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Abstract
We develop a stress-released stoichiometric silicon nitride (Si3N4) fabrication process for dispersion-engineered integrated silicon photonics. To relax the high tensile stress of a thick Si3N4 film grown by low-pressure chemical vapor deposition (LPCVD) process, we grow the film in two steps and introduce a conventional dense stress-release pattern onto a ∼400nm-thick Si3N4 film in between the two steps. Our pattern helps minimize crack formation by releasing the stress of the film along high-symmetry periodic modulation directions and helps stop cracks from propagating. We demonstrate a nearly crack-free ∼830nm-thick Si3N4 film on a 4” silicon wafer. Our Si3N4 photonic platform enables dispersion-engineered, waveguide-coupled microring and microdisk resonators, with cavity sizes of up to a millimeter. Specifically, our 115µm-radius microring exhibits an intrinsic quality (Q)-factor of ∼2.0×106 for the TM00 mode and our 575µm-radius microdisk demonstrates an intrinsic Q of ∼4.0×106 for TM modes in 1550nm wavelengths.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Silicon nitride (SiN) offers an attractive material platform for integrated nonlinear [1–4] and quantum light sources [5–7] on a silicon chip. Compared to silicon, SiN exhibits a lower intrinsic linear and nonlinear two-photon absorption losses in the telecommunications window (1.3 µm ∼ 1.6 µm) due to the wider bandgap of ∼5 eV. To reduce the undesirable extrinsic absorption from N-H bonds (at ∼1520 nm) due to the presence of H in the forming gases, low-pressure chemical vapor deposition (LPCVD) of stoichiometric SiN (i.e., Si3N4) at a high temperature (∼780 °C) can effectively reduce the formation of N-H bonds. Besides, Si3N4 features a moderate Kerr nonlinearity with nonlinear refractive index, n2, of ∼ 2.5×10−15 cm2W-1 [8], which is an order of magnitude smaller than that of Si while an order of magnitude larger than that of silica. Leveraging the mature silicon complementary metal-oxide-semiconductor (CMOS) fabrication process, researchers have demonstrated ultra-low-loss Si3N4 waveguides [9], ultra-high-quality (Q) microresonators [10–12] and ultra-low-threshold microring optical parametric oscillators (OPOs) [10] among other devices.
For a phase-matched nonlinear frequency conversion in the Si3N4 platform, it is well-known that one can engineer the dispersion of Si3N4 waveguides and microring resonators to be slightly anomalous [13] to compensate for the Kerr phase shift introduced by the pump. Previous work shows that a highly confined Si3N4 waveguide requires a thickness of exceeding 700 nm to attain an anomalous dispersion in the 1550nm wavelengths [14]. Whereas our previous modeling results suggest that Si3N4 whispering-gallery-mode (WGM) microdisks (with a 300nm-thick silica upper-cladding layer) require a Si3N4 thickness of ∼800 nm to attain an anomalous dispersion for transverse magnetic (TM)-polarized WGMs [15,16].
However, thick LPCVD Si3N4 films exhibit a large tensile stress (due to the shrinkage of the film after the high-temperature growth). This limits the film thickness to <400 nm typically before cracks are formed. To release the film stress, researchers demonstrated a temperature-cycling method to alleviate the film shrinkage, along with using manually scribed trenches in the rim region of the wafer to stop cracks initiated due to wafer handling from propagating inward [17]. Further, researchers developed a twist-and-grow process to deposit thick Si3N4 films through rotating the wafer by 45° in between two steps of the film deposition to re-distribute the uniaxial strain [18].
Recently, the photonic Damascene process utilizing additive fabrication processes has demonstrated a thick Si3N4 film of 1.5 µm by introducing a dense stress-release pattern [19]. An integral step of the process is the chemical mechanical polishing (CMP), which however could exhibit a non-uniformity in the removal rate of the film across the wafer [20]. This could compromise the fabrication of large-area devices such as mm-sized microdisk resonators. Only waveguide-based structures have been demonstrated on such a platform.
In this paper, we report a subtractive fabrication method for depositing a thick stress-released Si3N4 film using a conventional dense stress-release pattern. We demonstrate an 830nm-thick Si3N4 film nearly without cracks forming in the photolithography writing region on a 4” wafer. Our waveguide-coupled microresonators reveal intrinsic quality-factor (Q0) values of ∼2×106 for 115µm-radius microrings and of ∼4×106 for mm-sized microdisks in TM polarization.
2. Device fabrication
2.1. Si3N4 film deposition with a dense stress-release pattern
Figure 1(a) illustrates our conventional checkerboard-like stress-release pattern design. It comprises a periodic array of ∼5µm-size squares, with unit cells of two squares positioned in the 45° direction. Alternate rows (columns) are spaced edge-to-edge by ∼9 µm. Adjacent rows (columns) are shifted edge-to-edge by ∼7 µm. This gives a critical spacing of ∼2.8 µm between two square corners in a unit cell. The pattern has four mirror-reflection symmetry axes (in the x-, y-, 45° and 135° directions) and is four-rotation symmetric.
Fig. 1. (a) Schematic illustration of the checkerboard-like stress-release pattern. The dashed lines indicate the symmetry axes for the pattern. (b) Schematic cross-sectional view of a film deposited on a patterned (oxide-coated) Si wafer with surface modulations slightly exceeding the film thickness. (c) Schematics of the devices surrounded by the stress-release pattern. (d) Schematic layout on a 4” wafer. The black dashed-line window indicates the stepper writing region. The red solid-line window indicates the effective (usable) device region. The gray solid-lines indicate the manually scribed trenches. (e) Schematic illustration of the effects of the manually scribed trenches, which can stop most of the cracks from propagating into the device region but can also initiate cracks.
Such a pattern with a high degree of spatial symmetry and a moderately high modulation frequency can release the stress reasonably uniformly and effectively [21]. A periodic recession can periodically interrupt the stressed film and thus can release the stress in the modulation direction. A two-dimensional periodic recession modulating with a high degree of spatial symmetry and a high spatial frequency can release the stress of the film uniformly in all in-plane directions. We ensure the recession etched depth is slightly exceeding the film thickness to fully release the stress across the film thickness (Fig. 1(b)).
The high spatial frequency also helps minimize the recovery of the driving force for the cracks [22]. One needs to decrease the driving force of a crack down to the crack resistance. Abruptly changing steps or recessions can perturb the driving force of the crack. While multiple periodic abruptly changing steps (such as those in a checkerboard-like pattern) can avoid the crack from recovering its driving force in an overstressed film. The design of the relative shifts between adjacent rows (columns) helps intercept cracks that propagate in between alternate rows and columns.
The checkerboard-like pattern can be readily stacked and densely packed such that the pattern can surround each device and the overall stress-release area can be scaled, as illustrated in Fig. 1(c). The pattern is at least ∼30 µm away from the devices. The pattern needs to be aligning to and subtracting the future patterned devices. We also include five etched parallel trenches with a width of 5 µm at the boundary of a die to partially release the stress in the modulation direction and one etched trench between devices to partition each device. The pattern fills all the blank areas on the wafer in the photolithography writing region (75 mm × 75 mm) surrounding the devices, as illustrated in Fig. 1(d).
In addition, we use manually scribed trenches in the rim region of the wafer (∼1 cm from the wafer edge) following [17]. Such trenches can stop most of the cracks initiated from the wafer edge from propagating into the device region but can also initiate cracks due to the unintentional stress from the trenches, as illustrated in Fig. 1(e).
2.2. Fabrication process
Figures 2(a)-(g) schematically illustrate the fabrication process. The fabrication starts with a 4” silicon wafer covered with a 4.5µm thermal oxide as an under-cladding layer. We deposit by LPCVD a layer of Si3N4, with a thickness of <400 nm (Fig. 2(a)). Such a thickness is within a typical tolerance of LPCVD Si3N4 films on a wafer without forming cracks under our furnace conditions. We then apply the checkerboard-like dense stress-release pattern surrounding the device regions using i-line (365 nm) photolithography. The etch depth is ∼1.2 µm, exceeding the targeted total Si3N4 film thickness of ∼830 nm (Fig. 2(b)), so that the pattern interrupts abruptly and periodically the film to be deposited on top to release the stress. We further manually define trenches in the rim region of the wafer (∼1 cm from the wafer edge) following [17]. We then deposit a second layer of Si3N4 film to achieve the targeted thickness (Fig. 2(c)).
Fig. 2. (a)-(g) Fabrication process flow for fabricating Si3N4 devices on a stress-released 4” silicon wafer.
We measure the film thickness by an ellipsometer. The measured refractive index for the Si3N4 film is ∼1.98 at 1550 nm, suggesting the film is stoichiometric.
We deposit a ∼700nm-thick low-temperature oxide (LTO) as an etching hard mask (Fig. 2(d)). The LTO also serves to prevent delamination of the Si3N4 film. We remark that we can store the LTO-covered Si3N4 film for months without delamination or crack extension.
We pattern waveguide-coupled microrings and mm-size microdisks using the same photolithography. The coupling gap spacing between the bus-waveguide and the microresonator is limited by the photolithography to ∼400 nm. We etch the hard mask by reactive-ion etching using C4F8/H2/He-based etchants. We transfer the pattern to the Si3N4 film using C4F8/SF6-based etchants (Fig. 2(e)). We remove the residual hard mask by buffered oxide etchant (BOE).
We note that the root-mean-square (RMS) value of the surface roughness of the Si3N4 film after deposition is ∼227 pm while after the BOE etch is ∼339 pm. This reveals that the BOE etch is slightly over-etched and has roughen the Si3N4 surface. If the etch time is well-controlled to only removing the hard mask (allowing a tolerance of over-etch of within 5%), it is possible to minimize the etching to the Si3N4 surface. The over-etch, however, does not seem to significantly affect the optical modes in the devices for our ridge waveguide design.
We address wafer bowing by removing the backside Si3N4 film (Fig. 2(f)), and we observe no significant bowing afterwards. To our observations, our method of releasing the film stress does not significantly impact the bowing.
To remove any remaining H-bonds in the Si3N4 film, we perform a high-temperature annealing at 1150 °C under a N2 ambient for 4 hours. Finally, we clad the device with a ∼300nm-thick LTO, followed by another annealing at 1100 °C under a N2 ambient for 2.5 hours (Fig. 2(g)).
To enable smooth bus-waveguide facets for fiber end-coupling (with a tapered width of 4 µm), we dry-etch the facets and open dicing trenches through the under-cladding using C4F8/H2/He-based etchants, followed by etching the silicon substrate using deep reactive-ion etching, with a total etch depth of ∼150 µm.
Figure 3(a) shows a 900nm-thick Si3N4-film-coated 4” test wafer with the stress-release pattern and the manually defined trenches. The dashed-line window defines the effective device region with an area of 4725 mm2. We exclude from the photolithography writing region the four corner dies (4 × 15 mm × 15 mm), where we do not apply scribed trenches at the far corners and thus they tend to be particularly subjected to cracks formed from the wafer rim region due to wafer handling. Although the scribed trenches can stop most of the cracks initiated from the wafer edge, some cracks penetrate into the effective device region. There are also cracks initiated due to the stress from the trenches. When the cracks encounter the stress-release pattern, they typically can be stopped after interacting with several square elements. Within the effective device region, we observe no cracks initiated from within the region. This indicates that the pattern can release the stress effectively and minimize the recovery of the driving force of the crack.
Fig. 3. (a) Picture of a 4” test wafer with a 900nm-thick Si3N4 film. The red dashed-line window indicates a unit die. The white dashed-line window indicates the effective (usable) device region with an area of 4725 mm2. Manual trenches are scribed outside the region. (b), (c) Optical micrographs of the waveguide-coupled (b) 115µm-radius microring and (c) 575µm-radius microdisk surrounded by the stress-release pattern from an 830nm-thick Si3N4-film-coated wafer. (d) SEM image of a waveguide-coupled microdisk in the coupling region after Si3N4 patterning.
Figures 3(b), (c) show the optical micrographs of our fabricated waveguide-coupled (b) 115µm-radius microring and (c) 575µm-radius microdisk resonators surrounded by the stress-release pattern. The coupling waveguide has a width of ∼1.2 µm, which supports multiple modes in 1550nm wavelengths. For the microring, the waveguide width has a designed width of 2 µm.
Figure 3(d) shows a scanning electron micrograph (SEM) of the waveguide-to-microdisk coupling region before the LTO cladding (after process step (e)). We attribute the relatively rough sidewalls to the un-optimized photolithography and etching processes. We note that there are unintended residues introduced during the Si3N4 etching, which are outside the waveguide sidewalls and do not significantly overlap with the waveguide modes. We attribute the unintended residues to two possible mechanisms. First, the residues can be due to the residue photoresist attaching to the sidewalls after the photolithography. We plan to add a descum step after the photolithography. Second, the residues can be due to the re-deposition of polymers inside the etcher chamber. As we adopt SF6/C4F8 as the etchant with a gas flow of 30:85, the large flow rate of C4F8 may introduce polymers to the surface. To cope with this, we will fine tune the etching gas composition.
Figures 4(a), (b) show the 2.5-dimensional (2.5-D) finite-element-method (FEM) simulated mode amplitude distributions in ∼1550 nm wavelengths for (a) the fundamental TM (TM00) mode in an 115µm-radius microring and (b) the TM1,4214 WGM, with the fundamental radial order and the azimuthal order of 4214 in a 575µm-radius microdisk.
Fig. 4. (a), (b) 2.5-D FEM simulations for (a) the TM00 mode in a 115µm-radius microring and (b) the first-radial-order TM-polarized WGM in a 575µm-radius microdisk.
2.3. Stress-release pattern study
We measure the stress of the wafer on two test wafers with and without the checkerboard-like stress-release pattern. We deposit 300nm-thick Si3N4 films on two 4” silicon wafers coated with the same 3µm-thick thermal oxide in the same process run. We apply the stress-release pattern by transferring the pattern onto the oxide layer of one of the two wafers. We only deposit the Si3N4 films up to 300nm thick on both the wafers to ensure that there is no crack formation in order to properly measure the stress of the wafers. We measure the wafer bowing of the wafers twice using the film-stress measurement system SMSi 3800, namely after the Si3N4 film deposition and after the backside Si3N4 film is removed. We then calculate the overall stress of the film through the well-known Stoney equation [23,24]. The measured stress of the film without the pattern is 1125 ± 215 MPa while the measured stress of the film with the pattern is 944 ± 103 MPa. Thus, our experiments reveal that the pattern releases the overall stress of the wafer by ∼16%.
We gather statistics on two test wafers with Si3N4 film thicknesses of 900 nm and 980 nm. We apply the manually scribed trenches along with the stress-release pattern on the 900nm-thick Si3N4-film-coated wafer (shown in Fig. 3(a)) while the 980nm-thick Si3N4-film-coated wafer only has the stress-release pattern. We observe that even without the manually scribed trenches the checkerboard-like pattern can effectively stop the cracks. We do not transfer the device patterns onto these two wafers. We analyze the penetration depths of the cracks through the checkerboard-like pattern. We define the penetration depth in terms of the number of rows/columns of squares for stopping a crack. Figure 5(a) shows the histogram of the penetration depths on the 900nm-thick Si3N4-film-coated wafer. From an arbitrarily chosen majority of 62 cracks initiated in the wafer rim region (due to handling the wafer), we observe an average penetration depth of 1.8 rows/columns of squares with a standard deviation of 1.0. Figures 5(b), (c) show two optical micrographs of the cracks being stopped after 1 and 4 rows/columns of squares.
Fig. 5. (a) Histogram of the number of rows/columns of squares for stopping a crack on a 900nm-thick Si3N4 film. (b), (c) Optical micrographs of the cracks being stopped. The numbers 1 and 4 denote the numbers of rows/columns of squares before the cracks are stopped. (d) Histogram of the number of rows/columns of squares for stopping a crack on a 980nm-thick Si3N4 film. (e), (f) Optical micrographs of the cracks being stopped. The numbers 2 and 5 denote the numbers of rows/columns of squares before the cracks are stopped.
While on the 980nm-thick Si3N4-film-coated wafer, we study an arbitrarily chosen majority of 75 cracks, with an average penetration depth of 2.0 rows/columns of squares and a standard deviation of 1.1, as shown in Fig. 5(d). Figures 5(e), (f) show two optical micrographs of the cracks being stopped after 2 and 5 rows/columns of squares. Our experiments thus reveal that the cracks penetrated the stepper writing region can be effectively terminated within five rows/columns of squares of the checkerboard-like pattern. All the cracks are successfully terminated before reaching the device areas in the effective device region with an area of ∼4725 mm2.
We also observe that most of the cracks can penetrate through the five parallel etched trenches, as shown in Figs. 5(b), (c) and (f). The cracks are redirected to the modulation direction (perpendicular to the line extension direction) but not terminated, as a result of releasing the stress in only the modulation direction.
3. Transmission spectra characterization and analysis
3.1. Device characterization
We measure the transmission and OPO spectra from our fabricated microresonators. Figure 6(a) schematically illustrates the experimental setup. We scan the wavelength-tunable continuous-wave laser wavelength in 1550nm wavelengths in a constant rate (∼20 nm/s). The relatively high wavelength-scanning rate is adopted to minimize influences from low-frequency laser instabilities. The laser light is 50/50 split into two arms, with one for device characterization and the other for simultaneous wavelength calibration. For device characterization, we amplify the laser light using an erbium-doped fiber amplifier (EDFA) followed by a variable optical attenuator (VOA), and launch the light into the chip using a singlemode polarization-maintaining lensed fiber. We collect the output-coupled light using a long-working-distance objective lens with a numerical aperture (N.A.) of 0.55, followed by a polarization analyzer fixed at either transverse electric (TE) or TM polarization. The light is then split into two arms, with one measured by a high-speed photodiode and displayed by a real-time oscilloscope for measuring transmission spectra in the time domain, and the other measured by an optical spectrum analyzer (OSA) for measuring OPO spectra.
Fig. 6. (a) Experimental setup for transmission and OPO measurements. PC: polarization controller, PD: photodiode, VOA: variable optical attenuator, BS: beam splitter, PBS: polarizing beam splitter, OSA: optical spectrum analyzer, LWD: long-working distance, SG: signal generator, PM: phase modulator, M: mirror. (b) Calibration for the FSR of the MZI using a phase modulator.
For wavelength calibration, we use a free-space asymmetric Mach-Zehnder interferometer (MZI) with a path-length difference of ∼7 m as a frequency-ruler [25]. This enables a relative frequency calibration with a frequency resolution down to the tens of MHz level, which is reasonable for extracting the resonance linewidth (∼hundreds of MHz in our case) and the dispersion. We measure the MZI transmission by another high-speed photodiode and display the spectrum by the same real-time oscilloscope.
To calibrate the free spectral range (FSR) of the MZI (and thus the frequency resolution), we phase-modulate the laser light to generate frequency sidebands. This generates two satellite resonance dips symmetrically spaced with a well-defined frequency shift from the microresonator resonance. Figure 6(b) shows as an example of the simultaneously measured transmission spectra for a microdisk and the MZI. The laser light is phase-modulated at a frequency of 600.00 MHz. The two satellite resonance dips are symmetrically spaced by 1200.00 MHz. We calibrate the FSR of the MZI to be 42.36 ± 0.37 MHz by averaging the measurements over a total of 67 resonances across the transmission spectrum and from two microdisks.
Figure 7(a) shows the measured normalized transmission spectra from a 115µm-radius microring in TE and TM polarizations. The spectra are normalized to the fiber-to-lens transmission spectra without the chip. The insertion loss for both TM and TE modes are ∼10 dB, dominated by the bus-waveguide input/output-coupling losses. We attribute the modulations in the TE transmission spectrum to the multimode interference between the two waveguide transverse modes in the bus waveguide. For each polarization, we observe waveguide modes with two transverse orders (TE00, TE10; TM00, TM10). Through the FEM simulation as shown in Fig. 4(a), we obtain the resonance frequencies for all the supported modes. The FEM-calculated FSRs for different modes are: ∼199.6 GHz for the TE00 modes, ∼191.2 GHz for the TE10 modes, ∼196.3 GHz for the TM00 modes and ∼189.9 GHz for the TM10 modes. We identify the orders in the transmission spectra by comparing the observed FSRs with the FEM-simulated FSRs.
Fig. 7. (a) Measured transmission spectra from a 115µm-radius microring in TE and TM polarizations. i, ii: Resonance lineshapes with curve fitting considering i. backward scattering (κ0/2π = 83 MHz, κe/2π = 82 MHz, κbs/2π = 302 + i16 MHz) and ii. Fano interference (κ0/2π = 137 MHz, κe/2π = 43 MHz). (b), (c) Extracted Q factors from the spectra for the (b) TE00 and (c) TM00 modes.
3.2. Resonance lineshape analysis
To better characterize the resonance lineshapes for measuring the Q factors and the wavelength-dependence of the cavity FSR in the presence of dispersion, we analyze the transmission cavity resonances based on the coupled-mode theory (CMT) in the time domain. Our modeling accounts for (i) the backward scattering caused by the cavity sidewall roughness [26] and (ii) the coherent interference between the cavity resonance and the background transverse modes in the coupling waveguide. The backward scattering induces a weak cross-coupling from the forward to backward propagating modes, and vice versa, leading to a mode splitting that results in an asymmetric resonance doublet (Fig. 7(a)i). Whereas the coherent interference results in asymmetric Fano resonances (Fig. 7(a)ii). We express the coupled-mode equations as [26–28]:
By solving the coupled-mode equations (1) in steady state, we obtain the power transmission as:
Figures 7(a)i and 7(a)ii show examples of two particular resonance lineshapes fitted with Eq. (2). We adopt an under-coupling condition ($\kappa_{e}<\kappa_{0}$) for the resonance fits, motivated by the relatively wide coupling gap spacing and the phase mismatch between the straight bus-waveguide and the microring. Inset (i) features a curve-fitted resonance doublet accounting for only the backward-scattering cross-coupling (A = 1). The mode splitting of ∼300 MHz is essentially given by $\kappa_{bs,re}$. We note that in the case that $\kappa_{bs}$ is real ($\kappa_{bs,im}$ = 0), critical coupling occurs with $\kappa_{e}^{2}=\kappa_{0}^{2}+\kappa_{b s}^{2}$ [26]. Inset (ii) features a curve-fitted asymmetric Fano resonance lineshape accounting for only the coherent background interference ($\kappa_{bs}$=0).
We note that the mode splitting exhibits asymmetric linewidths and extinction ratios. The coupling between the forward and backward propagating modes results in two standing waves that exhibit two different spatial distributions. Thus, they could encounter slightly different losses as their local field maxima and minima overlap with different surface roughness features and non-uniformities.
We extract from the resonance fits the loaded Q-factor, QL = ω0/κ, the intrinsic Q-factor, $Q_{e}=\omega_{0} / \kappa_{e}$, and the external coupling Q-factor, Qe = ω0/κe. Figures 7(b), (c) show the extracted Q-factors for the (b) TE00 and (c) TM00 modes spanning across 1500 nm ∼ 1620 nm. We observe overall increasing trends for the QL and Q0 values, and an overall decreasing trend for the Qe values with wavelength for both the TE00 and TM00 modes. We attribute the intrinsic loss to the waveguide sidewall scattering loss (which decreases with wavelength) and the residual material absorption loss. We observe no significant loss near the ∼1520nm N-H resonance. The overall decreasing trend for the Qe values with wavelength is consistent with an increasing mode spatial overlap across the coupling gap. We attribute the apparent overall larger Qe values for the TE00 modes than for the TM00 modes to complications from the stronger coherent background interference in the TE modes (as shown in Fig. 7(a)).
We attribute the dips displayed in the QL and Q0 values (and the peaks displayed in the Qe values) to accidental degeneracies, and thus mode couplings between different transverse modes (TE00 and TE10, TM00 and TM10) or different polarization modes, as they are not completely orthogonal in the ridge waveguides. Different microring azimuthal-order modes in different transverse modes or polarizations can degenerate accidentally and overlap spatially. We do not account for such mode couplings explicitly in the CMT analysis (Eq. (1)). Their effects are displayed as local rises in the κ and κ0 values as an internal loss. As $\kappa_{e}=\kappa-\kappa_{0}$, the extracted Qe has local peaks.
We obtain the spectral-averaged QL and Q0 values over the entire measured wavelength range for both the TE00 and TM00 modes. The TE00 modes reveal a spectral-averaged QL value of ∼1.2×106, which corresponds to a spectral-averaged κ of ∼160 MHz and a spectral-averaged cavity finesse (FSR/κ) of ∼1200. We extract a spectral-averaged Q0 value of ∼1.6×106, with a standard deviation of ∼4×105 (including the accidentally coupled resonances, as they are not easy to be decoupled in this case). While the TM00 mode reveal a spectral-averaged QL value of ∼1.1×106, corresponding to a spectral-averaged κ of ∼180 MHz and a cavity finesse of ∼1100. We extract a spectral-averaged Q0 value of ∼2.0×106, with a standard deviation of ∼3×105 (after subtracting the accidentally coupled resonances).
We measure the microring transmission spectra with the same device design (radius: 115 µm, width: 2 µm, height: 830 nm) distributed on five arbitrarily selected dies on the wafer. We extract the spectral-averaged Q0 values for the TM00 modes from 1545 nm to 1570 nm. For one particular die that experiences stronger mode couplings in this wavelength range, we exclude those resonances for a fair comparison. Figure 8 shows the spectral-averaged Q0 values distribution over the five dies (denoted by the corresponding row (R) and column (C) of the wafer). The spectral-averaged Q0 values vary from ∼1.48×106 to ∼1.88×106. We remark that the variation for the extracted TM00 mode dispersion parameter (D2) values from three of the dies is within 1 MHz (see section 3.3).
Fig. 8. Extracted Q0 distribution from five waveguide-coupled 115µm-radius microrings of the same design from five different dies on the same wafer (R: Row, C: Column).
3.3. Dispersion analysis
We extract the cavity dispersion from the change in FSR over wavelengths. We Taylor-expand the resonance frequency, $\omega_{\mu}$, with respect to the relative azimuthal mode order, µ, at the probe/pump frequency, $\omega_{\mu}$ = ω0 [13]:
Figure 9(a) shows the measured FSR values for the TE00 and TM00 modes as a function of µ over ∼70 FSRs, considering the probe/pump wavelength of ∼1565 nm. We apply quadratic fits to extract the D2/2π values of 6.7 MHz for the TE00 modes and of 10.2 MHz for the TM00 modes, which correspond to $\beta_{2}$ of -178 ps2/km and of -270 ps2/km, respectively. The TE00 and TM00 modes are in the anomalous dispersion regime.
Fig. 9. (a) Extracted FSR values as a function of relative mode number given pumping at ∼1565 nm (µ = 0). (b) Measured OPO spectrum from a 115µm-radius microring when pumping at the TM00 mode with a QL of ∼9.3×105 upon a power of ∼17 dBm in the waveguide.
We observe at least two abrupt changes in the FSR values for the TM00 modes around µ = 0 and µ = 27, which we attribute to mode couplings between different transverse modes. We can observe the coupling between the TM00 and TM10 modes at µ = 0 in the transmission spectrum shown in Fig. 7(a), as denoted by the red dashed lines. We remark that such mode couplings can give rise to an anomalous dispersion within a narrow spectral band even in the case that the resonator is operating in the normal dispersion regime, and thus can initiate OPO [30].
The parametric gain for OPO occurs at where the anomalous dispersion compensates for the pump-induced phase modulation (satisfying the phase-matching condition) by [31]: $2 \gamma P_{p}, \gamma=n_{2} \omega / c A_{e f f}$ 0, where γ = n2ω/cAeff is the third-order nonlinear parameter, Aeff is the effective mode area, c is the speed of light in free space, Pp is the pump power, $\Delta \beta=\left(\beta_{p}-\beta_{s}\right)-\left(\beta_{i}-\beta_{p}\right)$ is the wavenumber ($n_{e f f}(\omega) \omega / c$) mismatch between the pump ($\beta_{p}$), the signal ($\beta_{s}$) and the idler ($\beta_{i}$), and neff is the effective refractive index. Energy conservation gives $\omega_{s}-\omega_{p}=\omega_{p}-\omega_{i}=\Delta \omega$, where we adopt arbitrarily $\omega_{s}>\omega_{p}>\omega_{i}$. The wavenumber mismatch is given by $\Delta \beta \approx \beta_{2} \Delta \omega^{2}$.
We pump at the high-Q mode at ∼1565 nm with tens of milliwatt power to generate OPO. Figure 9(b) shows the measured OPO spectrum when pumping at the TM00 mode of a 115µm-radius microring, with a QL value of ∼9.3×105 upon a power of ∼17 dBm in the coupling waveguide. We observe OPO sidebands generated at 15 FSRs (∼23.6 nm) away from the pump resonance wavelength. We remark that the OPO threshold power is slightly lower than 17 dBm.
Following the aforementioned theoretical analysis, with Aeff ≈ 1.16 µm2 (according to the FEM simulation result, as shown in Fig. 4(a)) and β2 of -270 ps2/km, we estimate $\Delta \omega \cdot(\lambda / \omega)$ is ∼23 nm, where λ is the wavelength in free space, which is consistent with our experimental results.
3.4. Microdisk characterization
Figure 10(a) shows the measured TM-polarized normalized transmission spectrum from a 575µm-radius microdisk. The 1.2µm-wide coupling waveguide mainly couples to two radial-order WGMs, labeled as M1 and M2. The coupling waveguide wraps along the microdisk circumference by an arc angle of 10° to lengthen the interaction length. Only for wavelengths >1548 nm we observe resonances with an extinction ratio significantly exceeding the background interference modulations and noise fluctuations.
Fig. 10. (a) Measured TM-polarized transmission spectrum from a 575µm-radius disk resonator supporting two distinct radial-order WGMs labeled as M1 and M2. (b) Extracted Q factors for M1 mode. (c) FSR values for M1 mode as a function of relative mode number with a pumping wavelength of ∼1565 nm (µ = 0).
We remark that it is quite difficult to keep track of one particular WGM over wavelengths in such a mm-sized microdisk for two reasons. Firstly, mode couplings occur frequently at accidentally degenerated azimuthal orders of different radial-order modes, and thus resulting in mode splitting or destructive interferences. Secondly, we observe two sets of radial-order modes and their mode interferences in some wavelength regions as our coupling waveguide propagates two transverse-order modes. It turns out that it is more difficult to keep track of M2 mode than M1 mode, though they exhibit similar Q values.
We successfully keep track of M1 mode from ∼1548.3 nm to 1619.3 nm, spanning a total of 212 azimuthal orders, and we study a total of 175 resonances. Figure 10(b) shows the extracted QL,0,e distributions for M1 mode. The Q0 increases moderately with wavelength, which we attribute to the combined effects of a reduced sidewall scattering loss yet a reduced optical confinement. We obtain a spectral-averaged Q0 value of ∼4.0×106, with a standard deviation of ∼6.7×105. The Qe decreases with wavelength as expected from an increased modal spatial overlap, with overall larger Qe values than those in microring modes (Fig. 7(c)), possibly due to a weak coupling (a larger phase mismatch) between the coupling waveguide and the WGM. The mm-sized microdisk exhibits a finesse of ∼800.
Figure 10(c) shows the measured FSR distribution for M1 mode as a function of $\mu$. We extract from the quadratic fit the dispersion parameter D2/2π of ∼0.6 MHz, indicating the mode is in the anomalous dispersion regime (an order of magnitude less than that of the TM00 modes in the microring, as shown in Fig. 9(a)).
We do not observe OPO from the 575µm-radius microdisk under a pump power of ∼23 dBm inside the waveguide. However, we do observe OPO from a smaller-size microdisk with a radius of 345 µm [33]. Figure 11 shows the OPO spectrum from a 345µm-radius microdisk by pumping at ∼ 1565.83 nm with under 50 mW in the waveguide. We reason that with a larger cavity size, the cavity finesse is smaller given the two microdisks exhibit similar Q-factors.
Fig. 11. Measured OPO spectrum from a 345µm-radius microdisk resonator upon a pumping power of ∼17 dBm in the waveguide in TM polarization.
4. Summary and discussion
In conclusion, we develop a subtractive fabrication process for stress-released Si3N4-based integrated photonic devices, with a demonstrated film thickness of ∼830 nm by introducing a conventional dense stress-release pattern in between two Si3N4-film depositions. Our process enables the fabrication of dispersion-engineered integrated photonic devices, featuring high-Q (∼106) microring and mm-size disk resonators. We demonstrated OPO in the microring, with the generated sidebands at frequencies consistent with the dispersion analysis. We also observed OPO in a microdisk. Our fabrication method is compatible with the conventional CMOS fabrication process without requiring CMP.
Table 1 compares the performance among different fabrication processes. Our method can realize 4”-wafer-scale thick Si3N4 film fabrication with a large effective device area. We define the effective device region (crack-free region) by the photolithography writing region (75 mm × 75 mm) excluding the four corner dies (4 × 15 mm × 15 mm). We are able to consistently attain crack-free areas of ∼4725 mm2 on three 4” wafers using the checkerboard-like stress-release pattern for both releasing the stress and stopping the cracks, with LPCVD Si3N4 film thicknesses of 830 nm, 900 nm and 980 nm. In our existing layout the largest waveguide-coupled resonator circuit is a 1.84mm-diameter microdisk side-coupled with a bus waveguide of ∼4mm long. Compared with the method in [18], our method allows us to deposit an overstressed Si3N4 film where the crack may have already been initiated. We believe that our method could also make the film more robust against unintentional stress due to wafer handling. Currently our demonstrated cavity intrinsic Q values are still lower than the state-of-the-art, which we attribute mainly to the relatively rough waveguide/microdisk sidewalls due to un-optimized Si3N4 patterning and etching.
Table 1. Comparison among fabrication processes
We summarize our design principle of the dense stress-release pattern as follows: First, a two-dimensional periodic modulation with a high degree of spatial symmetry, a (moderately) high spatial modulation frequency and a recession slightly deeper than the film thickness can be effective in releasing the stress of the film uniformly and stopping the cracks effectively. Second, it is also essential to adopt a pattern that is suitable for densely packing to fill up blank areas of a wafer and to surround device regions effectively.
We believe that our method of using subtractive fabrication processes and a conventional stress-release pattern design is potentially scalable to larger-size wafers. This assumes that the cracks formation is due to the film strain reaching the breaking threshold, which primarily depends on the film thickness and the substrate thickness and does not directly depend on the wafer size. We also assume a scalable (stackable) stress-release pattern like our demonstrated checkerboard-like stress-release pattern (and other specially designed two-dimensional stress-release patterns with a similar high degree of spatial symmetry of periodic modulations [21]). Further studies are needed.
Funding
Research Grants Council, University Grants Committee (16202615, 16203317).
Acknowledgments
We thank the Nanosystem Fabrication Facility (NFF) of the HKUST for device fabrication and helpful discussions. We thank Ms. Qianni Zhang and Mr. Sam Lai for fruitful discussions.
Disclosures
The authors declare no conflicts of interest.
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