Overcoming physical approximation limitations of nanometal thin film thickness measurement by physics-informed neural networks.

Non-destructive and precise thickness measurement of nanometre metal thin films, especially at the sub-10 nm scale where accurate measurement poses significant difficulties, is crucial for micro-nano device manufacturing. However, in thickness measurement for nanometre metal thin films based on the sample current method, the description of the relationship between secondary electron yield (SEY, σ) and film thickness relies on physical approximations of the secondary electron emission process. This leads to the construction of nonlinear piecewise functions, which consequently impairs the model's accuracy. To address this limitation, a physics-informed neural networks (PINN)-based high-precision thickness measurement model for nanometre metal thin films is proposed. The model takes the physical mechanism of secondary electron emission as a constraint and integrates a small amount of experimental SEY data for training. By embedding physical equations into neural networks, the model successfully learns the complex non-linear relationship between SEY and film thickness. In tests on Au, Ag, and Ti films, the PINN model demonstrates superior stability in thickness prediction error compared to the physical approximation model (PAM), maintaining the error within 10%. This method enables real-time thickness measurement during scanning electron microscope (SEM) surface observation, representing a precise and non-destructive nanometre thin film thickness measurement technique.