Thermo-optic coefficient and nonlinear refractive index of silicon oxynitride waveguides

Integrated waveguiding devices based on silicon oxynitride (SiON) are appealing for their relatively high refractive index contrast and broadband transparency. The lack of two photon absorption at telecom wavelengths and the possibility to fabricate low loss waveguides make SiON an ideal platform for on-chip nonlinear optics and for the realization of reconfigurable integrated quantum lightwave circuits. Despite this, very few studies on its linear and nonlinear optical properties have been reported so far. In this work, we measured the thermo-optic coefficient dn/dT and the nonlinear refractive index n2 of relatively high (n ∼ 1.83 at a wavelength of 1.55 μm) refractive index SiON by using racetrack resonators. These parameters have been determined to be dndT=(1.84±0.17)× 10−5 K−1 and n2 = (7 ± 1) × 10−16 cm2W−1.


I. INTRODUCTION
Quantum information science is rapidly developing relying on generation of quantum states of light via emission from quantum dots, 1 colour centres 2 or via frequency conversion mechanisms exploiting material nonlinearities. 3Silicon photonics is one of the most promising technological platforms for the development of chip-scale densely-integrated quantum devices. 4,5ifferent types of material nonlinearities in Si enable frequency conversion via χ (3)6 and χ (2) , 7 while its thermo-optical coefficient dn/dT allows for efficient tuning of interference in complex photonic devices. 8Nonetheless, important free-carrier and two photon absorption issues, as well as the band-to-band absorption below ∼ 1µm of wavelength, limit the use of Si in several applications. 9,10he quest for Si-based transparent dielectrics has led to intense studies of alternative materials such as silicon nitride (Si 3 N 4 ), 11 doped silica oxides 12 or oxynitrides. 13These materials typically possess χ (3) optical nonlinearities 14 and dn/dT 15,16 from one (nitrides) to two orders (silica) of magnitude lower than those of silicon.Due to the relatively low refractive indices, thicker guiding components are required when these materials are used.High optical quality Si 3 N 4 offers the best modal confinement, but may accumulate undesired stress at thicknesses over 200 nm, requiring thus specific design and processing solutions. 17,18ere, we report on the study of linear (thermo-optic) and nonlinear χ (3) optical properties of relatively high (n ∼ 1.83 at a wavelength of 1.55 µm) refractive index SiON.The detailed characterization, performed on a SiON resonator, revealed a thermo-optic coefficient close to the one of Si 3 N 4 , and a nonlinear refractive index which is nearly three times the one of SiO 2 .In the meanwhile, this material can be grown to relatively high thicknesses (> 1µm), offering thus an alternative to the Si 3 N 4 platform for the design of nonlinear and quantum optical integrated photonic circuits.

II. DEVICE FABRICATION AND EXPERIMENTAL SETUP
The device under test is an integrated racetrack resonator in the All-Pass filter configuration. 19 sketch of the top-view of the device is reported in Fig. 1(a).
The fabrication starts with a deposition of a silicon oxynitride film on top of a 5 µm thermal SiO 2 grown on 6-inch Si wafers.The 600 nm thick SiON layer was grown from a mixture of silane (SiH 4 , 50 sccm), ammonia (NH 3 , 65 sccm) and nitrous oxide (N 2 O, 100 sccm) gases using a parallelplate plasma enhanced chemical vapour deposition (PECVD) chamber at 3 00 • C. The devices were patterned using an i-line optical lithography and defined via dry reactive-ion etching followed by 1.5 h annealing in an N 2 atmosphere at 975 • C to densify (8 %) the guiding material and to release the excess H 2 .Following the work of Bossi et al., 20 from the refractive index at a wavelength of 850 nm n SiON = (1.839± 0.001), we estimate a Si 3 N 4 molar fraction of (73 ± 2)%, and a SiO 2 molar fraction of (27 ± 2)%.
The racetrack resonator has a cross section of 1.2 × 0.55 µm 2 and bending radius of R = 50 µm, while the coupling with the bus waveguide is realized by means of a straight section of length L = 20 µm and a coupling gap of 1.05 µm.The waveguides are single mode for both Transverse Electric (TE) and Transverse Magnetic (TM) polarization at the probe wavelength around 1550 nm.The mode is confined between the lower thermal oxide cladding and the upper one, constituted by a double stack of 400 nm Borophosphosilicate glass (BPSG) and a 2 µm thick PECVD SiO x layer.The cross-section of the device is reported in Fig. 1(b).
Three separate experimental setups have been used to investigate the device.The thermo-optic coefficient is determined by using a standard, thermally controlled, passive characterization waveguide setup.We used a C-band tunable Continuous Wave laser (CW), fiber coupled to a polarization controller, which is butt-coupled to the waveguides by means of tapered lensed fibers using a piezoelectric positioning stage.The coupling losses have been estimated with the cut-back technique, which results (6 ± 0.5) dB, equally divided between input and output.With the same technique, the propagation losses have been measured to be (2.0 ± 0.5) dB/cm for both TE and TM polarization at 1550 nm.
As it is possible to see from Fig. 1(c), the device is placed in thermal contact with a Peltier cell, whose temperature can be set in the range of 25-75 • C, with an accuracy of ±1 • C. The output power is monitored using a germanium photodetector.The laser wavelength is scanned over the linewidth of the resonator at different fixed temperatures, in order to track the resonance wavelength.
The experimental set-up used to determine the n 2 coefficient makes use of an additional CW tunable laser, called "idler" hereafter, which is combined to the pump laser and injected to the input port of the resonator to stimulate the Four Wave Mixing (FWM) process (see Fig. 1(c)).The laser background spontaneous emission is filtered down to a level below 110 dBm.The generated signal inside the resonator is filtered from the co-propagating pump and idler beams by using two cascaded Dense Wavelength Division Multiplexing (DWDM) modules, and directed to a photon counter (ID Quantique ID220) operating in Free Running mode, with a detection efficiency of 5% and a dead time of 40 µs.The DWDM modules achieve a signal isolation of more than 100 dB.
As discussed in Section IV, the determination of the nonlinear refractive index requires the knowledge of the extrinsic and of the total quality factors of the pump, the signal and the idler resonances.These have been extracted by measuring simultaneously the intensity and the phase of the light transmitted from the resonator as a function of wavelength.The latter has been probed by placing the sample into one arm of a free space Mach-Zehnder interferometer, as it is sketched in Fig. 1(d).For this measurement, we implemented only one C-band tunable laser, whose polarization was set at the input by a three-paddle polarization controller.The light was in and out coupled to the input/output waveguide by using two microscope objectives.The Mach-Zehnder was set in a nearly balanced regime (both in amplitude and phase) by using a delay line and a variable optical attenuator placed in the free arm.Three output signals were recorded at the output of the interferometer, which are the light transmitted from the sample I s (when the light in the free arm is blocked), the one coming from the free arm I ref (when the light in the arm which contains the sample is blocked), and their interference I.The phase is than retrieved by the relation φ = arccos

III. DETERMINATION OF THE THERMO-OPTIC COEFFICIENT
The thermo-optic coefficient has been measured by evaluating the resonance shift ∆λ as a function of the temperature variation ∆T with respect to a reference temperature of T = 28 • C. The temperature variation changes the effective index by a quantity ∆n eff (∆T ), so that each resonance gets shifted from the "cold" wavelength λ 0 by: As shown in the inset of Fig. 2, the quantities λ 0 and ∆λ(∆T ) can be extracted from the experiment.In the investigated range of temperatures the shift ∆λ is found to be linear.In order to compute the effective index shift, it is necessary to determine accurately the "cold" effective index n eff (λ 0 ).This has been shown to be quite difficult for resonators with a short free spectral range. 22Therefore, the effective index n eff (λ 0 ) has been computed by Finite Element Method (FEM) simulations.Due to the fact that the waveguide mode extends also into the cladding (the confinement factor of the fundamental TE and TM modes are 0.74 and 0.6 respectively), the quantity ∆n eff /∆T is not directly the thermo-optic coefficient of the waveguide core material, but it contains information about the thermo-optical properties of both the cladding and of the core materials.
In order to decouple the two contributions, the quantity ∆n eff /∆T is computed by FEM simulations as a function of the thermo-optic coefficient of only the bulk material Γ SiON , while the refractive index of the oxide cladding n ox is modelled as n ox (∆T ) = n ox,0 + Γ ox ∆T, where n ox , 0 is a reference refractive index at ∆T = 0 K, and Γ ox = 0.95 × 10 5 K 1 is the thermo-optic coefficient of the oxide, 15 which is kept fixed during the simulation.The quantity (∆n eff /∆T ) exp extracted from the experiment, is then compared to the one computed through numerical simulations, named (∆n eff (Γ SiON , Γ ox )/∆T ) theo .The best estimate of the thermo-optic coefficient of SiON is assumed to be the value of Γ SiON which matches the experimental result.
Fig. 2 reports the quantity (∆n eff /∆T ) theo as a function of Γ SiON (black squares), together with (∆n eff /∆T ) exp (red dot).(∆n eff /∆T ) exp matches the simulated one if Γ SiON = (1.84 ± 0.17) × 10 5 K 1 .For comparison, in Fig. 2 we also indicate the thermo-optic coefficient of silica Γ ox = 0.95 × 10 5 K 1 FIG. 2. Simulation of the quantity ∆n eff /∆T as a function of the thermo-optic coefficient of the waveguide core material.The red dot shows the experimental value, which is found from the analysis of the shift of the resonance wavelength as a function of temperature (shown in the inset).The solid blue lines mark the values of the thermo-optic coefficient of silica and of stoichiometric silicon nitride reported in Ref. 15.   and the one of stoichiometric silicon nitride Γ Si 3 N 4 = 2.5 × 10 −5 K −1 , both reported in Ref. 15.We point out that these values depend on the fabrication procedure, so they have to be only considered as indicative guidelines for the reader.The thermo-optic coefficient of SiON is approximately the 74% of the one of Si 3 N 4 .
Note that the simulation in Fig. 2 does not take into account the impact of the photoelastic effective index shift due to the accumulated stress in the waveguide, as a consequence of the temperature variation.This is however a reasonable approximation, as we estimated with a FEM simulation a maximum average stress (compressive and biaxial) of only 30 MPa in the waveguide core at 65 • C. By assuming as a first approximation the same stress-optical coefficients of stoichiometric Silicon Nitride for the Silicon Oxinitride core, 23 this leads to a photoelastic effective index shift of 3.47 × 10 7 K 1 .This value is actually two orders of magnitude lower than the one induced by the thermo-optic effect, and thus can be safely included within the error bar of our measurement.

IV. DETERMINATION OF THE NONLINEAR REFRACTIVE INDEX
The nonlinear refractive index is determined from the efficiency η of stimulated FWM.This quantity is defined as the ratio between the power of the converted signal P s and the one of the stimulating idler P i , and depends on the power enhancement factors |FE(ω j )| 2 (here, j = p, s, i labels the pump, the signal and the idler frequency respectively) and the nonlinear coefficient γ nl as: in which L is the resonator perimeter and P p is the pump power in the waveguide.The nonlinear refractive index n 2 appears in the definition of γ nl as: 6 where c is the speed of light, n g is the group index, n SiON is the bulk refractive index and A eff is the effective area, defined as in Ref. 24.Stimulated FWM is performed by tuning the pump and the idler laser frequencies ω p and ω i into two resonances orders of the resonator, shown in Fig. 3(a), and by monitoring the generated signal power at the frequency ω s = 2ω p ω i .Since the group velocity dispersion of the implemented waveguides is non-zero at the pump wavelength, the converted signal frequency ω s does not match perfectly the eigenfrequency ω 0s of the resonator, but has a normalized detuning δ = ω 0s −ω s ω 0s .From the simultaneous fit of the intensity and of the phase of the light transmitted from the resonator, shown in Fig. 3, the total and the extrinsic quality factors Q tot and Q ext have been extracted.The information carried by the phase is crucial for determining the extrinsic and the intrinsic quality factors, since their values can be exchanged without affecting the resonance linewidth and extinction ratio, which are the only quantities that can be extracted from a measurement of the intensity.As shown in Fig. 3(b), for all the three wavelengths involved in the FWM process, the phase jump across the resonance is always less than π, indicating that the resonator is undercoupled.The extrinsic quality factor must then be higher than the intrinsic one.Once Q tot and Q ext have been determined, the field enhancements can be computed from the relation: where τ rt = Ln g /c is the roundtrip time of light within the cavity (n g can be extracted from the measurement of the resonator free spectral range FSR through the relation n g = λ 2 LFSR ).Eq. 4 can be readily derived using temporal coupled mode theory. 25These quantities are reported in Table I for the TE and TM polarization.
The on chip power has been estimated from the measurement of the power before entering into the chip, and from the knowledge of the propagation and coupling losses.Finally, Eq. 2 and Eq. 3 have been used to extract the value of n 2 .Table II summarizes all these quantities.
The value of n 2 results to be (6 ± 1) × 10 16 cm 2 W 1 for the TE polarization, and (8 ± 1) × 10 16 cm 2 W 1 for the TM one.As expected, these values present a clear match due to the isotropic behaviour of the SiON amorphous structure.
Moreover, this value lies between the nonlinear refractive index of silica 26 (n 2 ∼ 2.36 × 10 16 cm 2 W 1 ) and the one of stoichiometric silicon nitride 27 (n 2 ∼ 2.4 × 10 15 cm 2 W 1 ).Let us state that by performing the same calculations which led to the results in Table II considering a non-vanishing nonlinearity in the cladding region, the value of n 2 still lies within the bounds set by the experimental error.On average, the nonlinear refractive index of SiON is approximately three times larger than the one of SiO 2 , and the 29.1% of the one of Si 3 N 4 .

V. CONCLUSIONS
In this work, an experimental characterization of the thermo-optic coefficient and of the nonlinear refractive index of silicon oxynitride waveguides has been performed.The thermo-optic coefficient results to be dn dT = (1.84 ± 0.17) × 10 5 K1 , close to the one of stoichiometric silicon nitride.The average nonlinear parameter n 2 results to be isotropic and equal to n 2 = (7 ± 1) × 10 16 cm2 W 1 , which is almost a factor of three larger with respect to the one of silica.
In addition to the well known appealing properties of the SiON, such as low insertion and propagation losses, wide transparency window from the visible to the infrared, lack of multi-photon absorption effects, CMOS compatibility and stress-free fabrication, in this paper we evaluated a sizable thermo-optic coefficient and nonlinear refractive index.The result reported here envisages that SiON has thermal and nonlinear optical properties which are competing to the other silica or silicon based materials.Hence, SiON is an excellent trade-off platform for the design of nonlinear and quantum optical integrated photonic circuits, in which thermal reconfiguration and nonlinear parametric processes constitutes fundamental operations.

FIG. 3 .
FIG. 3. (a) Normalized transmission of the resonator, with the polarization set to TM.The signal (blue), pump (yellow) and idler (red) resonance orders involved in the FWM process are highlighted with different colors.(b) Measured (black) and simulated (red) intensity and phase of the light transmitted.From left to right, the panels refer respectively to the signal, the pump and idler resonance orders.
, but by

TABLE I .
Measured resonance wavelength λ 0 , total quality factor Q tot , extrinsic quality factor Q ext , normalized detuning δ, roundtrip time τ rt and field enhancement |FE| relative to the pump, the idler and the signal TE and TM resonances.

TABLE II .
List of the main parameters which appear in Eq. 2 and Eq. 3.