A new precise positioning method for piezoelectric scanner of AFM

Highlights

• The paper proposed a new method named dynamic polynomial fitting method to model the hysteresis model of the PZT.

• The inverse model is used as the feedforward controller, combined with the intelligent fuzzy feedback controller, is utilized to AFM scanner to improve its lateral positioning accuracy significantly.

Abstract

Atomic Force Microscopy (AFM) plays a vital role in nanoscience and nanotechnology due to its nanoscale resolution. However, the realization of highly precise measurement for AFM is still a challenge. A main factor is the positioning accuracy of the piezoelectric scanner (PZT), affected significantly by the hysteresis of PZT. The paper reports a new dynamic polynomial fitting method modeling hysteresis to achieve the inverse model of the PZT. The inverse model is used as the feedforward input, combined with the fuzzy feedback controller proposed in our former paper, to correct the nonlinear errors induced by the hysteresis. The method is demonstrated to be effective in improving the positioning accuracy of the lateral PZT. Its accuracy can achieve 1 nm.

Introduction

As a powerful nanoscale measurement instrument, Atomic Force Microscopy (AFM) [1] is useful in many fields, such as chemistry, material science, biology, semiconductor industry and so on. AFM is mainly composed of a cantilever, a piezoelectric scanner, a controller and a computer. A probe attached to the end of the cantilever is applied to contact with the sample. The acting force upon this contact is detected by an optical lever. The driver in z direction will move to recover the mechanical state of the cantilever back to a set point value under the feedback controller [2], [3]. The piezoelectric scanner will scan in XY directions point by point. By recording the outputs of the feedback controller and the scanner, a three-dimensional image could be achieved.

Nowadays, the piezoelectric driver is used as the scanner in most commercial AFMs depending on its high positioning precision. However, the piezoelectric driver has hysteresis, nonlinearity and resonance, affecting its positioning accuracy seriously. Most of all, the hysteresis is difficult to eliminate. The paper focuses on the compensation of the hysteresis. Recently, many methods have been proposed to eliminate the positioning errors induced by hysteresis shown in Fig. 1, such as changing the driving power, applying feedforward controller and feedback controller. The driving power of PZT is commonly voltage source type. Therefore, the piezoelectric effect indicates that the driving displacement of PZT is linear to the charge quantity. So the designs of linear driving power are developed, such as charge source, mixed source and switch type source [4], [5], [6].They are demonstrated to be effective in improving the poisoning accuracy of PZT. But it is high cost. The conventional voltage source is still used commonly in commercial AFMs. The feedforward controller is based on the hysteresis inverse model achieved by many modeling methods, such as Bouc-Wen [7], [8], Duhem [9], Preisach [10], Prandtl–Ishlinskii model [11], [12] and so on. But the modeling methods are static, meaning that the model cannot describe the relationship between the hysteresis outputs and the inputs with changing rate. While the input of the scanner is changing upon time, it will induce great model errors (up to several micrometers). The feedback controller can be utilized with some new controllers [13], such as adaptive controller [14], dynamic controller [15], fuzzy controller [18] and so on [16], [17]. The intelligent fuzzy controller proposed in our former paper [18] can significantly improve the positioning accuracy of PZT.

The paper reports a dynamic polynomial fitting method to achieve the hysteresis model of the piezoelectric driver. Based on the inverse model, a feedforward controller is achieved. Combined with the original intelligent feedback controller proposed in our former paper [18], the new controller is proved to be efficient to improve the positioning accuracy of the driver.