Optimal design of a flexure hinge-based XYZ atomic force microscopy scanner for minimizing Abbe errors

Abstract

To establish of standard technique of nanolength measurement in a two-dimensional plane, a new ͑AFM͒ system has been designed. In this system, measurement uncertainty is dominantly affected by the Abbe error of the XYZ scanning stage. No linear stage is perfectly straight; in other words, every scanning stage is subject to tilting, pitch, and yaw motion. In this article, an AFM system with minimum offset of XYZ sensing is designed. And, the XYZ scanning stage is designed to minimize the rotation angle because Abbe errors occur through the multiply of offset and rotation angle. For XY stage, optimal design is performed to minimize the rotation angle by maximizing the stiffness ratio of motion direction to the parasitic motion direction of each stage. For the Z stage, the optimal design of maximizing the first-resonant frequency is performed. When the resonant frequency increases, the scan speed is improved, thereby reducing errors caused by sensor drift. This article describes the procedures of selecting parameters for the optimal design. The full range of the XYZ scanner is 100 m ϫ 100 m ϫ 10 m. Based on the solution of the optimization problem, the XYZ scanner is fabricated. And tilting, pitch, and yaw motion are measured by autocollimator to evaluate the performance of XY stage.

Dimensionless design graphs for three types of annulus-shaped flexure hinges

“…Due to this advantages flexure hinges are commonly used in precision engineering [1][2][3], metrology [4] and aerospace fields [5] for example.…”

Multi-Objective Design Optimization of an Over-Constrained Flexure-Based Amplifier

“…According to Equation (1), the displacement ratio R and the input stiffness Kin can be expressed as: 2 …”

“…[1][2][3][4][5]. A compliant mechanism with flexure hinges is regarded as one of the best and has been implemented in these fields due to its incomparable merits including no friction, lubrication and backlash, reduced weight, low clearance, and being easy to manufacture, integrally.…”

Design and control of a 6-degree-of-freedom precision positioning system

“…Shao et al [19] presented a novel precision tilt positioning mechanism for inter-satellite optical communication.Furthermore, combinations of in-plane and out-of-plane system have been explored and utilized. A flexure hinge-based XYZ atomic force microscopy scanner was presented by Kim et al [20]. In Ref.…”

“…From the above literature review, it can be seen that most of the existing precision positioning systems are featured by oneto three-DOF motions [10][11][12][13][14][15][16][17][18][19][20][21][22], which cannot meet the needs of manipulations in some cases. For example, an atomic force microscope designed for nanometrology in Ref.…”