Ultra-precision Stage Research Articles

H2 norm based parameter optimization of multiple tuned mass dampers for resonance suppression

Flexible dynamic behavior of ultra-precision motion stage significantly deteriorates control performance. To tackle this problem, this paper presents an [Formula: see text] norm based parameter optimization of multiple Tuned Mass Dampers (TMDs) for resonance suppression applied on linear flexible structures, assuming all parameters of multiple TMDs are independent, and considering locations of TMDs as variables. Linear flexible structures with multiple TMDs are modeled as a closed-loop control system through modeling in steps. Genetic algorithm is implemented employing [Formula: see text] norm as the optimization criterion. The effectiveness of the optimization is numerically verified on a free-free thin plate. The effects of uncertainties in TMDs parameters, linear flexible structure parameters, and TMDs failure on the vibration suppression effect are studied. The proposed modeling and optimization methods are promising for application to various flexible structures with provided modal frequencies and mode shape matrix.

Learning Synchronous Control Based on Intelligent Methods for Ultra-Precision Stage Systems

Learning Synchronous Control Based on Intelligent Methods for Ultra-Precision Stage Systems

Non-contact ultra-precision metrology of superfine cylinders with a developed two-dimensional coordinate measuring device

To address the issue of measuring force of a stylus that can move and/or hook up the measured workpiece with a small dimension in the contact measurement, a spectral confocal displacement sensor and an ultra-precision linear stage are employed to develop a two-dimensional coordinate measuring machine instead of the conventional stylus contact measurement to avoid the measuring force problem, by which the non-contact ultra-precision metrology can be achieved. A coordinate modeling-dividing method is proposed for the diameter and roundness measurement of the small cylindrical workpieces with a diameter of 0.5 mm and length of 50 mm, whose cross-sectional circle is divided into several equal arcs to be scanned by the developed two-dimensional coordinate measuring machine. Thus, a set of arcs, each of which consists of large numbers of coordinate points, can be obtained. The radius of each arc can be fitted by the least square method, and the arc profile can be characterized by a series of data processing. The diameter and roundness of the measured workpiece can be obtained by averaging these fitted arcs’ radii and stitching these arc profiles together, respectively. A preliminary measurement uncertainty analysis is carried out to verify the developed device and proposed method.

공간형 위치 결정 스테이지를 위한 타원형 및 포물선형 2 자유도 플렉셔 힌지에 대한 해석

With advancements in semiconductor manufacturing processes and the development of precision processing technology, flexure hinge-based ultra-precision positioning stages are widely used. In the flexure hinge, axial and bending stiffness properties greatly influence positioning performance. This study examined the stiffness properties of elliptic and parabolic 2-degrees-of-freedom (DOF) hinges, which have not been extensively discussed. The Timoshenko beam theory was applied to derive the stiffness equations for the axial and bending directions of each hinge. The stiffness properties were examined in several design conditions by comparing theoretical and finite element analyses. Based on the results of the analyses, an empirical formula in exponential form for the design of an elliptic hinge was constructed through surface-fitting. The elliptic hinge was found to be a better alternative to a circular hinge under certain design conditions by adjusting two design parameters. In the future, we will develop sophisticatedly designed hinges with improved axial and bending stiffness properties compared to the existing circular and elliptic hinges.

Precision Flux Control of Linear Reluctance Actuator Using the Integral Sliding Mode Method

The performance of the actuator is becoming increasingly important in the ultra-precision stage. However, the traditional Lorentz motors with given mechanical parameters cannot provide enough force for the next-generation motion stage in the semiconductor industry since they achieve a physical limit of power factor. To tackle this problem, this study develops a novel-driven approach and its control strategy for high-dynamic stages. Explicitly, the proposed method utilizes a linear reluctance motor as an actuator, which could promote the continuous thrust significantly. A heuristic optimization-based Bouc–Wen model is established to describe the nonlinear behavior of the novel actuator. Also, a flux control algorithm based on the integral sliding mode is derived and adjusted for precision thrust generation. Comparative simulations on a specific linear reluctance motor confirm the effectiveness and superiority of the proposed method and show that it has the ability to conquer the force nonlinearity of the novel actuator.

Development of a cross-scale 6-DOF piezoelectric stage and its application in assisted puncture

Micro-nano manipulation technology has been widely applied in ultra-precision fields such as micro-nano manufacturing and biomedical engineering. Multi-DOF ultra-precision stage is one of its key components. This study proposes a 6-DOF piezoelectric stage (6-DOF-PS) to solve the problem that few existing 6-DOF stages can take the characteristics of large range, high resolution and low coupling into account together. The optimal mechanism design scheme of the proposed stage was chosen by comprehensively considering three critical factors of the workspace, the parameter sensitivity of connecting rods and inertia load moment. The structure design and working principle of the 6-DOF-PS were introduced. A prototype of the 6-DOF-PS was fabricated and a series of experiments were performed. The experiment results showed that it achieved 6-DOF motion with the large range of 5 mm × 5 mm × 5 mm × 68° × 68° × 360° and the high resolution of 22.6 nm × 18.9 nm × 12.4 nm × 0.12 µrad × 0.13 µrad × 0.40 µrad, and the maximum coupling error was 5.03% in the 6-DOF motion. Therefore, 6-DOF motion with large range, high resolution and low coupling was achieved through this stage. Furthermore, it also had a good load carrying capacity. Finally, its application experiments in assisted puncture were carried out, the position and posture of the vascular models were adjusted by the 6-DOF motion, and the puncture operation was completed successfully with the assistance of the proposed 6-DOF-PS.

A Reflective-Type Heterodyne Grating Interferometer for Three-Degree-of-Freedom Subnanometer Measurement

A heterodyne grating interferometer (HTGI) able to simultaneously measure the three-axis translational displacements of ultra-precision motion stages with a sub-nanometer resolution is demonstrated. The HTGI is composed of two main parts, a reflective planar grating with a uniform micron-scale period in two orthogonal directions, and a reading head. Thanks to the reflective grating, the reading head design manages to make main optical paths common and located on the same side of this compact structure, potentially resulting in low Abbe errors and environmental variations. Relying on a laboratory-made dual-frequency laser source at 780 nm, two heterodyne interferometric measurement modules for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> -/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y</i> -direction motions and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i> -direction motion were realized based on first-order and zeroth-order diffraction, respectively. Experiments show that the proposed HTGI, in all three axes, can distinguish a 0.5 nm step or even better, perform an up to 2.5×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> 10linearity in a range of 80 μm, and hold a 5 nm stability within 300 s. These performances confirm that the proposed HTGI can greatly benefit nanoscience and technology, where multi-axis ultra-precision positioning is required, such as wafer stage in next-generation lithography machine, and so forth.

Frequency-Domain Data-Driven Adaptive Iterative Learning Control Approach: With Application to Wafer Stage

The feedforward control is becoming increasingly important in ultra-precision stages. However, the conventional model-based methods cannot achieve expected performance in new-generation stages since it is hard to obtain the accurate plant model due to the complicated stage dynamical properties. To tackle this problem, this article develops a model-free data-driven adaptive iterative learning approach that is designed in the frequency-domain. Explicitly, the proposed method utilizes the frequency-response data to learn and update the output of the feedforward controller online, which has benefits that both the structure and parameters of the plant model are not required. An unbiased estimation method for the frequency response of the closed-loop system is proposed and proved through the theoretical analysis. Comparative experiments on a linear motor confirm the effectiveness and superiority of the proposed method, and show that it has the ability to avoid the performance deterioration caused by the model mismatch with the increasing iterative trials.

Precise Compensation for Positional Accuracy of Ultra-Precision Air-Bearing Motion Stage Based on the Self-Calibration Method

In this paper, a high-efficiency self-calibration method was proposed, which was successfully applied to the ultra-precision air-bearing motion stage. Firstly, digital grating focusing, camera vision measurement and position synchronous output signal control were integrated, which can effectively improve the acquisition accuracy of stage positional data. Then, based on the least square algorithm the systematic error compensation value of motion stage can be quickly obtained through the fitting processing of three different measurement views. The experimental results showed that the proposed self-calibration measurement system can successfully realize ultra-precision air-bearing stage accurate location, and the orthogonality and shrinkage were controlled within 1 arcsec and 300 nm, respectively. This compensation method can effectively avoid the problems of high cost and poor environmental anti-interference in the laser interferometer measurement system, and will have a broad application prospect in the fields of high-end lithography and ultra-precision machining.

LFT-Structured Uncertainty State-Space Modeling for State Feedback Robust Control of the Ultra-Precision Wafer Stage

This paper presents linear-fractional-trans-formation (LFT)-structured uncertainty state-space modeling for robust control of the multiple-input multiple-output (MIMO) ultra-precision wafer stage with flexible structures to meet the challenges of vibration-dependent model uncertainties. Specifically, based on the modal MIMO state-space model, a parametric uncertainty model related with flexible modes is presented, and the uncertainty parameters are structured to a diagonal matrix with the LFT method. Meanwhile, a multiplicative uncertainty model is employed to express the uncertainty in high frequency with respect to ignored high-order modes. Thus, the final uncertainty model is structured with uncertainty parameters and high-frequency uncertainty. Based on the proposed uncertainty model, a comprehensive robust control scheme is proposed. Specifically, the weighting function matrixes are designed by the loop-shaping approach, and a $\mu$ analysis is employed to achieve a nonconservative solution with respect to the structured uncertainty. A standard stability criterion of a $\bf{M} \boldsymbol{\Delta}$ structure system is then utilized to determine the system stability by the largest structure singular value. Comparative experiments on a developed ultra-precision wafer stage are finally conducted, and the results validate that the proposed method achieves significant improvements on control performance, robustness, and robust stability in all exposure fields.

Real-time displacement calculation and offline geometric calibration of the grating interferometer system for ultra-precision wafer stage measurement

For ultra-precision wafer stage measurement in a photolithography scanner, real-time six-degree-of-freedom displacement calculation and offline geometric calibration methods are proposed to solve the multiple nonlinearities caused by rotation-translation coupling, Abbe error, and cosine error of the grating interferometer system with non-ideal geometry. First, the interference signal phase-shift model related to the displacements of the center of mass of the wafer stage is established. Then, through double approximations, the displacement calculation process is efficiently reduced to polynomials of substitution variables of phase-shift to improve the real-time performance of computing. Finally, the non-ideal geometry of the nonlinear computing model caused by manufacturing and assembly errors is calibrated offline by solving overdetermined equations set up by redundant measurement to improve the calculation precision. The proposed methods are verified through ZEMAX simulation.

Semi-active joint for ultra-precision positioning using sliding/rolling bearings

A novel semi-active joint for connecting mechanical (i.e., sliding/rolling) bearings or guideways to an ultra-precision motion stage is presented. The semi-active joint enables the benefits of bearing/guideway friction on in-position stability while avoiding its adverse effects on rapid ultra-precision positioning. The joint is equipped with solenoids that switch its stiffness from low, during settling, to high once the stage gets into position. A two-step scheme is implemented to mitigate adverse effects of switching on positioning performance. Experiments demonstrate up to 81% and 60% improvements in settling time and in-position stability, respectively, compared to cases with solely low- or high-stiffness joints.

A New Linear Motor Force Ripple Compensation Method Based on Inverse Model Iterative Learning and Robust Disturbance Observer

Permanent magnet linear motors (PMLMs) are gaining increasing interest in ultra-precision and long stroke motion stage, such as reticle and wafer stage of scanner for semiconductor lithography. However, the performances of PMLM are greatly affected by inherent force ripple. A number of compensation methods have been studied to solve its influence to the system precision. However, aiming at some application, the system characteristics limit the design of controller. In this paper, a new compensation strategy based on the inverse model iterative learning control and robust disturbance observer is proposed to suppress the influence of force ripple. The proposed compensation method makes fully use of not only achievable high tracking accuracy of the inverse model iterative learning control but also the higher robustness and better iterative learning speed by using robust disturbance observer. Simulation and experiments verify effectiveness and superiority of the proposed method.

Yaw error correction of ultra-precision stage for scanning beam interference lithography systems

The stage yaw error is a key factor affecting the phase distortion of gratings produced by scanning beam interference lithography system. In order to solve this problem, a coarse-fine dual-stage mechanism is proposed, in which an ultra-precision fine positioning stage with yaw error correction function is developed. To achieve nanoscale positioning and sub-microradian yaw motion accuracy, four Lorentz motors are used to drive the fine stage. The internal coupling factors and the mechanism of Lorentz motors motion control are analyzed. Besides, the Abbe error caused by the yaw error is investigated. Positioning and scanning experiments are conducted and the outcomes show that maximum yaw error is 0.33 μrad during constant velocity scanning, which completely meets the grating fabrication requirements.

An adaptive 2DoF P-PI controller based on an improved just-in-time learning technique for ultra-low-velocity linear stages driven by PMLSMs

In this paper, an adaptive two-degree-of-freedom (2DoF) proportional/proportional-integral (P-PI) controller is presented for ultra-precise linear motion stages driven by permanent magnet linear synchronous motors (PMLSMs) under ultra-low-velocity conditions. The adaptive 2DoF P-PI controller is designed based on reliable position output predictions obtained via just-in-time learning (JITL). To implement the JITL method, the current velocity commands, current position outputs and former position outputs are employed to formulate the JITL model. To guarantee high real-time performance and high prediction accuracy, the JITL method with an improved database (JITLIDB) is presented. Through comparative experiments, JITLIDB is shown to effectively reduce computation time by virtue of its use of a layered database structure to decrease the computational burden and a forgetting factor to prevent the JITL database from infinitely increasing in size. Based on the JITL predictions, a 2DoF P-PI parameter updating algorithm is designed, which is proven to guarantee that the system position errors converge to zero using the Lyapunov method. Through ultra-low-velocity simulations using the proposed adaptive 2DoF P-PI controller based on JITLIDB, it is shown that the proposed controller achieves satisfying performance. These simulations correspond to experiments performed on an ultra-precision air-bearing linear stage driven by a PMLSM. Finally, comparative experiments are presented, in which the proposed adaptive 2DoF P-PI controller based on JITLIDB achieves superior ultra-low-velocity error performance compared with a traditional 2DoF P-PI controller with fixed parameters.

Adaptive model-based feedforward to compensate Lorentz force variation of voice coil motor for the fine stage of lithographic equipment

This paper presents an adaptive model-based feedforward combined with PID feedback controller based on model identification to compensate the variation of the Lorentz force. In the previous work, we applied an analytical model to calculate the magnetic flux density and Lorentz force for the rectangular Voice Coil Motor (VCM) used in ultra-precision motion stage. This analytical model indicates the Lorentz force will change when coil of the VCM moves in the permanent magnet air gap, and the simulation and experiment results verify the effectiveness of this phenomenon. In order to improve the tracking and positioning performance of the fine stage, an adaptive controller is applied to the VCM to compensate the Lorentz force variation, and the step experiment verify it is effective to decrease the positioning error for the fine stage.

High accurate squareness measurement squareness method for ultra-precision machine based on error separation

Traditional measurement methods of squareness for ultra-precision motion stage have many limitations, especially the errors caused by the inaccuracy of standard specimens. On the basis of error separation, this paper presents a novel method to measure squareness with an optical square brick. The angles between the guideways and the four lines of brick section are measured based on the fact that sum of interior angle of a quadrilateral is 2π, and the squareness is obtained. A squareness measurement experiment was performed on a profilometer with a modified optical square brick. Experimental results show that the squareness accuracy between X and Y axes is not influenced by the accuracy of brick, and the measurement repeatability reaches 0.22 arcsec. Finally, a verification experiment to the proposed method was carried out with a high accurate standard specimen, and the error between the two methods is 1.06 arcsec. According to the error results and simulation analysis of the measurement system, the measurement error based on error separation is 0.06 arcsec. The proposed method is able to achieve a very high accurate squareness measurement with auxiliary components of normal accuracy, and can be applied to measure the accuracy class of sub-arcsec squareness.

Dynamic modeling method for air bearings in ultra-precision positioning stages

Air bearings have been widely used in ultra-precision positioning stages due to the property of nearly zero friction or wear. Small vibration of the bearing reduces the overall moving and positioning precision of the stage and hampers its applications in fabrication facilities requiring nanometer moving and positioning precision. In order to improve system precision, knowledge of the dynamic characteristics of air bearings is the first and crucial step. However, it is still a challenge to set up an accurate dynamic model for air bearings due to the system complexity. In this article, a novel method for the dynamic modeling of air bearing is proposed, which takes into account the dynamics in both the moving direction and the supporting direction. An ultra-precision positioning dual stage is investigated using the proposed dynamic modeling method. This stage has two sets of air bearings and can be used in integrated circuit fabrication equipments. Moreover, dynamic behaviors of the ultra-precision positioning dual stage are studied and compared with experimental results to validate the effectiveness and accuracy of the proposed method.

초정밀 듀얼 스테이지를 위한 고댐핑 저진동 제어기 개발

In this study, a cross-damped low vibration controller was developed to reduce vibration in ultra-precision dual stage driven by master/slave principle. In master-slave structure, the master stage leads the driving motion and the slave stage follows it so as to maintain a constant gap between two stages. In this structure, a small perturbation of master stage makes big oscillations in slave servoing stage, so a low damped master stage composed of voice coil motor makes a long vibration in settling area after driving motion profile. In this research, an effective feedback damping algorithm for increase the damping characteristics of the dual stage was developed. The designed velocity damping algorithm improves the system stability and reduces the settling time of the whole system. Simulation and experimental results show that the developed algorithm reduces settling time and improves the regulating performance.

Modeling and analysis of a novel rectangular voice coil motor for the 6-DOF fine stage of lithographic equipment

This paper presents a novel rectangular voice coil motor (VCM) used in ultra-precision motion stage. The new analytical model of magnetic field is proposed to calculate the Lorentz force, this analytical model indicates that Lorentz force will change when coil of the VCM moves in the permanent magnet air gap. The result of finite element analysis and experiment are used to verify this analytical model. This method offers a theoretical basis for the design and optimization of the VCM.