Design and Optimal Control of a Magnet Assisted Scanning Stage for Precise and Energy Efficient Positioning

Scanning stages are characterized by repeated back and forth motions and are widely used in advanced manufacturing processes like photo-lithography, laser-scribing, inspection, metrology, 3D printing, and precision parts assembly, many of which are closely related to the semiconductor (i.e., integrated circuit) manufacturing industry. In order to deliver more high- performance semiconductor chips, i.e., to keep up with predictions made by Moore’s Law, the scanning stages employed by the industry need to move faster while maintaining nanometer-level precision. Achieving these two goals simultaneously requires extensive use of thermal and vibration-induced error mitigation methods, because the motors, and subsequently the surrounding stage components, become heated and flexible parts of scanning stages are easily excited by their aggressive motions (with high acceleration/deceleration). Most of the available solutions tackle the heat and vibration mitigation problems separately, even though the two problems originate from one source, i.e., the large inertial loads generated by the scanning stage’s actuators. Much benefit (e.g., size and cost reductions) can be achieved by considering the two problems simultaneously by addressing their root cause. This dissertation proposes a design-based approach to simultaneously mitigate thermal and vibration-induced errors of scanning stages. Exploiting the repeated back-and-forth motions of scanning, permanent magnet (PM) based assist devices are designed to provide assist force needed during the motion reversal portions of scanning trajectories. The PM-based assist devices store the kinetic energy of the moving table during deceleration and release the stored energy when the table accelerates. Consequently, the force requirements of the primary actuator decrease, thus lowering its heat generation due to copper (resistive) losses. Moreover, the reaction forces borne by the PM assistive devices are channeled to the ground, bypassing the vibration isolated base upon which the scanning stage rests, thus reducing unwanted vibration. To increase the force density of the PMs, a 2D Halbach arrangement is adopted in a prototype scanning stage. Moreover, an efficient and low-cost servo system, optimized for versatility, is integrated into the scanning stage for automatic positioning of the PMs. The designed magnet assisted scanning stage is an over-actuated system, meaning that it has more control inputs than outputs. For the best utilization of its actuators, a feedforward approach for optimal allocation of control efforts to its actuators is developed. The stage, controlled with the optimal feedforward control inputs, achieves significant reductions of actuator heat and vibration-induced errors when applied to typical scanning motions used in semiconductor manufacturing (silicon wafer processing). To further improve the positioning accuracy of the stage, an Iterative Learning Control (ILC) approach for over-actuated systems is developed, exploiting the repeated motion of scanning stages. The optimal ILC update law is designed, considering model and input force uncertainties, for robust monotonic convergence of tracking errors, and the resultant control force is efficiently allocated to multiple actuators. Applied to the magnet assisted scanning stage, the proposed ILC approach additionally reduces tracking errors arising from the mismatch between the model and actual system, thus significantly improving the positioning accuracy of the stage.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/149847/1/yydkyoon_1.pd

Disturbance attenuation with multi-sensing servo systems for high density storage devices

Ph.DDOCTOR OF PHILOSOPH

Scanning micro interferometer with tunable diffraction grating for low noise parallel operation

Large area high throughput metrology plays an important role in several technologies like MEMS. In current metrology systems the parallel operation of multiple metrology probes in a tool has been hindered by their bulky sizes. This study approaches this problem by developing a metrology technique based on miniaturized scanning grating interferometers (μSGIs). Miniaturization of the interferometer is realized by novel micromachined tunable gratings fabricated using SOI substrates. These stress free flat gratings show sufficient motion (~500nm), bandwidth (~50 kHz) and low damping ratio (~0.05). Optical setups have been developed for testing the performance of μSGIs and preliminary results show 6.6 μm lateral resolution and sub-angstrom vertical resolution. To achieve high resolution and to reduce the effect of ambient vibrations, the study has developed a novel control algorithm, implemented on FPGA. It has shown significant reduction of vibration noise in 6.5 kHz bandwidth achieving 6x10-5 nmrms/√Hz noise resolution. Modifications of this control scheme enable long range displacement measurements, parallel operation and scanning samples for their dynamic profile. To analyze and simulate similar optical metrology system with active micro-components, separate tools are developed for mechanical, control and optical sub-systems. The results of these programs enable better design optimization for different applications.Ph.D.Committee Chair: Degertekin, Levent; Committee Co-Chair: Kurfess, Thomas; Committee Member: Adibi, Ali; Committee Member: Danyluk, Steven; Committee Member: Hesketh, Pete

Performance-driven control of nano-motion systems

The performance of high-precision mechatronic systems is subject to ever increasing demands regarding speed and accuracy. To meet these demands, new actuator drivers, sensor signal processing and control algorithms have to be derived. The state-of-the-art scientific developments in these research directions can significantly improve the performance of high-precision systems. However, translation of the scientific developments to usable technology is often non-trivial. To improve the performance of high-precision systems and to bridge the gap between science and technology, a performance-driven control approach has been developed. First, the main performance limiting factor (PLF) is identified. Then, a model-based compensation method is developed for the identified PLF. Experimental validation shows the performance improvement and reveals the next PLF to which the same procedure is applied. The compensation method can relate to the actuator driver, the sensor system or the control algorithm. In this thesis, the focus is on nano-motion systems that are driven by piezo actuators and/or use encoder sensors. Nano-motion systems are defined as the class of systems that require velocities ranging from nanometers per second to millimeters per second with a (sub)nanometer resolution. The main PLFs of such systems are the actuator driver, hysteresis, stick-slip effects, repetitive disturbances, coupling between degrees-of-freedom (DOFs), geometric nonlinearities and quantization errors. The developed approach is applied to three illustrative experimental cases that exhibit the above mentioned PLFs. The cases include a nano-motion stage driven by a walking piezo actuator, a metrological AFM and an encoder system. The contributions of this thesis relate to modeling, actuation driver development, control synthesis and encoder sensor signal processing. In particular, dynamic models are derived of the bimorph piezo legs of the walking piezo actuator and of the nano-motion stage with the walking piezo actuator containing the switching actuation principle, stick-slip effects and contact dynamics. Subsequently, a model-based optimization is performed to obtain optimal drive waveforms for a constant stage velocity. Both the walking piezo actuator and the AFM case exhibit repetitive disturbances with a non-constant period-time, for which dedicated repetitive control methods are developed. Furthermore, control algorithms have been developed to cope with the present coupling between and hysteresis in the different axes of the AFM. Finally, sensor signal processing algorithms have been developed to cope with the quantization effects and encoder imperfections in optical incremental encoders. The application of the performance-driven control approach to the different cases shows that the different identified PLFs can be successfully modeled and compensated for. The experiments show that the performance-driven control approach can largely improve the performance of nano-motion systems with piezo actuators and/or encoder sensors

Modeling and analysis of a class of linear reluctance actuators for advanced precision motion systems

Reluctance actuators (RA) are a type of electromagnetic actuator that offer high forces for short range motions. The RA takes advantage of the electromagnetic reluctance force property in air gaps between the stator core and mover parts. The mover accelerates because the stator generates the magnetic flux that produces an attractive magnetic attraction between the stator and mover. Hysteresis and other non-linearities in the magnetic flux have an impact on the force and have a nonlinear gap dependency. It is demonstrated that the RA has the capacity to produce a force that is effective and suitable for millimeter-range high-acceleration applications. One application for the RA is the short-stroke stage of photolithography machines for example. The RA is available in a wide variety of configurations, such as CCore, E-Core, Maxwell, and Plunger-type designs. The RA requires precise dynamic models and control algorithms to help linearize the RA for better control and optimization. Some nonlinear dynamics include magnetic hysteresis, flux fringing, and eddy currents. The RA is shown to have a much higher force density than any other traditional actuator, with the main disadvantage being the nonlinear and hysteretic behaviour which makes it hard to control without proper dynamic and control models in place. It is important to model the RA accurately for better control. The output force can be significantly impacted by unequal offsets or asymmetries between the mover and stator. In the thesis that follows, a review of RA systems is performed, an investigation that shows the importance of including the mean path length (MPL) term for higher accuracy, a technique for calculating the force of various asymmetrical instances for the C-core RA is demonstrated. This thesis documents currently available knowledge of the RA such as available applications, configurations, dynamic models, measurement systems, and control systems for the RA. The findings presented can allow for future control systems to be designed to counteract multi-axial asymmetric issues of the RA