1. Introduction

Silicon nitride (Si₃N₄) integrated planar waveguide and ring resonator structures [1] are attractive platforms for resonant nonlinear frequency conversion [2]. Moreover Si₃N₄ has been used for ultra-low loss integrated waveguides [3], particularly in the optical telecom band, where well established silicon on insulator waveguides [4, 5] suffer from two-photon and free carrier absorption. Besides low absorption, the waveguide dispersion plays a central role for parametric frequency conversion. In particular this applies to microresonator based optical frequency comb generation via the χ⁽³⁾ non-linearity (”Kerr-combs”) [6], which has recently also been demonstrated in Si₃N₄ [7]. In this scheme a set of equidistant optical frequencies is generated with a spacing corresponding to the free spectral range (FSR) of the resonator. Such integrated and CMOS-compatible microresonator frequency combs potentially offer a level of compactness and integration that is presently not attainable in mode-locked laser based combs and can moreover access GHz repetition rates [8]. Microresonator based frequency combs are promising for applications like the calibration of astronomical spectrographs [9], on chip optical interconnects [2], long range data communication [10] and optical arbitrary waveform generation [11]. Moreover recently Kerr-comb generation has recently been demonstrated in the visible [12] and the mid-infrared [13]. It is well known that the attainable spectral bandwidth of Kerr-combs is limited by the resonator dispersion, that leads to a wavelength dependent FSR of the resonator [14, 15]. The resonator dispersion is described as

2. Fabrication

The resonators and coupling waveguides are fabricated as follows. First, a bottom cladding layer of 4 μm thick silicon dioxide (SiO₂) is grown onto a 100 mm prime silicon wafer via wet oxidation. The thickness of the bottom cladding is chosen such that the compressive stress of the SiO₂ cancels out the tensile stress of the Si₃N₄. A 750 nm thick stoichiometric Si₃N₄ layer is grown with low-pressure-chemical-vapor-deposition (LPCVD) from dichlorsilane (SiH₂CL₂, 30 sccm) and ammonia (NH₃, 180 sccm). The Si₃N₄ growth rate is 2.75 nm/min at a temperature of 775°. To avoid excessive stress buildup and successive cracking of the Si₃N₄ film, the deposition is carried out in two equal deposition steps with intermediate cooldown to room temperature [22]. The dielectrics are etched from the backside of the wafer via reactive-ion-etching (RIE) to avoid buildup of static charges during the following electron beam lithography step. After electron beam lithography (using positive ZEP520A resist), the waveguide and resonator patterns are transferred into the waveguide core layer via RIE in SF₆ and CH₄ chemistry. The etch parameters have been carefully optimized to achieve low roughness while maintaining verticality and selectivity. The sidewall angle is approximately 78°. The ZEP520A is then stripped in an oxygen Plasma. Large remaining Si₃N₄ patches, which can lead to cracking during subsequent thermal annealing, are removed utilizing photolithography and an additional RIE step. After cleaning using Piranha etch the waveguides and resonators are thermally annealed for 3 hours in a nitrogen atmosphere at a temperature of 1200 °C to eliminate residual hydrogen from the Si₃N₄ structures and to reduce optical absorption in the near-infrared [1]. HfO₂ with a thickness of 55 nm is grown on top of the waveguides and resonators by atomic layer deposition (ALD) from tetrakis(ethylmethylamino)hafnium (TEMAH) and water (c.f. Fig. 1) at 200 °C. The low deposition temperature in ALD is beneficial due to the reduced thermal stress on the thick Si₃N₄ structures. Finally, 3 μm thick low-temperature silicon dioxide (SiO₂) is deposited on top on the structures. The critically coupled optical quality factors Q of the resonators are up to 1 million with HfO₂ clad resonators having slightly smaller quality factors (up to Q ≈ 6 · 10⁵) due to the formation of small irregularities on the surface (c.f. Fig. 1) during deposition. These are expected to vanish with further optimized ALD parameters and wafer preparation. The circumference of the chips is defined via an additional photolithography step and all dielectrics are etched with a single RIE step. To facilitate cleaving of the wafer and clear space to approach the coupling facet with tapered-lensed fibers for input and output coupling of light, a 130 μm deep anisotropic silicon RIE etch is performed. To reduce losses from fiber-to-chip coupling the bus waveguides are tapered [23] to a width of 150 nm and terminated 6 μm away from the etched coupling facet.

 

Fig. 1 Scanning electron micrograph of the cross-section of a HfO₂ (green) coated Si₃N₄ (yellow) resonator before the SiO₂ top cladding deposition. The Si₃N₄ core has a base width of 1700 nm and a height of 750 nm. The HfO₂ coating thickness is 55 nm. The detachment of the HfO₂ film on the lower right side of the resonator was caused by the cleaving process. Inset: Optical micrograph of a 50 μm radius ring resonator and coupling waveguide.

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3. Experiment

The resonator dispersion is characterized employing frequency-comb-assisted-diode-laser spectroscopy [19] (c.f. Fig. 2a). Here, a mode-hop-free external cavity diode laser (ECDL) is scanned between 1545 nm and 1615 nm. The spectrum of the resonator in transmission is recorded while a beat note with a self-referenced, stabilized fiber-laser frequency comb (Menlo Systems GmbH) with repetition rate of 250 MHz is generated. The beat signal is split and bandpass filtered at 30 MHz and 75 MHz to create two sets of accurate frequency calibration markers. All traces are recorded on a fast oscilloscope in peak detection mode with 10 million sampling points. To extend the span of the measurement the frequency comb is amplified in a dispersion compensated erbium-doped-fiber amplifier (Menlo Systems GmbH) and broadened in SMF-28. The intensity of the scanning laser is actively stabilized using a Mach-Zehnder interferometric intensity modulator. The measurement span is limited by the mode-hop free scanning range of the ECDL and the signal-to-noise ratio of the beat note generation.

 

Fig. 2 (a) Setup for frequency-comb-assisted-diode-laser spectroscopy; FPC, fiber polarization controller; MZI, Mach-Zehnder intensity modulator; BP, bandpass; DC-EDFA, dispersion compensated erbium-doped-fiber-amplifier. (b) Calibrated transmission spectrum of a 55 nm ALD-coated ring resonator with radius 301 μm and input polarization aligned to the TM11 mode. (c) Wavelength dependence of the free-spectral-range (FSR) over the measurement span of 8.7 THz, corresponding to 120 subsequent FSRs, based on 16 consecutive scans (symbols) in alternating direction. The red line is a linear fit from which both FSR D₁/2π of 75.04 GHz and dispersion D₂/2π of 350 kHz are determined.

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The resonance positions are fitted with symmetric double Lorentzian functions to account for modal coupling of counter-propagating modes [24]. The cross-section of the ring resonators are designed to feature anomalous dispersion at 1.55 μm and support both fundamental TE(TM)11 and first higher order TE(TM)21 modes. While in larger resonators (e.g. 301 micron radius) the excitation of higher transverse order modes is suppressed by the phase matching condition, these modes can be excited in smaller resonator geometries. Different mode families are identified via their FSR (c.f. Figs. 3a and 3b). These different FSR lead to periodic crossings of mode families [19] and to the formation of hybrid modes due to modal coupling [25]. These effects are observable as spectral variation of the resonance depth (c.f. Fig. 2b). Data points strongly affected by modal coupling to higher order modes are discarded before the dispersion D₂ is extracted from a linear fit of the measured FSR over the full spectral span (c.f. Fig. 2c) [19]. Another systematic error arises from wavelength dependent waveguide transmission due to interference of higher order and fundamental waveguide modes and asymmetric resonance line shapes [26]. Each dispersion measurement corresponds to 16 scans in alternating scan direction to cancel thermal shifts of resonance positions [27] and reduce the statistical error from calibration and double-Lorentzian fitting. Multiple measurement points in Fig. 3 and Fig. 4 correspond to different resonators with different coupling waveguide separation.

 

Fig. 3 (a) Simulations (lines) and measurements (symbols) of FSR D₁/2π and dispersion D₂/2π as function of wavelength of TE11 (a,c) and TM11 (b,d) modes for different HfO₂ ALD coating thickness applied to 301 μm Si₃N₄ ring resonators with base width of 1700 nm and Si₃N₄ height of 750 nm. (e) Dispersion D₁/2π at 1.55 μm as function of HFO₂ coating thickness and Si₃N₄ thickness for TE11 mode. The black solid line marks the transition from normal to anomalous dispersion. (f) Same as (e) for TM11 mode.

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Fig. 4 Simulated resonator dispersion D₂/2π at 1.55 μm for the TE11(a) and TM11(b) mode as function of ring radius and ring base width for Si₃N₄ ring resonators without HfO₂ coating and Si₃N₄ height of 750 nm. The black solid line marks the transition from normal to anomalous dispersion. (c) Comparison of dispersion simulations (lines) and measurements (symbols) for TE11 and TM11 mode for 24 μm, 37 μm and 50 μm ring resonators with a base width of 1700 nm at wavelength 1.58 μm. Dashed lines show the resonator dispersion D₂ if constant β₂ is assumed (c.f. Eq. (2)). Deviations from simulations and measurements are due to additional normal dispersion introduced by the finite radius of the ring resonators. (d,e,f) Same as (a,b,c) but with 55 nm HfO₂ coating.

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4. Simulations and discussion

We simulate the dispersion of integrated Si₃N₄ based ring resonators with a fully-vectorial axially-symmetric finite-element model [28] employing a commercial FEM solver (COMSOL Multiphysics). The model includes the angled sidewalls as well as the shape of the conformal coating on top of the waveguide edges (c.f. Fig. 1). The material dispersion is determined via spectral ellipsometry and included iteratively (similar to Ref. [19]) into the simulations. The resonator dispersion D₂ directly follows from the calculated mode resonance frequencies. The results of the simulations for varied HfO₂ coating thickness are shown in Fig. 3 and we find that both the magnitude and bandwidth of anomalous dispersion can be significantly increased. While the low wavelength zero-dispersion point (ZDP) is only weakly but quadratically shifted (TE11: 0.0021 nm/nm², TM11: 0.0067 nm/nm²), the long wavelength ZDP strongly linearly shifts towards mid-infrared wavelength for increased HfO₂ thickness (TE11: 26 nm/10 nm, TM11: 27 nm/10 nm). The simulations are compared to measurements of 301 μm ring resonators shown in Fig. 2c. We measure an increase of anomalous dispersion D₂/2π at 1.58 μm from 340 kHz to 490 kHz for the TE11 mode for a coating thickness of 55 nm. The TM11 mode, i.e. the mode with the major electric field component out of the resonator plane, is more strongly affected by the coating. We measure that ring resonators without HfO₂ coating have normal dispersion (−180 kHz) while similar resonators coated with 55 nm HfO₂ feature anomalous dispersion (350 kHz). Figures 3e and 3f show simulations of the 301 μm ring resonator dispersion D₂/2π at 1.55 μm as function of both HfO₂ coating thickness and Si₃N₄ core thickness. To decouple the HfO₂ coating thickness on the sidewalls and the base width of the resonator in Figs. 3e and 3f, the base width of the resonators is chosen such that the total base width after coating is 1700 nm. The interpretation of the increase of anomalous dispersion upon coating is as follows: For thin HfO₂ coatings, with only a few percent of the optical power contained in the HfO₂ coating, the increase of anomalous dispersion and anomalous dispersion bandwidth is mainly due to the increased waveguide cross section [29] of the now composite Si₃N₄/HfO₂ resonator core. Comparable results could thus also be achieved utilizing thicker Si₃N₄ layers, which however are very difficult to fabricate due to the high intrinsic stress of Si₃N₄. For thick HfO₂ coatings the material dispersion of HfO₂, which has a zero dispersion point around 1.8 μm, more strongly influences the ring resonator dispersion especially towards mid-infrared wavelengths. Also, from both the quadratic dependence of the low wavelength ZDP as well as Fig. 3e, it is apparent that the formation of a HfO₂ slab waveguide on the wafer introduces additional normal dispersion especially towards shorter wavelengths. Note that increased anomalous dispersion for a Si₃N₄ ring resonator of fixed thickness could also be achieved through partial or full removal of the SiO₂ top cladding, which however would sacrifice full encapsulation of the device. Coating with HfO₂ facilitates large and broadband anomalous dispersion without aforementioned drawbacks.

For a constant group-velocity-dispersion β₂ it is expected that the total dispersion scales as D₂/2π ∝ 1/R² (c.f. Eq. (2)). Thus, the ring radius not only determines the FSR D₁/2π of the resonator but is also crucial for obtaining large values of resonator dispersion D₂/2π. For whispering-gallery-mode resonators it has been observed that smaller wavelengths travel closer to the outer rim of the resonator and additional normal dispersion is introduced even for large radii and negligible bending loss [19]. Figure 4 presents measurements and simulations, which show that this effect also applies for ring resonators with strong radial confinement, such as integrated waveguide rings, and its alteration for resonators coated with HfO₂. Similar effects have been numerically studied for bent silicon waveguides [30]. In Figs. 4a and 4b, simulations of the dispersion D₂/2π as function of waveguide width and ring radius are presented.

We find a maximum of anomalous dispersion as function of ring radius, due to the interaction of the ∝ 1/R² scaling and the additional normal dispersion, and ring base width. The decrease toward small base width is due to decreased anomalous waveguide dispersion [18]. The decrease toward large base width is due to the transformation of the waveguide like resonator mode to a disc like resonator mode. We observe that coating with HfO₂ leads to a strongly increased dispersion which is shifted towards narrower ring base widths and smaller ring radii. The shift towards smaller radii is due to the increased confinement and supplements the increased anomalous dispersion (c.f. Eq. (2)). The shift towards smaller base width is due to the 110 nm HfO₂ on the waveguide sidewalls (TE11) as well as due to the increased confinement (TM11). The predictions of the numerical simulations are confirmed by measurements on ring resonators with a Si₃N₄ base width of 1700 nm and ring radii of 24 μm, 37 μm and 50 μm (c.f. Figs. 4c and 4f).

5. Conclusion

In summary, we have demonstrated both numerically and experimentally that dispersion of Si₃N₄ based waveguides can be engineered to be more anomalous through conformal coating with HfO₂ which is in particular favorable for applications such as low phase noise Kerr-comb generation. To facilitate measurements, we have extended the measurement span of frequency comb assisted diode laser spectroscopy to more than 8 THz maintaining MHz resolution and accuracy to resolve the dispersion of integrated ring resonators (values as small as x100 below the cavity decay rate can be measured). Using this unique method of directly measuring the dispersion of traveling wave microresonators with large FSR we have been able to demonstrate that the total Si₃N₄-ring resonator dispersion for small ring radii is always normal. Our results also show how HfO₂ coating can be used to extend the difficult fabrication of thick Si₃N₄ based waveguide devices effectively reducing the necessary thickness of high stress, low loss stochiometric Si₃N₄ layers. The low process temperature of ALD and the high conformity should make ALD a versatile tool in microresonator fabrication and also be compatible to a variety of materials. This includes materials with high intrinsic stress such as Si₃N₄ and with low softening or melting points such as chalcogenide glasses or even polymers. The large transparency window of HfO₂ is especially promising for applications in the mid-infrared wavelength region.