Modeling and simulation of the capacitive accelerometer

Table of Contents

1. INTRODUCTION

1.1 Overview of MEMS

1.2 Silicon Micro Accelerometers

1.2.1 Electromechanical Accelerometers

1.2.2 Piezoelectric Accelerometers

1.2.3 Piezoresistive Accelerometers

1.2.4 Electrostatic Accelerometers

1.2.4.1 Electrostatic-Force-Feedback Accelerometers

1.2.4.2 Differential -Capacitance Accelerometers

1.2.5 Resonant Accelerometers

1.3 MEMS Modeling and Simulation

2. ACCELEROMETER: FROM THEORY TO DESIGN

2.1 Operational Principles

2.1.1 Open-Loop Design

2.1.2 Force-Balance Design

2.1.3 Comparisons

2.2 Capacitive Accelerometer

2.2.1 Position Measurement with Capacitance

2.2.2 Noise Analysis

3. MODELING AND SIMULATION OF THE ACCELEROMETER

3.1 Overview of SUGAR

3.2 Nodal Analysis Approach

3.2.1 A simple example of the MEMS structure

3.2.2 Linear Beam Model

3.2.3 Nonlinear Beam Model

3.2.4 Nonlinear Gap Model

3.2.5 Gap Model with Contact Forces

3.3 Simulation Program based on SUGAR

3.4 Simulation Results

3.4.1 Single Capacitive Accelerometer

3.4.2 Differential Capacitive Accelerometer with a Single Beam

3.4.3 Differential Capacitive Accelerometer with Two Symmetric Beams

3.4.4 Two Parallel Beams Accelerometer

3.4.5 Four Symmetric Beams Accelerometer

3.5 Experimental Calibration Set-up and Experimental Results

3.5.1 Fabricated Sensor and Calibration Set-up

3.6 Comparison of the simulation and experimental results

4. CONCLUSIONS

4.1 Concluding Remarks

4.2 Future Work

Research Objectives and Themes

This master thesis investigates the modeling and simulation of various capacitive microaccelerometer structures using the SUGAR tool within a MATLAB environment. The primary research objective is to develop and validate mathematical models for different structural configurations, comparing simulation results against experimental data obtained from fabricated sensors to optimize performance parameters such as sensitivity, resonant frequency, and linear working range.

• Microelectromechanical Systems (MEMS) fabrication and design principles.
• Comparative analysis of open-loop versus force-balance accelerometer designs.
• Nodal analysis and finite element modeling of structural beams and gaps.
• Simulation of capacitive sensing techniques and noise characterization.
• Experimental validation using custom-built calibration systems.

Excerpt from the Book

Summary of Chapters

1. INTRODUCTION: This chapter provides an overview of MEMS technology, including historical development and the diverse applications of silicon microaccelerometers, while categorizing various types of acceleration sensing mechanisms.

2. ACCELEROMETER: FROM THEORY TO DESIGN: This section details the fundamental physics and operational principles of accelerometers, contrasting open-loop and force-balanced design methodologies and their respective performance trade-offs.

3. MODELING AND SIMULATION OF THE ACCELEROMETER: This chapter focuses on the implementation of SUGAR for MEMS modeling, presenting the mathematical derivation of linear and nonlinear beam models, simulation results for various specific sensor structures, and a validation against experimental data.

4. CONCLUSIONS: This section summarizes the modeling outcomes and experimental validations, while offering perspectives on future improvements, particularly regarding advanced structural designs and enhanced sensitivity methods.

Keywords

MEMS, Capacitive Accelerometer, Micro-electromechanical Systems, SUGAR, Nodal Analysis, Finite Element Analysis, Resonant Frequency, Force-Balance, Open-Loop, Silicon Micromachining, Sensitivity, Brownian Motion Noise, Sensor Calibration, MATLAB, Modeling and Simulation

Frequently Asked Questions

What is the primary focus of this research?

The thesis focuses on the accurate modeling and efficient simulation of capacitive microaccelerometers using the SUGAR simulation tool to predict performance characteristics like sensitivity and frequency response.

What are the central thematic areas?

The core themes include MEMS structural design, numerical modeling techniques (nodal analysis), capacitance-based sensing, and the comparison of simulation models with real-world experimental sensor performance.

What is the core research objective?

The primary goal is to establish a simulation-driven design workflow that reduces development costs and time while ensuring accurate performance predictions for complex micro-electromechanical structures.

What scientific methods are applied?

The research employs nodal analysis and ordinary differential equations (ODEs) implemented in MATLAB via SUGAR, alongside experimental validation using a centrifugal acceleration calibration test set-up.

What topics are discussed in the main body?

The main body covers the mathematical derivation of linear/nonlinear beam and gap models, the simulation of various accelerometer topologies (single, differential, parallel, symmetric), and the comparative analysis of simulation vs. experiment.

Which keywords best characterize the work?

Key terms include MEMS, Capacitive Accelerometer, SUGAR, Nodal Analysis, Finite Element Analysis, Sensitivity, and Sensor Calibration.

How does the author handle non-linear effects in the beam models?

The author implements a level-2 nonlinear beam model that accounts for geometric nonlinearities, such as axial shortening and the influence of axial forces on bending stiffness.

Why was the SUGAR tool chosen for this project?

SUGAR was selected because it leverages the MATLAB environment, allowing designers to describe MEMS devices in a netlist format similar to SPICE, making it highly flexible for modeling and optimization.

What role does the "Brownian motion noise" play in the sensor design?

The author identifies Brownian motion noise as a fundamental limit for high-performance silicon accelerometers, noting that it is inversely proportional to the proof mass and thus becomes critical as devices are miniaturized.