Contact-free handling using actively controlled electrostatic levitating fields

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(1)Contact-free Handling Using Actively Controlled Electrostatic Levitating Fields.

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(3) Contact-free Handling Using Actively Controlled Electrostatic Levitating Fields. PROEFSCHRIFT. ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnificus Prof. ir. K.C.A.M Luyben, voorzitter van het College voor Promoties, in het openbaar te verdedigen op dinsdag 18 September 2012 om 12.30 uur door. Shao Jü WOO. werktuigkundig ingenieur geboren te Dordrecht..

(4) Dit proefschrift is goedgekeurd door de promotoren: Prof. dr. ir. J. van Eijk Prof. dr. T. Higuchi. Samenstelling promotiecommissie: Rector Magnificus, Prof. dr. ir. J. van Eijk, Prof. dr. T. Higuchi, Prof. dr. H. Bleuler, Prof. dr. ir. P.P.J. van den Bosch, Prof. dr. ir. J. Compter, Dr. H. Vermeulen, Prof. dr. ir. J.L. Herder, Prof. dr. ir. G.C.A.M. Janssen,. voorzitter Technische Universiteit Delft, promotor University of Tokyo, promotor Ecole Polytechnique Fédérale de Lausanne Technische Universiteit Eindhoven Technische Universiteit Eindhoven ASML Veldhoven Technische Universiteit Delft en Universiteit Twente Technische Universiteit Delft, reservelid. The experimental work described in this thesis was conducted within the “Higuchi Ultimate Mechatronics” Project at the Kanagawa Academy of Science and Technology (KAST), Kawasaki city, Kanagawa 213-0012, Japan.. Contact-free Handling Using Actively Controlled Electrostatic Levitating Fields Woo, Shao Jü Delft University of Technology, Faculty 3mE, Dep. Precision and Microsystems Engineering, Mechatronic System Design (MSD) Keywords: Electrostatic levitation, contact-free, cleanroom, semiconductors, flat panel display, lateral restriction force, cost-effective, lossy dielectrics, capacitive displacement sensor, relay control, hysteresis control, describing function method, Filippov’s method Copyright © 2012 by Woo, Shao Jü All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without the prior permission of the author. Printed by Druckzentrum ETH Zentrum, Zürich, Switzerland..

(5) To my parents and my siblings To Verena To Sean Yung Qi.

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(7) Contents List of Main Symbols ......................................................................................................... xiii Chapter 1 Introduction......................................................................................................... 1 1.1 Motivation .................................................................................................................... 1 1.1.1 Background ........................................................................................................... 1 1.1.2 Electrostatic Versus Magnetic Forces................................................................... 1 1.2 Potential Applications .................................................................................................. 3 1.2.1 Semiconductor Manufacturing ............................................................................. 4 1.2.2 Flat Panel Display Manufacturing ........................................................................ 6 1.2.3 Nanotechnology .................................................................................................... 9 1.3 Literature Overview ................................................................................................... 11 1.4 Aim and Scope of Thesis ........................................................................................... 13 1.5 Outline of Thesis ........................................................................................................ 14 Chapter 2 Design and Analysis of an Electrostatic Suspension System ........................ 17 2.1 Introduction ................................................................................................................ 17 2.2 The Stator Electrode as Electrostatic Force Actuator ................................................ 18 2.2.1 Basic Relationships ............................................................................................. 18 2.2.2 Design of Stator Electrode Structure and Voltage Distribution ......................... 20 2.2.3 Electrostatic Suspension Force Calculation ........................................................ 22 2.2.4 Influence of Electric Fringing Fields .................................................................. 24 2.2.5 Influence of Suspended Object Obliqueness ...................................................... 25 2.3 Passive Squeeze-Film Damping ................................................................................ 27 2.3.1 Relative Translational Motion between Two Parallel Surfaces ......................... 28 2.3.2 Relative Rotational Motion between Two Surfaces ........................................... 29 2.4 Basic Principle of an Electrostatic Suspension System ............................................. 31 2.4.1 Open-loop Dynamic Model ................................................................................ 31 2.4.2 Closed-loop Dynamic Model .............................................................................. 33 2.5 Three-Degrees of Freedom Electrostatic Levitator ................................................... 35 2.5.1 Stator Electrode Geometries ............................................................................... 35 2.5.2 Kinematic Model ................................................................................................ 36 2.5.3 Open-loop Electromechanical Model ................................................................. 38 2.5.4 Linearized Open-loop Electromechanical Model ............................................... 38 2.5.5 Feedback Control Design .................................................................................... 40 2.6 Electrostatic Suspension of Flexible Bodies .............................................................. 46.

(8) viii. Contents 2.6.1 Introduction ......................................................................................................... 47 2.6.2 Electrostatic Actuator Structure .......................................................................... 47. 2.7 Alternative Electrostatic Suspension Principle Based on Motion Control of the Stator .......................................................................................................................................... 48 2.8 Prototype Voltage-Controlled Electrostatic Levitators ............................................. 52 2.8.1 Suspended Objects .............................................................................................. 52 2.8.2 Stator Electrodes ................................................................................................. 52 2.8.3 Mechanical Structure .......................................................................................... 53 2.8.4 Feedback Controller ............................................................................................ 55 2.9 Experiments ............................................................................................................... 56 2.10 Conclusions .............................................................................................................. 60 Chapter 3 Lateral Electrostatic Force .............................................................................. 61 3.1 Introduction ................................................................................................................ 61 3.2 Origin of Lateral Electrostatic Restriction Forces ..................................................... 61 3.3 Lateral Force Measurement Apparatus ...................................................................... 65 3.3.1 Measurement Procedure ..................................................................................... 67 3.3.2 Experimental Results .......................................................................................... 68 3.4 Improved Stator Design for Increase of Lateral Electrostatic Restriction Force ...... 70 3.4.1 Computation of Lateral Electrostatic Force........................................................ 71 3.5 Experimental Work .................................................................................................... 71 3.5.1 Experimental Apparatus ..................................................................................... 71 3.5.2 Experimental Results .......................................................................................... 72 3.6 Conclusions ................................................................................................................ 75 Chapter 4 Design of Integrated Capacitive Displacement Sensors................................ 77 4.1 Introduction ................................................................................................................ 77 4.2 Capacitance Transducer for Displacement Measurement ......................................... 78 4.3 Basic Switched Charge-Discharge Capacitive Sensor .............................................. 79 4.4 A Novel Stray-immune Capacitive Sensor Design ................................................... 81 4.4.1 Switched Charge-Discharge Capacitive Sensor Modelling ............................... 83 4.4.2 Improved Stray Capacitance Rejection Capability ............................................. 88 4.4.3 Charge Injection .................................................................................................. 92 4.5 Prototype Charge-Discharge Capacitance Transducer .............................................. 92 4.5.1 Switching Control Signals .................................................................................. 92 4.5.2 Selection of Analog Switches ............................................................................. 92 4.5.3 Selection of Analog Switches ............................................................................. 93.

(9) Contents. ix. 4.5.4 A Minimal Hardware Realization based on the DG403 Analog Switch ............ 94 4.6 An Oscillation Circuit based Capacitance Transducer .............................................. 95 4.6.1 Principle and Modelling of the Oscillation Circuit............................................. 95 4.7 Experiments ............................................................................................................... 97 4.7.1 Measurement Apparatus ..................................................................................... 97 4.7.2 Measurement Results .......................................................................................... 98 4.8 Conclusions .............................................................................................................. 100 Chapter 5 Electric Field and Force Modeling for Electrostatic Levitation of Lossy Dielectric Plates ................................................................................................................. 101 5.1 Introduction .............................................................................................................. 101 5.2 Stator Electrode Structure for Dielectrics ................................................................ 103 5.2.1 Electric Charging Mechanisms ......................................................................... 103 5.2.2 Stator Electrode Structure ................................................................................. 104 5.2.3 Electric Suspension Devices for Suspending Glass Panels .............................. 107 5.2.4 Restrictive Force Generation ............................................................................ 107 5.3 Theoretical Modeling ............................................................................................... 107 5.3.1 Background to the Electrostatic Problem ......................................................... 107 5.3.2 Boundary Conditions ........................................................................................ 110 5.3.3 First-order Taylor Series Approximation of the Inter-electrode Potential ....... 112 5.3.4 Solution to the Laplace Equation ...................................................................... 114 5.3.5 Electrostatic Levitation Force ........................................................................... 117 5.3.6 Transient Response under a Step Input in the Applied Voltages ..................... 120 5.4 Numerical Results and Discussion........................................................................... 122 5.4.1 Truncated Model ............................................................................................... 123 5.4.2 Electric Potential and Field Components.......................................................... 125 5.4.3 Frequency Response of Field Components ...................................................... 128 5.4.4 Comparison with Experimental Data ................................................................ 128 5.4.5 Optimization of Electrode Pattern .................................................................... 132 5.5 Conclusions .............................................................................................................. 133 Chapter 6 A Cost-effective and Simple Relay Driven Electrostatic Levitator Based on Squeeze-Film Damping ..................................................................................................... 135 6.1 Introduction .............................................................................................................. 135 6.2 Principle of Operation .............................................................................................. 137 6.3 Three-DOF Electrostatic Levitator .......................................................................... 139 6.4 Multi-DOF Electrostatic Levitator for Flexible Bodies ........................................... 141.

(10) x. Contents 6.5 Electromechanical Systems Modeling ..................................................................... 142 6.5.1 Hybrid Systems: an Introduction and Overview .............................................. 142 6.5.2 Kinematic Model of Levitated Disk ................................................................. 145 6.5.3 Open-loop Mechanical Subsystem Dynamics .................................................. 146 6.5.4 Relay with Hysteresis ....................................................................................... 147 6.5.5 Electrical Subsystem Dynamics ....................................................................... 147 6.5.6 Algebraic Force Transmission Relationship..................................................... 149 6.5.7 Linearized Open-loop Electromechanical Model ............................................. 149 6.5.8 Linearized State-Space Model of the Closed-Loop Dynamics ........................ 152 6.6 Closed-loop System Analysis Using Describing Function Analysis ...................... 153 6.6.1 One-DOF Open-loop Dynamic Model ............................................................. 154 6.6.2 One-DOF Closed-loop System Dynamics ........................................................ 154 6.6.3 Analytical Proof of Existence of Limit cycles.................................................. 156 6.6.4 Describing Function of Modified Relay ........................................................... 157 6.6.5 Prediction of Limit Cycles ................................................................................ 158 6.6.6 Stability Proof ................................................................................................... 161 6.7 Advanced Closed-loop System Analysis ................................................................. 162 6.7.1 Theory of Filippov Systems.............................................................................. 163 6.7.2 Stability Analysis of 1-DOF Levitator Using Filippov’s Method .................... 166 6.7.3 Calculation of Switching Period ....................................................................... 168 6.7.4 Derivation of the Monodromy Matrix of the 1-DOF Levitator ........................ 170 6.8 Simulation of Levitation in Vacuum ....................................................................... 172 6.9 Experimental results ................................................................................................ 175 6.9.1 Experimental Electrostatic Levitators............................................................... 175 6.9.2 Experiments Performed with 4-inch Silicon Wafers ........................................ 177 6.9.3 Experiments Performed with Glass Panels ....................................................... 183 6.9.4 Experiments Performed with Highly Flexible Aluminum Sheets .................... 186 6.10 Conclusions ............................................................................................................ 186. Chapter 7 Active Electrostatic Levitation Using Hysteresis Voltage Control ............ 191 7.1 Introduction .............................................................................................................. 191 7.2 Principle of Operation .............................................................................................. 192 7.3 Three-DOF Electrostatic Levitator .......................................................................... 194 7.4 Multi-DOF Electrostatic Levitator for Flexible Bodies .......................................... 195 7.5 Electromechanical Systems Modeling ..................................................................... 196 7.5.1 Kinematic Model and Open-loop Mechanical Subsystem Dynamics .............. 196.

(11) Contents. xi. 7.5.2 Electrical Subsystem Dynamics........................................................................ 196 7.5.3 Algebraic Force Transmission Relationship ..................................................... 199 7.6 Linearized Open-loop Electromechanical Model .................................................... 199 7.6.1 Linearized Mechanical Subsystem Dynamics .................................................. 200 7.6.2 Linearized Electrical Subsystem Dynamics ..................................................... 202 7.6.3 Composite Feedback Controller ....................................................................... 202 7.6.4 Linearized Closed-loop System Dynamics ....................................................... 205 7.7 Closed-loop System Analysis Using Describing Function Analysis ....................... 206 7.7.1 Describing Function of Switching Amplifier Element ..................................... 207 7.7.2 One-DOF Closed-loop System Dynamics ........................................................ 209 7.7.3 Prediction of Limit Cycle.................................................................................. 210 7.7.4 Proof of Stability ............................................................................................... 210 7.8 Closed-loop System Analysis Using Filippov’s Method......................................... 211 7.8.1 State-Space Model ............................................................................................ 213 7.8.2 Problem Statement and Proposed Solution ....................................................... 214 7.8.3 Calculation of Duty Ratio ................................................................................. 214 7.8.4 Calculation of Switching Period ....................................................................... 215 7.8.5 Derivation of the Monodromy Matrix of the 1-DOF Levitator ........................ 219 7.9 Simulation Results ................................................................................................... 223 7.9.1 Atmospheric Conditions ................................................................................... 223 7.9.2 Vacuum Conditions .......................................................................................... 225 7.10 Experimental Results ............................................................................................. 226 7.10.1 Experimental Electrostatic Levitator .............................................................. 226 7.10.2 Results and Discussion ................................................................................... 227 7.11 Conclusions ............................................................................................................ 231 Chapter 8 Conclusions and Future Research................................................................. 233 8.1 Conclusions .............................................................................................................. 234 8.1.1 A Generic Electrostatic Levitator ..................................................................... 234 8.1.2 Electrostatic Potential on the Suspended Object .............................................. 234 8.1.3 Lateral Electrostatic Force ................................................................................ 235 8.1.4 Capacitive Displacement Sensor ...................................................................... 235 8.1.5 Cost-effective Electrostatic Levitator Designs ................................................. 236 8.1.6 Alternative Levitator Concept Based on Motion Control of the Stator ............ 237 8.1.7 Modelling and Analysis .................................................................................... 238 8.2 Future Research........................................................................................................ 240.

(12) xii. Contents. Appendix A Derivation of Equations of Motion ............................................................ 243 A.1 The Lagrange Equations of Motion ........................................................................ 243 A.2 Quad-Electrode Pattern ........................................................................................... 244 A.3 Tri-Electrode Pattern ............................................................................................... 245 Appendix B Solution to the Laplace Equation ............................................................... 247 Appendix C Piecewise Quadratic Lyapunov Functions ................................................ 251 Bibliography ...................................................................................................................... 255 Summary ............................................................................................................................ 262 Samenvatting ..................................................................................................................... 265 Acknowledgements ........................................................................................................... 269 List of Publications ........................................................................................................... 272 Curriculum Vitae .............................................................................................................. 274.

(13) xiii. List of Main Symbols. List of Main Symbols Greek Symbols: ߜ݀௜ Small perturbation in the ݀௜ from its reference value ߜζ Small perturbation in ߜ from its reference value ߜߠ Small perturbation in ߠ from its reference value ߜܳ௞ Small perturbation in ܳ௞ , ݇ = ‫ݖ‬, ߠ, ζ, from its ref. value ߜܸ௜ Small perturbation in ܸ௜ from its reference value ߜ‫ݖ‬ୡ Small perturbation in ‫ݖ‬ୡ from its reference value Permittivity ߳ Permittivity of dielectric plate (chapter 5) ߳ୢ Permittivity of air ߳଴ Angular rotation about y-coordinate axis ζ ζ଴ Reference value of the angular rotation ζ Viscosity of air ߟୟ Angular rotation about x-coordinate axis ߠ ߠ଴ Reference value of the angular rotation ߠ Damping ratio ߦ Free electric charge density ߩ୤ Electric surface charge distribution or ߪୱ surface conductivity Conductivity of suspended dielectric plate ߪୢ Electric potential Φ Charging voltage in charge-discharge capacitive sensor ߶ୡ Electric potential on levitated object ߶ୢ ߶௜ Electric potential on electrode ݅ ߶୮,௜ Electric potential on inner electrode (‫ܧ‬୮,௜ ) ߶୬,௜ ߰ ߬ ߬ୱ ߯ୣ ߱ ߱୪୧୫ ߱୬. Electric potential on outer electrode (‫ܧ‬୬,௜ ) Squeeze number Charge relaxation time Switching time delay Susceptibility Angular frequency Angular frequency of limit cycle Natural angular frequency. m rad rad N, Nm V m F/m F/m F/m rad rad N∙s/ m2 rad rad C/m3 C/m2 Ω-1 S/m V V V V V V – s s – rad/s rad/s rad/s.

(14) xiv. List of Main Symbols. Vectors and Matrices: m Vector containing the perturbations in the local air gaps, ௜ Electric displacement vector C/m2 Electric field vector V/m Tangential electric field component vector V/m ୲ Electric force density vector N/m3 ୣ Electric force vector N ୣ Identity matrix – Conduction current vector A/m2. Surface current density vector A/m. Damping matrix N∙s/m, N∙s/rad Derivative feedback control matrix. ୈ V∙s/m, V∙s/rad Integral feedback control matrix V/m, V/rad. ୍. ୮ Proportional feedback control matrix V/m, V/rad Force-displacement matrix N/m. ୱ Force-voltage matrix N/V. ୴ Mass matrix. kg,kg∙m2 Unit normal vector to the surface of a dielectric plate m

(15) ୘ m, rad , Perturbation vector ୡ ζ Saltation matrix – Stress tensor N/m2 Force transformation matrix – ୤ ϯ. ୤. Pseudoinverse of force transformation matrix ୤. –. ୰ ૙ . Geometrical transformation matrix Bias voltage vector State vector Fundamental solution matrix. – V – –. Roman Symbols: ௜ Total suspension area of electrode unit Capacitance Capacitance between the sensing and stator electrode ୣ୶ Capacitance between stator electrodes E୮,௜ and E୬,௜ ௜ ୶ ୮,௜ ୱ୦ ୢ,୸ ୢ,஘ , ୢ,ζ. Unknown capacitance to be measured Parasitic capacitance Capacitance between signal wire and cable shield Squeeze-film damping constant associated with ୡ Squeeze-film damping constants associated with , ζ. m2 F F F F F F N∙s/m N∙s/rad.

(16) xv ݀ ݀଴ ݀௜ ݀௜,଴ ‫ܦ‬୰ ݁ E௜ ݂ୡ ݂ୢ ݂ୣ,௜ ݃ ℎ ݅ ‫୶୶ܫ‬ ݅ୱୣ୬ୱ ݇ୱ ݇୴ ‫ܮ‬ ݉ ‫݌‬ ‫݌‬ ‫݌‬ୟ ܳ୸ ,ܳ஘ ,ܳζ ‫ݎ‬ୢ ‫ݏ‬ ‫ݐ‬ ‫ݐ‬ௗ ܶୡ ܶୗ୍ ܳ ܸ ܸ௜. List of Main Symbols Air gap separation Reference air gap separation Air gap separation at the geometrical center of electrode ݅ Reference value of local air gap separation ݀௜ Duty ratio Position error of 1-DOF levitator Stator electrode ݅ Charge-discharge frequency Squeeze-film damping force Electrostatic force exerted by electrode ݅ Gravitational constant Hysteresis threshold. Current Moment of inertia Sensing current Force-displacement constant Force-voltage constant Length of rectangular plate Mass of levitated object Pressure Pitch Ambient pressure Generalized forces Radius of disk Discrete switching variable or Laplace variable Time Thickness of plate Charge-discharge cycle period Suspension initiation time Electric charge Voltage Difference between the electric potentials on stator electrode E௜ and the suspended disk (chapter 2) or difference between electrostatic potentials on the inner (‫ܧ‬୮,௜ ). m m m m – m – Hz N N m/s2 m A kg∙m2 A N/m N/V m kg N/m2 m N/m2 N, Nm m – s m s s C V V. and outer (‫ܧ‬୬,௜ ) electrode (chapter 6) or difference between electrostatic potentials on the inner (‫ܧ‬୮,௜ ) ܸ଴. and outer (‫ܧ‬୬,௜ ) electrode divided by two (chapter 7) Absolute reference value of the stator voltage ܸ௜. V.

(17) xvi ܸ୭ ܸୖ,௜ ܸୱ,୮ ,ܸୱ,୬ ܹ ‫ݓ‬ ‫ݓ‬ୣ ‫ݔ‬, ‫ݕ‬, ‫ݖ‬ ‫ݔ‬ୡ , ‫ݕ‬ୡ , ‫ݖ‬ୡ ‫ݖ‬ୡ,଴. List of Main Symbols Steady-state output voltage of the charge converter (chapter 4) Ripple in voltage. V V. Applied dc terminal voltages (chapters 6 and 7) Width of rectangular plate Width of electrode bar divided by 2 (chapter 5) Electric field energy Position coordinates Position coordinates of the center of mass Reference value of ‫ݖ‬ୡ. V m m J m m m. Abbreviations: ac Alternating current AMB Active magnetic bearing CMOS Complementary metal-oxide-semiconductor dc Direct current DEP Dielectrophoresis DOF Degrees of freedom DSP Digital signal processor FPD Flat panel display KAST Kanagawa Academy of Science and Technology LCD Liquid crystal displays MIMO Multi-input multi-output PID Proportional-Integral-Derivative SISO Single-input single -output TTL Transistor–transistor logic.

(18) Chapter 1 Introduction 1.1 Motivation 1.1.1 Background Stated in a rather general sense, this thesis is on the use of electrostatic fields and forces for actuation and to a lesser degree for sensing. As most of us undoubtedly know, the history of electrostatics dates back to as early as 500 B.C. when the ancient Greeks observed and recorded the mechanical effects of electric and magnetic fields on matter. However, it was not until the nineteenth century when the actual scientific foundation was established for electricity and magnetism. By using an electrical torsion, Coulomb (1736-1806) performed accurate electrostatic force measurements and from these enunciated his famous empirical inverse square law. Around the same time Oersted (1777-1851) and Ampere (1775-1836) conducted experiments on the influence of magnetic forces on various objects. Based on these electromechanical experiments and on Faraday’s work, Maxwell unified the subjects of electrostatics and magnetostatics into a general electromechanical dynamic theory. The industrial application of electromagnetics is truly myriad and encompasses fields far too numerous to mention them all. An important and distinctive property of magnetic and electric field forces is certainly their capability to mediate forces to all kinds of objects in a non-invasive and contact-free fashion. This property has created the technological field of contact-free suspension and levitation. In general, contact-free mediation of forces to objects prevents them from being contaminated and allows, for instance, friction-free motion, active control of the object’s dynamics in multiple degrees of freedom, and reduction of energy consumption. Furthermore, it enables non-invasive handling of objects, which is vital in manipulating biological cells and other living matter without damaging them. These inherent features render contact-free handling particularly attractive for applications in the biomedical field and in clean-room and vacuum environments. 1.1.2 Electrostatic Versus Magnetic Forces It is an established fact that the past two decades has witnessed a spectacular increase in the use of magnetic fields for contact-free suspension, handling, actuation, and processing of objects in a large variety of technical and scientific applications. In particular, the industrial deployment of active magnetic bearings (AMBs) in the domain of rotating machinery, which include vacuum pumps, turbo-compressors, and machine tools, has reached a highly mature level. AMBs are predominantly being used to eliminate traditional bearing problems, such as mechanical wear and lubrication. The literature on AMBs is.

(19) 2. Chapter 1. Introduction. vast. As a starting point for the interested reader we refer to classical works on AMBs such as Refs. [1,2,3]. Compared to contact-free magnetic suspension, however, contact-free electrostatic suspension at the macroscale has not been studied extensively. Both have in common that active feedback control of the attractive field is required to stabilize the suspended object. Macroscopic electrostatic levitators are characterized by air gap separations that range from several tens of micrometers to a few hundreds of micrometers, while the levitated objects can have physical dimensions ranging from millimeters to meters. The question then arises as to why this is the case. Undoubtedly, a major reason for this lies in the fact that under atmospheric conditions macroscale electrostatic actuators offer attainable electric energy densities several orders of magnitude weaker than their magnetic counterparts. Moreover high-voltages are required whose magnitudes typically range from several hundred to over a thousand volt. The maximum attainable value for the electric energy density is dictated by the breakdown field strength of air which in turn is dependent on the air gap, as shown in Figure 1.1. The energy density increases in tandem with the breakdown field strength as the air gap decreases. At typical air gap separations of several hundreds of micrometer, macroscopic electrostatic levitators offer electric energy densities of up to 1 × 10ଷ J/m3. Note that the energy density argument is also one of the reasons that electrostatic actuation is commonly applied in micro-electromechanical systems (MEMS) and nanotechnology systems.. Figure 1.1: Maximum attainable energy densities for electrostatic (Paschen’s curve) and magnetic fields under atmospheric conditions. Source: Ref. [7]..

(20) 1.2. Potential Applications. 3. MEMS are typically in a micron-scale dimensional regime and fabricated using wellestablished semiconductor micro-machining techniques by the selective etching of silicon substrates [4,5] or deposited thin films [6]. As shown in Figure 1.1, at gap separations below 5 µm the maximum attainable energy density in the gap of electrostatic microactuators approaches values which are of the same order of magnitude as that of magnetostatic micro-actuators. At submicron levels, electrostatic micro-actuators even have the potential to dominate magnetostatic ones. One major advantage that electrostatic micro-actuators have over magnetostatic ones is that they are compatible with the materials and processes of silicon micro-fabrication technologies. In spite of these shortcomings macroscopic electric field-based handling we assert that it can prove its usefulness and even superiority over its magnetic counterpart in the following two select cases: •. The material of the object to be levitated directly belongs to the class of dielectrics or semiconductors, examples of which are glass and silicon, respectively. This is in stark contrast with magnetic fields, which can only exert forces on a rather limited class of materials, i.e., ferromagnetic materials, which belong to the class of metallic conductors. As a matter of fact, electric fields can impart forces to virtually all materials known in a contact-free manner. Magnetic levitation of dielectrics or semiconductors can only be realized indirectly by placing them on a carrier which is levitated magnetically. Direct levitation of these materials renders levitator constructions which are generally less complex and smaller in size.. •. The levitation system operates in vacuum. In this case, the attainable energy density is no longer restricted by the breakdown field strength of air. Thus, the very absence of air enables the generation of substantially higher energy densities. In this context, it is interesting to note that the future trend in industrial integrated circuit (IC) manufacturing processes is towards making large sections of the process line operate in vacuum.. These two cases on their own open up a large variety of potentially innovative technical and scientific applications and motivated the research underlying this thesis.. 1.2 Potential Applications As indicated in the previous section, the motivation for the research underlying this thesis has an applied nature and stems from the potentially significant innovations which contactfree electrostatic field-based handling can offer in certain identified areas of industrial and scientific applications. The technological significance of electrostatic levitation is particularly reflected in its inherent capability to solve long-standing and highly critical chemical and particulate contamination control problems in vacuum and clean-room.

(21) 4. Chapter 1. Introduction. applications [8]. These problems arise from the direct mechanical contact through which dielectric and semiconductor materials, such as glass substrates and silicon wafers, are commonly handled by process equipment in these areas. Particulate contamination can either cause immediate product yield loss or eventual device reliability failures. Apart from these macroscale applications, applications in the area of nanotechnology can be envisioned. This area has actually experienced strong growth in the use of levitating electric fields for the handling of various nanoscale particles as evidenced by the published body of literature. In that sense, one cannot strictly speak of potential applications. The levitating principle frequently used at the nanoscale is different from the principle at the macroscale and cannot be simply transplanted to the latter. Even though the thesis is geared toward macroscopic applications, we shall discuss this interesting area of application for the sake of completeness. In the next sections we shall briefly discuss the above mentioned areas of application. 1.2.1 Semiconductor Manufacturing It is well known that in the semiconductor manufacture device performance, reliability, and product yield of silicon circuits are critically affected by the presence of chemical contaminants and particulate impurities on the substrate or device surface. More specifically, particulate contamination on the wafer surface hinders the proper functioning of microcircuits by interrupting or shorting conduction paths or by altering the capacitance of a circuit component. Generally, potential sources of particulate contamination are (i) valves, fittings, and other mechanical components in process gas delivery systems, (ii) wafer handling equipment, (iii) human clean-room operators [8]. The latter category is known to generate considerable airborne particulate contamination. During the past decade wafer handling equipment such as robotic manipulators have rapidly been introduced to replace human clean-room operators in the semiconductor industry [9] as they generate airborne particulates at a reduced rate. Table 1.1 summarizes the various types of common airborne molecular contaminants (AMC) in the clean-room, their sources, and effects. One of the major sources of VLSI and ULSI circuit yield loss is particulate contamination added to wafers as they pass through processing equipment. This has resulted in considerable efforts to design processing equipment cleanly by improvements such as •. “soft” pumping and venting. •. in-situ cleans [10,11]. •. Clean design of robotic manipulators in order to keep airborne molecular contamination from particles and outgassing produced by the robotic manipulator to a minimum. This is done by utilizing specialized engineering materials that resist shedding and flaking for the fabrication of exposed surfaces. The surfaces.

(22) 1.2. Potential Applications. 5. of clean-room robotic manipulators are usually either painted with polyurethane or ground to eliminate dust and oxidation. Furthermore, mechanical caps and joints are tightly sealed. The electrical wires and cables are normally concealed inside the robot manipulator to avoid accidents and the spread of contaminants [11]. Figure 1.2 shows a typical example of an arm construction of a clean-room robotic manipulator for the handling of silicon wafers.. Table 1.1: Summary of types of common airborne molecular contaminants (AMC) in the clean room, their sources, and effects [56]. AMC Class. Contaminants. Sources. Effects. Molecular acids.. Fluoride, chloride, bromide, sulfates, phosphates, nitrogen/oxygen compounds.. Etch chambers, diffusion furnances, CVD processes, wet benches using HCl, HF, BOE.. − Hazing of reticles, wafers, optics of exposure & metrology tools. − Corrosion of Al & Cu metal lines.. Molecular bases.. Ammonia, amines, amides, triemthylamine, triethylamine, cyclohexylamine, dimethylamine, methylamine, dimethylamine, ethanolamine, morpholine.. − Ammonia sources: CVD, HMDS, CMP, slurries, wafer cleaning processes, TiN films deposition hazing, particle formation, dimethylamine, methylamine, Si3N4 films deposition. − Amines sources: photoresist strippers, polymers, epoxies, TMAH decomposition. − Amides sources: solvents such as NMP dimethyl acetamide, polyimides.. Neutralizes photo-acids in resists Rxn with acid vapors can cause hazing, particle formation, and nitrides on wafer surface.. Molecular condensables.. Dibutyl phthalate, NMP, organophospates, siloxanes, hexamethyldisiloxane, PGMEA.. Outside air, process chemicals, outgassing from filter, sealants, walls, adhesives, floors, wafer shippers, FOUPs, pods, gaskets, sealing tape, bagging materials, flame retardants.. − Hazing of exposure tool optics and masks from silicones & HMDS by-products. − Delamination of PR and ARCs − Unwanted n-doping of wafers. − Interference with thin film metrology.. Molecular dopants. Boron, phosphorus, organophosphorus, arsenic, antimony. Outside air, degradation of HEPA & ULPA filters, exhaust from RIE, EPI, CVD processes, flame retardants.. Unwanted n- and p-doping of wafers.. Molecular metals.. Organo-metallic compounds.. Cross-contamination of wafers, plastic additives containing organo-tin and organo-bismuth compounds, corroding ductwork.. Particulates in air and on wafers..

(23) 6. Chapter 1. Introduction. Figure 1.2: Clean-room robotic manipulator for handling silicon wafers. Source: Brooks Automation. 1.2.2 Flat Panel Display Manufacturing Another major area of potential application that can be identified constitutes Flat Panel Display (FPD) manufacturing [12]. The technologies and processes used in FPD manufacturing bear similarities to those employed in semiconductor manufacturing. Therefore, both suffer from similar manufacturing problems which are linked to the level of cleanliness. The primary differences from semiconductor manufacturing are the relatively large line widths of the electronic circuitry, the small number of metal layers, and above all the much larger substrate area. The global FPD market is still growing at a rapid pace, with the prevalent technology being liquid crystal displays (LCDs). As the popularity of LCD displays for notebook PC's, smart phones/tablets, and TVs continues to increase, manufacturing facilities based mainly in South-Korea, Taiwan and to a lesser extent in Japan are rapidly expanding production of displays to keep up with growing market demand. Figure 1.3 depicts a chart in which the growing demand for glass substrate is shown graphically. The basic structure of LCDs may be thought of as two glass substrates sandwiching a layer of liquid crystal. As substrate material, soda-lime glass is widely used, because of its high productivity and excellent flatness over a large area [13]. One can distinguish between two primary types of LCDs, the more advanced active matrix LCD (AMLCD) and the basic passive matrix LCD (PMLCD). As part of the ongoing expansion of production of displays, there is pressure to increase the total area of glass substrates for the purpose of increasing through-put and decreasing manufacturing costs. Each glass substrate has on it a number of displays being processed in parallel. Currently the size of glass substrates is approaching 2.2×2.5 m. Substrates of this size are commonly referred to as 8th-generation panels..

(24) 1.2. Potential Applications. 7. Figure 1.3: LCD substrate glass supply versus demand. Source: http://www.semi.org. Table 1.2 gives an overview of the various panel generations. Concurrently, substrates are becoming thinner (< 0.5 mm). The net result is that the panels are bulky and very prone to structural mechanical deformation and in addition require larger handling equipment than those in integrated circuit manufacturing. Clearly, faced with the relatively short life cycle of panel generations, the challenge for handling equipment manufacturers is to cope with the market needs for new tools capable of handling high-volume production of large glass substrates.. Table 1.2: Glass panel dimensions and area by generation [9]. Generation. Dimensions [m]. Area [m2]. 1. 0.30×0.40. 0.120. 2. 0.37 ×0.47. 0.174. 3. 0.55×0.65. 0.358. 4. 0.75×0.90. 0.675. 5. 1.10×1.30. 1.430. 6. 1.50×1.85. 2.775. 7. 1.87×2.20. 4.114. 8. 2.20×2.50. 5.500. During the LCD manufacturing process, glass substrates are conventionally being handled by insulated robotic manipulators (Figure 1.4) to secure chemical resistance and prevent metallic contamination as much as possible [8,11]. Nevertheless, the inevitable direct mechanical contact between the handling equipment and glass substrate acts as a major source of problems, as it results in contamination due to particulate generation and electrostatic charging of the substrate through tribo-electric effects [14-16]. Electrostatic.

(25) 8. Chapter 1. Introduction. charging of the glass substrate raises its electrostatic potential causing air-borne particles to be attracted to it. The resulting electrostatic discharge damages the devices and constitutes an important factor affecting product yield and device reliability [11].. Figure 1.4: MOTOMAN robot for handling future 10th-generation extra-large LCD glass substrates. Source: Yaskawa Corp.. Transportation of glass substrates between various processing stations in the clean-room is increasingly being performed using conveyors with built-in air bearings (Figure 1.5). The air bearings float the glass substrates on a thin film of pressurized air. Linear motion is realized using e.g. friction wheels or rollers that are in direct contact with the substrate.. Figure 1.5: Air-floating conveyer for transporting glass substrates. Source: Asahi Kohsan Co. Ltd..

(26) 1.2. Potential Applications. 9. As a result, there is minimal amount of surface contact combined with reduced glass deformation. The drawbacks of these systems are that they cannot be used in vacuum environments, possess relatively large footprints and are bulky, and require accurate finishing of the air nozzles. The above described critical problems could be eliminated to a great extent by adopting fully contact-free handling of the glass panels utilizing electrostatic levitation processes. In addition to levitation, conveyance of the panels can also be realized using electrostatic forces. Apart from enhancing contamination control, electrostatic levitation could provide truly uniformly distributed suspension forces, leading to minimal mechanical deformation of the panel, which altogether can be expected to result in significantly improved device reliability and yield. 1.2.3 Nanotechnology Nanotechnology has been hailed as one of the most important technologies in the 21st century, together with information technology and biotechnology. Nanotechnology is defined as the creation and utilization of materials, devices, and systems through the control of matter on the nanometer-length scale, that is, at the level of atoms, molecules, and supra-molecular structures [17]. It is widely accepted that the birth of the concept of nanotechnology is marked by Nobel Laureate Richard Feynman’s now famous lecture held in 1959 entitled There’s plenty of room at the bottom [18]. In this lecture he envisioned the fabrication of materials and devices at the atomic/molecular scale. For this to happen Feynman put forward that a new class of miniaturized instrumentation would be needed to manipulate and measure the properties of these nanostructures. Because of their novel properties, nanostructured materials offer potential applications in electronics, biotechnology and information technology. The capability to handle matter with dimensions in the submicron and lower range is indispensable in nanotechnology and is fundamental to scientific disciplines as diverse as materials science, chemistry, physics, engineering, medicine, and biology. The main approach to making nanostructures is the so-called “bottom-up” approach where nanostructures are assembled from particles, ultimately atoms or molecules, using chemical techniques. This “bottom-up” approach is often referred to as molecular engineering. Central to molecular engineering is the process of self-assembly of atoms into structures and in particular the problem of artificial self-replication and integration [17]. Generally, handling may involve, for example, sorting (conducting) dielectric particles with respect to size or dielectric properties. Typical “top-down” mechanically oriented methods that have been applied are, for example, based on downsized mechanical grippers [19]. Apart from the tremendous efforts required to micro-fabricate these three dimensional silicon-based structures, problems, inherent to mechanical handling, arise among which are detrimental adhesive capillary, Coulomb and van der Waals forces..

(27) 10. Chapter 1. Introduction. Moreover, contacting micro-particles mechanically can result in undesirable side-effects; for example, touching biological cells can trigger complex chains of physiological reactions. Therefore, top-down techniques capable of handling either many particles simultaneously or individual particles in a fully contact-free manner are to be preferred. Dielectrophoresis offers a solution and has already been applied successfully to biological cells and other dielectric particles [20, 21]. It is based on the interaction of a nonuniform electric field with dielectric particles suspended in aqueous liquids. This field induces a dipole on the dielectric particle, which interacts with the nonuniform field and, as a result, produces a dielectrophoretic force on the particle. The magnitude of the dielectrophoretic force is related to the particle’s size, dielectric properties, and conductivity, as well as the electric and hydrodynamic properties of the surrounding aqueous medium. The majority of dielectrophoresis studies reported in the literature employs AC electric fields to produce the dielectrophoretic forces on particle suspensions. In the case that the applied field is alternating, the polarization of a particle is frequency dependent as the time needed by the movement of charge to form a dipole is finite. Wang et al. derived the general time-averaged dielectrophoretic force acting on a polarized, conductive particle in a nonuniform AC electric field [57,58]. His equation reveals that the dielectrophoretic force consists of two independent terms: •. A term associated with the real (in-phase) component of the induced dipole moment in the particle and the spatial nonuniformity of the electric field magnitude.. •. A term associated with the imaginary (out-of-phase) component of the induced dipole moment in the particle and the spatial nonuniformity of the electric field phase. This term only exists if the particles are subjected to travelling-wave fields. The force component related with this term can either propel the particle in the same or in the opposite direction of travel of the field.. In the context of levitation we now consider the case that the field is non-rotating, i.e. there is no travelling-wave component. The time-averaged dielectrophoretic force is then given by the expression [57,58] ଶ ⟨ୈ୉୔ ⟩ = 2π୫ ଷ Re େ୑ ∇

(28) ୰୫ୱ (1.1) , where ୫ denotes the permittivity of the liquid medium in which the particles are suspended, is the radius of the particle,

(29) ୰୫ୱ is the rms value of the electric field strength, and େ୑ denotes the Clausius-Mossotti factor which is given by ∗ ୮∗ − ୫. େ୑ = ∗ , ∗ ୮ + 2୫. (1.2).

(30) 1.3. Literature Overview. 11. ∗ are the complex permittivities of the particle and its suspending medium, where ୮∗ and ୫ respectively, defined as ௞∗ = ௞ − ௞ ⁄, = , . Here denotes the electrical conductivity and is the angular frequency of the applied electric field. The sign of the factor Re

(31) େ୑ plays a key role in realizing levitation. In the case that Re

(32) େ୑ < 0, ⟨ୈ୉୔ ⟩ would direct particles upwards where the field strength exhibits its minima, thus repelling them. This is also referred to as negative dielectrophoresis. The implication of this is that the levitation process would be passive by nature, i.e. unlike macroscopic levitation no active feedback control would be required to stabilize the suspended particles. It is common that the frequency spectrum of Re

(33) େ୑ shows positive values at low frequencies and negative values at higher frequencies. The crossover frequency is typically in the MHz range. To assess the applicability of negative dielectrophoresis under conditions typical for the potential macroscopic applications discussed in the previous sections we make use of the following two limiting cases: ୮ − ୫ ୮ − ୫ lim Re

(34) େ୑ = , lim Re

(35) େ୑ = . (1.3) ఠ→଴ ఠ→ஶ ୮ + 2୫ ୮ + 2୫. As surrounding medium either air or vacuum is used. Therefore we have the conditions ୮ > ୫ and ୮ > ୫ which leads to limఠ→଴ Re

(36) େ୑ > 0 and limఠ→ஶ Re

(37) େ୑ > 0. In other words there is no crossover in the frequency spectrum of Re

(38) େ୑ and hence no repulsion can be achieved for the envisioned macroscopic applications.. 1.3 Literature Overview In the following literature overview we restrict ourselves to work exclusively devoted to the contact-free handling using actively controlled attractive electrostatic fields. Despite the fact that research on (sub)micron-scale levitating devices is outside the scope of this thesis they will be included in the overview as well. As mentioned in the introduction, juxtaposed with magnetic levitation, relatively little work has been performed in the field of electrostatic levitation of macroscopic objects. One of the earliest applications of electrostatic levitation has been reported by Knoebel, who suspended an aluminum rotor in a vacuum gyroscope for use in spacecraft navigation instrumentation [24]. In the field of materials processing noncontact measurement of the electrical resistivity of molten metal samples has been studied by means of electrostatic levitation and noncontact heating of the sample in a vacuum chamber [25]. In the nineties, a comprehensive research program on electrostatic levitation, targeting applications in clean-room and vacuum manufacturing technology, was launched by Prof. Toshiro Higuchi at the Kanagawa Academy of Science and Technology (KAST). The work presented in this thesis was partially performed within the framework of this research program..

(39) 12. Chapter 1. Introduction. The electric suspension of silicon wafers and aluminum disks were initially reported [30,31]. Furthermore, the successful suspension of quartz and soda-lime glass panels and disks, which are in fact (lossy) dielectrics, has been demonstrated by adopting a novel stator electrode structure possessing many boundaries over which potential differences are generated [33,34]. In analyzing the dynamic behavior of the levitator a very simple lumped RC model was used which assumes a uniform electrostatic field. The work on the suspension of lossy dielectrics was subsequently extended by adding propulsion [35]. An electrostatic variable-capacitance motor [36] and an induction motor [37] were also studied in which the rotor is levitated and rotated simultaneously using specially designed electrostatic electrode structures. Simple and cost-effective levitator concepts based on switching control schemes were also developed [38,39]. Besides levitation, combined levitation and propulsion has been investigated as well in the KAST research program. This led to a working prototype of a linear electric levitator capable of transporting an aluminum hard disk in the lateral direction [32]. The lateral electrostatic force exerted on levitated (semi)conducting disks/panels plays an important role in both stationary and transportation devices [30,31,32]. In the former it acts as a passive restoring force in the event of externally applied lateral disturbances or inertial forces when accelerating the stator. In the latter it provides the propulsion forces. The lateral force is produced by fringing fields and is much weaker than the suspension forces. Outside of the KAST research program, a method for automatic release of a levitated object without external control commands in electrostatic levitation systems was reported in Ref. [40]. The same authors proposed tilting control as a means to increase lateral stability of a levitated aluminum disk during lateral acceleration [41]. Furthermore the development of a high-voltage dc power amplifier for use in electrostatic levitation systems has been reported [42]. High-voltage dc power amplifiers are commonly employed in levitators to amplify the low output voltage signals of the feedback controller in order to produce the high-voltage signals necessary for suspension. Han et al. [43] proposed a nonlinear compensation scheme to deal with the nonlinear, uncertain dynamics of electrostatic bearing systems. Their nonlinear compensation algorithm was experimentally investigated on a three-degree-of-freedom electrostatic bearing supporting a spherical rotor. In a subsequent study a suspension control scheme without bias voltage was developed to achieve a steady levitation of the spherical rotor [44]. We conclude this overview with examples of micro- and nano-scale realizations of the feedback-control based suspension schemes used in the macroscopic levitators. One of the first to report on micro-electric bearings were Kumar et al. who succeeded in the contactfree suspension of a small flat plate covered with a thin copper layer [26]. Furthermore, a micro-motor was proposed in which the rotor is stably levitated using three independent resonant circuits [27]. Electrically levitated rotors were also demonstrated in a micromachined gyroscope and in a variable-capacitance micro-motor [28,29]. Jones developed feedback-controlled two-electrode devices for levitating biological cells [46]. The same.

(40) 1.4. Aim and Scope of Thesis. 13. authors also studied the use of feedback-controlled dielectrophoretic forces generated by a cone-plate electrode structure for stably levitating single biological cells [47].. 1.4 Aim and Scope of Thesis The central theme in this thesis is the development of devices in which attractive electric fields are feedback controlled to achieve contact-free suspension of conducting and dielectric materials. This principle is universally applicable regardless of the object’s dimensions. Generally speaking, however, implementing it on downscaled or (sub)microndevices is easier to realize chiefly because the applied voltages are in a regime that can be generated easily using standard integrated circuit components. The scope of this thesis is restricted entirely to electrostatic levitation processes at the macroscopic scale. Ultimately, the aim of the electrostatic levitator designs developed in this thesis is to enhance contamination control and improve device yield in semiconductor and FPD manufacturing. The design and implementation of the levitators developed during the course of the research follows a typical mechatronic approach as it integrates specific areas of mechanical engineering, electrical and computer engineering. In order to provide a realistic impetus to the underlying handling technologies, the philosophy underpinning the designs of these levitators is sought to adhere to the following guiding principles: •. Cost-effectiveness and simplicity of construction1.. •. Small footprint and reduced exposed surfaces.. •. Scalable to many degrees of freedom multi-electrode levitators without incurring excessive and prohibitive system costs.. The first two guiding principles promote cleanliness as they result in reduced (airborne) molecular contamination by the levitator from particles caused by shedding and flaking, and from outgassing. The main research objectives of this thesis can now be formulated as follows:. 1. 1.. Demonstrate theoretically and experimentally that the array of levitators designed according to the first guiding principle are feasible without sacrificing suspension performance.. 2.. Contribute to a better understanding of the weak lateral electrostatic force on the levitated object by studying it both theoretically and experimentally, and increase the associated lateral stiffness by improving the stator electrode design.. 3.. Develop a capacitive sensor for measuring the displacement of the levitated object which can be integrated into the stator electrode. This serves the objective. We take the liberty of quoting Leonardo da Vinci: "Simplicity is the ultimate sophistication.".

(41) 14. Chapter 1. Introduction of preserving the planar structure of the stator which ties in with the second guiding principle. While designing the sensor, special attention should be paid to minimizing the influence of stray capacitances on the measurement. 4.. Develop an accurate analytical model describing the dynamics of the electrostatic field and forces exerted by a regular array of bar electrodes on a lossy dielectric plate. Based on this model we intend to gain an improved understanding of the influence of key stator electrode parameters and electrical properties of the dielectric plate on the levitation force dynamics.. These research objectives should culminate in the development of a rigorous analytical modeling framework along with design rules that would support the systematic and optimal design of the presented electrostatic levitators.. 1.5 Outline of Thesis Chapters 2, 3, 4, 6 and 7 describe various macroscopic electric suspension devices. Chapter 2 introduces the principle of a general electrostatic levitator for the contact-free suspension of conducting disks or panels, which includes the electrode structure, feedback control design and electromechanical modeling. The structure of the presented levitator structure can be considered as conventional, that is, it consists of a feedback controller, high-voltage dc power amplifiers, displacement sensors, and a stator electrode structure. Simple guidelines based on the assumption of uniform electric fields are established for the design of suitable stator electrode patterns and applied voltage distributions, which guarantee electric potentials on disks/panels close to zero volts. Chapter 3 deals with the passive stabilizing lateral electric forces exerted by the fringing fields on the levitated object. A measurement apparatus specially designed and built for measuring these weak forces is presented. Furthermore, an improved stator electrode design aiming at increasing the lateral electric forces is described. Experimental results demonstrate greatly improved lateral suspension stiffness characteristics. Chapter 4 investigates the integration of capacitive sensing elements onto the stator electrodes for the purpose of displacement measurement of the levitated object. As a result, one obtains a compact stator construction exhibiting an improved level of cleanliness of the levitator. Two different capacitive sensor designs are studied. A charge-discharge capacitive transducer design with improved stray capacitance immunization capabilities is developed. In addition a simple and cost-effective capacitance gap sensor using the oscillation principle is designed and realized. These features makes this particular sensor fit nicely into the cost-effective levitator design philosophy presented in chapter 6. Chapter 5 is devoted to the development of an analytical model for the electrostatic levitation field between a lossy dielectric plate and a generic stator electrode structure.

(42) 1.5. Outline of Thesis. 15. consisting of a regular planar array of parallel bar electrodes. Atmospheric humidityrelated surface conduction on the plate is explicitly taken into account in the model since it has a profound effect on the field dynamics. Based on this model, the electrostatic levitation force is calculated using the Maxwell stress tensor formulation. The levitation force dynamics are investigated by evaluating the transient response of the field under a step in the applied voltages. The associated rate of electric charge build up on the plate is theoretically predicted for soda-lime glass substrates, typically used in the manufacturing of LCDs, as a function of electrode geometry, air gap separation, ambient humidity, and step voltage magnitudes. Chapter 6 presents a relay driven switching control based electrostatic levitator whose development was ultimately driven by the search for cost-effective and simple electrostatic levitators. The repercussions of this design are far reaching as it provides a practical basis for the realization of large scale multi-electrode levitators for the suspension of flexible sheet-like objects. A full mathematical model describing the kinematics, dynamics and suspension forces is developed for the suspension of disks. Based on this model, a closedloop stability analysis is carried out for a one-degree-of-freedom model using two different methods, i.e. the classical describing function method and Fillipov’s method. Experimental results for various objects consisting of different materials, i.e. a silicon wafer, glass substrate and highly flexible aluminum sheet, are presented. The levitator design proposed in Chapter 7 is inspired by the relay controlled levitator presented in Chapter 6. Its design deviates fundamentally from the latter in that it enables the inclusion of active damping into the system by means of, for example, derivative control. This asset is of great advantage in vacuum environments where the absence of air squeeze film damping can lead to unacceptably large oscillation amplitudes in the position of the levitated object. Despite this added feature the proposed levitator largely retains the cost-effectiveness and simplicity of the relay controlled levitator concept. Similar to the relay controlled levitator, the classical describing function method and Fillipov’s method are both employed in analyzing the closed-loop stability of a one-degree-of-freedom model. Chapter 8 summarizes the main results of this work and presents a brief outlook on future research directions..

(43) 16. Chapter 1. Introduction.

(44) Chapter 2 Design and Analysis of an Electrostatic Suspension System 2.1 Introduction The primary objective of this chapter is to introduce the main functional blocks of a general electrostatic suspension system and provide a mathematical model describing its electromechanical dynamics. Due to the tight interconnection existing between electrostatics and electromagnetism, it is not surprising that the functional principle of an electrostatic suspension system reveals a strong analogy with the well-known active magnetic suspension systems that are based on controlled dc electromagnets. Both types of suspension systems necessitate the use of closed-loop feedback control to stabilize the position and attitude of the suspended object. This necessity will be explained analytically on the basis of a simple one-DOF electrostatic actuator suspending a conducting, rigid body object while being operated in an open-loop fashion. Pertaining to the geometries of the suspended objects, only basic thin circular (disks) and rectangular shaped (panels) bodies are considered. These objects may either be conducting or semiconducting. The principle of electrostatic levitation is elucidated using a one-DOF levitator which is followed by the presentation of a levitator that is capable of actively suspending a disk in three degrees of freedom. For this levitator, whose stator electrode consists of four identical planar circular segment electrodes, we shall derive an elaborate mathematical model of its electromechanical dynamics. Furthermore, this chapter provides guidelines on selecting the applied voltage distribution coupled with the design of the stator electrode pattern in order to establish a zero volt electrostatic potential on the suspended object. This particular condition is highly desired in clean-room applications where contamination of the suspended object has to meet stringent requirements. A nonzero electrostatic potential on the surface of the suspended object would obviously result in the attraction of contaminating foreign particulates due to electrostatic effects. Clean-room applications which could benefit from this condition are, e.g., in the area of silicon wafer and LCD glass substrate handling. Based on the developed theory a prototype electrostatic suspension device was designed and constructed for the levitation of 4-inch silicon wafers. Suspension experiments have been carried out successfully on this prototype levitator and their data will be presented. Although an analytical and theoretical treatment of electrostatic suspension of flexible bodies lies outside the scope of this thesis we will nevertheless touch briefly on this interesting topic and defer the presentation of experimental results obtained on an actual functioning prototype suspension device until chapter 6..

(45) 18. Chapter 2. Design and Analysis of an Electrostatic Suspension System. 2.2 The Stator Electrode as Electrostatic Force Actuator 2.2.1 Basic Relationships In an electrostatic suspension system, the stator electrode constitutes the (electrostatic) force actuator. Structurally, it is composed of individual stator electrodes whose number depends on the number of DOFs of the suspended object that have to be regulated. Generating an electrostatic field can be most easily performed by arranging the individual stator electrodes as planar electrode structures, forming parallel-type of plate capacitors with the suspended object. This is schematically illustrated in Figure 2.1 using a 1-DOF system consisting of an electrostatic force actuator combined with a conducting object. The electrostatic actuator consists of two rectangular, perfectly conducting electrodes Eଵ and Eଶ , both having an effective suspension area ‫ܣ‬. Note that the assumption that the suspended object consists of conducting material implies that its surface is an equipotential surface. It is therefore labeled as the third electrode Eଷ in this system of conductors. Upon applying electrostatic potentials ߶ଵ and ߶ଶ to the stator electrodes, an electrostatic field is created instantaneously between the electrodes and the suspended object, and electrostatic charges build up on the surfaces of the electrode and suspended object facing each other. In this simple example, the suspended object is assumed to undergo vertical movements ‫ݖ‬ only; therefore, angular motions are excluded. Between each of the stator electrodes and the suspended object capacitances are formed. φ1. φ2. E2. E1. −−−−−−−−−− d. C2d. C1d. − − − − − − − − − − φd Z. E 3: Conducting object. zc X. Figure 2.1: One-DOF electrostatic force actuator suspending a conducting object.. In general, the capacitance is a function of the electrode geometry and dielectric permittivity of the medium filling the gap between the stator and suspended object. Its definition is given by.

(46) 2.2. The Stator Electrode as Electrostatic Force Actuator ௜௝ =. 19. ௜௝ , ௜ − ௝. (2.1). where ௜௝ is the capacitance between electrode and , ௜௝ is the charge on electrode . induced by the potential difference ௜ − ௝ ; ௜ represents the potential on electrode and. ௝ represents the potential on electrode . Applying Eq. (2.1) to the one-DOF system of Figure 2.1 yields ଵୢ =. ଵୢ ଶୢ , ଶୢ = , ଵ − ୢ ଵ − ୢ. (2.2). where the subscript “d” denotes the suspended object. Evaluation of the capacitance for any system consisting of conductors on the basis of Eq. (2.1) can be done using the fourth law of Maxwell, which is also known as Gauss’s law, ∙ =

(47) ௜௝ ,. (2.3). ௜ − ௝ = ∙ ,. (2.4). ௌ೔. ௏೔. and the well-known relationship. ௅೔ೕ. where the electric flux density is related to the electric field intensity according to the linear relationship = , in which is the permittivity of the medium, the elemental vectors and designate the well-known element of surface and line in magnitude and orientation, respectively,

(48) ௜௝ is the electric charge density on electrode induced by the. potential difference ௜ − ௝ , ௜௝ is any path from electrode E௜ to electrode E௝ , and ௜. denotes the volume of electrode E௜ enclosed by the surface S௜ . Inserting Eqs. (2.2) and (2.3) into Eq. (2.1) yields ௜௝ =. ∮ௌ ∙ . ೔. ௅ ∙ ೔ೕ. =. ∮ௌ ∙ . ೔. ௅ ∙ . .. (2.5). ೔ೕ. In accordance with practical electrostatic suspension systems the suspended object and the stator electrodes are assumed to be closely spaced such that the air gap separation is small compared with the transverse dimensions. This condition allows us to neglect the electric fringing fields, which exist at the edges of the suspended object and do not pass straight from the stator electrodes to the suspended object. Therefore, a uniform electric field is assumed, which leads to the well-known relationship ௝ୢ = ௝ ⁄ ௝ ,. (2.6). where is the index number of the suspended object, ௝ is the area of electrode , and ௝ is the gap between electrode and the suspended object..

(49) 20. Chapter 2. Design and Analysis of an Electrostatic Suspension System. Remark 1 The local electric surface charge distribution ୱ , induced on the suspended object can be calculated if the electric field is known. The latter can be solved from the Laplace equation with proper boundary conditions. On the basis of the general electroquasistatic boundary continuity condition ∙ ଵ ଵ − ଶ ଶ = ୱ ,. (2.7). where ଶ = 0 in the case of perfectly conducting media, the following relationship between the surface charge distribution and potential can be derived

(50) , , , ௭ୀ଴. ୱ , = ୬ , , = 0 = −. (2.8). where the derivative of the potential should be taken along the outward normal on the surface of the suspended object. Consider now the following stator voltage distribution for the given one-DOF system:

(51) ଵ = + and

(52) ଶ = −. Using Eq. (2.4) we obtain ୢ. ୢ. ୉భ. ୉భ. ∙ = − ∙ ,. (2.9). or equivalently

(53) ଵ −

(54) ୢ = −

(55) ଶ −

(56) ୢ , which leads to a disk potential of zero, i.e.

(57) ୢ = 0. 2.2.2 Design of Stator Electrode Structure and Voltage Distribution In this section we shall derive general expressions for the suspension force using the energy method embodied by Eq. 2.9. To compute the electrostatic force output, it is imperative to know the potential of the object as a function of the electric potential

(58) ௞ and the capacitance ௞ୢ associated with stator electrode E௞

(59) ୢ =

(60) ୢ