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All Theses and Dissertations
2003-06-17
Development of In-Plane Compliant Bistable
Microrelays
Troy Alan Gomm
Brigham Young University - Provo
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Development of In-Plane
Compliant Bistable Microrelays
by
Troy Gomm
A thesis submitted to the faculty of
Brigham Young University
in partial fulfillment of the requirements for the degree of
Master of Science
Department of Mechanical Engineering
Brigham Young University
August 2001
Copyright © 2001 Troy A. Gomm
All Rights Reserved
BRIGHAM YOUNG UNIVERSITY
GRADUATE COMMITTEE APPROVAL
of a thesis submitted by
Troy Gomm
This thesis has been read by each member of the following graduate committee
and by majority vote has been found to be satisfactory.
Date
Larry L. Howell, Chair
Date
Spencer P. Magleby
Date
Richard H. Selfridge
BRIGHAM YOUNG UNIVERSITY
As chair of the candidate’s graduate committee, I have read the dissertation of Troy A.
Gomm in its final form and have found that (1) its format, citations, and bibliographical
style are consistent and acceptable and fulfill university and department style requirements; (2) its illustrative materials including figures, tables, and charts are in place; and
(3) the final manuscript is satisfactory to the graduate committee and is ready for submission to the university library.
Date
Larry L. Howell
Chair, Graduate Committee
Accepted for the Department
Craig C. Smith
Graduate Coordinator
Accepted for the College
Douglas M. Chabries
Dean, College of Engineering and Technology
ABSTRACT
DEVELOPMENT OF IN-PLANE
COMPLIANT BISTABLE MICRORELAYS
Troy A. Gomm
Department of Mechanical Engineering
Master of Science
Bistable microrelays have many possible applications and have the potential to
reduce the size, weight, power consumption, and cost of products in which they are used.
This research outlines the current state of microrelays, presents three new compliant
bistable micromechanisms, and characterizes their performance as microrelays. The
characterization includes a treatment of a new force-tester, a preliminary contact
resistance study, contact-force measurements, switching time measurements, insertion
loss, AC isolation, breakdown voltage, and DC isolation. This document also includes
recommendations for further research.
ACKNOWLEDGMENTS
This research could not have been completed without the help of many people. I
would like to thank my wife Amanda and our kids for their support, encouragement, and
faith. I’d also like to thank Dr. Larry Howell for his guidance and his evenings spent
proofing my thesis, Scott Lyon, Nathan Masters, Daniel Wilcox, and Chris Lott for their
help in testing, Jonathan Wittwer for his help with the force tester, and Kimberly Jensen
for the scanning electron micrographs used in this paper.
TABLE OF CONTENTS
CHAPTER 1
1.1
1.2
1.3
BACKGROUND AND THESIS OBJECTIVE ........................................................................................1
INTRODUCTION TO MEMS............................................................................................................2
OUTLINE .......................................................................................................................................3
CHAPTER 2
2.1
2.2
2.3
2.4
2.4.1
2.4.2
2.5
RELAY DESIGN ..................................................................................................29
INTRODUCTION ...........................................................................................................................29
MECHANISM DESIGN CONSTRAINTS ...........................................................................................29
MECHANISM DESIGN TRADEOFFS ...............................................................................................30
Isolation.................................................................................................................................31
Contact Performance ............................................................................................................32
Switching Time ......................................................................................................................32
Tradeoffs ...............................................................................................................................32
INCREASING DEFLECTION ...........................................................................................................32
INCREASING CONTACT FORCE ....................................................................................................33
DESIGN STEPS .............................................................................................................................34
DESIGN CHOICES FOR THIS RESEARCH........................................................................................35
CHAPTER 5
5.1
5.2
BISTABLE MICROMECHANISMS......................................................................13
INTRODUCTION ...........................................................................................................................13
OVERVIEW ..................................................................................................................................13
MECHANISMS..............................................................................................................................14
Linear Displacement Bistable Mechanism ............................................................................15
Young Mechanism .................................................................................................................20
Fully Compliant Bistable Mechanism ...................................................................................24
ACTUATION METHODS ................................................................................................................26
TIMs ......................................................................................................................................26
Manual Actuation..................................................................................................................27
CHAPTER 4
4.1
4.2
4.3
4.3.1
4.3.2
4.3.3
4.3.4
4.4
4.5
4.6
4.7
SURVEY OF PRIOR WORK..................................................................................5
INTRODUCTION .............................................................................................................................5
ACTUATION METHODS .................................................................................................................5
MICRORELAY TYPES .....................................................................................................................7
CONTACT TYPES ...........................................................................................................................7
Materials .................................................................................................................................8
Motion .....................................................................................................................................8
TYPICAL PERFORMANCE ...............................................................................................................9
CHAPTER 3
3.1
3.2
3.3
3.3.1
3.3.2
3.3.3
3.4
3.4.1
3.4.2
INTRODUCTION....................................................................................................1
FORCE TESTER..................................................................................................37
INTRODUCTION ...........................................................................................................................37
FORCE TESTER PRINCIPLES .........................................................................................................37
vii
5.3
5.4
USING THE FORCE TESTER ..........................................................................................................39
FORCE TESTER ACCURACY .........................................................................................................39
CHAPTER 6
6.1
6.2
6.2.1
6.2.2
6.2.3
6.3
6.4
6.5
6.5.1
6.5.2
6.5.3
6.6
INTRODUCTION ...........................................................................................................................41
EXPERIMENTAL SETUP ................................................................................................................41
Testing Microdevices.............................................................................................................41
Contact Designs.....................................................................................................................41
Layout of Experiment.............................................................................................................43
FABRICATION RESULTS ...............................................................................................................44
TAKING MEASUREMENTS............................................................................................................46
ANALYSIS ...................................................................................................................................47
Line Resistance......................................................................................................................47
Bulk Voltage Measurements ..................................................................................................47
Contact Resistance ................................................................................................................47
CONCLUSIONS .............................................................................................................................49
CHAPTER 7
7.1
7.2
7.3
7.4
7.5
7.5.1
7.5.2
7.5.3
7.6
SWITCHING TIME ...............................................................................................67
INTRODUCTION ...........................................................................................................................67
EXPERIMENTAL SETUP ................................................................................................................67
TAKING MEASUREMENTS............................................................................................................67
ANALYSIS ...................................................................................................................................69
Linear Displacement Bistable Mechanism ............................................................................69
Fully Compliant Bistable Mechanism ...................................................................................70
Young Mechanism .................................................................................................................70
CONCLUSIONS .............................................................................................................................71
CHAPTER 9
9.1
9.2
9.3
9.4
9.4.1
9.4.2
9.5
CONTACT FORCE ..............................................................................................53
INTRODUCTION ...........................................................................................................................53
PREDICTED VALUES ....................................................................................................................54
EXPERIMENTAL SETUP ................................................................................................................60
TAKING MEASUREMENTS............................................................................................................60
ANALYSIS ...................................................................................................................................62
Linear Displacement Bistable Mechanism ............................................................................62
Fully Compliant Bistable Mechanism ...................................................................................64
Young Mechanism .................................................................................................................65
CONCLUSIONS .............................................................................................................................66
CHAPTER 8
8.1
8.2
8.3
8.4
8.4.1
8.4.2
8.4.3
8.5
CONTACT RESISTANCE....................................................................................41
AC CHARACTERISTICS.....................................................................................73
INTRODUCTION ...........................................................................................................................73
EXPERIMENTAL SETUP ................................................................................................................73
TAKING MEASUREMENTS............................................................................................................75
ANALYSIS ...................................................................................................................................76
Contact-to-Contact Crosstalk................................................................................................76
AC Isolation...........................................................................................................................78
CONCLUSIONS .............................................................................................................................79
CHAPTER 10
VOLTAGE CHARACTERISTICS ....................................................................81
10.1
INTRODUCTION ...........................................................................................................................81
10.2
EXPERIMENTAL SETUP ................................................................................................................81
10.3
TAKING MEASUREMENTS............................................................................................................82
10.3.1
Breakdown Voltage...........................................................................................................82
10.3.2
Isolation ............................................................................................................................82
10.4
ANALYSIS ...................................................................................................................................83
10.4.1
Breakdown Voltage...........................................................................................................83
10.4.2
Isolation ............................................................................................................................84
viii
10.5
CONCLUSIONS .............................................................................................................................85
CHAPTER 11
SUMMARY.......................................................................................................87
11.1
SUMMARY...................................................................................................................................87
11.2
CONCLUSIONS .............................................................................................................................90
11.3
RECOMMENDATIONS FOR FURTHER RESEARCH ..........................................................................91
11.3.1
Optimization Research .....................................................................................................92
11.3.2
Product Research .............................................................................................................93
LIST OF REFERENCES ................................................................................................................95
APPENDIX A
ANSYS INPUT FILE FOR FULLY COMPLIANT BISTABLE MECHANISM
POTENTIAL ENERGY CURVE CALCULATION ..........................................................................99
APPENDIX B
FORCE TESTER PARTIAL DERIVATIVES AND GEOMETRY...................103
PARTIAL DERIVATIVES FOR EQUATION (5.4) ..........................................................................................103
APPENDIX C
MEASUREMENTS FROM CONTACT RESISTANCE TESTS .....................105
CONTACT VOLTAGE MEASUREMENTS AT 2 MA ......................................................................................105
PROBE TO PROBE VOLTAGE MEASUREMENTS AT 2 MA ..........................................................................109
APPENDIX D
MEASUREMENTS FROM CONTACT FORCE TESTS................................111
LINEAR DISPLACEMENT BISTABLE MECHANISM DATA ..........................................................................111
FULLY COMPLIANT BISTABLE MECHANISM DATA .................................................................................114
YOUNG MECHANISM DATA ....................................................................................................................117
APPENDIX E
MEASUREMENTS FROM AC CHARACTERISTICS TESTS ......................119
CONTACT-TO-CONTACT MEASUREMENTS FOR YOUNG MECHANISM RELAY ..........................................119
AC ISOLATION MEASUREMENTS FOR YOUNG MECHANISM RELAY ........................................................119
CONTACT-TO-CONTACT MEASUREMENTS FOR LDBM RELAY ...............................................................120
AC ISOLATION MEASUREMENTS FOR LDBM RELAY .............................................................................120
APPENDIX F
MEASUREMENTS FROM DC TESTS ..........................................................121
BREAKDOWN VOLTAGE MEASUREMENTS...............................................................................................121
ISOLATION MEASUREMENTS ...................................................................................................................122
ix
LIST OF FIGURES
Figure 3.1 – Ball on Hill Analogy: Balls A and C are in stable equilibrium positions,
ball B is in an unstable equilibrium position, and ball D is in a neutral
equilibrium position................................................................................................ 14
Figure 3.2 – Linear Displacement Bistable Mechanism .............................................. 15
Figure 3.3 – Functionally Binary Pinned-Pinned Segment (a) and half segment used
for
analysis (b)................................................................................................... 16
Figure 3.4 – Pseudo-rigid body model of the FBPP segment...................................... 16
Figure 3.5 – Pseudo-rigid body model – symmetrically divided................................. 17
Figure 3.6 – Potential energy curve for linear displacement bistable mechanism.... 19
Figure 3.7 – One of many possible Young mechanism configurations – top:
fabricated stable position; bottom: second stable position ................................. 21
Figure 3.8 – Schematic of Young mechanism configuration shown in Figure 3.7 (a)
with its pseudo-rigid body counterpart (b)........................................................... 21
Figure 3.9 – Generic pseudo-rigid body model of a Young mechanism. The Pins (A
& B) with torsional springs represent the compliant segments.......................... 22
Figure 3.10 – Potential energy curve for Young mechanism ...................................... 23
Figure 3.11 – Fully compliant bistable mechanism – top: small size mechanism in
second stable position; bottom: large size mechanism in fabricated position... 24
Figure 3.12 – Schematic of one leg of the Fully Compliant Bistable Mechanism ..... 24
Figure 3.13 – Potential energy curve for Fully Compliant Bistable Mechanism...... 25
Figure 3.14 – Thermomechanical In-plane Microactuator (TIM) ............................. 27
x
Figure 4.1 – Illustration of the distance between signal lines and the actuation
current paths. The central path is the signal line (which is open in this picture)
and the paths on the left and right are the actuation current paths. ................. 31
Figure 4.2 – Potential energy curve for the Fully Compliant Bistable Mechanism.
Regions a and b would be locations with poor contact force while region c
would provide optimal contact force..................................................................... 34
Figure 5.1 – Variables for equation (5.1). The large arrow shows the direction of
force for the flexible segment cross section (left) ................................................. 38
Figure 5.2 – Force tester. Schematic (left) and scanning electron micrograph (right)
................................................................................................................................... 38
Figure 6.1 – Cross-sections of contact designs. (a) IFAB, (b) V1, (c) V2, (d) V3,
(e) V4A, (f) V4B, and (g) V4C designs. Note that because gold is a poor
structural material, in designs with GOLD extending beyond POLY2, the gold
generally breaks and falls to the substrate below. ............................................... 42
Figure 6.2 – Layout of the contact study....................................................................... 43
Figure 6.3 – SEM pictures of contact designs. IF34 (top left), V1 (top right), V2
(middle left), V3 (middle right), V4A (bottom left), V4B (bottom right)........... 45
Figure 6.4 – SEM picture of contact design V4C......................................................... 46
Figure 6.5 – Graphical summary of voltage measurements. The values shown are in
Volts with a 2 mA load. Shown is a dot plot of the actual measured values (top)
and a plot of measurement means with 3σ error bars (bottom)......................... 48
Figure 6.6 – Graphical summary of contact resistance measurements. Shown are
the mean values (dots) and 3σ confidence intervals. The upper limits of the
Average, IF23, IF 11, and IF22 resistance measurements are 1434.7 Ω, 1395.8
Ω, 2181.2 Ω, and 1149.0 Ω respectively................................................................. 49
Figure 7.1 – Predicted contact force as a function of shuttle deflection for the Linear
Displacement Bistable Mechanism (top) and the Fully Compliant Bistable
Mechanism (bottom)............................................................................................... 54
Figure 7.2 – A general pseudo-rigid-body four-bar mechanism ................................ 56
Figure 7.3 – Predicted contact force as a function of ∆θ2 for the Young mechanism59
Figure 7.4 – Setup of contact force tests ....................................................................... 60
Figure 7.5 – Video images of contact force tests .......................................................... 61
xi
Figure 7.6 – Contact force measurement for Linear Displacement Bistable
Mechanism with 3σ error bars for both force and deflection ............................ 63
Figure 7.7 – Contact force measurements for Fully Compliant Bistable Mechanism.
First measurement (top) and second measurement (bottom) ............................. 64
Figure 8.1 – Linear Displacement Bistable Mechanism relay .................................... 68
Figure 8.2 – Surrogate Fully Compliant Bistable Mechanism (Masters, 2001) ........ 69
Figure 8.3 – Spring contacts for Young mechanism testing. The contact gap is
circled on the right. ................................................................................................. 70
Figure 9.1 – Young mechanism relay used for AC characteristics test. Circles
represent probe locations for the contact-to-contact crosstalk test and squares
represent probe locations for the AC isolation test. ............................................ 74
Figure 9.2 – Linear Displacement Bistable Mechanism relay used for AC
characteristics test. Circles represent probe locations for the contact-to-contact
crosstalk test and squares represent probe locations for the AC isolation test. 74
Figure 9.3 – Electrical diagram of experimental setup. R1 represents the resistance
of the air gap in parallel with the nitride layer and substrate. R2 is a 1 kΩ
resistor...................................................................................................................... 75
Figure 9.4 – Contact-to-contact crosstalk measurements for Young mechanism relay
(top) and LDBM relay (bottom) ............................................................................ 76
Figure 9.5 – AC isolation measurements for Young mechanism relay (top) and
LDBM relay (bottom) ............................................................................................. 78
Figure 10.1 – Relay used for voltage characteristics tests. White dots indicate probe
positions for the isolation tests ............................................................................... 82
Figure 10.2 – Results of breakdown voltage test for relay .......................................... 83
Figure 10.3 – Steps of the breakdown process captured on video.............................. 84
Figure 10.4 – Results of isolation test for relay ............................................................ 84
Figure 11.1 – Relay layout for LDBM (top) and FCBM (bottom) ............................. 88
Figure 11.2 – Relay layout for Young mechanism ....................................................... 89
xii
LIST OF TABLES
Table 2.1 – Attributes of relays in the current literature............................................ 11
Table 3.1 – Variable values for LDBM potential energy curve calculations............. 20
Table 3.2 – Variable values for Young mechanism potential energy curve
calculations .............................................................................................................. 23
Table 3.3 – Variable values for Fully Compliant Bistable Mechanism potential
energy calculations (variable names correspond to Ansys input file variables) 26
Table 5.1 – Variable values for equation (5.3) ............................................................. 40
Table 6.1 – Summary of probe-to-probe measurements (in Volts) ............................ 50
Table 7.1 – Variable values for Young mechanism contact force calculations ......... 59
Table 7.2 – Variable values for LDBM contact force calculations............................. 63
Table 11.1 – Comparison of relay performance parameters ...................................... 89
Table 11.2 – Comparison of performance parameters for selected relays ................ 90
xiii
CHAPTER 1
1.1
INTRODUCTION
Background and Thesis Objective
MEMS relays have many possible applications and have the potential to reduce
the size, weight, power consumption, and cost of products in which they are used. In
applications such as telecommunications switching in base stations and hand-held
devices, one type of relay that will be valuable is a bistable microrelay – a microrelay that
only requires power to switch from one state to another. Bistable microrelays offer
potential advantages over current microswitches, such as field effect transistors in that
they require zero power consumption to remain in the switched position and their motion
produces large gaps between contacts – which is desirable for high voltage switching and
high breakdown voltages.
One difficulty for many bistable micromechanisms is that they require the use of
large-clearance pin joints that can cause reliability problems for the mechanism. For
example, in high frequency applications, moving linkages cause impacts in the pin joint
that cause the joint to quickly fill with debris (Tanner et al., 1998) - leading to wearout
failure.
Recent research in compliant mechanisms application has yielded micro-scale
compliant structures capable of bistable behavior (Parkinson et al., 2000; Baker et al.,
2000). These mechanisms have the potential to solve several problems associated with
1
current MEMS relays. Specifically, compliant structures could replace mechanisms that
rely solely on pin joints to achieve their motion. This would allow microrelays to be
fabricated more easily and operate more reliably.
The purpose of this research is to determine the feasibility and method of using
compliant bistable mechanisms as microrelays. Specifically, the contributions of this
research are: first, the system integration of three compliant bistable micromechanism
designs and an actuator to create relays, and second, the characterization of their
performance using common relay performance metrics. The scope of the research is
limited to these contributions and will not include optimization of the relays’
performance, customization of the relays for a particular application, or development of
the relays to ready them for marketing. However, recommendations for further research
in those areas are included.
1.2
Introduction to MEMS
“Micro Electromechanical Systems” (MEMS) is the term used to describe
electromechanical devices that are fabricated on the scale of microns. Popular MEMS
devices include sensors, optical switches, and micromirror arrays such as Texas
Instruments’ Digital Light Processor. These devices are generally fabricated on silicon
substrates using integrated circuit fabrication processes such as photolithography and
surface micromachining.
Because of their small size and method of fabrication, MEMS devices have the
potential to be fabricated on-chip with integrated circuits to form a complete system on a
single die. A common example is the automotive airbag sensor developed by Analog
Devices.
2
The field MEMS is still in its early stages of development and few MEMS
devices have matured into marketable products. Most research in the field is focused on
developing new or improved fabrication processes and MEMS devices. This research
represents an effort to develop MEMS devices with the potential of achieving
marketability.
1.3
Outline
To familiarize the reader with the state of the art in MEMS relays in general,
Chapter 2 surveys prior work in the field. Chapter 3 reviews bistability in general,
reviews the prior work related to the three bistable micromechanisms and actuation
techniques used in this research, and shows a common potential energy analysis of the
mechanisms. Chapter 4 covers the general design of the relays developed for this
research while chapter 5 covers a force measurement device used for several tests.
Chapters 6 through 10 cover the characterization of the relays and Chapter 11
summarizes the research both qualitatively and quantitatively, and includes
recommendations for future research.
3
CHAPTER 2
2.1
SURVEY OF PRIOR WORK
Introduction
The body of research regarding microrelays is fairly substantial – partly due to the
explosive growth of the telecommunications industry with its extensive use of relays and
also because of pressure to achieve high component densities. The purpose of this
section is to outline the major areas of existing research in MEMS relays. To do so, the
following will be discussed:
2.2
–
Actuation Methods
–
Relay Types
–
Contact Types
–
Typical Performance
Actuation Methods
There are three main methods of MEMS relay actuation: electrostatic, thermal,
and magnetic. These three are described in detail below.
Electrostatic actuation involves creating a voltage difference between two
members. The members are pulled together through electrostatic attraction. This force is
generally negligible for macro devices, but is significant when used in MEMS devices.
Several electrostatically actuated relays of various geometries have been developed
5
including out of plane deflection (Grétillat et al., 1999; Yao and Chang, 1995; Yao et al.
1999; Zavracky, 1997) and in-plane deflection (Tang et al. 1990).
There are two main subcategories of thermal actuation: geometric and bi-material.
Bi-material thermal actuators use material with different coefficients of thermal
expansion. The materials are fabricated in layers and achieve deflection through uneven
expansion during heating. Such devices are generally heated by running current through
the bi-material structure (Sun et al., 1998) but some use an additional layer for a heating
current path (Zhang et al. 1999).
Geometric thermal actuators use only one material to achieve their deflection.
Examples include offset ground location (Pan and Hsu, 1997), variable cross-section
(Comtois et al., 1997), and angled leg (Cragun and Howell, 1999).
Magnetic actuators have also been used in MEMS relays. This type of actuation
is typically used because of its low voltage (but high current) capability. Magnetic
actuators generally have a coil – through which current can flow to produce a magnetic
field – and a movable member composed of either a ferromagnetic material or a polymer
magnet. An example of magnetic actuation is the relay presented by Taylor, Brand, and
Allen (1998). An example of a polymer magnet-based system is the actuator presented
by Lagorce, Brand, and Allen (1999). The geometry constraints for the coils of these
types of actuators have generally limited them to providing out-of-plane deflections.
The three types of actuation listed above cover the bulk of the existing literature.
There are other types of actuation – such as the use of heat to move a mercury microdrop
(Simon et al., 1997) – but these are generally more difficult to manufacture, less robust,
and only comprise a small portion of the literature.
6
One other actuation technique worth mentioning is the use of multiple energy
domains. For example, the microrelays designed by Zhou, Sun, and Carr (1999) use bimaterial thermal actuation to achieve a large deflection and then “clamp down” with
electrostatic attraction.
2.3
Microrelay Types
There are two main categories to differentiate micro relay operation:
–
Latching vs. non-latching
–
Normally open vs. normally closed
Latching relays (Form P) are those that consume power to switch positions (i.e.
from “off” to “on”) while non-latching relays consume power both to switch and to
remain in the switched position. Non-latching relays may be designated as either
normally open – when no power is being consumed, the contacts are open (Form A), or
normally closed – when no power is being consumed, the contacts are closed (Form B).
Nearly all of the micro relays developed thus far are non-latching and normally
open (Yao and Chang, 1995; Schile et al., 1998; Taylor et al. 1998; Grétillat et al., 1999;
Yao et al. 1999; Zhou et al. 1999). There are some latching relays (Sun et al., 1998) but
these generally have required a complex control signal and mechanical design to achieve
their latching ability.
2.4
Contact Types
Many different types of contacts have been used in conjunction with MEMS
relays. However, there are two basic attributes that may be used to categorize relay
contacts: their material and their motion.
7
2.4.1
Materials
Gold is the primary material used to fabricate current MEMS relay contacts. This
is due to its high electrical conductivity, softness, and availability in commercial
processes (Kruglick and Pister, 1999). Other contact materials have also been used
including nickel to gold (Grétillat et al., 1999), nickel-iron to gold (Taylor et al., 1998),
and even mercury (Simon et al., 1997; Lee and Kim, 2000).
2.4.2
Motion
There are two main types of contact configurations – as described by their contact
motion – horizontal and vertical. Vertical motion contacts move out of plane to make
contact and the connection is made by the top or bottom surface of the contact.
Horizontal contacts move in-plane and make the connection with the side of the contact.
Contact materials used to achieve low contact resistance are generally not good
structural materials (gold for example) so the contact will often have a structural portion
that has some layer or coating of contact material. Because of this, vertical motion
contacts are used much more frequently due to the comparative ease of fabricating
horizontal layers (Yao and Chang, 1995; Schile et al., 1998; Taylor et al. 1998; Grétillat
et al., 1999; Yao et al. 1999; Zhou et al. 1999). Horizontal contacts are less common due
to the difficulty of depositing contact material on the vertical walls that will make contact
(Kruglick and Pister, 1999).
8
2.5
Typical Performance
The relays found in the current literature are embodied in a wide variety of
designs and, therefore, exhibit a wide range of performance attributes. The important
attributes of microrelays are:
–
Switching time: Low switching times are preferred as they allow for a higher
range of switching frequencies. This is usually specified in a unit of time, but is
sometimes measured as the maximum frequency at which the relay is capable of
operating.
–
Displacement: Large displacements are generally preferred because the larger the
displacement the larger the isolation (in terms of resistance and in terms of
breakdown voltage between the signal lines and the actuation lines).
–
Actuation power: To reduce Joule heating and general power consumption, low
actuation power is desired. Most papers specify this attribute as actuation voltage,
current, power, or some combination of the three. Because actuator resistance is
generally not specified, when only voltage or current is specified, the actuation
power cannot be calculated.
–
Hold power: For applications with low switching frequencies or high hold times
(the switch is left “on” for a long time) low hold power (the power required to
hold the relay in the actuated position) is desired. This is generally not specified
in the literature, but can generally be deduced from the actuation power, actuation
method, and the behavior of the relay.
9
–
Physical size: A small physical size is desirable as it leads to increased component
densities. In several cases, only component sizes are specified. In these cases, the
overall relay system size is extrapolated from component sizes and device images.
–
Contact resistance: Low contact resistance is desired to decrease signal
attenuation and reflection (for high frequency signals). This attribute is almost
universally specified in the literature.
–
Breakdown voltage: High breakdown voltages (the voltage required for dielectric
breakdown between contacts along the signal line) are desired to increase the
reliability of the relay. Additionally, there are FCC requirements for breakdown
voltage in telecommunications system components. Although this attribute is
very important in the telecommunications industry, most papers do not specify the
breakdown voltage of the relay.
–
Isolation: High isolation, in terms of effective impedance or breakdown voltage
between the contacts and the actuation lines, is desired to increase relay
reliability. This attribute is rarely specified in the literature. It is specified either
as a voltage or as effective impedance.
–
Contact force: High contact forces are generally more desirable as they lead to
decreased contact resistance and decreased sensitivity to contact corrosion or
other contact imperfections. This attribute is also rarely specified in the literature,
as it is generally difficult to measure—especially in relays with vertical motion
(out of plane) contacts. When it is specified is often a calculated rather than a
measured value.
10
The attributes of relays in the current literature are summarized in Table 2.1
(Grétillat et al., 1999; Kruglick and Pister, 1999; Shiele et al., 1998; Simon et al., 1997;
Sun et al., 1998; Taylor et al., 1998; Yao and Chang, 1995; Yao et al., 1999; Zavracky et
al., 1997; Zhang et al., 1999; Zhou et al., 1999). In comparison to these relays, it is
believed that the main areas in which the relays developed in this research can make a
contribution are breakdown voltage, isolation, and hold power because of the large
deflections of the mechanisms and their bistable motion.
Table 2.1 – Attributes of relays in the current literature
Attribute
High
Actuation Current
600 mA
Actuation Voltage
150 V
Actuation Power
320 mW
Hold Power
320 mW
Breakdown Voltage > 400 V
Contact Force
500 µN
Contact Resistance
300 Ω
Displacement
16 µm
Isolation >1600 V
Low
50 nA
0.53 V
1 µW
0
>3 V
3 µN
22.4 µΩ
0.5 µm
Size 2.E+06 µm2 1E+04 µm2
Switching Time
5 ms
2 µs
11
CHAPTER 3
3.1
BISTABLE MICROMECHANISMS
Introduction
The mechanisms used in this research were developed previously. While all three
were developed at Brigham Young University, they were developed and analyzed
independently. The purpose of this chapter is to review bistable mechanisms in general,
review the mechanisms to be used in this research, and to include a simultaneous analysis
of all three mechanisms so they may be more easily compared. This chapter contains
some original work in the analysis of the potential energy curves of the mechanisms.
3.2
Overview
A bistable mechanism is a device that has two stable equilibrium positions. For
example, a light switch can rest at either the “on” or “off” position.
An equilibrium position is a position in which the mechanism has no acceleration.
Equilibrium positions of a mechanism can be found by finding where the derivative of a
mechanism’s potential energy equation equals zero. An equilibrium state is unstable if
small disturbances cause the mechanism to deviate from its position and not return. If the
mechanism returns to the equilibrium position after being disturbed, the position is a
stable equilibrium position. If the mechanism is disturbed and stays in the disturbed
position, it is in neutral equilibrium.
13
B
D
C
Gravity
A
Figure 3.1 – Ball on Hill Analogy: Balls A and C are in stable equilibrium positions, ball
B is in an unstable equilibrium position, and ball D is in a neutral equilibrium position.
A given equilibrium position can be found to be stable or unstable by taking the
second derivative of the mechanism’s potential energy equation. If the second derivative
is negative at the equilibrium position, it is an unstable equilibrium. If it is positive, the
equilibrium position is stable. Figure 3.1 shows the common “Ball on a Hill” analogy for
equilibrium positions.
3.3
Mechanisms
A compliant mechanism is a mechanism that derives some (partially compliant)
or all (fully compliant) of its motion from the deflection of its members. Three compliant
bistable mechanisms will be used for this research:
–
A linear displacement bistable mechanism (Baker et al., 2000)
–
A Young mechanism (Jensen et al., 1999)
–
A fully compliant bistable mechanism (Parkinson et al., 2000)
14
Figure 3.2 – Linear Displacement Bistable Mechanism
3.3.1
Linear Displacement Bistable Mechanism
The Linear Displacement Bistable Mechanism (LDBM) (Baker et al., 2000) is
composed of a central slider with an array of functionally binary pinned-pinned (FBPP)
segments (“legs”) on each side (Figure 3.2). Because the segments have pin joints on
each side, they can only support loads acting in-line with the pins. The segments cannot
support any other loads including moments. Because of this, the segments act as linear
springs with non-linear force-deflection relationships. By fabricating the FBPP segments
at an angle to the slider, the device achieves its bistable behavior.
The potential energy curve and, therefore, the equilibrium positions of the LDBM
can be found using the Pseudo-Rigid Body Model (Howell and Midha, 1995) and treating
the legs of the mechanism as FBPP segments. The Pseudo-Rigid Body Model is a
method of modeling compliant mechanisms by accurately approximating flexible
segments with rigid segments and torsional springs. In this case, it allows the FBPP
15
Figure 3.3 – Functionally Binary Pinned-Pinned Segment (a) and half segment used for
analysis (b)
Figure 3.4 – Pseudo-rigid body model of the FBPP segment
segment to be analyzed using standard kinematic analysis – instead of by the use of
elliptic integrals, which are required for an exact solution.
Because of symmetry, the arc can be divided at the midpoint for analysis (Figure
3.3). The pseudo-rigid body model of the FBPP segment is shown in Figure 3.4, and the
model for the half segment is shown in Figure 3.5. The symmetry is maintained by
requiring that the link lengths, torsional spring constants (KΘleft and KΘright), and link
angles (Θleft and Θright) be equal.
In order to analyze the model, the torsional spring constant and the pseudo-rigid
body link length must be found. The pin joint distance from ground is determined by the
16
Figure 3.5 – Pseudo-rigid body model – symmetrically divided
non-dimensional “fundamental radius factor”, γ, and is given by L(1-γ) where L is the
arc-length of the symmetrical half-segment. γ is related to the nondimensionalized initial
curvature (κ0) of the segment and may be calculated with equations (3.1) and (3.2)
(Edwards et al., 1999):
γ = 0.8063 − 0.0265κ 0
0.500 ≤ κ 0 ≤ 0.595
(3.1)
γ = 0.8005 − 0.0173κ 0
0.595 ≤ κ 0 ≤ 1.500
(3.2)
where:
κ0 =
L
R0
(3.3)
the R0 is the segment’s radius of curvature.
Another important factor required to analyze the model is the non-dimensional
“characteristic radius factor,” ρ (Howell and Midha, 1996). In order to take into account
the initial curvature of the segment, the length of the rotating link in the pseudo-rigidbody model is determined by ρL, which is given by:
17
2
a
 b 
ρ =  i − (1 − γ ) +  i 
L
 L
2
(3.4)
where ai and bi are the initial horizontal and vertical coordinates (respectively) of the
segment end and are given by:
L
sin κ 0
κ0
(3.5)
L
(1 − cos κ 0 )
κ0
(3.6)
ai =
and
bi =
With equations (3.5) and (3.6), the torsional spring constant for the pseudo-rigidbody model may be calculated with the following:
K = ρK Θ
EI
L
(3.7)
where KΘ for an initially curved segment is given as (Edwards et al., 1999):
K Θ = 2.568 − 0.028κ 0 + 0.137κ 02
(3.8)
The potential energy, V, for a half-segment may now be calculated by:
V =
1
2
K (Θ − Θ i )
2
(3.9)
where Θi is the initial pseudo-rigid-body model link angle. For the full mechanism, the
potential energy is given by:
Vmech = 4nV half − segment
where n is the number of segments per side (ex: 4 for Figure 3.2).
18
(3.10)
900
Potential Energy (µ N µ m)
800
700
600
500
400
300
200
100
0
0
10
20
30
40
50
60
70
80
90
100 110
Deflection (µ m)
Figure 3.6 – Potential energy curve for linear displacement bistable mechanism
A more useful potential energy curve than V as a function of ∆Θ is V as a function
of shuttle deflection δ. The relationship between δ and Θ is given by:
 x 2 + ( y − δ )2 − 2(1 − γ )L 
i

Θ = cos  i


2ρL


−1
(3.11)
where yi is the pin-to-pin distance in the δ direction and xi is the pin-to-pin distance in the
direction perpendicular to δ.
The potential energy curve for the linear displacement bistable mechanism is
shown in Figure 3.6. The mechanism geometry used and the results of the intermediate
calculations necessary to generate the potential energy curve are shown in Table 3.1.
19
Table 3.1 – Variable values for LDBM potential energy curve calculations
Variable
R0
L
κ0
γ
ai
bi
ρ
KΘ
Young’s Modulus (E)
Width
Height
I
K
Θi
xi
yi
Segments per side
3.3.2
Value
Unit
144 µm
122.94 µm
0.8538
0.7857
108.54 µm
49.37 µm
0.7799
2.644
1.69E+11 Pa
4 µm
2 µm
10.667 µm4
30236 µN*µm
0.5309 Radians
210 µm
55 µm
3
Young Mechanism
According to Jensen et al., 1999, a Young mechanism is one that:
•
Has two revolute joints, and, therefore, two links, where a link is defined
as the continuum between two rigid-body joints (Midha, et al., 1994)
•
Has two compliant segments, both part of the same link
•
Has a pseudo-rigid-body model which resembles a four-bar mechanism
Figure 3.7 shows the type of Young mechanism to be used in this research. The pseudorigid-body model for the mechanism is shown in Figure 3.8.
20
Figure 3.7 – One of many possible Young mechanism configurations – top: fabricated
stable position; bottom: second stable position
Figure 3.8 – Schematic of Young mechanism configuration shown in Figure 3.7 (a) with
its pseudo-rigid body counterpart (b)
The potential energy, V, of the mechanism is given by:
V =
(
1
K A ψ 2A + K B ψ 2B
2
)
(3.12)
where KA and KB are the torsional spring constants and ψA and ψB are the relative angular
deflections of the torsional springs. The relative angular deflections are given by:
ψ A = (θ 2 − θ 2 i ) − (θ 3 − θ 3i )
(3.13)
ψ B = (θ 4 − θ 4 i ) − (θ 3 − θ 3i )
(3.14)
21
Figure 3.9 – Generic pseudo-rigid body model of a Young mechanism. The Pins (A & B)
with torsional springs represent the compliant segments.
where the i subscript denotes the initial value of the given angle (Figure 3.9 illustrates the
locations of the various angles).
The torsional spring constants KA and KB can be calculated with the following
equation:
K = γK Θ
EI
l
(3.15)
where γ and KΘ may be approximated as (Howell and Midha, 1995):
γ ≈ 0.85
K Θ ≈ 2.65
(3.16)
and l is the actual length of the flexible segment (r = γl).
The potential energy curve for the Young mechanism is shown in Figure 3.10.
The parameters and necessary intermediate calculations used to calculate the potential
energy curve are shown in Table 3.2.
22
1000
Potential Energy (µN µm)
900
800
700
600
500
400
300
200
100
0
-10
0
10
20
30
40
∆θ 2 (degrees)
Figure 3.10 – Potential energy curve for Young mechanism
Table 3.2 – Variable values for Young mechanism potential energy curve calculations
Value
Unit
Actual
PRBM
l1
121.0
µm
l2
129.0
µm
l3
235.8
µm
l4
229.0
µm
121.0 µm
r1
r2
109.7 µm
216.5 µm
r3
r4
194.7 µm
0degrees
θ1
12degrees
θ2
-26.23degrees
θ3
-22degrees
θ4
IA
20.83
µm
IB
4.5
µm
61478 µN µm
KA
KB
7480 µN µm
2.65
KΘ
0.85
γ
Variable
23
Figure 3.11 – Fully compliant bistable mechanism – top: small size mechanism in second
stable position; bottom: large size mechanism in fabricated position
Figure 3.12 – Schematic of one leg of the Fully Compliant Bistable Mechanism
3.3.3
Fully Compliant Bistable Mechanism
The Fully Compliant Bistable Mechanism (Parkinson et al., 2000) is a single-
piece, linear-displacement mechanism (Figure 3.11). The mechanism is composed of a
central slider with compliant “legs” on either side. The legs have a variable cross-section
– with the ends being thin and flexible while the centers are thick and rigid. The ends of
the legs are connected to flexible “T”-segments that are, in-turn, anchored to the
substrate.
24
4000
Potential Energy (mN mm)
3500
3000
2500
2000
1500
1000
500
0
0
10
20
30
40
50
60
70
Deflection (mm)
Figure 3.13 – Potential energy curve for Fully Compliant Bistable Mechanism
The behavior of the mechanism may be qualitatively visualized by considering
the central slider to act as a classic rigid-body slider, the slender ends of the legs to act as
pin-joints with torsional springs, and the T-segments to behave as linear springs. This is
illustrated in Figure 3.12. While this model is helpful in visualizing the behavior of the
mechanism, the potential energy curve for the mechanism is best calculated with a nonlinear finite element solver.
The potential energy curve for the specific geometry to be used in this research
was calculated using Ansys – a commercial non-linear finite element solver. The curve is
shown in Figure 3.13 and the command file used to generate the data for the curve is
given in Appendix A. The geometry used to calculate the potential energy curve is given
in Table 3.3.
25
Table 3.3 – Variable values for Fully Compliant Bistable Mechanism potential
energy calculations (variable names correspond to Ansys input file variables)
3.4
Variable
l1
l2
Value
64
96
Unit
µm
µm
l3
146.4
µm
l4
77
µm
h1
3.5
µm
h2
h3
h4
bb
2.5
10
2.5
3.5
µm
µm
µm
µm
thetad
7
Degrees
ex
169e9
Pa
Description
Length of the T-segment
Length of the flexible
portion of the leg closest
to the T-segment
Length of the rigid portion
of the leg
Length of the flexible
portion of the leg closest
to the slider
Width of l1 (the cubed
dimension of the area
moment of inertia)
Width of l2
Width of l3
Width of l4
Thickness of the
mechanism
Angular offset of the legs
from normal to the slider
Young’s Modulus
Actuation methods
For the bistable mechanisms discussed above, there are currently two main
methods of actuation: Thermal In-plane Microactuators (TIMs) (Cragun and Howell,
1999) and direct manual actuation.
3.4.1
TIMs
Figure 3.14 shows a typical thermomechanical in-plane microactuator (TIM).
The actuator is composed of two mechanically grounded electrical contact pads on either
side, long, slender legs, and a movable shuttle. The legs are angled slightly off
perpendicular from the shuttle and Joule heating causes them to expand. The angle of the
26
Figure 3.14 – Thermomechanical In-plane Microactuator (TIM)
legs and the symmetry about the main axis of the shuttle causes the shuttle to deflect
when the legs expand.
These actuators generate higher reaction forces than other types of actuation (such
as electrostatic comb drives) but generally have smaller deflections. To overcome this
limitation, the TIMs used for these mechanisms use a “staged” configuration. To achieve
large deflections, TIMs have been used in a staged configuration. In this configuration,
two axially aligned TIMs push toward each other. They are connected by a “stage” that
consists of a movable shuttle and with angled legs. The motion of the TIMs cause the
stage shuttle to move perpendicular to the axis of the TIMs, and the slight angle of the
staged portion of the actuator amplifies the deflection of the TIMs.
3.4.2
Manual Actuation
Before the integration of the compliant bistable micro-mechanisms and the TIMs,
the mechanisms were switched using direct manual actuation. This was done by using an
electrical probe to put the mechanism from one stable position to another. While this is
27
an unacceptable actuation method for a relay, it does serve the purpose of actuating
mechanisms in their early stages of development.
28
CHAPTER 4
4.1
RELAY DESIGN
Introduction
Each of the mechanisms described in the previous chapter are specific instances
of three mechanism families. Mechanisms with widely varying performance
characteristics may be designed within any given family by specifying various
geometries. The purpose of this chapter is to outline the principles that should be
employed when designing relays based on any of the three mechanism families.
4.2
Mechanism Design Constraints
When designing a specific instance of a mechanism family, there are generally
more unknowns (in the form of geometric specifications) than there are constraints. For
example, there are several different variations of the Linear Displacement Bistable
Mechanism that could achieve the same reaction force at a given displacement. It is,
therefore, necessary to further constrain the design of the mechanism to fit the particular
relay application.
There are two basic ways to constrain the relay design:
–
Specify the mechanism’s deflection required to make contact
–
Specify the desired contact force
29
The values for these constraints are chosen based on the desired performance of the relay.
Ideally a designer would have the contact to be used fully characterized (i.e. resistance as
a function of contact force, signal current, and signal frequency). The designer would
then use the desired application’s target resistance and/or switching time to constrain the
contact force.
Additionally, the ideal design scenario would have the mechanism / contact type
combination’s isolation fully characterized (as a function of signal frequency and
mechanism design). The designer would then use a target isolation to constrain the
deflection. Other performance parameters, such as switching time, are also directly
affected by contact force and deflection decisions and play a role in further constraining
the relay design.
Because of time and financial constraints, these sorts of full characterizations are
generally not feasible; characterizing the isolation, for example, would take hundreds or
thousands of iterations to fully quantify how isolation varies with a mechanism family’s
design. However, a general, qualitative look at how design changes modify the
mechanism’s performance as a relay is valuable.
4.3
Mechanism Design Tradeoffs
In order to make good design decisions, it is important to understand how
deflection and contact force affect the performance of the relay and the mechanism in
general. Outlined in this section are the following performance areas:
–
Isolation
–
Contact Performance
–
Switching Time
30
Figure 4.1 – Illustration of the distance between signal lines and the actuation current
paths. The central path is the signal line (which is open in this picture) and the paths on
the left and right are the actuation current paths.
4.3.1
Isolation
In general, increasing the distance between the signal lines and the actuation
current paths increases isolation (see Figure 4.1). Each of the three bistable mechanisms
used in this research require two actuation circuits – one to move the mechanism from its
fabricated state to its second stable equilibrium, and another to move it back. Because
the contacts are located between the mechanism’s unstable equilibrium position and its
second stable position, increasing the total deflection of the mechanism tends to increase
the isolation between the signal line and one actuation circuit (the one on the right in
Figure 4.1). Isolation between the signal line and the second actuation circuit may be
increased by increasing their separation.
31
4.3.2
Contact Performance
In general, for most contact designs, high contact force is desirable. Higher
contact force leads to decreased contact resistance.
4.3.3
Switching Time
In general, switching time is a function of the deflection required to move from
the initial stable equilibrium to the contacting position. The further the required
deflection, the slower the switching time.
Switching time is also a function of the amount of potential energy stored at the
unstable equilibrium position. The more energy stored, the more quickly the device will
move from the unstable equilibrium position to the contact, reducing the switching time.
Because of the high reaction forces imparted from the TIMs, devices with greater
potential energy at the unstable equilibrium position do not switch significantly slower
than those with less potential energy at the unstable equilibrium position.
4.3.4
Tradeoffs
The main tradeoff seen with designing relays based on the three mechanism
families is that increasing deflection increases isolation but also increases switching time.
Additionally, if force is increased by making the compliant members more stiff, the
maximum stress in the mechanism will increase – potentially reducing the mechanism’s
reliability.
4.4
Increasing Deflection
There are several ways to modify the design of the three mechanisms to increase
the deflection. One method would be to increase the overall scale of the device
32
geometry. This would generally lead to lower contact forces if the compliant members
are not proportionally stiffened.
Another method would be to move the contacts further from the unstable
equilibrium position. This would also lead to reduced contact force and increased
switching time if some other change is not also made. It would also lead to decreased
isolation because the signal line would be moved closer to the second actuator’s current
path.
Additionally, each mechanism family has unique ways of increasing the total
deflection. For example, the Linear Displacement Bistable mechanism could be designed
with its legs at a greater angle from perpendicular to the shuttle, or an additional length of
rigid silicon could be added to the rigid segment of the Young mechanism.
4.5
Increasing Contact Force
There are two main methods of increasing the contact force. First, the compliant
segments of the mechanism may be stiffened. This would increase the contact force and
decrease the switching time, but the maximum stresses would be increased.
Second, the contacts may be moved closer to the unstable equilibrium of the
mechanism. This is a good solution because the contact force and isolation (for the
LDBM and the FCBM) would increase while the switching time would decrease (the
isolation would increase because the signal line would move closer to the center of the
two actuation current lines – it is generally closer to the second actuator because the first
actuator is offset by the mechanism).
An important point is that the potential energy curves discussed in Chapter 3 are
helpful in determining the ideal location for the contacts. The steeper the potential
33
4000
Potential Energy (mN mm)
3500
c
3000
2500
a
2000
b
1500
1000
500
0
0
10
20
30
40
50
60
70
Deflection (m m )
Figure 4.2 – Potential energy curve for the Fully Compliant Bistable Mechanism.
Regions a and b would be locations with poor contact force while region c would provide
optimal contact force.
energy curve, the higher the reaction force at that position. Optimally, the contacts
should generally be placed toward the center of the region between the unstable
equilibrium position and the second stable equilibrium position where the downward
slope of the potential energy curve is at a maximum (see Figure 4.2).
4.6
Design Steps
Based on the above discussion, a designer should follow these steps when
designing a relay based on one of the three mechanism families used in this study:
–
Determine the critical performance characteristics of the relay
–
Chose the basic geometry to give the required deflection, contact force, and
associated performance attributes (such as switching time)
–
Prototype the relay and test the performance parameters
34
–
Modify the design based on the above discussion to compensate for any
deficiencies in isolation or switching time
4.7
Design Choices for this Research
For this research, the three mechanisms used were chosen based on their bistable
behavior, their compliant (partially or fully compliant) nature, and accessibility for the
research.
The system designs for the relays used in this research were chosen using the
method outlined above. Two main factors played into this decision. First, the relays for
this research were not designed for a specific product application so the designs had no
specific targets for the relay performance characteristics. Second, the mechanisms have
never been tested as relays so their performance characteristics as functions of design
have not been measured. Future designers of these types of relays will be able to use the
results of this research to help optimize designs for specific applications.
For these reasons, the same geometry as that used to calculate the potential energy
curves of Chapter 3 was used to fabricate the relays for this research. The specifics of
contact design and location are given in Chapters 6 & 8.
35
CHAPTER 5
5.1
FORCE TESTER
Introduction
In order to measure the contact force of the mechanisms used for relays in this
research, as well as to characterize the contacts studied in this research, it is necessary to
measure forces on-chip. This is a difficult task at the micro-level and cannot be done
directly with current technology. In order to indirectly measure such forces, a force tester
was developed.
5.2
Force Tester Principles
The basic principle behind the force tester is the use of beam deflection to infer
reaction force. The force tester consists of an array of beams in mechanical series
connections. Figure 5.2 shows a schematic of the beam system in its initial fabricated
position and its deflected position as well as a scanning electron micrograph of a
fabricated force tester. The entire device is constrained as a slider that may only translate
in the direction of the force to be tested.
Using small deflection (Bernoulli-Euler) assumptions, the reaction force, F, may
be calculated by:
F=
NEbh 3
d
L3
37
(5.1)
F
d
b
L
h
Figure 5.1 – Variables for equation (5.1). The large arrow shows the direction of force
for the flexible segment cross section (left)
F - Test
F - Probe
Figure 5.2 – Force tester. Schematic (left) and scanning electron micrograph (right)
where b is the out-of-plane thickness of the beams (see Figure 5.1), d is the deflection of
the central rigid members, E is the Young’s modulus of the material (polycrystalline
silicon in this case), h is the in-plane width of the beam (in the direction of deflection), L
is the length of the individual beams, and N is the total number of deflecting beams (12
for the force tester in Figure 5.2).
38
5.3
Using the Force Tester
The tester is used by pushing the large rigid section (at the bottom of the images
above) with a probe. The tester slides forward and the central rigid segments push
against the test structure. The deflection of the flexible segments is measured optically,
by comparing the relative motion of the central rigid segments to the large rigid segment.
The force can then be calculated using equation (5.1).
5.4
Force Tester Accuracy
Equation (5.1) is a linear approximation of the force-deflection relationship. In
order to improve the accuracy of the equations while maintaining the ease of analysis of
linear approximation, an equation for the approximation error may be used. This
equation is found by comparing the linear solution to the closed-form elliptic integral
solution (Bisshop and Drucker, 1945) and curve-fitting the error function (Wittwer,
2001). For the case of a vertical load on a cantilever beam (the loading case for this
mechanism), the equation for force error, εP, evaluated for 0 < d/L < 0.75 is:
2
3
d 
d 
d 
d
ε P = 0.0040   − 1.0760  + 0.1697   + 0.3390  
L
L
L
L
4
(5.2)
Including the force error given in equation (5.2), equation (5.1) may be rewritten as:
F=
NEwh 3 d 1
L
1+ εP
(5.3)
The values of the variables for equation (5.3) are shown in Table 5.1 with the exception
of N, which is 12 for the contact resistance measurements (Chapter 6) and 4 for the
contact force measurements (Chapter 7).
39
Equation (5.3) gives a percent error of less than 0.03%, but there is another source
of error for the force measurement – variability of the equation’s parameters. Each of the
parameters in equation (5.3) are somewhat uncertain and can be well represented as
normally distributed random variables. As such, a mean and standard deviation may be
calculated for each parameter. For example, Young’s modulus of polycrystalline silicon
for this manufacturing process has a mean value of 162 GPa and a standard deviation of
14 GPa (Sharpe et al., 1999). The variance of each parameter may be used to calculate
the total variance of F with the following equation:
2
2
2
2
2
 ∂F  2  ∂F  2  ∂F  2  ∂F  2  ∂F  2
σ 2F = 
 σb + 
 σh + 
 σd + 
 σL
 σE + 
 ∂E 
 ∂b 
 ∂h 
 ∂d 
 ∂L 
(5.4)
The equations for each of the partial derivatives for the equation above as well as the
specific values for the force tester geometry used in this research are given in
Appendix B. The uncertainties used for equation (5.4) are shown in Table 5.1 with the
exception of σd, which is calculated for each deflection measurement.
Using equations (5.3) and (5.4), the measured deflection of the force tester may be
converted to a force and a force uncertainty. The user of the tester can determine both the
force and a confidence interval for that force.
Table 5.1 – Variable values for equation (5.3)
Variable
Mean
b
E
h
L
3.5 µm
162 GPa
3 µm
150 µm
Standard
Deviation
0.06 µm
14 Gpa
0.05 µm
0.05 µm
40
CHAPTER 6
6.1
CONTACT RESISTANCE
Introduction
A relay’s contact resistance is one of its most important performance parameters.
A well-designed contact with low contact resistance can help the relay achieve low power
consumption and low signal attenuation. For these reasons, a preliminary study of
contact design – focusing on contact resistance – is included in this research.
6.2
Experimental Setup
6.2.1
Testing Microdevices
In order to test the microdevices in this research, a standard microscope probe
station was used for all test in Chapters 6 through 10. This consists of a stereoscopic
microscope with a CCD video camera and a stage for the mounting of vacuum probe
holders. Standard microprobes with an electrical connection through the probe station
were used.
6.2.2
Contact Designs
Fifteen contact designs were used for this study. Nine of the designs were based
on the layout shown in Figure 6.1(a). To make these nine designs, the offset of Poly2
41
B
GOLD
GOLD
POLY2
POLY2
POLY2
POLY1
POLY2
POLY1
POLY1
A
(b)
(a)
GOLD
GOLD
POLY2
POLY2
POLY2
POLY1
POLY1
POLY2
(c)
(d)
GOLD
GOLD
POLY2
POLY2
POLY2
POLY2
POLY1
POLY1
POLY1
POLY1
(e)
(f)
GOLD
POLY2
POLY2
POLY1
POLY1
(g)
Figure 6.1 – Cross-sections of contact designs. (a) IFAB, (b) V1, (c) V2, (d) V3,
(e) V4A, (f) V4B, and (g) V4C designs. Note that because gold is a poor structural
material, in designs with GOLD extending beyond POLY2, the gold generally breaks and
falls to the substrate below.
42
from Poly1 was set at 1, 2, and 3 microns. For each of these levels, the offset of Gold
from Poly 1 was set at 1 micron less than the Poly2 offset, the same as the Poly2 offset,
and 1 micron more than the Poly2 offset. The naming scheme for this contact design is
“IFAB” where A is the offset of Poly2 from Poly1 and B is the offset of Gold from
Poly1. For example, IF23 would have a Poly2 layer that extends 2 microns beyond Poly1
and a Gold layer that extends 3 microns beyond Poly1. For this contact design, the
geometry of both the stationary and the movable sides of the contact is identical.
The remaining six of the fifteen designs are designated with a V followed by a
Figure 6.2 – Layout of the contact study
number 1 through 4. Design V4 has 3 variations, A through C. Of the 15 designs, all
have contact areas that are flat and perpendicular to the direction of motion except for
contact V3, which has an angled, tooth-shaped design. Cross-sections for the V
designated designs are shown in Figure 6.1(b-g).
6.2.3
Layout of Experiment
In general, the resistance of a contact is a function of the contact force. Therefore,
this experiment was laid out with a force tester (as described in Chapter 5) for each
contact design. Each force tester is capable of exerting and allowing for the measurement
of up to 1401 µN of force with a standard deviation of 145 µN. Figure 6.2 shows a photo
of the layout taken with a scanning electron microscope (SEM).
The contacts with the pads are mechanically grounded, while those without pads
are attached to a slider mechanism. The force testers slide independent of the contacts
and are able to push the contacts together to make an electrical connection.
43
Figure 6.3 – Layout of the contact study
The contacts on the sliding contact bar are connected by a gold line to provide a
current path. Each design has five copies per force tester. This allows for redundancy in
case of damage to the contacts. Additionally, multiple contacts per contact bar would
provide a means of separating the line resistance from the contact resistance.
6.3
Fabrication Results
Scanning electron microscope images of each of the contact designs are shown in
Figures 6.4 and 6.5. It can be seen from these images that gold protrusions generally
break and fall to the substrate. Additionally, misalignment of layers can be seen (IF34
image). This is probably due to inexact alignment of layer masks prior to photoresist
exposure.
44
Figure 6.4 – SEM pictures of contact designs. IF34 (top left), V1 (top right), V2 (middle
left), V3 (middle right), V4A (bottom left), V4B (bottom right)
45
Figure 6.5 – SEM picture of contact design V4C
6.4
Taking Measurements
To measure the contact resistance, three probes are necessary. Two probes are
used to make the electrical connection by touching two of the contact pads. The third
probe is used to push the force gauge against the contact bar and close the contact.
Because of the physical scale and equipment involved, it is impossible to
consistently apply the same amount of force each time a contact is tested. Therefore, a
high and a low force were used – a small force gauge deflection for the low force and a
large deflection for the high force. These positions were recorded on a videocassette for
use in making optical measurements of the deflections.
A multichannel circuit analyzer (HP 4145A) was used to apply a current of 2 mA
through the contacts and to measure the resulting voltage. The current was applied and
voltage measured several times each time a contact was tested. Measurements were
made on three different arrays on dies from three different wafers. Appendix C shows
the raw data from these measurements.
46
6.5
6.5.1
Analysis
Line Resistance
Line resistance was negligible in our measurements. The measurement variability
on single sets of contacts was significant, with standard deviations ranging from 0.0023
V (1.15 Ω) to 0.5199 V (260 Ω) with an average standard deviation of 0.1039 V (52 Ω).
Because of this, no difference could be found when comparing measurements of voltage
across the outer contacts with measurements of voltage across neighboring contacts.
Line resistance, therefore, was not separated from the total measured resistance.
6.5.2
Bulk Voltage Measurements
Figure 6.6 shows a graphical summary of the voltage measurements (with a 2 mA
load). The top graph is a dot plot of the actual measured voltages for each contact. The
bottom graph shows the mean voltage for each contact with error bars at plus and minus
three standard deviations. The bottom graph is ordered by ascending means.
6.5.3
Contact Resistance
To isolate the contact resistance from the bulk system resistance, voltage
measurements (with a current of 2 mA) were taken with two probes touching the same
gold pad. This measurement data is given in Table 6.1 (measurements of voltage with
the probes directly touching are also shown in Table 6.1, but were used for comparison
purposes only and were not factored in to the probe-to-probe voltage mean or variance).
The mean voltage was found to be 0.011893 V with a standard deviation of 0.003860 V.
47
3
Volts
2
1
V4C
V3
IF23
V4B
V2
Average
V4A
V1
V4B
IF34
IF33
IF32
IF23
IF22
IF21
IF12
IF11
IF10
0
Volts
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
IF22
IF11
V1
IF21
V3
V4C
IF33
V4A
IF32
IF12
IF34
1.0
0.5
0.0
Contact Type
Figure 6.6 – Graphical summary of voltage measurements. The values shown are in
Volts with a 2 mA load. Shown is a dot plot of the actual measured values (top) and a
plot of measurement means with 3σ error bars (bottom).
The mean voltage was subtracted from each of the individual contact voltage
measurements. The standard deviation of the bulk system voltage was included by taking
the square root of the sum of the contact voltage variance and bulk system variance
(standard deviation squared). The modified contact voltages and standard deviation were
divided by 0.002 A to convert to Ohms. It is important to note that these values represent
the resistance of both of the contacts in the current path. The measurements may be
48
1000.0
Resistance (Ohms)
900.0
800.0
700.0
600.0
500.0
400.0
300.0
200.0
100.0
IF22
IF11
V1
IF23
Average
V4B
IF21
V3
V4C
IF33
V4A
IF32
IF12
IF34
0.0
Contact Type
Figure 6.7 – Graphical summary of contact resistance measurements. Shown are the
mean values (dots) and 3σ confidence intervals. The upper limits of the Average, IF23,
IF 11, and IF22 resistance measurements are 1434.7 Ω, 1395.8 Ω, 2181.2 Ω, and
1149.0 Ω respectively.
divided by 2 to isolate the resistance of the individual contacts. The resistances are
summarized in Figure 6.7.
6.6
Conclusions
There are two main factors involved in choosing a contact: low mean resistance,
and low variation in resistance measurements. From the graphs shown above it is clear
that the five contact designs with the lowest mean resistance are IF34, IF12, IF32, V4A,
and IF33 with respective mean resistance values of 49.2 Ω, 74.9 Ω, 77.3 Ω, 131.0 Ω, and
192.3 Ω. This could be misleading, though, because for IF32, half of the devices tested
showed no contact at all (a fact that is not included in the mean resistance calculations)
even though the voltage was quite low when contact was made.
49
Low variation is also important for achieving consistent contact results. The
contact designs with the lowest standard deviations are IF32, V4B, IF21, IF34, and IF12.
Again, it is important to consider that for contact design IF32, half of the devices showed
no contact – a fact that is not included in the calculation of standard deviation. Based on
low mean resistance and low standard deviations, designs IF34 and IF12 appear to be the
best choices.
For the relays used in this research, contact designs IF11 and V3 were used.
Because of the long manufacturing lead time associated with fabricating these devices,
the decision of which contact to use had to be made before the contact study was
complete. From the initial tests it seemed as though IF11 would achieve the lowest
contact resistance (see the low grouping of points for IF11 on the dot plot of Figure 6.6).
However, after further testing it is clear that other contact designs would be superior in
terms of mean resistance and variability. The V3 contact design was also chosen because
of its tooth shape, which could be an important distinguishing factor for measurements of
contact resistance. It is important to note that these choices of contacts still allow for the
Table 6.1 – Summary of probe-to-probe measurements (in Volts)
Probe to Probe
Mean
Std Dev
Probe to Probe on Gold Close Mean
Std Dev
Probe to Probe on Gold Far
Mean
Std Dev
All
Mean
Std Dev
1
0.024000
0.000000
0.013333
0.001000
0.007667
0.000816
0.014300
0.006300
50
Set
2
3
0.010000 0.010000
0.000000 0.000000
0.011778 0.006000
0.002333 0.000000
0.015778 0.016750
0.000667 0.001035
0.012833 0.011000
0.002823 0.004771
4
----0.010000
0.000000
0.010000
0.000000
All
0.014118
0.006575
0.010538
0.003467
0.013067
0.003850
0.012411
0.004678
testing of critical performance parameters of the relays. It is recommended that
optimization of the relay should start with the use of the contact designs mentioned
above.
51
CHAPTER 7
7.1
CONTACT FORCE
Introduction
Contact force is another important relay performance parameter. High contact
forces can help lower contact resistance and reduce bounce on closing. Additionally the
factors that lead to higher contact forces also lead to faster switching times.
It is very difficult to measure contact force. There are several factors that
contribute to this difficulty, with the primary factor being stiction. Stiction is the term
used to describe the nonlinear adhesion between movable mechanical structures and the
substrate. Stiction can be increased or reduced by changing the fabrication process or
modifying the release process, but it is very difficult to predict or measure the effects of
such process changes.
Analytical predictions of contact force were combined with the results of contactforce measurements to characterize the behavior of the three compliant bistable
mechanisms as relays. This also gives a preliminary treatment of stiction and its effects
on relay performance.
53
30
Contact Force ( N)
20
10
0
0
10
20
30
40
50
60
70
80
90
100
110
-10
-20
-30
Deflection ( µ m )
100
50
Contact Force ( N)
0
-50
0
10
20
30
40
50
60
70
-100
-150
-200
-250
-300
-350
Deflection ( µ m)
Figure 7.1 – Predicted contact force as a function of shuttle deflection for the Linear
Displacement Bistable Mechanism (top) and the Fully Compliant Bistable
Mechanism (bottom)
7.2
Predicted Values
There are several ways to predict the contact for the mechanisms in this study.
The most straightforward method is to use the potential energy calculations given in
Chapter 3. For the Linear Displacement Bistable Mechanism (LDBM) the potential
energy equation (3.9) may be differentiated (symbolically or numerically) with respect to
54
deflection to find the predicted contact force. Because the Fully Compliant Bistable
Mechanism’s (FCBM) potential energy curve was found using finite element analysis, its
contact force cannot readily be found symbolically. It may, however, be found by
numerically differentiating the potential energy values calculated by finite element
analysis. For both of these mechanisms, the results of the numeric differentiation is
shown in Figure 7.1. It is important to note that when taking the derivative, the sign of
the results must be inverted (multiplied by –1) to find the correct value for contact force.
The maximum predicted contact force for the LDBM is 23.4 µN at 88 µm and the
maximum predicted contact force for the FCBM is 70.6 µN at 44 µm.
Finding the predicted contact force is more difficult for the Young mechanism.
Because the potential energy equation (3.12) is in terms of relative angular deflections,
there is not a linear deflection with which to differentiate to find contact force. However,
the contact force may be calculated using virtual work as described by Howell, 2001.
To use the virtual work method of analyzing a mechanism, one may start with the
following:
δW = Aδθ 2 + Bδθ 3 + C δθ 4
(7.1)
where δW is the change in total system virtual work, δθi is the change in angles i = 2, 3,
and 4, and A, B, and C are the total moments about the joints of angles 2, 3, and 4,
respectively. A, B, and C can be expressed as functions of the mechanism geometry and
loads shown in Figure 7.2 with the following:
A = (− X 2 a 2 − Y2 b2 − r2 X 3 )sin θ 2
+ (− X 2 b2 − Y2 a 2 + r2 Y3 ) cos θ 2
+ M 2 + T1 + T2
55
(7.2)
Figure 7.2 – A general pseudo-rigid-body four-bar mechanism
B = (− X 3 a3 − Y3b3 )sin θ 3
+ (− X 3b3 − Y3 a3 ) cos θ 3
(7.3)
+ M 3 − T2 − T3
C = (− X 4 a 4 − Y4 b4 )sin θ 4
+ (− X 4 b4 − Y4 a 4 ) cos θ 4
(7.4)
+ M 4 + T3 + T4
Because there are no loads on members 2 and 4 and no moment on segment 3 on
contact, the equations for A, B, and C may be simplified to:
A = − r2 X 3 sin θ 2 + r2 Y3 cos θ 2 + T2
56
(7.5)
B = (− X 3 a 3 − Y3 b3 ) sin θ 3 + (− X 3 b3 − Y3 a 3 ) cos θ 3 − T2 − T3
(7.6)
C = T3
(7.7)
In the above equations, Ti is the torque of each torsional spring in the pseudorigid-body model. It is expressed as:
Ti = − K i ψ i
(7.8)
ψ 2 = (θ 2 − θ 2o ) − (θ 3 − θ 3o )
(7.9)
ψ 3 = (θ 4 − θ 4o ) − (θ 3 − θ 3o )
(7.10)
where
and θio is the initial position of angle θi.
The principle of virtual work (the change in total system virtual work must be
zero) may be applied and equation (7.1) may be divided by δθ2 to obtain:
A+ B
The terms
δθ 3
δθ
+C 4 = 0
δθ 2
δθ 2
(7.11)
δθ 3
δθ 4
and
are kinematic coefficients and have the values:
δθ 2
δθ 2
r sin (θ 4 − θ 2 )
δθ 3
= h32 = 2
r3 sin (θ 3 − θ 4 )
δθ 2
(7.12)
r sin (θ 3 − θ 2 )
δθ 4
= h42 = 2
r4 sin (θ 3 − θ 4 )
δθ 2
(7.13)
and
57
Solving equation (7.11) for force would give X3 and Y3 forces, but contact force is
the force normal to the face (contacting surface) of the contact. If the contact force Fc is
located at P3 (in Figure 7.2), then X3 and Y3 may be expressed as:
X 3 = Fc sin (Θ 3o + θ 3 )
(7.14)
Y3 = Fc cos (Θ 3o + θ 3 )
(7.15)
and
where Θ3o is the angle between normal to the contact face and normal to the pseudorigid-body model link 3 and can be found by:
 (1 − γ )(l4 sin θ 4o − l2 sin θ 2o ) 

Θ 3o = sin −1 
R3


(7.16)
where li is the actual length (as opposed to pseudo-rigid-body model length) of the ith
flexible segment, R3 is the actual length of the rigid segment, and γ is the fundamental
radius factor as described in Chapter 3.
Substituting equations (7.14) and (7.15) into equations (7.5) and (7.6),
substituting equations (7.5) through (7.7) into equation (7.11) and solving for Fc yields:
Fc =
h32 (T2 + T3 ) − T2 − T3 h32
Hh32 − r2G
(7.17)
where
H = [− sin (Θ 3o + θ 3 )a3 + cos (Θ 3o + θ 3 )b3 ]sin θ 3
(7.18)
G = sin (Θ 3 o + θ 3 )sin θ 2 + cos (Θ 3o + θ 3 ) cos θ 2
(7.19)
+ [− sin (Θ 3o + θ 3 )b3 − cos (Θ 3o + θ 3 )a3 ]cos θ 3
and
58
5.00E-03
Contact Force (µN)
0.00E+00
0
5
10
15
20
25
30
35
40
-5.00E-03
-1.00E-02
-1.50E-02
-2.00E-02
-2.50E-02
-3.00E-02
∆θ2 (degrees)
Figure 7.3 – Predicted contact force as a function of ∆θ2 for the Young mechanism
The predicted contact force for the Young mechanism may be calculated using
equation (7.17). The graph of contact force as a function of ∆θ2 is given in Figure 7.3.
The maximum contact force for the mechanism is calculated to be 0.00319 µN at a ∆θ2 of
17º. The variable values used to calculate contact force graph for the Young mechanism
are given in Table 7.1.
Table 7.1 – Variable values for Young mechanism contact force calculations
Variable
l1
l2
l3
l4
r1
r2
r3
r4
θ1ο
θ2o
θ3o
θ4o
K1
K2
a3
b3
γ
Value
Unit
121.0 µm
129.0 µm
235.8 µm
229.0 µm
121.0 µm
109.7 µm
216.5 µm
194.7 µm
0 degrees
12 degrees
-26.23 degrees
-22 degrees
61478 µN µm
7480 µN µm
190 µm
70 µm
0.85
59
Figure 7.4 – Setup of contact force tests
7.3
Experimental Setup
To allow for contact force measurement, the force tester described in Chapter 5
was placed next to each of the three mechanisms (Figure 7.4). The number of legs was
reduced to 4 to allow the testable range of the force tester to be closer to the expected
range of predicted contact force for the three mechanisms.
7.4
Taking Measurements
To measure the contact force, each mechanism was switched from its fabricated
position to its second stable equilibrium position. The force testers were then manually
60
Figure 7.5 – Video images of contact force tests
pushed toward the mechanism. When the mechanism was in contact with the force tester,
the tester was used to push the mechanism back through its unstable equilibrium position
– to snap back to its original position.
This process was captured under a microscope and videotaped. Images from the
tape were digitized (Figure 7.5) and imported into an image analysis program (Scion
Image from Scion Corporation) and the force tester deflections were measured. The raw
measurement data is given in Appendix D.
61
7.5
7.5.1
Analysis
Linear Displacement Bistable Mechanism
In order to calculate the force applied to the force tester the displacement of the
force tester’s central rigid members is needed. Additionally, to measure the uncertainty
of the force calculation, the measurement error is required. Because the image analysis
software gives distances in terms of pixels, the measurements must be calibrated. To do
this, an object with a known dimension was measured six times in at each displacement
step (see Appendix C for values used). The actual dimension was divided by the average
of this calibration measurement to find a calibration number.
The deflection of the central rigid members and the displacement of the force
tester as a whole were each measured six times. Each of these measurements were
multiplied by the calibration number to convert from pixels to microns. The deflections
and the standard deviation of the deflections were used with equations (5.3) and (5.4) to
calculate the force and the force error at each displacement. The results of the
measurements are summarized in Figure 7.6. The variable values used to calculate the
contact force curve are shown in Table 7.2.
From the plot it can be seen that the measured values have the same shape as the
predicted value curve but are significantly offset. This offset is a measure of the stiction
at the location of the device, on the die used for the test. The average value of the offset
is 365 µN. Because this value is significantly higher than the maximum predicted
reaction force, the mechanism does not move to a stable equilibrium position as soon as it
passes its unstable equilibrium position. Instead, it remains in any position to which it is
moved.
62
600
500
Force (µN)
400
300
Experimental
Theoretical
200
100
0
0
20
40
60
80
100
-100
Deflection (µm)
Figure 7.6 – Contact force measurement for Linear Displacement Bistable Mechanism
with 3σ error bars for both force and deflection
Table 7.2 – Variable values for LDBM contact force calculations
Variable
Value
Unit
53 µm
R0
L
81.59 µm
0.8538
κ0
0.7857
γ
ai
52.97 µm
bi
51.34 µm
0.7583
ρ
2.8496
KΘ
Young’s Modulus (E) 1.69E+11 Pa
Width
4 µm
Height
2 µm
I
10.667 µm4
K
47738 µN*µm
0.9788 Radians
Θi
xi
100 µm
yi
35 µm
Segments per side
2
63
100
Contact Force ( N)
80
60
40
20
Experimental
Theoretical
0
-20 20
25
30
35
40
45
50
55
-40
-60
-80
Displacem ent ( µ m )
100
Contact Force ( N)
80
60
40
20
Experimental
Theoretical
0
-20 20
25
30
35
40
45
50
55
-40
-60
-80
Displacem ent ( µ m )
Figure 7.7 – Contact force measurements for Fully Compliant Bistable Mechanism. First
measurement (top) and second measurement (bottom)
7.5.2
Fully Compliant Bistable Mechanism
The deflection and displacement measurements, along with their associated
standard deviations were calculated using the method described in the Linear
Displacement Bistable Mechanism section above. Force calculations were also made in
the same manner. The results of the measurements and calculations are shown in
Figure 7.7. The lower limits of the 3σ error bars stop at zero. This is because a negative
contact force does not make sense physically.
64
These contact force measurements do not follow the curve as closely as those of
the LDBM. However, the results are consistent with repeated measurement.
Additionally, it is interesting to note that 73% of the 3σ error bars enclose the predicted
values. The stiction is clearly lower at the mechanism location on the die tested (a
different die was used than that for the LDBM). This conclusion is supported by the fact
that the mechanism would move to a stable equilibrium position immediately after
passing its unstable equilibrium position.
There are several possible causes for the lower measured contact force (compared
to that of the LDBM) and difference in shape of the predicted and measured values of
contact force. First, the mechanisms tested were on different dies due to poor
manufacturing yield of the devices. Process variations in both the fabrication and the
release of the dies could easily cause the lower measured contact force. Second, the
surface area parallel to the substrate is much smaller for the FCBM. This also results in
lower stiction. Finally, the predicted contact force curve does not account for variations
in material properties or feature dimensions. These variations would certainly change the
shape of the contact force curve.
7.5.3
Young Mechanism
Although data for the Young mechanism contact force is included in Appendix D,
no graph is included in this section. There were several problems using the force tester
with the Young mechanism. First, the force tester was not able to measure the force
normal to the contact face because while the mechanism rotates, the force tester is
constrained to move in a straight line. The difference in motion also caused the contact
to exert more force on one side of the force tester than the other.
65
The second problem in measuring the Young mechanism contact force was
geometry incompatibility. The Young mechanism would get caught on the slider portion
of the force tester and be unable to move further.
The final problem was the low reaction force provided by the Young mechanism.
Because the forces were so low, stiction prevented the mechanism from moving to its
stable equilibrium positions.
7.6
Conclusions
According to the predictions, both the Fully Compliant Bistable Mechanism and
the Linear Displacement Bistable Mechanism have the potential to impart a large contact
force. This indicates that they would perform well as relays in terms of the contact force
performance parameter.
The Young mechanism, on the other hand seems problematic at best. The current
configuration imparts very little contact force. While this could be changed by modifying
the geometry, the fact that the mechanism achieves its motion through rotation will not
change. This not only makes it difficult to measure the contact force, but placing
contacts will also be difficult because both their location and rotation must be calculated.
For all three mechanisms, stiction is a problem. Stiction makes verification of the
contact force predictions difficult, but more importantly, it reduces the amount of force
imparted to the contact. This can be seen by the fact that the LDBM was unable to freely
move to its stable equilibrium positions. The FCBM, on the other hand, had much lower
stiction and was able to move to its stable positions.
66
CHAPTER 8
8.1
SWITCHING TIME
Introduction
Switching time is a critical relay performance parameter. Shorter switching times
mean higher frequency ranges and therefore expanded application possibilities. Because
of the physical scale and time scale involved, predicting the switching time of a micromechanism is difficult. It is therefore important to obtain measurements of switching
time to characterize a mechanism’s performance as a relay.
8.2
Experimental Setup
Full relays were used to test switching time. The full relays include the
mechanism, contacts, and actuators. An example of the Linear Displacement Bistable
Mechanism relay is shown in Figure 8.1.
8.3
Taking Measurements
To measure the switching time, the actuation voltage and the contact voltage were
plotted simultaneously on a digital oscilloscope. The time separation of the two voltage
steps indicated the switching time.
For the LDBM relay, the contact voltage that was measured was the voltage
between one contact and the common ground (the same ground used for the actuation
circuit). This was done because a layout error caused the contacts to connect directly to
67
Figure 8.1 – Linear Displacement Bistable Mechanism relay
the substrate – connecting them electrically. For the Young mechanism and the Fully
Compliant Bistable Mechanism, a separate DC power source was used to place a voltage
across the contacts. A resister was placed in series with the contacts and the voltage
across the resister was measured as the contact voltage.
The same layout error that caused the contacts to connect to the substrate
prevented the actuators for the Fully Compliant Bistable Mechanism from functioning.
Therefore, another fully compliant bistable mechanism design was used as a comparable
for the FCBM’s switching time. The mechanism was recently developed at Brigham
Young University (Masters, 2001), and is shown in Figure 8.2.
68
Figure 8.2 – Surrogate Fully Compliant Bistable Mechanism (Masters, 2001)
8.4
8.4.1
Analysis
Linear Displacement Bistable Mechanism
The switching time of the LDBM was measured to be 340 µs with a standard
deviation of 20 µs. A current pulse of 85 mA was used to achieve contact and measure
the switching time. This is well within the range of the switching times of current
microrelays. The geometry of the LDBM used is the same as that given in Table 3.1 with
2 legs per side rather than 3.
69
Figure 8.3 – Spring contacts for Young mechanism testing. The contact gap is circled on
the right.
8.4.2
Fully Compliant Bistable Mechanism
The switching time of the surrogate FCBM was measured to be 452 µs with a
standard deviation of 68 µs. A current pulse of 55 mA was used to achieve contact and
measure the switching time. This is also well within the range of the switching times of
current microrelays.
8.4.3
Young Mechanism
The switching time of the Young mechanism was not measurable. The reason for
this is that the mechanism failed to make contact with more than one contact at a time.
Because the Young mechanism gains its motion through rotation, it is necessary to
predict the angle of the mechanism at contact. Such predictions are difficult and highly
variable due to the poor pin joint tolerances inherent in the manufacturing process.
Although both fixed contacts and contacts mounted on flexible springs (shown in
Figure 8.3) were tried, neither method provided an electrical contact with which to
measure the switching time.
70
8.5
Conclusions
The LDBM and the FCBM should perform well as relays, in terms of switching
time. The Young mechanism would have to be tested further – perhaps using high-speed
photography – before any definite statements about its switching time performance could
be made. It is important to note that while the measured switching times appear to fall in
the middle of the range of switching times of current relays, it is generally only out-ofplane relays that have extremely low switching times. The switching times measured for
these mechanisms are very low for in-plane microrelays.
From observing the tests, it seems as though the actuators design plays as
important a role in determining switching time as the mechanism design. This is because
the contacts are fairly close to the mechanisms’ unstable equilibrium positions. The
mechanisms are therefore pushed all the way to contact by the actuators. The power used
to actuate the mechanisms could be reduced so that the mechanisms would be pushed just
past their unstable positions, but this would increase switching time. This was verified by
reducing the actuation current on the surrogate FCBM to 50 mA. At the lower current,
the switching time was increased from 452 µs to 600 µs – a 33% increase in switching
time for less than a 1% power reduction.
It is recommended that future research in this area begin with fabrication of a
FCBM with actuators that are not attached to the substrate (this may be done by
enclosing ANCHOR features with POLY0 in the MUMPS process). Future attempts at
optimizing the switching time of the relays should begin with a thorough quantitative
study of the effects of actuator design, contact location, and applied current on switching
time.
71
CHAPTER 9
9.1
AC CHARACTERISTICS
Introduction
AC characteristics of current microrelays are generally not documented because
most microrelays are designed for DC or low frequency signal use. The relays studied in
this research are also intended for DC or low frequency use. However, there are two AC
signal characteristics that are of interest: contact-to-contact crosstalk and AC isolation.
Contact-to-contact crosstalk refers to the ratio of the output signal to the input signal,
where the output signal is induced across the open contact. AC isolation is the ratio of
the signal induced in the actuation circuit (by the input signal) to the input signal.
9.2
Experimental Setup
Because the contact-to-contact crosstalk and AC isolation are dependent upon
contact design and actuation circuit layout rather than the design of the mechanism used,
only the Linear Displacement Bistable Mechanism relay and the Young mechanism relay
were used. This is due to the fact that the motion of the LDBM and the FCBM are
similar (linear displacement with a central shuttle) so they can both use the same contact
design and actuation circuit layout. Figures 9.1 and 9.2 show the relays used for the AC
characteristics tests as well as the probe locations for each of the tests.
73
Figure 9.1 – Young mechanism relay used for AC characteristics test. Circles represent
probe locations for the contact-to-contact crosstalk test and squares represent probe
locations for the AC isolation test.
Figure 9.2 – Linear Displacement Bistable Mechanism relay used for AC characteristics
test. Circles represent probe locations for the contact-to-contact crosstalk test and
squares represent probe locations for the AC isolation test.
74
R1
O-Scope
Probe 2
On Pad
Probe 1
On Pad
R2
O-Scope
Figure 9.3 – Electrical diagram of experimental setup. R1 represents the resistance of the
air gap in parallel with the nitride layer and substrate. R2 is a 1 kΩ resistor.
9.3
Taking Measurements
For both the contact-to-contact crosstalk and the AC isolation tests, a function
generator (Tektronix CFG253) was used to apply AC sine wave signals from 1 Hz to
1 MHz. All signals (applied and measured) shared a common ground. A digital
oscilloscope was used to measure the amplitude of both the input signal and the induced
signal. For each measurement, the oscilloscope averaged 8 samples of several periods.
In order to differentiate between signals induced on-chip and signals induced by
the setup of the experiment (ex: signal wire or probe-to-probe crosstalk), the probe
closest (electrically) to ground was lifted off the die and the induced signal was
measured. The probe locations for the tests are shown in Figures 9.1 and 9.2, an
electrical diagram of the experimental setup is shown in Figure 9.3, and the raw
measurement data is given in Appendix E.
75
0.12
Output / Input
0.1
Pad to Pad
System Noise
0.08
0.06
0.04
0.02
0
1
10
100
1000
10000
100000
1000000
10000
100000
1000000
Frequency (Hz)
Output / Input
0.2
0.18
Pad to Pad
0.16
System Noise
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
1
10
100
1000
Frequency (Hz)
Figure 9.4 – Contact-to-contact crosstalk measurements for Young mechanism relay (top)
and LDBM relay (bottom)
9.4
9.4.1
Analysis
Contact-to-Contact Crosstalk
The results of the contact-to-contact crosstalk measurements for both the Young
mechanism relay and the LDBM relay are shown in Figure 9.4. The horizontal axis is
frequency (on a log scale) and the vertical axis is the ratio of the induced signal amplitude
(in volts) to the input signal amplitude (also in volts). It can be seen from the graphs that
for both the Young mechanism relay and the LDBM relay crosstalk becomes measurable
76
at around 10 kHz. An interesting feature of the LDBM graph is the large amount of
system noise measured at 10 kHz. This spike was measure several times (so it is not
simply a statistical outlier). The exact nature of the large measurement is not known, but
may be due to system resonance. It is recommended that future tests include measures to
isolate the cause of this large reading.
77
0.14
Output / Input
0.12
Pad to Pad
System Noise
0.1
0.08
0.06
0.04
0.02
0
1
10
100
1000
10000
100000
1000000
10000
100000
1000000
Frequency (Hz)
Output / Input
0.2
0.18
Pad to Pad
0.16
System Noise
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
1
10
100
1000
Frequency (Hz)
Figure 9.5 – AC isolation measurements for Young mechanism relay (top) and LDBM
relay (bottom)
9.4.2
AC Isolation
The results of the AC isolation measurements for both the Young mechanism
relay and the LDBM relay are shown in Figure 9.5. The axes are the same as those for
Figure 9.4. From the graphs, it can be seen that for both the Young mechanism relay and
the LDBM relay AC Isolation begins to decrease at around 10 kHz. As in the contact-tocontact crosstalk graph, a large, unexplained spike in system noise was repeatedly
measured at 10 kHz.
78
9.5
Conclusions
For relays designed for DC to low frequency use, the relays used in this research
perform well. From the AC characteristics tests it can be seen that AC signals do not
adversely affect relay performance, in terms of contact-to-contact crosstalk and AC
isolation, until around 10 kHz. This suggests that these relays are suitable for lowfrequency applications, but would be unacceptable for high-frequency applications (most
notably RF switching).
The factors that are thought to affect both the contact-to-contact crosstalk and the
AC isolation of the relays include pad / actuation current path separation, nitride
thickness, relative current line orientation (parallel vs. perpendicular), current line /
contact pad areas, and dielectric strength between pads. These are thought to be the
important factors because they are the main contributors to resistance and capacitance
between the contacts and between the contacts and the actuation circuits. In order to
optimize the AC performance of the relays, future research should begin with a study to
quantitatively characterize the contacts and actuation circuits as functions of these
factors. Another avenue for further research would be to test the relays with better
equipment to reduce the system noise and isolate the AC characteristics of the relays.
Some factors that may contribute to system noise include wire shielding, wire length, and
probe separation.
79
CHAPTER 10
10.1
VOLTAGE CHARACTERISTICS
Introduction
The voltage characteristics of a relay are important performance parameters for
determining its potential applications. The higher the voltage that the relay can
withstand, the broader the potential applications.
10.2
Experimental Setup
The physical layout of the voltage experiment was the same as that of the AC
characteristics experiments (Chapter 9) and the switching time experiments (Chapter 8).
The relay shown in Figure 10.1 and two small contact pads (each 92 µm by 92 µm
separated by a 2 µm gap) were used for the tests. The small pads were included in the
test to determine the effect of very small separation distances. Also, the breakdown
voltage and was not measured separately for each mechanism because the voltage
characteristics are dependent upon pad design and current line layout rather than on the
mechanism used to move the contact.
81
Figure 10.1 – Relay used for voltage characteristics tests. White dots indicate probe
positions for the isolation tests
10.3
10.3.1
Taking Measurements
Breakdown Voltage
To measure the open circuit, contact-to-contact breakdown voltage, a high voltage
power supply (Stanford Research Systems PS310) was used. The voltage was applied to
the two contact pads with the relay in the open position. The current limit on the power
supply was set to 0.1 mA and the voltage was slowly increased until the current limit
tripped. The voltage characteristics measurements are given in Appendix F.
10.3.2
Isolation
The same equipment was used to measure isolation (contact-to-actuation current
line breakdown voltage). The difference in setup was that the voltage was applied to a
82
0.1
0.09
Current (mA)
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0
100
200
300
400
500
Voltage
Figure 10.2 – Results of breakdown voltage test for relay
contact pad and the closest section of the current line (rather than to the two contact
pads). The location of the isolation measurement is shown on Figure 10.1.
10.4
10.4.1
Analysis
Breakdown Voltage
The results of the breakdown voltage test on the relay are summarized in Figure
10.2. It should be noted that for the equipment used, 0.01 mA is the lowest current
measurement that can be displayed so should be considered to be effectively zero current
flow. From the figure, it can be seen that current begins to leak at around 400 V. The
pad separation for this test was 33 µm.
The tests using the small pads were more dramatic. Because of the small
separation, the pads experience dielectric breakdown rather than current leakage. The
current was effectively zero until the point of breakdown, so a plot of applied voltage
versus current is not included. The breakdown voltage was measured twice (with
83
Figure 10.3 – Steps of the breakdown process captured on video
Current (mA)
0.1
0.09
Breakdown
0.08
Isolation
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0
100
200
300
400
500
Voltage
Figure 10.4 – Results of isolation test for relay
different sets of pads) and found to be 350 V and 360 V. Figure 10.3 shows the steps of
the breakdown process captured on video.
10.4.2
Isolation
The results of the isolation test, along with a comparison to the breakdown
voltage test, are summarized in Figure 10.4. It can be seen from the graph that current
begins to leak at around 200 V. This lower voltage can be explained by the lower
84
separation (25 µm for the isolation test as opposed to 33 µm for the breakdown test) and
the large size of the pad on the actuation circuit (the uppermost pad as seen in
Figure 10.1).
10.5
Conclusions
The relay layouts used in this research perform well in terms of breakdown
voltage. The 400 V breakdown characteristic is on the upper end of the range of current
microrelays (see Table 2.1). This performance characteristic could be easily improved by
increasing the separation between the contact pads. The tests also show that attempts to
decrease the pad separation (perhaps to increase component density) could result in
catastrophic failure.
It is important to note that the tests characterized the relays only for currents in
excess of 0.01 mA. It is recommended that future research of the voltage characteristics
of the relays begin with studying the voltage ranges that yielded a 0.01 mA current in the
above tests with a finer current resolution. This could be done by placing a large resistor
(on the order of megaohms) in series with the device to be tested, measuring the voltage
across the resistor, and using the voltage measurement to calculate the current flow
through the device.
The isolation measured for this relay layout is quite low. This performance
characteristic could be improved by designing an actuation current path separated by a
greater distance from the contact pads. It is recommended that future attempts to
optimize the relay design (in terms of the tradeoffs between breakdown voltage, isolation,
and component density) include a study to quantify the effects of pad size and separation.
85
It is also recommended that the effects of switching high voltage signals be
studied. Such research should investigate the possibility of arcing – during the initial
switch closure, during contact bounce after closure, and during switch opening. This
research is important because arcing can lead to contact welding and reduce the useful
life of the relay.
86
CHAPTER 11
11.1
SUMMARY
Summary
The purpose of this research was to investigate the feasibility and method of using
compliant bistable mechanisms as microrelays. There were three main contributions of
this research. First, existing mechanisms and actuators were integrated into a coherent
switching system. Second a preliminary investigation of several possible horizontal
contact designs was performed to discover feasible contacts to allow the switching
systems to behave as relays and switch electrical signals. Third, the performance of the
relays was characterized and compared to that of current microrelays.
The relay designs used for this research are shown in Figures 11.1 and 11.2. A
summary of the performance of the relays presented in this research compared to that of
the high and low values of current microrelays is given in Table 11.1. Table 11.2
compares the performance of three representative current microrelays with those
characterized in this research.
87
Figure 11.1 – Relay layout for LDBM (top) and FCBM (bottom)
88
Figure 11.2 – Relay layout for Young mechanism
Table 11.1 – Comparison of relay performance parameters
Attribute
Actuation Current
Actuation Voltage
Actuation Power
Breakdown Voltage
Contact Force
Contact Resistance
Displacement
Isolation (DC)
Literature
High
600 mA
150 V
320 mW
> 400 V
500 µN
300 Ω
16 µm
>1600 V
Literature
Low
50 nA
0.53 V
1 µW
>3 V
3 µN
22.4 µΩ
0.5 µm
—
LDBM
Relay
85 mA
11 V
935 mW
> 475 V
23.4 µN
49.2 Ω
88 µm
> 235 V
FCBM
Relay
85 mA
11 V
935 mW
> 475 V
70.6 µN
49.2 Ω
44 µm
> 235 V
Size 2.E+06 µm2 1E+04 µm2 1.92E+6 µm2 1.93E+6 µm2
Switching Time
5 ms
2 µs
340 µs
452 µs
* see Figure 3.9
89
Young
Mechanism
Relay
55 MA
8V
440 MW
> 475 V
0.00319 µN
49.2 Ω
17º (∆θ2)*
> 235 V
8.6E+5 µm2
—
11.2
Conclusions
Both the Linear Displacement Bistable Mechanism and the Fully Compliant
Bistable Mechanism should work well as relays. Both mechanisms have good values of
contact force, switching time, and breakdown voltage. The large deflections of the two
mechanisms lead to high breakdown voltages and isolations. This should make them
suitable for higher voltage applications – such as telecommunications components for
which the FCC requires high breakdown voltages.
The power consumption of both mechanisms is quite high compared to current
microrelays. However, there are two things to keep in mind when considering the power
consumption. First, power consumption is a function of actuator design and can be
changed by optimizing the actuators’ power performance. Second, because the
mechanisms are bistable, power usage is only required during switching and not to hold
the switch in either the “on” or “off” positions. This feature should make the relays
appealing for applications in which the “on” or “off” hold time is high – such as DSL line
Table 11.2 – Comparison of performance parameters for selected relays
Taylor et al.
Attribute
1998
Actuation Type
Magnetic
Actuation Current
600 mA
0.53 V
Actuation Voltage
Actuation Power
320 mW
320 mW
Hold Power
Breakdown Voltage
>3 V
Contact Force
Contact Resistance 22.4–38.6 mΩ
Displacement
Isolation (DC)
Size
Switching Time
Shiele et al.
1998
Electrostatic
50–70 nA
20–150 V
1–10.5 µW
1–10.5 µW
Sun et al.
1998
Thermal
LDBM
FCBM
Thermal
Thermal
85 mA
85 mA
11 V
11 V
10–12 mW
935 mW
935 mW
0
0
0
> 400 V
> 475 V
> 475 V
21 µN
23.4 µN
70.6 µN
2.1–35.6 Ω
49.2 Ω
49.2 Ω
10–80 Ω
10 µm
10 µm
>1600 V
2
2.08 mm 0.03–0.7 mm2
0.5–5 ms
2.6–33 µs
90
16 µm
0.1–0.5 ms
88 µm
44 µm
> 235 V
> 235 V
2
2
1.92 mm
1.93 mm
340 µs
452 µs
diagnostic equipment.
A drawback of the LDBM is its pin joints. These provide a mechanism for
mechanical wear and can lead to wearout – or Weibull – failure distribution. The FCBM,
on the other hand, has no pin joints so would tend to follow a random failure – or
exponential – failure distribution. Because electrical components also tend toward
random failure distributions, the FCBM may be more suited for integration with on-chip
electronics.
The Young mechanism is the least suited for relay applications. The first reason
for this conclusion is the fact that it has pin joints, which provide a mechanism for
mechanical wearout failure. The second reason is the mechanism’s rotational motion.
This motion makes prediction of correct contact position difficult, and combined with the
poor tolerances of the pin joints, it is nearly impossible to place the contacts in a position
that will provide a good electrical contact. The third reason is the mechanism’s low
contact force. The forces imparted by the mechanism are so low that the contact
resistance for the relay would probably suffer.
11.3
Recommendations for Further Research
The recommendations for further research fall into two categories. The first is
optimization research. This refers to research intended to improve the performance of the
relays. The second category is product research. This refers to research intended to
prepare the relays for production and marketing.
91
11.3.1
Optimization Research
One of the biggest problems in testing and using the mechanisms is stiction. The
amount of stiction varies widely from die to die and from release to release. It is
recommended that research be performed to allow accurate measurements of stiction and
quantify the effects of process variations on it. This would hopefully lead to an improved
release process to reduce the overall stiction. Another area of stiction research would be
to study methods of reducing the effects of stiction on mechanism motion. For example,
the POLY0 layer in the MUMPS process has been seen to decrease the effects of stiction
when placed under floating pin joints.
The next area for relay optimization research is to perform a more in-depth
contact study. It is recommended that such a study use more designs and a factorial
experimental layout to quantify the effects of design changes on contact resistance. This
would hopefully lead to a predictive model that could be used to evaluate potential
designs before fabrication. Another area of contact research would be to study the
robustness of each design to misalignment and other process variations.
It is recommended that the mechanisms be analyzed to determine possible
configurations that could achieve higher contact forces. The results of such research
would be a model that would optimize the mechanism design to maximize contact force
given constraints such as physical size and desired deflection.
To more fully characterize the Young mechanism and other rotational
mechanisms, it is recommended that a rotational force tester be developed. This would
help with validating contact force models and possibly with better understanding the
effects of stiction.
92
It is recommended that research be performed on optimization of relay switching
time. This should begin with a thorough quantitative study of the effects of actuator
design, contact location, and applied current on switching time. Such research should
lead to a predictive empirical or analytical model of switching time.
To improve the AC performance of the relays, it is recommended that future
research begin with a study to quantitatively characterize the contacts and actuation
circuits as functions of contact design and line and contact separation. Another avenue
for further research would be to test the relays with better equipment to reduce the system
noise and isolate the AC characteristics of the relays. The results of such research would
be an optimized layout for the contacts and the actuation circuits.
In regards to the voltage characteristics of the relays, it is recommended that
future research include a factorial study of breakdown voltage and current leak with
separation distance as a factor and size of each pad as two additional factors. This will
help optimize the relay design in terms of the tradeoff between isolation, breakdown
voltage, and component density. It is also recommended that a low-current (less than
0.01 mA) study be performed to more fully characterize the relays, as well as research
into the possibility of arcing between the fixed and moving portions of the contacts.
11.3.2
Product Research
It is recommended that the first area of research toward making the relays a
marketable product be a reliability study. Such a study would characterize all of the relay
performance parameters as a function of relay life (in terms of switching cycles).
The next recommended area of product research is packaging. It is recommended
that methods of electronics packaging be surveyed to gain an understanding of
93
appropriate methods of packaging microrelays. Such research should also include the
effects of packaging on performance parameters; particularly power consumption,
breakdown voltage, contact-to-contact crosstalk, and isolation as the are highly dependent
upon their environment (vacuum, noble gasses, etc.)
It is also recommended that relay designs for RF switching be researched. For
high frequency signals, a single current line is not sufficient to route the signal. Instead,
waveguide structures (a signal line with a ground line on either side) must be used. A
waveguide relay design would be radically different from the designs presented in this
research.
Finally, it is recommended that issues related to high-volume production of
microrelays be researched. Such research would include optimization of manufacturing
yield and an assessment of the financial viability of high-volume production of
microrelays. In conjunction with this research, it is recommended that a marketing study
be performed to assess the potential size to the microrelay market as well as the specific
applications of interest to potential customers.
94
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International Reliability Physics Symposium Proceedings, March 30 - April 2, 1998, pp.
26-35.
Taylor, William P., Brand, Oliver, and Allen, Mark G., 1998, “Fully Integrated
Magnetically Actuated Micromachined Relays,” IEEE Journal of
Microelectromechanical Systems, Vol. 7, No. 2, June 1998, pp. 181-191.
Wittwer, J.W., 2001, “Effects…,” M.S. Thesis, Brigham Young University,
Provo, Utah.
Yao, J. Jason and Chang, M. Frank, 1995, “A Surface Micromachined Miniature
Switch for Telecommunications Applications with Signal Frequencies from DC up to 4
GHz,” The 8th International Conference on Solid-State Sensors, and Eurosensors IX,
Stockholm Sweden, June 15-29, 1995, pp. 384-387.
Yao, Z. Jamie, Chen, Shea, Eshelman, Susan, Denniston, David, and Goldsmith,
Chuck, 1999, “Micromachined Low-Loss Microwave Switches,” IEEE Journal of
Microelectromechanical Systems, Vol. 8, No. 2, June 1999, pp. 129-134.
Zavracky, Paul M., Majumder, Sumit, and McGruer, Nicol E., 1997,
“Micromechanical Switches Fabricated Using Surface Micromachining,” IEEE Journal
of Microelectromechanical Systems, Vol. 6, No. 1, March 1997, pp. 3-9.
Zhang, Yanwei, Zhang, Yongxia, and Marcus, R. B., 1999, “Thermally Actuated
Microprobes for a New Wafer Probe Card,” IEEE Journal of Microelectromechanical
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Actuation,” J. Micromech. Mecroeng., 9, 1999, pp. 45-50.
97
Appendix A
ANSYS INPUT FILE FOR FULLY
COMPLIANT BISTABLE
MECHANISM POTENTIAL ENERGY
CURVE CALCULATION
/BATCH
*SET,l1,64e-6
*SET,l2,96e-6
*SET,l3,146.4e-6
*SET,l4,77e-6
*SET,h1,3.5e-6
*SET,h2,2.5e-6
*SET,h3,10e-6
*SET,h4,2.5e-6
*SET,bb,3.5e-6
*SET,thetad,6
*SET,ex,169e9
*SET,ldiv1,10
*SET,ldiv2,20
*SET,ldiv3,10
*SET,ldiv4,20
*SET,pi,acos(-1)
*SET,thetar,thetad*pi/180
*SET,I1,bb*h1*h1*h1/12
*SET,I2,bb*h2*h2*h2/12
*SET,I3,bb*h3*h3*h3/12
*SET,I4,bb*h4*h4*h4/12
*SET,A1,bb*h1
*SET,A2,bb*h2
*SET,A3,bb*h3
*SET,A4,bb*h4
*SET,dy,65e-6
*SET,steps,30
*SET,dely,-dy/steps
/PREP7
ET,1,BEAM3
R,1,A1,I1,h1,1.2, , ,
R,2,A2,I2,h2,1.2,0,0,
R,3,A3,I3,h3,1.2,0,0,
99
R,4,A4,I4,h4,1.2,0,0,
UIMP,1,EX, , ,ex,
UIMP,1,DENS, , , ,
UIMP,1,ALPX, , , ,
UIMP,1,REFT, , , ,
UIMP,1,NUXY, , , ,
UIMP,1,PRXY, , , ,
UIMP,1,GXY, , , ,
UIMP,1,MU, , , ,
UIMP,1,DAMP, , , ,
UIMP,1,KXX, , , ,
UIMP,1,C, , , ,
UIMP,1,ENTH, , , ,
UIMP,1,HF, , , ,
UIMP,1,EMIS, , , ,
UIMP,1,QRATE, , , ,
UIMP,1,VISC, , , ,
UIMP,1,SONC, , , ,
UIMP,1,MURX, , , ,
UIMP,1,MGXX, , , ,
UIMP,1,RSVX, , , ,
UIMP,1,PERX, , , ,
k,1,0,-l1/2
k,2,0,l1/2
k,3,0,0
k,4,l2*cos(thetar),l2*sin(thetar)
k,5,(l2+l3)*cos(thetar),(l2+l3)*sin(thetar)
k,6,(l2+l3+l4)*cos(thetar),(l2+l3+l4)*sin(thetar)
l,1,3,ldiv1
l,2,3,ldiv1
l,3,4,ldiv2
l,4,5,ldiv3
l,5,6,ldiv4
mat,1
type,1
real,1
lmesh,1,2
real,2
lmesh,3
real,3
lmesh,4
real,4
lmesh,5
FINISH
/SOLU
ANTYPE,0
NLGEOM,1
NROPT,AUTO, ,
LUMPM,0
EQSLV, , ,0,
PREC,0
PIVCHECK,1
SSTIF
PSTRES
TOFFST,0,
DK,1,all,0
100
DK,2,all,0
DK,6,ux,0
DK,6,rotz,0
*DO,i,1,steps
DK,6,uy,i*dely
lswrite,i
*ENDDO
save
lssolve,1,steps
FINISH
/POST1
set,last
/dscale,1,1
pldi,1
/output,output
/output
*DO,i,1,steps
set,i
etable,tpe,sene
/output,output,,,append
ssum
/output
*ENDDO
/POST26
ksel,s,kp,,6
nslk,s
*get,nkp6,node,0,num,max
nsel,all
ksel,all
NSOL,2,nkp6,U,Y,uy
RFORCE,3,nkp6,F,Y,fy
101
FORCE TESTER PARTIAL
DERIVATIVES AND GEOMETRY
Appendix B
Partial Derivatives for Equation (5.4)
∂F Nbh 3 d 1
=
∂E
L3 1 + ε P
∂F NEh 3 d 1
=
∂b
L3 1 + ε P
∂F 3NEbh 2 d 1
=
1+ εP
∂h
L3
∂F NEbh
=
∂d
L3
3
(1 + ε P ) − d  ∂ε P 
 ∂d 
(1 + ε P )2
 ∂ε 
3(1 + ε P ) − L P 
∂F NEbh
 ∂L 
=
4
∂L
L
(1 + ε P )2
3
∂ε P 0.0040 2.1520d 0.5091d 2 1.3560d 3
=
−
+
−
∂d
L
L2
L3
L4
∂ε P − 0.0040d 2.1520d 2 0.5091d 3 1.3560d 4
=
+
−
+
∂L
L2
L3
L4
L5
103
MEASUREMENTS FROM CONTACT
RESISTANCE TESTS
Appendix C
Contact Voltage Measurements at 2 mA
Contact
IF10
IF10
IF11
IF11
IF11
IF11
IF11
IF11
IF11
IF11
IF11
IF11
IF11
IF11
IF11
IF11
IF11
IF11
IF11
IF11
IF11
IF11
IF12
IF12
IF12
IF12
IF12
IF12
IF12
IF12
Set
2
3
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
3
3
3
3
3
1
1
1
1
1
1
1
1
Low*
35.0000
35.0000
0.5340
0.5420
0.5420
0.5440
0.5540
0.5540
0.5520
0.5580
0.5540
0.5560
2.0599
2.2579
2.2059
2.2540
2.2880
2.5500
2.5990
2.2949
2.2960
2.3600
0.0400
0.0520
0.0700
0.0720
0.3000
0.3520
0.1260
0.2800
High*
from pad
35.0000
35.0000
0.6260
1
0.6640
1
0.6240
1
0.6120
1
0.6040
1
0.6060
1
0.6060
1
0.6000
1
0.6360
1
0.6480
1
2.4700
2
2.4860
2
2.2800
2
2.4300
2
2.4979
2
2.5200
3
2.8929
3
2.7520
3
2.8430
3
2.5349
3
2
2
2
2
2
2
2
2
105
to pad
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
5
5
5
Contact
IF12
IF12
IF12
IF12
IF12
IF12
IF12
IF12
IF12
IF12
IF12
IF12
IF12
IF12
IF12
IF12
IF12
IF21
IF21
IF21
IF21
IF21
IF21
IF21
IF22
IF22
IF22
IF22
IF22
IF22
IF22
IF22
IF22
IF22
IF22
IF22
IF22
IF23
IF23
IF23
IF23
IF23
IF23
IF23
IF23
IF23
IF23
Set
1
1
1
1
1
1
1
2
2
2
2
2
3
3
3
3
3
1
1
1
1
1
2
3
1
1
1
1
1
1
1
1
1
1
1
2
3
2
2
2
2
2
3
3
3
3
3
Low*
0.0860
0.4540
0.1140
0.1840
0.1820
0.0720
0.0700
0.1620
0.1660
0.1640
0.1620
0.1700
0.1330
0.1840
0.1450
0.1630
0.1670
0.5600
0.5660
0.6320
0.6160
0.6240
35.0000
35.0000
1.7520
1.7840
1.7620
1.7540
1.7700
1.7560
1.7420
1.7599
1.7460
1.7460
35.0000
35.0000
0.1480
0.1500
0.1500
0.1500
0.1500
1.4640
1.4410
1.4400
1.4310
1.4370
High*
0.1640
0.1720
0.1720
0.1680
0.1660
0.1470
0.1370
0.1420
0.1650
0.1570
0.6100
0.6520
0.6480
0.6300
0.6240
35.0000
35.0000
2.0220
1.9000
2.0380
2.0940
1.9080
2.0620
1.9540
2.0959
2.0659
1.9280
2.0460
35.0000
35.0000
0.1500
0.1500
0.1500
0.1560
0.1540
1.4670
1.4640
1.4640
1.4550
1.4530
106
from pad
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
to pad
5
5
5
5
5
5
5
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
1
1
1
1
1
1
1
1
1
1
1
4
4
4
4
4
4
4
4
4
4
4
2
2
2
2
2
2
2
2
2
2
4
4
4
4
4
4
4
4
4
4
Contact
IF32
IF32
IF32
IF32
IF32
IF32
IF33
IF33
IF33
IF33
IF33
IF33
IF33
IF33
IF33
IF33
IF33
IF33
IF33
IF33
IF33
IF34
IF34
IF34
IF34
V1
V1
V1
V1
V1
V1
V1
V2
V2
V3
V3
V3
V3
V3
V3
V3
V3
V3
V3
V3
V3
V3
Set
2
2
2
2
2
3
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
2
3
2
2
2
2
2
2
2
2
3
3
3
3
3
Low*
0.1580
0.1600
0.1580
0.1600
0.1620
35.0000
0.4180
0.4500
0.4540
0.4680
0.4600
0.4760
0.4660
0.4620
0.4620
0.4440
0.2600
0.2600
0.2600
0.2620
0.2680
0.0320
0.0400
0.6380
0.6520
0.8120
0.8000
0.7360
0.7640
35.0000
35.0000
0.4640
0.4800
0.5600
0.4940
0.5020
0.2350
0.2350
0.2370
0.2370
0.2380
High*
from pad
0.1760
2
0.1760
2
0.1740
2
0.1720
2
0.1680
2
35.0000
0.4720
2
0.4960
2
0.4620
2
0.4720
2
0.4660
2
0.4640
2
0.4600
2
0.4660
2
0.4680
2
0.4680
2
0.2680
2
0.2680
2
0.2660
2
0.2640
2
0.2640
2
0.1880
2
0.1000
2
0.1500
2
0.1520
2
0.8480
1
0.9000
1
0.7200
1
1.0100
1
0.8200
1
0.9460
1
0.8600
1
35.0000
35.0000
1.3820
2
1.2900
2
1.2720
2
1.2260
2
1.2940
2
0.0400
2
0.0400
2
0.0700
2
0.2410
2
0.2490
2
0.2500
2
0.2490
2
0.2520
2
107
to pad
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
Contact
Set
Low*
V4A
1
35.0000
V4A
2
0.1440
V4A
2
0.1400
V4A
2
0.1400
V4A
2
0.1400
V4A
2
0.1380
V4A
3
0.3600
V4A
3
0.3900
V4A
3
0.4010
V4A
3
0.4010
V4A
3
0.4040
V4B
2
0.6640
V4B
2
0.6720
V4B
2
0.6460
V4B
2
0.6840
V4B
2
0.6520
V4B
3
35.0000
V4C
2
0.0900
V4C
2
0.0580
V4C
2
0.1340
V4C
2
0.0580
V4C
2
0.0960
V4C
3
0.8840
V4C
3
0.9570
V4C
3
0.9150
V4C
3
0.8710
V4C
3
0.9490
*35 means no contact or broken
High*
from pad
35.0000
1
0.1400
2
0.1440
2
0.1380
2
0.1380
2
0.1580
2
0.4470
2
0.4200
2
0.4250
2
0.4060
2
0.4010
2
0.6280
2
0.6260
2
0.6340
2
0.6320
2
0.6260
2
35.0000
0.0380
2
0.1020
2
0.0560
2
0.0380
2
0.0500
2
0.9020
2
0.8770
2
0.9650
2
0.7810
2
1.0300
2
108
to pad
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
Probe to Probe Voltage Measurements at 2 mA
Configuration
Probe to Probe on Gold (Close)
Probe to Probe on Gold (Far)
109
Set
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
3
3
Voltage
0.012
0.014
0.012
0.014
0.012
0.014
0.014
0.014
0.014
0.016
0.014
0.014
0.012
0.01
0.01
0.01
0.01
0.01
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.008
0.008
0.008
0.008
0.008
0.016
0.016
0.016
0.016
0.016
0.014
0.016
0.016
0.016
0.018
0.016
Configuration
Set
3
3
3
3
3
3
4
4
4
4
4
4
4
1
1
1
1
1
2
2
2
2
2
2
3
3
3
3
3
3
Probe to Probe
Voltage
0.018
0.016
0.016
0.016
0.016
0.018
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.024
0.024
0.024
0.024
0.024
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
In the table above, “on Gold” refers to the fact that the voltage was measured
from probe to probe with both probes touching the same pad of gold. Close and Far refer
to the distance between the probes. Close measurements had probe separation distances
of less than 100 µm while Far measurements had probe separation distances of about
800 µm.
110
Appendix D
MEASUREMENTS FROM CONTACT
FORCE TESTS
Linear Displacement Bistable Mechanism Data
Displacement Deflection
DisplacementDeflection Calibration Calibration Displ. Defl. Actual Actual
(pixels)
(pixels) Measurement Measurement Calib. Calib. Displ. Defl.
Step
1
11.05
102.00
78.00
214.000.41030.4065 4.5236 41.5328
1
11.05
99.00
78.01
212.000.41020.4104 4.5236 40.3112
1
10.00
100.00
78.01
214.000.41020.4065 4.0937 40.7184
1
10.00
100.00
78.00
213.000.41030.4085 4.0937 40.7184
1
11.05
100.00
78.00
214.000.41030.4065 4.5236 40.7184
1
11.00
100.00
79.00
215.000.40510.4047 4.5031 40.7184
2
12.00
94.01
80.01
215.000.40000.4047 4.7702 38.1897
2
13.00
92.00
81.00
215.000.39510.4047 5.1677 37.3731
2
12.04
92.01
81.01
214.000.39500.4065 4.7861 37.3772
2
10.00
94.00
80.00
214.000.40000.4065 3.9751 38.1856
2
13.00
93.01
80.00
213.000.40000.4085 5.1677 37.7834
2
12.00
93.00
81.00
214.000.39510.4065 4.7702 37.7794
3
23.00
83.00
80.02
215.000.39990.4047 9.2195 33.4054
3
23.00
82.00
80.00
216.000.40000.4028 9.2195 33.0029
3
25.00
84.00
81.00
216.000.39510.402810.0212 33.8078
3
23.00
84.00
79.00
216.000.40510.4028 9.2195 33.8078
3
24.00
84.00
80.00
216.000.40000.4028 9.6204 33.8078
3
24.00
83.00
79.00
218.000.40510.3991 9.6204 33.4054
4
51.00
69.00
78.00
214.670.41030.405320.6626 27.9643
4
49.00
71.00
78.00
214.670.41030.405319.8523 28.7748
4
50.00
69.00
79.00
214.670.40510.405320.2575 27.9643
4
50.00
68.00
78.00
214.670.41030.405320.2575 27.5590
4
48.00
69.00
80.00
214.670.40000.405319.4472 27.9643
4
50.00
69.00
81.00
214.670.39510.405320.2575 27.9643
5
58.01
66.00
79.03
214.670.40490.405323.5952 26.7484
5
58.03
65.00
78.06
214.670.40990.405323.6033 26.3432
5
59.00
67.00
76.01
214.670.42100.405323.9979 27.1537
5
60.00
67.00
80.02
214.670.39990.405324.4046 27.1537
5
57.04
66.00
80.06
214.670.39970.405323.2006 26.7484
5
59.03
67.01
79.01
214.670.40500.405324.0101 27.1578
111
Displacement Deflection
DisplacementDeflection Calibration Calibration Displ. Defl. Actual Actual
Step
(pixels)
(pixels) Measurement Measurement Calib. Calib. Displ. Defl.
6
69.00
62.00
79.00
214.670.40510.405327.4342 25.1273
6
71.00
62.00
80.00
214.670.40000.405328.2294 25.1273
6
69.00
64.00
79.00
214.670.40510.405327.4342 25.9379
6
66.00
62.00
81.00
214.670.39510.405326.2414 25.1273
6
65.00
62.00
82.00
214.670.39020.405325.8438 25.1273
6
67.00
63.00
82.02
214.670.39010.405326.6390 25.5326
7
83.00
62.00
78.00
214.670.41030.405333.2756 25.1273
7
84.00
63.00
80.00
214.670.40000.405333.6765 25.5326
7
82.00
62.00
79.01
214.670.40500.405332.8747 25.1273
7
82.00
62.00
80.00
214.670.40000.405332.8747 25.1273
7
84.00
65.00
82.00
214.670.39020.405333.6765 26.3432
7
83.00
65.00
80.01
214.670.40000.405333.2756 26.3432
8
102.00
61.00
82.00
214.670.39020.405340.5544 24.7220
8
101.00
64.00
80.00
214.670.40000.405340.1568 25.9379
8
100.00
63.00
80.00
214.670.40000.405339.7592 25.5326
8
100.00
63.00
79.00
214.670.40510.405339.7592 25.5326
8
100.00
64.00
82.00
214.670.39020.405339.7592 25.9379
8
100.00
61.00
80.00
214.670.40000.405339.7592 24.7220
9
119.00
63.00
79.00
214.670.40510.405347.9138 25.5326
9
119.00
62.00
80.00
214.670.40000.405347.9138 25.1273
9
119.00
63.00
80.00
214.670.40000.405347.9138 25.5326
9
119.00
65.00
78.00
214.670.41030.405347.9138 26.3432
9
120.00
64.00
82.00
214.670.39020.405348.3164 25.9379
9
119.00
63.00
78.00
214.670.41030.405347.9138 25.5326
10
135.00
63.00
79.00
214.000.40510.406554.2421 25.6125
10
136.00
65.00
78.00
214.000.41030.406554.6439 26.4256
10
135.00
63.00
78.00
213.000.41030.408554.2421 25.6125
10
135.00
64.00
81.00
213.000.39510.408554.2421 26.0191
10
137.00
66.00
81.00
215.000.39510.404755.0457 26.8322
10
136.00
65.00
81.00
215.000.39510.404754.6439 26.4256
11
153.00
67.00
79.00
214.670.40510.405361.2114 27.1537
11
153.00
70.00
80.00
214.670.40000.405361.2114 28.3696
11
156.00
69.00
81.00
214.670.39510.405362.4116 27.9643
11
155.00
68.00
82.01
214.670.39020.405362.0116 27.5590
11
153.00
67.00
79.00
214.670.40510.405361.2114 27.1537
11
153.00
70.01
79.00
214.670.40510.405361.2114 28.3736
12
175.00
75.00
80.00
214.670.40000.405368.8757 30.3960
12
174.00
73.00
79.00
214.670.40510.405368.4821 29.5854
12
175.00
71.00
81.00
214.670.39510.405368.8757 28.7748
12
175.00
73.00
83.00
214.670.38550.405368.8757 29.5854
12
176.00
72.00
83.00
214.670.38550.405369.2693 29.1801
12
175.00
73.00
82.00
214.670.39020.405368.8757 29.5854
In the table above, step 10 is bolded because it is the unstable equilibrium position
(measurements continue beyond this point because the stiction was greater than the
112
restorative force of the mechanism). The calibration measurements are pixel
measurements of features with known dimensions (32 µm for displacement and 87 µm
for deflection). The deflection and displacement calibration numbers are in units of
microns per pixel and are found by dividing the known dimension by the calibration
measurement.
113
Fully Compliant Bistable Mechanism Data
Displacement Deflection
Displacement Deflection Calibration Calibration Displ.
Step
(pixels)
(pixels) Measurement Measurement Calib.
0
0.00
72.00
53.00
53.000.6038
0
0.00
75.00
53.01
53.010.6037
0
0.00
75.00
53.01
53.010.6037
0
0.00
75.00
53.01
53.010.6037
0
0.00
72.00
53.00
53.000.6038
0
0.00
71.00
55.00
55.000.5818
1
15.03
71.00
53.00
53.000.6038
1
14.04
72.00
53.00
53.000.6038
1
14.04
71.00
54.00
54.000.5926
1
14.04
72.00
51.00
51.000.6275
1
12.00
71.00
54.00
54.000.5926
1
13.04
72.00
54.00
54.000.5926
2
17.00
71.00
54.00
54.000.5926
2
17.00
72.00
54.00
54.000.5926
2
18.03
71.00
54.00
54.000.5926
2
18.03
70.00
55.00
55.000.5818
2
19.03
71.00
54.00
54.000.5926
2
18.00
71.00
54.00
54.000.5926
3
24.00
70.00
54.01
54.010.5925
3
22.00
73.00
54.00
54.000.5926
3
23.00
71.00
54.01
54.010.5925
3
22.00
71.00
53.00
53.000.6038
3
23.00
72.00
55.00
55.000.5818
3
22.00
71.00
54.00
54.000.5926
4
26.00
75.00
55.00
55.000.5818
4
25.00
75.00
53.00
53.000.6038
4
27.00
73.00
54.00
54.000.5926
4
26.00
73.00
53.00
53.000.6038
4
26.00
74.00
54.01
54.010.5925
4
26.00
74.00
53.00
53.000.6038
5
30.00
78.00
54.00
54.000.5926
5
29.00
75.00
53.00
53.000.6038
5
30.00
76.00
53.00
53.000.6038
5
28.00
75.00
52.00
52.000.6154
5
29.00
77.00
55.00
55.000.5818
5
30.00
74.00
52.00
52.000.6154
6
34.00
77.00
54.00
54.000.5926
6
35.00
78.00
55.00
55.000.5818
6
34.00
78.00
54.00
54.000.5926
6
32.00
78.00
54.00
54.000.5926
6
32.00
76.00
53.00
53.000.6038
6
31.00
78.00
53.00
53.000.6038
114
Defl. Actual Actual
Calib. Displ. Defl.
0.6038 0.0000 43.2041
0.6037 0.0000 45.0043
0.6037 0.0000 45.0043
0.6037 0.0000 45.0043
0.6038 0.0000 43.2041
0.5818 0.0000 42.6041
0.6038 9.0500 42.7512
0.6038 8.4539 43.3533
0.5926 8.4539 42.7512
0.6275 8.4539 43.3533
0.5926 7.2256 42.7512
0.5926 7.8518 43.3533
0.5926 10.0435 41.9466
0.5926 10.0435 42.5374
0.5926 10.6521 41.9466
0.5818 10.6521 41.3558
0.5926 11.2429 41.9466
0.5926 10.6343 41.9466
0.5925 14.2230 41.4837
0.5926 13.0377 43.2615
0.5925 13.6303 42.0763
0.6038 13.0377 42.0763
0.5818 13.6303 42.6689
0.5926 13.0377 42.0763
0.5818 15.5056 44.7277
0.6038 14.9092 44.7277
0.5926 16.1020 43.5349
0.6038 15.5056 43.5349
0.5925 15.5056 44.1313
0.6038 15.5056 44.1313
0.5926 18.0636 46.9655
0.6038 17.4615 45.1591
0.6038 18.0636 45.7612
0.6154 16.8594 45.1591
0.5818 17.4615 46.3633
0.6154 18.0636 44.5570
0.5926 20.2138 45.7783
0.5818 20.8083 46.3729
0.5926 20.2138 46.3729
0.5926 19.0248 46.3729
0.6038 19.0248 45.1838
0.6038 18.4302 46.3729
Displacement Deflection
Displacement Deflection Calibration Calibration Displ.
Step
(pixels)
(pixels) Measurement Measurement Calib.
0
0.00
76.00
59.00
59.000.5424
0
0.00
76.00
58.01
58.010.5516
0
0.00
76.00
56.01
56.010.5713
0
0.00
77.00
58.01
58.010.5516
0
0.00
75.00
59.00
59.000.5424
0
0.00
76.00
58.00
58.000.5517
1
3.00
75.00
58.00
58.000.5517
1
2.24
74.00
57.00
57.000.5614
1
2.00
76.00
58.00
58.000.5517
1
2.00
73.00
58.00
58.000.5517
1
3.00
75.00
56.00
56.000.5714
1
2.00
73.00
58.00
58.000.5517
2
8.00
73.00
59.00
59.000.5424
2
11.00
72.00
56.00
56.000.5714
2
9.06
76.00
55.00
55.000.5818
2
7.07
72.00
57.00
57.000.5614
2
8.00
74.00
58.00
58.000.5517
2
9.06
72.00
57.00
57.000.5614
3
15.03
74.00
58.00
58.000.5517
3
15.00
74.00
58.00
58.000.5517
3
16.00
75.00
57.00
57.000.5614
3
15.03
75.00
58.00
58.000.5517
3
14.04
73.00
60.00
60.000.5333
3
16.00
74.00
59.00
59.000.5424
4
20.00
74.00
59.00
59.000.5424
4
19.00
75.00
58.03
58.030.5514
4
20.00
74.00
59.00
59.000.5424
4
19.03
72.00
58.00
58.000.5517
4
20.02
73.00
60.00
60.000.5333
4
20.00
73.00
59.00
59.000.5424
5
25.00
76.00
59.00
59.000.5424
5
26.00
76.00
57.00
57.000.5614
5
26.02
75.00
57.00
57.000.5614
5
25.00
77.01
57.00
57.000.5614
5
24.00
75.00
58.00
58.000.5517
5
25.00
75.00
59.00
59.000.5424
6
33.00
80.00
57.00
57.000.5614
6
32.00
80.00
57.00
57.000.5614
6
31.00
78.00
58.00
58.000.5517
6
31.00
80.00
58.01
58.010.5516
6
32.00
78.00
59.00
59.000.5424
6
32.00
78.00
57.00
57.000.5614
7
36.00
81.00
57.00
57.000.5614
7
35.00
83.00
57.00
57.000.5614
7
34.00
80.00
58.00
58.000.5517
7
34.00
81.00
57.08
57.080.5606
7
34.00
80.00
56.00
56.000.5714
115
Defl. Actual Actual
Calib. Displ. Defl.
0.5424 0.0000 41.9400
0.5516 0.0000 41.9400
0.5713 0.0000 41.9400
0.5516 0.0000 42.4919
0.5424 0.0000 41.3882
0.5517 0.0000 41.9400
0.5517 1.6699 41.7466
0.5614 1.2468 41.1900
0.5517 1.1132 42.3032
0.5517 1.1132 40.6334
0.5714 1.6699 41.7466
0.5517 1.1132 40.6334
0.5424 4.4935 41.0035
0.5714 6.1786 40.4418
0.5818 5.0889 42.6886
0.5614 3.9712 40.4418
0.5517 4.4935 41.5652
0.5614 5.0889 40.4418
0.5517 8.2472 40.6048
0.5517 8.2307 40.6048
0.5614 8.7794 41.1535
0.5517 8.2472 41.1535
0.5333 7.7039 40.0561
0.5424 8.7794 40.6048
0.5424 10.8787 40.2513
0.5514 10.3348 40.7952
0.5424 10.8787 40.2513
0.5517 10.3511 39.1634
0.5333 10.8896 39.7073
0.5424 10.8787 39.7073
0.5424 13.8362 42.0620
0.5614 14.3896 42.0620
0.5614 14.4007 41.5085
0.5614 13.8362 42.6209
0.5517 13.2827 41.5085
0.5424 13.8362 41.5085
0.5614 18.3147 44.3992
0.5614 17.7597 44.3992
0.5517 17.2047 43.2892
0.5516 17.2047 44.3992
0.5424 17.7597 43.2892
0.5614 17.7597 43.2892
0.5614 20.2073 45.4664
0.5614 19.6460 46.5890
0.5517 19.0847 44.9051
0.5606 19.0847 45.4664
0.5714 19.0847 44.9051
Displacement Deflection
Displacement Deflection Calibration Calibration Displ. Defl. Actual Actual
Step
(pixels)
(pixels) Measurement Measurement Calib. Calib. Displ. Defl.
7
34.01
81.00
57.01
57.010.5613 0.5613 19.0903 45.4664
In the table above, step 0 is used because when the mechanism moved past its
unstable equilibrium position, it was deflecting the force tester – which could not move
back any further. The process of measuring the contact force was repeated for this
mechanism.
116
Young Mechanism Data
Deflection
Deflection Calibration Deflection Actual Average
StepAngle (pixels) MeasurementCalibrationDeflection Angle
- 10.47
11.28
- 11.08
0.56
12.1
- 11.64
- 11.35
- 11.05
0 27.78
35.01
79.10
1.3401 45.8169 17.22
0.68
0 28.49
34.06
79.31
1.3365 44.5737
0 28.67
32.02
80.16
1.3224 41.9040
0 28.76
34.13
81.15
1.3062 44.6653
0 28.91
35.01
80.16
1.3224 45.8169 28.51
0 28.42
36.06
80.16
1.3224 47.1910
0.40
1 27.26
35.36
83.38
1.2713 46.1802 15.69
0.76
1 27.27
35.06
81.30
1.3038 45.7884
1 26.24
36.22
79.51
1.3332 47.3034
1 27.59
35.06
80.40
1.3184 45.7884
1 26.97
35.06
80.22
1.3214 45.7884 26.97
1 26.51
35.01
82.30
1.2880 45.7231
0.51
2 25.21
36.01
83.49
1.2696 47.2221 13.99
0.75
2 25.25
34.01
82.30
1.2880 44.5994
2 26.09
36.01
81.30
1.3038 47.2221
2 25.02
36.01
80.31
1.3199 47.2221
2 25.45
35.01
79.40
1.3350 45.9107 25.27
2 24.58
34.01
78.41
1.3519 44.5994
0.50
3
23.3
37.12
80.50
1.3168 49.1823 12.72
0.86
3 23.09
36.12
79.63
1.3312 47.8573
3 24.72
37.05
80.62
1.3148 49.0895
3 24.25
36.06
78.92
1.3431 47.7778
3 24.36
37.05
80.75
1.3127 49.0895 24.00
3 24.28
37.05
79.63
1.3312 49.0895
0.65
In the table above, the angle measurement is the measurement of the angle
between the line defined by the Young mechanism pin joints and the short flexible
segment. Step “-” is a measurement of the angle with the mechanism in its fabricated
position. This measurement is used to calculate the change in angle used as the x-axis of
the potential energy and contact force prediction curves for the Young mechanism. The
top bolded number in the Average Angle column with each step is the average difference
117
between the initial angle and the measured angle. The second bolded number is the
standard deviation of the average angle difference (calculated by taking the square root of
the sum of the squared standard deviation of the initial angle measurements and the
squared standard deviation of the step angle measurement). The third number in the
Average Angle column with each step is the average measured angle for that step. The
fourth number is the standard deviation of the measured angle for that step.
118
Appendix E
MEASUREMENTS FROM AC
CHARACTERISTICS TESTS
Contact-to-Contact Measurements for Young Mechanism Relay
Frequency (Hz)
1
10
100
1000
10000
100000
1000000
V1
4.56
4.56
4.56
4.43
4.27
4.24
4.24
No Probe
Contact
V2
V2
Pad to Pad System Noise
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.17
0.17 0.039813
0.039813
0.43
0.27 0.101415
0.063679
0.4
0.24
0.09434
0.056604
AC Isolation Measurements for Young Mechanism Relay
Frequency (Hz)
1
10
100
1000
10000
100000
1000000
V1
4.56
4.56
4.62
4.4
4.24
4.24
4.28
No Probe
Contact
V2
V2
Pad to Pad System Noise
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.29
0.035 0.068396
0.008255
0.4
0.27
0.09434
0.063679
0.5
0.24 0.116822
0.056075
119
Contact-to-Contact Measurements for LDBM Relay
Frequency (Hz)
1
10
100
1000
10000
100000
1000000
V1
4.58
4.48
4.48
4.41
4.36
4.36
4.36
No Probe
Contact
V2
V2
Pad to Pad System Noise
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.08
0.8 0.018349
0.183486
0.24
0.24 0.055046
0.055046
0.32
0.24 0.073394
0.055046
AC Isolation Measurements for LDBM Relay
Frequency (Hz)
1
10
100
1000
10000
100000
1000000
V1
4.58
4.48
4.48
4.41
4.36
4.36
4.36
No Probe
Contact
V2
V2
Pad to Pad System Noise
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.08
0.8 0.018349
0.183486
0.24
0.24 0.055046
0.055046
0.32
0.24 0.073394
0.055046
120
Appendix F
MEASUREMENTS FROM DC TESTS
Breakdown Voltage Measurements
Voltage
0
35
50
75
100
125
150
175
200
250
300
350
400
412
425
435
440
450
455
460
465
470
475
Current
(mA)
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.02
0.03
0.03
0.04
0.04
0.05
0.06
0.07
0.08
0.09
0.1
The equipment used to measure the current at each voltage could not read less
than 0.01 mA. Therefore, 0.01 mA should be considered essentially zero current flow.
121
Isolation Measurements
Voltage
0
50
100
150
200
210
215
220
225
230
235
237
Current
(mA)
0.01
0.01
0.01
0.01
0.02
0.03
0.03
0.04
0.05
0.07
0.09
0.1
The equipment used to measure the current at each voltage could not read less
than 0.01 mA. Therefore, 0.01 mA should be considered essentially zero current flow.
122