#### Document Type

Dissertation

#### Date of Award

Spring 5-31-2004

#### Degree Name

Doctor of Philosophy in Materials Science and Engineering - (Ph.D.)

#### Department

Committee for the Interdisciplinary Program in Materials Science and Engineering

#### First Advisor

Kenneth Rudolph Farmer

#### Second Advisor

Durgamadhab Misra

#### Third Advisor

Ken K. Chin

#### Fourth Advisor

Zhixiong Xiao

#### Fifth Advisor

Baoqing Li

#### Abstract

In this dissertation, theoretical analyses and optimization studies are given for three kinds of MEMS devices: thermal bimorph cantilevers, electrostatic torsion actuators, and variable capacitors. Calculation, simulation, and experimental data are used to confirm the device behavior and demonstrate the application of the design approaches.

For thermal bimorph cantilevers, an analytical model is presented which allows theoretical analysis and quantitative optimization of the performance based on material properties and device dimensions. Bimorph cantilevers are divided into two categories for deflection optimization: either the total thickness is constant, or the cantilever has one constant and one variable layer thickness. The optimum equations are then derived for each case and can be used as design rules. The results show that substantial improvements are possible over existing design approaches. Other parameters like static temperature distribution, power consumption, and dynamic behavior are also discussed, as are design tradeoffs such as feature size, application constraints, fabrication feasibility, and cost.

The electrostatic torsion actuator studies are conducted for two device types: round and rectangular. The first case describes an analytical study of the pull-in effect in round, double-gimbaled, electrostatic torsion actuators with buried, variable length electrodes, designed for optical cross-connect applications. It is found that the fractional tilt at pull-in for the inner round plate in this system depends only on the ratio of the length of the buried electrode to the radius of the plate. The fractional tilt at pull-in for the outer support ring depends only on the ratio of the length of the buried electrode to the outer radius of the ring and the ratio of the ring's inner and outer radii. Expressions for the pull-in voltage are determined in both cases. General relationships are also derived relating the applied voltage to the resulting tilt angle, both normalized by their pull-in values. Calculated results are verified by comparison with finite element MEMCAD simulations, with fractional difference smaller than 4% for torsion mode dominant systems. For the second case, a fast, angle based design approach for rectangular electrostatic torsion actuators based on several simple equations is developed. This approach is significantly more straightforward than the usual full calculation or simulation methods. The main results of the simplified approach are verified by comparing them with analytical calculations and MEMCAD simulations with fractional difference smaller than 3% for torsion mode dominant actuators. Also, good agreement is found by comparison with the measured behavior of a micro-fabricated full-plate device.

In the last topic, ultra-thin silicon wafers, SU-8 bonding and deep reactive ion etching technology have been combined for the fabrication of folded spring, dual electrostatic drive, vertical plate variable capacitor devices with displacement limiting bumpers. Due to the presence of the bumpers, the variable capacitor with parallel plate drive electrodes has two tuning voltage regimes: first a parabolic region that achieves roughly a 290% tuning range, then a linear region that achieves an additional 310%, making the total tuning range about 600%. The variable capacitor with comb drive electrodes has a parabolic region that achieves roughly a 205% tuning range, then a linear region that achieves an additional 37%, making its total tuning range about 242%. The variable capacitors have Q factors around 100 owing to the use of silicon electrodes other than lower resistivity metal.

#### Recommended Citation

Peng, Wuyong, "Optimization studies of thermal bimorph cantilevers, electrostatic torsion actuators and variable capacitors" (2004). *Dissertations*. 636.

https://digitalcommons.njit.edu/dissertations/636