Microring Resonator Dispersion Metrology with Neural Networks

Technical Summary: Microring Resonator Dispersion Metrology with Neural Networks

Problem Statement
Precise knowledge of resonator dispersion, arising from both geometric dimensions and material properties, is critical for high-performance nonlinear integrated photonics, such as optical parametric oscillators and frequency combs. While direct fabrication-level measurements (e.g., cross-section imaging or ellipsometry) offer limited insight, complete optical characterization for precise dispersion metrology is time-consuming and ill-suited for mass-scale foundry production. Existing non-destructive methods often fail to capture geometric dispersion contributions, and destructive analysis is impractical for wafer-scale process monitoring. There is a need for a rapid, non-destructive method to link measurable optical dispersion signatures to underlying device geometry and material parameters.

Methodology
The authors propose a machine learning (ML) framework utilizing three distinct neural network architectures trained on numerically generated datasets. The datasets simulate a silicon nitride (Si$_3$N$_4$) microring resonator with a fixed outer radius (23 $\mu$m) and varying ring heights (620–720 nm) and widths (750–950 nm). Material dispersion is modeled using Sellmeier-type equations with four distinct parameter sets (SM1–SM4) representing different ammonia-to-silane gas ratios during deposition.

The framework addresses three complementary problems:

1. Inverse Regression (Geometry Prediction): A deep neural network (20 hidden layers) predicts ring width and height from integrated dispersion ($D_{int}$) spectra.
2. Inverse Classification (Material Identification): A classification network identifies the specific Sellmeier model (gas ratio) used in the material based on $D_{int}$ data.
3. Forward Prediction (Dispersion Synthesis): A regression network predicts the coefficients of a sixth-order polynomial to reconstruct the full $D_{int}$ spectrum directly from ring dimensions, bypassing the need for repeated numerical simulations.

The study rigorously evaluates model robustness by introducing controlled noise ($\pm$50 MHz and $\pm$200 MHz) to simulate realistic measurement uncertainties and analyzes the impact of spectral downsampling (varying the number of $D_{int}$ data points used).

Key Results

• Geometry Prediction Accuracy: In noiseless conditions, the regression model achieves sub-nanometer accuracy (< 1 nm) for both width and height. Under realistic noise ($\pm$50 MHz), accuracy remains high with errors < 8 nm using approximately 45 dispersion samples. At higher noise levels ($\pm$200 MHz), errors increase to approximately 16 nm. The model demonstrates that height prediction is generally more robust than width prediction due to the higher sensitivity of $D_{int}$ to height variations.
• Material Classification: The classification network achieves > 99% accuracy in identifying the correct Sellmeier model across all noise conditions. This task proves significantly more robust to noise than dimension regression, as different gas ratios produce distinctively shaped $D_{int}$ profiles.
• Sampling Efficiency: The study finds that dispersion samples taken far from the pump frequency (where spectral curvature is higher) are most informative. While 45 samples are sufficient for high-precision systems, even reduced sampling (e.g., 6 samples) yields reasonable results for low-noise scenarios, though accuracy degrades with high gas ratios where $D_{int}$ curves flatten.
• Forward Prediction: The forward network successfully reconstructs dispersion spectra from geometric inputs with high fidelity, providing a rapid alternative to eigenmode solvers for design assessment.
• Noise Resilience: The models exhibit high resilience to frequency jitter and stochastic perturbations, functioning effectively as nonlinear filters that prioritize global spectral curvature over localized fluctuations.

Significance and Claims
The paper claims to establish a bidirectional machine learning framework that links measurable optical responses ($D_{int}$) to underlying fabrication parameters (geometry and material). The authors posit that this approach offers a rapid, non-destructive tool for wafer-scale quality control and process monitoring in photonic foundries. By demonstrating that a limited set of judiciously chosen resonance frequencies can enable accurate dimension prediction even with realistic measurement noise, the work suggests a pathway to overcoming the bottlenecks of current characterization methods. The ability to perform both inverse (characterization) and forward (design prediction) tasks within this framework highlights the potential of ML to accelerate the development and deployment of advanced photonic systems without requiring destructive testing or exhaustive optical sweeps.