Microring Resonator Dispersion Metrology with Neural Networks

TL;DR

The paper tackles non-destructive, wafer-scale dispersion metrology for microring resonators by leveraging three neural-network models trained on numerically generated $D_{ m int}(bc)$ datasets: (i) inverse prediction of ring geometry from dispersion, (ii) classification of the Si$_3$N$_4$ Sellmeier dispersion model, and (iii) forward reconstruction of the $D_{ m int}$ spectrum from ring dimensions via a compact polynomial representation. It demonstrates sub-nanometer width/height predictions in noiseless data and robust performance under realistic noise (50–200 MHz), with around 45 dispersion samples sufficing for <8 nm width accuracy, and classification accuracy exceeding 99%. The forward model shows high-fidelity spectrum reconstruction from dimensions, enabling rapid dispersion-engineering and design-stage verification. These findings support rapid, non-destructive quality control and process monitoring in photonic foundries, bridging measurable optical responses to fabrication parameters and enabling scalable dispersion metrology.

Abstract

Precise knowledge of resonator dispersion, from both geometric and material contributions, is essential for reliable high-performance nonlinear integrated photonics devices, such as optical parametric oscillators, frequency doublers, and integrated optical frequency combs. However, direct measurements at the fabrication level provide limited knowledge, whether through destructive cross-section imaging or non-destructive ellipsometry, while complete optical characterization that enables precise dispersion metrology is time-consuming and poorly suited for mass-scale foundry fabrication. In this work, we develop a machine learning framework to solve three complementary problems: (i) predicting resonator geometric dimensions, (ii) identifying the correct material dispersion, and last, but not least, (iii) precisely reconstructing the integrated dispersion spectrum directly from ring dimensions. These three neural networks together enable both inverse and forward characterization of microring resonators. Using numerically generated datasets based on Sellmeier-type material models, we demonstrate <1 nm ring dimension prediction accuracy without noise, <8 nm prediction accuracy with ~45 dispersion samples under a realistic frequency measurement noise level (50 MHz), and ~16 nm prediction accuracy at a higher noise level (200 MHz). The Sellmeier model classification exceeds 99% accuracy in all cases. Importantly, dispersion sampled far from the pump resonances proves most informative, reducing full-spectrum characterization requirements. The forward-prediction network reconstructs dispersion spectra from the ring dimensions with high accuracy. Our results highlight the potential of machine learning applied to dispersion data as a rapid, non-destructive tool for wafer-scale quality control and process monitoring in photonic foundries.

Figures (11)

• Figure 1: (a) Dissipative Kerr soliton (DKS) microcombs convert a single frequency laser to a frequency comb, often in Si$_3$N$_4$ microring resonators. The properties of the frequency comb depend on the dispersion of the microring resonator, quantified by the integrated dispersion $D_\text{int}$, which describes the deviation of the microring mode frequencies from a uniformly spaced grid. $D_\text{int}$ depends on (b) the resonator geometry, and in particular, the ring width ($RW$) and ring height ($RH$) and (c) the refractive index dispersion of the constituent materials. For Si$_3$N$_4$, its dispersion will be impacted by different gas precursor ratios in the growth process (labeled SM1 to SM4 here, and described in further detail later). (d) Example simulated $D_\text{int}$ curves for different geometric and material parameters. (e) Here, we use neural networks to understand how well we can extract geometric and material parameters given $D_\text{int}$ data. We further consider how well this extraction works in the presence of noise on the $D_\text{int}$ data associated with measurement uncertainty, and what level and types of downsampling of $D_\text{int}$ data can still lead to good parameter extraction.
• Figure 2: Integrated dispersion curves ($D_{\rm{int}}/2\pi$) as a function of mode index for Si$_3$N$_4$ films grown with the four precursor gas ratios outlined in Table \ref{['tab:si3n4_disp']}: (a) 3:1, (b) 5:1, (c) 7:1, and (d) 15:1. Each sub-panel contains 441 distinct $D_{\rm{int}}/2\pi$ curves that span a thickness variation between 620 nm and 720 nm (10 nm step size) and ring width variation between 750 nm and 950 nm (10 nm step size).
• Figure 3: Schematic diagrams of the three neural network architectures used in this study: (a) Regression model for predicting the ring width and height from the integrated dispersion ($D_\text{int}(\mu)$). (b) Classification model for identifying the Sellmeier model from dispersion data. (c) Another regression model for predicting the coefficients of a $6^{\rm{th}}$ order polynomial fitting the integrated dispersions from the ring widths and heights. To emphasize that we regress on the polynomial coefficients, not on the integrated dispersion directly, we use an asterisk.
• Figure 4: Performance of the regression neural network trained and tested on datasets generated using the Sellmeier model 1. (a) and (b) Predicted versus true values for ring width and ring height, respectively. (c) Error distribution in the actual width–height plane. We calculate the overall error with the formula $\sqrt{(w_a-w_p)^2+(h_a-h_p)^2}$, where $w$ and $h$ represent width and height, and subscripts $a$ and $p$ refer to actual and predicted values.
• Figure 5: Histograms of the absolute prediction errors for (a) height and (b) width, respectively, for the regression neural network studied in Fig. \ref{['fig:NN3_SM1']}. In 49 out of 50 test cases, the errors remain below 1 nm.