Molecular-absorption-induced thermal bistablity in PECVD silicon nitride microring resonators

The wavelength selective linear absorption in communication C-band is investigated in CMOS-processed PECVD silicon nitride rings. In the overcoupled region, the linear absorption loss lowers the on-resonance transmission of a ring resonator and increases its overall quality factor. Both the linear absorption and ring quality factor are maximized near 1520 nm. The direct heating by phonon absorption leads to thermal optical bistable switching in PECVD silicon nitride based microring resonators. We calibrate the linear absorption rate in the microring resonator by measuring its transmission lineshape at different laser power levels, consistent with coupled mode theory calculations.


Introduction
Interplay of free carrier and thermal nonlinearities in high quality factor (Q) small mode volume (V) optical resonators gives rise to various phenomena including self-pulsation and bistable switching [1][2][3][4]. Plasma-enhanced chemical vapor deposition (PECVD) produced materials, such as silicon nitride (SiN x ) and hydrogenated amorphous silicon (a-Si:H), are promising for the CMOS-compatible platform for low loss waveguide and resonators [5]. Along with experimentally demonstrated thermal and Kerr nonlinearities in PECVD grown devices [6][7][8], few works were found on studying the linear absorption mechanism leading to the thermal nonlinearities, where the electronic transitions related absorptions are weak in the wide bandgap materials. Different from electronic transitions, molecular/phonon absorption turns the optical energy directly to atomic lattice vibration and heat, represented by wavelength selective linear loss in waveguide (with bandwidth tens of meV) and thermal bistability in resonators [9][10]. In PECVD grown SiN x waveguides, the secondary harmonics of hydrogen-bond absorb the nearinfrared (near-IR) light ~0.816 eV [11]. Near the absorption peak at 1520 nm, the thermal heating induced nonlinearity effectively shifts the cavity resonance [10] and clear bistable switching is shown in the ring with quality factor versus mode volume ratio (Q/V)=10 15 cm -3 .
The resonator induced Purcell factor is ~10 7 for light-mater interaction at resonant wavelength [12]. The close investigation of the passive absorption process in resonators is useful for developing low power all optical bistable switch [13][14][15] and chemical sensors in infrared (IR) or mid-IR range [16]. Inversely, well understanding of the molecular absorption related linear and nonlinear response in resonators would provide useful information for optimizing their active functionalities, such as parametric oscillation, Raman amplification, cascaded four-wave mixing, where minimizing the linear absorption is a fundamental step towards low power and stable operation [17][18][19][20][21][22][23][24][25].

Device fabrication
SiN x films are grown by low-frequency low-temperature (350 o C) PECVD (follow recipe No. 5 in [26]). The 80 sccm: 4000 sccm SiH 4 :N 2 ratio and the 400W RF power control the deposition rate at 22.8A/s. PECVD silicon nitride has a Si/N ratio from 0.8 to 1, a density of 2.5 to 2.8g/cm 3 , and refractive index of ~ 2.0 at 1550 nm wavelengths. The optical bandgap is estimated to be 3 to 4 eV [27]. We probe the components of silicon nitride film by the transmission Fouriertransform infrared (FTIR) methods.
With the low-temperature growth, low interlayer stress allows the SiN x deposition thickness up to 0.65 μm ( Fig. 1(a)). Deep-UV lithography defines the 1 μm waveguide and ring widths with highly repeatable geometry, followed-by an optimized dry etch with high aspect ratios. The high aspect ratio allows good extinction between TE and TM polarizations ( Fig. 1(b)). The optical properties of the waveguide, including refractive index and propagation losses can be optimized by controlling the plasma frequency, precursor gas ratio, and thermal annealing [26,28]. The characteristic absorption wavelength at 1520 nm arises from the superposition of molecular rotations and vibrations. We verified the defects states absorption by FTIR spectroscopy (Fig. 2(a) and Fig. 2(b)). The small band around 485 cm -1 is associated with Si breathing vibrations [29]. The absorption band at 863 cm -1 is due to stretching vibration of Si-N bonds [30]. The bending vibration of Si-N bonds in the alpha-modification of crystalline silicon nitride is at 910 cm -1 [31][32]. The bands located around 3356 and 1155 cm -1 correspond to stretching and bending vibrations of N-H bonds. The Si-H bonds stretching mode is at 2205 cm -1 .
Phonon modes beyond 4000cm -1 could be a mix of high order phonon modes and the defects modes in the composite [11]. We performed the post-fabrication annealing at 800-1000 o C to reduce the molecular bonds, but annealing changes the cladding/core material morphology and led to extra scattering loss.

Measurement
Continuous-wave (CW) light generated from tunable laser (AQ4321) is sent onto chip through polarization controller and lensed fiber. An automatic power control circuit built in Ando laser AQ4321 maintains the optical output stability within +/-0.01 (0.05) dB or less in 5 minutes (1 hour). With integrated spot size converter, the total fiber-chip-fiber loss is reduced to 14 dB. The output light is collected by both a slow power meter and a high-speed near-IR photoreceiver (New Focus Model 1554B, DC to 12 GHz bandwidth). The fast photoreceiver is connected to the digital phosphor oscilloscope (Tektronix TDS 7404, DC to 4 GHz bandwidth).

Linear absorption dependent quality factors in the over-coupled region
By scanning the tunable laser from 1480 nm to 1560 nm, we measured the power transmission for a range of waveguide lengths from 25 mm to 44 mm with 5 mm discrete steps. The fitted transmitted power versus waveguide length with linear model gives a propagation loss of 4.3 dB/cm at 1550 nm, and a -13.5 dB insertion loss from the two facets of waveguides. However, we observed the total loss is strongly wavelength dependent, arising largely from molecularbond absorption in the bulk nitride [11]. The propagation loss has an absorption peak at 1520 nm with 37.2 nm (20 meV) full-width half-maximum ( Fig. 2(b)). The maximum loss is 6.8dB/cm at 1520 nm and reduces to 2.3dB/cm when the wavelength is detuned 25 nm away from the absorption peak. The propagation scattering loss due to scattering is mostly wavelength independent and about 2 dB/cm.
The wavelength-dependent linear absorption ( Fig. 2(b)) is presented by the dip in waveguide transmission spectrum (black solid curve in Fig. 2(c)). The propagation loss composes of waveguide sidewall roughness scattering and material absorption in near-IR. The material absorption near 1520 nm is mostly induced by middle band defects absorption. The coupling matrix gives the linear absorption dependent on-resonance transmission [33][34] as: here t is the field transmittance between ring and waveguide. α(λ)=exp(-α L (λ)L/2) is the roundtrip field transmission of the ring cavity with circumference L (2π×40m), and intrinsic propagation coefficient α L . α L is wavelength dependent for the PECVD grown silicon nitride waveguide, and derived from our waveguide transmission measurements. We plot the onresonance transmission (T res ) as a function of the field transmittance α for the resonances (inset of Fig. 2(c)). As the round-trip transmittance (1-α()) decreases from 0.99 to 0.9, the onresonance transmittance drops from 0.75 to 0.2 in the overcoupling region (red curve in the inset of Fig. 2(c)). The on-resonance transmission is minimized at the critical coupling point, where the round-trip transmittance has the same value as ring-waveguide field transmittance (t = 0.89).
The trend is opposite as the linear absorption keeps increasing into the undercoupling region. With the wavelength-dependent linear loss, the resonator quality factor over the whole spectrum is plotted in Fig. 2(d). The increasing quality factor with higher linear propagation loss is due to the approach into critical coupling regime between the ring and the waveguide. The total Q factor (experimentally measured as  res /, where  res and  are obtained by applying Lorenzian fit to individual resonance) of a microring resonator coupled to a single waveguide can be expressed as [35][36]: where n eff =1.6 is the effective refractive index of silicon nitride waveguide. λ 0 is the resonance wavelength of the ring, t' is the field transmission coefficient between the ring and waveguide. By fitting the model to the measured data, we obtained the field transmission coefficient t' = 0.93. It is noted that the trend is inverse with t' = 1. The maximized linear absorption and ring quality factor near 1520 nm form an ideal condition for investigating the optical nonlinearity from the light matter interaction. With the wavelength dependent linear loss (black line in Fig. 2(c)), equation 2 predicts the correspondent quality factor (circles in Fig. 2(d)), which is comparable to experimental measurement (crosses in Fig. 2(d)).
We measured three rings with radii of ~20, 40

Thermal induced bistable switching
Comparing the resonances at different wavelengths, the linear loss modifies the ring-waveguide coupling coefficient. The linear loss enlarges extinction ratio in the overcoupling region. The steepened transmission spectrum shows higher the quality factor. With fixed ring-waveguide coupling coefficient, we model the nonlinear cavity transmissions with time-domain nonlinear coupled mode theory for the intracavity photon and temperature dynamics [37]: where a is the amplitude of resonance mode; ΔT is the cavity temperature shift. P in is the power carried by incident CW laser wave. κ is the coupling coefficient between waveguide and cavity, adjusted by linear absorption in waveguide. ω L -ω 0 is the detuning between the laser frequency (ω L ) and cold cavity resonance (ω 0 ). The thermal induced dispersion is ΔωT=ω 0 ΔT(dn/dT)/n.  Fig. 1(a).
The side coupling loss rate of the ring (ω 0 /Q in /2) is 72.5 GHz, and the linear absorption rate (1/ lin ) is 2.5 GHz (Fig. 3(a)). The coupling and intrinsic quality factors are 85,000 and 1,500,000 respectively. The transmission lineshape evolves from symmetric Lorentzian to unsymmetrical bistable one as the input power increases from 20 μW (Fig. 3(a)) to 156 μW ( Fig. 3(b)). Good model-experiment correspondence at different input power levels is obtained by maintaining the same parameter space (Fig. 3(c)). The power dependent transmission spectrum for TM modes near the1520nm resonance is similar to the TE modes, confirming the linear absorption related thermal nonlinearity is polarization insensitive. As the intensity built-up factor is proportional to Q 2 /V, the switching energy dramatically reduces with linear absorption (inversely proportional to α×Q 2 /V), and minimized to 1.38pJ near chemical bond absorption peak at 1520nm. For the ring resonance far away from the molecular absorption dip (1560nm), the transmission spectrums at different power levels (from 20 to 156W) have the same symmetric Lorentzian lineshape, but with slightly shifted resonance wavelength.
The tuning efficiency increases to a peak value at 80 pm/mW for the resonances at 1520 nm wavelength (for both TE and TM polarizations), and drops to 10 pm/mW near 1610 nm resonance under optimized polarization and coupling control. Fig. 3(d) plots cavity resonance shift versus the input power. The straight linear relation implies negligible contribution from higher order nonlinear absorption such as two-photon absorption and free-carrier absorption related thermal nonlinearities. Near the absorption peak, the input/output transfer function shows clear bistability when the laser detuning (δ=(λ L -λ res0 )/(Δλ/2)) is set at δ = 3.42 and 3.72 (inset of Fig. 3(d)), where λ L , λ res0 , and Δλ are laser wavelength, cold cavity resonance and cavity bandwidth respectively.
The optical absorption in near 1520 nm is dominated by absorption from the N-H bonds.
Through the model-measurement correspondence at different power levels, the linear absorption lifetime in the ring resonator is 400 ps (Fig. 3). Higher linear absorption (absorption rate) lowers the extinction ratio in linear region (dashed red line in Fig. 3(a)) and increases cavity resonance shift at nonlinear region (dashed red line in Fig. 3(b)). The transmission spectrum measurement at different power levels are shown in Fig. 3(c), with the parameter space given in Table 1. We also performed two-wavelength bistable operation to achieve the all optical bistable switch functionality, with one pump laser power changes the refractive index through thermaloptic dispersion and another probe laser to separately monitor the resonance shift [14,40]. One cw pump laser is set on mode near 1540 nm and the wavelength of another probe laser is set near resonance of another adjacent mode. The power of the probe laser is below 22W not to trigger nonlinear response. The output of the pump power is blocked by a 30 dB notch filter, and only the probe power is collected by the photodetector. We clearly observe transmission of probe laser decreases as nonlinearity shifts as the cavity resonance approaching probe laser wavelength.
The probe laser transmission is minimized at pump power level shifting the resonance onto the probe laser wavelength. The output power of the probe laser increases as the pump power keep increasing and shifting the resonance away from the probe laser wavelength (Fig. 4(a)). The plot of the probe detuning versus the pump power dropped into the resonator gives the linear relation between cavity resonance shift efficiency at 55 pm/mW at 1540 nm (inset of Fig. 4(a)), consistent with the value ins Fig. 3(d) [41]. The related thermal dynamics is measured at both positive and negative pump laser-cavity detunings in Fig 4(b). We observed the first-order exponential decay of the probe transmission, when a step-input function (to 1 mW) is entered on the cw pump laser. The exponential fit gives thermal lifetime of ~150 s for the nitride ring resonator system. The measured lifetime may be related to the heat dissipation to substrate rather than the core-cladding system (τ th,c ) given in table I (also in [42]), and is consistent with other chemical bond absorption related thermal nonlinearities [16].

Conclusions
The wavelength selective molecular absorption modifies the linear absorption of the PECVD silicon nitride ring resonators, and led to thermal bistability. The absence of free carrier dispersion could improve the stability of thermal bistable switching. Three independent models are compared to experimental data for correlating the linear loss in waveguide to microring resonator behavoir. With fixed scattering loss, higher linear loss from material absorption steepens the extinction ratio in the overcoupling region, and enhances the empirical quality factor of the resonator. The phonon absorption, coupled with enhanced Q factors, leads to pico joule level bistable switching in the wide bandgap material based microring resonator. The power dependent nonlinear transmission spectrum is numerically described by the couple mode theory.