Robust mass damper design for bandwidth increase of motion stages
Citation for published version (APA): Verbaan, C. A. M. (2015). Robust mass damper design for bandwidth increase of motion stages. Eindhoven: Technische Universiteit Eindhoven. Integrated circuits (IC's) are widely used in devices nowadays to control process parameters. Examples are transportation vehicles, medical equipment, computers and phones, and industrial plants. The amount of IC's in all types of products has increased tremendously during the last decades. This functionality became
... onality became usable by miniaturization of the IC's, which enabled to apply more components within the size of an IC, combined with a decrease in production cost. The most important step in the production of IC's is the illumination of the IC pattern on the surface of a wafer which is provided with a photo-sensitive layer. This illumination is executed after positioning the wafer with respect to the optical column by means of a motion stage. Mechanical vibrations in the motion stage take long to fade naturally and compromise image quality as they limit the control systems' bandwidth. They are related to design specific natural frequencies of the motion stage. This thesis presents the idea of adding mechanical damper devices to the motion stage to increase the damping of these natural frequencies. This leads to a fast decrease of the vibration amplitude by dissipating the energy stored in the vibrations. The result is an increase in control bandwidth, which allows increased productivity and hence lower prices. Analyses have been performed on complex stage designs to quantify the performance improvement. Experimental validation showed the correspondence between theory and practice. This thesis proves a damper concept that enables further increase of density hence functionality of IC's. The boundaries of the societal impact are not easily identified. iv v Summary Robust Mass Damper Design for Bandwidth Increase of Motion Stages In the production of integrated circuits (e.g. computer chips), optical lithography is used to transfer a pattern onto a semiconductor substrate, which is called wafer. This wafer is fixed on top of a motion stage which positions the wafer's surface with respect to the optical column used for projection of the pattern. The accuracy of the motion system largely determines the minimum feature size that can be projected and the speed of the motion stage is a measure for the throughput. Both the accuracy and the velocity of the motion stage are determined by a position control system which exists of a feedback loop with a PID + controller and a feedforward path. The gain of the feedback loop, which has to be high to counteract disturbances, is usually limited by flexible behavior of the stage mechanics. The resonance frequencies as well as the modal damping values of these resonances determine to what extent bandwidth limitations exist. An increase of the modal damping, which is usually low in high-precision mechanical designs, results in a decreased amplification factor at these resonances and, therefore, provides additional room to increase the controllers' frequency dependent gain. This thesis addresses the challenge to increase the modal damping of the bandwidth limiting resonances of motion stages. This modal damping increase is realized by adding passive elements, called robust mass dampers (RMDs), at specific stage locations. These RMDs exist of a mass, mounted to the stage by a parallel spring and a high-damping dashpot and provide robust and broad banded damping to the flexibilities. The theoretical advantages of RMDs for an abstracted stage model and ideal damper models are used as a starting point and a closed-loop criterion is derived as performance measure for further optimization A robust mass damper design is presented based on a high-viscosity fluid in order to maintain linear time-invariant behavior and the performance limitations of this damper are investigated. Especially, the linear visco-elastic behavior introduces differences with respect to an ideal damper model. Multi-mode Maxwell models are created to take this behavior into account. Subsequently, two complex motion stage designs are elaborated and RMDs are designed in order to maximize the performance. The damper parameters that have to be determined are mass, stiffness and damping. In both cases, the optimal RMD parameters are obtained by executing optimization algorithms. These optimizations include models, obtained by finiteelement modal analyses and RMD models which include the linear visco-elastic fluid model. vi The first motion stage design is optimized based on an open-loop criterion for modal damping increase between 1 and 4 kHz. Experimental validation shows that a suppression factor of over 24 dB is obtained in this frequency range. In addition, a suppression of 19 dB is visible up to 6 kHz. Transient time responses show an amplitude decrease rate which is 20 times faster for the damped stage than for the undamped stage. In addition, the optimization results show that a larger suppression factor can be obtained by applying linear viscoelastic materials compared to applying purely viscous damping. The second motion stage design is optimized under closed-loop conditions and in addition to the RMD properties as listed before, the controller parameters are included in the optimization. RMDs are designed and experimental identification of both the undamped and damped stage is performed. For the stage with RMDs, a low-frequency sensitivity improvement of 9 dB is proven in the vertical direction of motion for a PID + controller by experimental validation on a six degree of freedom experimental motion stage. This corresponds to an increase of the bandwidth frequency of 50 %. In addition to the improvements in input-output behavior (frequency response function), the stage shows inherently better damped behavior for a number of modes. This improves the spatial behavior for modes that are not observed in the FRF. The theoretical and experimental results show that there is great potential of using the Robust Mass Dampers as an add-on to high-precision motion stages with high bandwidths.