Nonlinear Modeling of MEMS Fixed-Fixed beams

📝 Abstract

This dissertation presents a new coupled electro-mechanical model that is an improvement on the classical parallel-plate approximation. The model employs a hyperbolic function to account for the beam deformed shape and electrostatic field. Based on this, the model can accurately calculate the deflection of a fixed-fixed beam subjected to an applied voltage and the switch capacitance-voltage characteristics without using parallel-plate assumption. For model validation, the model solutions are compared with ANSYS finite element results and experimental data. It is found that the model works especially well in residual stress dominant and stretching dominant cases. The model shows that the nonlinear stretching can significantly increase the pull-in voltage and extend the beam maximum travel range. Based on the model, a graphene nanoelectromechanical systems (NEMS) resonator is simulated and the agreement with the experimental data is excellent. The proposed coupled hyperbolic model demonstrates its capacity to guide the design and optimization of both RF microelectromechanical system (MEMS) capacitive switches and NEMS devices.

💡 Analysis

This dissertation presents a new coupled electro-mechanical model that is an improvement on the classical parallel-plate approximation. The model employs a hyperbolic function to account for the beam deformed shape and electrostatic field. Based on this, the model can accurately calculate the deflection of a fixed-fixed beam subjected to an applied voltage and the switch capacitance-voltage characteristics without using parallel-plate assumption. For model validation, the model solutions are compared with ANSYS finite element results and experimental data. It is found that the model works especially well in residual stress dominant and stretching dominant cases. The model shows that the nonlinear stretching can significantly increase the pull-in voltage and extend the beam maximum travel range. Based on the model, a graphene nanoelectromechanical systems (NEMS) resonator is simulated and the agreement with the experimental data is excellent. The proposed coupled hyperbolic model demonstrates its capacity to guide the design and optimization of both RF microelectromechanical system (MEMS) capacitive switches and NEMS devices.

📄 Content

Nonlinear Modeling of MEMS Fixed-Fixed Beams

by

Xi Luo

Presented to the Graduate and Research Committee of Lehigh University in Candidacy for the degree of Doctor of Philosophy

in

Electrical Engineering

Lehigh University May, 2016 ii

Approved and recommended for acceptance as a dissertation in partial fulfillment of the requirements for the degree of Doctor of Philosophy.

Date

Dr. James C. M. Hwang, Dissertation Advisor, Chair

Accepted Date

         Committee Members: 

                            Dr. Douglas Frey 

                                  Dr. Svetlana Tatic-Lucic 

                              Dr. Herman F. Nied 

                               Dr. Richard P. Vinci 

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Acknowledgments

I greatly appreciate my advisor Professor James C. M. Hwang’s guidance, support, and encouragement through my Ph.D. study. He provided me a wide range of advanced research topics and also trained me to be an independent researcher by working on these topics. I also would like to thank Professor Herman F. Nied for his valuable help and suggestions on my dissertation. Moreover, I would like to thank Professor Douglas Frey, Professor Svetlana Tatic-Lucic, and Professor Richard P. Vinci for their help and support. I am grateful to my former and current colleagues at Compound Semiconductor Technology Laboratory (CSTL), particularly, Dr. Subrata Halder, Dr. David Molinero, and Dr. Cristiano Palego who provided valuable contribution to my growth in research. I am also thankful to the help from Dr. Weike Wang, Dr. Laura Jin, Dr. Yaqing Ning, Vahid Gholizadeh, Mohammad Asadi, Xiao Ma, Zhibo Cao and Kevin Xiong, who have made my graduate research at CSTL an enjoyable experience. I would also like to express my gratitude to Dr. Charles Goldsmith at MEMtronics Corp. for providing precious device samples and helpful discussions.
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I owe my deepest gratitude to my family members, my wife Jin Wang, my parents and parents-in-law. Without your support and sacrifice, I cannot go this far.

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Table of Contents List of Figures …………………………………………………………………………………………….. vii Abstract ……………………………………………………………………………………………………. 1 Chapter 1 Introduction ………………………………………………………………………………….. 3 1.1 RF MEMS Capacitive Switches Background ……………………………………. 4 1.2 Pull-in Voltage Calculation …………………………………………………………….. 5 1.3 Nonlinear Stretching Effect …………………………………………………………….. 9 1.4 Small Length Scale Effect …………………………………………………………….. 10 1.5 Organization of the Dissertation ……………………………………………………. 11 References ……………………………………………………………………………………………. 12 Chapter 2 Theory and Parallel-plate Models ………………………………………………….. 15 2.1 Comparison of Analytical and Computational Approaches ……………….. 15 2.2 Parallel-plate Assumption in Electromechanical Structure ………………… 19 2.2.1 Parallel-plate Theory and Effect of Length Ratio ……………………….. 19 2.2.2 Effect of Bending and Residual Stress ………………………………………. 23 2.2.3 Nonlinear Elastic Restoring Force ……………………………………………. 38 2.2.4 Geometric Design for Linear Material Behavior ………………………… 43 References ……………………………………………………………………………………………. 51 Chapter 3 Theory and Hyperbolic Models ……………………………………………………… 55 vi

3.1 Hyperbolic Model ……………………………………………………………………….. 55 3.1.1 Limitations on Parallel-plate Approximation ……………………………… 55 3.1.2 Hyperbolic Model and Electrostatic Field ………………………………….. 58 3.1.3 Hyperbolic Model Coefficient Determination …………………………….. 62 3.1.4 Nonlinear Spring Constant and Pull-in Voltage ………………………….. 63 3.2 Effects of Stationary Electrode Thickness and Substrate …………………… 66 References ……………………………………………………………………………………………. 79 Chapter 4 Experimental Validation and Disc

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