$N$_{4}$ waveguide [32]. Trimming methods specific to Si$_{3}$N$_{4}$ devices are described in Refs. [25], [30] and [32]. Each of the described methods have both relative advantages and disadvantages. For example, physical ageing is known to alter the refractive index of polymers due to volume relaxation [33], which contributes to resonance drift over an extended period of time. Such relaxation has also been observed for trimmed SiO$_{2}$ cladding and is discussed in more detail in Sec. 5 of this work. Laser trimming requires direct UV exposure on a translation stage which is challenging at the wafer-scale. Further, the study in [30] makes use of dissociation and rearrangement of chemical bonds in nitrogen-rich Si$_{3}$N$_{4}$, and the application is thus of limited utility for stoichiometric Si$_{3}$N$_{4}$ devices.

Of significant relevance to the current work is the study by Spector et al. [21] in which various claddings were applied to silicon micro-ring resonators, with optical response being trimmed through micro-heaters formed via silicon doping close to the MRRs. One of these claddings consisted of SiO$_{2}$, deposited via Plasma-Enhanced-Chemical-Vapour-Deposition (PECVD) at a relatively low temperature of 150°C. Such oxides are considered of low-quality and their optical properties are susceptible to low temperature processing. The authors showed that for a silicon MRR of 13.0-$\mathrm{\mu}$m diameter, a shift of 1.7 nm could be induced. However, the cladding SiO$_{2}$ relaxes in this case after 24-hour storage in ambient atmosphere, and the resonance reverts close to its original wavelength. The authors demonstrated significant improvement in stability for a spun layer of HSQ, although this process required a bake of 475°C and trimming was not achieved using integrated heaters.

Here we demonstrate an alternative resonance trimming technique utilizing local annealing of an MRR, permanently changing the refractive index of a waveguide cladding consisting of SiO$_{2}$ deposited through a sputtering, Physical Vapour Deposition (PVD) process. This technique makes use of integrated micro-heaters, fabricated in a CMOS-compatible process. The electrical nature of the trimming is compatible with an efficient, automated process that could be achieved through probe contact and optical feedback, for multiple devices on a single wafer. The use of micro-heaters has been described previously in both [21] and [24]. It may be argued that this approach presents limitations in terms of the thermal power that may be delivered by the heaters, and the need for a micro-heater to be associated with each element that requires trimming. Certainly, this latter point pertains to a trade-off between ease of use of electrically-based trimming, and increased circuit complexity. We do note though that the integration of micro-heaters is commonplace for certain applications, for example as described in [24].

While our approach is similar in nature to that of Spector et al. [21] we note that our deposition process is performed at room temperature. It may thus be applied at the end of a process flow either as a cladding material for an entire wafer (for example, such cladding-free Si$_{3}$N$_{4}$ wafers are supplied by LioniX [10,34] as in the current case), with the added requirement of processing of integrated heaters at a temperature less than that used for trimming; or the cladding may be applied selectively into regions defined by previous processing, for instance within a photonics foundry. Such "windows" are widely used for applications in sensing and ion implantation, for example [35,36]. We thus extend the trimming process to temperatures as low as 50°C. We also report results on the long-term stability of our approach which shows relaxation ranging from 7.3% – 13.3% for furnace trimmed MRRs which have been stored in atmospheric ambient for 570 days. We suggest that this alternative trimming technique may find use in applications which would benefit from its flexibility, ease of application and apparent stability.

2. Device fabrication and post-process trimming

The post-fabrication trimming technique discussed in this paper is based on the modification of refractive index of SiO$_{2}$ after deposition and annealing at an appropriate temperature. The modification is permanent in nature. When applied to SiO$_{2}$ co-located with an MRR the modification in the refractive index changes the effective index of the optical mode in the waveguide, thus shifting the resonance wavelength. By varying the annealing temperature and duration, it is possible to shift the resonance within a wide range of wavelengths.

We implement the trimming technique on foundry-fabricated silicon nitride MRRs, acquired from LioniX [10,34]. The waveguide core layer is 200 nm-thick Si$_{3}$N$_{4}$ deposited by low-pressure chemical vapour deposition (LPCVD) on an 8-$\mathrm{\mu}$m buried oxide (BOX). The refractive index of the LPCVD Si$_{3}$N$_{4}$ is 1.996 at 1550 nm [37]. Both the bus waveguide and the waveguide defining the ring resonator are 1 $\mathrm{\mu}$m in width. The schematic of the device is shown in Fig. 1(a). Fiber-to-chip coupling is achieved by aligning 2.5 $\mathrm{\mu}$m-spot size lensed fibers to each edge facet of the bus waveguide. After receipt of the devices from the foundry, a Torr International CRC-600 radio frequency (RF) sputtering tool was used to sputter-deposit silicon dioxide (SiO$_{2}$) on the Si$_{3}$N$_{4}$ MRRs as a cladding material. The sputtering target was a 3-inch 99.99% pure SiO$_{2}$ disk and the deposition was carried out at room temperature. The samples were cleaned with acetone, isopropanol alcohol and deionized water before deposition of SiO$_{2}$. To independently investigate the change in index of the SiO$_{2}$ as a function of annealing, a cleaned Si wafer was simultaneously deposited upon, cleaved into 1 cm$^{2}$ samples, which were then annealed and characterized using ellipsometry. RF power during sputter deposition was set at 120 W and the sputter gas argon flow was set at 5 sccm. The deposition rate under these conditions is $\sim$160 nm/hr. Chromium heaters were fabricated on top of the cladding layer after the SiO$_{2}$ deposition. Because the refractive index of the SiO$_{2}$ cladding is susceptible to relatively low temperature change, the formation of metal heaters was performed at room temperature throughout the entire process. Specifically, patterning was achieved by maskless photolithography with a Heidelberg $\mathrm{\mu}$PG 101 Micro Pattern Generator. Chromium was deposited with the same RF sputtering tool used for the SiO$_{2}$ deposition at 55 W RF power and 5 sccm argon flow rate. The deposition rate is $\sim$300 nm/hr. The resulting heaters are 150 nm thick. Figure 1(b) shows the cross-sectional structure along the dashed line of the device after deposition, overlaid with the simulated TE mode profile, while a planar optical image is shown in Fig. 1(c). Each heater consists of a metal heating ring that is directly above the Si$_{3}$N$_{4}$ ring cavity with two metal pads for electrical contact placed within the ring circumference.

 

Fig. 1. (a) Schematic representation of a Si$_{3}$N$_{4}$ ring resonator and the integrated heater. (b) Cross-sectional view and dimensions of the device along the dashed line in (a). Simulated mode profile is overlaid on top. (c) Microscope image of the sample after formation of heaters.

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3. Results

3.1 Ellipsometry measurement of refractive index modification

To characterize the permanent change in refractive index after deposition and annealing of the SiO$_{2}$, the silicon samples with sputtered oxide were annealed at different temperatures in a tube furnace in an inert nitrogen ambient. Isothermal annealing was performed on the same sample for a total of 1 min, 3 min, 5 min and 10 min. The refractive index at a wavelength of 1.55 $\mathrm{\mu}$m before and after each annealing was measured with a J. A. Woollam variable-angle spectroscopic ellipsometer (VASE). The refractive index of the SiO$_{2}$ film is $\sim$1.455 immediately after deposition. The change in refractive index is plotted in Fig. 2.

 

Fig. 2. Ellipsometry measurements of the change in refractive index of sputter-deposited SiO$_{2}$ film on a Si wafer. The dashed lines are included to guide the eye.

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The refractive index of the sputtered oxide follows a decreasing trend with increasing annealing duration and temperature, with a faster rate of change at higher temperatures. To provide an estimate of the change in refractive index at higher temperatures, a sample was also annealed at 1000 °C for 15 minutes. A reduction of 0.025 was achieved, which is consistent with the simulation work in [38] where the authors reported a decrease of $\sim$0.03 in refractive index after annealing of an ion beam sputtering (IBS) deposited SiO$_{2}$ film at 1300 K. We also compared the effect of the annealing environment and found no significant difference in film refractive index between samples annealed in nitrogen and samples annealed in ambient atmosphere. This comparison has significance if the trimming technique is to be employed in air. While one might anticipate modification in the annealing response of our structures at elevated temperatures (given the presence of oxygen and other reactive elements in air), the limited temperatures used here do not induce any modification of the sputtered film refractive index compared to annealing in nitrogen.

3.2 MRR resonance trimming

To demonstrate the resonance trimming technique, silicon oxide was sputter-deposited on Si$_{3}$N$_{4}$-based MRRs, thus acting as the waveguide cladding material. For easy identification of the resonances, the rings were chosen to have radii of 100 $\mathrm{\mu}$m with a free spectral range (FSR) of 2.23 nm. The coupling gap between the bus waveguide and the ring resonator was 0.9 $\mathrm{\mu}$m. We carried out both low-temperature (below 100 °C) and high-temperature (between 200 and 500 °C) annealing on two different samples.

Sample 1 (low temperature) was heated to 50 °C, 55 °C and 60 °C for 15 minutes at each temperature and Sample 2 (high temperature) was heated to 200 °C, 250 °C, 350 °C, 400 °C, 450 °C and 500 °C for 15 minutes at each temperature. Both samples were annealed in a tube furnace in an inert nitrogen ambient. The annealing time is sufficient to approach the saturated resonance shift for each temperature. Optical measurements were made after each annealing step to locate the resonance wavelengths near 1550 nm. Example measurement results for Sample 1 are shown in Fig. 3(a). A shift of 400 pm compared to the unannealed sample (RT) was achieved after annealing at 50 °C for 15 min, increasing to 900 pm at 60 °C.

 

Fig. 3. Transmission spectra of sputter oxide cladded silicon nitride MRRs for (a) low-temperature and (b) high-temperature annealing. Measurement data and calculated shift from ellispsometry are compared in (c). The inset of (c) shows the measured refractive index under different annealing conditions.

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Figure 3(b) shows the resonance wavelength of Sample 2 before annealing and after each annealing step from 200 °C to 500 °C. The resonance monotonically shifts to shorter wavelengths when annealed at increasingly higher temperature, which is consistent with the decrease in refractive index of the oxide cladding determined from ellipsometry measurements described in Sec. 3.1. A maximum shift of 4.4 nm was observed after the sample was annealed at 500 °C. This is almost twice the FSR of the ring resonator under test.

The change in refractive index of the SiO$_{2}$ was characterized using ellipsometry, in a manner identical to that described in Sec. 3.1. A silicon wafer was placed next to Sample 2 in the same SiO$_{2}$ deposition run, subsequently cleaved into 1 cm$^{2}$, with each being annealed at 200 $^{\circ }$C, 300 $^{\circ }$C, 400 $^{\circ }$C or 500 $^{\circ }$C for 15 minutes. The refractive index of the deposited SiO$_{2}$ film was measured using ellipsometry after each annealing step. The measured refractive index is shown in the inset of Fig. 3(c). Using the measured refractive indices of SiO$_{2}$; the known refractive index of Si$_{3}$N$_{4}$; and the geometry of the waveguide, the optical mode profile was then simulated using the commercial software Synopsis’ FEMSIM Suite in RSoft [39], and the effective index extracted. It is known [40] that for an MRR subjected to a resonance shift, the central wavelength $\lambda _{\textrm {res}}$, resonance wavelength shift $\Delta \lambda$, change of effective index $\Delta n_{\textrm {eff}}$ and group index $n_{\textrm {g}}$ are related by:

In Fig. 3(c) we compare the measured resonance shift of the MRR with that determined by Eq. (1), as a function of annealing temperature. The measured resonance shift is the difference between the resonance wavelength before any annealing was performed and after each annealing step. There is excellent agreement between the data sets, confirming that the oxide cladding and the modification of its refractive index is responsible for the trimming of the MRRs; and also providing evidence that we are tracking the same resonance order as a function of annealing temperature.

The microscopic mechanism for the change in refractive index is not investigated in this study. However, annealing is known to alter the structure and thus the optical properties of sputtered-deposited silicon oxide [38,42]. The consistency between the refractive index reduction in this study and [38] suggests SiO$_{2}$ film expansion during the annealing process, associated with atomic reconfiguration and a decrease in film density. In further agreement with [38] elevated temperature annealing promotes the removal of defects within the film and improves its stability.

In order to quantify the propagation loss in the waveguides cladded with sputtered SiO$_{2}$, the internal Q-factor of an identically processed MRR with a radius of 300 $\mathrm{\mu}$m was measured to be in the order of $2\times 10^5$. The loss is calculated from fitting of the MRR spectrum (not shown) to be 1.9 dB/cm for as-deposited SiO$_{2}$, and 1.5 dB/cm after the sample was annealed at 300 $^{\circ }$C for 15 min. We note that these loss values guide the application of this trimming technique towards optical systems with similar propagation loss, but we further note that the sputtering process is flexible in nature and lower-loss claddings could be developed.

3.3 Demonstration of on-chip trimming with integrated micro-heaters

The integration of individual micro-heaters with the MRRs enables the trimming technique to be applied to each device without process crosstalk. This has significant potential for automated, wafer-scale trimming through the application of a controlled electrical signal. Prior to presenting such on-chip micro-annealing results, we describe how the integration of heaters affects the MRR optical transfer. Figure 4(a) shows the resonance spectrum of a 100-$\mathrm{\mu}$m radius ring resonator near 1550 nm before and after micro-heater formation. The resonance red-shifted by 85 pm after the definition of the micro-heater. Both the changes in resonance wavelength and in Q-factor are relatively minor and have negligible effect on the overall outcome of the trimming process.

 

Fig. 4. (a) The resonance spectrum of a silicon nitride MRR before (black dotted line) and after (blue solid line) the integration of an on-chip heater. (b) Two MRRs (green and blue line) are trimmed with on-chip metal heaters to match the resonance of a third MRR (red).

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We demonstrate the trimming method with in-situ micro-heaters on a sample chip containing multiple single-channel ring resonators. These resonators are located in within 30 $\mathrm{\mu}$m to one another with nominally identical radii of 100 $\mathrm{\mu}$m but different coupling gaps of 0.7 $\mathrm{\mu}$m, 0.9 $\mathrm{\mu}$m and 1.2 $\mathrm{\mu}$m respectively between the bus and the ring. While the coupling condition due to the change in gap width varies in a predictable manner, the variation in resonance wavelength between the rings is unpredictable due to the variation in fabrication conditions. The optical spectra associated with the three MRRs are shown in Fig. 4(b). By application of an electrical power of 41.9 mW to a heater associated with a 0.9-$\mathrm{\mu}$m gap size MMR and 19.7 mW to another heater associated with a 1.2-$\mathrm{\mu}$m gap size MMR for a total of 15 minutes each, the respective resonance point of the rings was permanently trimmed to match the resonance of the third ring with a 0.7-$\mathrm{\mu}$m coupling gap (resonance wavelength of 1550.5 nm). The precision of this technique is indicated by the wavelength spacing between the three rings which decreased to $<$20 pm ($\sim$1.8 GHz). Although the rings were located on the chip within 30 $\mathrm{\mu}$m of one another, we did not observe any significant cross-modification in terms of the trimming process. This observation is supported by thermal simulation carried out with Ansys’ Lumerical HEAT module, where temperature distribution in the waveguide/heater cross-sectional plane was calculated as shown in Fig. 5. The temperature of an adjacent Si$_{3}$N$_{4}$ waveguide at a distance of 30 $\mathrm{\mu}$m away is estimated to be 22 $^{\circ }$C, 25 $^{\circ }$C and 30 $^{\circ }$C when the temperature of heater is fixed at 100 $^{\circ }$C, 300 $^{\circ }$C and 500 $^{\circ }$C, respectively, with the second case being a realistic representation of the maximum heater capacity (See Sec. 4.). This confirms that the effect of thermal cross-talk is insignificant even at elevated temperatures achievable through maximum heater power dissipation.

 

Fig. 5. Temperature profile in the plane normal to Si$_{3}$N$_{4}$ waveguide and the heater in a thermal simulation. Temperature of the heater is fixed at (a) 100 $^{\circ }$C, (b) 300 $^{\circ }$C and (c) 500 $^{\circ }$C. Temperature at the core of the associated waveguide is simulated to be (a) 75.0 $^{\circ }$C, (b) 216.2 $^{\circ }$C and (c) 360.5 $^{\circ }$C. Temperature at the core of the adjacent waveguide at a distance 30 $\mathrm{\mu}$m away is simulated to (a) 21.5 $^{\circ }$C, (b) 25.8 $^{\circ }$C and (c) 30.5 $^{\circ }$C.

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4. Efficiency of the on-chip heaters

Integrated heaters are required in many photonic circuits to actively control the system through the thermo-optic effect [16-20]. Critical to the current work is an estimate of the temperature achieved in the core of the silicon nitride waveguide. Figure 6(a) shows an MRR optical spectrum with the local heater dissipating 20.6 mW of electrical power. At elevated temperatures, the measured resonance wavelength is determined by a combination of the permanent trimming due to the change in cladding index and the dynamic thermo-optic effect. We have shown in Sec. 3 that a post-annealing permanent reduction of the refractive index of the SiO$_{2}$ film shifts the resonance wavelength to lower values, while during annealing (at elevated temperature) the thermo-optic effect contributes to an increase in refractive index in both the SiO$_{2}$ film and the Si$_{3}$N$_{4}$ waveguide core. As a result, when the sample is being heated the resonance wavelength moves to the right and counteracts the effect of permanent trimming. After the sample is cooled to room temperature, the permanent trimming is the sole contributing factor to the wavelength shift. We note that the evolution in the spectrum between 5 and 10 minutes is negligible, as shown in the inset of Fig. 6(a). The shift due to the thermo-optic effect alone is identified as the shift from the wavelength during trimming (after 5 minutes of electrical power application), to the wavelength after the sample is cooled to room temperature. A total shift of 0.16 nm was observed, which compared with Fig. 3(a), corresponds to an expected annealing temperature of 30 $^{\circ }$C to 40 $^{\circ }$C.

 

Fig. 6. (a) The resonance spectrum of a silicon nitride MRR before trimming (red), during trimming at the 5^th min (green), 10^th min (purple) and after trimming is complete (brown); (b) failure condition for a heater-integrated MRR by application of 840 mW electrical power. The micro-heater is damaged after 20 min.

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It is possible to estimate the change in modal effective index in Eq. (1). This can then be compared to the value determined by modal simulations and the increase in temperature can be calculated from the thermo-optic coefficient of silicon oxide $\partial n_{\textrm {SiO}_{2}}/\partial T = 0.96 \times 10^{-5}/^{\circ }$C [43] and silicon nitride $\partial n_{\textrm {Si}_{3}\textrm {N}_{4}}/\partial T = 2.45 \times 10^{-5}/^{\circ }$C [44]. The temperature in the core of the waveguide is then estimated to be 40 $^{\circ }$C for 20.6 mW of electrical power dissipation, in agreement with the comparison made previously.

In order to demonstrate the working limit of the in-situ heaters, one heater was driven to its failure threshold of 840 mW. After 20 minutes of operation at this power the heater exhibited open circuit behaviour. Figure 6(b) shows the total resonance shift of the associated ring resonator after the device was returned to room temperature. For our heater design, this then represents the maximum trimming possible via integrated annealing. Comparing with Fig. 3(b), the total shift suggests a core temperature of 225 $^{\circ }$C. This is comparable to the performance of Cr/Au heaters reported in [19], where an increase of 54 $^{\circ }$C was obtained with a power of 300 mW for an 8-$\mathrm{\mu}$m wide heater and 1.5-$\mathrm{\mu}$m thick silicon oxide cladding (compared to 10 $\mathrm{\mu}$m width and 3 $\mathrm{\mu}$m thickness in this work).

5. Resonance stability of the trimmed devices

From the perspective of power dissipation of an optical device, resonance trimming is preferred over steady-state, thermo-optic tuning when a permanent adjustment of the system’s transfer function is desired. However, the trimmed resonance may not be stable over an extended period of time. Previous studies which utilize changes in cladding index to trim device resonances have discussed issues relating to the long-term effect of relaxation of trimmed resonance wavelengths. In [21] trimmed Si MRR cladded with PECVD oxide underwent more than 500 pm shift after 1 day of storage in open air (essentially total relaxation to their original resonances). Reference [22] reported a Si MRRs trimmed with electron beam induced compaction of SiO$_{2}$ cladding to a total of 4.91 nm experience a further red shift of 0.15 nm along the trimming direction 5 days after the irradiation. Photo-induced trimming of chalcogenide-cladded Si MRRs in [27] observed a 0.16 nm drift of a device trimmed to a total of 6.7 nm. Further, the authors noted that the drift was proportionate to the total trim.

It is therefore pertinent to discuss the stability of our trimmed devices. We observed the temporal drifting of two sets of devices: furnace annealed resonators (MRR $\#$1 – $\#$8) belonging to Sample 1 and Sample 2 demonstrated in Sec. 3.2, and devices trimmed with in-situ heaters presented in Sec. 3.3 and Sec. 4. (MRR $\#$9 – $\#$11). Devices were stored at room temperature in an atmospheric environment and under room lighting for 570 days for MRR $\#$1 – $\#$8 and 99 days for MRR $\#$9 – $\#$11 before characterization was repeated. Figure 7 shows the overall wavelength trim and subsequent relaxation of the above devices. Resonances from all MRRs showed a relaxation towards the initial wavelengths, suggesting a structural relaxation of the SiO$_{2}$ cladding and the possibility to re-trim the devices. Four resonators on Sample 1 (all 100 $\mathrm{\mu}$m in radii) which were annealed at a maximum of 60 $^{\circ }$C showed an average resonance relaxation of 70 pm after an initial shift of 870 pm, accounting for 8.1% of the total trimming range; for resonators annealed at 500 $^{\circ }$C (Sample 2), an average relaxation of 540 pm was observed across 4 rings with a trimming range of 4.43 nm, corresponding to 12.3% of the initial shift. The stability of devices trimmed with micro-heaters is demonstrated with MRR $\#$9 – $\#$11, where $\#$9 and $\#$10 showed 20 pm and 55 pm relaxations, respectively. MRR $\#$11, which experienced a higher trimming range of 1.4 nm after its associated heater was driven to failure threshold, showed a relaxation of 270 pm, equivalent to 19% of the overall induced shift. These observations are in broad agreement with those of [27] that the magnitude of the resonance drift depends on the overall induced shift.

 

Fig. 7. Initial and final wavelength of trimming of 11 MRRs, and their relaxation after 570 days (MRR $\#$1 – $\#$8) and after 99 days ($\#$9 – $\#$11). MRR $\#$1 – $\#$8 were furnace annealed and MRR $\#$9 – $\#$11 were trimmed with in-situ heaters.

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The uncertainty of the measurements was also investigated using an untrimmed MRR from the same chip to account for measurement variation. A spread of 44 pm in the resonance wavelength from the control sample is observed across 7 hours of measurement in a single day, with an associated single standard deviation of 16 pm. This represents the variation from external factors including environmental effects and measurement set-up drift. Thus, 44 pm indicates the lower limits of uncertainty for the stability measurement, and goes to explain to some degree the large relaxation fraction of MRR $\#$9 and $\#$10.

6. Conclusion

We have presented a robust post-fabrication trimming technique via on-chip annealing with integrated resistive micro-heaters on a silicon nitride photonic platform, for waveguides clad with SiO$_{2}$. This process utilizes room temperature sputter-deposited SiO$_{2}$ as cladding material which upon heating changes the resonance wavelengths of ring filter devices. External annealing at 500 $^{\circ }$C results in a resonance shift up to 4.4 nm. Precise trimming with control better than 20 pm was demonstrated on two single-channel rings on the same chip using the micro-heaters. In this case a maximum of 1.4 nm resonance shift was achieved prior to micro-heater failure. This method offers a low-cost, energy-efficient and CMOS-compatible solution to compensate for fabrication variances. Because the essence of this method is the annealing of cladding oxide, it is possible for it to be applied to many photonic platforms.