Machine learning driven measurement of high-aspect-ratio nanostructures using Mueller matrix spectroscopic ellipsometry

Abstract

Accurate fabrication of high-aspect ratio (HAR) structures in applications from semiconductor devices to x-ray observatories is essential for their optimal performance because their performance directly depends on their structure. High-efficiency critical-angle transmission (CAT) gratings enable high-resolution x-ray spectroscopy in astrophysics, but their performance is only ideal when certain performance-critical parameters, like the bar tilts introduced during deep reactive-ion etching, are tuned to precise values. Traditional measurement methods like small-angle x-ray scattering (SAXS) are accurate, but limit the development of robust control algorithms to nudge performance-critical parameters toward favorable values because they are slow and often destructive. We present a fast, accurate, nondestructive measurement method using Mueller matrix spectroscopic ellipsometry and machine learning. Given a HAR structure, we train on rigorous coupled-wave analysis simulation data to predict Mueller matrix spectra from input performance-critical parameter values. We then invert this forward problem by freezing our network weights, measuring experimental Mueller matrix spectra, and vanilla gradient descending on performance-critical parameters to values that correspond to the input Mueller matrix spectra. Introducing machine learning to invert the forward problem reduces computation time, and experimental results demonstrate close agreement between our method’s determined tilt and SAXS measurements. Our accurate, fast measurement method paves the way for the development of robust control algorithms that adjust fabrication parameters in response to measurement, ensuring optimal performance in not only CAT gratings but also HAR structures embedded in applications from semiconductor to microelectromechanical systems fabrication.