Foundry-enabled wafer-scale characterization and modeling of silicon photonic DWDM links

3.1 Wafer-scale optical parameter extraction

First, we investigate the optical properties and geometric parameters of silicon waveguides. We use a large sweep of asymmetric, or imbalanced, Mazh–Zehnder interferometers (AMZIs) with varying waveguide width and arm length imbalance (Figure 3e) across two wafers fabricated by AIM Photonics in dedicated full-reticle wafer runs. The MZIs are grating-coupled with de-embedding structures to subtract the loss envelope of the grating couplers, as shown in a representative test structure in Figure 3f. Because a large sweep of waveguide widths is used, Euler bends are employed to maintain single-mode operation within multimode waveguides; interference fringes from higher order modes could interfere with the optical parameter extraction. The transmission spectrum of each AMZI across the wafer is measured with an optical sweep using a broadband tunable laser covering the S-, C-, and L-bands. A peak-finding algorithm is used to extract the wavelength locations of each interference fringe. From here, we utilize an ordinary least squares (OLS) regression to derive fitting parameters for the group index of the AMZI following the procedure outlined in ref. [48]. Because the fringe order of the interferometer must be known to find the effective index, we must use a method to infer it. The smaller the length imbalance of the AMZI, the larger the accuracy of the inferred fringe order. A mode solver simulation sweep across waveguide width and wavelength was performed to allow us to compare the extracted group index to that of the simulated group index. By minimizing the error between these, we can find the waveguide width that corresponds to the extracted group index. The effective index at this waveguide width can then be used to infer the fringe order of the measured device, ensuring a more accurate effective index extraction.

Figure 3:

Wafer-scale characterization of waveguide effective and group index. (a) Wafermap of effective index at wavelength of 1,550 nm across wafer 1. (b) Wafermap of effective index at wavelength of 1,550 nm across wafer 2. (c) Wafermap of group index at wavelength of 1,550 nm across wafer 1. (d) Wafermap of group index at wavelength of 1,550 nm across wafer 2. (e) Micrograph of chip containing asymmetric Mach-Zehnder interferometers (AMZIs) with varying width and length imbalances. (f) Micrograph of representative grating-coupled AMZI test structure.

AMZIs were measured on two wafers. We plot the wafermaps of the effective index and group index for each of the two wafers at the single mode waveguide width of 480 nm. The effective index is shown in Figure 3a and b for the first and second wafer, respectively, and the group index is shown in Figure 3c and d for the first and second wafer, respectively. It is clear that there is a radial relationship shown in each of the four wafermaps. To demonstrate this statistically, we mapped the locations of the reticles to polar coordinates in reference to the center of the wafer and performed an OLS regression. The correlations for radial relationships for effective index were 0.507 and 0.623 for each wafer, respectively, and for group index, 0.527 and 0.502, respectively. As suggested by the slanted bullseye appearance of the wafermaps, there also exists a planar relationship. Again, we performed an OLS regression, this time using Cartesian coordinates and projecting across the wafer at varying angles. This way, we understand not only the strength of the planar relationship, but also the angle at which the plane is situated. The correlations and angles for planar relationships for effective index were 0.351 (264.15 deg) and 0.174 (245.18 deg) for each wafer, respectively, and for group index, 0.355 (259.72 deg) and 0.291 (258.72 deg), respectively. These trends could be explained by temperature variations in the process.

The resulting extracted wafer-scale optical parameters are displayed in Figure 4. The effective and group indices averaged over the 64 reticles across each wafer are shown in Figure 4a and b, respectively. The effective and group indices are calculated across waveguide widths supporting only a single mode up to those supporting many higher order modes. As expected, both parameters head toward an asymptote at highly multimode waveguide widths, as their behavior starts to exhibit that of a slab mode. The high consistency between wafers is noteworthy for each parameter. Additionally, the standard deviation for both the effective index and group index is displayed in Figure 4c and d, respectively. There is a clear trend that larger waveguide widths experience drastically reduced statistical variation in both effective index and group index. This is explained by the mode being less perturbed proportionally by etching biases due to the much larger width. Further, the mode of larger waveguides is more confined and is less affected by changes in sidewall. There is relatively low variation between the two measured wafers, despite the two wafers being from different lots. We expect wafer-to-wafer variations to be lower within the same lot compared to variability between wafers from different lots.

Figure 4:

Effective and group index statistics across waveguide width. (a) Effective index averaged across each wafer at different waveguide widths at wavelength of 1,550 nm. (b) Group index averaged across each wafer at different waveguide widths at wavelength of 1,550 nm. (c) Standard deviation of effective index averaged across each wafer at different waveguide widths. (d) Standard deviation of group index averaged across each wafer at different waveguide widths.

We measured microdisk modulators and filters on our latest 300 mm wafer taped out with AIM Photonics. The transmission spectrum of a representative microdisk modulator is shown in Figure 5a, the wafermap displaying the resonance locations across the wafer is shown in Figure 5b, and a histogram of the distribution is displayed in Figure 5c. Similarly, the transmission spectrum, wafermap, and histogram for the microdisk filter are shown in Figure 5d–f, respectively. The variation of the modulator is slightly higher than that of the filter (standard deviation of 0.65 nm vs. 0.6 nm) due to the modulator junction width being slightly smaller to reduce series resistance and factoring in variations of the doped junction in the modulator. However, both demonstrate high robustness to variations compared especially to microring resonators. Microrings of a similar radius demonstrated standard deviations on the order of multiple nanometers, further solidifying these as robust devices.

Figure 5:

Wafer-scale microresonator characterization. (a) Transmission spectrum of a microdisk modulator. (b) Wafermap of microdisk modulator resonance location across the wafer. (c) Histogram and statistical data of microdisk modulator. (d) Transmission spectrum of a microdisk filter. (e) Wafermap of microdisk filter resonance location across the wafer. (f) Histogram and statistical data of microdisk filter.

3.2 Implications for link energy consumption

With a suite of devices now measured and analyzed at the wafer-scale, we can use these results to calculate power consumption to inform component and link design (Table 1). The variation of effective index, extracted from the AMZI test structures, can be converted mathematically to waveguide phase error. This phase error due to fabrication variations must be compensated for by thermal tuning of the device. In our scalable link architecture, the devices that are sensitive to these waveguide phase errors are the interleavers. Therefore, we can calculate the required thermal tuning per thermo-optic phase shifter within the interleaver. Accounting for 3σ variation allows us to cover about 99.7 % of all devices, statistically speaking. From the effective index standard deviation of 480 nm wide waveguides, we calculate a 3σ phase error of 7.887 radians. Assuming a tuning efficiency of 25 mW P _π , on average 31.38 mW would be required. However, as we noted previously, moving to a larger waveguide width reduces the variation of optical parameters significantly. Therefore, using wider waveguides in the interleavers enables higher robustness to fabrication variations and an associated reduced energy consumption. Using the same tuning efficiency, 1,200 nm wide waveguides would exhibit a 3σ phase error of 2.154 radians, leading to an average tuning power of 8.57 mW. This is a significant reduction. Moreover, the 3σ phase error being less than π enables easier alignment to channels. Moving on to the microdisks, using the numbers reported in Figure 5 and the device FSR [49], we have 3σ phase errors of 0.451 and 0.416 radians for the microdisk modulators and filters, respectively. This leads to an associated average tuning power of 5.91 and 2.46 mW, respectively. The filter exhibits a larger tuning efficiency due to no RF contact vias and closer placement to the optical mode. Using a thermal undercut of the substrate significantly improved the thermal tuning efficiency of devices [50]. If we apply those improvement factors here to these already robust components, then the average tuning power required would now be 1.34 mW, 0.37 mW, 1.18 mW, and 0.49 mW for the 480 nm waveguide phase shifter, 1,200 nm waveguide phase shifter, microdisk modulator, and microdisk filter, respectively. The resulting power consumption that each component contributes to the link is calculated and displayed in Table 1. Clearly, utilizing robust component designs and strategies to improve tuning efficiency, such as thermal undercut, are imperative to reducing the power consumption of links due to thermal tuning requirements.

3.3 Wafer-scale link parameter extraction

First, we look at one of the primary contributors to the link loss budget – the power penalties associated with modulation. Important to understanding the power penalties associated with the resonant modulator, shown in Figure 6a, is the depletion response of the device (Figure 6b). The insertion loss (IL) and extinction ratio (ER) vary depending on the driving voltage of the modulator and carrier detuning from the resonant wavelength. As shown in Figure 6c, the IL, ER, and associated power penalties can be calculated based on the detuning of the carrier from the resonant wavelength. The total power penalty is given by the following equation:

where

and r is the linear extinction ratio. As the extinction ratio increases and approaches infinity, the power penalty associated with the ER approaches zero, while the power penalty associated with on–off keying approaches 3 dB (equal distribution of ‘1’s and ‘0’s), for 3 dB total. There are diminishing returns of power penalty after achieving an ER of at least 10 dB. A large depletion response is necessary for a small insertion loss while maintaining a low driving voltage. In addition, the optical modulation amplitude (OMA) is shown to be maximal at the minimum of the total power penalty; the OMA normalized to the input power is defined as

where P ₁ is the ‘on’ state optical power, P ₀ is the ‘off’ state optical power, and P _in is the input optical power. With the ability to calculate these power penalties from the depletion response, we measured the depletion response of disk modulators across a wafer. The calculated total power penalty, including OOK and ER penalties and IL, is shown in the wafermap in Figure 6d. With a driving voltage of only 1 V, the mean total power penalty is 7.78 dB, with a standard deviation of 0.41 dB. Since the resonant modulators are critically coupled, fabrication variations can cause a moderate change in the extinction ratio, resulting in the larger standard deviation. However, moving toward resonant modulators that are slightly over-coupled will help to reduce this standard deviation, as the extinction ratio of over-coupled modulators are less sensitive to fabrication variations.

Figure 6:

Microdisk modulator power penalties. (a) Micrograph of a microdisk modulator. (b) Depletion response of microdisk modulator demonstrating changing spectrum with varied applied reverse bias to the junction. (c) Power penalties, insertion loss, and optical modulation amplitude of modulator as function of detuning wavelength. (d) Wafermap of total power penalty of modulators in each reticle.

Coupling between fiber and chip has traditionally also been a challenge in terms of contending with excess losses [51], [52], [53]. Although grating couplers are available, we use edge couplers for both higher coupling efficiency and larger optical bandwidth, important for broadband DWDM links. A representative edge coupler is shown in Figure 7a. The substrate below the silicon nitride edge coupler is partially removed and backfilled with silicon dioxide. This dramatically improves the mode matching between the cleaved SMF28 mode and that of the silicon nitride waveguide, thereby dramatically improving the possible coupling efficiency. Low-loss and broadband escalators enable coupling between silicon nitride and silicon device layers. Using a periscope fiber array, we obtained wafer-scale per-facet coupling losses by measuring a loopback structure in each of the 64 reticles. The loss per coupler is shown in Figure 7b, with a mean coupling efficiency of 0.924 dB and standard deviation of only 0.036 dB. These sub-dB edge couplers demonstrate high robustness to variations in both fabrication and positioning of the fiber array (similar process to that used when attaching the fiber array), critical to realizing ultra-broadband links.

Figure 7:

Wafer-scale insertion loss of edge couplers and microdisk filters. (a) Micrograph of an edge coupler with substrate removed underneath. (b) Wafermap of per-facet coupling losses between edge couplers and cleaved SMF28. (c) Micrograph of a microdisk filter. (d) Wafermap of insertion loss seen at the drop port of add-drop microdisk filters.

On the receiver side, wavelength-selective resonant filters must be used to filter out and drop each encoded carrier. Assuming a large enough filter bandwidth (or alternatively, lower quality factor) is used to avoid attenuating parts of the signal, the main parameter of interest is the insertion loss seen at the drop port of the device. If critical coupling is not achieved, the insertion loss can become quite high, straining the link loss budget. We utilize microdisk filters for their robustness to fabrication variations (Figure 7c). Another advantage is that the cavity loss is small, owing to the supported whispering gallery mode. This allows a simple symmetric coupling scheme to produce low insertion loss add-drop filters; a wafermap of the insertion loss seen at the drop port of microdisk filters is shown in Figure 7d. The mean and standard deviation insertion loss is 0.225 dB and 0.047 dB, respectively. Introducing a slight asymmetry to the coupling can reduce this loss even further.

3.4 Implications for link optical power budget

The various insertion losses and power penalties of each component within the link measured from test structures are tallied in Table 2. Statistical information is included where mass-measurement was possible, however all values are based on measured data. To better understand the system-level implications of component-level variability in integrated photonic links, we perform a Monte Carlo simulation using the available statistical data obtained from wafer-scale measurements. While one-off measurements provide estimates of link loss, they do not capture the full distributional behavior of the link budget. A Monte Carlo approach enables us to propagate measured variations, including insertion losses, coupling efficiencies, and modulation power penalties, through the full link architecture. This allows for a more accurate estimation of performance metrics such as link yield for a given power budget and worst-case design margins (e.g., 3σ link loss). Using the available wafer-scale measurements, 200,000 Monte Carlo simulations were performed on the link budget (Figure 8). The resulting mean link loss was 18.407 dB, and the corresponding standard deviation was 0.418 dB. Given a receiver sensitivity for error-free operation at 16 Gbps per channel [49], incorporating the 3σ link loss into our tabulated link budget as the margin allows us to describe the expected behavior of 99.7 % of links (Table 2). By statistically sampling from the known distributions of each component, we gain insights into opportunities for targeted yield improvement through component-level optimization.

Figure 8:

Monte Carlo simulations (n = 200,000) showing total link loss incorporating statistical variations of components from wafer-scale measurements. Mean and standard deviation link losses were 18.407 dB and 0.418 dB, respectively.