MECHANICAL DYNAMICS AND THERMALLY-INDUCED … › edsnu › mcgruer › thesis › ...intermodulation formulations have also been applied to an Ohmic contact RF MEMS switch. The resulting

MECHANICAL DYNAMICS AND THERMALLY-INDUCED

INTERMODULATION IN AN OHMIC CONTACT-TYPE MEMS SWITCH FOR RF AND MICROWAVE

APPLICATIONS

A Thesis Presented

by

Zhijun Guo

to

The Department of Electrical and Computer Engineering

in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

in the field of

Electrical Engineering

Northeastern University Boston, Massachusetts

August, 2007

Table of Contents

Page ii

HTable of Contents

HTable of Contents .............................................................. ii

Abstract.............................................................................. v

List of Figures.................................................................. vii

List of Tables .................................................................. xiii

Acknowledgement .......................................................... xiv

Chapter 1. Introduction.................................................... 1

Chapter 2. Background of RF MEMS Switch................ 3

2.1 History and Development of MEMS Technology............................3

2.2 RF MEMS Switch ............................................................................5

2.2.1 Operation and Category of RF MEMS Switch ...............................................................................5

2.2.2 Performance and Characteristics of RF MEMS Switches ............................................................11

2.2.3 Applications..................................................................................................................................12

2.2.4 Failure Mechanisms and Reliability Issues...................................................................................14

References ............................................................................................18

Chapter 3. Mechanical Dynamics of a MEMS Switch 22

3.1 Dynamic Response of MEMS Switch ............................................22

Table of Contents

Page iii

3.2 Finite Element Analysis (FEA) ......................................................26

3.3 Lumped Parameter Modeling of a Cantilever Beam ......................27

3.4 Geometry of the Microswitch.........................................................30

3.5 Finite Element Modeling................................................................32

3.6 Electrostatic Actuation ...................................................................33

3.7 Squeeze-Film Damping ..................................................................34

3.8 Effect of Perforation .......................................................................39

3.9 Nonlinear Contact Model with Adhesion .......................................43

3.10 Dual-Pulse Scheme for Actuation ................................................45

3.11 Results and Discussion .................................................................50

3.11.1 Simulation Results ......................................................................................................................50

3.11.2 Comparisons Between Experiments and Simulations ................................................................58

Chapter 4. Intermodulation Distortion......................... 70

4.1 Intermodulation Effect....................................................................71

4.2 Theoretical Analysis of Intermodulation Distortion.......................74

4.3 Thermally-Induced PIM in MEMS Switch ....................................77

4.4 Design of a Model System .............................................................80

4.4.1 Design Considerations ..................................................................................................................80

4.4.2 Microfabrication ...........................................................................................................................81

4.4.3 Mathematical Analysis .................................................................................................................84

Table of Contents

Page iv

4.5 Results and Discussion ...................................................................96

4.5.1 Model Predictions.........................................................................................................................96

4.5.2 Static and Transient Electrical Resistance ....................................................................................98

4.5.3 Comparison Between Experiment and Simulation .....................................................................102

4.5.4 Prediction of Intermodulation in an RF MEMS Switch .............................................................106

References ..........................................................................................109

Chapter 5. Summary and Future Work ..................... 112

5.1 Dynamic Simulation.....................................................................112

5.2 Intermodulation Distortion ...........................................................114

Appendix A.................................................................... 117

Abstract

Page v

Abstract

RF MEMS switches have demonstrated superior electrical performance compared

with semiconductor switches. However, the failure mechanisms of the microswitch are

not yet fully understood.

We first developed a full dynamic model based on the built-in capabilities of

ANSYS® in combination with a finite difference method for squeeze-film damping. The

model includes the real cantilever structure, electrostatic actuation, the 2-D non-uniform

squeeze-film damping effect, and a nonlinear spring to model the contact tip impact on

the drain.

Meanwhile, we developed an analytical model for designing a dual-pulse

actuation scheme for the microswitch in an effort to optimize its dynamics during

operation, i.e. fast closing, minimum bouncing and oscillation, and gentle contact or

reduced impact force. Simulation results show that switch bounce has been dramatically

reduced or completely eliminated by using the open-loop dual-pulse actuation method.

Moreover, the impact forces have also been reduced as a result of the reduced velocity on

initial contact. The experiment is consistent with the simulation. However, it is found that

the reduction in bounce is very sensitive to the pulse voltages and the times of the dual-

pulse.

Second, the thermally-induced intermodulation distortion has been investigated

both theoretically and experimentally in a test structure. It is shown that the thermally-

induced intermodulation distortion can be predicted from the device geometry, the

thermal and electrical conductivities of the materials, and the difference frequency of a

Abstract

Page vi

two-tone input signal. The intermodulation is largest in the low difference frequency

limit. As the difference frequency is increased to a value which is comparable to the

reciprocal of the thermal time constant of the device, the intermodulation distortion starts

to decrease rapidly, approaching zero at high difference frequencies. In the high

frequency regime, the thermal conductivity of the substrate is the dominant material

property for intermodulation distortion.

The predictions agree well with the experimental measurements. The derived

intermodulation formulations have also been applied to an Ohmic contact RF MEMS

switch. The resulting technique can be conveniently used to predict the thermally-induced

intermodulation and provide guidelines for reducing it in MEMS, NEMS or other

devices.

List of Figures

Page vii

List of Figures

Figure 2-1 An example of a typical three terminal MEMS switch..................................... 6

Figure 2-2 A metal-to-metal contact-type RF MEMS switch ............................................ 9

Figure 2-3 (a) An example of capacitive MEMS RF switch and (b) the electrical CRL

circuit ................................................................................................................................ 10

Figure 2-4 Schematic representation of switches in a series and shunt configuration ..... 10

Figure 2-5 (a) and (b) broadside MEMS switches, (c) inline MEMS switch ................... 11

Figure 3-1 Dynamic behavior of a RF MEMS switch, the step curves are for the step

voltage for actuation. The traces are recorded using oscilloscope which show the transient

‘in contact’ and ‘out of contact’ after actuation [see Reference (3)] ................................ 25

Figure 3-2 Side view of a typical cantilever beam ........................................................... 27

Figure 3-3 The lumped mechanical model for a cantilever beam. ................................... 28

Figure 3-4 Gap of the cantilever vs. applied voltage ........................................................ 29

Figure 3-5 The electrostatic force and spring force vs. normalized gap for a voltage-

controlled electrostatic actuator. ....................................................................................... 30

Figure 3-6 SEM micrograph of the Northeastern University MEMS switch. .................. 31

Figure 3-7 The top view as well as the dimensions of the Northeastern University RF

MEMS switch where w1 = 80 µm, w2 = 10 µm, w3 = 16 µm, w4 = 30 µm, L1 = 30 µm and

L2 = 24 µm. ....................................................................................................................... 32

Figure 3-8 The side view of the microswitch where h1 = 6.3 µm, h2 = 0.6 µm and h3 =

0.38 µm. ............................................................................................................................ 32

Figure 3-9 Grid of finite elements of half of the switch for ANSYS® simulation. .......... 33

List of Figures

Page viii

Figure 3-10 Electrostatic force between two parallel plates ............................................. 34

Figure 3-11 Schematic representation of the finite difference method............................. 38

Figure 3-12 The displacement of the microswitch contact tip vs. the contact force. ....... 45

Figure 3-13 (a) Lumped spring-mass system, (b) a typical profile for a dual-pulse

actuation method, and (c) the desired gradual close for a dual-pulse actuation ............... 46

Figure 3-14 The relationship between the contact force, where ta is the actuation time, ton

is the turn-on time, and Fa is the applied force. Note that ta and ton are normalized to the

period of the first natural frequency, and Fa is normalized to a force Fth which

corresponds to threshold voltage. ..................................................................................... 49

Figure 3-15 The actuation time, ta, and the turn-on time, ton, for a dual voltage pulse

method as a function of actuation voltage Va. Note that ta and ton are normalized to the

period of the first natural frequency, and Va is normalized to the threshold voltage........ 49

Figure 3-16 Contact tip displacements of the switch at actuation voltages of (a) 70V, (b)

74V, and (c) 81V............................................................................................................... 51

Figure 3-17 The simulated contact tip velocity as a function of time for an actuation

voltage of 81V................................................................................................................... 52

Figure 3-18 The top view as well as the dimensions of the Northeastern University RF

MEMS switch where w1 = 80 µm, w2 = 10 µm, w3 = 16 µm, w4 = 30 µm, L1 = 30 µm and

L2 = 24 µm. ....................................................................................................................... 53

Figure 3-19 Comparison of displacements at different locations of the switch (see Figure

3-7) with an actuation voltage of 74 V. ............................................................................ 53

Figure 3-20 (a) Electrostatic force, Fe, (b) squeeze-film damping force, Fd, and (c) the

ratio, ⎜Fd/Fe⎜, of their relative values with an actuation voltage of 74 V. ........................ 54

List of Figures

Page ix

Figure 3-21 Evolution of the squeeze-film pressure distribution across the actuator at an

actuation voltage of 74 V. ................................................................................................. 55

Figure 3-22 Comparison of the simulated microswitch contact tip displacement for cases

with and without the slip-flow effect ................................................................................ 56

Figure 3-23 Impact forces, together with the static contact forces, of the switch with

actuation voltages of (a) 70V, (b) 74 V, (c) 78 V, and (d) 81 V, respectively. ................ 57

Figure 3-24 Displacement of the contact tip using a dual pulse actuation, Va = 88 V, ta =

0.8, Vh = 67 V, and ton = 1.05 µs. The inset shows the impact force for this dual pulse

actuation. The static force for a single-step actuation voltage of 67 V gives a static force

of 15 µN. ........................................................................................................................... 58

Figure 3-25 A schematic representation of the circuit and instruments used for

experimental measurement. .............................................................................................. 59

Figure 3-26 Switch voltages (solid lines) measured by oscilloscope and the corresponding

single step actuation voltages (dotted lines) of 70 V, 74 V, and 81 V.............................. 60

Figure 3-27 Close and open times versus actuation voltage, where Tc1, To1, Tc2, To2 are 1st

close time, 1st open time, 2nd close time, and 2nd open time, respectively. The scattered

dots are experimental results and the lines are from simulations. .................................... 61

Figure 3-28 Comparison between the simulated and measured opening and closing times

for an actuation voltage of 81 V. The horizontal axis is the number of closings or

openings of the switch. ..................................................................................................... 62

Figure 3-29 Comparison between simulation (a) and experiment (b) for a dual pulse

actuation, the insets show the corresponding pulses......................................................... 63

List of Figures

Page x

Figure 3-30 Oscilloscope traces of the switch voltage for a dual voltage pulse actuation

with V h = 74 V, and 81 V, respectively. The inset shows the corresponding actuation

dual voltage pulses. ........................................................................................................... 63

Figure 3-31 Oscilloscope traces of the switch voltage for dual voltage pulses: (a1)

[0.95Va, ta, 0.95Vh, ton], (a2) [Va, ta, Vh, ton], and (a3) [1.05Va, ta, 1.05Vh, ton], where Va =

1.35 Vth, Vh = 1.03 Vth, ta = 0.5 µs and ton = 0.8 µs............................................................ 64

Figure 3-32 Oscilloscope traces of the switch voltage for dual voltage pulses: (b1) [(Va,

0.89ta, Vh, 0.89ton], (b2) [Va, ta, Vh, ton], and (b3) [(Va, 1.11 ta, Vh, 1.11ton], where Va =

1.35 Vth, Vh = 1.03 Vth, ta = 0.5 µs and ton = 0.8 µs............................................................ 65

Figure 3-33 Simulated contact tip displacement of the switch at pressures of 1 atm and 10

atms for an actuation voltage of 74 V. .............................................................................. 66

Figure 4-1 Schematic representation of a nonlinear system ............................................. 74

Figure 4-2 Generation of harmonics in a nonlinear system.............................................. 75

Figure 4-3 Generation of IMD (2nd and 3rd order) in a nonlinear system ......................... 75

Figure 4-4 The 3rd order intermodulation power and output power versus input power. 77

Figure 4-5 The geometry and dimensions of the device, not to scale (dimensions in µm).

........................................................................................................................................... 81

Figure 4-6 The wafer-level layout of the device............................................................... 82

Figure 4-7 The die-level layout of the device................................................................... 82

Figure 4-8 The layout of the device.................................................................................. 82

Figure 4-9 The process flow of the fabrication of the device ........................................... 83

List of Figures

Page xi

Figure 4-10 (a) SEM micrograph of the fabricated device. (b) Cross-sectional view of a

device, not to scale, where W1 = W3 = 160 µm, W2 = 12 µm, H1 = 1062 Å, H2 = 500 µm

and H3 = 1 µm................................................................................................................... 84

Figure 4-11 The three-dimensional view of the device on a pryex glass substrate .......... 85

Figure 4-12 The cross-sectional device-on-substrate schematic showing the heat

generated by tungsten as uniformly distributed over a semicircle with a radius of half the

width of the device, i.e. r1 = W2/2, and is transferred to the ambient through conduction.

The arrows illustrate the isotropic nature of heat conduction, r2 = H2 + H3, not to scale. 86

Figure 4-13 The circuit configuration in which the microstructure is in series with a load

where RS and RL are for source resistance and load resistance, respectively. RSW represents

the resistance of the device that is variable with input power. ......................................... 93

Figure 4-14 (a) The electrical resistance variation showing a sinusoidal-type variation

with a frequency of 2ω, i.e. R = sin(4πft+∆). (b) The input sinusoidal signal with a

frequency of f = 3.2 kHz, i.e. I = I0sin(2πft). .................................................................... 97

Figure 4-15 Variation of the resistance of the device as a function of the frequency. The

input power for a 50 ohm load is 40 mW. ........................................................................ 98

Figure 4-16 The third-order intermodulation distortion of the device as a function of

difference frequency ∆f = f2 - f1, f2 = 10 MHz. The input power for a 50 ohm load is 40

mW.................................................................................................................................... 98

Figure 4-17 The electrical resistance of the device as a function of the measuring current

using a four point probe test setup .................................................................................... 99

Figure 4-18 Block diagram of the measurement system for the transient electrical

resistance of the microscale devices ............................................................................... 101

List of Figures

Page xii

Figure 4-19 The transient electrical resistance of the device with different applied

voltages ........................................................................................................................... 102

Figure 4-20 Block diagram of the experimental setup for the two-tone intermodulation

measurement, where f1 and f2 are two tone signals and SSPA is for solid-state power

amplifier. This figure is provided by Professor Elliot Brown from University of

California at Santa Barbara. ............................................................................................ 103

Figure 4-21 Output spectrum of the intermodulation distortion with respect to the total

input power of the device for cases: (a) Pin = 72 mW, (b) Pin = 36 mW, and (c) Pin = 18

mW, where f1 = 10 MHz, ∆f = f2 - f1 = 6.4 kHz. The measurements were conduced by

Professor Elliot Brown from University of California at Santa Barbara ........................ 105

Figure 4-22 Comparison of the modeled third-order intermodulation distortion with

experimental measurement at different power levels, the frequency of the first tone signal

is f1 = 10 MHz, the difference frequency is ∆f = f2 - f1 = 6.4 kHz. The measurements were

conduced by Professor Elliot Brown from University of California at Santa Barbara... 105

Figure 4-23 The solid model of a quarter of the Ohmic contact-type RF MEMS switch

......................................................................................................................................... 107

Figure 4-24 The simulated electrical resistance of the microswitch as a function of

current which flows through the switch.......................................................................... 107

Figure 4-25 Intermodulation sideband power relative to input power as a function of

power transmitted by switch ........................................................................................... 108

List of Tables

Page xiii

List of Tables

Table 2-1 Comparison of RF MEMS Actuation Mechanism ............................................. 9

Table 3-1 Flow Regimes and Their Knudsen Number ..................................................... 36

Table 4-1 Physical Properties of Device Materials Used in the Model ............................ 84

Acknowledgement

Page xiv

Acknowledgement

I would like to take this chance to express my deepest thanks and gratitude to my

supervisor, Professor Nick McGruer, for his continuous support and guidance throughout

my research in the past five years. His wide knowledge, dedication, and enthusiasm in

research deeply impressed me and taught me what a true scientific researcher should be. I

would also like to express my greatest thankfulness to my advisor, Professor George

Adams. His kind help and wholehearted support are indispensable for the completeness

of my thesis and have benefited me a lot. They support me in every possible way to

enhance my academic capabilities and skills to the highest level. I learned a lot of lessons

and values from their great personality. Professor Elliot Brown from University of

California at Santa Barbara is also greatly appreciated for his help with intermodulation

testing of our fabricated devices. Without his help, this thesis can not be completed.

I would also like to thank my committee member Dean Paul M. Zavracky for his

valuable comments and suggestions. His attendance to my thesis defense is greatly

appreciated, although he has an extremely busy schedule as Dean of School of

Technological Entrepreneurship.

Also, I would thank all faculty, staff and students in the microfabrication lab for

their helpful discussions and friendship.

August 6, 2007

Chapter 1.Introduction

Page 1

Chapter 1. Introduction

This thesis deals with microelectromechanical systems (MEMS) switch

technology for radio frequency (RF) and microwave frequency applications. Since RF

MEMS switches hold great potential for replacement of the existing semiconductor-based

switches as the next-generation switching components in both industrial and military

applications, RF MEMS switches technology has received considerable attention.

However, the RF MEMS switches still have problems such as long-term reliability which

are being intensively investigated. Therefore, the emphasis of this thesis is placed on the

understanding of the dynamics, which are relevant to the reliability of the switch, and the

thermally-induced intermodulation effect in micro-/nano-scale micromechanical devices

for RF and microwave application. The intermodulation distortion due to Ohmic heating

is not well understood and it may become significant when RF MEMS switches are used

for high-power applications which require high fidelity of the signals.

In the first part, the development of a comprehensive mechanical dynamic model

will be the focus of the MEMS switch dynamic study. This model will include all

important aspects such as the real geometry, squeeze-film damping, contact, etc. that are

relevant to the performance of the microswitch. The goal of the dynamic model of the

microswitch is to simulate its dynamic response during operation for a better

understanding of the switch dynamics. Furthermore, the model can be utilized as a design

tool to predict or to optimize the dynamic performance of the Ohmic contact-type switch.

Chapter 1 Introduction

Page 2

The second part of this thesis is on the intermodulation effect due to the Ohmic

heating in microscale mechanical devices. The work consists of development of

analytical models and experimental verification of the predicted results. The emphasis for

the intermodulation effect is on the fundamental understanding of this signal distortion as

a function of difference frequency, materials properties, etc. It is aimed at deriving some

closed-form expressions for convenient prediction of intermodulation distortion in micro-

/nano- scale structures. The organization of this thesis is shown as follows:

Chapter 1 is the outline of the thesis and the primary content and structure of this

thesis is presented. The background of RF MEMS switch technology will be given in

Chapter 2, with an emphasis on the current status of RF MEMS switches and the major

problems which hinder the widespread application of the RF MEMS switches.

Mechanical dynamics of the RF MEMS switches will be concentrated on in Chapter 3.

This includes previous work about modeling and simulation of RF MEMS switches and

development of the comprehensive dynamic model in this thesis. The comparison

between the simulated results and measurements will also be made. In Chapter 4, an

introduction to the intermodulation effect will be first given, then the development of the

analytical model is described, followed by the design, fabrication and testing of the

fabricated micromechanical structures. And last, Chapter 5 is a summary of the thesis and

the future work.

Chapter 2. Background of RF MEMS switch

Page 3

Chapter 2. Background of RF MEMS

Switch

This section provides an overview of the technology of MEMS with an emphasis

on RF MEMS switches. We summarize the current status of the development for RF

MEMS switch and identify the issues which may hinder the widespread applications of

RF MEMS switches.

2.1 History and Development of MEMS Technology

MEMS is the acronym of Micro-Electro-Mechanical Systems. As its name

implies, MEMS is a technology which deals with devices in multiple physical domains

on a micrometer scale. In other words, devices manufactured by using MEMS technology

could involve combined disciplines such as electronic, electrical, mechanical, optical,

material, chemical, and fluids engineering.

The development of this emerging MEMS technology involves integrating

mechanical elements with conventional microelectronics using silicon-based

micromachining technology. The compatibility of MEMS technology with silicon-based

integrated circuits (IC) enables electronics to sense or control environments on the

same chip. The mechanical advantages of MEMS components allow microelectronics to

operate with improved electrical performance. MEMS devices gather information from

its environment by measuring mechanical, acoustics, thermal, biological, optical,

Chapter 2. Background of MEMS

Page 4

magnetic and chemical phenomenon. The MEMS devices can also be utilized to react to

changes in that environment through the mechanical movements of the MEMS actuators

by responding, moving, pumping, positioning and directing. The low cost of MEMS

devices is enabled by batch fabrication which often adopts the infrastructure for IC

fabrication.

In the 1980s, the basic ideas about MEMS were developed although the progress

was slow. The first MEMS device with demonstrated functionality was a gold resonating

MOS gate structure1DPT. The MEMS devices have found applications in the field of sensors

and actuators for automobiles, inkjet printers, and photo projectors. Typical MEMS

devices which were developed in the early days were resonating MOS gate structures1,

surface micromachined switches 2 , crystalline silicon based torsional scanning

micromirrors 3 PT, microaccelerometers4DPT, silicon micromachined gyroscopes5DPT, inkjet printer

headsD6DPT, and piezoresistive silicon-based MEMS pressure sensors.7

With the development of advanced technology for micro/nano-fabrication and the

appearance of information technology (IT) in the 1990s, devices made by means of

MEMS technology have found a great variety of potential applications. One of the most

attractive applications for MEMS devices is that for RF and microwave/millimeter

integrated circuits. RF MEMS technology has been used to manufacture

micromechanical devices which exhibit superior electrical performance over

conventional counterparts, as discussed before. RF MEMS devices are used in systems in

which directing, switching, varying, and routing of signals or reconfiguration of the

system are required.


Page 5

The replacement of conventional devices or supplement conventional devices

with RF MEMS devices enables the operation of systems with enhanced performance. To

date, RF MEMS technology has already been utilized to implement high quality

devices/components such as switchesTPD8DPTP-DDDTD14DTP, high Q varactors (variable capacitor)TPD15DPT, high Q,

highly linear inductors,TPD16 DPT and RF resonatorsTPD17 DPTP-DDTD19 DTP circuits such as filtersTPD20 DPTP,TD21 DTP, voltage-

controlled oscillators (VCO) PD22DPTP,TD23DTP, low-loss phase shifters TPD24DPTP-DDTD26DTP, and subsystems/systems

e.g. high-efficiency power amplifiersTPD27DPT, phased array antennas P�23�,P TPD28DPT and reconfigurable

antennas.29

2.2 RF MEMS Switch

In this section, we will give an overview of microswitches which are intended to

be used for applications in the RF, microwave and millimeter wave regimes. This

includes operation principles, classifications, characteristics, and applications with an

emphasis on promised functionality and the reliability concerns. Also, we will summarize

the current status of RF MEMS switches and identify the issues which must be addressed

properly before they are widely accepted as a mainstream product in industry.

2.2.1 Operation and Category of RF MEMS Switch

RF MEMS switches are devices that use mechanical movement to achieve an

open (“break”) or short (“make”) circuit condition in an RF transmission line or an

antenna. As an example, a three terminal electrostatically actuated MEMS switch is

shown in Figure 2-1. In the 1990s, a MEMS switch, although it was far from mature and

had poor reliability, designed for microwave applications was demonstrated by Dr Larry


Page 6

Larson at Hughes Research LabsTPD30DPT. A group at Northeastern University, sponsored by

Analog Devices Inc, developed an electrostatically actuated, normally open switch that

consists of a surface micromachined electroplated gold cantilever beam and three

electrical terminals: drain, source and gate. When an actuating voltage is applied to the

gate, the resulting electrostatic force deflects the beam, causing its free end to move

against the contacts. By adding a fourth terminal, the design becomes a relay in which

two terminals are used for actuation while the other two are switched.

Figure 2-1 An example of a typical three terminal MEMS switch

When the switch is used as a part of a circuit, the cantilever beam is pulled down,

and the switch closes, ‘making’ a closed circuit. When the beam is lifted up by the

restoring force, the circuit ‘breaks’, thus an open circuit forms. This simple “break” and

“make” mechanism of the microswitch makes it technologically feasible and viable as an

emerging new device.

RF MEMS switches are generally classified according to the actuation mechanism,

contact type, and configuration in a circuit. Actuation mechanisms for MEMS switches

are diverse and invoke several physical phenomena that produce a mechanical movement

from a different physical domain. The primary actuation methods are: electrostatic,

Anchor Cantilever

RF out

RF in Actuation electrode Contacts


Page 7

piezoelectric, thermal, electromagnetic, and bimetallic. The various actuating

mechanisms offer different voltage and current handling capabilities, require different

power levels to actuate, and operate at different speeds. Electrostatic designs are the

fastest and draw the least control power, while thermal actuation delivers high power

handling and larger actuating forces. The following gives a brief description about the

mechanisms and the pros and cons for any individual mechanism.

Electrostatic: this mechanism is the commonly used actuation scheme in RF

MEMS mainly due to its ease of technological implementation, no off-state power and

very little power consumption during switching, and compatibility with normal CMOS

processing. It involves the creation of Coulomb force elicited by the positive and/or

negative charges, set by applied voltages between certain mechanical structures. For an

actuation with considerable electrostatic force, most devices requires a large voltage,

usually 30V or higher. For handheld devices such as cellular phone in wireless

communication applications, one has to build a CMOS integrated up-converter to

increase the usually used 5 volt control voltageDPT. Attempts are also made to reduce the

actuation voltage by novel structure designs TPD31DPTP-DDTD33DTPor by using other actuation mechanisms.

Piezoelectric actuation: this actuation mechanism takes advantage of the inverse

piezoelectric effect: a voltage across certain surfaces of a ferroelectric material, e.g. PZT

(Lead Zirconate Titanate, piezoelectric ceramic material), causes elastic deformation of

the materials, which gives larger contact force for a smaller actuation voltage in contrast

with electrostatic actuation. The RF MEMS switch using piezoelectric actuation has

shown good performance for a low actuation voltage 34DPTP,TD35DTP.


Page 8

Electromagnetic actuation: Electromagnetic methods of actuation rely on

aligning the magnetic moment in a magnetic material, usually soft magnetic materials, by

an external magnetic field. The magnetostatic force exerted by the external magnetic field

on the switch can turn the switch ON or OFF, depending on the direction of the applied

current. This is a novel method and has some advantages compared to other methods but

requires special processing involving magnetic materials TPD36DPTP-46DT P. Among the RF MEMS

switches, the design by MicroLab shows promising for applications since it overcomes

the large power consumption of conventional magnetically actuated switches.

Electrothermal: Electrothermal actuation involves using two materials with

different thermal expansion coefficients. When the materials are heated, the composite

beam bends away from the material with the higher thermal expansion coefficient TPD 47DPT, thus

providing mechanical movement. Another thermal method employs shape memory alloys

(SMA), which involves a solid phase change for some special materials. At low

temperatures, the SMA has a martensitic crystalline structure, which is more flexible and

allows relatively large elastic deformations. When the temperature is raised,

transformation to austenitic phase takes place and the material loses its flexibility and

thus the strain is recovered. Currently, these thermal methods have not been very popular

despite the latching properties due to the required power consumption and slow

switchingTPD48DPTP,TD49DTP.

As discussed above, each actuation mechanism has its own advantages and

disadvantages. One may choose the actuating mechanism for benefiting a specific

application while tolerating the drawbacks associated with it. A table by Rebeiz 50 is

reproduced in


Page 9

Table 2-1 Table 2-1 to summarize the main characteristics of the above mentioned

mechanism.

Table 2-1 Comparison of RF MEMS Actuation Mechanism

Voltage (V) Current (mA)

Power (mW) Size

Switching time (µs)

Contact force (µN)

Electrostatic 20-80 0 0 small 1-200 50-1k Electrothermal 3-5 5-100 0-200 large 300-10k 500-1k Magnetostatic 3-5 20-150 0-100 medium 300-1k 50-200 Piezoelectric 3-20 0 0 medium 50-500 50-200

MEMS switches can also be categorized as metal-metal contact or Ohmic

contactTPD 51 and metal-insulator-metal, or capacitive coupling 52 DPT, based on the contact

characteristic during switching. The metal-metal contact switches use metal to metal

direct contact to achieve an Ohmic contact, as shown in Figure 2-2TPD53DPT. This type of switch

Figure 2-2 A metal-to-metal contact-type RF MEMS switch

can be used in a broad frequency range from DC to W band (75 – 111GHz).

The capacitive switch utilizes a thin dielectric layer between two metal electrodes to

achieve a closed circuit, as shown in Figure 2-3. This switch is an example of practical

MEMS capacitive shunt MEMS switches and was developed by Goldsmith13 et al at

Raytheon (formerly Texas Instruments). This switch is based on a fixed-fixed metal (Al


Page 10

or Au) beam design. The anchors are connected to the coplanar-waveguide (CPW)

ground plane, and the membrane is, therefore, grounded. As its name implies, this type of

switch is only applicable to high frequency signals.

Figure 2-3 (a) An example of capacitive MEMS RF switch and (b) the electrical CRL circuit

Due to its intrinsic contact characteristics, a capacitive MEMS switch has to be

designed to have a large contact area for smaller insertion loss, but large contact area

results in poor isolation. Therefore, a trade-off has to be made for optimized performance

of capacitive switches.

In addition, MEMS RF switches may be grouped as series and shunt types from

the configuration topology in a circuit, as shown in Figure 2-4.

Figure 2-4 Schematic representation of switches in a series and shunt configuration


Page 11

The broadside and the inline switch for contact-type switches are shown in Figure

2-5 54DPT. The actuation of the broadside switch is in a plane that is perpendicular to that of

the transmission line, while the inline switch is actuated in the same plane as the transmi-

Figure 2-5 (a) and (b) broadside MEMS switches, (c) inline MEMS switch

ssion line.

2.2.2 Performance and Characteristics of RF MEMS

Switches

Much attention has been paid to RF MEMS switch technology since the first

micromechanical membrane-based switch was demonstrated by Petersen using

electrostatic actuation 55 . This is mainly due to the fact that conventional switching

devices such as GaAs-based metal-semiconductor field effect transistors (MESFETs) and

PIN diodes for high-speed switching can not meet the demanding requirements for RF

applications. For instance, silicon FETs can handle high power signal at low frequency,

but the performance drops off dramatically as frequency increases; others, such as GaAs

MESFETs work well at moderately high frequencies but only at low power levels. For


Page 12

frequency greater than 1 GHz, these semiconductor switches have a large insertion loss

(typically 1- 2 dB) in the closed circuit state and a lower electrical isolation (typically 20

– 25 dB) in the open-circuit state. Also, the inherent junction capacitance of the

semiconductor based switches exhibits a larger nonlinear current versus voltage behavior,

leading to larger intermodulation distortion. However, the MEMS switches have a 3 Prd P

order input intercept point (IP3) better than 65 dBm 54. This low loss, high isolation, and

high linearity are advantages of conventional electromagnetically-actuated mechanical

relays. On the other hand, like semiconductor switches, the MEMS switches have

smaller size, less weight, and fast switching in contrast to the electromagnetically

actuated mechanical relays. Therefore, MEMS switches combine the merits of both

semiconductor switches and mechanical relays.

2.2.3 Applications

As mentioned above, RF MEMS switches have low insertion loss, high isolation,

and high linearity for RF applications, compared with semiconductor-based solid-state

switches. At the same time, RF MEMS switches occupy little space, are not sensitive to

acceleration, have extremely low power consumption, have an extremely high cutoff

frequency of 20 – 80 THz, in contrast to 0.5 – 2 THz for MESFETs and 1.0 – 4.0 THz for

PIN diodes50 and are compatible with low cost silicon based IC technology. So, RF

MEMS switches have potential applications in a wide variety of areas. RF MEMS

switches can be used as a discrete switching component to switch signals. RF switches

can also be used as the building blocks of circuits such as phase shifters, which are

suitable for modern communications, automotive, and defense applications, low-loss


Page 13

tunable circuits (matching networks, filter, etc) and high performance automatic

instrument testing systems, or subsystems or systems such as reconfigurable phased-array

antennas. Due to the cost of hermetic packaging of MEMS switches, the switches may

first be used in defense and high-value commercial applications. The following details

some example applications of RF MEMS switches:

Band switching and T/R Duplexers (TDD) in mobile phone or cellular phones56

Almost all the cellular or mobile phones on the market use a transmit/receive (T/R)

switch, or a band switch, and/or duplexers to interface the antenna and the chipset. The

use of any one or a combination of switching devices depends on the number of bands,

which is determined by the cellular phone system operator. Currently, compound

semiconductor such as GaAs and PIN diodes switches provide a reasonably good solution

to switching due to their power handling and flexibility. The overall performance of the

mobile phone or cellular phone could be greatly improved after RF MEMS switches

replace semiconductor-based counterparts in a multiband switching networks or T/R

switches in a T/R duplexer.

High frequency high Q digitized capacitor banks and phase-shifting networks��8�:

The semiconductor switches, e.g. back-biased Schottky diodes, which are commonly

used in digital capacitor banks, have a low Q factor (Q ~ ωC/G in microwave and

millimeter wave applications). The RF MEMS switch may provide a high Q factor for

high frequency applications due to its inherent low loss characteristics.

Phase shifting is a popular control function at microwave and millimeter wave

frequencies. The reduction of occupation area and increase in accuracy in time-delay

phase shifting can be achieved using RF MEMS switches. One approach is to use a


Page 14

coplanar-waveguide transmission line periodically with RF MEMS switches equally

distributed along the lineTPD57DPT.

Applications in the defense area include phased array antennas, phased-array

radar, and satellite communications58 . Antennas used in military airborne crafts are

required to be able to handle high-data rates and possess large steering angles at

frequencies as high as Ku band (12.2 – 12.7 GHz). State-of-the-art phased array antennas

(PAA) are generally used for this application. The constructive interference of radiation

at PAA is realized through a high efficiency time-delay phase-shifting network, which

can be made possible through RF MEMS switches due to their intrinsically low insertion

loss and low-power consumption.

Other applications of RF MEMS switches are in automotive smart antenna, anti-

collision airbags, automotive GPS systems, base-stations for cellular phones, automatic

instrumentation, wireless LAN’s, data communications, digital personal assistants,

Bluetooth devices, etc.

2.2.4 Failure Mechanisms and Reliability Issues

As can be seen from the preceding discussions, the main driving force for much

effort on research and development of RF MEMS switches is their superior electrical

performance compared with existing semiconductor-based switches. As an emerging

technology, besides some inherent drawbacks with RF MEMS switches such as slow

switching speed, there are still concerns associated with RF MEMS switch technology.

To better understand the current status and potential problems, the following provides a

brief description of the issues related to the long-term reliability of microswitches, and


Page 15

identifies some specific aspects which must be addressed before the RF MEMS switch is

widely accepted.

Compared with other actuation mechanisms, electrostatic actuation has the

advantages of being fast, easy to implement, and having virtually no power consumption.

However, electrostatic discharge (ESD) may cause failures to MEMS devicesTPD59DPTP- DDTD61DTP. The

sudden build-up of a static charge on the MEMS device may result in potentials of over

one thousand volts, causing parts of the actuator or contact melt and weld together, which

may lead to the failure of the switch. It is generally recommended that proper precautions

should be taken before transport or handing of RF MEMS switches.

In general, electrostatically actuated MEMS switches use a relatively high

actuation voltage, usually on the order of 20 - 120V. From an application perspective,

high actuation voltages are not desired. To reduce the actuation voltage, one may use the

following methods: 1) increase the actuation area, 2) decrease the gap between the

electrodes, although this may decrease the electrical isolation during opening, 3) design

switches which have lower spring constant.

Alternatively, one may also provide an intermediary step that enables an RF

MEMS switch to operate at much lower voltages. A dc-dc voltage converter and

controller may be integrated with a high-voltage RF MEMS device to create a low-

voltage solution.

In addition to the above aspects which are relevant to RF MEMS switch

technology, another major concern about RF MEMS switches is its long-term reliability.

So far, the failure mechanisms are not completely understood, although it is observed that

the failure of a well-designed MEMS switch associated with mechanical malfunction


Page 16

such as mechanical fatigue or even fracture is not usually a problem. It is also found that

most failures of current RF MEMS switches are associated with their contacts. The

reasons for mechanical failure at contact are very diverse and complicated. This is due to

the fact that contributing factors from different physical domains may have different

effects on failures. For instance, a simple Ohmic contact type switch may fail as a result

of a permanent stiction, or fail to open. The stiction may be caused by the increased

adhesive force during cycling, or due to degradation of contact with a larger contact area,

The second mode of failure associated with contact is the increase of resistance at the

contact after cycling. The switch is considered to fail if the contact resistance is larger

than a few ohms during operation.

It is believed that the reliability of the switch could be enhanced if one can

address the following issues properly:

(1) Contact materials: minimum adherence force at the contact interfaces is

desired for a better contact, near zero adherence force would be ideal;

(2) Actuation scheme: an optimized actuation scheme gives an optimum dynamic

behavior in terms of low impact force, reduced bounces;

(3) Thermal issues: low temperature of the switch is anticipated even when

handling high power;

(4) Resistance increase: it is often related to the chemically contaminated or

physically damaged contact.

In this thesis, we will deal with items (2) and (3). To study the dynamics of the

switch, we have used a finite element package ANSYS® and a finite difference method to

develop a comprehensive dynamic model. This model includes the complete structure of


Page 17

the switch, squeeze-film damping, nonlinear contact, etch holes, and adherence force.

Afterwards, we use the model to optimize the dynamic performance of the switch. Also,

the simulated results are compared with the experiments. We also need to establish a

thermal model to investigate the thermally-induced intermodulation. Specifically, we first

build an analytical model to quantitatively examine the intermodulaton effect and design

the test device, and subsequently, make measurement on the fabricated device. Also, we

applied the developed method to predict the intermodulation distortion for a RF MEMS

switch. The intermodulation is caused primarily by Ohmic heating, since it is found that

the intermodulation caused by the change in contact resistance from the change in contact

force from the signal is much smaller than the thermally-induced intermodulation62.


Page 18

References

TP

1H. C. Nathanson, W. E. Newell, R. A. Wickstrom, and J. R. Davis, Jr. “The Resonant Gate Transistor,”

IEEE Trans. Electron Devices, vol. 14, pp. 117-133, March 1967. 2 P. M. Zavracky and R. H. Morrison Jr., “Electrically actuated micromechanical switches with hysteresis,”

in Tech. Dig. IEEE Solid State Sensor Conf. Hilton Head Island, SC, June 6 - 8, 1984. 3K. E. Peterson, “Silicon torsional scanning mirror,” IBM J. Res. Develop., vol. 24, no. 5, pp. 631 – 637,

1980. 4ADXL105 datasheet, HTUhttp://www.analog.comUTH . 5P. Greiff, B. Boxenhorn, T. King, and L. Niles, “Silicon monolithic micromechanical gyroscope,” in Tech.

Dig. 6th Int. Conf. Solid-State Sensors and Actuators Transducers’ 91, San Francisco, CA, pp. 966 - 968,

June 1991. 6G. T. A. Kovacs, Micromachined Transducers Sourcebook, Boston, MA: McGraw-Hill, 1998. 7J. Brysek , K. Petersen, J. Mallon, L. Christel, F. Pourahmadi, Silicon Sensors and Microstructures, San

Jose, CA, 1990. 8E. R. Brown, “TRF-MEMS switches for reconfigurable integrated circuits,” IEEE Trans. Microwave and

Techniques, vol. 46, no.11, pp.868 - 880, 1998. T 9 J. Jason Yao, “RF MEMS from a device perspective,” J. Micromech. Microeng. vol.10, R.9 – 38, 2000T 10T. Zlatoljub D. Milosavljevic, “RF MEMS Switches”, Microwave Review, vol. 10, no.1, pp.1 - 9, June

2004. 11 T. Gabriel M. Rebeiz, “RF MEMS switches: status of the technology”, the 12PthP international

conference on solid-state sensors, actuators and microsystems, pp.1726 - 1729, Boston, June 8-12 2003.T 12T.S. Lucyszyn, “Review of radio frequency microelectromechanical systems technology”, IEE Proc. Sci.

Meas. Technol. vol. 151, no.2, pp.93 - 103, 2004.T 13 C. L. Goldsmith, Zhimin Yao, S. Eshelman, D. Denniston, “Performance of low-loss RF MEMS

capacitive switches”, IEEE Microwave and Guided Wave Letters, vol. 8, no. 8, pp.269 – 271, Aug. 1998. 14P. M. Zavracky, S. Majumder, N. E. McGruer T “Micromechanical switches fabricated using nickel

surface micromachining, ”J. Micromechanical Systems, vol. 6, pp. 3 - 9, 1997. 15 M. Innocent, P. Wambacq, S. Donnay, H. Tilmans, M. Engels, H. DeMan and W. SansenT “Analysis of

the Nonlinear Behavior of a MEMS Variable Capacitor,” Nanotech, vol.1, pp.234 – 237, 2002. 16 Imed Zine-El-Abidine, Michal Okoniewski and John G McRory, “Tunable radio frequency MEMS

inductors with thermal bimorph actuators,” J. Micromech. Microeng , vol.15, pp.2063 - 2068, 2005. 17Brian Bircumshawa,, Gang Liu, Hideki Takeuchi, Tsu-Jae King, Roger Howe, Oliver O’Reilly, Albert

Pisano “The radial bulk annular resonator: towards a 50 Ω RF MEMS filter”, The 12th International

Conference on Solid State Sensors, Actuators and Microsystems, pp.875 - 878, Boston, June 8 - 12, 2003.


Page 19

18S. Pacheco, P. Zurcher, S. Young, D. Weston and W. Dauksher, “RF MEMS resonator for CMOS back-

end-of-line integration,” 2004 Topical Meeting on Silicon Monolithic Integrated Circuits in RF Systems,

Atlanta, GA, USA, pp. 203 - 206, Sept.8 - 10, 2004. 19 K. M. Strohm, F. J. Schmuckle, B. Schauwecker, J. F. Luy, “Silicon Micromachined RF MEMS

Resonators,” IEEE MTT-S Int. Microwave Symposium Digest, pp.1209-212, 2002. 20 S. V. Robertson, L. P. B. Katehi and G. M. Rebeiz,T “Micromachined W-band filters,” IEEE

Transactions on Microwave Theory and Techniques, vol. 44. no. 44, pp.598 – 606, 1996. 21James Brank, Jamie Yao, Mike Eberly, Andrew Malczewski, Karl Varian and Charles Goldsmith, “RF

MEMS-based tunable filters,”International Journal of RF and Microwave Computer-Aided Engineering,

vol.11, no.5 , pp. 276 – 284, 2001. 22D. Ramachandran, A. Oz, V. K. Saraf, G. Fedder and T. Mukherjee “MEMS-enabled Reconfigurable

VCO and RF Filter,” Proceedings of the 2004 IEEE Radio Frequency Integrated Circuits Symposium

(RFIC), pp. 251-254, Fort Worth, TX, June 6-8, 2004. 23 M. Behera, V. Kratyuk, Yutao Hu, and K. Mayaram, “Accurate simulation of phase noise in RF MEMS

VCOs” in Proceedings of the 2004 International Symposium on ISCAS ,V.3, pp.23 - 26 May 2004. 24A Malczewski, S. Eshelman, B. Pillans, and J. Ehmke, “X-band RF MEMS phase shifters for phased

array applications,” IEEE Microwave and Guided Wave Letters, 1999. 25Y Liu, A Borgioli, A. S Nagra, R. A York,” K-band 3-bit low-loss distributed MEMS phase shifter”,

IEEE Microwave and Guided Wave Letters, vol. 10, no. 10, pp.415 – 417, 1999. 26 B. Pillans, S. Eshelman, A. Malczewski, J. Ehmke, and C. Goldsmish, “Ka-band RF MEMS phase

shifters,” IEEE Microwave and Guided Wave Letters, vol. 9, no.12, pp. 520 – 522, December 1999. 27Atsushi Fukuda, Hiroshi Okazaki, Tetsuo Hirota and Yasushi Yamao, “Novel Band-Reconfigurable High

Efficiency Power Amplifier Employing RF-MEMS Switches,” IEEE Trans. Electron, vol. E88, no. 11,

2005. 28K. Suzuki, S. Chen, T. Marumoto, Y. Ara, and R. Iwata, "A Micromachined RF Microswitch Applicable

to Phased-Array Antennas," IEEE MTT-S Symp Dig., Anaheim, pp.1923 - 1926, 1999. 29Kiriazi, J., H. Ghali, H. Ragaie, H. Haddara, “Reconfigurable Dual-Band Dipole Antenna on Silicon

Using Series MEMS Switches,” Antennas and Propagation, IEEE Society International Conference, 22–27

June, vol. 1, pp. 403 – 406, 2003. 30L. E. Larson, R. H. Hackett, M. A. Melendes, and R. F. Lohr, “Micromachined microwave actuator

(MIMAC) technology-a new tuning approach for microwave integrated circuits,” in Microwave and

millimeter-wave monolithic circuits symposium digest, Boston MA, pp. 27 - 30, June 1991. 31P. T. Sergio P. Pancheo, Linda P. B. Katehi and T. C. Nguyen, "Design of Low Actuation Voltage RF

MEMS Switch," Microwave Symposium Diges, IEEE MTT-S International, pp. 165 -168, 2000. 32 Shyh-Chiang Shen and Milton Feng, “Low Actuation Voltage RF MEMS Switches with Signal

Frequencies From 0.25 GHZ to 40 GHz," IEDM Technical Digest, pp. 689–692, 1999.


Page 20

33 Balaraman,D., Bhattacharya,S.K., Ayazi,F., Papapolymerou,J.,” Low cost low actuation voltage copper

MEMS switch,” Microwave Symposium Digest, IEEE MTT-S International, vol.2 , pp.1225 -1228, 2002. 34Hee-Chul Lee, Jae-Hyoung Park, Jae-Yeong Park, Hyo-Jin Nam and Jong-Uk Bu, “Design, fabrication

and RF performances of two different types of piezoelectrically actuated Ohmic MEMS switches,”

Micromech. Microeng. vol.15, pp.2098 - 2104, 2005. 35G. Klaasse, B. Puers and H. A. C. Tilmans, “Piezoelectric actuation for application in RF-MEMS

switches,” SPIE-Int. Soc. Opt. Eng. Proceedings of Spie – the International Society for Optical

Engineering, vol.5455, no.1, Strasbourg, France, pp.174-80, Apr.29-30, 2004. 36Cho Il-Joo, Song Taeksang, Baek Sang-Hyun and Yoon Euisik, “A low-voltage push-pull SPDT RF

MEMS switch operated by combination of electromagnetic ctuation and electrostatic hold,” 18th IEEE

International Conference on Micro Electro Mechanical Systems, Miami Beach, FL, USA, pp.32-35, Jan.30-

Feb.3, 2005. 37 W. P. Taylor and M. G. Allen, “Integrated magnetic microrelays: normally open, normally closed, and

multi-pole devices,” Proceedings of International Solid-State Sensors and Actuators (Transducers ’97), pp.

1149–1152, 1997 38J. A. Wright, Y.-C. Tai, and G. Lilienthal, “A magnetostatic MEMS switch for DC brushless motor

commutation,” Proceedings of Solid-State Sensor and Actuator Workshop, pp. 304–307, 1998. 39 J. A. Wright and Y. C. Tai, “Micro-miniature electromagnetic switches fabricated using MEMS

technology,” Proceedings of 46th Annual International Relay Conference: NARM’98, pp. 131 –134, 1998. 40J. Wright, Y. C. Tai, and S.-C. Chang, “A large-force, fully integrated MEMS magnetic actuator,”

Proceedings of International Solid-State Sensors and Actuators (Transducers ’97), pp. 793–796, 1997. 41H. A. C. Tilmans, E. Fullin, H. Ziad, M. D. J. Van de Peer, J. Kesters, E. Van Geffen, J. Bergqvist, M.

Pantus, E. Beyne, K. Baert, and F. Naso, “A fully-packaged electromagnetic microrelay,” Proceedings of

IEEE International MEMS Conference, pp. 25 – 30, 1999. 42E. Fullin, J. Gobet, H. A. C. Tilmans, and J. Bergqvist, “A new basic technology for magnetic micro-

actuators,” Proceedings of IEEE International MEMS Conference, pp.143 – 147, 1998. 43J. W. Judy and R. S. Muller, “Batch-fabricated, addressable, magnetically actuated microstructures”,

Proceedings of Solid-State Sensor and Actuator Workshop, pp.187 – 190, 1996. 44L. K. Lagorce, O. Brand, and M. G. Allen, “Magnetic microactuators based on polymer magnets,”

Journal of Microelectromechanical Systems, vol. 8, pp. 2 – 9, 1999. 45M. Ruan, J. Shen and B. Wheeler, “Latching micromagnetic relays,” Journal of Microelectromechanical

Sysstems, vol. 10, no. 4, pp. 511 - 517, 2001. 46W. P. Taylor, O. Brand, and M. G. Allen, “Fully integrated magnetically actuated micromachined relays,”

Journal of Microelectromechanical Systems, vol. 7, pp.181 – 191, 1998.


Page 21

47T. Blondy, P. Cros, D., Guillon, P., Rey, P., Charvet, P., Diem, B., Zanchi, C., Quoirin, J.B.” Low voltage

high isolation MEMS switches,” Topical Meeting on Silicon Monolithic Integrated Circuits in RF Systems,

pp. 47 – 49, 2001. 48P. T. Lai, B..K., Kahn, Harold, Phillips, S. M., Heuer, A. H., Quantitative Phase Transformation Behavior

in TiNi Shape Memory Alloy Thin Films, Journal of Materials Research, vol. 19, no. 10, pp.2822 - 2833,

2004. 49 H. Kahn, M. A. Huff, and A. H. Heuer, “The TiNi shape-memory alloy and its applications for MEMS,”

J. Micromech. Microeng vol.8,T pp. 213 - 221, 1998.T 50 G. M. Rebeiz, RF MEMS Theory, Design, and Technology, John Wiley & Sons, Inc., Hoboken, NJ, pp.4,

2003. 51P. M. Zavracky, N. E. McGruer, R.H. Morrison and D. Potter “Microswitches and Microrelays with a

View Toward Microwave Applications,” Int. J. RF Microwave: CAE’ vol. 9, no. 4, pp 338 – 347, 1999. 52S. Pacheco, C. T.-C. Nguyen, and L. P. B. Katehi, “Micromechanical electrostatic K-band switches,”

Proceedings IEEE MTT-S International Microwave Symposium, Baltimore, Maryland, pp.1569 - 1572,

June 7-12, 1998. 53S. Majumder, J. Lampen, R.Morrison and J. Maciel “An Electrostatically Actuated Broadband MEMS

Switch,” Proceedings of Sensors Expo. Pp.23 - 26, Boston, Sept. 2002. 54Gabriel M. Rebeiz, Jeremy B. Muldavin, “RF MEMS switches and switch circuits,” IEEE microwave

magazine, pp.59 – 71, Dec. 2001. 55 K. E. Petersen, “Micromechanical membrane switches on silicon,” IBM Journal of Research and

Development, vol. 23, pp. 376 – 385, July 1979. 56 http://rfdesign.com/mag/radio_rf_mems_mobile/index.html 57N. S. Barker and G. M. Rebeiz, “Distributed MEMS True-Time Delay Phase Shifters and Wide-Band

Switches,” IEEE Trans. Microwave Theory Tech., vol.46, Apr. 1998. 58 G. M. Rebeiz, J. B. Muldavin, “RF MEMS switches and switch circuits,” IEEE Microwave Magazine,

pp.59 - 71, Dec. 2001. 59 S. A. Gasparyan and H. Shea, “Designing MEMS for reliability,” SPE Micromachining and

Mierafabrication Conference. Short Course M34, San Francisco, October 2001. 60T. Ono, Y. S. Dong, and M. Esashi, “Imaging of micro-discharge in a micro-gap of electrostatic actuator,”

in Proc. 13th Annu. Int. Conf.Micro Electro Mechanical Systems (MEMS 2000), pp.651 – 656, Jan. 2000. 61J. W. Minford and O. Sneh, “Apparatus and method for dissipating charge from lithium niobate devices,”

U.S. Patent 5, 949, 944, Oct. 2, 1997. 62 J. Johnson, G. G. Adams, N. E. McGruer, “Determination of intermodulation distortion in a contact-type MEMS microswitch,” IEEE Trans. Microwave Theory and Tech. vol. 53, pp. 3615 -3620, 2005.

Chapter 3. Dynamics of Microswitch

Page 22

Chapter 3. Mechanical Dynamics of a

MEMS Switch

In this chapter, we will develop a comprehensive dynamic model using ANSYS®

(a software package based on the finite element method) in combination with a finite

difference method. First, we give a brief introduction to work on dynamics of MEMS

devices with an emphasis on RF MEMS switches. Then, we describe the modeling based

on finite element analysis, and after that we will describe models which are parts of the

comprehensive model for simulating dynamics of the switch This model includes solid

modeling of the switch using ANSYS®, electrostatic actuation, non-uniform squeeze-film

damping based on the Reynolds equation including compressibility and slip-flow, effects

of perforation of the beam on damping, nonlinear elastic contact and adherence force

during unloading. Finally, we present the experimental measurements and make

comparisons between the simulated results and the experimental measurements.

3.1 Dynamic Response of MEMS Switch

As mentioned in Chapter 1, MEMS switches promise to replace conventional

solid-state switches in many high frequency applications due to their enhanced

performance. For these applications, MEMS switches must be designed to be able to

operate for 1 to a few hundred billion cycles. The reliability of MEMS switches is

believed to be strongly connected to the dynamics of the actuation. It has been


Page 23

experimentally observed that most failures occur at the contact, either because of stiction

due to large adherence force, or due to a substantial rise of the electrical resistance.

Impact force can flatten and increase the area of the contact leading to increased

adherence force. Contaminated contact and/or damaged contact resulting from fracture,

pitting, hardening, etc may cause switch resistance to increase. It is generally assumed

that if the contact resistance of the switch is 5 Ω or more, which corresponds to an

insertion loss of 0.5 dB in a 50 Ohm environment, the switch fails.

In general, the characterization of mechanical dynamics of the switch includes

actuation and release time, switching speed, impact force at contact, and bounce. All of

these properties are critical for the successful development of RF MEMS switches. But

among them, switching speed, impact force and bounce may be most critical, because

they are most relevant to the reliability of the switch.

During operation, the contact tip on the cantilever beam makes contact with the

drain, or signal transmission line. Before making steady contact, the contact tip usually

bounces several times due to the elastic energy stored in the deformed materials of the

actuator. The existence of bouncing behavior increases the effective closing time of the

switch. Meanwhile, the contact may be damaged by the impact force. This instantaneous

high impact force may induce local hardening or pitting of materials at the contact area.

The switch contact may also stick to the drain because of large adherence forces caused

by high impact force. Also, the bounces may facilitate material transfer, or contact wear-

out, which is not desired for a high-reliability switch. It has been experimentally observed

that the switches bounce a few times before making permanent contact1 -DPTDDDDDTD5DTP. Elimination,

or at least reduction, of bounces is highly desirable for microswitches to operate with


Page 24

longer lifetime and better performance. To control the dynamic behavior of the switch, it

is necessary to develop full dynamic models to simulate the dynamic response of the

microswitch.

Most dynamic models on MEMS switches account for only certain aspects of the

switch such as the squeeze-film damping, but contact characteristics and adhesions of the

microswitches during operation are not taken into account. For instance, Czaplewski et

al. 6 used a dynamic model to predict the dynamics of a Ohmic RF MEMS switch. But

the contact, squeeze-film damping, and adhesion effects have not been taken into account

in this model. The analytical analysis presented by Steeneken et al. 4 about the dynamics

of a capacitive RF MEMS switch mostly deals with the squeeze-film damping as well as

the slip-flow effects. Recently, Granaldi and Decuzzi 7 presented a one-dimensional

dynamic model which mainly focuses on the switching time and bouncing of a cantilever

based microswitch. In this model, the squeeze-film damping and the spring restoring

force have been lumped into two parameters, thus it does not take into account the

nonuniformity across the actuator and the nonlinearity of the damping force. Gee et al.8

presented a one-dimensional dynamic model and examined the effect of the dynamics of

the switch on its opening time. In that model, they used a fourth-order beam deflection

equation and included the adhesion force due to both van der Waals type forces and

metal-to-metal bonds. The one dimensional dynamic model developed by McCarthy et

al.3 based on a finite difference method for squeeze-film damping was used to simulate

the dynamics of the RF MEMS switch both before and after the contact. In that model,

the squeeze-film damping effect and a simple spring contact have been included, and the

spring shows the bouncing features after initial contact, as shown in Figure 3-1. It is seen


Page 25

that the number of bounces increase with increasing actuation voltage, resulting in longer

time to close. But the nonuniformity and nonlinearity of the squeeze-film damping as

well as the bowing of the microswitch has been neglected.

In this work, we develop a model which will cover almost all important aspects

pertaining to the dynamics of the switch. This includes the complex two-dimensional (2-

D) geometry, squeeze-film damping, compressibility, slip-flow, and the effect of

perforation of the mobile structures, nonlinear contact, and adhesive force during

unloading. This reveals the dynamic response of the switch both before and after closure.

Furthermore, we develop an open-loop actuation strategy for operation of the switch with

enhanced performance. We measure the dynamic response of the microswitch. And last, a

comparison between the modeling and the experimental measurement is made. The

following will present the development of the models in more detail.

Figure 3-1 Dynamic behavior of a RF MEMS switch, the step curves are for the step voltage for actuation. The traces are recorded using oscilloscope which show the transient ‘in contact’ and ‘out

of contact’ after actuation [see Reference (3)]

T im e after actuation (µs)

0 10 20

Sw

itch V

olta

ge

(V)

0 .0

0.1

0.2

0.3

0.4

0.5

Actu

atio

n V

olta

ge

(V)

0102030405060


0 10 20

Sw

itch V

olta

ge

(V)

0 .0

0 .1

0.2

0.3

0.4

0.5

Actu

atio

n V

olta

ge

(V)

0102030405060


0 10 20

Sw

itch V

olt

0 .0

0.1

0.2

0.3

0.4

0.5

Actu

atio

n

0102030405060


Page 26

3.2 Finite Element Analysis (FEA)

The finite element method is a numerical technique which has been used to solve

complex nonlinear problems in fields of research such as mechanical structures, fluid

mechanics, heat transfer, vibrations, electric and magnetic fields, acoustic engineering,

civil engineering, aeronautic engineering, and even in weather forecasting. The common

characteristic of FEA is the mesh descretization of a continuous domain into a set to

discrete sub-domains. In doing analysis of solid mechanics, a complex solid structure is

divided into a finite number of elements, and these elements are connected at points

called nodes. The stresses of each element are balanced by those of neighboring elements

and ultimately by the forces exerted on the exterior or at the boundaries. The

displacement of each node is determined by the overall displacement constrained by the

boundary conditions. Compared with analytical methods, FEA allows the simulation of a

generally complex geometry, and examination of the three-dimensional effects both

locally and globally.

In the modeling and simulation of dynamics of the RF MEMS switch, we used

ANSYSP®P version 10.0, a FEA package from ANSYS Inc. The procedure of performing

simulation involves building solid model, material property designation, meshing, set-up

of boundary conditions, solving and post-processing. Before we go into the details of the

simulation, we need to introduce the aspects associated with the dynamics of the switch

such as lumped-parameter modeling, geometry and dimensions, electrostatic actuation,

squeeze-film damping, effect of etch holes, nonlinear contact, and adhesion.


Page 27

3.3 Lumped Parameter Modeling of a

Cantilever Beam

Cantilever beams are often used as actuators in MEMS devices. The reasons

include the better understanding of the mechanical behavior and ease of fabrication. For

instance, cantilever beams are used in some inline series RF MEMS switches and

broadside switches, as discussed in Chapter 2. For applications of moving switches,

adjusting elements, valves and grippers, a DC voltage is applied, whereas for resonant

devices, an AC component is added to the driving voltage to excite the harmonic motions

of the beam. A simple cantilever beam is shown in Figure 3-2.

Figure 3-2 Side view of a typical cantilever beam

Since one end of the cantilever beam is free standing, the residual stress within the

beam is released. However, the released unloaded beam can also be deformed by the

nonidealities, which gives rise to take-off angle, and the existence of the stress gradient

over the cross section of the cantilever, which creates curvature of the released part of the

beam. Thus, the total deflection curve of an unloaded beam mainly consists of two

components: the take-off angle and the curvature.

The first natural resonance frequency of a cantilever beam in transverse vibration

as shown in figure is governed by the general equation9

Cantilever beam

g


Page 28

eff

eff

MK

fπ21

0 = (3-1)

where KBeffB and MBeffB are the effective stiffness or spring constant and mass of the beam,

The effective spring constant of a cantilever-type structure depends on the force

distribution over the beam, Young’s modulus, and geometry 10. The effective mass for a

uniform cantilever beam is MBeffB = (33/140) M, where M is the mass of the cantilever

beam11.

The static and dynamic behavior of a cantilever beam, as shown in Figure 3-2,

with electrostatic actuation, can be modeled using a simplified lumped one dimensional

mass-spring system with a voltage-controlled parallel-plate capacitor, as shown in Figure

3-3 .

Figure 3-3 The lumped mechanical model for a cantilever beam.

As can be seen from Figure 3-3, the bottom electrode is fixed and the top

electrode having a mass of MBeffB is suspended by a spring with stiffness of KBeffB and a

damper with damping constant b. In the following static analysis, the damping effect has

been neglected for simplification. The normalized gap with respect to the initial gap

versus the applied voltage which is normalized with respect to the pull-in voltage is

shown in Figure 3-4.

Keff b

VMeff

g


Page 29

Figure 3-4 Gap of the cantilever vs. applied voltage

It can be seen that the system becomes unstable at g = (2/3)gB0 B due to the existence

of a forward feedback. At equilibrium when g > (2/3)gB0B, the electrostatic force pulling the

upper electrode down balances the spring restoring force which pulls the electrode upTPD12DPT.

If the sign convention is assigned a positive sign for forces that increase the gap, the net

force on the upper electrode at voltage V and gap g is:

)(2 02

2

ggkgAVFnet −+−= ε (3-2)

where gB0 B is the gap at zero volts and zero spring extension. For this system to be stable at

the equilibrium point, the net force, FBnetB = 0, and the derivative of Eqn (3-2) has to be

less than or equal to zero. Then, at pull-in we have:

32

2 PIPI

gAVk ε= (3-3)

032 gg PI = (3-4)

A

kgVPI ε27

8 30= (3-5)

Stable

Unstable


Page 30

To better understand the pull-in phenomenon, we normalized the voltage to the

pull-in voltage as PIVV /=ν , and the displacement to 0/1 gg−=ς . At equilibrium, we

can get:

ςς

ν=

− 22

)1(274 (3-6)

The normalized force, the left hand side of Eqn (3-6) as a function of normalized

gap ζ with a variable voltage as a parameter, is shown in Figure 3-5. It can be seen that

there exist two equilibrium states for ν ≤ 1, and one of them is stable. The stable

equilibrium point is specified by the condition that the derivative of Eqn (3-2) is negative.

When ν = 1, the system is at pull-in state, and when ν > 1, the system becomes unstable,

as discussed above.

Figure 3-5 The electrostatic force and spring force vs. normalized gap for a voltage-controlled electrostatic actuator.

3.4 Geometry of the Microswitch

The microswitch under investigation was fabricated at Northeastern University using the

standard micromachining technology. The details of the fabrication process can be found


Page 31

in the doctoral dissertation by Majumder 13. The switch is based on a cantilever-beam

type mechanical structure, as shown in Figure 3-6. The source, the actuator and the drain

of the microswitch is made of electroplated gold, and the gate is sputtered gold.

Figure 3-6 SEM micrograph of the Northeastern University MEMS switch.

The source end of the microswitch is attached to the substrate. The contacts

indicated on the figure make contact with the lower drain metallization (barely visible) in

the on-state.

The cantilever beam is actuated through the electrostatic force between the top

electrode, i.e. actuator, and the bottom electrodes, i.e. gate. The initial separation

between the top and bottom electrode is 0.6 µm before actuation. The top view along

with the dimensions of the microswitch is shown in Figure 3-7. The side view along with

the dimensions of the microswitch is shown in Figure 3-8.

ActuatorSource Drain

Gate

Contact


Page 32

Figure 3-7 The top view as well as the dimensions of the Northeastern University RF MEMS switch

where w1 = 80 µm, w2 = 10 µm, w3 = 16 µm, w4 = 30 µm, L1 = 30 µm and L2 = 24 µm.

Figure 3-8 The side view of the microswitch where h1 = 6.3 µm, h2 = 0.6 µm and h3 = 0.38 µm.

3.5 Finite Element Modeling

ANSYS® is a well established simulation tool which utilizes finite element

techniques. The properties of MEMS switches can be examined both locally and globally

using ANSYS®. The top and side views of the switch are shown in Figure 3-7 and Figure

3-8. Only half of the switch is simulated by utilizing the symmetry of the switch. The

electrode and beam of the switch are discretized to rectangular structures, i.e. regular

mapped mesh grids, as shown in Figure 3-9, which are used for both electrostatic

actuation and implementation of the finite difference method to solve the Reynolds

equation for the squeeze film damping. The rest of the microswitch is meshed using free

meshing. Element solid45 is used for the whole mechanical three-dimensional structure,

whereas surface element surf22 is used for the surface which is subject to electrostatic

and squeeze-film damping forces. Element link8 is used to simulate the contact between

Source Gate

h1h2 h3

Drain

w3

w4

w2

A

L2L1

w1

BBeamFixed

Fixed


Page 33

the contact tip and the drain of the switch. The total number of elements is 634 consisting

of 598 solid45, 35 surf22 and 1 link8 element. There are three layers through the

thickness.

Figure 3-9 Grid of finite elements of half of the switch for ANSYS® simulation.

3.6 Electrostatic Actuation

As discussed above, electrostatic actuation is one of the most popular actuation

mechanisms for MEMS devices. The main reasons are its near zero-power consumption

and its ease of implementation. The electrostatic force between two parallel plates is

established through the Coulomb force on oppositely polarized charges. The charges at

the surface of two conductors are accumulated by an electric field, which is created by a

voltage applied to the plates with a distance of h, as shown in Figure 3-10 . Note that the

fringing effect has been neglected in the model.

ActuatorBeam


Page 34

Figure 3-10 Electrostatic force between two parallel plates

The pressure between two parallel plates separated by a distance g is given as:

22

2gVFELEε

= (3-7)

where ε B0B is the permittivity of free space, V is the voltage difference between the

electrodes, and g is the distance between the electrodes. In applying the electrostatic force

to the elements of the switch, we assume that the forces between two opposite elements

of opposite electrodes can be approximated by the electrostatic force between the two

parallel plates. This is because the gap is much smaller than the length of the switch, thus

the local two opposite elements is close to be parallel.

3.7 Squeeze-Film Damping

MEMS devices which are electrostatically actuated often have a large electrode

area and a smaller gap between electrodes, which gives a large electrostatic force and fast

speed. Such devices exhibit a damping force. The damping forces originate from

deformed structural materials, or damping from the viscosity of the surrounding fluid.

The damping mechanisms associated with these damping forces are called structural and

squeeze-film damping, respectively. In the latter case, the damping force is due to the fact

that a displacement of small magnitude has to squeeze air out of the narrow gap. The

V hE field


Page 35

viscosity of the air limits the flow rate, which gives rise to a pressure at the surface of the

moving electrode. The distribution of the gas film pressure varies across the electrode

surface. The total damping force, which affects the mechanical dynamics, and ultimately

the design and control of the device, is often known as squeeze-film damping.

As early as the 1960s, LangloisTPD 14 DPT and Gross TPD 15 DPT investigated the squeeze-film

damping phenomenon from a theoretical perspective. Griffin 16DPT and Blech 17 linearized

the Reynolds equation for it to be suitable for structures which undergo vibrations of

small amplitude. The linearized Reynolds equation is widely utilized in analyzing

squeeze-film damping effects. Since the Reynolds equation is derived from Navier-

Stokes equations, which describes viscous, pressure and inertial mechanisms in fluid

mechanics, it holds true only under certain circumstances. The assumptions are as follows:

1) inertial effect is negligible; 2) the surfaces move perpendicular to each other; 3) the gas

thin film is isothermal; 4) the gap, i.e. g, dimension is much smaller than the lateral

dimensions, W and L, thus pressure does not vary across gap.

In general, the force due to squeeze-film damping effect consists of two

components: 1) spring force due to the compressibility; 2) the dissipative force arising

from the viscous flow. The relative importance of the two components in squeeze-film

effect is measured by the squeeze number. For a two-dimensional system, the squeeze

number is related to the geometry and the properties of the gas film as follows 18:

20

212gPL

a

ωµσ = (3-8)

whereµ is viscosity of air gas, L is the lateral dimension of the moving structure, ω is the

frequency of oscillation of the structure, PBa B is the ambient air pressure, and gB0 B is the initial


Page 36

gap between the two electrodes. If the squeeze number is small, the dissipative damping

force is dominant over the spring force, otherwise the spring force dominates.

One of the important characteristics associated with squeeze-film damping is the

slip-flow effect, which may dramatically change the damping force. This becomes more

important when the gap thickness (i.e. characteristic length) is comparable to the mean

free path of the gas molecules and the tangential component of the gas velocity at the

boundary is no longer zero.

Fluid or gas flows are generally categorized based on the Knudsen number. The

Knudsen number is defined as the ratio of the mean free path, LBmB, of a fluid to the

characteristic length, LBcB, of the flow region:

c

mn L

LK = (3-9)

Also, the mean free path of a typical gas is inversely proportional to the pressure 19D The

flow regimes which follow different principles are listed in Table 3-120.

Table 3-1 Flow Regimes and Their Knudsen Number

Flow Regimes KBn B number Continuum flow &l

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MECHANICAL DYNAMICS AND THERMALLY-INDUCED … › edsnu › mcgruer › thesis › ...intermodulation formulations have also been applied to an Ohmic contact RF MEMS switch. The resulting