Mechanical Design and Modeling of
MEMS Thermal Actuators for RF
Applications
by
Dong Yan
A thesis
presented to the University of Waterloo
in fulfillment of the
thesis requirement for the degree of
Master of Applied Science
in
Mechanical Engineering
Waterloo, Ontario, 2002
c
°Dong
Yan, 2002
I hereby declare that I am the sole author of this thesis.
I authorize the University of Waterloo to lend this thesis to other institutions or individuals for
the purpose of scholarly research.
Dong Yan
I authorize the University of Waterloo to reproduce this thesis by photocopying or other means,
in total or in part, at the request of other institutions or individuals for the purpose of scholarly
research.
Dong Yan
ii
The University of Waterloo requires the signatures of all persons using or photocopying this
thesis. Please sign below, and give address and date.
iii
Acknowledgements
First of all, I would like to sincerely thank my supervisors, Dr. Amir Khajepour and Dr.
Raafat Mansour, for all they have done for me. Their support, knowledge, advice, patience and
troubleshooting skills made my research achievement possible.
I also would like to thank my friends and colleagues. In alphabetic order, they are Saeed
Behzadipour, David Gairns, Arash Narimani, Tong Qu, Neil Sarkar, Aden Seaman, Yu shen,
Ehsan Toyserkani, Wilson R. Wang, Huizhong Yang. Their friendship and support made my
life more colorful and enjoyable.
The financial support of this project was provided by Natural Sciences and Engineering
Research Council of Canada (NSERC) and COM DEV International Ltd. Without their continuous support, this project would not have been possible.
Finally, I would like to express my deepest appreciation to my family. Their endless support
and encouragement made all of this possible.
iv
Abstract
Micro electro mechanical system (MEMS) technology has shown its bright future in many
different fields, especially in space and radio frequency (RF) systems. By using MEMS technology, we can greatly shrink the cost and the footprint of RF circuits since all the off-chip
components such as inductors and capacitors can be fabricated and integrated into a whole
single chip at one time. Our research is directed by the purpose of developing more powerful
RF components.
This thesis describes an analytical model of a two-hot-arm horizontal thermal actuator at the
beginning. The experimental results are provided to prove the accuracy of the analytical model.
It then documents the design and model of a bidirectional vertical thermal actuator. This new
novel vertical thermal actuator has the ability to bend up and down without any modification,
so it is supposed to have twice the amount of deflection than the traditional vertical thermal
R
°
actuator. The numerical simulation is done by using commercial software Coventorware . It
shows a good agreement with the analytical result. At the end, this thesis documents a new
design of multiport switch with a latching mechanism and an improvement of tunable capacitor
by using bidirectional vertical thermal actuators.
v
Contents
1 Introduction
1
1.1
Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2
Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.3
Thesis overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
2 Background
8
2.1
Introduction to MEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2
MEMS actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3
2.4
8
2.2.1
Electrostatic actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.2
Thermal actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.3
Other actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Micromachining techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.1
Bulk micromachining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.2
Wafer bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.3
LIGA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.4
Surface micromachining . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.5
Flip chip technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Micromachining foundry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3 Two-hot-Arm Horizontal Thermal Actuator
25
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2
Electrothermal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2.1
Analytical solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
vi
3.2.2
3.3
Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Mechanical analysis
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.1
Analytical solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.2
Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4
Fabrication process and experiments . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.5
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4 Bidirectional Vertical Thermal Actuators
49
4.1
Mechanical design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2
Electrothermal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.3
4.4
4.2.1
Analytical solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2.2
Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Mechanical analysis
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.3.1
Analytical solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.3.2
Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5 RF Applications of Horizontal and Vertical Thermal Actuators
69
5.1
Multiport switch with a latching mechanism . . . . . . . . . . . . . . . . . . . . . 69
5.2
Tunable capacitor with U-shaped vertical thermal actuators . . . . . . . . . . . . 73
5.3
Fabrication and future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6 Conclusions
76
vii
List of Tables
2.1
MUMPs process layers and their Properties . . . . . . . . . . . . . . . . . . . . . 23
3.1
Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2
Geometrical data of the two-hot-arm thermal acutator . . . . . . . . . . . . . . . 33
4.1
Geometrical data of the U-shaped vertical thermal acutator . . . . . . . . . . . . 58
viii
List of Figures
2-1 The schematic view of MEMS chip [1] . . . . . . . . . . . . . . . . . . . . .
9
2-2 The schematic diagram of electrostatic microactuator . . . . . . . . . . . 11
2-3 (a) Comb-drive electrostatic microactuator. [2] (b) electrostatic micromotor [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2-4 The schematic diagram of thermal pneumatic microactuator . . . . . . . 13
2-5 The thermal bimetallic microactuator with the cantilever prototype . . 13
2-6 Various Bulk-micromachining Structures[3] . . . . . . . . . . . . . . . . . . 15
2-7 the schematic diagram of LIGA process [3] . . . . . . . . . . . . . . . . . . 17
2-8 Processing steps of typical surface micromachining [3]. . . . . . . . . . . 18
2-9 The schematic diagram of flip chip process [4] . . . . . . . . . . . . . . . . 21
2-10 Cross section of MEMS motor fabricated by MUMPs [5] . . . . . . . . . 22
2-11 Cross section of MEMS motor after releasing process [5] . . . . . . . . . 24
3-1 A traditional thermal actuator (one hot arm) . . . . . . . . . . . . . . . . 26
3-2 Schematic diagram of two-hot-arm thermal actuator . . . . . . . . . . . . 26
3-3 (a) Schematic top view of two-hot arm thermal actuator. (b) Simplified one dimensional coordinate system. . . . . . . . . . . . . . . . . . . . . 27
3-4 The schematic cross section of the actuator for thermal analysis . . . . 28
3-5 The schematic diagram of boundary conditions . . . . . . . . . . . . . . . 31
3-6 The analytical result of temperature distribution along the outer and
inner hot arms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3-7 The numerical result of temperatue distribution of the two-hot arm
thermal actuator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
ix
3-8 Maximum temperature as a function of input voltage: Comparison
between analytical and simulation results. . . . . . . . . . . . . . . . . . . 35
3-9 (a) The plane frame structure simplified for the thermal actuator with
six redundants. (b) The bending moment of the outer hot arm due to
the virtual force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3-10 (a) The bending moment diagram of a unit force in the deflection
direction (b) The bending moment diagram of a unit force in the
force direction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3-11 Deflection of the actuator tip as a function of input voltage . . . . . . . 41
3-12 Numerical result of the deflection of two-hot-arm thermal actuator
with 10v input voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3-13 Deflection meter coupled to a two-hot-arm thermal actuator . . . . . . 42
3-14 Overview of the whole chip after HF release. . . . . . . . . . . . . . . . . . 43
3-15 Experiment equipment for measuring the deflection of thermal actuators 44
3-16 Comparison of experimental result with the analytical and numerical
results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3-17 The touching of the outer and inner hot arms at high actuating voltage 45
3-18 A curve found in the inner hot arm as seen in SEM . . . . . . . . . . . . 46
3-19 Two modes of the traditional thermal actuator operation [6]. . . . . . . 47
3-20 Back bending of the two-hot-arm thermal actuator . . . . . . . . . . . . . 47
3-21 Over etching of the teeth of the deflection meter. . . . . . . . . . . . . . . 48
4-1 3D schematic view of a vertical thermal actuator showing a cross section through the hot and cold arm.[7] . . . . . . . . . . . . . . . . . . . . . 50
4-2 3D View of the U-shaped vertical thermal actuator . . . . . . . . . . . . 51
4-3 2D schematic top view of the U-shape VTA . . . . . . . . . . . . . . . . . 52
4-4 Simplified one dimensional coordinate system . . . . . . . . . . . . . . . . 53
4-5 Schematic cross section of the VTA for thermal analysis . . . . . . . . . 53
4-6 3D schematic diagram of the element 3 with the cross section . . . . . . 55
4-7 (a) The boundary conditions of temperature continuity. (b) The boundary conditions of the rate of the heat conduction . . . . . . . . . . . . . . 56
x
4-8 Temperature distribution along the top layer of VTA . . . . . . . . . . . 59
4-9 Numerical result of temperature distribution of the U-shaped VTA
R
°
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
using Coventorware
4-10 Comparison of the maximum temperature as a function of input voltage. 60
4-11 (a) The schematic 3-D view of U-shaped VTA, (b) Four bar linkage
representing for the U-shaped VTA. . . . . . . . . . . . . . . . . . . . . . . 62
4-12 (a) The hinged rigid frame for mechanical analysis, (b) schematic of
the spring coefficient analysis in y direction.
(c) schematic of the
deflection of the U-shape VTA. . . . . . . . . . . . . . . . . . . . . . . . . . 63
4-13 (a)The bending moment of the top layer long beam due to the virtual
force, (b) The bending moment of the top layer long beam due to the
thermal expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4-14 The hinged rigid frame with three deflection directions . . . . . . . . . . 65
4-15 (a) The deflection without torsional springs. (b) the deflection with
two torsional springs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4-16 Deflection of the tip of the U-shaped vertical thermal actuator as a
function of input voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5-1 (a) Schematic of latching mechanism in 3D view. (b) Detail of the
latching mechanism.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5-2 (a) Top view of the multiport switch. (b) Closed-up of the multiport
switch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5-3 Top view of the tunable capacitor with U-shaped vertical thermal
actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5-4 Schematic diagram of S-shaped connection and detail of the connection. 75
xi
Chapter 1
Introduction
1.1
Motivation
The greatest promise of microelectromechanical systems (MEMS) lies in the ability to produce
mechanical motion on a small scale. Such devices are typically low power and fast, taking advantage of such microscale phenomena as strong electrostatic forces and rapid thermal responses.
MEMS-based sensors have been widely deployed and commercialized. MEMS technologies also
show prospective applications in optics, transportation aerospace, robotics, chemical analysis
systems, biotechnologies, medical engineering and microscopy using scanned micro probes [8].
The explosive growth of data traffic such as the internet has produced a pressing need for
large capacity communication network. Satellites and radio frequency (RF) systems are the
important components for the communication network. The emergence of on-chip, discrete RF
MEMS has attached the attention of the wireless industry that is interested in smart phones,
Bluetooth and so on. MEMS-based RF systems may play a significant role in making such
products possible. By using MEMS-based RF components, the footprint of RF circuits can be
greatly shrunk by including all the off-chip components such as inductors and capacitors into
on-chip components. At the same time, the performance can also be increased by reducing
signal delay time and noise effects through the applications of on-chip components.
These outstanding advantages and promising applications of MEMS based RF components
become a driving motive force for many MEMS designers, including the author of this thesis,
to concentrate their research efforts on designing novel RF MEMS devices. However one of
1
the fundamental problems that most of MEMS designers have to face is the limitation of the
access to fabrication foundries. Although more and more clean rooms have been founded with
the financial support of government and industries, there is still a solid community of MEMS
researchers who do not have their own clean room. Fortunately, those MEMS researchers who
do not have their own clean room still can manage to do their research with the facilities of a
number of commercially available fabrication foundries. Cost and time are other issues for most
MEMS researchers. Modeling MEMS devices is one solution to these issues. Before any MEMS
design is submitted fabrication, MEMS researchers should be able to grasp the properties of the
MEMS designs as much as possible through modeling. Accurate models of MEMS devices also
can release MEMS researchers’ work on device level design and allow them to focus on system
level design. In this thesis, research effort is directed at these two motivations: the excellent
properties of MEMS based RF components and the crucial need for the accurate modeling of
MEMS devices.
1.2
Literature review
The first impressive review of the applications of silicon as mechanical material, more than electronic material, was published by Kurt Petersen in 1982 [9]. Almost at the same time, Howe
[10] first proved the evolution of a very useful method to build micromechanical elements using
technologies that were developed first to build microelectronic devices for the integrated circuits
in seminal work done in 1982. R. T. Howe demonstrated techniques to fabricate microbeams
from polycrystalline silicon (polysilicon) films [10]. With the encouragement of this demonstration, Howe built the first prototype polysilicon MEMS, a chemical vapor sensor which was
a fully integrated micromechanical and microelectronic system [11]. With the development of
the micromachining techniques, many complex devices have been produced and some of them
are already commercialized. An impressive example of a commercial MEMS that makes use
of surface micromachining to build a fully integrated accelerometer is the AD-XL50 microaccelerometer produced by Analog Devices Inc. for use in automobile airbag deployment systems
[12].
The impact of MEMS is very wide and deep. The feasibility of MEMS has been proven
2
in several markets including the automotive industry. MEMS technology has also received the
attention of the wireless industry because of its advantages such as low cost, higher performance,
reduced size and weight, and increased reliability. Therefore, a tremendous research effort
has focused on the development of MEMS based components in the wireless and microwave
technology area. The tunable capacitor (or variable capacitor) is one of the most important and
active branches in the area of applying MEMS technology to passive and active components,
such as inductors, switches and filters. According to the actuating mechanism, a tunable
capacitor can be categorized into two types: electrostatic and electro-thermal.
In the category of electrostatic actuating mechanisms, tunable capacitors take two forms:
parallel plate and interdigitated (or comb-drive). In the parallel plate approach, the top plate is
suspended in a certain distance from the bottom plate by suspension springs, and this distance
is used to vary in response to the electrostatic force between the plates induced by an applied
voltage. Young, et al [13] reported a tunable capacitor designed for monolithic low-noise voltagecontrolled oscillators (VCOS) . In this work, the new tunable capacitor consists of a thin sheet
of aluminum suspended in air approximately 1.5 µm above the substrate. A DC voltage results
in an electrostatic force pulling the movable plate closer to the substrate, hence increasing the
capacitance. Theoretically, a tuning range of up to 50% can be achieved. The required tuning
voltage depends on the suspension dimension. Experimental work has also been done and the
result shows that the tuning range is 16%. The conclusion of this work was also highlighted
that the aluminum micromachined tunable capacitors constitute an attractive alternative to
conventional varactor diodes as the tuning element in VCOS for personal communication devices
because this technology requires no changes of the underlying IC process.
In order to improve the tuning range of parallel plate tunable capacitors, Aleksander Dec
and Ken Suyama have documented two new tunable capacitors in [14], and [15]. In [14], Dec et
al presented two new tunable capacitors with two and three plates respectively. Polysilicon was
chosen as the structural material for tunable capacitors due to its good mechanical properties.
Several tunable capacitors have been fabricated by the standard polysilicon surface micromachining process, which features three layers of polysilicon and one gold layer. For the two plate
tunable capacitor, the fixed plate was anchored under the suspended plate; while with the three
plate tunable capacitor, the suspended plate is placed in the middle of the three plates. The
3
measurements of the tuning range of the two and three plates tunable capacitors are 1.5:1 and
1.87:1, respectively. These two designs have greatly increased the tuning range of the tunable
capacitor with a slight modification of the fabrication process. Another new tunable capacitor
with one suspended top plate and two fixed bottom plates has been proposed by Jun Zou et al
[16]. One of the two fixed plates and the top plate form a variable capacitor, where as the other
fixed plate and the top plate are used to provide electrostatic actuation for capacitance tuning.
The controllable tuning range of 68% has been achieved experimentally. Its fabrication process
is also completely compatible with the existing standard IC fabrication technology. Instead
of polysilicon and aluminum, other materials such as the dielectric material [17] can be used.
Instead of the parallel plate style tunable capacitor, J. Jason Yao et al have designed, fabricated
and experientially tested an interdigitated “comb” structure tunable capacitor [17], [18]. With
the special fabrication process, the continuous and controllable tuning range is up to 300%.
A tunable capacitor can also be built using an electro-thermal actuating mechanism. Compared to electrostatic, tunable capacitors actuated by thermal actuators have several advantages
[19]:
• Avoiding the static charges collecting on the plates
• Improvement in the reliability of tuning
• Approximately linear capacitance tuning
• Lower driving voltages
A flexible integration of MEMS tunable capacitors can also be obtained by using flip-chip
transfer technology. After flip chip transformation, the low resistivity silicon substrate, which
has high loss at high frequencies, can be removed to improve the performance of the tunable
capacitor. The tunable capacitor with an electro-thermal actuator has some disadvantages such
as lower tuning and more space requirements.
A series mounted MEMS tunable capacitor with an electro-thermal actuator was reported
by Zhiping Feng et al [19]. The electro-thermal actuator has been used to drive the top plate
of the tunable capacitor to move vertically (the vertical direction is defined as the direction
perpendicular to the substrate). The MEMS structure was mounted on the alumina substrate
4
by using flip chip technology. The tuning range of this type capacitor was reported to be 2:1. In
[20], Huey D. Wu et al have presented another tunable capacitor with a thermal actuator array
that can be actuated horizontally (the horizontal direction is defined as the direction parallel
to the substrate). Experiments have shown two interesting observations. The first is the range
of the capacitance change, which achieved a very impressive 2.6 pF. The corresponding gap
variation should be from 2 to 0.2 µm. The second observation is the excellent repeatability and
resolution of the capacitance-vs-voltage relationship. Small voltage changes such as 0.1 Volt
result in visible capacitance variations.
These two inspiring observations obtained more researchers’ attention. Kevin F. Harsh et al
improved the tunable capacitor by replacing the thermal actuator array with vertical thermal
actuators that have the motion perpendicular to the substrate [4]. The advantages of the vertical
thermal actuator are the larger deflection in the direction perpendicular to the substrate and
more robust for flip-chip transfer process. The capacitor can be tuned from approximately 0.5
to 3.5 pF by using the control voltage less than 1 V.
Obviously, the performance of a thermal actuator becomes a key factor for the performance
of a tunable capacitor Compared with widely-used electrostatic forces, thermal expansion can
provide larger forces and it is also easier to control. However a single-material actuator based
solely on the thermal expansion of a beam would have a small deflection relative to the size
of the actuator. Differential expansion of a laminate made of two materials of unequal thermal expansion coefficients, the bimetallic or bimorph, [21] can be used to amplify deflection.
Horizontal thermal actuators, one of the most famous thermal actuators designed by John H.
Comtois and Victor M. Bright, takes advantage of the shape to create a “bimetallic” effect
using a single material [22]. The current passes through all the structure when the thermal
actuator is activated. Internal Joule heating causes elastic structures to expand and generate
deflection when the structures are mechanically constrained. Such actuators were also reported
in [6], [23], [24].
Vertical thermal actuators were also mentioned in [22]. The actuation theory of a vertical
thermal actuator is similar to that of a horizontal actuator. The only difference is that the
current passes through two layers in the case of the vertical thermal actuator instead of one layer
in horizontal actuator. The structures are mechanically constrained in two layers, not in one
5
layer like the horizontal thermal actuator. So the different thermal expansion of the structures
generates the vertical motion out of the plane. Based on the same idea, some modifications of
the vertical thermal actuator have been well documented in [25], [26], [4].
Modeling of the thermal actuator began with the horizontal thermal actuator in [23]. Finite
element method also has been employed to analysis the horizontal thermal actuator in [23], [27].
The analytical model of the thermal actuator was presented by Qing-An Huang and Neville Ka
Shek Lee in [28] , [24]. In the electro thermal analysis, they simplified the thermal analysis of
the horizontal thermal actuator as one dimensional problem. Then, force method and virtual
work have been used to solve thermal mechanical problem. The analytical result is in good
agreement with the experimental results.
1.3
Thesis overview
The objective of this thesis consists of two main parts: the analysis of a two-hot arm horizontal
and vertical thermal actuator; and an improved design of a tunable capacitor and multiport switch with latching mechanism for radio frequency (RF) applications. Chapter 1 briefly
clarifies the motivation of this thesis work and takes a look at the previous research in the area
of tunable capacitor and thermal actuator.
The definition of MEMS is given in Chapter 2. Chapter 2 also explains and compares
different MEMS actuators, followed by a discussion of the basic fabrication techniques and
their limitations, which are the constrains for the design and analysis of the MEMS devices.
Multi Users MEMS Process (MUMPs) is highlighted in Chapter 2 because all of the devices in
this thesis are fabricated using MUMPs.
Chapter 3 documents the analytical solution of the two-hot arm horizontal thermal actuator.
Numerical and analytical results are also provided for comparisons. In Chapter 4, a new and
novel vertical thermal actuator is designed and modeled. The difference of the new vertical
thermal actuator from the traditional vertical thermal actuator is that the new vertical thermal
actuator can be bent in two directions, up and down. This allows the actuator to have twice
the deflection compared to traditional vertical actuators. By applying a similar approach, the
analytical solution to the vertical thermal actuator is also obtained. The analytical results are
6
also in good agreement with the numerical results.
Based on the analytical modeling of the two types of thermal actuators, two RF components,
a tunable capacitor and a multi-port switch are designed in Chapter 5. The latching mechanism
is also explained and applied to this type of switch.
Chapter 6 concludes the thesis. The key findings are highlighted and recommendations for
the future work in this area are presented.
7
Chapter 2
Background
2.1
Introduction to MEMS
With the advent of integrated circuit (IC) fabrication technology in the 1960s, human being’s
ability to make physically small objects received a big progress. Since the circuits still perform
the same function when they are scaled down by factors, competition occurred to develop ways
of integrating more and more circuits on a semiconductor wafer. From the economic side, that
is beneficial since the greater the number of circuits, the greater the profits. Such an exemplary
success in mass production as appeared in IC industry has been achieved, and researchers
are motivated to apply the concepts of integrated electronics manufacturing to mechanics,
optics and fluidics with the hope of acquiring the same improvements in performance and cost
effectiveness experienced by the semiconductor industry. That resulted in the advent of MEMS
technologies
MEMS is the acronym for Microelectromechanical Systems. In Europe, it is also called Microsystems. By now, there is still no generally accepted definition for MEMS. Some researchers
depict it as the integration of miniaturized sensors, actuators and signal processing units, enabling the whole system to sense, decide and react [3]. Other MEMS engineers consider a
typical MEMS device as [29] :
• A device that consists of a micromachine and microelectronics, where the micromachines
are controlled by microelectronics. Quite often, microsensors are involved in the control
8
system by providing signals to the microelectronics.
• A device that is fabricated using micromaching technology and an integrated circuit (IC)
process, i.e., technologies of batch fabrication.
• A device that is integratedly born, without individual assembly steps for the main parts
of the device except for the steps required for packaging.
More generally speaking, MEMS is simultaneously a toolbox, a physical product and a
methodology all in one [30]. As the name implies, “Micro” establishes the size definition,
“Electro” intimates that either electricity or electronics is involved and “mechanical” infers
that some moving parts should be included. From the physical point view, MEMS is usually
the integration of mechanical elements and electronics on a common silicon wafer using microfabrication technologies. The electronics can be fabricated by IC process sequence (e.g., CMOS)
and the mechanical elements are constructed by micromachining methods that are compatible
with the IC fabrication process. Figure 2-1 depicts MEMS characteristics. The sensors and
Mechanical Elements
Electronics Elements
Figure 2-1: The schematic view of MEMS chip [1]
actuators can be made of mechanical elements, and signal processing and control units can be
built by using electronics circuits. So, the whole system can be integrated on a single chip without any extra assembly process. The motivation for integrating the whole system on a single
chip is miniaturization and parallel processing which leads to inexpensive fabrication in large
quantities. It also has the ability to make devices with the functions that cannot be realized
with traditional technologies.
9
In the beginning of 1990s, MEMS emerged with the development of IC fabrication processes,
in which sensors, actuators and control functions are cofabricated in silicon [31]. With the strong
financial support from both governments and industries, MEMS research has achieved remarkable progress. MEMS technology has proven its outstanding and revolutionary capability in
many different fields. There are numerous MEMS applications that have been commercialized
such as microaccelerometers, microsensors, inkjet printer head, micromirrors for projection, etc.
In addition to these less-integrated MEMS devices, more complicated MEMS applications also
have been proposed and demonstrated for their concepts and possibilities in such varied fields
as biomedical, chemical analysis, microfluidics, data storage, display, optics wireless communications etc. [32], [33]. With more and more energy and effort injected, some new branches
of MEMS technologies have appeared such as microoptoelectromechanical systems (MOEMS)
and micrototal analysis systems (µTAS) because of their potential applications’ market.
MEMS technologies do face a lot of challenges. First of all, from the design point view,
MEMS computer aided design (CAD) software packages are still very time consuming and not
powerful enough to include all the real factors that affect the operation of MEMS devices at one
time. The complexity of MEMS design is also a big issue for MEMS designers. Typical MEMS
devices, even simple ones, manipulate energy in several physics domains. That requires that
the MEMS designer must understand and find ways to control complex interactions between
these domains. Secondly, in the fabrication side view, the cost issue for a state-of-the-art silicon
foundry is also a barrier most MEMS designers have to face. High initial investment limits the
speed of the MEMS development. Packaging can also affect the performance of MEMS devices
and becomes one of the most fundamental problems in MEMS research. Due to the diversity of
MEMS devices, each new MEMS device almost needs a totally new and particular packaging
method.
2.2
MEMS actuators
A microactuator is the key device for the MEMS to perform physical functions. They are maybe
required to drive the resonator to oscillate at their resonant frequencies. They could be needed
to produce the mechanical output based on the particular microsystems: they maybe drive
10
micromirrors as a scanner or a switch; they also could actuate micropumps for microfluidic
systems. Because of the scaling consideration, the electromagnetic force that is most commonly
used in macro actuators is not the only driving force for microactuators [32].With the efforts of
researchers, more and more different actuation principles, such as electrostatic force, thermal
expansion, piezoelectric force, and shape memory alloys, have been used to design various
structures for specific applications. This results in the fact that more and more different,
powerful and fancy microactuators have been designed, fabricated, and applied [34]. A brief
introduction is given to the microactuators according to their different actuation principles.
2.2.1
Electrostatic actuators
For a simple parallel-plate style electrostatic microactuator, the electrostatic force is created by
applying the voltage across the two plates. The schematic diagram of this kind of electrostatic
microactuator is shown in Figure 2-2. Usually the two plates are separate by dielectric material
+ + + + + + +
V
- - - - - - - -
Figure 2-2: The schematic diagram of electrostatic microactuator
such as air. The force generated by applying a voltage can be given by
F =
V 2 ∂U
2∂d
where F is the electrostatic force, V is the applying voltage, d is the distance between the two
plates, U is the energy stored in the two-plate capacitor, which can be obtained by
CV 2
2 ,
and
C is the capacitance.
The electrostatic microactuator is one of the most popular microactuators in MEMS applications. The well-known electrostatic microactuators include comb-drive microactuators [35],
11
and wobble micromotors [36]. Figure 2-3 shows scanning electron microscope (SEM) pictures
of these two electrostatic microactuators.
(b)
(a)
Figure 2-3: (a) Comb-drive electrostatic microactuator. [2] (b) electrostatic micromotor [2]
From the fabrication point of view, the electrostatic microactuator can be easily integrated
on a chip because all fabrication processes are compatible with traditional IC fabrication. Since
there is no current consumption during actuation, the electrostatic microactuator consumes no
power. But in order to have a large deflection or force, high actuating voltage is needed. Also,
hysteresis makes the electrostatic microactuator hard to control.
2.2.2
Thermal actuators
Thermal actuation has been extensively employed in MEMS. It includes a broad spectrum
of principles such as thermal pneumatic, shape memory alloy (SMA) effect, bimetal effect,
mechanical thermal expansion, etc. [31]. The thermal pneumatic microactuator uses thermal
expansion of a gas or liquid or the phase change between liquid and gas to create the actuation.
As shown in Figure 2-4, a thermal pneumatic actuator is made of a cavity that contains a
volume of fluid with a thin membrane as one wall. Current passed through a heating resistor
causes the liquid in the cavity to expand and deform the membrane.
Shape memory alloy effect occurs in some alloys in which a reversible thermal mechanical
transformation of the atomic structure of the metal happens at a certain temperature. At low
temperature, the SMA is kept at the desired deformed shape. When the temperature rises
above a threshold value, the deformed SMA is transformed back to the original shape. A
12
Liquid
Heat
element
Cavity
Figure 2-4: The schematic diagram of thermal pneumatic microactuator
thermal bimetallic microactuator consists of two different materials that are layered together.
Figure 2-5 shows a cantilever bimetallic structure. When it is heated, a deflection is generated
by the different thermal expansion between the two materials. The more different the two
materials’ thermal expansion coefficients, the more deflection is generated. The principle of the
Metal layer
Elastic layer
Figure 2-5: The thermal bimetallic microactuator with the cantilever prototype
mechanical thermal expansion microactuator is similar to that of the bimetallic microactuator.
The only difference is that the mechanical thermal expansion microactuators are made of the
same material. The operation procedure of mechanical thermal expansion microactuators will
be explained in detail in Chapter 3 and 4.
Thermal actuators can generate relatively large force and displacement at low actuating
voltage. The deflection can linearly increase as the control voltage is increased within a large
13
range. Mechanical thermal expansion actuator and bimetallic actuator also can be integrated
in a chip easily. However the high power consumption and low switching frequency are concerns
for applications of thermal actuators.
2.2.3
Other actuators
Other actuators such as magnetic actuators and piezoelectric actuators have also been developed
for some special applications [37], [38]. Microactuators are often fabricated by electroplating
techniques, using nickel or its compositions. Since nickel is a ferromagnetic material, it can be
used in actuators by using the electromagnetic effect.
The principle of the piezoelectric actuator is based on the inverse piezoelectric effect. When
a voltage is applied to an asymmetric crystal lattice, the material will be deformed in a certain
direction. Although these two actuators can provide large forces, the fabrication process needs
to be further developed.
2.3
Micromachining techniques
The motivation for micromachining MEMS devices is the same as for integrated circuits: microfabrication allows miniaturization and parallel processing which leads to inexpensive fabrication
in large quantities. This can be used to make cheap products, large arrays, integrated systems
and devices with the functions that cannot be realized with traditional technologies.
Micromachining is the set of design and fabrication tools that precisely machine and form
structures and elements at a scale well below the limits of human perceptive capability−the
microscale. Micromachining is the underlying foundation of MEMS fabrication, and a key
factor for MEMS processes. In general, micromachining is such a process that selectively
etches away parts of the silicon wafer or adds new structural layers to form the mechanical and
electromechanical devices.
The well-established integrated circuit (IC) industry played an important role in fostering
an environment suitable for the development and growth of micromachining technologies. Many
tools and processes used in the design and micromachining of MEMS products are borrowed
from the IC technology. Bulk and surface micromachining are two basic and major microma-
14
chining techniques. Wafer bonding can be used as the post process of bulk micromachining.
LIGA (lithographe, galvanoformung, abformung) has been used in high-aspect ratio applications. In some special applications, the substrate is required to have some particular properties
which silicon does not have. The flip chip technique is applied to solve this problem. The goal
of this section is to briefly introduce these basic micromachining techniques.
2.3.1
Bulk micromachining
The bulk micromachining technique is one of the most popular micromachining techniques.
The term bulkmicromachining comes from the fact that this type of micromachining is used to
realize micromechanical structures within the bulk of a single crystal silicon wafer by selectively
removing (‘etching’) wafer material. Bulk micromachining allows selective removal of significant
amounts of silicon from a substrate to form three dimensional mechanical structures such as
membranes, trench holes and so on (Figure 2-6). The crystal orientation of the wafer plays a
Figure 2-6: Various Bulk-micromachining Structures[3]
decisive role. Different etchants such as solutions of potassium hydroxide (KOH), hydrazinewater have different etching rates in different crystal orientations of silicon [9], [39]. A high
aspect ratio can also be reached for micromechanical components that can be formed directly
15
from the silicon wafer.
Although bulk micromachining is a mature technique, it has some fundamental limitations.
For instance, the wafer’s crystallographic planes determine the maximum obtainable aspect
ratios. The higher aspect ratios can requires larger sizes as compared with other micromachining
techniques. Also, it is difficult to get complex structures from bulk micromachining. One
approach to solve this problem is the wafer bonding technique.
2.3.2
Wafer bonding
Bulk micromachining has the limitation in forming complex three dimensional microstructures
in a monolithic format. One of the solutions is through the separate fabrication of the various elements of a complex system followed by subsequently assembling them. Wafer-to-wafer
bonding is a technique that enables virtually seamless integration of multiple wafers. Wafer
bonding for MEMS can be categorized into three major types: anodic bonding, intermediatelayer bonding-assisted bonding and direct bonding [31].
Anodic bonding is usually established between a sodium glass and silicon for MEMS. A
voltage is applied between the glass and silicon, and at the same time, the heater also provides
the bonding temperature around 180~500 0 C. During the bonding process, a new strong and
hermetic chemical bond is formed between the glass and silicon. Intermediate layer assisted
bonding requires an intermediate layer that can be metal, polymer, solders, glass, etc., to fulfill
the bonding between wafers [40]. Direct bonding is also called silicon fusion bonding, which is
used for silicon wafer to silicon wafer bonding. This type of bonding is based on the chemical
reaction between OH-groups present at the surface of native silicon or grown oxides covering
the wafers [41].
2.3.3
LIGA
With the development of the MEMS technologies, complex microstructures that are thick and
three dimensional are required. Therefore, research and effort of micromachining techniques
are directed towards achieving high aspect ratio and three dimensional devices. LIGA process
is one of those micromachining techniques.
LIGA is an acronym for lithography, electroforming and micromolding (in German, litho16
graphe, galvanoformung, abformung). The LIGA process is a technique for fabrication of
three-dimensional microstructures with high aspect ratios having heights of several hundred
micrometers, which is not possible with silicon-based micromachining techniques. With the
LIGA process it is possible to make more complex microstructures and to work in the third
dimension. Different plastics, metal ceramics or combinations of these can be used in connection with the LIGA process in order to produce difficult and complex structures. A schematic
diagram of the LIGA process is shown in Figure2-7.
Figure 2-7: the schematic diagram of LIGA process [3]
2.3.4
Surface micromachining
Unlike bulk micromachining, surface micromachining does not remove material from the bulk
silicon, but constructs structures on the surface of the silicon wafer by adding (“depositing”)
thin films. A thin film is deposited wherever either an open area or a free-standing mechanical
structure is desired, is called a sacrificial layer. The thin film out of which the free-standing
structure is made, is called the structure layer. Finally the given mechanical structure is defined
through removing the sacrificial layer and releasing the structure layer (Figure 2-8).
Surface micromachining requires a compatible set of structural materials, sacrificial materials and chemical ethants. First of all, these materials have to be suitable for the application.
Then, for the structure materials, they must have good mechanical properties such as high yield
17
Figure 2-8: Processing steps of typical surface micromachining [3].
18
and fracture stress, minimal creep and fatigue, also good wear resistance. The sacrificial materials also need good mechanical properties in order to prevent the devices from the fabrication
process. The etchants have to have excellent etch selectivity, which means they have to etch
the sacrificial materials quickly without affecting the structure materials.
The dimensions of surface micromachined structures can be several orders of magnitude
smaller than bulk micromachined structures. The surface micromachined devices are also very
easy to integrate in IC circuits since the IC circuits are also made of the silicon wafer. As
its name implies, surface micromachined devices are usually planar structures. The assembly
process has to be added to build three dimensional devices.
2.3.5
Flip chip technique
Traditionally, flip chip technology is defined as mounting the chip to a substrate with any kind
of interconnect materials and methods (e.g., fluxless solder bumps, tape-automated bonding
(TAB), wire interconnects, conductive polymers, anisotropic conductive adhesives, metallurgy
bumps, compliant bumps, and pressure contacts), as long as the chip surface (active area)
is facing the substrate [42]. Flip chip components are predominantly semiconductor devices;
however, with the development of flip chip technology, MEMS devices are also beginning to
be used in flip chip form. The boom in flip chip technologies results not only from flip chip’s
advantages in size, performance, flexibility, reliability and cost over other technologies, but also
from the widening availability of flip chip materials, equipment and devices. Using flip chip
technologies in MEMS devices, performances can be greatly improved because of the following
advantages:
• Smallest size: eliminating the packages and bond wires reduces the required area.
• Highest electrical performance: eliminating bond wires reduces the delaying inductance
and capacitance of the connection. (The inductance of a single solder bump is less than
0.05nH, compared to 1nH for a 125-um-long and 25-um-diameter wire [30])
• Greatest I/O density: unlike wire bonding which requires that bond pads are positioned
on the periphery of the die to avoid crossing wires, flip chip allows the placement of bond
pads over the entire die.
19
• Most rugged: flip chips are mechanically the most rugged interconnection method because
they are solid little blocks of cured epoxy when completed with an adhesive underfill.
Besides these general properties, flip chip technologies are attractive to the MEMS industry
because of their abilities to integrate a system on a chip through packaging a number of different
dies on a single substrate. One of the most attractive features of any MEMS fabrication service is
the number of structural layers available to MEMS designers. Most MEMS fabrication processes
have a limited number of structure layers because of time and cost issues. The more structure
layers the process has, the longer time and more expensive the process needs. One of the most
popular MEMS commercial foundries, Muti-User MEMS Processes (MUMPs), is only a threelayer surface micromachining polysilicon process [5]. It is the bottleneck for MEMS designers
to design more complex structures. As one solution, flip chip technologies can give designers
more room and more releasable layers to construct their designs. Flip chip technologies also
can transfer MEMS devices to other substrates. This technique can be used to produce highly
advanced micromechanical systems that are better suited to radio frequency (RF), microwave,
or optical applications where specific material properties or additional structural layers are fatal
[4]. Figure 2-9 illustrates the flip chip technique.The process starts with an unreleased MEMS
device; gold transfer bumps are placed on all the transfer pads and one anchor pad. The transfer
pads are only connected to the host substrate with the sacrificial SiO2 layer. When the SiO2
layer is dissolved in hydrofluoric acid (HF), the transfer pads and thus the MEMS devices are
completely disconnected from the host substrate. Because of permanent connection to the host
substrate, the anchor not only prevents the substrate from contacting the device after release,
but also suspends the substrate to act as a shield during the release and drying process. Before
bonding the MEMS devices to other substrates, the gold bumps on the MEMS host substrate
are pressed against a smooth glass substrate. This pressing step is required to flatten any
trailing wires from the top of the bump left by the wire-bonding machine. In addition, pressing
the bumps provides better planarity across the bumps during the actual bonding. Then the
entire structure is flip chip bonded to a target substrate. The silicon substrate is anchored at
an anchor bump. Once released, the substrate can be removed sagely by using clamps to break
the anchor without damage to the device. After bonding and releasing, the flip chip devices
are rinsed in methanol to displace the HF in order to prevent HF further etching from within
20
Figure 2-9: The schematic diagram of flip chip process [4]
the devices. After several minutes in a methanol rinse, the devices are super-critically dried in
a special drying chamber that uses liquid CO2 to displace the methanol. Without this step,
the evaporating methanol would pull devices downward into contact with the substrate and
destroy the devices. After these steps, the MEMS device is transferred to another substrate
successfully.
2.4
Micromachining foundry
The Multi-user MEMS processes or MUMPs is a three-layer polysilicon surface micromachining
process derived from work performed at the Berkeley Sensors and Actuators Center (BSAC)
at the University of California in the late 80’s and early 90’s. It is a commercial program
that provides the international industrial, governmental and academic communities with costeffective, proof-of concept surface micromachining fabrication [5]. This process has the general
features of a standard surface micromachining process as follows:
• Polysilicon is used as the structure material,
21
• Deposited silicon oxide is used as the sacrificial layer,
• Silicon nitride is used as electrical isolation between the polysilicon and the substrate,
• Metal (usually gold) is the top layer of the device and can be used as conductive layer.
Figure 2-10 shows the cross section of an electrostatic motor fabricated by the MUMPs
process. This device includes all the layers that are available in the MUMPs process. In order
Figure 2-10: Cross section of MEMS motor fabricated by MUMPs [5]
to make the process as general as possible, MUMPs process defines all the layers’ thickness and
their functions. All MEMS designers have to follow these definitions and design rules. These
definitions and design rules limit the designers to design more complex devices, but they make
it possible for many different designs to be put on a single silicon wafer in one single fabrication
process. Also, the standardization of the fabrication process reduces the fabrication cost and
lets more and more designers submit their designs. In this thesis, all the actuators are designed
by the following MUMPs design rules. Table 2.1 shows the main limitations of MUMPs process
and a brief introduction of each layer’s function.
The MUMPs process begins with 100 mm n-type silicon wafers of 1-2 Ω-cm resistivity. In
order to prevent or reduce charge feed through to the substrate from electrostatic devices on
the surface, these wafers are highly doped with phosphorus. Next, a 600 nm silicon nitride
layer is deposited on the wafers as an electrical isolation layer. A 500 nm polysilicon film-Poly
0 is deposited right after this step. The poly 0 is the only layer that can not be released in
the MUMPs process, so it is typically used as a ground plane or for routing purposes. Poly 0
is then patterned by photolithography, a process that includes the coating of the wafers with
22
Material Layer
Silicon Nitride
Poly0
First oxide
First oxide
Poly1
Second oxide
Second oxide
Poly2
Metal
Table 2.1: MUMPs process layers and their Properties
Thickness Lithography level name Function
0.6 µm
Insulator
0.5 µm
Poly0 and hole0
Conductive layer
2.0 µm
Dimple
Release friction
2.0 µm
Anchor1
fix poly1 on substrate
2.0 µm
Poly1 and hole1
Structure layer
0.75 µm
Poly1-poly2-via
Connection with poly1 and poly2
0.75 µm
Anchor2
fix poly1 on substrate
1.5 µm
Poly2 and hole2
Structure layer
0.5 µm
Metal and metal hole
Conductive layer
photoresist, exposure of the photoresist with the appropriate mask and developing the exposed
photoresist to create the desired etch mask for subsequent pattern transfer into the underlying
layer. After the photolithography process, the poly 0 layer is etched in a special system.
A 2.0 µm phosphosilicate glass (PSG) sacrificial layer is then deposited and annealed. The
layer of PSG, known as First Oxide, will be removed at the end of the whole MUMPs process
to free the first mechanical layer of polysilicon. This sacrificial layer can be patterned by
photolithography with masks such as Dimple and Anchor 1. After patterning first oxide, the
first structural layer of polysilicon (Poly 1) is deposited at a thickness of 2.0 µm. The polysilicon
is lithographically patterned using a mask designed to form the first structural layer Poly 1.
After Poly 1 is etched, a second PSG layer (Second Oxide) is deposited and annealed. The
second oxide can be patterned by two different etch masks : Poly 1_Poly 2_VIA and Anchor
2, with different objectives. The Poly 1_Poly 2_VIA level provides the etch holes in the second
oxide down to the Poly 1 layer in order to make mechanical and electrical connections between
Poly 1 and Poly 2 layers. The second structural layer, Poly 2, is then deposited with 1.5 µm
thickness. As Poly 1 patterned, Poly 2 structural layer is patterned by the second designed
mask Poly 2. The Poly 1 and Poly 2 layers are the mechanical structural layers in MUMPs
process because they both can be released by etching the first oxide and second oxide at the
end of the process.
A 0.5 µm metal layer is the final deposited layer in the MUMPs process. It provides for
probing, bonding, electrical routing and highly reflective mirror surfaces. The metal layer is
lithographically patterned by the mask named metal. The release process can be done by MEMS
23
designers in their own facility. The process of releasing chips is performed in the following steps.
First chips are immersed in acetone for 3 minutes, and then in De-ionized (DI) water for 30
seconds. These two steps can strip photoresist off. After that, chips are put in the 49% HF
etchant for 1.5-2 minutes to etch oxide away. This is followed by several minutes in DI water
and then alcohol for 2 minutes to reduce friction followed by at least 10 minutes in an oven at
1100 C. Figure 2-11 shows the device after sacrificial oxide release.
Figure 2-11: Cross section of MEMS motor after releasing process [5]
24
Chapter 3
Two-hot-Arm Horizontal Thermal
Actuator
In this chapter, modeling of a two-hot-arm horizontal thermal actuator is documented. Finite
element analysis and experiment results are also provided.
3.1
Introduction
A typical thermal actuator is shown in Figure 3-1. In the thermal actuator, the hot arm is
usually thinner than the cold arm, so the electrical resistance of the hot arm becomes higher
than the cold arm. When an electric current passes through the cold and hot arms, the heat
generated in the hot arm is much more than that of the cold arm. It causes that the temperature
of the hot arm to become much higher than the cold arm. Since the cold and hot arms are made
of the same material and same thermal expansion coefficient, the temperature difference causes
the hot arm to expand more than the cold arm. This results in the rotation of the actuator.
Although traditional thermal actuators can generate much larger deflection than electrostatic
actuators without the need of a high actuating voltage, there are still some limitations in
traditional thermal actuators. Ideally, the flexure is expected to be as thin as possible. When
the flexure becomes thinner, more deflection of the thermal actuator tip can be generated by
the different thermal expansion between hot and cold arms. But, if the flexure is thinner than
the hot arm, the temperature of the flexure could be higher than that of the hot arm which
25
anchor
cold arm
dimple
hot arm
direction of motion
flexture
Figure 3-1: A traditional thermal actuator (one hot arm)
might result in over heating. Also, in order to keep it elastically deflecting, the flexure should be
long enough. However, if the flexure is too long, the deflection of the thermal actuator tip will
be reduced. Since the current passes through the flexure and the cold arm, the resistance of the
flexure and cold arm also contributes to the actuator’s overall resistance. The power consumed
in the flexure and cold arm does not contribute to the desired movement of the thermal actuator
tip. Only power dissipated in the hot arm is directly transferred into the intended movement
of the thermal actuator tip. Since the resistance of flexure and cold arm is comparable with
the hot arm, the efficiency issue of electrical power consumption should be concerned.
Some efforts have been directed at resolving these limitations of traditional thermal actuators and improving their efficiency. David M. Burns and Victor M. Bright designed a new
thermal actuator which has two hot arms [43]. The two-hot arm thermal actuator is shown in
Figure3-2. In this new thermal actuator, the electric current only passes through the outer and
outer hot arm
flexure
dimple
cold arm
inner hot arm
anchor
Figure 3-2: Schematic diagram of two-hot-arm thermal actuator
inner hot arms. This avoids the cold arm and flexure to being part of the electric circuit. It
dramatically increases the efficiency since all the power consumed in the actuator contributes
to the deflection of the thermal actuator tip. The flexure can also be thinner than the hot arm
because no current passes through the flexure.
Obviously, the new two-hot arm thermal actuator has improved the limitations of the tra26
ditional one. As mentioned before, thermal actuators have been widely used in many MEMS
applications; in order to reduce the design circle and simplify MEMS design work, modeling of
this new two-hot arm thermal actuator is discussed in the following sections.
3.2
3.2.1
Electrothermal analysis
Analytical solution
A diagram of the two-hot arm thermal actuator is shown in Figure 3-3 (a). The two-hot arm
thermal actuator is usually fabricated by surface micromachining. The size of the cross section
of the actuator is much smaller than the actuator length. So the electrothermal analysis of
the two-hot arm actuator is generally simplified as a one dimensional problem [28]. The twohot arm thermal actuator shown in Figure 3-2 can be treated as two line shape microbeams
connected in series. Figure 3-3 (b) shows the coordinate system for thermal analysis. Since the
Lg
Wh
Wc
Wf
Lf
Lc
L3
L2
L1
(a)
x=0
x=L1
x=L1+Lg
x=L1+Lg+L2
(b)
Figure 3-3: (a) Schematic top view of two-hot arm thermal actuator. (b) Simplified
one dimensional coordinate system.
current only passes through the outer and inner hot arms, the coordinate does not include the
cold arm and flexure.
27
There are three mechanisms of heat flow: conduction, convection and radiation. Conduction
is the transport of energy from high temperature to low temperature region. Convection is the
heat transfer between the air and the solid interface when there is a temperature difference.
Radiation is the energy emitted from a body due to its temperature [44]. According to the
finite element analysis [23], heat dissipation through radiation to ambient can be neglected in
comparison with heat losses through conduction to the anchor substrate which is considered as
a heat sink, and heat losses through air to the substrate due to convection. As shown in Figure
3-4, the heat flow equation is derived by examining a differential element of the microbeam of
thickness tsi , width wh , and length dx [28]. When the heat flow is under steady-state conditions,
wh
PolySi
Air
Si3N4
X
t si
ta
tn
X+dX
text
Si
Figure 3-4: The schematic cross section of the actuator for thermal analysis
resistive heating power generated in the element is equal to the heat conduction and convection
out of the element
·
dT
−kp wt
dx
¸
·
dT
+ J ρwtdx = −kp wt
dx
x
2
¸
x+dx
+
Sdxw(T − Ts )
RT
(3.1)
where T and Ts are the beam and substrate temperatures, respectively; kp is the thermal
conductivity of polysilicon, J is the current density, ρ is the resistivity of polysilicon, and S is
the shape factor which accounts for the impact of the shape of the element on heat conduction
to the substrate [45]. This geometric factor represents the ratio of heat loss from the sides and
bottom of the beam to the heat loss from the bottom of the beam only. RT is the thermal
resistance between the polysilicon microbeam and the substrate if the microbeam is wide enough
28
[28]. The thermal resistance, RT , is given by:
ta
tn
+
kv
kn
RT =
(3.2)
where ta and tn are the thickness of air above the nitride and the thickness of nitride on
the substrate, respectively, and kv and kn are the thermal conductivity of air and nitride,
respectively. The shape factor, S , is given by [45]
S=
tsi ta
(2
+ 1) + 1
wh Tsi
(3.3)
where tsi is the thickness of the polysilicon and wh is the width of the hot arm. Usually, the
resistivity ρ is related to the temperature of the polysilicon. The resistivity can be assumed here
to have a linear temperature coefficient, ξ , so the resistivity becomes a function of temperature
ρ = ρ0 [1 + ξ(T − Ts )]
(3.4)
where ρ0 is the resistivity of polysilicon at room temperature. The current density can be
written as
J=
V
ρL
(3.5)
where V is the voltage applied to the outer and inner hot arm, L is the length of the polysilicon
that current passes through. After taking the limit as dx → 0 in Equation (3.1) and simplifying
the results, the following equation is produced
d2 T
S(T − Ts ) J 2 ρ
−
=
dx2
kp RT t
kp
(3.6)
Substituting Equations (3.5) and (3.4) into Equation (3.6), the final equation for the thermal
model is found to be
d2 T
V2
1
S(T − Ts )
−
=
2
2
dx
kp RT t
L ρ0 kp 1 + ξ(T − Ts )
(3.7)
In the following we linearize Equation (3.7) and derive its analytical solution. In Equation (3.7),
the second term of the right hand side is nonlinear. After using the Taylor series expansion and
29
dropping all therms except the first two, Equation (3.7) becomes
d2 T
V2
S(T − Ts )
−
=
[1 − ξ(T − Ts )]
dx2
kp RT t
L2 ρ0 kp
In order to simplify the above equation, some variables have been changed and the above
equation is rewritten as:
d2 T
= A2 Tθ − B
dx2
(3.8)
where
Tθ = T − Ts
B=
A2 =
V2
L2 ρ0 kp
S
+ Bξ
kp RT t
Solving Equation (3.8) and applying the solution to the outer and inner hot arms, the
temperature distribution of the outer and inner hot arms is obtained. Equation (3.9) is the
temperature distribution of the outer hot arm and Equation (3.10) is the inner hot arm temperature distribution
T1 = Ts +
B1
+ C1 eA1 x + C2 e−A1 x
A21
(3.9)
T2 = Ts +
B2
+ C3 eA2 x + C4 e−A2 x
A22
(3.10)
where Ci (i = 1 to 4) are some constants to be obtained. B1 and A1 are the same as B and
A, respectively, except that L is replaced by L1 , V is replaced by V1 and w is replaced by wh .
B2 and A2 are also the same as B and A, respectively, except that L is replaced by L2 , V is
replaced by V2 and w is replaced by wh . V1 and V2 are the voltages across the outer hot arm
and inner hot arm, respectively. They can be given by
V1 =
V
(L1 + Lg )
L1 + L2 + Lg
V2 =
V
L2
L1 + L2 + Lg
Figure 3-5 shows the boundary conditions that are needed to solve constants Ci . The qi
30
q1
q2
Tm
q3
Ts
Figure 3-5: The schematic diagram of boundary conditions
(i = 1 to 3 ) are the rates of heat conduction, Tm is the temperature of the joint between the
outer and inner hot arms. The anchor pads can be assumed to have the same temperature
as the substrate. According to the continuity of the temperature and rate of heat conduction,
five boundary conditions are obtained for Equations (3.9) and (3.10). They can be written in
matrix form as:
A×C =B
(3.11)
where






A=




1
1
0
0
0
0
0
1
1
0
eA1 (L1 +Lg )
e−A1 (L1 +Lg )
0
0
−1
0
0
eA2 L2
e−A2 L2
−1
A1 eA1 (L1 +Lg ) −A1 e−A1 (L1 +Lg ) A2 eA2 L2 −A2 eA2 L2 −R_cold

1
−B
A21



− B2

A22


B =  −Ts − B12
A1


2
 −Ts − B
A22

−Ts R_cold
31
























c1


 c2


C =  c3


 c4

Tm











and R_cold is the thermal resistance of the cold arm of the thermal actuator. It can be
calculated by
R_cold =
π
h
2wh ln w
wc
Equation (3.11) is written in matrix format so that the thermal problem can be solved in the
same way. For the given process parameters such as ρ0 and ξ, material properties parameters
and drive voltage, the temperature distribution along the outer and inner hot arm can be
obtained from Equations (3.9) to (3.11).
3.2.2
Simulation results
To simulate the temperature distribution of the two-hot arm thermal actuator, the parameters
in [28] and [5] have been used. All the parameters are listed in Tables 3.1 and 3.2.
Table 3.1: Material
Material Properties
Young’s modulus E
Poisson’s ratio v
Thermal expansion coefficient K
Thermal conductivity of polysilicon kp
Thermal conductivity of air kv
Thermal conductivity of nitride kn
Resistivity of polysilicon ρ0
Properties
Value
162 × 109
0.22
4.7 × 10−6
41 × 10−6
0.026 × 10−6
2.25 × 10−6
20
Unit
Pa
C −1
W · µm−1 · C −1
W · µm−1 · C −1
W · µm−1 · C −1
Ω · µm
R
°
The analytical result is calculated by Matlab . Figure 3-6 shows the temperature distribution along the outer and inner hot arms for the specified input voltage. From the figure, the
maximum temperature appearing in the middle of the outer hot arm is clearly shown. At the
middle of the inner hot arm, the temperature is a little bit lower than the maximum temperature
because the length of the outer hot arm is longer than that of the inner hot arm, which means
the resistance of the outer hot arm is bigger than that of the inner hot arm. Since the outer hot
32
Table 3.2: Geometrical data of the two-hot-arm thermal acutator
Geometrical data
Value Unit
The length of the outer hot arm L1 252
µm
The length of the inner hot arm L2 220
µm
The length of the cold arm Lc
162
µm
The length of the flexure Lf
38
µm
The length of the gap Lg
2
µm
The thickness of polysilicon tsi
2
µm
The thickness of air ta
2
µm
The thickness of nitride tn
0.6
µm
550
Vb=5v
Temperature (K)
500
450
400
350
300
0
50
100
150
200
250
300
350
400
450
500
Position of outer and inner hot arm (µ m)
Figure 3-6: The analytical result of temperature distribution along the outer and
inner hot arms
33
and inner hot arms are both connected to the anchor, the temperature at those points are equal
to the substrate temperature T s. At the joint point between the outer hot arm and inner hot
arm, the temperature has a great jump. This is because the cold arm is also connected at that
point. The cold arm becomes a heat sink and brings the temperature down. The numerical
R
°
result is generated by a commercial software Coventorware
MemETherm solver. This solver
can compute the thermal field and the electrical potential resulting from an imposed voltage
or current flow through a resistive material. In this simulation, three different physical domain
boundary conditions, electrical, thermal and mechanical, are applied. In the electrical boundary
condition, the actuating voltage is applied across the outer and inner hot arms. All of the three
anchors are set to the substrate temperature for the thermal boundary conditions since they
are connected to the substrate. For the mechanical boundary conditions, these three anchors
are also fixed in all directions. The simulation result is shown in Figure 3-7. Obviously, the
Figure 3-7: The numerical result of temperatue distribution of the two-hot arm
thermal actuator.
analytical results of the temperature distribution for the two-hot arm thermal actuator have
good agreement with the numerical simulation results. The error of the maximum temperature
between them is less than 10%. In Figure 3-7, the temperature of the cold arm is almost the
same as the substrate temperature, which agrees with the physical meaning. The maximum
temperature as a function of the input voltage is shown in Figure 3-8. It clearly shows that the
maximum temperature increases with the input voltage and the analytical result interpreted
34
R
°
here is in good agreement with the numerical result obtained from Coventorware .
Max temperature vs Voltage
1300
Analytical results
Simulation results
1200
1100
Maximum Temperature (C)
1000
900
800
700
600
500
400
300
0
1
2
3
4
5
6
7
8
9
10
Voltage (V)
Figure 3-8: Maximum temperature as a function of input voltage: Comparison between analytical and simulation results.
3.3
3.3.1
Mechanical analysis
Analytical solution
As the operating principle of the two-hot arm thermal actuator explained before, it is essential
to know the linear thermal expansion of the outer and inner hot arms in order to find the
mechanical deflection of the actuator. The temperature distribution of the outer and inner hot
arms has been obtained from Equations (3.9) and (3.10), respectively. Based on that, the linear
thermal expansion of the outer hot arm ∆L1 , inner hot arm ∆L2 and the gap ∆Lg can be given
by:
∆L1 = α
Z
0
L1
(T1 − Ts )dx = α(
B1
C1 A1 L1 C1
C2 −A1 L1 C2
L1 +
e
−
−
e
+
)
A1
A1 A1
A1
A21
35
(3.12)
Z
L2
B2
C3 A2 L2 C3
C4 −A2 L2 C4
L2 +
e
−
−
e
+
)
2
A2
A2 A2
A2
A2
0
·
¸
Z L1 +Lg
B1
C1 A1 L1 C2 −A1 L1 A1 Lg
∆Lg = α
(T1 − Ts )dx = α
L
+
(
e
−
e
)(e
−
1)
g
A1
A1
A21
L1
∆L2 = α
(T2 − Ts )dx = α(
(3.13)
(3.14)
where α is the thermal expansion coefficient of the polysilicon. The structure of the two-hot
arm thermal actuator shown in Figure 3-2 is similar to a plane-frame structure with three fixed
bases for elastic structure engineering. Deflection analysis of such structures has been well
documented in [46]. Deflection analysis of the one-hot arm has also been done by using the
force method [24]. The force method is applied to analyze the bending moment of the actuator
due to the thermal expansion. The two-hot arm thermal actuator is a statically indeterminate
structure with the degree of the indeterminacy of 6. Each constraint can be released and
replaced by two forces and one moment in the directions of Xi (i = 1 to 6). The six redundants
are shown in Figure 3-9 (a). Following the force method [46], the six redundants Xi (i = 1 to
X3
X2
X6
X1
X5
X4
(a)
L1
P=1
(b)
Figure 3-9: (a) The plane frame structure simplified for the thermal actuator with
six redundants. (b) The bending moment of the outer hot arm due to the virtual
force
36
6) can be obtained by solving a set of simultaneous equations:














f11 f12 f13 f14 f15 f16



f21 f22 f23 f24 f25 f26  


f31 f32 f33 f34 f35 f36  



f41 f42 f43 f44 f45 f46 



f51 f52 f53 f54 f55 f56 

f61 f62 f63 f64 f65 f66
X1


∆Lg
 
 
X2   ∆L1 − ∆L2
 
 
X3  
0
=
 

X4 
∆Lg
 
 

X5 
∆L1
 
X6
0














(3.15)
where each item of the right hand side of Equation (3.15) represents the displacement of Xi in
their own direction. For example, ∆Lg is the displacement of the force X1 in the X1 direction.
fij represents the flexibility coefficient which is defined as the deflection at i direction due to
the unit force acting in the j direction. It can be found by diagram product of the bending
moments due to respective six unit redundants, Xi (i = 1 to 6 ). f11 is shown as an example
to calculate those coefficients.
As we mentioned, the subscript of each flexibility coefficient includes two directions: the
deflection direction and the force direction. The first step to calculate the flexibility coefficient is
to draw the bending moment diagrams caused by two unit forces acting at these two directions,
respectively. Figure 3-10 shows the bending moment diagrams. For the flexibility coefficient
f11 , the deflection and force directions are the same, so the bending moment diagrams of these
two unit forces are also similar to each other in the figure. After the bending moment diagrams
are drawn, each element’s bending moment is calculated, i.e. each hatched area in Figure 3-10
(a). For element 1, the hatched area is 12 L22 . Then, we need to find the bending moment with
regards to each hatched center point in Figure 3-10 (b). For element 1, it is 23 L2 . Finally, for
each element, we should multiply these two items together, and sum all the elements together
to get the flexibility coefficient f11
f11 =
1 L32
L3
+ L22 Lg + 1 + L22 L1 − L21 L2 )
(
EIh 3
3
37
(3.16)
(1)
X1
(a)
(1)
X1
(b)
Figure 3-10: (a) The bending moment diagram of a unit force in the deflection
direction (b) The bending moment diagram of a unit force in the force direction.
The following equations give the other flexibility coefficients’ expression:
f21 = −
1
(2L1 L2 Lg + L2 L2g − L21 Lg )
2EIh
f31 = −
f41 =
1
(L1 L2 + L2 Lg + L22 − L21 )
2EIh
1
(2L31 − L21 L2 + 2L2 Lg L3 + 2L2 L1 L3 − L21 L3 )
2EIh
f51 =
1
(2L21 Lg − 4L1 L2 Lg − 3L2g L2 )
2EIh
f61 = −
1
(2L1 L2 + 2L2 Lg − L21 )
2EIh
f12 = f21
f22 =
f32 =
¢
1 ¡
3L1 L2g + L3g
3EIh
¢
1 ¡
2L1 Lg + L2g
2EIh
38
f42 =
¢
1 ¡
2L3 L1 Lg − L2g L2 − L21 Lg
2EIh
f52 =
f62 =
2L1 L2g
EIh
¢
1 ¡
2L1 Lg + L2g
2EIh
f13 = f31 ; f23 = f32
f33 =
f43 =
1
(L1 + L2 + Lg )
EIh
1
(L2 − L1 L3 − L3 Lg )
2EIh 1
f53 =
1
(3L2g + 4L1 Lg )
2EIh
f63 =
1
(L1 + Lg )
EIh
f14 = f41 ; f24 = f42 ; f34 = f43
f44 =
L3f
3EIf
+
Lc (L3 + Lf )(2L3c + 6Lc Lf L3 )
1
+
(6L23 Lg + L31 + 3L1 L23 − 3L3 L21 )
2
2EIc (3Lc + 6Lc Lf )
3EIh
f54 = −
f64 = −
L2f
2EIf
−
1
(2L1 Lg L3 + 2L2g L3 − L21 Lg )
EIh
Lc (L3 + Lf )
1
−
(4L3 Lg − L21 + 2L1 L3 )
2EIc
2EIh
f15 = f51 ; f25 = f52 ; f35 = f53 ; f45 = f54 ;
f55 =
f65 =
4L2g L1
8L3g
+
EIh
3EIh
1
(2Lg L1 + 2L2g )
EIh
f16 = f61 ; f26 = f62 ; f36 = f63 ; f46 = f64 ; f56 = f65
f66 =
Lf
1
Lc
(L1 + 2Lg ) +
+
EIh
EIf
EIc
(3.17)
In the above equations, E is the Young’s modulus of polysilicon, Ih , Ic and If are the moment
of inertia for the hot arm, cold arm and the flexure, respectively. Once the six redundants are
obtained, the deflection of the actuator tip can be calculated by the virtual work method [46].
39
A virtual force P is applied to the free end of the actuator normal to the hot arm. The bending
moment of the outer hot arm due to the virtual force is shown in Figure 3-9 (b). The bending
moment due to the virtual force as a function of the position of the outer hot arm is given by
M = (L1 − x)P
(3.18)
The bending moment of the outer hot arm due to the thermal expansion, i.e. the moment of
the outer hot arm due to the six redundants, can be represented as
M=
2
X
Mi
(3.19)
i=1
M1 = X1 x + X1 (L2 − L1 ) − X2 Lg − X3
M2 = X4 x + X4 (L3 − L1 ) − 2X5 Lg − X6
where M1 is the bending moment of the outer hot arm caused by the redundants X1 , X2 and
X3 , and M2 is the bending moment of the outer hot arm caused by the redundants X4 , X5 and
X6 . M is the total bending moment of the outer hot arm caused by the thermal expansion.
According to the method of virtual work [46], the deflection in the free end of the actuator can
be written as
u=
Z
L1
MM
1
Ma L31 L1 Ma − Mb 2
+
L1 + L21 Mb )
dx =
(−
EIh
EIh
3
2
(3.20)
where Ma and Mb are the variables that can be explained by the following equations:
3.3.2
Ma = X1 + X4
(3.21)
Mb = X1 (L2 − L1 ) − X2 Lg − X3 + X4 (L3 − L1 ) − 2X5 Lg − X6
(3.22)
Simulation results
R
°
The mechanical analysis is simulated by Coventorware with MemETherm solver. The ana-
lytical and numerical solutions of the deflection as a function of the input voltage are shown in
40
Figure 4-12. It is clear that good agreement is achieved. One thing that should be highlighted
12
Analitical Results
Simulation Results
10
Displacement ( µ m)
8
6
4
2
0
1
2
3
4
5
Voltage (v)
6
7
8
9
Figure 3-11: Deflection of the actuator tip as a function of input voltage
here is when the input voltage is increased, the analytical results cannot accurately predict the
numerical results anymore. The reason is that at high working voltage, the temperature of the
actuator becomes extremely high and nonlinear effects become more important. The first two
terms of the Taylor series of the nonlinear part in Equation (3.7) is not accurate enough to
represent the whole nonlinear part. It should be also noted that at that high working voltage, the temperature of the actuator is almost equal to the melting point of the material, and
therefore the operating voltage of the thermal actuator is usually much lower than that voltage.
Furthermore, the inner and outer hot arms may touch each other [43] at high actuating voltage
due to large deflection as seen in Figure 3-12. At 10v, the two-hot arm thermal actuator has
more than 10 µm deflection and the touching between the outer and inner hot arms is found
in the box shown in the figure.
41
Figure 3-12: Numerical result of the deflection of two-hot-arm thermal actuator with
10v input voltage
3.4
Fabrication process and experiments
The two-hot arm thermal actuator presented here has been fabricated using the 44th production
run of the Multi-User MEMS Processes (MUMPs). The whole thermal actuator is constructed
out of one polysilicon layer, here polysilicon-1 layer is used. In order to reduce the friction
effect, dimples are used on the cold arm to reduce the amount of polysilicon in direct contact
with the silicon nitride layer. A deflection meter is also placed in front of the tip of the two-hot
arm thermal actuator to make it easy to measure the deflection (Figure 3-13). After the chips
Dimple
Deflection Meter
Figure 3-13: Deflection meter coupled to a two-hot-arm thermal actuator
arrived, HF release process was done to release thermal actuators out of the substrate. This
process was proceeded in the clean room of the University of Waterloo. Figure 3-14 shows the
scanning electron micrograph (SEM) of the whole chip.
42
Figure 3-14: Overview of the whole chip after HF release.
43
In this experiment, a power supply with at least 15V (DC) tuning range was needed to
provide the actuating voltage. Two DC probes were employed to add the actuating voltage
on the thermal actuators. In order to capture the deflection of the thermal actuator at each
actuating voltage, a CCD camera was installed on the top of the probe station. When the
power supply was tuned from 2 volts to 11 volts, the camera was used to record pictures of
the deflection of the actuators at each voltage. The exact deflection of the thermal actuator
at any actuating voltage was then obtained by enlarging the picture at the deflection zone. A
SEM of deflection meter is also provided to compare with these pictures in order to increase
the accuracy. Figure 3-15 shows the experimental equipment.
Figure 3-15: Experiment equipment for measuring the deflection of thermal actuators
The experimental data is plotted in Figure 3-16 . Comparing with the analytical and
numerical results, a good agreement is achieved.
3.5
Discussion
In Figure 3-12, the simulation results show that the outer and inner hot arms could touch
each other at high actuating voltage. This phenomenon has been seen during the experiments.
44
14
analitical result
test
simulation
12
Deflection um
10
8
6
4
2
0
1
2
3
4
5
6
Voltage
7
8
9
10
11
Figure 3-16: Comparison of experimental result with the analytical and numerical
results
Figure 3-17 shows the touching of the outer and inner hot arms when the actuator is subjected
9.0v voltage. Another interesting phenomenon that was observed in the experiments was that
Figure 3-17: The touching of the outer and inner hot arms at high actuating voltage
the touching of the two hot arms occured, the thermal actuator was not able to move back to
its original place even without any actuating voltage. When the voltage was applied again, the
thermal actuator moved to the same distance as before. After zooming at the middle of the
two hot arms, a curve was found in the inner hot arm (Figure 3-18 ). This curve could be the
reason for the fact that the thermal actuator had undergone plastic deformation. As a result,
the inner hot arm becomes shorter and draws the thermal actuator to move down a little bit
45
Figure 3-18: A curve found in the inner hot arm as seen in SEM
as seen in the tests.
A traditional thermal actuator can operate in two modes [6]. Figure 3-19 shows both modes
of operation for the actuator. In the basic mode, the thermal actuator is operated as described
before. The back-bent mode occurs after the driving current is increased above the level required
for the maximum deflection resulted in a reshaping of the hot arm. After reshaping, the hot
arm is shorter than its original length and therefore the thermal actuator moves to a negative
position. A back-bent thermal actuator still can be used as a traditional thermal actuator
except the zero-deflection position has been shifted. For the two-hot arm thermal actuator,
back bending is also found in the experiments, when we applied 11v voltage and removed the
voltage after a few seconds. Figure 3-20 shows the back bending of the two-hot arm thermal
actuator.
At high actuating voltage, two different phenomena are found: the touching of the two hot
arms and back bending. Both of them are not desirable for most thermal actuator applications.
One of these two problems’ solutions is to create an accurate model. According to the model, we
should keep the thermal actuator’s working voltages far away from those “dangerous” voltages.
Fabrication tolerance also should be concerned. For example, when we do the HF release, the
time we put the chips in the HF etchant can affect the final geometry of thermal actuators
dramatically. Further experiments are needed to be proceed to achieve average fabrication
46
Figure 3-19: Two modes of the traditional thermal actuator operation [6].
Figure 3-20: Back bending of the two-hot-arm thermal actuator
47
tolerance. Figure 3-21 shows the over etching during the HF releasing process. The teeth of
the deflection meter should be rectangular, but they become rounded after etching.
Over etching
Figure 3-21: Over etching of the teeth of the deflection meter.
48
Chapter 4
Bidirectional Vertical Thermal
Actuators
In this chapter, a novel bidirectional vertical thermal actuator is designed. Thermal analysis and mechanical analysis are presented. The numerical simulation results obtained from
R
°
Coventorware are also provided to compare with the analytical results. Good agreement is
achieved.
4.1
Mechanical design
The horizontal thermal actuator discussed in the previous chapter was operated by different
thermal expansions between the hot and cold arms. The same hot and cold arms structure can
also be used to create a vertical thermal actuator that can have the motion perpendicular to
the substrate. One version of a vertical thermal actuator is shown in Figure 4-1 [22]. In the
traditional vertical thermal actuators, the hot arm is above the cold arm and is separated by an
air gap. At one end, the arms are connected together with a via, while at the other end, they
are anchored separately on the substrate. The flexure connects the cold arm to the anchor to
finish the current pass. The driving current passes through the hot and cold arms and results
in the generation of thermal energy. Similarly, as the horizontal thermal actuator, the hot arm
is thinner than the cold arm, so the hot arm has a higher electrical resistance and thermal
resistance. The hot arm thus has a larger thermal expansion than the cold arm. As the hot
49
via
hot arm
cold arm
gap
flexure
anchor
Figure 4-1: 3D schematic view of a vertical thermal actuator showing a cross section
through the hot and cold arm.[7]
arm expands, it drives the tip of the vertical actuator downward towards the substrate. The
traditional vertical thermal actuator can also be designed for upward motion, however, both
motions cannot be achieved by one actuator.
Obviously, the traditional vertical thermal actuators have the same limitations as those of
the traditional horizontal thermal actuators. Theoretically speaking, the thinner the flexure,
the larger the deflection of the tip of the vertical thermal actuator. But the flexure cannot
be thinner that the hot arm, otherwise the temperature of the flexure is higher than that of
the hot arm. Also, the power consumed by the cold arm has no contribution to the deflection
of the tip of the actuator. In this work, research has been directed towards improving the
traditional vertical thermal actuator shown in Figure 4-1, and it has resulted in a novel Ushape bidirectional vertical thermal actuator depicted in Figure 4-2.
This new vertical thermal actuator (VTA) can either bend upward or downward without
any modification. The bending direction of the new VTA depends on where the voltage is
applied. When the voltage is applied across anchors 1 and 2 in Figure 4-2, the current only
goes through the top layer, and it expands due to the increase of its temperature. Thus, the
50
anchor 3
anchor 1
flexure
top
layer
via
anchor 4
bottom
layer
anchor 2
Figure 4-2: 3D View of the U-shaped vertical thermal actuator
actuator’s tip is deflected downward to the substrate. For deflecting the actuator upward, the
voltage is simply switched from anchors 1 and 2 to anchors 3 and 4. The U-shape VTA is more
electrically efficient than the traditional actuator since no electrical power is wasted in the cold
arm when the U-shape vertical actuator is operated. This bidirectional motion indicates that
the new vertical thermal actuator has almost twice amount of displacement compared to the
conventional VTA at the same size.
In the following sections, electro-thermal and mechanical analysis of the U-shape vertical
thermal actuator are presented. Simulation results are also provided with which the design
process could be simplified significantly
4.2
4.2.1
Electrothermal analysis
Analytical solution
A schematic top view diagram of the U-shape VTA is shown in Figure 4-3. Since the U-shape
VTA is fabricated by using surface micromachining, the electro-thermal analysis of the U-shape
VTA can be simplified as one dimensional heat transfer problem similar to the thermal analysis
of the two-hot arm thermal actuator. As mentioned in the above section, when the U-shape
VTA is operated, the current only passes through one layer of the actuator. In the following
analysis, the current is assumed to pass through the top layer of the actuator. The actuator
51
Wb2
Wb1
Lb2
Lb1
Le
W2
W1
L1
L2
Figure 4-3: 2D schematic top view of the U-shape VTA
shown in Figure 4-2 can be seen as several microbeams connected in series. The coordinate
system for the thermal analysis is shown in Figure 4-4. In this coordinate system, there are five
microbeams connected to each other. The two short and long bars of the microbeams have the
same dimensions. In order to simply the analysis, the two short bars are numbered as element
1, the two long beams are named as element 2, and the connection between two long beams is
shown as element 3.
The thermal analysis of the U-shape VTA is similar to the thermal analysis of the two-hot
arm thermal actuator. Only the heat loss through conduction and convection is concerned, and
the heat that is dissipated through radiation to the ambient is neglected based on the previous
finite element analysis [23]. As seen in Chapter 3, the heat flow equation can be derived from
a differential element of the microbeam shown in Figure 4-5. Under steady-state conditions,
ohmic power generated in the element is equal to heat conduction and convection out of the
element
·
dT
−kp wt
dx
¸
·
dT
+ J ρwtdx = −kp wt
dx
x
2
¸
x+dx
+
Sw(T − Ts )dx
RT
(4.1)
The definitions of parameters in Equation (4.1) are similar to those in Equation (3.1). Using
52
element 1
element 2
X=Lb1
element 3
X=Lb1+L1
X=Lb1+
2L1+Le
X=Lb1+
L1+Le
X=2Lb1+
2L1+Le
Figure 4-4: Simplified one dimensional coordinate system
PolySi2
Air
PolySi1
X
t p2
Lg
tp1
tv
tn
X+dX
Air
Si3N4
text
Si
Figure 4-5: Schematic cross section of the VTA for thermal analysis
53
the same procedure used in Section 3.2.1, the general solution to the temperature distribution
of each element of the U-shape VTA can be written as:
T = Ts +
B
+ C1 eAx + C2 e−Ax
A2
where Ci (i = 1 to 6 ) are the constants to be obtained. For simplification, A and B are
employed to represent two long terms during solving Equation (4.1). The subscript is assigned
to them for different elements in the following. For element 1, the temperature distribution is
B1
+ C1 eA1 x + C2 e−A1 x
A21
T1 = Ts +
(4.2)
where
B1 =
A21 =
Vb12
L2b1 ρ0 kp
Sb1
+ B1 ξ
kp RT 1 tp2
V
Lb1
2 (Lb1 + L1 ) + Le
¸
·
2 (Lg + tp1 + tv )
+1 +1
tp2
Vb1 =
Sb1 =
tp2
wb1
RT 1 =
tv + Lg
tp1
tn
+
+
kv
kn
kp
and Vb1 is the potential acted on element 1; Sb1 is the shape factor of element 1. For element
2, the temperature distribution is similar to element 1 except that Lb1 is replaced by L1 , and
wb1 is replaced by w1 , that is
T2 = Ts +
B2
+ C3 eA2 x + C4 e−A2 x
A22
where
B2 =
A21 =
Vb22
L21 ρ0 kp
S1
+ B2 ξ
kp RT 1 tp2
54
(4.3)
Vb2 =
Sb2 =
V
L1
2 (Lb1 + L1 ) + Le
¸
·
tp2 2 (Lg + tp1 + tv )
+1 +1
w1
tp2
Element 3 is the connection between the top layer and the bottom layer, the cross section of
element 3 is not rectangular like elements 1 and 2. Figure 4-6 shows the 3-D view of the cross
section of element 3. For element 3, under steady state, the heat flow Equation (4.1) takes the
top layer
via
current
Ac
bottom layer
Figure 4-6: 3D schematic diagram of the element 3 with the cross section
form
kp Av
d2 T
Se w2 (T − Ts )
=
− J 2 ρAc
2
dx
RT 2
(4.4)
where Av is the sum of the cross sections of the top layer, via, and bottom layer of the element
3, Ac is the cross section of the top layer in element 3, and Se is the shape factor for element
3. Solving Equation (4.4), the temperature distribution of element 3 can be obtained as
T3 = Ts +
B3
+ C5 eA3 x + C6 e−A3 x
A23
where
B3 =
Vb3 =
Vb32 Ac
L2e ρ0 kp Av
V
Le
2 (Lb1 + L1 ) + Le
55
(4.5)
Se w2
+ B3 ξ
kp RT 2 Av
·
¸
tp1 2tv
+1 +1
Se =
w2 tp1
A23 =
RT 2 =
tv
tn
+
kv
kn
In order to solve for constants ci (i = 1 to 6 ) in Equations (4.2), (4.3), and (4.5), at least six
boundary conditions are needed. Figure 4-7 (a) shows the boundary conditions that represent
Ts
Tm2
Tm1
Tm1
Tm2
(a)
Ts
q1
q2
q3
(b)
Figure 4-7: (a) The boundary conditions of temperature continuity. (b) The boundary conditions of the rate of the heat conduction
the continuity of temperature from one element to another. Since the U-shape VTA is symmetrical, the temperature distribution of the actuator also should be symmetrical. Therefore, the
temperatures of both ends of element 3 are equal to Tm2 , and the two joints between elements
1 and 2 are equal to Tm1 . Figure 4-7 (b) shows the boundary conditions of the rate of the
heat flow. Substituting all the boundary conditions into Equations (4.2), (4.3) and (4.5), the
56
following equations are obtained
AC = B
(4.6)
where

1
1
0
0
0
0
0

 AL
 e 1 b1
e−A1 Lb1
0
0
0
0
0



0
0
1
1
0
0
−1



e−A2 L1
0
0
0
0
0
eA2 L1

A=

0
0
0
0
1
1
0



0
0
0
0
0
eA3 Le e−A3 Le



A2
0
0
0
 A1 eA1 Lb1 −A1 e−A1 Lb1 −A2

0
0
λeA2 L1 −λe−A2 L1 eA3 L1 −e−A3 L1 0











B=









1
−B
A2
1
−Ts −
B1
A21
−Ts −
B2
A22
−Ts −
B2
A22
−Ts −
B3
A23
−Ts −
B3
A23
0
−RTs
kp w2 tp1 A3











C=










C1 

C2 


C3 


C4 


C5 


C6 



Tm1 

Tm2
57





















0
0
0
−1
−1
−1
0
−R
kp w2 tp1 A3





















Here λ is equal to w1 tp2 A2 Áw2 tp1 A3 , R is the thermal resistance of the bottom layer of the
U-shape vertical thermal actuator, and it is calculated by
R=
1 A2
KA
L1 Lb1
A1
L1
+
A2
Lb1
(4.7)
where A1 and A2 are the cross section area of the long bar and short bar, respectively. Solving
Equation (4.6) and substituting the given process parameters to Equations (4.2), (4.3) and
(4.5), the temperature distribution of the U-shape VTA can be obtained.
4.2.2
Simulation results
In the simulation of the temperature distribution of the U-shape VTA, all the material parameters are the same as those used in Chapter 3. The geometrical data are listed in Table 4.1.
Table 4.1: Geometrical data of the U-shaped vertical thermal acutator
Geometrical data
Value Unit
The length of the long beam of the top layer L1
177
µm
The length of the long beam of the bottom layer L2
217
µm
The length of the short bar of the top layer Lb1
50
µm
The length of the short bar of the bottom layer Lb2
60
µm
The width of the long beam of the top layer w1
10
µm
The width of the long beam of the bottom layer w2
18
µm
The width of the short bar of the top layer wb1
13
µm
The width of the short bar of the bottom layer wb2
15
µm
The length of the connection between two long beams Le 38
µm
The gap between the top layer and the bottom layer
0.75
µm
The thickness of the top layer Tp2
1.5
µm
The thickness of the bottom layer Tp1
2.0
µm
The thickness of air Tv
2
µm
The thickness of nitride Tn
0.6
µm
Figure 4-8 shows the temperature distribution of the U-shaped vertical thermal actuator.
The input voltage is 5V, and the other parameters are listed in Tables 4.1 and 3.1. Since
the U-shaped vertical thermal actuator is symmetrical about its center line, the temperature
distribution also should be symmetrical about its center line. The above analytical results show
that characteristic. The maximum temperature appears in element 2 rather than element 3
58
700
Vb = 5v
650
600
element 1
element 2
Temperature
550
element 3
500
450
400
350
300
0
50
100
150
200
250
300
350
400
450
500
Top layer position of vertical actuator
Figure 4-8: Temperature distribution along the top layer of VTA
because element 3 is the connection between the top and bottom layers. The bottom layer
becomes a heat sink which reduces element 3 temperature. Also, the cross section of element 3
is bigger than that of element 2 (Figure 4-6), hence element 3 has a bigger thermal capacitance
compared to element 2.
Figure 4-9 shows the numerical simulation of the same actuator using Coventorware software.
In this simulation, three different physical domain boundary conditions, electrical, thermal
and mechanical, are applied. In the electrical boundary condition, the actuating voltage is
added across anchors 1 and 2 in Figure 4-2. All of the four anchors are set to the substrate
temperature for the thermal boundary condition since they are connected to the substrate. For
the mechanical boundary conditions, these four anchors are also fixed in all directions. The
simulation results are shown in Figure 4-9. The temperature distribution is in good agreement
with the analytical results. The maximum temperature as a function of the input voltage is also
provided in Figure 4-10. Like the two-hot arm thermal actuator and for the same reason, the
analytical results are in better agreement with the numerical results at low voltage. However,
the difference at high input voltages is acceptable.
59
Figure 4-9: Numerical result of temperature distribution of the U-shaped VTA using
R
°
Coventorware
1100
Analytical results
Simulation results
1000
Maximum Temperature (K)
900
800
700
600
500
400
300
0
1
2
3
4
5
6
7
Voltage (V)
Figure 4-10: Comparison of the maximum temperature as a function of input voltage.
60
4.3
4.3.1
Mechanical analysis
Analytical solution
The linear thermal expansions of the top and bottom layers are the essential inputs for the
mechanical analysis of the U-shape vertical thermal actuator. Based on Equation (4.3), the
thermal expansion of the top layer can be obtained from
∆L1 = α
Z
0
L1
(T − Ts )dx = α
·
¸
B2
C3 A2 L1
C4 −A2 L1
L
+
(e
−
1)
−
(e
−
1)
1
A2
A2
A22
(4.8)
where the parameters’ definitions are similar as those in section 3.3.1. Here, the thermal
expansions of elements 1 and 3 of the top layer are neglected in comparison with the thermal
expansion of element 2. From Figure 4-9, it is clear that the temperature of the bottom layer is
also increased. Since, no current passes through the bottom layer, the temperature distribution
along the bottom layer is a simple linear heat conduction problem. The thermal expansion of
the bottom layer can be calculated by
∆L2 = α
Z
0
L2
1
(T − Ts )dx = α (Tm2 − Ts ) L2
2
(4.9)
where Tm2 is the tip temperature of the bottom layer as shown in Figure 4-7 (a).
Since the U-shape VTA is symmetrical, it can be simplified to that shown in Figure 4-11a.
In this section, it is intended to convert the continuous model shown in Figure 4-11a to a lumped
model four-bar linkage shown in Figure 4-11 (b). In this model, element 1 (short bar) is treated
as a torsional spring, because when the tip of the U-shape vertical thermal actuator is bent
upward or downward, element 2 (long beam) rotates about element 1 (short bar).
The deflection of the VTA can be calculated by the following steps. First, the deflection
of the structure shown in Figure 4-12 (a) can be obtained by using the same method used in
Section 3.3.1. After that, the spring coefficient KT of the structure in the y direction at the tip
of the actuator can be found (Figure 4-12 (b)). Then, the whole structure in Figure 4-11 (b)
can be redrawn as the one in Figure 4-12 (c).
In Section 3.3.1, the fixed base of the plane rigid frame was represented by three force
components. But here, the base of the plane rigid frame shown in Figure 4-11 (b) is hinged
61
top layer
bottom layer
via
cross section
(a)
Kb1
Kb2
(b)
Figure 4-11: (a) The schematic 3-D view of U-shaped VTA, (b) Four bar linkage
representing for the U-shaped VTA.
and therefore two force components can be used when the hinged base is released (Figure 4-12
(a)). The two force components (X1 and X2 ) can be calculated by solving Equation (4.10):


f11 f12
f21 f22


X1
X2


=
∆L1 − ∆L2
0


(4.10)
where fij represents the flexibility coefficients, and they all can be obtained by
f11 =
L2 Lg L2 L1
L32
L31
+ 2 + 2 −
3EI2
EIg
EI1
3EI1
f21 =
L21 Lg L2 Lg L1 2L2g L2
−
−
2EI1
EI1
3EIg
f12 = f21
f22 =
L3g
L2g L1
+
3EIg
EI1
where E is the Young’s modulus of polysilicon, I1 , I2 and Ig are the moment of inertia for the
62
KT
X2
X1
(a)
(b)
Deflection
u
y
KT
Kb1
Kb2
(c)
y
Figure 4-12: (a) The hinged rigid frame for mechanical analysis, (b) schematic of
the spring coefficient analysis in y direction. (c) schematic of the deflection of the
U-shape VTA.
63
top and bottom layer long beams and the via, respectively. Once the two force components are
achieved, the deflection of the end of the rigid frame without torsional spring (Figure 4-12 (a))
can still be calculated by using the virtual work method. The bending moment of the top layer
long beam due to the virtual force is shown in Figure 4-13 (a).The bending moment due to the
L1
P=1
(a)
X2Lg
X1(L2-L1)-X2Lg
(b)
Figure 4-13: (a)The bending moment of the top layer long beam due to the virtual
force, (b) The bending moment of the top layer long beam due to the thermal
expansion
virtual force as a function of the position of the top layer long beam is given by
M = L1 − x
The bending moment due to the thermal expansion is shown in Figure 4-13 (b). It can be
obtained by
M = X1 x + X1 (L2 − L1 ) − X2 Lg
According to the virtual work method, the deflection of the hinged rigid frame without the
torsional springs (Figure 4-12 (a) ) can be found as
1
u=
EI1
Z
0
L1
M M dx =
1
1
1
1
(− X1 L31 + X1 L21 L2 − X2 L21 Lg
EI1 3
2
2
(4.11)
In order to find the stiffness coefficient KT in Figure 4-12 (b), three deflections are assigned
64
to the hinged rigid frame structure (Figure 4-14).By using the force method, the stiffness matrix
V3
V2
V1
Figure 4-14: The hinged rigid frame with three deflection directions
of the structure in Figure 4-14 can be obtained

k11 k12 k13


 k21 k22 k23

k31 k32 k33

∆1


F1


 


 

  ∆2  =  F2 

 

∆3
F3
(4.12)
where kij is the stiffness coefficient. The definition of a stiffness coefficient is analogous to the
definition of the flexibility coefficient: a typical coefficient kij represents the force at i due to a
unit displacement applied at j [46, lea]. ∆i is the deflection in i direction and Fi is the force at
i direction. The stiffness coefficient kij can be given by
k11 =
3EI2 3EI1
+
L32
L31
k21 =
3EI2
L22
k31 =
3EI1
L21
k12 = k21
k22 =
3EI2 4EIg
+
L2
Lg
65
k32 =
3EIg
Lg
k13 = k31
k23 = k32
k33 =
3EI1 4EIg
+
L1
Lg
Let F2 and F3 equal to zero, the stiffness coefficient in the direction of V1 can be found from
equation 4.12.
KT = k11 +
k23 k31 − k33 k21
k32 k21 − k22 k31
k12 +
k13
k22 k33 − k23 k32
k22 k33 − k23 k32
(4.13)
where KT is the stiffness coefficient of the hinged frame in the direction of V1 .
Figure 4-15 shows the steps of how to find the final deflection of the U-shape vertical thermal
actuator. In Figure 4-15 (a), the thermal expansion can generate the deflection u at the tip
of the actuator, it can be treated as an equivalent force F acting at the tip and generates the
same deflection. Hence, the value of force F is uKT . When the two torsional springs are added
to the structure shown in Figure 4-15 (b), the final deflection of the U-shape vertical thermal
actuator can be obtained from
uf =
KT
KT +
Kb1
L21
+
Kb2
L22
u
(4.14)
where Kb1 and Kb2 are the torsional spring coefficients of the top and bottom layer short bars,
respectively.
4.3.2
Simulation results
R
°
The deflection as a function of the input voltage is simulated by Coventorware with MemETherm
solver. The analytical solution is also provided which is in a good agreement with the simulation
results ( Figure 4-16).
66
KT
u
(a)
Kb1
1
uf
2
Kb2
(b)
Figure 4-15: (a) The deflection without torsional springs. (b) the deflection with
two torsional springs
67
7
Analytical results
Simulation results
6
Displacement ( µ m)
5
4
3
2
1
0
0
1
2
3
4
5
6
7
Voltage (V)
Figure 4-16: Deflection of the tip of the U-shaped vertical thermal actuator as a
function of input voltage
4.4
Conclusion
The lumped model developed in this chapter for the mechanical deflection of VTA does not
need prior experiments for tuning the model as opposed to the model in [47]. The simulation
R
°
results obtained from Coventorware have a good agreement with the analytical results.
The U-shape VTA presented here has been fabricated by using the 46th production run of
MUMPs. The top layer is fabricated by using poly2 and the bottom layer is constructed out
of poly1. The four anchors are made of the stack of the poly0, poly1, poly2 and gold layers.
Here, the gold is used to reduce the contact resistance when we use probes to apply a voltage
on the VTA.
In order to measure the vertical deflection of VTA, an optical measuring system has to
be developed. The other way to measure the vertical deflection of VTA is to measure other
properties that can represent the deflection of VTA. For example, the capacitance of a tunable
capacitor can be used for deflection measurement. Further Experiments will require special
equipment which will be prepared in the future.
68
Chapter 5
RF Applications of Horizontal and
Vertical Thermal Actuators
In this chapter, a new multiport switch with a latching mechanism is designed. An improvement
is proposed to increase the tuning range of a tunable capacitor by using bidirectional vertical
thermal actuators.
5.1
Multiport switch with a latching mechanism
MEMS technology has proven its ability in the application of wireless communication, especially
in the RF field. Many single-pole-single-throw (SPST) RF MEMS switches have been designed,
fabricated and modeled. Some companies also have commercialized SPST RF switches based
on MEMS technology. However, multiport switches (N-pole-N-throw, NPNT ) are still under
investigation.
The new design of a MEMS switch with a latching mechanism is presented here. This novel
design can be used to build multiport switches or a switch matrix. The new multiport switch
consists of a horizontal thermal actuator, which has been well documented in Chapter 3, as
the actuation part, and electrostatic actuating cantilevers as the switching part. The switching
part also could be the U-shape vertical thermal actuator, which depends on the application and
the requirements for the multiport switch. For a low speed switch and large switching distance,
the U-shape vertical thermal actuator is a good choice.
69
A general latching mechanism structure is shown in Figure 5-1 (a). It includes two horizontal
thermal actuators and one bidirectional vertical thermal actuator. The actuating sequence is
as follows: first the horizontal thermal actuators are actuated. When plate A is moved away
from plate B, the vertical actuator is activated, it brings plate B downward to the substrate.
Then, the horizontal thermal actuators are released, they bring plate A back to the original
position. After that, the vertical actuator is also released. Because plate A is brought back
first and blocks the way of plate B, it cannot go back to its original position any more. Before
actuation, plate A was under plate B, after actuation, plate A is above plate B, so two different
states of plate B are generated, which can be treated as the switch’s two states: “on” and “off”,
respectively. A closed view of the latching mechanism is shown in Figure 5-1 (b). The white
arrows show the moving direction of the two plates.
The three dimensional structure of the multiport switch is shown in Figure 5-2. This
structure is similar to the one shown in Figure 5-1. Electrostatic cantilever beam actuators
have been used instead of the vertical thermal actuators as the switching part in order to
increase the switching speed. Some holes are also considered on the cantilever beam. These
holes can decrease the damping effect when the switch is activated at high speed. Meanwhile,
these holes can also reduce the stiffness of cantilevers, which means less electrostatic actuating
force, i.e. less input voltage is required to actuate the switch. The purpose of putting holes on
the plate is analogous to the purpose of putting holes on the cantilever beams. The actuating
sequence is similar to the above explanation of the latching mechanism structure.
Each cantilever beam can carry one RF signal. Any of the cantilever beams can be the
signal input port and the others are signal output ports. For example, if the signal input port
is cantilever beam A, and the signal is to be sent out through cantilever beam B, cantilever
beams A and B should be actuated together, and cantilever beam C should be left quiescent.
So, cantilever beams A and B will be changed from one state to another together and connected
through the substrate.
The most important advantage of this type multiport switch is that there is no power
consumption in the quiescent state. The number of the ports the switch can have depends on
the properties of the horizontal thermal actuators and the working frequency. Obviously, the
more ports the switch has, the larger the force the horizontal thermal actuator needs to move
70
Vertical thermal
actuator
Horizontal
thermal actuator
(a)
B
A
(b)
Figure 5-1: (a) Schematic of latching mechanism in 3D view.
latching mechanism.
71
(b) Detail of the
A
B
C
Electrostatic cantilever
actuator
Horizontal thermal
actuator array
(a)
(b)
Figure 5-2: (a) Top view of the multiport switch. (b) Closed-up of the multiport
switch.
72
the plate. If the distance of the two cantilever beams is too small, the signals will “talk” to
each other (cross talk) at high frequency, which affects the property of the multiport switch.
This compromise has to be made.
5.2
Tunable capacitor with U-shaped vertical thermal actuators
The tunable capacitor has been introduced in Chapter 1. Its advantages attract many researchers’ attention. The tunable capacitor with vertical thermal actuators documented in [4]
has shown the tuning range up to the factor of seven. In Chapter 4, the U-shape vertical thermal actuator was designed, modeled and simulated. The results showed the ability of this type
thermal actuator to have larger deflection than the traditional vertical thermal actuators. So
the tuning range of the tunable capacitor can be greatly increased by replacing the traditional
vertical thermal actuator with the U-shape vertical thermal actuator. Figure 5-3 shows an
overview of the new tunable capacitor with the U-shape vertical thermal actuator.
RF singal line
DC power line
U-shape thermal
actuator
Figure 5-3: Top view of the tunable capacitor with U-shaped vertical thermal actuators
With the increase of the deflection of the vertical thermal actuator, the connection between
the actuator and the capacitor plate has to be redesigned. Ideally, the connection should have a
73
small stiffness in the horizontal direction and a large stiffness in the vertical direction. The small
stiffness in the horizontal direction allows the vertical thermal actuators to lift the capacitor
plate easily. The large stiffness in the vertical direction can keep the capacitor plate in the same
plane with the vertical thermal actuator. Based on these requirements, a new design is shown
in Figure 5-4. A S-shaped spring connection is employed here. Obviously, the stiffness of the
S-shaped spring in the horizontal direction is very soft. One special structure is also built to
make the stiffness of the S-shaped spring in vertical direction larger. The cross section of this
structure is zoomed in Figure 5-4. When the U-shape vertical thermal actuator is bent up, the
connection between the tip of the U-shape vertical thermal actuator and the S-shaped spring is
bent down because of the weight of the capacitor plate. But after a certain bending degree, the
two separated poly1 parts of the U-shape vertical thermal actuator and the S-shaped spring
will touch each other, it absorbs most further bending moment and makes the stiffness of the
S-shaped spring stronger in the vertical direction.
5.3
Fabrication and future work
The multiport switch with a latching mechanism and the tunable capacitor with vertical thermal
actuators has been fabricated using the 46th production run of MUMPs. All the pads are not
anchored on the silicon substrate. And they are covered by gold in order to transfer devices
to the other substrate. The purpose of transferring devices to another substrate is to reduce
the effect of the silicon substrate on the RF properties of devices because silicon is conductive
material and lossy for RF signal.
A flip chip bonding machine is needed to transfer devices to another substrate. A vacuum
environment is also required to test devices’ RF properties. The required flip chip bonding
machine is not available yet and Designing a vacuum chamber for RF properties tests is also
under the way. All of these work will be done in my PhD program and experimental results
will be provided in future work
74
A
A
U-shape vertical
thermal actuator
S-shape spring
connection
poly2
poly1
Figure 5-4: Schematic diagram of S-shaped connection and detail of the connection.
75
Chapter 6
Conclusions
In this thesis, a two-hot-arm horizontal thermal actuator model was documented in Chapter
3. Some special phenomena, such as back bending, were found during the experiments. In
Chapter 4, a bidirectional vertical thermal actuator was designed, modeled and simulated.
Chapter 5 discussed applications of these two types of thermal actuators. A multiport switch
with a latching mechanism was developed for RF applications by using thermal actuators. An
improvement of the tunable capacitor was also proposed by employing the novel bidirectional
vertical thermal actuator.
The traditional and well-known one-hot-arm horizontal thermal actuator has been well
documented in many previous published works. Because of its numerous advantages, such as
large displacement, low actuating voltage, and so on, many research effort focuses on this area,
which results in the arising of the two-hot-arm horizontal thermal actuator with larger deflection
and more cost-efficient power consumption. According to the best knowledge of the author,
modeling of two-hot-arm horizontal thermal actuator is first reported here. The numerical
simulation and test results were also provided to corroborate the modeling. Comparing with
the analytical results, a good agreement was achieved. In the experiments, we also found the
fact that the inner and outer hot arm would touch each other at large deflections. At large
deflections, the temperature was also high enough to make structure material-polysilicon to
become soft. therefore, keeping the actuating voltage less than 8V was suggested here based
on the geometry data provided in Chapter 3. Back bending was also reported in the test
results at one-hot-arm thermal actuators, here it was found in the experiments of two-hot-arm
76
thermal actuator. When increasing the driven current and time above a certain level, back
bending occurred. During this process, the inner and outer hot arm deforms. After removing
the current, both of hot arms were shorter than their original length due to plastic deformation.
Based on the strategy of the two-hot-arm horizontal thermal actuator, A U-shape vertical
thermal actuator was designed. This novel actuator had the ability to move bidirectionally
without any remodification, which indicated twice deflection of the traditional vertical thermal
actuators. A new lumped model method was employed to calculate the deflection of the novel
R
°
bidirectional thermal actuator. Simulation results using Coventorware were provided to show
the accuracy of the analytical results.
By applying two-hot-arm thermal actuators and bidirectional vertical thermal actuators, a
multiport switch with a latching mechanism, and an improved tunable capacitor were designed.
A multiport switch is a key device for a communication network. Some multiport switches with
electrostatic actuators need voltage supply when they stay at “on” state. The new multiport
switch with a latching mechanism do not need any power supply for maintaining its on or off
status. The latching mechanism keeps the switch in the desired state. A tunable capacitor is
an important component for a system with a tuning capability. The tuning range of a tunable
capacitor is a significant property. By using new bidirectional vertical thermal actuators, the
tuning range of a tunable capacitor can be greatly increased.
In order to measure the deflection of the new vertical thermal actuator, some future work is
needed. Because of the fabrication limitation, vertical thermal actuators should be transferred
to another substrate in order to test the ability of bidirectional motion. An optical system is
also needed to measure the vertical deflection. For capturing the RF properties of multiport
switches and tunable capacitors they also need to be transferred to another substrate. All the
device transformation can be done by using flip chip technologies.
77
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