Piezoelectric actuators (PEAs) are extensively used for scanning and positioning in scanning probe microscopy (SPM) due to their high precision, simple construction, and fast response. However, there are significant challenges for instrument designers due to their nonlinear properties. Nonlinear properties make precise and accurate control difficult in cases where position feedback sensors cannot be employed. However, the performance of PEA-driven scanners can be significantly improved without position feedback sensors if an accurate mathematical model with low computational costs is applied to reduce hysteresis and other nonlinear effects. Various methods have been proposed for modeling PEAs, but most of them have limitations in terms of their accuracy and computational efficiencies. In this research, we propose a variant DenseNet-type neural network (NN) model for modeling PEAs in an AFM scanner where position feedback sensors are not available. To improve the performance of this model, the mapping of the forward and backward directions is carried out separately. The experimental results successfully demonstrate the efficacy of the proposed model by reducing the relative root-mean-square (RMS) error to less than 0.1%.

Rapid advancement in the nanotechnology and semiconductor industries has driven the demand for fast, precise measurement systems. Atomic force microscopy (AFM) is a standout metrology technique due to its high precision and wide applicability. However, when operated at high speeds, the quality of AFM images often deteriorates, especially in areas where sharp topographic features are present. This occurs because the feedback speed of the Z-scanner cannot keep up with the sample height changes during raster scanning. This study presents a simple variable scan speed control strategy for improving AFM imaging speed while maintaining the image quality obtained at low scan speeds. The proposed strategy aims to leverage the similarity in the height profiles between successive scan lines. The topographic information collected from the previous line scan is used to assess the surface complexity and to adjust the scan speed for the following line scan. The AFM system with this variable speed control algorithm was found to reduce the scan time needed for one AFM image by over 50% compared to the fixed-speed scanning while maintaining the similar level of accuracy. The calculated mean square errors (MSEs) show that the combination of speed adjustments and preemptive surface topography prediction has successfully allowed us to suppress the potential oscillations during the speed adjustment process, thereby enhancing the stability of the adaptive AFM system as well.