mechanical dynamics and thermally-induced … › edsnu › mcgruer › thesis ›...
TRANSCRIPT
-
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.
-
Chapter 2. Background of RF MEMS switch
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
-
Chapter 2. Background of MEMS
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
-
Chapter 2. Background of RF MEMS switch
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.
-
Chapter 2. Background of MEMS
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
-
Chapter 2. Background of RF MEMS switch
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
-
Chapter 2. Background of MEMS
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
-
Chapter 2. Background of RF MEMS switch
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
-
Chapter 2. Background of MEMS
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
-
Chapter 2. Background of RF MEMS switch
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
-
Chapter 2. Background of MEMS
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
-
Chapter 2. Background of RF MEMS switch
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
-
Chapter 2. Background of MEMS
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
-
Chapter 2. Background of RF MEMS switch
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.
-
Chapter 2. Background of MEMS
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.
-
Chapter 2. Background of RF MEMS switch
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.
-
Chapter 2. Background of MEMS
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.
-
Chapter 2. Background of RF MEMS switch
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
-
Chapter 3. Dynamics of Microswitch
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
-
Chapter 3. Dynamics of Microswitch
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
-
Chapter 3. Dynamics of Microswitch
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
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
T im e after actuation (µs)
0 10 20
Sw
itch V
olt
0 .0
0.1
0.2
0.3
0.4
0.5
Actu
atio
n
0102030405060
-
Chapter 3. Dynamics of Microswitch
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.
-
Chapter 3. Dynamics of Microswitch
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
-
Chapter 3. Dynamics of Microswitch
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
-
Chapter 3. Dynamics of Microswitch
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
-
Chapter 3. Dynamics of Microswitch
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
-
Chapter 3. Dynamics of Microswitch
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
-
Chapter 3. Dynamics of Microswitch
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
-
Chapter 3. Dynamics of Microswitch
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
-
Chapter 3. Dynamics of Microswitch
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
-
Chapter 3. Dynamics of Microswitch
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
-
Chapter 3. Dynamics of Microswitch
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