Integrating physics-based simulations, machine learning, and Bayesian inference for accurate detection and metrology of elongated nanoscale analytes using high-frequency capacitance spectroscopy

Elongated analytes are simple general-purpose model systems for nucleic acid strands, bacteriophages, nanoplastic fibers, nanotubes, nanorods, etc., and are characterized by numerous unknowns (e.g., material composition, length, orientation, etc.) that are difficult to measure accurately in real-time. This paper aims to advance the state-of-the-art of nanoscale sensing and metrology for these elongated, high aspect-ratio analytes, utilizing advanced data analysis methods specially developed for high-frequency capacitance spectroscopy measurements at nanoelectrode arrays. A model-based approach is proposed, integrating: (1) advanced supervised learning algorithms trained on an extensively augmented dataset derived from accurate physics-based numerical simulations; (2) a Markov Chain Monte Carlo (MCMC) Bayesian estimation framework for the parameters extraction task. The proposed algorithm achieves substantial speed enhancements while maintaining high accuracy, even at the resolution limits of the sensor. The test case is developed for multispectral capacitance images of 200-1000 nanometers long nanorods captured with an advanced 256 × 256 pixels nanocapacitor array. The proposed approach minimizes the need for time-consuming, physics-based simulations in sensor behavior prediction and Bayesian inference iterations. It is applicable to other elongated nanoscale analytes whose state is defined by many parameters. As a result, a robust and scalable solution for efficient and precise metrology of elongated analytes is established for high parallelism and high throughput nanocapacitor array sensor applications.