High-speed AFM imaging via iterative learning-based model predictive control

Abstract

Atomic force microscopy (AFM) imaging has been broadly used for material topography characterization and observation of dynamic material morphology revolution. However, current efforts on high-speed AFM imaging are still limited. In this study, we propose an iterative learning-based model predictive control (IL-MPC) scheme to achieve high-speed AFM imaging. Integrated with the conventional PI feedback control, the IL-MPC scheme is used in the feedforward path to ensure accurate tracking of the sample topography by the AFM z-axis piezo at high imaging speed. Particularly, IL-MPC combines a model predictive controller (MPC) with an iterative learning controller (ILC), where the MPC ensures the fast convergence of the ILC with the existence of line-to-line sample topography variation and the ILC ensures the precision tracking of the sample topography by dealing with the modeling uncertainty of MPC and the nonlinearities of AFM piezo actuator. Moreover, the proposed IL-MPC can be implemented in time domain so that the computation complexity is greatly reduced compared to other frequency-domain iterative learning feedforward approaches. For validation and demonstration, both the proposed method and the conventional contact-mode AFM are applied to image a silicon calibration sample with square pitches (step height: 178 nm). The experiment results show that the proposed technique can increase the scanning speed to scan rate of 50Hz (with linear tip velocity of 1.7 mm/s) while maintaining the imaging quality.