Athermal silicon nitride angled MMI wavelength division (de)multiplexers for the near-infrared

WDM components fabricated on the silicon-on-insulator platform have transmission characteristics that are sensitive to dimensional errors and temperature variations due to the high refractive index and thermo-optic coefficient of Si, respectively. We propose the use of NH3-free SiNx layers to fabricate athermal (de)multiplexers based on angled multimode interferometers (AMMI) in order to achieve good spectral responses with high tolerance to dimensional errors. With this approach we have shown that stoichiometric and N-rich SiNx layers can be used to fabricate AMMIs with cross-talk <30dB, insertion loss <2.5dB, sensitivity to dimensional errors <120pm/nm, and wavelength shift <10pm/°C. Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. 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Introduction
Wavelength division (de)multiplexing (WDM) devices are important elements required to increase the capacity of data-links and high speed telecommunication photonic systems.The most popular WDM integrated technologies include arrayed waveguide gratings (AWG) [1], planar concave gratings (PCG) [2] and micro-ring resonators (RR) [3].These components usually require sophisticated design processes and complex fabrication steps to achieve low insertion losses and improved spectral responses.More recently, an alternative technology based on dispersive selfimaging in multimode waveguides has also been used to obtain angled multimode interferometers (AMMI) for WDM in the near infra-red (NIR) and mid infra-red (MIR) [4][5][6].These AMMI structures have a distinctive ease of fabrication, high tolerance to dimensional errors and low insertion losses compared to other WDM approaches [7].
The vast majority of WDM components have been fabricated on the mature silicon-oninsulator (SOI) platform.However, their transmission characteristics tend to be strongly sensitive to temperature variations due to the relatively high thermo-optic coefficient of Si (1.8x10 -4 /°C).In fact, the thermal shift produced in the central wavelength of these devices is of the order of 70-100pm/°C in the NIR region [2,3,8].As a result, they require active temperature control or complex compensation techniques to stabilize the wavelength drift in order to preserve their performance at different temperatures.
To tackle this situation, we propose using a recently demonstrated silicon nitride (SiN x ) platform [9][10][11] with low propagation losses and potentially lower thermo-optic coefficient to fabricate AMMI (de)multiplexers .With this approach we aim to combine the distinctive advantages of the AMMI structures with the advantages of the SiN x platform in order to demonstrate athermal (de)multiplexers with low insertion losses and spectral tolerance to dimensional errors with a relatively simple fabrication process (i.e.single lithography and single etching steps).
In this paper, we report the design, fabrication and characterisation of two AMMI triplexers for the O (1260-1360nm) and C (1530-1565) telecommunication bands.We discuss the spectral characteristics of both devices and the effect that the refractive index (n) of three different SiN x layers have on them.Finally, we detail the effect that both temperature and dimensional variations have on the central wavelength of the devices.To the best of our knowledge, the study in this paper is the first demonstration of SiN x AMMI (de)multiplexers for WDM in the NIR wavelength regime.

Design and fabrication
Figure 1 shows the basic structure of an AMMI.It consists of a multimode waveguide of width W M DW with input/output waveguides of width W IO .Opposed to conventional multimode interferometers (MMI), the input/output waveguides of the device are tilted at an angle θ t .Similarly, the input/output waveguides are tapered from its single-mode width to W a before entering the multimode waveguide to increase the fidelity of the devices.The axial positions of the output waveguides respect to the input (L i ) are designed to match the dispersive self-imaging condition of an MMI given by Equation 1where, n e f f is the effective index of the fundamental mode in the multimode region of the device and λ i is the design wavelength of the ith output channel [6].
The two AMMI triplexers were designed to operate at different wavelength windows within the O band (1270-1320nm) and the C band (1520-1570nm), respectively.Before running simulations, W M DW was fixed at 25µm so that the dimensions of the designed devices could be comparable to those of previously demonstrated AMMIs on SOI [4,5].The rest of the structural parameters were then optimised to provide spectral responses with insertion losses (IL) <2dB and cross-talk (XT) ≈15-20dB using FIMMWAVE with a refractive index of 2.0 for SiN x .
Figure 2 shows the IL of the devices as a function of W a using an initial θ t of 0.3 radians.From these results, W a was selected to be 9µm as this value minimises the IL for both wavelength bands.Similarly, θ t was then adjusted to minimise the XT between adjacent channels.Initial values for (L i ) were calculated to provide a channel spacing (∆λ) ≈15nm using equation 1. Figure 3 depicts the precise (L i ) values obtained for both devices after simulations were performed.Table 1 shows the optimised design parameters for both devices.Table 1.Optimised design parameters for the 3-channel AMMI Tapered grating couplers were used to effectively couple light into the devices via optical fibres.Each coupler consists of a single-mode waveguide tapered up to a 10µm wide waveguide, where surface gratings are incorporated.The period of the gratings was selected to be either  Several structures were included in the final mask layout to optimize and measure the designed devices.A set of AMMIs with different lengths was considered to account for fabrication errors and to calibrate the output lengths for the desired wavelengths.In addition, AMMI structures with W M DW with variations of ±20 and ±40nm were added to study the sensitivity of the devices to dimensional variations.Finally, a separate structure with two tapered grating couplers connected back-to-back was included for normalization purposes.
The structures were fabricated on three different SiN x layers with a thickness of 300nm.These layers were deposited on 6" Si wafers with a 2µm thermally-grown SiO 2 layer using the NH3-free plasma enhanced chemical vapour deposition (PECVD) process detailed in [9].Table 2 summarises the optical properties of each SiN x layer.
The structures were defined using electron beam lithography on a high-resolution resist (ZEP520A) with a thickness of 450nm spun on the wafers.The design was then transferred to the SiN x using inductively coupled plasma etching (ICP) with a target etch depth of 300nm and a SF 6 :CHF 3 chemistry.Finally, a 1µm thick layer of PECVD SiO x was deposited on top of the Table 2. Optical properties of the SiN x layers.The refractive index (n) was estimated from ellipsometry measurements.The propagation losses (PL) were measured using the cutback method as described in [9].The spectral response of the devices was characterised using two tunable laser sources with wavelength tuning ranges between 1260-1360nm (Agilent 8164B) and 1520-1620nm (Agilent 8163B).The polarisation of the light launched into the devices was controlled to ensure that only TE modes were allowed to propagate.Similarly, the chips were placed on a thermal stage to control the temperature at which the measurements were taken, so that the effect of the temperature on the spectral response of the devices could also be studied.A separate structure consisting of two tapered grating couplers connected back to back was used for normalization purposes.Table 3 shows the spectral response of the designed AMMIs fabricated in the three different SiN x materials.The most evident effect of changing the refractive index (n) of the SiN x layer is the shift introduced in the central wavelength (∆λ i ) of the AMMI's channels.In this case, λ i is shifted to shorter wavelengths when the n is decreased from its stoichiometric value (n = 2), while the opposite occurs when n is increased.This means that with lower n we need shorter lengths to output the desired wavelengths, while with higher n we require longer lengths.This result is important because it means that it is possible to reduce the overall footprint of the AMMI devices by using SiN x layers with lower n.In fact, it also means that AMMIs on SiN x can have shorter L i than AMMIs with the same W M DW on SOI because of their lower n. Figure 6 shows that the observed wavelength shift has a relatively linear behaviour that can be quantified between 1.10-1.20nm/0.01RIU at both wavelength bands.

Refractive Index
The change in the n of the SiN x layers not only affects ∆λ i , but also the overall spectral performance of the devices.The data on Table 3 show that ∆λ increases with decreasing n.As a result, the devices fabricated on SiN x layers with low n tend to have a reduced channel count compared to their counterpart on SiN x layers with high n.Nevertheless, the BW of the devices remains between 50-60% of ∆λ's value, which is important to ensure a lower device sensitivity to wavelength shift.Moreover, the IL non-uniformity across the channels and their XT decrease as n is reduced below its stoichiometric value (n=2) improving the performance of the devices.
In general, it can be said that the spectral characteristics improve with lower n, while they worsen with higher values.As a result, we can not only reduce the footprint of the devices using SiN x layers with lower n, but we can improve their performance in terms of BW and XT.In fact, the XT observed in the C-band for the N-Rich AMMI is not only better than that of the stoichiometric AMMI, but is better than the typical 15-25dB XT exhibited by other WDM devices fabricated on SOI [1,2].
Finally, it is important to note that the IL increases for the devices that were not fabricated in the stoichiometric material because their design was not optimised for the refractive index of the corresponding SiN x .Hence, the IL can be reduced by optimising the design for the refractive index of the material layer.The sensitivity of the λ i shift with respect to the fabrication error in the width of the AMMI's multimode waveguide was also studied (∆W M DW ). Figure 7 shows the experimental results obtained in both wavelength bands for the devices fabricated on the stoichiometric and N-rich SiN x .In this case, it can be observed that the AMMIs have almost a linear sensitivity ∆λ/∆W M DW close to 100pm/nm regardless of the n of the SiN x layer used.Table 4 shows that this value is comparable to the sensitivity of 100pm/nm observed on AMMIs previously reported on the SOI platform, [5], which in fact is already about one order of magnitude lower than that of other conventional (de)multiplexer devices [12].

AMMI Width
These results confirm that SiN x AMMIs have the high tolerance to dimensional errors observed in SOI AMMIs.However, SiN x devices are known for having a considerably higher tolerance to dimensional variations due to the lower refractive index contrast between the SiN x core and the cladding.In this case, the lack of an improved tolerance can be attributed to the width of the multimode waveguide.For single mode waveguides, the refractive index change observed with dimensional variations in SOI is ≈ 6x10 -2 , while that observed in SiN x is one order of magnitude smaller ≈ 7x10 -3 .This smaller refractive index change translates into a lower sensitivity to dimensional variations in SiN x waveguides.In the case of the MDW with W M DW = 25µm, the refractive index change observed in both SOI and SiN x is negligible.As a result, comparable ∆λ/∆W M DW is expected in both platforms.The sensitivity could be potentially reduced by increasing W M DW in order to decrease further the refractive index sensitivity of the multimode waveguide, but that would mean increasing the overall footprint of the devices as L i scales with W M DW 2 .Figure 8 shows the central wavelength (λ i ) measured for the different AMMI devices as a function of temperature.It can be observed that in all cases λ i increases its value as the temperature increases resulting in wavelength shifts (∆λ/∆T) between 5 and 50pm/°C that depend on the n of the SiN x layer.The devices fabricated on the stoichiometric material have the lowest shift around 10pm/°C in both wavelength bands.On the other hand, ∆λ/∆T is higher for the devices fabricated on the N-rich layer with values close to 30pm/°C probably due to the presence of dangling bonds.Similarly, ∆λ/∆T reaches values almost as high as 50pm/°C for the devices on the Si-rich layer due to the presence of dangling bonds and the increased amount of Si atoms with a high thermo-optic coefficient within the material.Table 5 summarizes the temperature sensitivity of different WDM devices.The ∆λ/∆T for the devices on the stoichiometric and N-rich layers is at least ≈ 8 times and 4 times better than that observed in similar (de)multiplexer devices on silicon, respectively.Moreover, it is comparable to the values observed on silica AWG devices with the advantage of having a less complex fabrication process than some compensation techniques used for Si devices.

Conclusions
We have demonstrated the fabrication of AMMI structures on SiN x layers as an alternative to conventional SOI (de)multiplexers.We have shown that stoichiometric SiN x layers can be used to fabricate AMMIs with XT<20dB and IL<3dB.This performance is comparable to the state of art of AMMIs on the SOI platform with the advantage of having a ∆λ below 10pm/°C, which is at least 8 times lower than the one observed in typical SOI (de)multiplexers.We have also demonstrated that devices fabricated on N-rich layers have the potential to achieve XT values even below 30dB with a ∆λ/°C of 20pm/°C.These XT values are lower than the typical 15-25dB observed in other WDM devices fabricated on SOI.
In addition, we have demonstrated that the AMMI devices fabricated in SiN x require smaller L i thus reducing their overall footprint, whereas the footprint of other SiN x structures, such as AWGs and PCGs, increases by almost an order of magnitude due to their lower refractive index contrast compared to SOI.Nevertheless, the size of the multimode waveguide limits the tolerance to fabrication errors of the devices to values close to 100pm/nm which are comparable to those of other AMMIs in SOI.The sensitivity to dimensional variations could be reduce by increasing W M DW at a price of increased device footprint.
As a result, we have proved that SiN x AMMIs are a convenient option to fabricate athermal (de)multiplexers with a good tolerance to fabrication errors and temperature variations with a relatively simple fabrication process.The studied devices have the potential to be used for commercial applications that are sensitive to temperature variations, but there is still room for improvement.In fact, both the size and the performance of the AMMIs could be improved by optimizing the design for SiN x layers with a refractive index close to a N-rich composition because L i decreases and the spectral performance of the devices improves with lower n.

Fig. 2 .
Fig. 2. IL as a function W a for the C and O bands when W M DW = 25µm and θ t = 0.3rad.

Fig. 3 .
Fig. 3. Optimised L i for the: (a) O-band and (b) C-band when W M DW = 25µm with optimised θ t .

Fig. 4 .
Fig. 4. Top view of the fabricated AMMI devices at the interfaces with the multimode waveguide.

Figure 5 (
Figure5(c) and 5(d) present the transmission spectra of the two devices fabricated on the stoichiometric SiN x (Wafer 1) measured at 20°C.The IL for both is below 2.5dB with a nonuniformity of less than 1dB across all the channels.The average 3dB bandwidth (BW) and XT for the device operating at the O-band are 7nm and <18dB respectively, while they are 10nm and <20dB for the C-band device.These experimental results are in good agreement with the theoretical simulations in 5(a) and 5(b).Moreover, the spectral response of the devices is similar to that of previously demonstrated SOI AMMIs, which have IL≈1.5-3dB,BW≈10nm and XT<15-25dB[4,5].

Fig. 6 .
Fig. 6.Central wavelength (λ i ) as a function of the refractive index of the SiN x layers.

Fig. 7 .
Fig. 7. Sensitivity of the spectral shift as a function of the fabrication error in the width of the AMMI's multimode waveguide observed with devices fabricated on different material layers for the (a) O-band and (b) C-band.

Fig. 8 .
Fig. 8. Central wavelength as a function of temperature for AMMIs fabricated on different SiN x layers operating in the (a) O-band and (b) C-band.

Table 3 .
Summary of the spectral parameters of AMMIs fabricated SiN x layers with different refractive indices.

Table 4 .
Fabrication sensitivity for different WDM devices fabricated on SOI and SiN x .The waveguide geometry of the devices is specified by their width (W), height (H) and etch depth (ED).The sensitivity of the devices is given in both pm/nm and GHz/nm.(*This work)

Table 5 .
Temperature sensitivity for different WDM devices.Their waveguide geometry is specified by width (W) and height (H).(*This work)