Data-driven modeling and estimation of beam position drift for electron beam systems

Abstract

Electron beam systems (EBS) have reached a level of precision where residual beam position drifts, caused by thermal expansion, mechanical bending, and electronic effects, have become a dominant source of inaccuracy. These drifts arise from different interacting influence factors and are difficult to predict with first-principles models alone. Hence, this article presents a data-driven approach to model and estimate beam drift in EBS by including indirect ambient measurements. Principal component analysis is used to extract static impact variables from temperature, pressure, and other sensor data. These variables are embedded into a linear state-space model that accounts for dynamic effects, from which an adaptive Kalman filter is derived for real-time drift estimation between calibration measurements. The developed estimator avoids covariance windup, enforces parameter sparsity, and allows physically motivated constraints. Finally, the proposed method is validated by measurement data from a semiconductor electron beam tool, demonstrating accurate drift estimation in a wide range of scenarios.