Serial-kinematic monolithic nanopositioner with in-plane bender actuators

Abstract

This article describes a monolithic nanopositioner constructed from in-plane bending actuators which provide greater deflection than previously reported extension actuators, at the expense of stiffness and resonance frequency. The proposed actuators are demonstrated by constructing an XY nanopositioning stage with a serial kinematic design. Analytical modeling and finite-element-analysis accurately predicts the experimental performance of the nanopositioner. A $10\mathrm{\mu }\mathrm{m}$ range is achieved in the X and Y axes with an applied voltage of +/-200 V. The first resonance mode occurs at 250 Hz in the Z axis. The stage is demonstrated for atomic force microscopy imaging.

Introduction

Nanopositioning devices are a class of short-range motion stages with resolution on the nanometer scale or below [1]. Applications include atomic force microscopy [2], [3], [4], [5], [6], [7], [8], data storage [9], nanofabrication [10], [11], cell surgery [12], and precision optics [13].

Piezoelectric tube scanners were the first common nanopositioning systems used in Atomic Force Microscopy (AFM) [14]. Since these are constructed from a single piece of piezoelectric ceramic, they are known as monolithic structures which provide both actuation and some motion guidance [15], [16]. The travel range of piezoelectric tubes is determined by the length, radius, and tube wall thickness. They tend to be long (e.g. 50 mm) and thin (e.g. 7 mm diameter) which can be difficult to integrate due the significant vertical height. There is significant scope to explore other monolithic geometries that are similar in cost but provide improved performance and alternative dimensions.

The most common class of nanopositioners are flexure-based devices [17], [18], [19], [20], [21], [22], [23], [24], [25]. In these designs, metal flexures guide a central stage which is driven by piezoelectric stack actuators. Metal flexure-based nanopositioners provide the highest performance metrics with respect to displacement gain, resonance frequency, cross-coupling, and load size. However, they are also much larger, heavier, and more costly than monolithic devices like piezoelectric tubes. In addition, assembling and preloading piezoelectric stack actuators are required to avoid damage to the stack actuators [26]. Preload mechanisms require careful design considerations and precise machining which increase manufacturing time and cost.

There is significant demand for low profile positioning systems in applications such as optical microscopy [27], atomic force microscopy [28], and in particular, scanning electron microscopy (SPM) where the load-lock area is typically less than 10 mm in height [29], [30]. Products designed for these applications include the SuperFlat AFM from Kleindiek nanotechik [28], the P-541 and P-542 Series from Physik Instrumente [31], and the Nano-Bio and Nano-LPS Series from Mad City Labs [27].

This work combines monolithic and flexure-based designapproaches which results in a vertical thickness of less than 1 mm, which is an order of magnitude less than current metal flexure based devices. The advantages of the proposed approach over metal flexure designs are generalized by lower vertical height; lower mass; no preload mechanism; compatibility with vacuum and low temperature applications. The proposed method is light weight, which makes it suitable for applications such as camera stabilization and optical scanning from small-scale air vehicles [32]. The simple mechanical structure of the proposed method also avoids the need for stack actuators and the resulting preloading requirements. Since bonding or encapsulation materials are not required, the reported monolithic design can also be easily adapted to high-vacuum and cryogenic applications.

The disadvantages of the proposed method stem from the low vertical height that results in low vertical stiffness. This results in higher vertical cross-coupling and a lower payload capability compared to metal flexure devices. The most useful range of payload masses for the proposed method is less than 10 g.

Microelectromechanical systems (MEMs) are another class of monolithic flexure-based nanopositioners [33]. These devices provide the smallest size and the opportunity to integrate sensing mechanisms [33], [34], [35]. MEMs based nanopositioners are best suited to payload masses in the milligram range. The proposed methods represent an intermediate point between MEMs based nanopositioners and metal-flexure based nanopositioners.

This article describes a new actuation method for monolithicnanopositioners using in-plane bending actuators. As illustrated in Fig. 1, Fig. 2, each actuator is made from a thin piezoelectric beam with four top electrodes and a grounded bottom electrode. When opposite voltages are applied to the top electrodes, the resultant deflection is shown in Fig. 3. A unique feature of this design is that the moving end deflects in a plane and does not rotate. Compared to a piezoelectric bimorph bender, the motion is lateral rather than vertical [36].

The methods described herein are compared to previous and future work in Fig. 1, including the previous beam extension actuators (top), the topic of this work (middle), and future work (bottom). Other related work has also included closed-loop [37] and feedforward [38] control of extension actuators. Future work (bottom) aims at extending the monolithic concept to a bimorph structure which enables vertical and angular motion [39], [40].

A summary of the application characteristics of extension [41] and in-plane bending actuators are listed in Table 1. In-plane bending actuators provide increased flexibility in the choice of travel range since the deflection is proportional to the actuator length squared, rather than directly proportional [41]. The beam width of an in-plane bending actuator can be used to control the trade-off between stiffness and travel range. In practice, reduced in-plane stiffness is not expected to be a significant disadvantage since the operating speed is limited by the first resonance mode, which is an out-of-plane mode primarily determined by the material thickness and is similar for both approaches.

A preliminary version of this work was presented at the IEEE International Conference on Advanced Intelligent Mechatronics in 2018 [42] which used Euler–Bernoulli beam theory to estimate the static deflection of each bender, and a lumped mass and stiffness approach to estimate the combined deflection and stiffness. This modeling approach does not capture the out-of-plane dynamics which are the lowest frequency and most significant eigenmodes of the system.

Compared to [42], the present work uses a combination of Euler–Bernoulli beam theory and Hamilton’s principle to predict the total deflection in each axis and the first resonance modes in both the lateral and vertical directions. This work also extends on [42] with an experimental measurement of resonance modes, measurement of the cross-coupling between axes, and application to atomic force microscopy imaging.

In the remainder of the article, Section 2 outlines the structural design, fabrication, and actuating principles of the nanopositioner. Sections 3 Electromechanical model of an active flexure, 4 Electromechanical model of the piezoelectric nanopositioner present a reduced-order model of an active flexure from which the dynamics of the nanopositioner are predicted. Section 5 presents finite element analysis (FEA) of the device which validates the modeling of the nanopositioner. Section 6 presents the experimental performance of the device which examines the range, cross-coupling, non-linearity, and modal characteristics. Section 7 demonstrates the use of the nanopositioner for atomic force microscopy.