Robust mass damper design for bandwidth increase of motion stages

This chapter introduces the research objective of this thesis, which focusses on bandwidth limitations of high-precision motion stages. A brief overview is given regarding the history of IC production and the application of motion stages in this field. Performance limiters are listed, of which one is elaborated in this thesis. Specifically, the performance limiting behavior of the stage’s mechanical design in terms of flexible modes and the relation with the modal damping of these modes is studied. Subsequently, the goals of the thesis are listed and research objectives are defined in order to structure the problem and present sub problems. Finally, the outline of the thesis is presented and the relations between the topics are visualized in a table. Chapter 1 – Introduction 2 1.1 IC production and lithography In 1958, the first functional integrated circuit (IC) was presented and in the years afterwards the applications for these types of circuits grew enormously. Already in 1965, Gordon E. Moore wrote an article in which he predicted the increase of functionality of integrated circuits for the next decade [61]. This prediction estimated the miniaturization factor of components on integrated circuits, which proved to be correct, and after 1975, this observation became driving in further miniaturization. Nowadays, the idea behind 'Moore's law' is such widespread that planning trajectories for the development of these components were – and often are – based on this observation instead of technological possibilities and difficulties [62,80]. In this way it might be seen as a self-fulfilling prophecy. Since the publication by Moore, many publications have elaborated upon the difficulties in maintaining the miniaturization rate over time [45,56,73] and the new possibilities that have been developed to satisfy this prediction [96]. The miniaturization of ICs lead to 1) an increase of functionality per volume, and 2) a decrease in energy consumption per IC operation. In addition to the continuous miniaturization, 3) the cost price per integrated circuit has tremendously decreased, which enabled to implement these devices in a large part of industrial machines and consumer products. The key production step determining the performance of ICs is the projection of the functional pattern on the surface of a substrate. The substrate is a thin round silicon disc called wafer. Figure 1.1: Image of the illumination process. The light beam subsequently passes: optical components to condition the light; the reticle which contains the pattern to be projected and, finally, illuminates the pattern on the surface of the wafer. Robust Mass Damper Design for Bandwidth Increase of Motion Stages 3 The functional pattern of an IC is projected in a scanning motion in a machine that is called a wafer scanner. See Figure 1.1 for an impression of the illumination process. The smallest feature size that can be produced is related to the wavelength of the light and the accuracy of the wafer scanner. These properties, therefore, determine the miniaturization rate. The scanner’s throughput is related to the scanner’s speed and therefore to the production cost of an IC. The quality of the projected pattern is mainly a function of: • the quality of the optical system, which includes 1) the light source in which the used wave length is important, 2) the optical path and the components that are applied in the optical column, 3) abilities to adapt the projection pattern by optical corrections and 4) the quality of the projection surface and the 5) properties of the photosensitive resist, and • the accuracy of the motion system that takes care of the positioning of the wafer (and reticle, with the original image) with respect to the optical column. The maximal throughput is mainly limited by: • the sensitivity of the resist with respect to the applied wavelength of the projection light and, therefore, by the output power of the light source, and • the velocity of the motion system and the achievable accelerations and related settling times. The second points for both projection quality and throughput are related to the motion stage’s performance and are further subject of this thesis. 1.2 Motion stages The performance of high-tech motion systems improved significantly during the past decades. Especially, in the field of lithographic systems, very fast and accurate motion stages have continuously been developed: • the accelerations and velocities have been increased, • the accuracies have been increased, • the wafer diameter and therefore the wafer area has been increased. It is expected that these trends will continue in the future. To enable these developments, the complexities of the systems have manifold during the past decades. Roughly 3 decades ago, a wafer scanner contained: • a single level wafer stage with three in-plane position control loops, • a single DoF controlled reticle stage. Nowadays, this device contains: Chapter 1 – Introduction 4 • a serial double wafer stage principle with both stages fully position controlled (12 loops), • a serial double reticle stage principle with both stages fully controlled (12 loops). With all functionality included, over 40 simultaneously operating position control loops are present in a modern wafer scanner. The points above clearly show the increasing importance of the position control systems in the performance. A high-precision motion system exists of a mechanical stage part, which accommodates for force actuators and position sensors. The acceleration forces are mainly created by an amplifier, with a setpoint trajectory and a feedforward control path. The system’s stabilization and robustness against disturbances is provided by feedback control: position measurements enable to calculate position errors and apply actuator forces to suppress these errors. The higher the controller gain can be designed the smaller the position error due to low-frequency disturbances will be. This principle is known as high gain feedback. 1.3 Performance limiters The controller gain in practical cases is limited by several factors: • limitations in actuator forces and amplifier currents, • the finite accuracy of the sensors, • the presence of time delays, • the presence of flexible dynamics in the mechanical components. Especially, the presence of flexible stage dynamics is becoming more and more limiting for the performance. The natural frequencies of motion stages are designed as high as possible to enable high controller gains. Materials with high specific stiffness and low density enable these high frequencies. In future stage designs however, the mechanical design for high natural frequencies will be increasingly difficult: the stage accelerations have to increase further to enable larger throughputs. In case of larger actuator sizes the stage mass increases and more energy will be dissipated, which causes thermal problems. A decrease of the stage mass enables to obtain large accelerations, however, without decreasing the stage’s outer dimensions, it limits the amount of structural material that can be distributed in the design phase and decreases the stage’s static stiffness. This approach makes it more difficult to obtain high natural frequencies. An additional drawback in these types of precision designs is the low damping present at these frequencies. The prevalent materials for these applications contain low material damping and interfaces are designed with low damping, hysteresis and friction. The resulting resonances can be counteracted by increasing the controller complexity with notch filters, however, the controller complexity is usually restricted by implementation limits and robustness problems at high frequencies. In addition, over-actuation and over-sensing can be applied in order to make non-rigid modes observable and controllable. These active Robust Mass Damper Design for Bandwidth Increase of Motion Stages 5 solutions however, lead to complex controllers and are able to cause unstable behavior of the closed-loop system. 1.4 Thesis goals The goal of this thesis is to explore mechanical design in order to adapt the dynamical behavior in such a way that the stage becomes better controllable. The hardware for control is considered to be fixed to enable comparison between different plants. The hypothesis is that the performance of the motion system can be increased by increasing the modal damping of the non-rigid body modes by making use of passive (local) added mechanical dampers. Such dampers change the dynamics of the original system and, therefore, the resulting natural frequencies and mode shapes differ from the original ones. In case of relatively small damper masses however, most new frequencies and mode shapes are highly comparable to the original ones, except for the damping, which has been substantially increased. The idea in this thesis is to apply large damping values in these passive dampers. This results in broad band damping of the mode shapes. This solution is inherently stabilizing the system due to the principle of energy dissipation. To enable investigation of the performance of a motion stage, firstly, a dynamic model of the stage is created and frequency responses are visualized. In this thesis, one of the most important assumptions is that the controller structure is fixed. This assumption allows investigating the performance increase that can be reached by adapting the plant characteristics. Design-specific performance limiting behavior is evaluated from a feedback control point-of-view. Secondly, the mechanical (passive) dampers are added to the stage model to improve the performance. The positions for these dampers is determined and properties for practical elaboration are included. Thirdly, the performance of the stage for one direction of motion is optimized. Different levels of motion stage elaboration are shown in this thesis. Simple and abstracted stage models are used t