## Abstract

A silicon/silicon-rich nitride hybrid-core waveguide has been proposed and experimentally demonstrated for nonlinear applications to fill the gap between the pure silicon waveguide and the pure silicon nitride waveguide with respect to the nonlinear properties. The hybrid-core waveguide presented here leverages the advantages of the silicon and the silicon-rich nitride waveguide platforms, showing a large nonlinearity γ of 72 ± 5 W^{−1} m^{−1} for energy-efficient four-wave mixing wavelength conversion. At the same time, the drawbacks of the material platforms are dramatically mitigated, exhibiting a reduced two-photon absorption coefficient *β*_{TPA} of 0.023 cm/GW resulting in an increased nonlinear figure-of-merit as large as 21.6. A four-wave-mixing conversion efficiency as large as −5.3 dB has been achieved with the promise to be larger than 0 dB. These findings are strong arguments supporting the silicon/silicon-rich nitride hybrid-core waveguide to be used for energy-efficient nonlinear photonic applications.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

The main motivations for developing integrated nonlinear optical devices compared to commercially available nonlinear fiber optics is to take advantage of their smaller size, higher energy-efficiency, and integration of multiple functionalities on óne chip [1]. In order to bring these motivations into reality, the ideal integrated waveguide for nonlinear optical devices is required to have a low linear and nonlinear loss, a large nonlinearity, and should be compatible with matured complementary metal-oxide-semiconductor (CMOS) fabrication technologies. Furthermore, to exploit the possibilities and benefits of integrating active silicon photonic devices like modulators and detectors for efficient signal processing, e.g. in the data center applications, the ideal nonlinear waveguide platform should also be easily integrated with the existing silicon-on-insulator (SOI) platform [2].

For compatibility to CMOS technology, crystalline silicon (Si) waveguides for nonlinear optics is a natural first choice as Si is the backbone of CMOS and possesses a large nonlinear index *n*_{2} of 2.8-14.5 x 10^{−18} m^{2}/W [3]. Indeed, an efficient four-wave mixing (FWM) conversion efficiency (CE) of −5.5 dB with a coupled pump power of 25 dBm has been achieved in a Si rib waveguide having a large nonlinearity γ of ~58 W^{−1} m^{−1} [4]. Even larger nonlinearities have been measured for silicon ridge waveguides going up to 307 W^{−1} m^{−1} [5] and ~588 W^{−1} m^{−1} [6]. Unfortunately, Si has a small bandgap of ~1.1 eV resulting in a large two-photon absorption (TPA) coefficient β_{TPA} of the waveguides (0.5, 0.8 and 0.6 cm/GW for [4], [5] and [6], respectively), and the associated free-carrier absorption (FCA) dramatically decreases and limits the nonlinear efficiency of c-Si waveguides. A *p-i-n* structure across the c-Si waveguide in order to actively sweep out the generated carriers can be applied to reduce the impact of FCA and increase the nonlinear efficiency. In this way, the FWM CE has been demonstrated to reach −4.4 dB [7] with the drawback of adding relatively complexities in the design, fabrication, and use of the waveguides. Amorphous silicon (α-Si) waveguides have also been demonstrated to exhibit a large γ even up to 1200 W^{−1} m^{−1} [8–10] but unfortunately α-Si material typically suffers from Stabler-Wronski degradation at higher powers [9] and still possess a large β_{TPA} of 0.25 cm/GW [10]. Alternatively, waveguides realized in deuterated silicon-oxynitride (Hydex) or silicon nitride (Si_{3}N_{4}) have been successfully utilized for parametric oscillation [11–15] and octave supercontinuum generation (SCG) [15], due to the very low propagation loss (6 dB/m [11] and 0.8 dB/m [14], respectively) and negligible nonlinear loss that is obtainable in the waveguides. However, the drawbacks of such waveguides are their weak mode confinements caused by small refractive indices (RI) of Hydex (<1.9) and Si_{3}N_{4} (<2.0) along with low nonlinearities (γ = 0.233 W^{−1} m^{−1} for the Hydex waveguides and γ = 1.2 W^{−1} m^{−1} for the Si_{3}N_{4} waveguide [16]) requiring large pump powers. Recently, silicon-rich nitride (SRN) waveguides have been attracting much attention for nonlinear optics due to a large RI of 2.1-3.1 along with TPA-free operation due to a large bandgap >2.2 eV [17–21]. Whereas SRN waveguides with a moderate excess of Si show an improved (comparing to Si_{3}N_{4}) γ of ~16 W^{−1} m^{−1} in [17], ~3 W^{−1} m^{−1} in [18] and ~9.3 W^{−1} m^{−1} in [19], a too high Si excess may result in TPA (β_{TPA} = 0.1 cm/GW for a Si:N ratio of ~1.7 [17]). Moreover, additional high-temperature (not being backend-CMOS compatible) fabrication steps will be inevitable for integrating Hydex and silicon nitride (Si_{3}N_{4}) waveguides in SOI platform. In an extreme case, ultra-silicon-rich nitride (Si_{7}N_{3}) waveguides with a large RI of 3.1 and a γ of 500 W^{−1} m^{−1} have been demonstrated to exhibit good performances for nonlinear optics [20,21]. However, it is still an open question how the Si_{7}N_{3} material platform perform for key nonlinear applications like octave-spanning SCG and frequency-comb generation and in high bit-rate communication experiments.

Here, we propose and experimentally demonstrate a Si/SRN hybrid-core waveguide (HCW), in which the waveguide core is comprised of Si and SRN. A similar structure utilizing a thin Si layer to enhance light confinement in a low-index waveguide having a high nonlinear index has recently been proposed [22]. However, the low index waveguide part consists of a CMOS-*in*compatible polymer and no experimental results are given. In our HCW, light will be confined partially in Si and partially in SRN to reduce TPA and FCA compared with a pure Si waveguide. Meanwhile, the nonlinearity is dramatically improved compared with a pure SiN waveguide. Linear characterizations and FWM experiments show a moderately low waveguide propagation loss of ~5.2 dB/cm, a large γ of 72 ± 5 W^{−1} m^{−1}, and a low β_{TPA} of 0.023 cm/GW, which reasonably result in a larger nonlinear figure of merit than a conventional silicon waveguide and higher power efficiency for nonlinear processes than the Hydex and Si_{3}N_{4} waveguides.

## 2. Structure, fabrication and linear characterization

Figure 1(a) shows a schematic of the proposed Si/SRN HCW, which comprises a thin Si layer with a SRN layer on the top. Width of the waveguide, thickness of the Si layer, and thickness of the SRN layer are denoted as *w*, *h*_{Si} and *h*_{SRN}, respectively. For the nonlinear properties of the presented waveguide structure, the power distribution of the guided mode is a key parameter. By using an eigenmode solver (Mode Solutions from Lumerical Inc.), we have calculated the power confinement ratio (*Γ*_{Power}) of the transverse-electric (TE) mode in the Si and in the SRN material with respect to the Si layer thickness *h*_{Si}, as shown in Fig. 1(b) for, *w* = 1200 nm and *h*_{SRN} = 400 nm. The wavelength is 1550 nm and the refractive indices (RIs) of Si and SiO_{2} are 3.478 and 1.444, respectively. The RI of SRN is extracted from ellipsometry by using a TaucLaurentz fitting model. The fitting shows a RI of 2.126 at 1550 nm and a TPA-free bandgap of 2.618 eV. Figure 1(b) also shows the effective index (*n*_{eff}) as a function of the silicon thickness and shows as expected an increase in *n*_{eff} as more light is confined in the Si layer at larger *h*_{Si}. To leverage a large confinement of the mode in Si but avoid the detrimental nonlinear losses in thick Si layers, we choose a moderately thin Si layer of 70 nm. Figure 1(c) shows the TE mode profile when *h*_{Si} = 70 nm, *h*_{SRN} = 400 nm, and *w* = 1200 nm. It is seen that the waveguide confines light nicely with the *n*_{eff} of 2.1 and a small effective mode area *A*_{eff} of 0.43 μm^{2}. Although the intensity in the Si layer is large, the relative power is small comparing with the power in the SRN layer and we find that *Γ*_{Power} in Si and SRN are ~26% and ~53%, respectively.

The proposed HCWs are fabricated from a silicon-on-insulator (SOI) wafer with a 1-μm SiO_{2} insulator layer and a 340-nm top Si layer, which is oxidized to thin down the Si layer to 70 nm. After etching away the oxidized layer with hydrofluoric acid (HF), a 400 nm-thick SRN film is deposited on the wafer by utilizing a reaction between dichlorsilane (SiH_{2}Cl_{2} at 80 sccm) and ammonia (NH_{3} at 20 sccm) at 830°C and 120 mTorr in a low-pressure chemical vapor deposition (LPCVD) machine. The film is characterized by using X-ray photoelectron spectroscopy (XPS) and shows ~20% of excess Si. A 60-nm thick aluminum (Al) film is patterned on the wafer by e-beam lithography and a lift-off process to act as the etching mask for the Si and SRN stack, which are dry-etched by using a gas mixture of tetrafluoromethane (CF_{4}, 20 sccm) and hydrogen (H_{2}, 10 sccm) gasses. After stripping the residual Al, the HCWs are covered by 1-μm of SiO_{2}. Figure 2(a) shows a scanning electron microscope (SEM) image of the cross section of a HCW before the Al stripping. By measuring the transmission of light in waveguides with 3 different lengths (4 mm, 11.5 mm, and 17 mm), the propagation and coupling losses to a tapered lensed fiber of the fabricated HCWs are extracted for different widths of the waveguides as shown in Fig. 2(b). For a given width and length, 6 identical waveguides are fabricated and measured to estimate the uncertainty from measurements and process variations indicated by the error bars in Fig. 2(b). The propagation loss α for the TE mode in the 900 nm, 1200 nm, and 1400 nm waveguides are 7.60 ± 0.61 dB/cm, 5.23 ± 0.28 dB/cm and 5.17 ± 0.35 dB/cm, respectively. The coupling loss for the waveguides with different widths varies slightly and is ~6 dB/facet. This relatively large coupling loss is due to a mode mismatch between the waveguides and the tapered lensed fiber and can be reduced by introducing an inverse tapered waveguide scheme [23].

We have also fabricated and characterized microring resonators (MRRs) based on the presented HCW and Fig. 2(c) shows the measured spectrum in an MRR with a width of 1200 nm, a coupling gap of 200 nm, and a bending radius *R* of 50 μm. The spectrum has been normalized to the transmission in a straight bus waveguide, and due to reflections between the waveguide facets, the normalized spectrum suffers from Fabry-Perot ripples. To extract the quality factor (Q) of the MRR, we fit the spectrum around 1535 nm with a Lorentzian curve as shown in Fig. 3(d), revealing a wavelength full-width at half maximum (FWHM) of 17 pm equal to a loaded Q-factor (*Q*_{load}) of ~88000. Due to a strong mode confinement of the waveguide, the MRR is under-coupled for the gap of 200 nm and the intrinsic *Q*_{int} can be calculated to ~1.1 x 10^{5} according to *Q*_{int} = 2*Q*_{load} / (1 + *T*_{0}^0.5), where *T*_{0} = 0.378 is the normalized transmission at the resonant wavelength (λ_{0} = 1535.015 nm). From the spectrum we find a free-spectral range (FSR) of 2.733 nm corresponding to a group index *n*_{g} of ~2.763, which is close to the calculated value of 2.807. We have also measured the resonance shift of an MRR with respect to a change in the temperature and a value of 53 pm/°C is extracted, reasonably falling in between that of a Si MRR (~83 pm/°C [24]) and that of a SiN MRR (~17 pm/°C [25]).

## 3. Nonlinear characterization

In order to characterize the nonlinear properties of the presented HCWs, we have carried out FWM experiments on the fabricated waveguides with the experimental setup shown in Fig. 3(a). The pump and probe signals from two continuous wave (CW) lasers are separately polarized by polarization controllers (PCs), amplified by erbium-doped fiber amplifiers (EDFAs), filtered by 1-nm band-pass filters, and combined in a 3-dB fiber coupler. After passing through a polarization beam splitter (PBS) and another PC, the two signals are injected into the HCWs by using a tapered lensed fiber. Here, the PBSs and the PCs are used to select the TE polarization for the two signals. The output light from the waveguides is collected by another tapered lensed fiber and analyzed by an optical signal analyzer (OSA). In order to monitor the input and output powers of the waveguides, two power meters are connected via two 20-dB fiber couplers positioned before and after the waveguides. During the measurements, we fix the wavelengths of the pump and the probe signals to 1550 nm and 1548.9 nm, respectively. Figure 3(b) shows the measured output FWM spectrum for an HCW width *w* = 1200 nm and a length *L* = 11.5 mm when the coupled input pump power (*P*_{pump}) is 81 mW (19.1 dBm). From Fig. 3(b), one can get an FWM conversion efficiency (CE) of −29 dB with the CE defined as the ratio of the output idler power to the output probe power.

We have also measured the CEs at different pump powers (red dots) for the fabricated HCWs, as shown in Fig. 3(c) for waveguides with widths *w* = 900 nm (top) and *w* = 1200 nm (bottom). Here, both waveguides are 11.5 mm long and the power of the input probe signal is fixed at 4.94 dBm. The linear curves (dashed red lines) with a slope of 2 are used to fit the measured data, and we can see both linear fittings match quite nicely, suggesting negligible nonlinear losses from e.g. TPA or FCA. Furthermore, the nonlinear parameter *γ* can be calculated from [26,27],

*L*

_{eff}is the effective interaction length of the pump and probe signals in the waveguide defined as

*L*

_{eff}= (1-e

^{-α}

*)/α. Here, we reasonably assume the phase matching condition being satisfied due to a small wavelength separation between the pump and the probe signals [27]. Thus, 20log(*

^{L}*γL*

_{eff}) is the interception of the linear fitting curves with the y-axis at zero and with

*L*

_{eff}= 6.23 mm for the 1200 nm-wide waveguide, we extract a nonlinear parameter

*γ*of 72 ± 5 W

^{−1}m

^{−1}. The extracted

*γ*is even larger (87 ± 3 W

^{−1}m

^{−1}) for the 900nm-wide waveguide due to the lower effective mode area and despite the larger waveguide loss (7.6 dB/cm, i.e.

*L*

_{eff}= 4.95 mm). Knowing the waveguide dimensions and the calculated nonlinear parameters, it is easy to calculate the nonlinear refractive index (

*n*

_{2}) of the waveguide materials as

*n*

_{2}= (

*γ*λ

*A*

_{eff})/(2π). Using the parameters of the waveguide with width 1200 nm, effective

*n*

_{2}of the HCW material is calculated to be 7.7 ± 0.6 x 10

^{−18}m

^{2}/W, which is reasonably falling in between that of our deposited SRN (2.1 ± 0.2 x 10

^{−18}m

^{2}/W [19]) and that of Si (2.8-14.5 x 10

^{−18}m

^{2}/W [3]).

In order to characterize the TPA coefficient (β_{TPA}) of the proposed HCW, we use a pulsed laser as the input source and the experimental setup is shown in Fig. 4(a). Here, the pulse train with a repetition rate of 10 GHz is generated by an erbium-doped glass oscillator pulse-generating laser (ERGO PGL) with the wavelength centered at 1550 nm. The Gaussian-like pulses are measured to have a full-width at half-maximum (FWHM) of 1 ps by an auto- correlator and are coupled into the waveguides after being amplified by an EDFA and filtered by a 5-nm band-pass filter. Two power meters are positioned before and after the waveguide to record the average input and output powers, respectively. Knowing the average powers and the repetition rate, one can calculate the peak powers, which in our case are 20.1 dB above the average powers. The dots in Fig. 4(b) shows the coupled output peak power from a 11.5 mm-long waveguide with width 1200 nm measured as a function of the coupled input peak power (coupling loss is 6 dB per coupling). It can be observed that, as the input power increases to above ~3W, the output light gradually saturates due to TPA and the associated FCA.

To estimate β_{TPA}, we fit the measured data with solutions to the equation [6],

*P*(z) is the peak power along the waveguide with

*P*(0) and

*P*(0.0115) being the input and output powers, respectively, and

*A*

_{eff}= 0.43 μm

^{2}for the measured waveguide. The first term on the right side in Eq. (2) represents the linear loss, which for low input powers can be extracted from the linear fit (dashed line) in Fig. 4(a) to be 5.54 dB/cm agreeing well with the obtained value from the cutback method (5.23 ± 0.28 dB/cm). The second and the third terms represent the TPA and FCA, respectively, with the relation [6],where ${\gamma}_{FCA}$ is the FCA coefficient,

*D*is the FCA cross section determined by the material, τ is the free carrier lifetime, and

*hν*is the photon energy. In the presented HCWs, the free carriers will mainly be generated in the silicon layer, so

*D*is chosen as 1.45 x 10

^{−17}cm

^{2}, similar to that for a silicon waveguide [28]. The lifetime τ can be estimated by [29],

_{bulk}is the carrier lifetime in the bulk silicon, which are several micro seconds and far larger than τ being usually at the level of nano seconds [30].

*S*

_{Si-SiO2}and

*S*

_{Si-SiN}are the interface recombination velocities between Si and SiO

_{2,}and between Si and SiN, respectively.

*S*

_{Si-SiO2}is 8000 cm/s [29,30] and

*S*

_{Si-SiN}is smaller than 10 cm/s due to the passivation of the silicon surface by the silicon nitride [31]. Thus, from Eq. (4), we can get a free carrier lifetime of ~0.78 ns, which is comparable with the measured value of ~0.8 ns for a silicon nanowire having a size of 445 nm x 220 nm [32]. Following this, β

_{TPA}is the only unknown parameter in Eq. (2) when solving the differential equation. Solid curves in Fig. 4(b) represents solutions to Eq. (2) for different β

_{TPA}and the best solution fitting the measured data is when β

_{TPA}= 0.023 cm/GW. Nonlinear Schrödinger equation (NLSE) is also solved to fit β

_{TPA}and τ by including the dispersion and the best fittings are obtained when β

_{TPA}= 0.014 cm/GW and τ = 780ps or β

_{TPA}= 0.023 cm/GW and τ = 500ps. These values agree well with the β

_{TPA}fitted by Eq. (2) and the τ from literatures. The small variations may come from the used calculated dispersion value (

*D*= −1832 ps/km/nm), which may be not exactly the same as the actual one. Thus, if a more accurate value of β

_{TPA}is needed, one can firstly measure the actual free carrier lifetime with a fast photodetector and then measure the dispersion value for solving the NLSE.

We have also carried out FWM experiments on the fabricated HCWs with the pulsed pump. The setup is similar with the one in Fig. 3(a) but now a pulse train generated by the ERGO PGL is used as the pump after being polarized by a fiber PC, amplified by an EDFA, and filtered by a 5-nm band-pass filter. The wavelength center and the repetition rate of the pulse train are kept to 1550 nm and 10 GHz, respectively, but the FWHM of the pulse is adjusted to 4.2 ps to decrease the peak power and the risk of burning waveguides during the measurements. For the probe part, the CW light will not be amplified and filtered but directly coupled by the 3-dB coupler after a fiber PC to avoid the noise produced by the spontaneous emission of the EDFA. The probe CW signal is fixed at 1557 nm and at a power of 5 dBm. When extracting the CEs as a function of the input pump power, we first integrate the measured spectra around the idler from 1538 nm to 1546 nm when the probe signal is on and off. Next, we calculate the difference of the two integrated powers to cancel off the added noise from the pump EDFA. Figure 4(c) shows the FWM CE measured and extracted as a function of the coupled input peak power *P*_{Pump} for waveguides with a length of 11.5 mm and widths of 900 nm (top) and 1200 nm (bottom). Lines (dashed) with slopes of 2 are also shown representing the case where β_{TPA} = 0 cm/GW. For similar input powers, the CEs in the pulsed pump FWM experiments are ~4 dB lower than the CEs obtained in the CW pump scheme shown in Fig. 3(c). This is caused by the phase mismatching between the pump and the probe being separated 7 nm in the pulsed pump experiments. When the *P*_{Pump} >1 W TPA and FCA start to limit the CE, nevertheless, a CE as large as −5.3 dB when *P*_{Pump} = 36.1 dBm is achieved, which could be further increased by using higher pump powers or longer waveguides.

## 4. Discussion

Table 1 lists previously reported and typical nonlinear parameters of some silicon-based and CMOS-compatible waveguide platforms along with values for our proposed Si/SRN HCW. Here, we use the nonlinear figure of merit (FOM) calculated as FOM = *n*_{2}/(λβ_{TPA}) to quantify the nonlinear efficiency and the figure of merit γ/α to quantify the nonlinear power efficiency of the waveguides. It is seen that while Si waveguides possess large nonlinear indices the nonlinear FOM is relatively small due to nonlinear losses induced by TPA and FCA. Although Hydex, Si_{3}N_{4}, and SRN waveguides can achieve a nonlinear FOM >> 1 due to the materials’ bandgaps (TPA-free) and negligible nonlinear losses, most of them have a low nonlinear power efficiency for applications e.g. without resonators. Highly enriched SRN – so-called ultra-silicon-rich nitride (USRN) – shows similar nonlinear parameters to a-Si but with a high FOM due to a vanishing TPA coefficient. However, as a-Si, the efficiency of USRN waveguides may suffer from larger material losses and stability issues due to the presence of Si-H and N-H bonds in the materials [20]. Our proposed HCW has a nonlinear FOM as large as 21.6, which is more than one order of magnitude larger than that of c-Si and has a γ/α of ~0.6, which is larger than most of the pure dielectric waveguide platforms. Moreover, the HCW platform concept can be seamlessly integrated with the SOI platform in order to e.g. realize doped regions in the Si around the waveguide to inject carriers into the HCW waveguide. In this way, one could realize modulators or sweep out the carriers generated by TPA increasing the nonlinear FOM further making the HCW concept an interesting choice for nonlinear photonics. On the other hand, the presented Si/SRN hybrid-core waveguides have more flexibilities of engineering the dispersion by tailoring the thicknesses of the Si and SRN layers e.g. a waveguide with 50nm-thick Si, 800nm-thick SRN and 1000nn width exhibiting a small dispersion of −700 ps/km/nm. However, one should note that this may give a little compromise of the nonlinearity of the waveguide.

## 5. Conclusion

We have proposed and experimentally demonstrated a novel silicon/silicon-rich nitride hybrid-core waveguide (Si/SRN HCW) for the integrated nonlinear optics. The presented HCW has a propagation loss of ~5.2 dB/cm, which can be attributed to the N-H bonds absorption in the SRN layer and the SiO_{2} cladding, the sidewall roughness and the roughness of the Si/SRN interface. Thus, the loss is expected to be decreased by annealing the SRN layer and the cladding as well at a high temperature, reducing the sidewall roughness e.g. by utilizing a soft mask instead of a metal mask as used here and polishing the top surface of the Si layer before thinning it down. The presented hybrid waveguide delivers an effective trade-off between the nonlinear figure of merit of SRN and the nonlinear power efficiency of Si by partially confining light in the Si and SRN. The two-photon absorption coefficient is measured to be only 0.023 cm/GW and the large nonlinear parameter to be ~72 W^{−1} m^{−1}, corresponding to a large nonlinear figure of merit of 21.6. Four-wave mixing experiments performed on the HCWs show a conversion efficiency of −29 dB using a continuous-wave pump power of 19.1 dBm, and a conversion efficiency of −5.3 dB using a pulsed pump with the peak power of 36.1 dBm. Furthermore, the low nonlinear loss suggests that larger conversion efficiencies and even parametric gain are possible in order to realize key nonlinear processes. The nonlinear efficiency can also be enhanced by dramatically reducing the free carrier lifetime [33] by carrier extraction or by using a ring resonator waveguide structure [34]. Together with the advantage of being seamlessly integrated with the existing SOI platform, the presented silicon/silicon-rich nitride hybrid-core waveguide concept paves an efficient and interesting way for on-chip platforms for nonlinear applications needed in e.g. future data centers.

## Funding

Det Frie Forskningsråd (Danish Council for Independent Research) (DFF-7107-00242), Villum Fonden (Villum Foundation) (VKR023112), Danish National Research Foundation through the SPOC research center of excellence (DNRF123), National Natural Science Foundation of China (61475138 and 61675177), and China Scholarship Council.

## Acknowledgments

The authors acknowledge Meicheng Fu for helping on the calculations and DTU Nanolab for the support of the fabrication facilities and Xiaoyan Wang acknowledges the support from China Scholarship Council (CSC).

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