Accurate, optics-based measurement of feature sizes at deep sub-wavelength dimensions has been conventionally challenged by improved manufacturing, including smaller linewidths, denser layouts, and greater materials complexity at near-atomic scales. Electromagnetic modeling is relied upon heavily for forward solutions to the inverse problem of optical measurements for parametric estimation. Machine learning (ML) approaches are continually under consideration, either as a means to bypass direct comparison to simulation or as a method to augment nonlinear regression. In this work, both ML approaches are investigated using a well-characterized experimental data set and its simulation library that assumes a 2-D geometry. The benefits and limitations of ML for optical critical dimension (OCD) metrology are illustrated by comparing a straightforward library look-up method and two ML approaches, nonlinear regression with radial basis functions (RBF) and multiple-output Gaussian process regression (GPR) that indirectly utilizes the simulation data. Both RBF and GPR generally improve accuracy over the conventional method with as few as 32 training points. However, as measurement noise is decreased the uncertainties from RBF and GPR differ greatly as the GPR posterior estimate of the variance appears to overestimate parametric uncertainties. Both accuracy and uncertainty must be addressed in OCD while balancing simulation versus ML computational requirements.
Proceedings of the SPIE
February 24-27, 2020
San Jose, CA
Metrology, Inspection, and Process Control for Microlithography XXXIV