Coupling error suppression method for high-rigidity flatbed scanners

ObjectiveIn the context of increasingly stringent requirements for micro-measurement precision in advanced manufacturing, semiconductor chips, and other fields, the coupling error of Atomic Force Microscope (AFM) stage scanners has become a critical bottleneck restricting measurement accuracy. This paper focuses on the coupling error control of high-rigidity bow-shaped stage scanners, achieving effective error suppression through theoretical modeling, parameter optimization, simulation verification, and experimental calibration. A tangential deformation model of the bow-shaped flexure hinge was constructed based on the segmented stiffness method, deriving the quantitative relationship between tangential force and coupling displacement. The sequential quadratic programming method was employed to optimize key parameters such as hinge length, width, and spacing, determining the optimal structural parameters that balance motion flexibility and anti-coupling capability. Simulation results demonstrated that the maximum equivalent stress of the scanner is far below the allowable stress of the material, and the first-order natural frequency of 314.38 Hz can avoid resonance interference. An orthogonal error calibration method based on two-dimensional self-traceable chromium grid reference material was proposed. After calibration in the closed-loop state, the coupling angle error was reduced to 0.018°, significantly improving measurement accuracy. This research provides a reliable technical solution for the performance optimization of metrological AFM scanners, with important engineering application value for promoting precise micro-dimension measurement in advanced manufacturing, semiconductor chips, and related fields. This research aims to address the critical coupling error issue in AFM stage scanners that severely limits measurement accuracy in nanotechnology applications. The primary goal is to develop an optimized design methodology for bow-shaped flexure hinges that balances motion flexibility and anti-coupling capability, overcoming the limitations of existing models that fail to adequately consider coupling deformation under tangential forces. Concurrently, this study seeks to establish a systematic parameter optimization approach that resolves the trade-off between load-bearing capacity and coupling error sensitivity, providing a superior solution to both traditional miniaturized structures with limited load capacity and large-size designs prone to significant coupling errors. A key objective is to minimize coupling errors originating from both mechanical system crosstalk and sensor feedback inaccuracies, thereby significantly improving the measurement precision of AFM systems for advanced manufacturing, semiconductor chips, and biomedicine applications. Ultimately, this research intends to create a comprehensive technical framework that ensures high-precision two-dimensional displacement while maintaining structural integrity and operational reliability, eliminating the major bottleneck restricting AFM measurement accuracy and enabling more reliable characterization of microstructures at the nanoscale.MethodsThis paper focuses on the coupling error control of stage scanners with high-rigidity bow-shaped structures and conducts multi-dimensional research. First, a tangential deformation model of the bow-shaped hinge is established based on the segmented stiffness method, revealing the quantitative relationship between tangential force and coupling displacement, providing a theoretical basis for error tracing. Second, a parameter optimization model targeting low stiffness in the motion direction and high stiffness in the tangential direction is constructed. The sequential quadratic programming method is used to optimize key parameters such as hinge length, width, and spacing, minimizing coupling deformation while satisfying load-bearing capacity and displacement range requirements. Third, Finite element simulation is used to verify the static performance and modal characteristics of the optimized structure, ensuring that its stiffness, stress, and natural frequency meet the design requirements. Finally, an orthogonal error calibration method based on two-dimensional self-traceable chromium grid reference material is proposed, combined with grating interferometer feedback control, to achieve accurate measurement and offline correction of coupling angles.Results and DiscussionsThe optimized bow-shaped flexure hinge parameters (L=11.63 mm, W=2.41 mm, D=1.98 mm, H=17 mm) achieved the design objective of low stiffness (0.7533 N/μm) in the motion direction while maintaining high tangential rigidity. Simulations confirmed the structural reliability, with a first-order natural frequency of 314.38 Hz well above operational frequencies, effectively avoiding resonance. The maximum equivalent stress of 9.07×107 Pa was significantly below the allowable stress of 2.8×108 Pa, ensuring structural safety. Experimental results demonstrated that the open-loop coupling angle error was 0.280°, already meeting commercial standards. After implementing the proposed calibration method using two-dimensional self-traceable chromium grid reference material, the closed-loop coupling angle error was reduced to 0.018°, representing a 93.6% improvement. This significant reduction confirmed the effectiveness of both the mechanical design optimization and the calibration methodology in suppressing coupling errors from both mechanical installation and sensor feedback crosstalk.ConclusionsThis research successfully developed a comprehensive solution for coupling error suppression in high-rigidity stage scanners. The segmented stiffness method provided an accurate theoretical model for tangential deformation, while sequential quadratic programming optimization achieved the optimal balance between motion flexibility and anti-coupling capability. Finite element simulations validated the structural performance with excellent static and dynamic characteristics. Most importantly, the proposed calibration method using self-traceable reference material effectively reduced coupling angle errors to 0.018°, significantly improving measurement accuracy. The integrated approach of theoretical modeling, structural optimization, simulation validation, and experimental calibration provides a reliable technical solution for metrological AFM scanner performance enhancement, with significant implications for precise micro-dimension measurement in advanced manufacturing and semiconductor industries.