Design, Fabrication and Testing of a Lateral Self-cleaning MEMS Switch
By Yong SHI
B.Eng., Materials Sciences and Applied Chemistry
The National University of Defense Technology, P. R. China, 1985
S.M., Aeronautics and Astronautics,
Massachusetts Institute of Technology, 2001
Submitted to the Department of Aeronautics and Astronautics
in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy in Aeronautics and Astronautics
At the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
August 2004
2004 Massachusetts Institute of Technology
All rights reserved.
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Departmen( of Aeronautics and Astronautics
Aug. 20, 2004
Certified by ...
......
... ......
... ... ... ... ... .
Sang-Gook Kim
~
Esther & Harold Edgerton Professor of Mech. Eng.
-
Thesis Supervisor
Certified by
... ... ... ... ... ... ..
L/
S. Mark-Sp
g
Professor of Arfonauticsnd Astronautics
Certified by ...... .
Charles Stark
"ra
fe2s
& Astro.
Certified by ... ... .
G e Barbastathis
Esther & Harold Edgerton Professor of Mech. Eng.
Certified by ...
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Pri~~pal Research Scientist
A ccepted by ... ... ... ... ... ... ... ... ... ... . ... ....
OF
T
. .... ... .....
... ... ... . . .....
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Professor of Aeronautics and Astronautics
Chair, Departmental Committee on Graduate Students
jo
OCT 15 2008
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AERO
Design, Fabrication and Testing of a Lateral Self-cleaning MEMS Switch
by
YONG SHI
Submitted to the Department of Aeronautics and Astronautics
On August 20, 2004 in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy in
Aeronautics and Astronautics
ABSTRACT
A lateral contact MEMS switch has been developed to address the need for a long life cycle,
low contact resistance RF switch. At the present time, there is no commercial MEMS switch
that meets all the requirements. The objectives of this research are to understand the
functional requirements and the failure modes of such MEMS switches, and to develop a
cost effective, compact and highly reliable direct contact MEMS switch.
Major switch performance parameters were investigated to determine the real functional
requirements of an RF switch, which leads to a novel switch design. This switch design is
characterized by the self-alignment of the contact surfaces, self-cleaning of the particles
generated from asperity fracture and deformation, and the anchoring method of the metal
contacts in the micro switch structures and the large stroke piezo-actuation by the strain
amplifying MEMS mechanism. The analytical model for the contact force - contact
resistance relation is established to predict the required contact force, while modeling of the
switch isolation provides the required displacement of the actuator.
The 5-mask fabrication process for the device consists of several steps including bottom
electrode lift-off, plating mold formation, electroplating, mold removal, switch structure
formation and device release. The major issue is the fabrication of the vertical sidewall of
gold for electrical contact. A fine control of electroplating current and temperature makes
deep and clean vertical metal walls. The device is released with XeF 2.
It has been demonstrated that a contact resistance lower than 0.1 is achieved for up to
10 billion operating cycles. The grooved surface exhibited the self-cleaning effect and the
parallel-beam design of the switch structure guaranteed the perfect contact during the switch
operation. In addition, no failure has been observed in the anchoring of the gold metal to
the switch structure. Finally, molded electroplating proved to be an effective way to create
vertical metal sidewall for electric contact. The electroplated gold surface is more uniform
and the microstructure is denser than that deposited by e-beam evaporation.
Thesis Supervisor: Sang-Gook Kim
Title: Esther & Harold Edgerton Assoc Professor of Mechanical Engineering
2
Acknowledgements
I would like to thank my advisor Prof. Sang-Gook Kim sincerely for his supervising and
supporting on this project, especially his encouraging and emphasizing on the way of
creative thinking, and the ability to balance looking into the "big pictures" as well as the
details in research.
My sincere thanks also go to all the memebres of the MIT Mcro/Nano Systems
Laboratory and my office mates Dr. Yongbae Jeon, Dr. J. H. Jeong, Dr. Cheewei. Wong, Dr.
Y. A. Song, Nick Conway, Raj Sood, Tarek A. El Aguizy, Clemens Mueller-Falcke, Sunil
Doddabasanagonda, Ray Hardin, the MIT Microsystems Technology Laboratory staff Dave
Terry, Kurt Broderick, Vicky Diadiuk, Dennis Ward and my friends Dr. Hanqin Li and Dr.
Hongwei Sun for their help and advice.
I would also like to thank Prof. Mark Spearing for the partial RA support and Prof. Carol
Livermore and Prof. Joel Voldman for the TA support during the course of this work.
Finally I want to thank my wife Zhihong Wang, my son Caleb and my daughter Isabel
for their love and making all this meaningful.
This project was originally funded by the Manufacturing Institute of MIT and the Korea
Institute of Machinery and Materials (KIMM).
3
Contents
ACK N O W LEDGEM ENTS .........................................................................................
3
CONTENTS.......................................................................................................................
4
LIST O F FIG URES .......................................................................................................
7
LIST O F TABLES .......................................................................................................
11
NO M EN CLATURE.....................................................................................................
13
1.
INTRODUCTION ..................................................................................
17
1.1
BACKGROUND AND M OTIVATION.................................................................
17
1.2
O BJECTIVES.................................................................................................
18
1.3
LITERATURE REVIEW ....................................................................................
19
General switch perform ances ....................................................................
M EM S Switch classification....................................................................
Contact m echanics and switch failure modes ...........................................
Sum mary..................................................................................................
19
21
23
24
1.4
APPROACH......................................................................................................
25
1.5
ORGANIZATION OF THE DOCUMENT .............................................................
26
RF M EM S SW ITCH DESIGN .............................................................
29
SWITCH FAILURE MODE ANALYSIS...............................................................
FUNCTIONAL DESIGN OF THE SW ITCH SYSTEM ..............................................
29
1.3.1
1.3.2
1.3.3
1.3.4
2.
2.1
2.2
2.2.1
2.2.2
2.3
2.3.1
2.3.2
2.3.3
2.3.4
2.3.5
2.4
2.5
2.5.1
2.5.2
Functional requirem ents: ........................................................................
D esign param eters:...................................................................................
30
30
30
SWITCH CONCEPT AND DESIGN ....................................................................
31
The general concept .................................................................................
The self-alignm ent of the contact surfaces ................................................
The self-cleanimg of the dam aged surface...................................................
Attaching of the gold contacts to the structure..........................................
Contact force adjustm ent.........................................................................
31
32
32
33
33
34
34
34
35
SWITCH MATERIALS SELECTION ..................................................................
SWITCH MODELING......................................................................................
Equivalent m odel ...................................................................................
Switch isolation........................................................................................
4
2.5.3
2.5.4
2.6
3.
Switch insertion loss.................................................................................
M icro strip transmission line design.........................................................
36
37
SU M M A RY ...................................................................................................
39
CONTACT MECHANICS AND CONTACT RESISTANCE............. 40
3.1
3.2
3.2.1
3.2.2
3.3
3.4
3.4.1
3.4.2
3.5
3.5.1
3.5.2
4.
CONTACT SURFACE CHARACTERIZATION.....................................................
C ONTACT M ECHANICS ..................................................................................
40
Hertz contact
...........................................
Plastic contact...........................................44
42
CONSTRICTION RESISTANCE .......................................................................
OVERALL CONTACT RESISTANCE ....................................................................
46
Elastic C ontact ........................................................................................
Plastic contact ..........................................................................................
47
48
C OM PUTING EXAM PLES..................................................................................
49
Contact resistance and force with a single asperity
...................
Contact resistance and force with distributed asperities
................
SWITCH ACTUATION.........................................................................
4.1
42
47
49
53
61
ACTUATION METHOD REVIEW ......................................................................
4.1.1
4.1.2
4.1.3
4.1.4
4.2
4.2.1
4.2.2
4.2.3
61
Force and displacement of micro actuators................................................
61
Work densities and frequencies of micro actuators
..................
65
Actuation efficiency of micro actuators ...
....................................
66
Driving voltage or current of micro actuators
..................... 67
PIEZOELECTRIC ACTUATOR.........
......................................................
68
The common operation modes
............................... 68
The transverse mode.............................................................
69
PZT actuator
.................
.......................................
69
4.3
ACTUATOR DESIGN AND SIMULATION.............................................................
71
Bow actuator
....... ..... ............................
...............................
M odal analysis mode..... .....................................
.......................................
Bow actuators used in parallel and series.......................................................
71
72
73
4.3.1
4.3.2
4.3.3
4.4
4.4.1
4.4.2
4.4.3
4.5
4.5.1
4.5.2
4.5.3
5.
5.1
5.2
SWITCH-ACTUATOR COUPLED ANALYSIS........................................................
73
Sliding condition.........................................................................................
73
Sw itch beam stiffness...................................................................................
75
Coupled analysis i arlea...........ndse...................................................76
SWITCH GEOMETRY AND THE SWITCH SCHEMA I .........................................
80
The switch geometry...................................................................................
The beam stiffness. ........................................
.......................................
Switch schem atics......................................................................................
80
81
82
DEVICE FABRICATION
HE.SWITHSCC.........
83
......................................
5.3
INTRODUCTION ....
.............................................................................
PROCESS EVALUATION...............................................................................
FABRICATION PROCESS FLOW.........................................................................
5.4
ISSUES AND PROBLEMS OF THE DEVICE FABRICATION..................................
91
Electroplating in general ...........................................................................
Electroplating m old..................................................................................
91
92
5.4.1
5.4.2
5
83
.83
86
5.4.3
5.4.4
5.4.5
E lectroplating...........................................................................................
Underplating ...........................................................................................
Other issues ..............................................................................................
95
97
100
FABRICATION RESULTS AND SUMMARY ........................................................
101
DEVICE TESTING RESULTS AND DISCUSSION ............................
106
6 .1
T E ST SET -U P .................................................................................................
106
6.2
CONTACT SURFACE CHARACTERIZATION......................................................
108
6.3
6.3.1
6.3.2
CONTACT RESISTANCE MEASUREMENT.........................................................
110
Dummy design resistance measurement......................................................
Contact resistance measurement.................................................................
110
111
6.4
HOT AND COLD SWITCH TEST........................................................................
114
Hot test.....................................................................................................
Cold T est ..................................................................................................
114
116
TEST RESUL TS DISCUSSION..........................................................................
118
5.5
6.
6.4.1
6.4.2
6.5
7.
RESEARCH SUMMARY, CONCLUSIONS AND CONTRIBUTIONS
..........................................................
...............................................
. 123
7.1
RESEARCH SUMMARY.................................................
123
7.2
CON CLU SION S ............................................................................................
124
7.3
7.3.1
7.3.2
7.3.3
7.3.4
7.4
7.4.1
7.4.2
7.4.3
7.4.4
CONTRIBUTIONS........................................................................................
125
MEMS switch design..............................................................................
M odeling..............................
..... ........... ........................................
MEMS switch fabrication .........................................................................
MEMS switch test and Analysis...............................
125
125
126
126
RECOMMENDATIONS FOR FUTURE WORK ...............................
126
.... ............................................ ..
D esign ............................................
..............................................
Fabncation............................
Device integration, packaging...................................................................
Testing................................................
126
127
127
128
.................................
REFERENCES ............................................
.............. 129
APPENDIX A ............................................................
P RO CESS D ETA ILS .................................................................
...........
......................
6
1 34
137
APPENDIX B..........................................................
M A TLA B SCR IPTS.......................................................................
134
...............................
137
List of Figures
Figure 2-1 Switch concept..........................................................................................
32
Figure 2-2 Mechanical anchoring of the contacts to the switch .....................................
33
Figure 2-3 MEMS switch simplified configuration ......................................................
35
Figure 2-4 Switch equivalent model.............................................................................
35
Figure 2-5 Insertion loss vs. contact resistance.............................................................
37
Figure 2-6 Micro-strip transmission line .....................................................................
38
Figure 2-7 Micro-strip impedance vs. the ratio of w/h .................................................
38
Figure 3-1 Sidewall surface of e-beam evaporated Gold................................................
41
Figure 3-2 A simple contact surface.............................................................................
42
Figure 3-3 Single asperity elastic contact ......................................................................
43
Figure 3-4 Volume conservation after plastic deformation............................................
45
Figure 3-5 Constriction resistance between surfaces Al and Ac ....................................
46
Figure 3-6 Contact resistance vs. contact force for single asperity ................................
52
Figure 3-7 Influence of asperity size on the contact force-contact resistance relation.........53
Figure 3-8 Contact force-contact resistance for varying plastic index............................
59
Figure 3-9 Comparison of the contact resistance-force relations from the single asperity
60
model and the distributed asperity model .............................................
7
Figure 4-1 Curved electrode electrostatic actuator.........................................................
61
Figure 4-2 PZT micro gripper......................................................................................
62
Figure 4-3 Comb drive actuator ............................................
63
Figure 4-4 Scratch drive actuator...........................................64
Figure 4-5 Actuator work density vs. cycling frequency ................................................
66
Figure 4-6 Principle of the transverse mode of piezoelectric actuator............................
69
Figure 4-7 Displacement
from a simple PZT actuator.................................................70
Figure 4-8 Bow actuator model.............................................72
Figure 4-9 Free body diagram of the switch beam ...........
..............................
74
Figure 4-10 The coupled switch -actuator system.................................76
Figure 4-11 Switch schematics .........................................
82
Figure 5-1 Su-8 structure with e-beam evaporated Gold................................84
Figure 5-2 Close-up view of the Gold film on the sidewall ..........................
85
Figure 5-3 Surface quality of the sidewall.................................85
Figure 5-4 Step 1: Growth of thermal oxide on the Si substrate and the 5 masks ............... 86
Figure 5-5 Step 2: Photolithography and bottom electrode lift-off................................87
Figure 5-6 Step 3&4: Thin Film PZT deposition, patterning and top electrode lift-off ....... 87
Figure 5-7 Step 5: Preparation of photo resist mold for electroplating.........................88
Figure 5-8 Step 6:Electroplating of the contact metal...............................88
Figure 5-9 Step 7: Electroplated contact metal after electroplating mold is removed .....
89
Figure 5-10 Step 8: Switch structural layer (Su-8) deposition and patterning..................89
Figure 5-11 Step 9: Device release by XeF2 etching
8
.......
............................
90
Figure 5-12 Positive photo resist mold cross-section....................................................
93
Figure 5-13 Su-8 mold cross-section on flat surface ......................................................
94
Figure 5-14 Su-8 mold after parameters trade-off.........................................................95
Figure 5-15 Plating results with un-cleaned mold ........................................................
96
Figure 5-16 Typical de-bonding between the Su-8 mold and substrate ..........................
99
Figure 5-17 Underplating at the edges of electrode.......................................................
99
Figure 5-18 Plated Gold contacts after mold removal.....................................................
102
Figure 5-19 SEM picture of device with two rows of actuators after it's released ......
103
Figure 5-20 SEM picture of device with single row of three actuators after it's released ... 103
Figure 5-21 SEM picture of the switch part of the released device ................
104
Figure 5-22 Picture of the released device showing the undercut of the release (darker area)
............................................................................................................
104
Figure 5-23 SEM picture of the contact area of the released device...............
105
Figure 6-1 Test set-up schem atic...............................................................................
106
Figure 6-2 The probe station and the measuring system.................................................
107
Figure 6-3 The actuator driving system ..........................................................................
107
Figure 6-4 SEM picture of the sidewall surface of gold by molded electroplating...... 108
Figure 6-5 SEM picture comparison of the contact surfaces ....................
109
Figure 6-6 AFM image of the mold surface....................................................................
109
Figure 6-7 Circuit for contact resistance measurement....................................................
111
Figure 6-8 Relationships between contact force and contact resistance............................
114
Figure 6-9 Contact resistance vs. number of operation cycles for hot test........................ 116
Figure 6-10 Contact resistance vs. number of operation cycles for cold test..................... 117
9
Figure 6-11 Picture of the device under testing using four-probe method........................
119
Figure 6-12 SEM picture of the contact area after the cycling test ................
121
Figure 6-13 Zoom-in SEM picture of the contact area after cycling test .........................
122
10
List of Tables
Table 1-1 Comparison of MEMS switch to traditional switches ....................................
19
Table 1-2 Performance review of MEMS switches developed by industry .....................
20
Table 1-3 Performances review of MEMS Switches developed by academia..................21
Table 1-4 Comparison of metal contacting and capacitive coupling..............................22
Table 2-1 Switch isolation for given geometry.............................................................
36
Table 3-1 Au Material properties and asperity size.......................................................
50
Table 3-2 Plastic index and surface topography...........................................................
58
Table 4-1 Actuator performance comparison...............................................................
65
Table 4-2 Actuation efficiency of micro actuators ........................................................
67
Table 4-3 Driving voltage or current comparison of different actuators for MEMS switch. 67
Table 4-4 Bow actuator size and performances ............................................................
72
Table 4-5 Modal analysis of the bow actuator ...............................................................
73
Table 4-6 Actuators performances summary...............................................................73
Table 4-7 Sw itch design m atrix ...................................................................................
80
Table 4-8 Switch Beam thickness ................................................................................
81
Table 6-1 Resistance measurements on dummy design B15D .........................................
111
Table 6-2 Resistance measurement on dummy design B25D ..........................................
111
11
Table 6-3 D riving voltage vs. contact resistance .............................................................
112
Table 6-4 Contact force Vs. Contact Resistance.............................................................
113
Table 6-5 Test matrix for long cycle contact resistance measurement..............................
115
Table 6-6 Hot contact resistance measurement (sample 1-15-8# at 12 V driving voltage) 115
Table 6-7 Hot contact resistance measurement (Sample 2-36-3 # at 9 V driving voltage).. 116
Table 6-8 Contact resistance measurement for cold test ............................................
12
117
Nomenclature
a
Contact radius
A,
Area of the contact surface
Contact radius at plastic deformation
b
Switch beam width
C11E
Stiffness under constant electric field
C
Off- state capacity of the switch
C,t
Capacity of PZT actuator
d
Gap between two switch contacts/distance between to contacts
Piezoelectric coefficient in 1-3 direction
D, D3
Electric displacement, electric displacement in 3 direction
E
Young's modulus of the switch beam material
Young's modulus of contact materails 1 and 2
EL, E3
Electric field and electric field in the 3 direction
e13
Piezoelctric coefficient in 1-3 direction
13
F
Force on the contact surface from the actuator
Force normal to the contact surface
FnT
Total contact force
Force paralell to the contact surface
X and y components of Fn
FS
Force on the actuator from the switch
Ge
Contact conductance
h
Switch structure thickness
H
Brinell hardness
I
Current
Stiffness matrix of the switch beam and actuator
KpzT
Stiffness of the PZT actuator
I
Length of the switch beam
Al,, Al
Deformation of the switch beam in x and y direction due to sliding
Moment on the switch beam
Mass matrix of the structure and actuator
n
Normal direction
N
Total number of asperties
P
Contact presure
14
Pc
Yield stress
PP01
Poling of the PZT
Q
Charge on the surface
q
Change generated by PZT actuator
Radius of the asperity
Contact resistance/constriction resistance
S21
SS,
S parameter of transmissiom coefficient from port 1 to port 2
Strain, strain in 1 direction
Compliance under constant electric field
SD
Compliance at open circuit
T, T,
Stress , stress in 1 direction
V
Voltage
w
Width of the microstrip (electrode width on the switch beam)
x
Sliding motion between two contact surfaces
zo
Characteristic impedance
indentation
Critical indentation when plastic deformation occurs
Plastic indentation
8s
Dielectric constanct at constant strain
15
ST
Dielectric constanct at constant stress
(z)
Asaperity height distribution fuction
(ppi, <p,
Potential and potential on surface A, and surface A,
Friction cofficient
0
Angle of the contact surface
Electrio-mechanical coupling term
p0
Resistivity
(-
Standard deviation of the asperity heights
Signal frequency
to,
Plastic index
Electric mode shape
Mechanical mode shape
16
1. Introduction
1.1
Background and Motivation
Radio frequency (RF) MEMS switches are devices that provide a short circuit or
open circuit in the RF transmission line by micro-mechanical movement. RF switches
usually operate at radio frequency to millimeter wavelength (frequencies of 0.1 to 100 GHz)
[1]. They have wide applications from satellite communication to wireless sensors. In the
past, semiconductor switches such as GaAs or InP p-i-n diodes as well as FET (Field Effect
Transistors) have been used to perform the switching function. In the last 15 years, the
performance of GaAs HEMT (high-electron mobility transistors) devices and silicon CMOS
(complementary metal-oxide-semiconductors) have had tremendous advances, but the
performance of the semiconductor switches has no significant improvements until the
emergence of the MEMS (Microelectromechanical
system) technology. The cut-off
frequency, which is an indication of the low-loss performances of the switch, is 1-2 THz for
GaAs p-i-n diodes and 0.2-0.5 TEIz for FET switches respectively, while this frequencies for
MEMS switches is 30 to80 THz, which are much higher that of semiconductor switches.
The isolation of MEMS switches could be as low as -40 dB at 40 GHz, while that of the
semiconductor switches is only about -5 dB [1].
17
Because of their broad range of applications, hybrid technology and the huge market
potential, RF MEMS switches have attracted a great deal of research interests. Different
kinds of MEMS switches have been developed by a number of companies and universities
[2]-[8]. Most of the current RF MEMS switches are designed with electrostatic actuators [3],
although there are some designs using thermal [4] or magnetic [5] actuators. One of the
major problems of MEMS switch is the low reliability or short lifecycle. The typical life cycle
requirement for a RF switch for radar systems and other instrumentation systems is over 40
to 100 billion cycles [1]. The best practice of the RF MEMS switch reported can achieve
about 10 billion life cycles. There is a big gap between the current technology and the market
requirement. To address these issues, the functional requirements of switches, which reflect
customers' demands, have to be investigated. The failure mechanisms of MEMS switches
and the contact mechanics and physics of the switching members have to be taken into
account. The primary goal of this research is to fully investigate the contact mechanics and
failure modes of MEMS switches, design and fabricate a low contact resistance and long
lifecycle RF MEMS switch.
1.2
Objectives
The objectives of this research are three-fold:
1) To investigate the functional requirements of MEMS switches, determine the key
factors that influence the major switch performance parameters, in order to design and build
a MEMS switch emphasizing the uniqueness of micro fabrication rather than just
miniaturizing a bulk conventional product.
2) To understand, model and analyze the mechanical behavior, contact resistance of
such a micro contact systems. In addition, the effect of adhesion and micro wielding
18
between the two contact surfaces are also studied to further investigate the failure modes of
MEMS switches.
3) To verify experimentally the model and analysis through the design, fabrication
and testing of a new MEMS switch. The major performance target is to achieve a low
contact resistance of less than 0.1 Q (about 0.5 0 is the current best practice) over its entire
life cycle.
The test and analysis results should provide guidelines for further switch
performance improvements in order to build a cost effective, robust and highly reliable
MEMS switch with a lifetime of more than 100 billion cycles.
1.3
1.3.1
Literature review
General switch performances
Petersen reported the first MEMS switch in 1979 [9]. Since then, a large number of
RF MEMS switches have been developed. Gabriel M. Rebeiz summarized the performance
of MEMS RF switches and those of traditional RF switches, which are compared in Table
1-1 [1].
Table 1-1 Comparison of MEMS switch to traditional switches
Voltage (V)
Power consluription
Switching time
Rs Q
Isolation(1-10 GHz)
Isolation (10-40
GHz)
Loss (1-100 GHZ)
RFMEMS
20-80
0.05-0.1 mW
1-300 ps
± 3-5
5-100 mW
1-100 ns
FET
3-5
0.05-0. 1mW
1-100 ns
0.5-2
-40~ -60 dB
-30-40 dB
2-4
-40--20 dB
-20 ~-5 dB
4-6
-30--10 dB
0 -- 5 dB
0.05-0.2 dB
0.3-1.2 dB
0.4-2.5 dB
19
PIN
From Table 1-1 we can see that the advantages of MEMS RF switches are the low
power consumption, high isolation and low insertion loss. Besides, MEMS switches are very
linear devices and require very low intermodulation. The disadvantages are the longer
switching time and higher driving voltages. The latter will be addressed further since it is
related to the actuation mechanism.
In Table 1-2 and Table 1-3, the performance of some of the recently developed
MEMS switches from both the industry and academia is compared [10].
Table 1-2 Performance review of MEMS switches developed by industry
cenhza
A
voage
CWmq,
es
Suik&
fte
Rentuie
Idagen
Less
IeMuIfesn
a
ydes
V
mW
ps
sN
A
4 G~r,
a
zakedenA
40-5e
0*
2-4
100
1-2
-44
Anabgmke
Baesb.ck
70-30
0
3-6
100
OaMn
Ueduk&
17-20
0
300
meteru
h
1000
> 6x10 10
>6x1013
1-2
-40
-0.15
>1x10'
-30
-0.25
>x10'
2000CreMa
n
SumwUg
nI.
DUIaR "
ST-jmaddia
nhual
5
200
10,000
3000
mdrsms
ed i
60
0
8-10
50-150
0.0-2
-50
-0.1
>1x10'
5-s
0
100
50-100
0.5-1
-35
-0.15
>5x10
2e-3
0
30-40
50-100
1-2
-44
-0.15
v1x10'
edkedk&
73
0
el
50-150
1-2
-40
-0.15
>lx10
nmr
5
0
300
100-200
-44
-0.5
>1x108
-50
-0.2
>1x108
xerU
e&
zedresds
dedredus
cretoa
maadeswK
5
0
500
50-150
NEC
Redkvsb
30-50
0
30-40
50-100
20
Table 1-3 Performances review of MEMS Switches developed by academia
University
Actuation
voltage
Power
Consumptian
Switch
time
Contact
force
Resistanc
e
Isolatio
n
lass
Proven life
time
V
mW
pS
pN
0
4 GHz,
dB
dB
cycles
Northeastr
Eletrostatic
60-80
0*
2-3
1-1.5
-40
-0.15
Michigan
Eletrostatic
30-40
0
26-30
0.5-1
-35
-0.15
Berkeley
Electrostatic
30-110
0
0.2-0.4
-37
-0.2
UCDavis
Thermal
6-8
30-40
10003000
-36
-0.5
Fraunhofer
Germany
Electrostatic
20-260
0
5-30
1-3
Beijing U.
Electrostatic
43-135
0
50
1
U. Illinois
Electrostatic
0
1-1.5
x107
-25
-0.1
It can be seen that the majority of the switches utilize electrostatic actuators that
require high driving voltages from 20 volt up to 260 volt. The typical ones need driving
voltages of 60-80 volts. The high voltage requires expensive dc-dc converter, which prevents
low cost RF MEMS switch eventually. The contact resistances of these switches range from
0.5 Q to 2 Q, while the life cycles can reach as high as 1010, although in several cases no
lifetime data is reported. In addition, most of MEMS switches cannot handle more than 2050 mW powers. Furthermore, they also need to be packaged in inert gas environment and in
very low humidity, which results in very high cost.
1.3.2
MEMS Switch classification
MEMS switches can be classified according to the actuation methods. These
included electrostatic [11], thermal-electric [12], electromagnetic [13-16], piezoelectric
[17,18]. Electrostatic actuators need higher driving voltages, while thermal-electric and
electromagnetic actuators require higher power consumption. This will be discussed in detail
in section 4.1.
21
According to the switch configurations, MEMS switches can be classified as vertical
contact [8] and lateral contact [19, 20, 21]. The dynamic behavior of lateral contact switches
is superior to many vertical contact switches. For example, the switch contact can be made
through a linear controllable motion provided by the thermal actuator as reported in [19],
which avoid pull-in (unstable condition) of the switch member. Pull-in is a phenomenon
typical for electrostatic actuators. However, the contact resistances of the lateral contact
switches are much higher due to the higher roughness on etched sidewall surfaces and the
contact materials for the existing switches. Lateral contact switch fabricated by bulk micromachining method [20,21] may also need wafer bonding which makes the process more
complex. To take advantage of the lateral contact switch, a new fabrication method has to be
developed to make smoother sidewalls for contact.
According to the switch contact methods, there are two types of switches: direct
metal contacting [8] and capacitive coupling [22]. Performances of switches with the two
methods are compared in Table 1-4 [10].
Table 1-4 Comparison of metal contacting and capacitive coupling
Power Handlig mW
Frequency range
GHz
Metal-metal
contact
0.5 - 5 available
10-100 low reliability
DC-60 GHz
Capacitive
contact
30-300
> 10 GHz
It can be seen that metal-metal contact switches provide large application frequency
ranges, however, capacitive contact switches are relatively more successful than metal-metal
22
contact switches. The major reasons are that metal-metal contact switches have low power
handling capability and their reliability is also relatively low. Contact resistance of a switch
controls its power-handling capacity, while the lack of an effective way to maintain a low
contact resistance reduces its reliability.
1.3.3
Contact mechanics and switch failure modes
Several types of contact mechanics models have been proposed. The Greenwood-
Williamson contact model is one of the basic "asperity-based-model" [23]. The model is
valid for an elastic contact. Chang et al [24] expanded this model by introducing plastic
deformation, so that the model can operate at both low and high contact force situation.
In addition, Negus-Yovanovich [25] has proposed a thermal contact model, while
Leung and Hyman [26] used numerical method called " thermal network analysis".
J. Tringe,
et al. [27] studies the contact problem of electroplated gold thoroughly.
They measured gold contact resistance of 100 mQ with a contact force of 100 tN. They
found that as a contact metal, gold is relatively inert, forming only modest contamination
layers, and there is no insulating oxide that must be broken with a large force in order to
obtain the required contact resistance. They observed that arcing could occur, causing
sufficient energy transfer to the contact surfaces to destroy the switch.
D. Hyman et al. [26] studied the contact physics of electroplated gold probe tip on
sputtered pure gold substrate. They found that heat dissipation is the critical design
parameter for maintaining a low contact resistance, a high power handling capability, and a
minimum of surface adhesion in a metallic contact switch. This limiting factor can be
addressed through the design of a proper heat sink and thermal modeling throughout switch
development. D. Hyman suggested that the switch contact electrodes should be fabricated of
23
films, which also have high thermal conductivities, with a minimum thermal path to a sink
substrate.
Y. Wang, et al. [19] developed low-voltage lateral-contact micro-relays which is
surface micro-machined in 2002. The thermal actuator has a length of 200 tm, width and
thickness of 2 gm, center offset of 10 gm. The maximum displacement calculated is 5.4 yxm.
The sidewall of the switch is sputtered gold with a thickness of 0.5 ym. It has a skin depth of
0.71 ytm at 12 GHz and 0.45 ym at 30 GHz. They believe sputtered gold has a higher
hardness that gives less surface damage for metallic micro-contacts. The structure of the
micro-relay is polycrystalline silicon. The actuator part and the contact head is connected
through a 0.6 tm low stress silicon nitride serving also as electric and thermal isolation. They
found that contact heads with round and square shapes showed better reliability than the
angled-shaped contact head. The failure modes they observed were due to metal contact
welding. Besides, surface roughness on the sidewall results in bad contact and a high
adherence force of gold also plays a role in contact degradation. They suggested that a gold
and nickel alloy be considered as the contact metal due to its small adherence force and
relatively low resistance.
1.3.4
Summary
Most MEMS RF switch designs utilize electrostatic actuators that require high
operation voltage and packaging in inert gas environment resulting in high cost. The switch
functional requirements are not fully investigated. Lateral metal-metal contact switches have
shown to have promising characteristics compared to other configurations, especially their
better dynamic behavior and their large application frequency range. However, the reliability
of this type of switches is low and the contact resistance of this type of switch is usually high
24
because their contact surfaces (sidewall) are usually etched, so that they have high surface
roughness.
1.4
Approach
Beginning with an extensive literature review to summarize the current status of
MEMS switch, the present research focuses on the conceptualization of novel switch
configuration and contact method to satisfy fully the requirements for an RF switch. Failure
analysis of currently available MEMS switches will be carried out to better understand the
switch function and also provide feedback for satisfying the functional requirements of RF
switches. There are several parameters which have been utilized to define the performance
of an RF switch, such as cut-off frequency, isolation, insertion loss, power carrying capacity,
switching speed, contact resistance and reliability etc. However, not all of these parameters
are independent. Contact resistance is one of the dominant factors. A low contact resistance
has positive influence on most of these operating parameters. These parameters will be
investigated to determine the major functional requirements for MEMS switches in order to
generate a decoupled and optimized design.
Low contact resistance is the primary requirement for high performance RF MEMS
switches. To achieve a low contact resistance, a higher contact force is required to generate a
sufficiently large real contact area through elastic-plastic deformation of the asperities
between the surfaces. Contact mechanics and contact resistance will be modeled to provide
guidelines for switch and actuator design.
The ability to maintain the low contact resistance directly influences the life cycles of
the switches. Switch design will focus on how to maintain the low contact resistance. Self-
25
cleaning switch configurations will be developed to satisfy this requirement. In the mean
time, the configurations should not dramatically increase the complexity for fabrication to
reduce the cost [28].
Different actuators will be compared with each other according to their
performance. An actuator for the switch will be selected and designed based on its
performance (displacement, force, driving voltage, controllability). Optimization of the
actuator will be conducted to improve the switch performance.
Finally the RF switch will be fabricated and tested. The contact resistance and long
term performance of the switch will be measured, analyzed and compared with the
theoretical prediction. Further suggestion and recommendation will be given for the
commercialization of the switch.
1.5
Organization of the document
This document is organized in the same way as the problem is approached.
Chapter 2 presents the analysis of the failure modes of currently available RF MEMS
switches, and also investigates the functional requirements of these types of switches. The
main switch performances will be examined and the major functional requirements of a
MEMS switch will be determined: contact resistance and isolation. These major functional
requirements are further investigated and decoupled into a set of independent functional
requirements. Each of the functional requirements is satisfied by an independent design
parameter. This leads to the novel design of the switch, which is a lateral contact series
switch and is capable of self-cleaning, self-alignment and maintaining a low contact
resistance over a long life cycle.
26
Chapter 3 presents the modeling of contact mechanics and contact resistance. A
higher contact force is required to generate large enough real contact area through elasticplastic deformation of the asperities on the contact surfaces. However, if the contact force is
too large, the frictional force will also be very large resulting in a high wear rate of the
contact materials. This obviously will reduce the life cycles of the switches. The modeling of
the contact resistance consists of more steps: surface characterization, real contact area
determination using Hertz 's law for elastic contact, and the contact resistance determination
using Holm's equation. For larger force, the deformation of the asperity is probably in plastic
region and is treated accordingly. The modeling provides the force and displacement
requirements for the low contact resistance requirements.
Chapter 4 presents the selection of the actuation methods. Based on the literature
review, a PZT actuator has been selected because of its high force and low driving voltage.
However, the displacement from piezoelectric actuators is relatively small. An amplification
mechanism is required to obtain the required displacement. Finite element analysis is applied
to verify and optimize the actuator design. After that, an actuator-switch coupled analysis is
conducted to determine the appropriate switch geometry. Chapter 5 discusses the key
fabrication issues of this MEMS switch and the corresponding fabrication results. Process
verification tests have been done to determine the method to deposit Au on the sidewall of
the structure for metal-metal contacts. Electroplating of Au is chosen to deposit the metal
film on the contact areas over E-beam evaporated Au. Pt by e-beam evaporation is used as
a seed layer. To obtain high quality contact metal by electroplating, the mold for
electroplating is critical. The mold should have near vertical sidewall and should be removed
easily after electroplating. Spin-on Su-8 has been chosen for the mold and also the switch
structure materials for its unique vertical sidewall and compatibility with the actuator. PZT
27
actuator is deposited using the sol-gel method. The final fabrication process utilizes five
masks. Special considerations have been given to ensure the process compatibility with
surface micro machining techniques, such as photolithography, lift-off, and XeF2 dry release
etc.
Chapter 6 presents the principle of the measurements, the design of the test set-up,
and the experiments conducted. The surface quality of the electroplated contact areas are
studied under SEM and compared with that of e-beam evaporated surface. The former is far
smoother than the latter. Contact-force and contact-resistance relationships are determined
and the results correlated with the theoretical prediction. Both dynamic tests (power on
when cycling) and static tests (power off when cycling) are conducted. The results have
demonstrated the self-cleaning effect of the modulated contact surface design.
Chapter 7 summarizes and concludes the research. Compared with the existing
MEMS switches, the uniqueness of the device lies in the self-alignment of the contact
surfaces, self-cleaning of the particles generated from asperity fracture and plastic
deformation, and the anchoring method of the metal contact to the micro switch structure.
By introducing a modulated surface to modify the tribological behavior of the contact
surfaces, low contact resistance of 0.1 Q can be maintained for billions of operating cycles
without sacrificing the benefits of MEMS switches such as low insertion loss, near zero
power consumption, and very high isolation.
28
2. RF MEMS Switch Design
2.1
Switch failure mode analysis
Failure analysis of currently available MEMS switches provides a deep understanding
of the switch functional requirements and also feedback for satisfying the functional
requirements. The major failure modes of MEMS switches are damage, pitting and surface
hardening of the contact area [26]. These are caused by the asperity fracture, plastic
deformation, and repeated impact from the opposite switching members, which gradually
reduces the real contact area and increases the contact resistance.
Another failure mode is micro welding between switching members. Micro welding,
which causes the switch fail to open, is due to Joule heating. The increase in contact
resistance results in the increase of Joule heating, which increases the local temperature, then
further increases contact resistance and causes more plastic deformation and micro welding.
In order to minimize the two failure modes, a mechanism to maintain low contact resistance
has to be developed.
Other failure modes are mostly decoupled from the system and can be easily
avoided. For example, adding a protecting circuit can minimize arcing, while packaging of
the device in inert gas environment can almost eliminate the deposition of organics and
contaminants on the contact area [29].
29
2.2
Functional design of the switch system
The switch performance is investigated to determine the real functional
requirements of an RF switch. There are several parameters which have been used to define
the performance of an RF switch, such as cut-off frequency, isolation, insertion loss, power
carrying capacity, switching speed, contact resistance and reliability etc. However, not all of
these parameters are independent. Contact resistance is one of the dominant factors. A low
contact resistance has a positive influence on most of these parameters. Another
independent parameter is the isolation that can be determined by the separation of the two
switching members. The functional requirements of a new RF MEMS switch can be
summarized as how to provide and maintain the low contact resistance and high isolation
over a high number of operating cycles.
2.2.1
Functional requirements:
" FR1: Provide low resistivity at contact
e FR2: Remove particles periodically between contact surfaces
" FR3: Provide low off-state capacitance
Each of the functional requirements is to be satisfied by an appropriate design
parameter or solution. The new design parameters are generated to meet individual
functional requirement it's associated with, but not to couple to other functional
requirements.
2.2.2
Design parameters:
" DP 1: Maximize true contact area by high force piezoelectric actuation
" DP2: Micro-grooved contact surface with limited sliding motion (self-cleaning)
30
9
2.3
2.3.1
DP3: Piezoelectric actuation with amplified strokes
Switch concept and design
The general concept
The switch design is shown in Figure 2-1. It is a lateral contact series switch that
consists of fixed switching members, movable switching members and the position stopper
to prevent excessive contact forces. Each switching member consists of two parallel beams
with angled contact surfaces at the tips that are floating and induce small scale sliding
between fixed and movable contacts. Gold or other noble metals are to be deposited on the
sidewall or the angled contact surfaces as well as the transmission line along the beams and
pads. When the movable members meet the fixed members under a linear controllable
motion, the physical contacts between the two pairs of angled surfaces will create a short
circuit in the transmission line from one of the fixed members to the other. When a certain
amount of separation (or gap) is maintained between the two pairs of angled surfaces, there
will be an open circuit between the two fixed members.
31
Contac
. .F.
urfac e
ixe d
Undulated
surface
n
sto
-- 25 pm
MovablI6
Figure 2-1 Switch concept
2.3.2
The self-alignment of the contact surfaces
Several novel ideas are devised for the new design. First of all, geometric or position
mismatch of the contact surfaces from device operation or fabrication will reduce the
normal contact area and even prevent a real contact. The two pairs of identical beams shown
in Figure 2-1 will deform equally in magnitude but opposite in directions. This will ensure a
good contact between the two pairs of surfaces during switch operation. A slight torsional
movement of the two pairs of beams can also compensate for any the contact surface
sidewall slope resulting from the fabrication process.
2.3.3
The self-cleaning of the damaged surface
The debris or loose particles generated on the contact area during operations are to
be cleaned through micro sliding motion between the two surfaces, and then trapped in the
micro grooves fabricated on one of the surfaces. The concept of undulation of low friction
surface was first developed by Suh [30,31] and this research adapts the micro-scale version
32
from it. Low contact resistance can thus be maintained throughout the long life cycles of the
switch.
2.3.4
Attaching of the gold contacts to the structure
Noble metals or alloys have weak adhesion to the sidewall of the switch structure,
such as Si or SU-8 (an epoxy). The connecting parts of the switch have been designed as a
series of dovetails. The contact metal is filled into these dovetail trenches, and thus is
embedded and anchored in the switch structures. Mechanically anchoring the contact metal
into the structure ensures the two have secure physical and mechanical connection as shown
in Figure 2-2.
Sftructue
Contact mnetals
4 pmrr
Figure 2-2 Mechanical anchoring of the contacts to the switch
2.3.5
Contact force adjustment
To achieve a low contact resistance, a higher contact force is required to generate a
sufficiently large real contact area through elastic-plastic deformation of the asperities
between the surfaces. However, if the contact force is too large, the frictional force will also
be very large resulting in a high wear rate of the contact materials. This obviously will reduce
33
the life cycle of the switches. The angle between the contact surfaces and the switch beams
provides the adjustment of the contact forces, which ensures the capability to optimize the
switch performance.
2.4
Switch materials selection
There are several materials that could be used as the structural materials both for the
switches and the actuators. The most commonly used material is Si since it is available as the
substrate materials and also its fabrication techniques are mature. However, we have chosen
SU-8 as the switch and actuator structural material. There are few reasons. First of all, SU-8
is a negative, epoxy-type, near-UV photoresist (365 nm) [32]. It can be patterned directly by
photolithography and the thickness of the structures can be as high as 2 mm with an aspect
ratio of up to 25. This will dramatically simplify the fabrication process avoiding deep
reaction ion etch and chemical-mechanical polishing (CMP) for Si structures. Besides, it has
been demonstrated that the sidewall of the SU-8 structure can be nearly vertical, which is
crucial for forming the switch contact surfaces. In addition, SU-8 is an epoxy resin with a
Young's modulus of about 4.4 GPa and a Poisson's ratio of about 0.22. Its low stiffness
allows the switch beams to deform or bend easier because this bending is required by the
self-cleaning mechanism.
This is also advantageous for the strain amplification PZT
actuator as can be seen later.
2.5
2.5.1
Switch modeling
Equivalent model
The proposed MEMS switch is a lateral contact series switch. For modelling
purpose, it is simplified as a configuration shown in Figure 2-3.
34
metal
Actuator
d
Substrae
Figure 2-3 MEMS switch simplified configuration
This lateral switch is equivalent to a capacitor at off state and a resistor at on state [1]
as is shown in Figure 2-4.
zo
Cs
zo
Off State:
zo
On State:
zo
Figure 2-4 Switch equivalent model
2.5.2
Switch isolation
Isolation is defined as the ratio of the power delivered to the load for an ideal switch
in the "ON" state to the actual power delivered to the load when the switch is in the "OFF"
state [33].
Isolation can be found from the transmission coefficient parameter, S21, as following
=
4w 2 CSz 2
(2-1)
Alternatively, isolation can also be expressed in decibel form
35
1OLog(S ) 2 = 20Log,1 2>CZ 0 |
(
(2-2)
For a given set of switch geometry and signal frequency, the isolation of the switch can be
computed as listed in Table 2-1, where the impedance is assumed to be 50 0.
Table 2-1 Switch isolation for given geometry
Thickness h
AVid th b pm
Gap
d
pm
pm
qe .ncy
Fr.
Frequency
GHz
Isolation
dB
4
-67
10
10
10
10
3
4
-62
10
10
5
40
-47
10
10
3
40
-43
It is shown from the table that the isolation is comparable to the existing MEMS
switches even with a small gap of 3 pm.
2.5.3
Switch insertion loss
The insertion loss is defined as the ratio of the power delivered to the load in the
"ON" state of the ideal switch to the actual power delivered by the practical switch, in the
ON state [33]. An idea switch is assumed to have no power loss.
Insertion loss can be determined from the S parameters:
InsertionLoss = -20Log(l
36
-
c
2ZO
Assuming the impedance is again 50 Q, the insertion loss vs. contact resistance is
shown in Figure 2-5.
0.8 0.7
0.6
0.
--
03
0
S0.20.10
1
2
3
4
5
6
7
8
Contact resistance ohm
Figure 2-5 Insertion loss vs. contact resistance
For a contact resistance of 0.1
2.5.4
, the insertion loss is only 0.01 dB.
Micro strip transmission line design
A micro strip transmission line [33] as shown in Figure 2-6 below has been used in
most RF MEMS design due to its simplicity of fabrication. The critical parameters of a micro
strip are the ratio of metal layer width to dielectric layer thickness (w/h). The candidate
material for the switch structure is SU-8, which has been explained in 2.4. The dielectric
constant of SU-8 is around 4.8 and the impedance of the transmission line can be chosen
from 50 to 100 Q depending on the application. From Figure 2-7 [33], it can be determined
that w/h should be around 1-2.5. In this research, a range of switch beam widths (w) and
heights (h) has been chosen and the ratio of w/h varied from 1- 2.5.
37
Figure 2-6 Micro-strip transmission line
1000
500
400
300
200
100
4)
Q
C
cc
E
50
40
30
20
.2
10
5
4
3
2
ItI
-7
6l
I
I 1
C4J Ci Id Ui
66660
-
N
M
lt
L
0
IN
0
000
M I-t L
w/h
Figure 2-7 Micro-strip impedance vs. the ratio of w/h
38
0
0
2.6
Summary
A novel MEMS switch was conceptualized based on switch performance analysis.
Several novel ideas are devised for the new switch design. First of all, compliant supports of
the contact surfaces deform accordingly to compensate for the geometric or position
mismatch of the two contact surfaces, resulting from either device operation or fabrication.
Second, the debris from damages generated on the contact area during operation are to be
cleaned through micro sliding motion between the two surfaces, and then trapped in the
micro grooves fabricated on one of the surfaces. Low contact resistance is thus maintained
throughout the long life cycles of the switch. Thirdly, noble contact metals and alloys, which
are to be used as contact materials for their low resistivity, have weak adhesion to the
sidewall. Anchoring the contact metal into the switch structure mechanically solves this
problem, so that the two have secure mechanical connection. The equivalent model of the
switch is established and the insertion loss and signal isolation loss has been predicted to
provide guideline for the design of the switch.
39
3. Contact Mechanics and Contact
Resistance
In this research, the primary goal is not to develop a better contact model, but rather use
the existing models to provide a guideline for the selection and design of the actuator. There
are several models for the mechanical contact behaviour of rough surfaces. Greenwood and
Williamson proposed the basic elastic contact model in 1958 [23].
The modeling of the
contact resistance consists of a few more steps. First the contact surface is characterized to
determine the distribution of asperity diameter and height, then, a single asperity contact
analysis is made to find the relation between contact force and the radius of the contact area
for either elastic or plastic contact. With the radius of contact, we can find the constriction
resistance for the single asperity. Finally, the total contact resistance is found by integrating
all the contact asperities over the whole area using Greenwood and Williamson's model.
3.1
Contact surface characterization
The contact resistance of two surfaces is closely related to the mechanical behaviour of the
two contact surfaces.
40
Ii
--
hi
If we zoom in any surface of a real material, we find that the surface consists of
asperities. An example is the sidewall surface of e-beam evaporated gold film by SEM as
shown in Figure 3-1.
/84nm
10nm
3.7
7G
Acc V Spot Magn
10 0 kV 3_0 80000x
Det WD
GSE 8.0
nm
200 nmn
4.1 Tourr
Figure 3-1 Sidewall surface of e-beam evaporated Gold
In general, we can assume that contact between a plane and a normally flat surface
covered with a large number of asperities; the asperities are all spherical and the heights vary
randomly. An example surface is presented schematically in Figure 3-2.
41
Z
d
\)
Reference
Figure 3-2 A simple contact surface
If the two surfaces come together until their reference planes are separated by a
distance d. Then the probability of making contact at any asperity of height z is
# (z)dz
prob(z > d)=
(3-1)
d
where * (z) is a probability function.
3.2
3.2.1
Contact mechanics
Hertz contact
To study the contact behaviour of the two surfaces, we can start with a simple case,
the contact of two spherical bodies as shown in Figure 3-3. Hertz first solved this problem
in the elastic regime [34].
42
m~
m.-.
U
2W -~
-
-
T~
W~~EL~
ZI
E1.,oD
R1
L2
Figure 3-3 Single asperity elastic contact
From the theory of elasticity, the vertical deformation can be expressed as
a = (ki + k)go
7 2a
(3-2)
2
The contact radius, a, is given by
a= (k +k 2 ) K
(3-3)
4p9
v2l
-
where
1
1 v
7E 2
R1 +R2
2RR 2
From force balance, we have
go 2
2a3
a 3
= F --> go =
"2ra
3F~
"2
43
(3-4)
Substituting equation (3-4) into equation (3-3) and simplifying, we have the normal contact
force
431
1
1
F, =-a3(-+-3
R R 2 ;r(k+ k 2 )
For
(3-5)
-> 0X, the contact radius, indentation and contact force can be related by the
R2
following equations
I I
3
4
F '=-ERI a 2
(3-6)
3
1
1-v
E
El
2
1
E2
Through these equations, contact radius a and the contact force Fn is related to each
other by the indentation a if the deformation is in elastic regime. They can be use to
determine the contact radius from the force applied.
3.2.2
Plastic contact
Under higher contact forces, plastic deformation will occur and the Hertz contact
solution is no longer valid. From the work of Tabor (1951), it can be shown that yield
occurs when the contact pressure
PC = 0.6 H
( 3-7)
where H is the Brinell hardness of the contact material.
Since the contact area is of prime interest while the actual shape of the deformed
asperity outside the contact is less important, W. R. Chang (1987) assumed that the volume
of the materials should be conserved after plastic deformation occurs as shown in Figure 3-4
[24].
44
c
ap
2a
Figure 3-4 Volume conservation after plastic deformation
From equation (3-6) and (3-7), it can be found that the critical indentation when
plastic deformation occurs is,
ac
0.3rH
(3-8)
2R
E
Based on the assumption, the control volume before and after plastic deformation is
constant. The diameter of the contact area after plastic deformation occurs can be expressed
as
a
(3-9)
(39)
2=RaC
Where C is related to the plastic indentation and can be expressed as
-- a-,
a
(3-10)
a=aC+a,
By substituting equation (3-10) into (3-9), the contact radius after plastic deformation
can be determined as
45
a
3.3
(3-11)
Ria (2 -- a
a
Constriction resistance
R. Holm (1967) [29] described the constriction resistance due to the geometry
change in a conductor. Assuming two arbitrary surfaces A1 and Ac with potential <p and <p
as shown in Figure 3-5.
A1
(Pi
n
Ac
(PC
Figure 3-5 Constriction resistance between surfaces Al and Ac
From Ohm's law, the constriction resistance is simply given by
- |P
where Q
-(| _ Q
(3-12)
I
IC
is the charge on the surface Ac and I is current through it.
46
1=::- dA
I
=
8P dA
a
Substituting in (3-12), we have
RC =
4xrC
Assuming the arbitrary Ac is circular with radius a, then
RC =
(3-13)
2a
This equation relates the contact radius with the constriction resistance. With all these
relations, we are able to determine the overall contact resistance.
3.4
3.4.1
Overall contact resistance
Elastic Contact
If the contact pressure P on an asperity satisfies
P < Pc = 0.6H,
The deformation of the contact material is in the elastic region.
If we assume the total asperities number is N, then the expected number of contacts
can be estimated as
n =N
(3-14)
$(z)dz
Since a=z-d, the contact area
(3-15)
Al= rzaa
47
The mean contact area is
(3-16)
fra(z - d)#(z)dz
The total expected area of contact is given by
(3-17)
A = irNR, J(z - d)#(z)dz
d
The total expected load is then
Fr
=
3NER2 f(z -
d) 2
(3-18)
#(z)dz
And the total conductance is
GC=
2NR12 -
-f(z
P
-d) 2
(3-19)
0(Z)dZ
d
This is the Greenwood and William model [23].
3.4.2
Plastic contact
If the contact pressure P on an asperity satisfies
P > Pc = 0.6H,
The deformation of the asperity subjected to such a high force will experience plastic
deformation, while the deformation of the other asperities might still be in elastic regime.
The critical indentation ac associated with this critical pressure is expressed in Equation (38). The total expected load is
F
=3
I d+ac
NER1I f (z -d)
3
2
00
#(z)dz+0.6;rRNH
J[2(z -d)-a,]#(z)dz
d+a,
48
(3-20)
The total conductance is
GC = 2NR2
df ,
V-
(z -d) 2
2NR-
#b(z)dz±
+
[2(z - d) -a ] 2 #(z)dz
1Jd
(3-21)
d
From this conductance equation, we can find the total contact resistance.
3.5
Computing Examples
To provide the actuator design guideline, we assume the contact requirement for the
proposed MEMS switch is 0.1 Q. The surface profile of the contact surface is similar to that
described in section 3.1. We will look at the contact behavior of two cases: 1). Single
asperity. 2). Distributed asperities.
3.5.1
Contact resistance and force with a single asperity
Assuming the contact resistance requirement is
RC = 0.1 Q
From (3-13),
(3-22)
2RC
From (3-6),
a = RI2a 2
Equalizing the two equations, we have,
p
2RC
1
1
R 2ca 2
1
49
a = P
2RR
(3-23)
Substituting (2-23) into (2-3),
1 3
F =-ER
R1 a 2
2
3
(3-24)
_E Cp
6 RI
R
To evaluate the force requirement, we choose Au to the contact material and its material
properties and asperity size are listed in Table 3-1.
Table 3-1 Au Material properties and asperity size
Parameters
Asperity radius
m
1.1xl1077.2
Young's modules GPa
Resistivity
Q.m
2.2 x 10-8
0.42
Poisson's ratio
2
Brinell Hardness GPa
Substituting the parameters in Table 3-1 into (3-23) and (3-24), we can find the indentation
and contact force,
a
= 1.1
x10~7
M
And F, =7.6 x10 4 N
The critical indentation when plastic deformation occurs can be found from (3-8),
50
06H )2
ac= 2E
=1.78x1'
0
(3-25)
R
m
The critical indentation ac << a , plastic deformation will occur.
For plastic contact, the contact radius can be found from (3-11). Equalizing it to (3-22),
I
I
2 = R 2(2a
2R
-- aC )2
Then,
2
(2a -ac)=
(3-26)
2RR2
Since the maximum contact pressure at plastic deformation is 0.6 H, then the contact
force
F = a2 x 0.6H
= TR1 (2a -ac) x 0.6H
Substituting in (3-26),
0.6H ,2
"4 R 2
(3-27)
=4.56 x 10-5 N
The indentation can be found from (3-26),
1
2
a = -ac +
8
2
I
R 2R2
=5.5 x 10-8
m
51
(3-28)
The analysis above indicts that to achieve a contact resistance of 0.1 Q, assuming single
asperity contact, the contact force requirement is about 45.6 pN. For the assumed asperity
size and material properties, the force-contact resistance relations are shown in Figure 3-6.
It can be seen that the elastic-plastic model predicts a low contact resistance for a given
contact force. Figure 3-7 shows the influence of the asperity size on the contact forcecontact resistance relationships for elastic contact. For a given contact force, the elastic
model predicts that the contact resistance of a larger asperity is lower. In the case of plastic
contact, the elastic-plastic model shows that the asperity size has no influence.
Contact resistance vs contact force for single asperity
Elastic model
-
0.9--
Elastic-plastic model
0.8
-
E 0-7
O.
Q0.6
0.5
t0.4
0
00.3 0.2 0.1
0
0
0.5
1
Contact force N
2
1.5
x10
Figure 3-6 Contact resistance vs. contact force for single asperity
52
Contact resistance vs contact force for single asperity
1.1
0.9
E 0. 8
0
0.7
0.6
B0.5
0
L)0.4
0
0.5
1
Contact force N
1.5
2
x10
Figure 3-7 Influence of asperity size on the contact force-contact resistance relation
3.5.2
Contact resistance and force with distributed asperities
We assume that the contact surface consists of multiple asperities as was described in
section 3.1. All the asperities have the same diameter but their heights vary according to a
certain distribution function. Greenwood analyzed the contact resistance and contact force
of steel surface by assuming two asperity distribution functions: exponential and Gaussian
[23]. He obtained very close results using the two different distribution functions. The
reason was probably that the uppermost of the asperities of the contact surfaces dominant
the contact behavior, although the height distribution tends to be a Gaussian.
To simplify the analysis and obtain a close form solution, we assume the asperity
heights follow an exponential distribution,
53
#(z)
(3-29)
= -e
where o- is the standard deviation of the asperity heights.
From equation (3-21),
d+a"
2NR2
= 2NR 2
(Z - d) Se
d+a
2NR2(.
I
0dz+r2d+ac [2(z -d)--a
C]2e
dz
a
2
p
2NR 2 a 2
[2(z - d) -a]1#(z)dz
d
Assuming z = as and h
GC
-
(z - d)2 #(z)dz + f(
1
as
h)2 e -Sds +
VfJ2Is-(h+
{J+
f
{G,
a)j
2a
T S
(3-30)
+G 1}
P
where
ha,
Ge, =
GC=I
a (s - h)S esds
s -(h+
e-si
). e-jds
GC, and GUI can be further evaluated. For G, , assuming s - h = x,
54
a,1
GC
x 2 e-'dx
=e
(3-31)
=-e
a
2
9
e
+
dx
where
dx = 2V(1
fe-
TX
x
3x
5x
1.3
2.5
3.7
(3-32)
Equation (3-32) can be rewritten as
f
dx=2x$(-1)"
n=O
X
(3-33)
n!(2n +1)
Substituting (3-33) into (3-31) and simplifying,
GCI= e-'
2
(ac
o-
a +E(-1)"
-e
e_=± n!(2n +1)
(3-34)
Similarly, assuming s - (h + aC ) = y for Ge11 ,
2-(h +a(
Gcjj = e
=
2o- f
y
2
e-'dy
(3-35)
g 2a
ac {Jo
2
-}'dy -2a
2eYdy
where
y2e-'dy
=
(3-36)
2
and
55
2a
2
'dy
=
ac
e
2c-
2a
+
I)(-1)
(3-37)
n!(2n +
n
Substituting (3-36) and (3-37) into (3-35), we have
c
GCII-
ac )
-- 7r +±
2a
e
2
ac
(2a)
2
! 2a)
2a)
2a-
n!(2n±+1)j
=0
(3-38)
Substituting (3-34) and (3-38) into (3-30), we have
GC=2 N(R o-)2
2)
pe
rac"N
e
+2o
± a
a
2
-0)
a
n! (2n +1)
n1=0
2
-
a- )
1n-0
(3-39)
To evaluate the contact force, we assume the same exponential distribution function of (329), and also z = os and h =
d
--.
Substituting them into (3-20), we have
7
1
FT =
3NER1 a
2
3
3
2
2
(s - h) e-ds + 0.67rR1NH(20-)
[s - (h+
h'
a
where
56
-i)]e'ds (3-40)
+a(
(s -h)
3
e
S'ds
e
S
+
(3-44)
3
2
C
and
+ 2aC)]e-Sds
[s-(h±
20-
(3-45)
e
-
2aSubstituting (3-44) and (3-45) into (3-40), we have
33
F
2,=0H (R o)f
3
+ 1.2;rNH(RIo-)(
-
(h'+ ac)
ac
RI
3
+ - GC,
2
-
}+
(3-46)
a
-1Ie
where GC, and Ge,, are given by equation (3-34) and (3-38) respectively.
Greenwood [23] defined plastic index
2
=(aC
(3-47)
(-
Substituting equation (3-8) into (3-47),
2E
2
0.6xrH R)
(3-48)
From (3-48), we can see that plastic index depends on both the material properties and the
surface topography.
57
The contact resistance and contact force relation can be evaluated by varying the plastic
index, a function of (o- / R,), and (o-R,). The parameters assumed in the evaluation are listed
in Table 3-2. Much larger or smaller plastic indexes give unrealistic results. Since we are just
making relative comparison, the number of asperity was chosen to be 200 and the asperity
radius was 110 nm if not specified. There was no special reason for this choice.
Table 3-2 Plastic index and surface topography
The derived multi-asperity elastic-plastic contact model is evaluated by varying the
plastic index and the results are compared to the Greenwood and William model as shown
in Figure 3-8. It can be seen that for low plastic index, which means that contact tends to be
elastic, the multi-asperity elastic-plastic contact model gives closer prediction comparing with
that from GW model.
Figure 3-9 shows that comparison of the results from the single asperity plastic contact
model and the multi-asperity elastic-plastic contact model. The latter predicts low contact
58
resistance under given contact force. Since it is almost for sure that the first single asperity
will experience plastic deformation during contact for most cases, the real contact resistance
might fall in between the predicted results of the two models.
10
Coitact resistance vs contact force for distributed asperties
T=0.5 5
T=0.45
plastic index 045
plastic index 0.55
plastic index 0.65
plastic index 0.85
--- GWmodel
-
Eo
0
T=O.85
GW
is
10
10
10
C
10tc
Contact force N
10
10
Figure 3-8 Contact force-contact resistance for varying plastic index
59
Comparison of the distributed and single asperity model
101
distributed model, plastic index 0.55
single asperity model
-
E
0
10
0
010'
10
10
10
10
10
10
Contact force, N
Figure 3-9 Comparison of the contact resistance-force relations from the single asperity
model and the distributed asperity model
60
-
_____
-
-_~~~
4. Switch Actuation
4.1
4.1.1
Actuation method review
Force and displacement of micro actuators
There are many kinds of micro actuators, which have been used for different
applications. A few of these actuators [35-40] are shown from Figure 4-1 to Figure 4-4 and
their performances are listed below in Table 4-1.
Figure 4-1 Curved electrode electrostatic actuator
61
1W
-W
-_
_
_
_
_
_
--
-. c
The curved electrode electrostatic actuator shown in Figure 4-1 has two fixed curved
electrodes and one floating movable beam electrode. When voltage is applied to the
electrodes, the movable electrode will deform according to the shape of the curved
electrode, and therefore, relatively high force and large displacement can be obtained
compared to a parallel plate actuator.
Flexible Hinge
Piezoactuator
Glass
Figure 4-2 PZT micro gripper
The PZT micro gripper shown in Figure 4-2 utilizes the transverse mode of the PZT
actuator (dark area in the center) and amplifies its displacement. When voltage is applied to
PZT, it will shrink laterally, then the two movable arms will rotate along the flexible hinge as
shown by the arrows.
62
A&
W-
-~--~
W
-~-~
Figure 4-3 Comb drive actuator
Figure 4-3 shows a platform driven by four comb drives in x-y directions. Each comb
drive consists of many fingers that form capacitors in parallel. Force and displacement can
be generated due to the area change of the capacitors when voltage is applied. A comb drive
does not exhibit pull-in and has wide applications.
63
__________
W
L,
Bushing
TA
Substrate.Wns
o
Figure 4-4 Scratch
drive actuator
Figure 4-4 shows the operating principle of a scratch drive actuator. The actuator
consists of a plate with a bushing moving on a substrate. When voltage is applied, the plate
will pull-in first and the bushing will deform gradually and stretch forward. After the voltage
is switched off, the actuator has moved forward. The process can be repeated and large
displacements can be obtained.
64
-
AL
-
-~
ihS...
Table 4-1 Actuator performance companison
6
pm
P mN
Size, pm
Conib Diive
40
1.4 x 10-3
1000 (136 fingers)
Curved Electrode
120
3.5
600x30x50
Scratch Drive
150
70 X 10-3
100x75 each
NI-Ti SMA
60
1000
2000*1000*5
AI/Si bimiorplh
11
11x10-3
100 L 3.3 t
PZT Microgripper
250
20
(>1000 L)
The Table 4-1 shows a few very typical micro actuators that could be used for
MEMS switches. They are mainly electrostatic and piezoelectric actuators. From the
comparison, it's obvious that the displacement from these actuators is very large, but the
force that can be provided is relatively small. For the purpose of switch actuators, there is
special requirement on the actuator force, which is the key for a low contact resistance. It
seems that shape memory alloy actuator and the PZT actuator can provide relatively large
force.
4.1.2
Work densities and frequencies of micro actuators
Energy density and the cycling frequency or actuation frequency are the two other
important parameters for actuators. Figure 4-5 compares the work densities and cycling
frequencies of commonly used actuators [41]. From this figure, we can see that PZT
actuator, electrostatic actuator and the electromagnetic actuator have relatively higher cycling
frequencies and also higher energy density.
65
.... a.S.
S.aWJ~~~
Thermo
SMA
107 ,Pneumatic
(F. 51v)
J/m 3
Thermal
expansion
106
Electromagnetic PZT
D]
U
105
Muscle
Electrostatic
N
104
m
Micro
U bubble
103
102
1
10
102
103
104
105
106
Cycling frequency HZ
Figure 4-5 Actuator work density vs. cycling frequency
4.1.3
Actuation efficiency of micro actuators
Actuation effciency is another important parameter for actuator selection. Prof. A. J.
Flewitt in the Department of Engineering at University of Cambridge has done extensive
research in micro actuators performances [42]. The actuation effciency of several micro
actuators is shown in Table 4-2. It is obvious that conductive polymer, electrostatic and
piezoelectric actuators have the relatively high actuation efficiency.
66
~
-
-.
~---
- -
--
~
U.
-
-
Table 4-2 Actuation efficiency of micro actuators
Micro actuator type
Actuation efficiency
TiNi SMA
0.01
Electrostatic
0.5
Electromagnetic
<0.01
Piezoelectric
0.3
Bimetallic
4.1.4
10-4
Thermopneumatic
0.1
Conductive polymer
0.6
Driving voltage or current of micro actuators
Among the actuators mentioned above, electrostatic, piezoelectric, thermal and
magnetic actuators are usually used for MEMS switch. A comparison of the driving
conditions of the different micro actuators is shown in Table 4-3[10].
Table 4-3 Driving voltage or current comparison of different actuators for MEMS switch
Acuator type
Electrostatic
Thermal
Magnetic
Piezoelectric
Voltage V
20-80
3-8
3-5
5
Current mA
<0.1
5-100
20-150
<0.1
67
Contact force pN
50-1000
500-3000
50-200
500-2000
-
From Table 4-3, we can see that the driving voltage needed by the electrostatic
actuator is too high, but the contact force it could provide is rather low. The thermal
actuator can operate at a low driving voltage and provide a large force, however it consumes
a significant amount of power due to the high current required. The magnetic actuator has
the similar problem. The PZT (piezoelectric) actuator seems to be an ideal candidate. It can
not only provide linear controllable movement for the required frictional movement of selfcleaning and self-alignment, but also provide a sufficiently large contact force and
displacement. Besides, it operates at low driving voltage and also has a high cycling
frequency. Therefore, we adopt PZT as the actuator material for the proposed the switch.
4.2
4.2.1
Piezoelectric actuator
The common operation modes
Generally, various one-dimensional modes of operation are possible depending on
the electric field direction, poling direction and application of loads.
There are three
common operating modes for piezoelectric actuators: longitudinal mode, transverse mode
and shear mode.
In the longitudinal mode, load and electric field are applied along the direction of
poling, while in shear mode, shear load and poling direction are in the plane of the structure,
the electric field applied is perpendicular to the plane. In the transverse mode, the load is
applied transverse to the poling direction and the electric field is applied along the poling
direction.
68
4.2.2
The transverse mode
The transverse mode is more suitable for surface micro fabrication. The transverse
mode utilizes transverse piezoelectric effects. We choose transverse mode although its
coupling term d, is smaller than that of longitudinal mode d33. The principle of the mode is
shown in Figure 4-6.
N-TT
Figure 4-6 Principle of the transverse mode of piezoelectric actuator
The transverse mode is characterized by the electric field E3 applied along the poling
direction and the normal load T1 applied perpendicular to the poling direction.
4.2.3
PZT actuator
As a thin film actuator, PZT actuator usually consists of an oxide layer, which is the
diffusion barrier, an adhesion layer between the oxide layer and the bottom electrode,
bottom electrode, the PZT thin film and the top electrode. It's a composite beam. The
lateral displacement from the PZT actuator can be predicted both analytically [43] and
numerically.
69
Assume a simple thin film PZT actuator consists of Pt 0.2 pm/PZT1 Pm
/Pt0.15pm /Ti0.15 Im /SiO2 0.3pm and the length of the actuator is 400 Pm. The
piezoelectric coefficient d, is assumed to be 100
xlo12
m/V. The displacement from the
analytical model [43] and finite element method (CoventorWare, a MEMS device simulation
software) is shown in Figure 4-7.
PZT actuator displacement vs. applied volatge
7.00E-01
6.00E-01
h-
.2 5.00E-01
E
C
4.00E-01
'U
-S
EU
3.00E-01
2.OOE-01
1.00E-01
0.00E+00
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
Voltage applied V
-+- analytical -U- Finite Elemen
Figure 4-7 Displacement from a simple PZT actuator
From Figure 4-7, it can be seen that the displacement from the thin film actuator is
very small, although the length of the actuator is already 400 pm and the driving voltage is as
high as 30 volt. However, PZT is a ceramic material with relatively high Young's modulus
and stored energy density. This makes it possible to amplify mechanically the displacement
from PZT actuator and to maintain the desired actuator stiffness.
70
4.3
4.3.1
Actuator design and simulation
Bow actuator
The bow actuator is designed and demonstrated by S. Kim and N. Conway [44,45].
The bow actuator consists of a thin film PZT with associated electrodes and a mechanism to
amplify the displacement generated from PZT as shown in Figure 4-8. When voltage is
applied to the top and bottom electrode of the thin film PZT, it will shrink laterally (in both
x
and y direction). The shrinkage in y direction will pull the amplification mechanism inward,
so that the compliant parallel guiding linkage structures (the amplification mechanism) on
both side of the PZT will deform outward along their flexible pivots. Therefore, amplified
displacement in x direction can be generated. To understand its dynamics and behaviours in
both lateral and out of plane direction, the bow actuator is simulated using FEM software
for MEMS device called CoventorWare (MEMCAD). The geometry and the simulated
performances of this actuator is listed in Table 4-4.
71
Top electrode
Thin film PZT
electrode
Pivots
_Amplification
11echanlis111
Y
25 jim
Y
Figure 4-8 Bow actuator model
The size of the bow actuator and the performances is listed in Table 4-4.
Table 4-4 Bow actuator size and performances
Actuator size
550 ptm x 400 pm x10 prm
PZT thin film size
Driving voltage
Max. displacement
400 pm x 100 pm x 0.5 pm
10 V
3.45 pm
Amplification
4.3.2
-5.5
Modal analysis
Modal analysis of the bow actuator is also done by using CoventorWare (a Finite
Element Analysis software for MEMS devices). The first three natural modes of the bow
actuator are summarized in Table 4-5.
72
Table 4-5 Modal analysis of the bow actuator
Mode
1st, out of plane
2nd, torsional
3rd, lateral
4.3.3
Frequency KHz
29.4
55.2
80.4
Bow actuators used in parallel and series
The bow actuators can be used either in parallel or in series depending on the
performance requirements. In this research, the bow actuators are used both in series and in
parallel. The performances of the actuators are summarized in Table 4-6, where TRSC refers
three actuators in a series (three rows single column) and DRDC refers four bow actuators
in two rows and two columns.
Table 4-6 Actuators performances summary
Design
Displacement pm
Stiffness laterally
Stiffness out of plane
3.0
6.0
9.0
N/n
140.0
140.0
47.0
N/m
4.5
1.0
0.2
A1 Single
Al DRDC
Al TRSC
4.4
Switch-actuator coupled analysis
4.4.1
Sliding condition
The two contact surfaces should have relative sliding motion to clean the damaged surfaces.
Condition for the sliding has to be determined to ensure it. The free body diagram of the switch is
shown in
Figure 4-9.
Figure 4-9 Free body diagram of the switch beam
73
F
Fny
Fnx
Ff
F,
tactuation
Figure 4-9 Free body diagram of the switch beam
From the diagram, we can find that:
F, = Fsin9
F, = F cos9
(4-1)
F, = pF, = pF cos0
To have sliding, the following conditions should be satisfied:
F
Ff
FsinO pFcosO => tan9
74
p
(4-2)
Assume p = 0.5
1[31], 0 = 26.60
450. The chosen angle for the switch structure is 450
to gaurantee the frictional motion.
4.4.2
Switch beam stiffness
From Figure 4-9,
1, = F, sin0 = F cos0 sin0
(4-3)
M,= F,l
(4-4)
Assuming the deformation of the beam due to sliding is AL ,
AlX = A/ cos0
(4-5)
Al, =Al sin 0
From beam theory, we can find the tip displacement
"X
AIX =
(4-6)
3EI,
Where
Ix=
12
hb3
Substituting in equation above,
A
- 4Fcos0sin0l'
Ehb 3
AX =
Rearranging, the stiffness of the switch beam becomes
3
Ehb 3
K= 2sin201
(4-7)
The max stress on the beam is
b
M2
Ix
3Eb
=
2
x
75
(4-8)
The dimension of the switch beam has to be determined based on the sliding motion
requirements and the maximum stress limit. This can be done by coupled switch-actuator
analysis.
4.4.3
4.4.3.1
Coupled analysis
The coupled system
The sliding between the two contact surfaces is enforced to clean the contact
surfaces. However, the magnitude of the motion should be minimized to avoid reducing the
stiffness of the switch beams significantly, so that the contact force is reduced. The
magnitude of the sliding motion can be determined through the coupled analysis. The
switch-actuator pair is a coupled system and can be simplified as an actuator working against
a structural spring as shown in Figure 4-10 assuming the deformation of the switch beams is
elastic.
PZT actuator
Switch
Figure 4-10 The coupled switch -actuator system
Hagood [46] et al has developed a model for this coupled system based on the Ritz
formulation, which consists of the actuator equation and sensor equation.
(M, +M,)F +(K, + K,)r -OV = Bff
O T r +(Cs
+Cp)V = Bqq
76
For quasi-static case, this expression can be simplified and expressed in matrix form for the
PZT actuator:
ET
K EZT
0
0
CPzr
x
V
}
F
Q
(4-10)
For the switch beam structure, the force-displacement relation can be written as
F, = K, x,
4.4.3.2
(4-11)
Compatibility and equilibrium
The state of the beam structure and the PZT actuator is related by compatibility and
equilibrium requirements.
Force equilibrium requires:
F=F
(4-12)
x = -x, = AlX
(4-13)
Compatibility requires
From equation (4-10), we have
(4-14)
KZT x-OV =F
Substitute in equation (4-12) and (4-13), we have
K, =
OV
-AlKPzr
AI X
x
(4-15)
77
4.4.3.3
Finding the coupling term
The coupling term ( can be found using the Ritz method. The electric and
mechanical mode shapes, which satisfy the prescribed voltage boundary conditions and the
geometric boundary conditions, can be assumed as:
(4-16)
PZT
'Px
(4-17)
TM
PZT
0
can be found using the expression derived by Hagood [46].
0
=
Ne,N,dVZT
VPZT
=
f/r
--1I e 1
PZT
VpI
1 cl
(4-18)
IITdVPZT
PZT
e31APZT
'PZT
Since e, is not a commonly available value for the electromechanical coupling, we can relate
it to d, which is available, using the constitutive equations.
4.4.3.4
Constitutive equations
For small stress and electric fields, piezoelectric materials follow a linear set governing
equations, which describe the electrical and mechanical interaction of the materials. The
equation can be expressed as
[SD
dJ{ T
DJL d
C' _ El
S
(4-19)
This equation can be simplified for the 1D transverse mode as:
dT
}[s,'
D3
dl
T
(4-20)
E3
78
Equation (4-20) can also be rearranged as
TDL3
e3,
CSj E3 ~
(4-21)
633
4.4.3.5
Determining the switch beam stiffness
From equation (4-20) and (4-21), we can find
e3 1
=
d
Substituting in equation (4-18)
O = daKPZT
(4-22)
Substituting in equation (4-15),
=
d31 V -Al
A
(4-23)
* KrzA
Since there is a gap d between the switch and the actuator, the equation above has to
be modified as
KS =
(Max.DispaementPZT - d) - AlX
AIX
KPzr
(4-24)
Using this equation and also the max. stress equation as constraints, the stiffness of
the switch beam can be determined based on the sliding motion AlI . After the beam width
and thickness are determined by other requirements such as isolation, the switch beam
length can be determined exactly based on beam theory from equation (4-7)
Ehb3
2 sin(2O)K,
(4-25)
79
4.5
4.5.1
Switch geometry and the switch schematic
The switch geometry
The final design matrix for the MEMS switch is listed in Table 4-7. The angle of the
switch contact surface is chosen to be 450, which gives the maximum possibility for the two
contact surfaces to slide on each other.
Table 4-7 Switch design matrix
o
1#
2#
3#
4#
5#
6#
7#
8#
0
45
45
45
45
45
45
45
45
Actuator
TRDC
TRSC
Groove size
pm
none
4x3
Beam
height pm
10
25
Gap pm
3
Beam
width pm
15
15
15
15
25
25
25
25
Beam
length pm
125
110
90
65
200
170
140
100
The groove size is chosen to be 4 pm long and 3 pm deep with a rounded comer
design, so that the length of each of the normal contact areas is about 2 pm. There are 12
such contact areas on one such surface. The reason for choosing the 2 pm length is that we
want the switch beams to experience the minimum deformation, 2 pm in this case, to
minimize the stress in the switch beams and also to maintain the required contact force. Two
pm is about the smallest feature size we can obtain with UV photolithography. Given the
contact area to be 2 pm long, the deformation of the switch beams has to be at least 2 pm in
order to completely clean the contact area during switch operation.
80
Based on the modelling results shown in Table 1-2, the gap between the two
contacts is chosen to be 3 ptm. This is a trade-off between the isolation requirement and the
actuator performance.
There are two types of switch structures: 15 prm and 25 pm wide. The actuators
TRSC means three actuators in series. TRDC means two columns of three-actuator series in
parallel. The beam length of the switch is determined by equation (4-25).
4.5.2
The beam stiffness
Based on the switch geometry listed in Table 4-7, the theoretical switch beam
stiffness can be determined by equation (4-7) as listed in Table 4-8. The Young's modulus,
Poisson's ratio and density of SU-8 are chosen to be 4 GPa, 0.22 and 1.22 g/cm' respectively
based on literature review.
The switch beam stiffness will be used for the prediction of the contact force.
Experimental method such as nano indentation and AFM will be used to verify the switch
beam stiffness.
Table 4-8 Switch Beam thickness
Width pm
15
25
Beam #
1#
Stiffness N/m
51.84
2#
76.07
3#
4#
1#
2#
3#
138.68
368.68
23.15
37.70
67.50
4#
185.22
81
4.5.3
Switch schematics
The most suitable switch configuration for the self-cleaning mechanism is a lateral
contact switch. Actuators are needed to provide the in-plane movement to perform the
ON/OFF switch function and the frictional movement between the two contact surfaces.
One of the switch schematics is shown in Figure 4-11, which includes the switch part and
the actuator part. The actuator part consists of three bow actuators in series. The outer
boundary line in the figure represents the substrate and the anchored point of the device. Of
course, the actuators can also be two rows of actuators in parallel or in other configurations.
Actuator part
Switch part
30 pm
Su-8 base
Figure 4-11 Switch schematics
The lateral contact configuration is not only suitable for self-cleaning, it is also good for
the co-fabrication of the actuators, the contacts and the structures, and reducing the cost,
which will be discussed in the following chapter.
82
5. Device Fabrication
5.1
Introduction
Several key fabrication issues had to be addressed. Method to deposit Au on the
sidewall of the structure has to be determined: e-beam evaporation or electroplating. The ebeam evaporation process is simple but the deposited film has less dense microstructure and
there is a geometric limit to evaporating film on the sidewall of a deep narrow gap. While the
electroplating process is more flexible to deposit metal in a narrow gap, but the mold for
electroplating is critical. The mold should have near vertical sidewalls and be removed easily
after electroplating. The process of making a near vertical sidewall with a positive photoresist
or SU-8 has to be developed. PZT is deposited using a sol-gel method and SU-8 could be
chosen as the switch structure material for its unique vertical sidewall and compatibility with
the actuator process.
It's possible to use SU-8 as both the electroplating mold and the
switch structure; however, SU-8 is very difficult to remove partially after electroplating.
5.2
Process evaluation
In order to determine which process to choose to fabricate the near vertical wall of
the metal contact, an initial evaluation test had to be done. SU-8 has been selected as the
structural material due to its property of forming a vertical sidewall and low stiffness. Then
83
-'-
,
--
- -L _;
-. M-.
_;k_
gold is e-beam evaporated on the sidewalls of the structure. To improve the adhesion
between gold film and Su-8, a 500 E Ti layer is deposited first.
The deposited gold film quality on the sidewall of the structure is inspected using
SEM and is shown in Figure 5-1, Figure 5-2 and Figure 5-3.
Figure 5-1 Su-8 structure with e-beam evaporated Gold
84
---
h, -iL
-- Mmm
Figure 5-2 Close-up view of the Gold film on the sidewall
Ace, V Spot Magn
10.0 kV 3 0 b0000x
Det
WD
GSE 8,0
I'M0nm
3.9 T orr
Figure 5-3 Surface quality of the sidewall
From the pictures shown above, it can be seen that the thickness of the gold film on
the sidewall is less than half of that deposited on the top surface. Besides, the film is also
85
very porous which exhibits poor electric and mechanical properties. The Su-8 structure used
here has a gap of about 10 prm. Since the real device wafer will have a gap of only 3-5 tm,
the e-beam deposition of gold on the sidewall will make even poorer sidewalls. As a result, ebeam evaporation is discarded and electroplating is chosen to make the vertical sidewalls of
gold as electric contacts.
5.3
Fabrication Process flow
The proposed device fabrication consists of several major steps, including bottom
electrode lift-off, plating mold formation, electroplating, mold removal, switch structure
formation and device release. The process requires 5 masks. For the initial fabrication, thin
film PZT is not included because the major challenge here is to verify the effects of the
modulated surface on the contact resistance. Figure 5-4 to Figure 5-11 shows the complete
process flow and the associated device pictures after each step. The detailed fabrication
parameters are shown in Appendix A.
4" wafer,tlernal Oxide
o MaSKS
Figure 5-4 Step 1: Growth of thermal oxide on the Si substrate and the 5 masks
86
1
Bottom Electrode
Figure 5-5 Step 2: Photolithography and bottom electrode lift-off
all
IIII
III
ofIf
III
ll
101
M
1Hf
Ill
Ill
aod
110
lt
Mask 2&3
PLT/ top elect rode
Figure 5-6 Step 3&4: Thin Film PZT deposition, patterning and top electrode lift-off
87
Mask 4
Photo resist mold
Figure 5-7 Step 5: Preparation of photo resist mold for electroplating
thermometer
wafer
stirrer
'Anode
Heater/stirrer
Fulse Electroplatmig
t
Figure 5-8 Step 6:Electroplating of the contact metal
88
Mold removal
Figure 5-9 Step 7: Electroplated contact metal after electroplating mold is removed
B
B1
BB
- B Mask 5
Su8 coat and pattern agan
Figure 5-10 Step 8: Switch structural layer (Su-8) deposition and patterning
89
Device release
Figure 5-11 Step 9: Device release by XeF2 etching
As shown in Figure 5-4, the fabrication begins with a 4" wafer (either n-type or ptype, but P-type is preferred due to a following process of plasma etching which favors ptype. For concept proving of the self-cleaning mechanism, high resistivity Si substrate is not
used). The figure on the right shows the masks, which is an overlap of the 5 masks. The
first process is the growth of 200 nm silicon oxide at 1050 0C.
Figure 5-5 shows the process for electrode lift-off. Thin negative photo resist AZ
5214 is used as the mold. After the mold is formed, e-beam evaporation is used to deposit
the metal (Ti/Au). Finally, the electrode is patterned via lift-off in acetone. The thickness of
the Ti and Au are 500 nm and 2.2 ptm respectively.
Figure 5-6 shows the deposition of thin film PZT and the lift-off of the bottom
electrode. These steps are shown here for the completeness of the fabrication process.
However, they are not included for the initial fabrication.
90
Figure 5-7 shows the photo resist mold for electroplating. The critical requirement
here is to have vertical sidewalls. The materials of the mold can be either AZ series positive
photo resist or Su-8, an epoxy, which is a negative tone photo resist. The mold shown in the
figure is from AZ 9260 photo resist with a sidewall angle of about 92.2 . The best vertical
angle is 90.1 with Su-8 as the mold material. This will be discussed later.
Figure 5-8 shows step 6, which is the electroplating of the contact metal. Details of
this process will be discussed later.
Figure 5-9 shows the electroplated contact metal after the photo resist mold is
removed.
Figure 5-10 shows the forming of the switch structure with Su-8; while Figure 5-11
shows the device after released with a XeF 2 etch.
5.4
Issues and problems of the device fabrication
The major issue for the device fabrication is the creation of the vertical sidewall of
gold for the electric contact. Molded electroplating has been chosen instead of e-beam
evaporation based on process evaluation. Thus, the issue becomes how to create the mold
with vertical sidewall for electroplating and how to electroplate the high quality contact
metal. The problems confronted during fabrication and how they were solved is summarized
below.
5.4.1
Electroplating in general
Electroplating is used to form the lateral metal contacts by molding electroplated
metal into a narrow gap of Su-8. The process consists of three major steps: electrode/seed
layer formation by e-beam evaporation, photo resist mold formation and electroplating itself.
Photo resist mold formation and the electroplating are the two key processes. For the
91
purpose of electric contact, the mold should have vertical sidewalls for a good contact of
switching. And the mold material should be able to survive the electroplating environment
(temperature, erosion). For the electroplating itself, there are several plating processes such
as DC electroplating, pulsed plating and pulse reverse plating. Pulsed electroplating is chosen
because it facilitates the nucleation of new grains, which could make finer-grained deposits.
Besides, it provides better deposition at the sharp comers, which is critical to the quality of
the micro-grooved contact.
The electroplating is conducted in a beaker on a hotplate as shown in Figure 5-8.
The plating controller controls the current, the voltage to the anode and also the frequency
of the plating. The plating solution used is Orotemp 24 from Technic Inc. The reaction of
the plating is a two-step process.
1) A fast equilibrium between the gold cyanide ion and a neutral reducible species:
Au(CN)j +->AuCN + CN2) A charge transfer reaction
AuCN + e- -> Au(s) + CN-
5.4.2
Electroplating mold
There are several issues related to making the required mold for electroplating and
also several parameters to optimize the electroplating process. Some of these requirements
are coupled, so a trade-off has to be made to ensure a working device.
5.4.2.1
Mold material
Both Su-8 [47] and positive photo resist [48] have been considered as a mold
material because they can all survive the electroplating environment. Su-8 has the reputation
92
of creating near vertical sidewalls, but it is not easy to be removed due to its cross-linked
epoxy structure after curing. A positive photoresist such as AZ9260 can be removed easily
by acetone, but it is difficult to form a near vertical sidewall.
5.4.2.2
Positive photo resist mold
At the beginning, positive photo resist was used to create the mold. On a substrate
without any features (blank wafer), a mold with near vertical sidewall is formed successfully
as shown in Figure 5-12. The sidewall angle is about 92.2 . However, in the real situation,
bottom electrode and the electroplating seed layer was already deposited on the substrate.
The bottom electrode and the seed layer prove to cause problem for forming the mold
between the two contacts, which is necessary to separate the two contacts. The positive
photoresist mold between the two contacts disappears after development. This is because
the resist is positive and the reflection/diffraction from the bottom electrode exposes the
nearby mold. SU-8 is eventually chosen as the mold material in this regard.
Figure 5-12 Positive photo resist mold cross-section
5.4.2.3
SU-8 mold
SU-8 has a similar problem as positive resist. It is relatively easy to create a mold with
vertical sidewalls on a flat surface as shown in Figure 5-13. However, the mold has also to be
93
formed between two electrodes to separate the two contacts. If SU-8 is exposed with a
normal dose, the pattern for the grooved contact cannot be formed (the pattern can not be
developed). The reason is also the reflection and diffraction from the electrode nearby and
the negative tone of SU-8. The exposure dose has to be reduced, so that the desired mold
pattern can be formed. However, if the exposure dose is reduced significantly, the adhesion
between SU-8 and the substrate would become poor and the mold would peel off during
electroplating. This happened at the early stage of the test.
Figure 5-13 Su-8 mold cross-sections on flat surface
To increase the adhesion between the Su-8 and wafer, dehydration process (30 min
@120 C) and UV cleaning (5 min) of the wafer are performed before the coating of the SU8. After the SU-8 is developed, an O2 plasma etch is done to remove the residue of SU-8 on
the electrode surface. Development time for the SU-8 is also increased to more than 10 min,
which is at least twice as long as the normal developing time, for the same reason. However,
it is still difficult to remove the residue completely.
94
-~
-~ -
~
-~
~
~-
-
The solution is to reduce the exposure dose to the minimum possible to form the
mold, then after the mold is developed, expose the SU-8 with an extra dose (adding the total
dose to the normal dose required) and hard bake the mold to increase the adhesion. The
picture in Figure 5-14 shows the sidewall of the SU8 mold after this trade-off, which is
acceptable.
-
~
~W
Figure 5-14 Su-8 mold after parameters trade-off
5.4.3
Electroplating
There are several process parameters, which have influence on the quality of the
plated metal deposit. The quality of the deposit including roughness, uniformity, purity,
density and electrical properties all depend on process parameters, such as, frequency,
current density, temperature. There are also several key issues related to plating including the
cleanness of the electrode, aspect ratio of the mold, underplating, which are all discussed
below.
95
-
5.4.3.1
Electrode cleanness
First of all, the cleaning of the electrode is found to be a critical problem. After Su-8
development, there is always some organics/polymer remaining on the electrode. These
residues prohibit the deposition of gold on the electrode. At the beginning, development
time for Su-8 is increased to remove the residue, however, it is still difficult to remove the
residue completely. Then, two plasma etch recipes are tried, one is just 02, another is
0 2 /CF4 . There is a trade-off between the etch time and residue removal. Longer etch times
will cause undercut of the mold at the gap of the two contact surfaces. However, if the etch
time is short, metal can only be deposited on a few spots on the electrodes as shown in
Figure 5-15. O2 plasma is reported to be able to remove the residue but was found it
ineffective. In the present work, the combination of 02 and CF4 is used and the results are
very good. Gold can be electroplated uniformly in the mold after this treatment.
Figure 5-15 Plating results with un-cleaned mold
5.4.3.2
Current density
The second issue is the current density control. Higher current density causes dark
metal deposit (indicating a very rough surface). The optimized current density is about 50
96
A/m 2 . Because the whole contact area to be plated is about 1 mm2 , a 0.05 mA current is
required. However, the minimum controllable current of the existing plating controller is 1
mA. This means a large dummy area on the wafer is required and this creates problems for
uniform electroplating on the desired area.
5.4.3.3
Plating frequency
Higher plating frequency produces finer grain size. The plating frequency is changed
from the initial test frequency of 266 Hz to 1000 Hz with a duty cycle of 10%. 1000 Hz is
the maximum possible frequency because the minimum controllable time is 1 ms for the
available controller. The actual plating frequency used is 1000 Hz.
5.4.3.4
Wetting
Wetting of plating solution on the mold proves to be another issue. It's found at the
early stage that it's very hard to deposit metal in mold with the fine feature (the grooves)
when the aspect ratio of the mold is very high. This is probably because the mold with fine
feature is hard to be wetted by the plating solution. The aspect ratio of the mold is reduced
from the initial value of 30/3 to 10/3 and the results become much better.
5.4.3.5
Agitation and temperature control
A stirrer is used to keep the plating solution uniform in ion concentration and in
temperature, resulting in uniform deposit thickness. The optimized temperature is about
62.5C.
5.4.4
Underplating
In addition to the parameters discussed above, underplating has to be solved to
obtain the required contacts. This problem is related to both the plating mold creation and
the electroplating process and is also observed by J. Voldman [49]. Underplating can cause
97
the switch to fail to operate. The reason is that there is always some de-bonding between the
SU-8 mold and the substrate, as shown in Figure 5-16. Electroplating can occur in the space
created by the de-bonding shown in Figure 5-17. Since the gap between the two contact
metal walls is only 3 micrometer, this underplating will be sufficient to create a short circuit
between the two contacts. The following measures have been taken to solve this problem:
1) Dehydration (30 min@ 120 C) and UV cleaning of the wafer (8 min) is performed
before the coating of SU-8.
2) Slower temperature ramp down rate after SU-8 is baked (2 C/min).
3) Etch the electrode of the mold with 0 2/CF 4 plasma in a short time (about 2 to 3
min).
4) Lower the electroplating temperature. The temperature is reduced from 65 C to
45 0C, without significant influences on the deposit quality.
5) Quick wet etch
A quick dip of about 30 sec in TFA, Transene (etch rate 28 A/sec at 25 'C) is used
to guarantee the removal of the underplated metal in the end.
98
Figure 5-16 Typical de-bonding between the Su-8 mold and substrate
Figure 5-17 Underplating at the edges of electrode
99
5.4.5
5.4.5.1
Other issues
Thicker bottom electrode
To get a better measurement of the contact resistance, it's necessary to minimize the
influence from the switch beam, i.e., the resistance from the beam has to be as small as
possible. The first electrode used is 0.2 pm thick. The resistance along the beams (the rmicrostrips) is very high, causing difficulty to find the exact value of the contact resistance. Ideally,
the thickness of the electrode should be around 2.5 pm, so the resistance on the beam is less
than 0.1 Q. However, the thickness of the AZ 5214 image inverse photo resist is only
around 1.8 pm. To achieve 2.5 pm metal film lift-off, we need at least 3.5 pm thick mold.
Double coating of AZ 5214 photo resist is used to satisfy this requirement. The actual
bottom electrode thickness achieved is about 2.2 pm.
5.4.5.2
Mold removal
The SU-8 mold is very hard to be etched. A technique has been developed to
remove the mold from the substrate after electroplating. The wafer is first immersed in
NMP (N-Methylpyrrolidone) and heated to about 80 'C for 1-2 hours in a water bath,
followed by a 15 second piranha clean. Piranha can attack Ti, which is used as adhesion layer
between the substrate and the gold layer, so the piranha time has to be controlled precisely.
5.4.5.3
Lead electrode for electroplating removal
To electroplate the metal contact, current has to be supplied to each of the contacts.
The whole wafer is at the same potential and all the contacts are connected. The contacts of
the switches have to be separated, which was done by dicing. The solution is to cut into the
substrate 10 pm deep to remove the electrode (150 pm wide) by die saw (220 pm wide
blade) before the Su-8 switch structure is formed.
100
5.4.5.4
Delamination of SU-8 after die saw
Die saw is also needed before the device is released for testing purposes. Using a
wide blade to cut SU-8 causes serious delamination even at very low cutting speed. The
delamination was prevented by cutting through the wafer in the middle of the wider streets,
which were cut previously, using a narrower blade (30 pm wide). The wider streets were cut
to remove the electrode lead for electroplating.
5.5
Fabrication results and summary
The switch devices have been fabricated successfully. Near vertical sidewalls of gold
for electric contact were obtained after the electroplating mold was removed. The contact
structures and the vertical sidewalls were shown in
Figure 5-18. The finally released devices were shown from Figure 5-19 to Figure
5-23. It has been demonstrated that molded electroplating is a better way to create near
vertical metal sidewalls for electric contact compared to e-beam evaporation. The fabrication
method is also fully compatible to the PZT actuator fabrication process, making it possible
to fabricate the switch and actuator simultaneously.
101
Figure 5-18 Plated Gold contacts after mold removal
102
Figure 5-19 SEM picture of device with two rows of actuators after it's released
Figure 5-20 SEM picture of device with single row of three actuators after it's released
103
Figure 5-21 SEM picture of the switch part of the released device
Figure 5-22 Picture of the released device showing the undercut of the release (darker area)
104
Figure 5-23 SEM picture of the contact area of the released device
105
6. Device
Testing
Discussion
6.1
Results
and
Test set-up
The test schematic is shown in Figure 6-1. The major components or electronics
used are listed below.
I
+
-
I
Power
Figure 6-1 Test set-up schematic
* RF-1 Microwave Probe Station
" Agilent 6614C Power Supply
" Trek 610C Amplifier
" BK Precision 401 1A 5MHz Function Generator
" HP 54602B Oscilloscope
" PZT stack actuator: max. Displacement 182.88 pm (at max. voltage 800 V), stiffness
45.2x10 6 N/m, capacitance 3.00 pF, diameter 30.86 mm, overall length 184.15 mm.
106
* MTI
2000 Fotonic sensor
The real set-up is shown in Figure 6-2 and Figure 6-3.
Figure 6-2 The probe station and the measuring system
Figure 6-3 The actuator driving system
107
--
a
6.2
i-
a
2
1- -
Contact surface characterization
Before the contact resistance is measured, the surface quality of the contact metal by
electroplating is studied with SEM (Scanning Electron beam Microscope) and AFM (Atomic
Force Microscope). The results are shown below and are compared with the surface by ebeam evaporation.
A
ec.V Spot Magn
25 0 kV 3.0
Det WD
h
1 50000x GSE 8 7
200 nm
2-1 Torr
Figure 6-4 SEM picture of the sidewall surface of gold by molded electroplating
108
--
I
M
5
Figure 6-5 SEM picture comparison of the contact surfaces
by molded electroplating (a) and e-beam evaporation (b)
The sidewall surface of the electroplated gold shown in Figure 6-4 is much smoother
than that achieved by e-beam evaporation in Figure 6-5, which is good for making electric
contact.
The surface of the Su-8 mold is also checked with AFM, which confirms the SEM
result, and it shown in Figure 6-6.
20.C nm
1.5
1.
1.0
.
.5
0.5
0.5
1.0
1.5
Figure 6-6 AFM image of the mold surface
109
2.01
m
6.3
Contact resistance measurement
The tests, which have been done for the MEMS switches, include the force-contact
resistance characterization tests and the long lifecycle performance tests. Contact resistance
is measured using the four-probe method, which measures the voltage drop at the contact
and also the current in the circuit directly. Two probes are used to connect the MEMS
switch with the measurement circuit, so that there is desired current in the circuit flowing
through the switch. Two other probes are used to measure the voltage drop exactly from
the input to the output pads. The resistance from the probes itself can be excluded. Then
contact resistance can be determined directly from these measurements.
6.3.1
Dummy design resistance measurement
Since the switch beam has a significant length, the resistance on the beam could be
significant, although the thickness of the gold film on the beam has already been increased to
about 2.2 tm. To measure the contact resistance correctly, the resistance from the switch
beam has to be measured first and then be subtracted from the whole loop resistance
measurement. The dummy designs, which have all the same dimension as the real devices
but have the contact area connected on purpose, give the best solution.
There are two beam-widths with 4 beam lengths each used in all the switch designs.
The measurements for the design B15D with beam width of 15 tm is listed in Table 6-1,
while the measurements for the design B25D with beam width of 25 tm is listed in Table
6-2.
110
Table 6-1 Resistance measurements on dummy design B15D
Device#
Beam#
V mV
I mA
RQ
1-6-1#
1#
38.6
51.2
0.7539
1-6-2#
2#
36.4
51.2
0.6914
1-6-3#
3#
31.4
51.2
0.6172
1-6-4#
4#
28.8
51.2
0.5234
Table 6-2 Resistance measurement on dummy design B25D
6.3.2
Device#
Beam#
V mV
I mA
RQ
1-47-6#
1#
34.6
50.1
0.6909
1-47-7#
2#
30.2
50.1
0.6028
1-47-8#
3#
28.6
50.1
0.5709
1-47-9#
4#
22.7
50.1
0.5234
Contact resistance measurement
As mentioned earlier, the contact resistance measurement circuit is very simple
which is shown in Figure 6-7.
-
A
Figure 6-7 Circuit for contact resistance measurement
111
The contact resistance is determined by the voltage and current measurement
subtracting the resistance from the switch beam.
R
=
(6-1)
R
The voltage to the driving actuator is gradually increased while the current and
voltage in the circuit is carefully monitored. When the two contact surfaces of the switch
merely contact each other, the readings from the voltage and current meters will fluctuate.
Further increasing the driving voltage will make a steady contact and the contact resistance
will drop accordingly.
Lateral movement is provided by a bulk linear piezoelectric stack actuator, which is
driven by a function generator and the associated amplifier shown in Figure 6-3. The
displacement from the stack actuator is calibrated with MTI Photonic sensor (on the right in
the figure).
The stack actuator is mounted on a linear stage, which provides position
adjustment in x-y-z directions. The tested sample is 1-15-8#, which has the same dimension
as the dummy design of 1-47-8#. The resistance on the beam is 0.5709 Q, which can be
found from Table 6-2. The driving voltage and contact resistance measurement is listed in
Table 6-3.
Table 6-3 Driving voltage vs. contact resistance
Driving V(V)
V (mV)
I (mA)
7.9
314.1
50.1
6.27
5.70
8.4
92.9
50.1
1.84
1.27
9
70.6
50.1
1.41
0.84
10
45.6
50.1
0.91
0.34
12
33.5
50.1
0.688
0.098
15
29.9
50.1
0.597
0.027
112
R+Rc
Q
Rc Q
The driving voltage can be converted to the displacement of the actuator, and then
the displacement of the actuator can be converted to a contact force based on the switch
stiffness. The stiffness of the switch is 67.5 N/m theoretically, while the effective
piezoelectric coefficient d33 of the piezo stack actuator is 0.2288 tm/V. This effective
piezoelectric coefficient is also verified using an MTL Fotonic sensor, which measures the
displacement from the piezo stack actuator directly. The actual gap between the two contacts
is about 2.0 pm. The force-resistance relationship is shown in Table 6-4 and Figure 6-8.
Table 6-4 Contact force Vs. Contact Resistance
Contact Force ( N)
Rc Q
0.48
5.70
4.83
1.27
14.09
0.84
29.53
0.34
60.41
0.098
106.73
0.027
113
Contact resistance vs. contact force
7
E
0
6
5
(0
(0 4
<a
I-
3
2
1
0
0
20
40
60
80
100
120
140
Contact force, micro Newton
Figure 6-8 Relationships between contact force and contact resistance
The force-contact resistance curves correlate with the theoretical prediction very
well.
Hot and cold switch test
6.4
6.4.1
Hot test
The switch is also subjected to accelerated switching tests simulating the real
operation and contact resistance is measured in two ways: hot test while the signal power is
on during cycling and cold test while the signal power is off during cycling.
The test frequency and number of cycles for both hot and cold tests are listed in
Table 6-5.
114
Table 6-5 Test matrix for long cycle contact resistance measurement
Test#
mCce
ie
'etrqenyH
Frequency H~z
Time rmn
Cycles
1
0
0
0
2
1
10
6.00x10 2
3
10
10
6.00x103
4
50
20
6.00x10 4
5
100
40
2.40x10 5
6
200
60
7.20x10 5
7
1000
168
1.01x10
8
2000
834
1.00x10 8
7
The hot test results are shown in Table 6-6, Table 6-7, and Figure 6-9.
Table 6-6 Hot contact resistance measurement (sample 1-15-8 # at 12 V driving voltage)
Test#
Voltage mV
Current mA
R+Rc Q
Rc Q
1
30.6
48.0
0.6375
0.0675
2
28.2
45.8
0.6157
0.0457
3
29.6
47.5
0.6232
0.0532
4
34.2
46.3
0.7387
0.1687
5
34.0
44.4
0.7657
0.1958
6
33.2
45.5
0.7297
0.1597
115
Table 6-7 Hot contact resistance measurement (Sample 2-36-3 # at 9 V driving voltage)
Test#
Voltage mV
Current mA
R+Rc Q
Rc Q
1
36.8
46.0
0.8000
0.2300
2
32.7
45.9
0.7124
0.1424
3
35.3
42.2
0.8365
0.2665
4
38.0
45.7
0.8315
0.2615
5
33.3
43.7
0.7620
0.1920
6
30.3
44.5
0.6809
0.1109
Contact resistance vs. switching cycles for hot test
0.4
-mme
-DrMng vottage 90
-+-DrMng votge I:I
E
.10.3
/
/
E 0.2
/
0.1
0
1.0E+00
1.OE+01
1.OE+02
1.OE+03
1.OE+04
1.OE+05
1.OE+06
Number of operation cycles
Figure 6-9 Contact resistance vs. number of operation cycles for hot test
6.4.2
Cold Test
As mentioned earlier, the cold test is conducted while the signal power is off during
cycling. The test results are shown in Table 6-8 and Figure 6-10.
116
Table 6-8 Contact resistance measurement for cold test
Test#
Voltage mV
Current mA
R+Rc Q
Rc n
0
30.5
38.9
0.784
0.098
6.00x10 2
28.9
37.6
0.769
0.104
6.00x103
28.4
36.1
0.787
0.085
6.00x10 4
27.8
36.9
0.753
0.060
2.40x10 5
27.8
36.1
0.770
0.088
7.20x10 5
27.1
35.8
0.757
0.081
1.01x10 7
29.6
37.1
0.798
0.113
1.00x108
28.5
37.5
0.760
0.076
1.00x109
29.3
37.2
0.788
0.099
E
0 0.4
4E
0
E
Contact resistance vs. number of cycles for cold test
0.40.3 -
E 0.3 S
0.2 0.
0.2
1-23-4#
U
I
0.0
1.OE+00 1.OE+02 1.OE+04 1.OE+06 1.OE+08 1.OE+10 1.OE+12
Number of switching cycles
Figure 6-10 Contact resistance vs. number of operation cycles for cold test
117
The long lifecycle tests show after about 10 billion cycles, the contact resistance has
been maintained almost constant. The test is being continued to reach 1011 cycles.
6.5
Test Results Discussion
The fatigue test of the switch provides better understanding of the switch function
and also feedback for further improvement to satisfy the functional requirements by
changing the corresponding design parameters.
In the hot test, the contact resistance varies more than in cold test conditions. The
reason might be that in a hot test situation, the impact from the actuation, and thermal effect
due to the Joule heating over the effective contact areas all has influence over the contact
resistance measurement.
While under static conditions, this influence might be less
significant. Because it took very long to run one switch cycling test and the time available
was really limited, no further test results were obtained from both the hot test and cold test.
Therefore no concrete conclusion can be made. Further tests are needed to explain the
phenomenon in the hot test situation. Figure 6-11 shows the picture of the device under
testing with the four probes providing the current in the circuit and also measuring the
voltage drop on the contact.
118
Figure 6-11 Picture of the device under testing using four-probe method
As discussed early, the first major failure mode of MEMS switches are contact
resistance increase caused by damage, pitting and surface hardening of the contact area
because of the asperity fracture, plastic deformation, repeated impact from the opposite
switching members, and the second major mode is micro-welding between switching
members because of heating due to contact resistance increase. The second mode is
obviously related to the first one. These two modes are mainly due to the increase in contact
resistance of the switch in operation. Since the actuation motion from the PZT actuator is
linear and controllable, impact from the switch member is minimized. However, there still
could be asperity fracture due to repeated contact, which would cause contact resistance
increase. The test results have shown that a low switch contact resistance has been
maintained almost constant for 101 cycles, which is a significantly large operating cycle. This
119
also implies that the major cause of the switch failure might be largely controlled. The debris
from the surface damage might be cleaned through the frictional motion of each switch
operation as expected. Although concrete evidence is still needed to verify the micro scale
self-cleaning mechanism, the test results of the contact resistance of 0.1 Q being maintained
for up to ten billion operating cycles supports the theory. Figure 6-12 shows the SEM
picture of the contact areas after the cycling test, which indicates that the micro grooves on
the contact surfaces have been flatted during the test. Figure 6-13 shows the zoom-in SEM
picture of the contact surfaces after the test. It seem that the surfaces has some scratches.
Further exploration is needed to study the effect of the undulated surfaces on micro scale
contacts.
120
Figure 6-12 SEM picture of the contact area after the cycling test
121
- AN,
Asiffiffims,.
Figure 6-13 Zoom-in SEM picture of the contact area after cycling test
122
7. Research Summary, Conclusions
and Contributions
7.1
Research summary
A new RF MEMS switch with self-cleaning lateral contacts was developed for
wireless, mobile communications. The switch was enabled by strain-amplified PZT
actuators, and was designed for improved robustness, compactness and reliability.
Compared with the existing MEMS switches, the uniqueness of the device lies in the selfalignment of the contact surfaces, self-cleaning of the particles generated from asperity
fracture and plastic deformation, and the anchoring method of the metal contact to the
micro switch structure. By introducing a modulated surface to modify the tribological
behavior of the contact surfaces, low contact resistance can be maintained for more than one
billion operating cycles without sacrificing the benefits of MEMS switches such as low
insertion loss, near zero power consumption, and very high isolation. Switch performances
analysis was made to determine the primary performances controlling factors, which led to
this novel design focusing on two primary: contact resistance and signal isolation. Special
measures have been taken to ensure the creation of the near vertical sidewall of the electric
contacts and the process compatibility with the PZT actuators, including lift-off, molded
electroplating, high-aspect-ratio polymer lithography and XeF2 dry release.
123
The cold switch cycling tests have shown that the contact resistance is maintained at
the level of 0.1 to 0.2 Q and has no obvious increase over the operating cycles tested. Low
contact resistance has been maintained for the ten billions of operating cycles. However, due
to the limited time available and the time consuming nature of the cycling test, no further
test results were available. The switch design is compatible to our thin film PZT actuating
technology and can be readily integrated into a fully functional MEMS switch.
Conclusions
7.2
It has been demonstrated that low contact resistance can be maintained for the
billions of operating cycles without sacrificing the benefits of MEMS switches by
introducing a modulated surface to modify the tribological behavior of the contact surfaces.
The cycling test results of the switch contact resistance supports that the groove design of
the switch contact surface has the self-cleaning effect through trapping the debris on the
damaged areas during the switch operation. However, further tests are needed to verify it.
The parallel beam design of the switch structure guarantees the perfect contact
during the switch operation. Even though the contact metal may wear after long lifecycle
operation, the contact can always be made due to relative motion of the two contact
surfaces.
It has also been demonstrated that the connection between gold metal wall and the
switch structure is very secure and reliable. It is reported and also shown in this research that
gold has poor adhesion with SU-8, however, there is no mechanical connection failure
observed between gold and the structure during the test because of the gold contact metal is
mechanically anchored in the SU-8 structure.
124
It has also been demonstrated that molded electroplating is a better way to create
near vertical metal sidewalls for electric contact compared to e-beam evaporation. The
electroplated gold surface is far more uniform than that of the e-beam evaporated surface
because of the uniform surface of SU-8 mold. The fabrication method is also fully
compatible to the PZT actuator fabrication process, making it possible for the co-fabrication
of the switch and actuator.
7.3
7.3.1
Contributions
MEMS switch design
The main contribution of this work is the modeling and analysis, design,
manufacturing and testing of an RF MEMS switch. The novel design of self-alignment of
the contact surfaces, self-cleaning of the particles generated from asperity fracture and plastic
deformation, and the anchoring method of the metal contact to the micro switch structure
are major contributions in the device design. By introducing the modulated surface, the
tribological behavior of the contact surfaces is modified. The debris from the damaged area
can be pushed and trapped in the grooves and low contact resistance is maintained and the
life cycles of the switch are increased dramatically.
7.3.2
Modeling
The major contribution is the modeling of the contact resistance for distributed
multi-asperity contact using the elastic-plastic indentation model developed by Chang.
Chang's elastic-plastic indentation model is a modification to Hertz's elastic indentation
model. However, it has not been seen that this model has been used for the contact
resistance modeling of distributed multi-asperity contact. By varying the plastic index defined
125
by Greenwood, it was found that this model might be more accurate for the contact of
surfaces with high plastic index.
7.3.3
MEMS switch fabrication
A novel fabrication technique to create the near vertical gold sidewalls for electrical
contact of the device was developed.
A series of problems has been solved including
evaluating the process of e-beam evaporation and molded electroplating, forming the vertical
electroplating mold, cleaning electrode for plating, preventing the mold peeling off during
plating, trading off parameters for high quality gold deposition and preventing debonding/underplating etc. The final structures satisfy the requirements of lateral electric
contact of the switch.
7.3.4
MEMS switch test and Analysis
Theoretical analyses, hot/cold tests have been conducted to evaluate the
performance of the switch. It as been experimentally verified, and tested the contact
resistance-force relation correlated with the theoretical prediction very well. Both the hot
and cold long lifecycle tests have been conducted to determine the long-term effect of the
modulated surfaces. It has been demonstrated that there is no obvious change in contact
resistance after the billion of operating cycles.
7.4
7.4.1
Recommendations for Future Work
Design
There are a few issues, which should be taken into account for the improvement of
the switch performance. First of all, the gap between the two switch contacts should be
increased. The designed gap of the two contacts is 3 Pm, however, the actual gap after
device fabrication is about 2 pm. This is because the SU-8 photo resist is negative and
126
during the device fabrication, SU-8 is slightly under exposed to avoid the influence from the
bottom electrode. Second, the influence of the size of grooves should be further
investigated. In the current design, the groove size is fixed (both width and depth). Third,
thorough modeling of friction and wear rate between the two contact surfaces will be critical
to further understanding the micro tribology and improving the switch performances.
7.4.2
Fabrication
For the fabrication, there are two possible ways to simplify the fabrication process
and potentially increase the yield. The first one is to choose a gold electroplating solution
that can be plated at room temperature. This will minimize the temperature influence on the
adhesion between the Su-8 mold and the substrate. The second is to explore the possibility
to use a single uniform layer of bottom electrode and later on etch the electrode between the
switch contacts. This might help build a better mold for electroplating because there will be
no diffraction/reflection from the bottom electrode. However, since the electrode is etched
away, the cross-section of the electrode underneath the mold is not covered. Metal can be
deposited on the cross-section during electroplating and eventually connect the two contacts,
which has to be addressed.
7.4.3
Device integration, packaging
Device packaging should be designed and the device should be kept in a vacuum or
inert gas environment to avoid contamination and increase the life cycles of the switches.
Low humidity is not really necessary because PZT actuator is not sensitive to it.
127
7.4.4
Testing
Further tests are needed to qualify the new switch. These tests include the cold
switching tests of up to 10" cycles, and also the hot tests, which determine the performances
of the switch when RE signal passes through.
Furthermore, the devices without the
microgrooves should also be tested. The results should be compared with those results
obtained from devices with the microgrooves and directly verify the effectiveness of the selfcleaning mechanism. The insertion loss and isolation of the switches for a given RF signal
has to be measured too. A better data acquisition system is needed to monitor the switch
performances in the real time.
128
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133
Appendix A
Process Details
A. 1 Process for the electroplating seed layer
Step
1
Process
Premetal
Description
Start with p-type 4" wafers
Piranha clean + HF dip
2
1st photo resist
HMDS, 30 sec
Image inverse resist AZ 5214E
Dispense 6 sec@ 0.5 Krpm
Spread 6 sec@0.75 Krpm
Spin 3 sec@2 Krpm
3
4
Prebake
2nd photo resist
5
6
Prebake
Exposure
10 min @90'C in oven, wait 10 min@RT
Image inverse resist AZ 5124E
Dispense 6 sec@0.5Krpm
Spread 6 sec@0.75 Krpm
Spin 30 sec@3 Krpm
30 min @90 0 C in oven
EV1, 365-450 nm wavelength at 10 mW/cm 2
Exposure time 1.5 sec
7
8
Postbake
Flood exposure
30 min @ 90'C in oven
EV1, 365-450 nm wavelength at 10 mW/cm2
Exposure time 60 sec
9
Develop
Developer AZ 422, about 120 min (till clear)
Photoresist thickness about 3.8Vm.
10
Metal deposition
E-beam evaporation
0.5 KA Titanium @ 1 A/sec
followed y 24 KA Au @ 5 A/sec
11
Lift-off
Wafers immersed in Aceton for 12 hours
Spray aceton, methanol and 2-propanol on wafers
For fine features, use ultrasound. Keep the power
and time of ultrasound the minimal (thinkness of Au
134
L
about 22 KA)
A. 2 Process for PZT film fabrication. Courtesy of Dr. Yongbae Jeon and Nicholas Conway
Step
1
Process
PT sol-gel coating
2
Pyrolysis
3
PZT sol-gel coating
4
Pyrolesis
5
Repeat step 3&4
6
Photo resist
7
8
Prebake
Exposure
9
10
11
Develop
Postbake
Wet etch
12
Strip photo resist
13
PZT annealing
Description
PT sol-gel solution El (Seed layer), 1 wt% PT
(125/100), Mitsubishi Materials Co., 3 Krpm on
PZT coater
Heat to 380 0 C for 1 min on a hotplate
Step down to 200 0 C for 1 min
Then 800 C form 1 min
PZT sol-gel solutionF2, 17 wt% PZT(125/52/48),
2 Krpm on PZT coater
Heat to 801C for 1 min on a hotplate
Then 380 0C for 5 mM on a hotplate
Step down to 200'C for 1 mM
The 800C for 1 min
About 0.2 pm obtained per coat after annealed
Allow wafer to cool down between coats
HMDS, 30 sec
Thick photo resist AZ 4620
Static dispense the resist
Dispense 9 sec @1.5 Krpm
Spread 60 sec@3.5 Krpm
Spin 10 sec@5 Krpm
900C for 30 min in a oven
EV1, exposure 45 sec total at interval of 15 sec with
15 sec wait
Developer AZ 440 for 3 min
90'C for 30 min in a oven
Etch in100 HCl (17%):20 BOE (4%):400 DI water
for < 10 sec. Spray with DI water afetr etch
Strip photoresist with aceton, methanol and 2propanol, dry with nitrogen
Put wafer on the stainless steel wafer holder and
ramp up to 380 0 C on a hot plate, move the wafer
with the hoder to the box furnace in air at 650 0C for
20 min.
135
A. 3 Process for mold formation, electroplating and mold removal
Step
Process
Description
1
2
3
Cleaning
Dehydrate
Su-8 coating
UV clean for 5 min
Bake the wafer for 30 min @1050 C
Su-8 2015, MicroChem. Co.
Static dispense
Spread 30 sec @ 0.5 Krpm
Spin 35 sec @ 4.75 Krpm
Yield 10 pm resist
4
Prebake
5
Exposure
Ramp to 600 C for 1 min, then 85' C for 4 min, then
down to RT naturally on the same hotplate
EV1, 350-450 nm wavelength at 10 mW/cm2
Exposure total of 8.7 sec at interval of 2.9 sec a and
wait for 15 sec
Ramp to 65' C for 1 min, then 940 C for 4 mi, then
ramp down to RT naturally on the same hotplate
6
Post exposure bake
7
Develop
Su-8 developer PGMEA, 3 min
Rinse with 2-propanol
Dry with Nitrogen
8
Flood exposure
EV1 , a flood of 8 sec exposure to increase the
curing degree of Su-8 and the adhesion of su-8 to
substrate
9
Hard bake
10
Mold cleaning
11
Electroplating
Ramp to 105' C for 60 min, then cool down
naturally
Plasma etch with 02 and CF 4. Recipe etchcln.rcp on
PlasmaQuest
Electroplating is done immediately after mold
cleaning.
Plating solution Orotemp 24 , Technic Inc.
Frequency 1 KHz, duty cycle 10%
Temprature 450 C to 65.50 C
Current
12
Mold removal
density 0.05 mA/mm2
The wafer is immersed in NMP at 80' C in a wafer
bath for about 60 min
Rinse with 2-propanol
10 sec Piranha dip
136
Appendix B
Matlab scripts
% Matleb scripts for the contact resistance modeling in
Chapter 3 Contact resistance
% 3.5 Computing examples
% 1.
single asperity contact
% Au material properties
R=0.1
% contact resistance requirement ohm
R10=110*10^(-9)
% asperity radius m
E1=77.2*10^9
% Young's modulus Pa
v=0.42
% Poisson's ratio
H=2*10A9
% Brenell Hardness
ro=2.2*10^(-8)
% resistivity ohm.m
000%%%%%%%%%%%%%%%%%0
%%%%%%%%%%%%%%%%%%%%%%%%
E=El/ (2* (1-vA2))
Fn=E*1/(6*RlO)*(ro/R)^ 3
% contact force
alfa=(3/4*Fn/(E*R1OAO .5))A (2/3)
% indentation
AlfaC=(0.3*3.14*H/E)A2*R1O
% critical indentation
P=3/2*Fn/(3.14*RlO*alfa)
% contact pressure
Pm=0 . 6*H
137
Alfal=roA2/(4*RA2*RlO)
% Alfa
>> AlfaC,
plastic deformation
Fnp=0.6*3.14*H*roA2/(4*RA2)
AlfaP=1/2*AlfaC+roA2/(8*RA2*RlO)
Fnl=(0:1:200)*10A(-6);
R1=110*1OA(-9);
% asperity radius
x1=6*Rl*Fnl;
Rsingl=ro*(xl/E)
(-1/3)
R2=220*10^(-9);
% asperity radius
x2=6*R2*Fnl;
Rsing2=ro*(x2/E).
A
(-1/3);
A
(-1/3);
R3=80*10A (9);
x3=6*R3*Fnl;
Rsing3=ro*(x3/E).
% asperity radius
yl=4*Fnl/(0.6*pi*H)
Rpla=ro*yl. A (-0.5);
figure
plot
(1)
(Fn1, Rsing3, Fnl,Rsingl,
xlabel('Contact force
',
Fn1,
Rsing2,
'.-')
N')
ylabel('Contact resistance Ohm')
legend
('R1=80 nm', 'R1=110 nm',
title('Contact
asperity')
resistance
'R1=220
vs contact
nm')
force
for
%-plot (Fn1, Rsing1,Fn1,Rsing2,'--', Fn1, Rsing3,
138
single
figure
plot
(2)
(Fn1, Rsingl,
Fn1, Rpla,'--')
xlabel('Contact force
N')
ylabel('Contact resistance Ohm')
legend
('Elastic model', 'Elastic-plastic model')
title('Contact resistance vs
asperity')
% 2.
contact
force for single
distributed asperities
00000000000000000000000000000000
% 1).
evaluate the value of the two series
%phi=[0.35, 0.45,0.55,0.65,0.85];
phi=0.55 % input from assumption, plastic index
i=1;
% evaluation of the infinite series
for n=0:1:176
fan=factorial(n);
d3n(i)=(-1).^n.*phi.^(-2*n)./(fan.*(2*n+1));
d3nHalf(i)=(-1).^n.*phi.^(2*n).*0.5.An./(fan.*(2*n+l));
i=i+1;
end
sumup=sum (d3n)
sumupHalf=sum(d3nHalf)
% phi =0.2315,
sumup=0.2052;
sumupHalf=0.2910
% phi=0.2 sump=0.1772, sumuoHalf=0.2507
% phi=0.55 sumup=0.4825, sumupHalf=0.6417
% phi=0.65 sumup=0.5590, sumupHalf=0.7137
% phi=0.45 sumup=0.3981, sumupHalf=0.5492
139
% 2).
Contact force and contact resistance
R1m=80*10A(-9);
%
input
from
assumption,
asperity
radius
N=200
asperities
%
input
from
assumption,
number
modified,
separation
of
cl=2*E/(0.6*pi*H);
dl=(phi/cl)^ 2
d2= (Rlm*phi/cl)^2
dev=(dl*d2)A0.5
Dl=dl
D2=d2*N
h=0.02:0.02:4;
%
to
be
normalized by asperity height STD
% proposed model
A=(pi/2)A0.5*exp(-l/(2*phiA2));
B=l/phi*sumup;
C=-l/phi*exp(-l/(2*phi^2)*sumupHalf);
Gc=2*N*d2AO .5./(ro*exp(h))*(A+B+C)
conductance
Rct=l. /Gc;
% Contact
% Contact resistance
Gcl=l./(exp(h)*phi)*(-exp(-l/phi^2)+sumup);
Gc2=exp(-h-l/(2*phiA2))*(pi/2+2AO.5/2*1/phi*exp(1/ (2*phi^2) ) - 2A0.5/2*1/phi*sumupHalf);
Fl=-l/phi^3*exp(-h-1/phiA2)+3/2*Gcl;
F2=(l/(2*phiA2)-l)*exp(-h-1/phi^2);
140
Fnt=4/3*N*E*d2*dl^0.5*F1+1.2*pi*N*H*d2*F2;
Contact force
sepa=h*dev;
%6
% separation
% Greenwood model
GcGW=N./(ro*exp(h))*(pi*d2)^0.5;
RcGW=1./GcGW;
FGW=piA0.5*N*E*d2*d1AO.5./exp(h);
%Rct3_a80=Rct;
%Fnt3_a80=Fnt;
figure
plot
(3)
(h, Fnt)
xlabel('separation')
ylabel('contact force')
figure
plot
(4)
(Fnt, Rct,
FGW, RcGW,
')
'.-
xlabel('Contact force')
ylabel('Contact resistance Ohm
legend
('Elastic-plastic model
title('Contact
resistance
distributed asperities')
figure
plot
'GW model')
vs
seperation
for
(5)
(Fnt, Rct,
Fn1,
Rpla,
xlabel('Contact force,
'--')
N')
ylabel('Contact resistance, Ohm')
legend
('distributed
model,
p lastic
index
0.55',
'single asperity model')
title('Comparison
asperity model')
of
the
141
dist ributed
and
single
figure
plot
(6)
(FGW, RcGW,
'.-')
xlabel('Contact force N')
ylabel('Contact resistance Ohm')
legend
('GW model')
title('Contact
resistance
distributed asperities')
figure
Rct3a,
plot
'--')
vs
contact
Fnt3,
Rct3,
force
for
(7)
(Fnt3_a80,
Rct3_a80,
-',
Fnt3a,
xlabel('Contact force N')
ylabel('Contact resistance Ohm')
legend
220 nm' )
('Asperity 80 nm' ,
title('Contact
resistance
'Asperity 110 nm', 'Asperity
vs
contact
force
for
different asperity sizes')
figure
%6 plot
FGW, RcGW,
(8)
(Fnt2, Rct2,
--
'
)
Fnt3,
Rct3,Fnt4,
Rct4,Fnt5,
Rct5,
xlabel('Contact force N')
ylabel('Contact resistance Ohm')
legend
0.55', 'plastic
('plastic
index
index 0.65', 'plastic
title('Contact
resistance
distributed asperities')
142
0.45',
index
'plastic
index 0.85',
'GW model')
vs
contact
force
for