Ensc 494
Project Report
Design of a Micro-Machined
Bistable Switch
Maria Trinh
Ian Foulds
Steven Liao
Sam Hu
Supervisors:
Dr. Ash Parameswaran
Robert Johnstone
September 7, 2001
Table of Contents
LIST OF FIGURES ....................................................................................................... III
LIST OF TABLES ......................................................................................................... III
1. INTRODUCTION......................................................................................................... 1
1.1 DEFINITION OF A BISTABLE SWITCH.......................................................................... 1
1.2 THE NEED FOR A BISTABLE SWITCH .......................................................................... 1
1.3 DESCRIPTION OF MUMPS TECHNOLOGY .................................................................. 1
2. DESIGN EVOLUTION ................................................................................................ 2
2.1 PROPOSED SOLUTIONS ............................................................................................... 2
2.1.1 Pull-Crown Design............................................................................................. 2
2.1.2 Push-Crown Design ........................................................................................... 3
2.1.3 Ladder Design, the Best Solution.................................................................... 5
3. IMPLEMENTATION OF THE LADDER DESIGN ................................................ 8
3.1 LIST OF COMPONENTS ................................................................................................ 8
3.2 DESCRIPTION OF DIMENSIONS .................................................................................... 9
3.3 CONSTRAINTS AND CALCULATIONS ......................................................................... 10
3.3.1 Cantilever Beams ............................................................................................. 10
3.3.2 Box Spring ........................................................................................................ 12
3.4 DESCRIPTION OF DIFFERENT DESIGN VARIATIONS ................................................... 13
3.5 DESIGN ISSUES ......................................................................................................... 15
4. FUTURE RESEARCH ............................................................................................... 15
5. CONCLUSION............................................................................................................ 16
ii
List of Figures
FIGURE 1: BISTABLE SWITCH STATE DIAGRAM ................................................................... 1
FIGURE 2: PULL-CROWN DESIGN, FIRST STABLE STATE...................................................... 2
FIGURE 3: PULL-CROWN DESIGN, SECOND STABLE STATE.................................................. 3
FIGURE 4: PUSH-CROWN DESIGN, FIRST STABLE STATE ..................................................... 4
FIGURE 5: PUSH-CROWN DESIGN, TRANSITION STATE ........................................................ 4
FIGURE 6: PUSH-CROWN DESIGN, SECOND STABLE STATE ................................................. 5
FIGURE 7: LADDER DESIGN, FIRST STABLE STATE .............................................................. 6
FIGURE 8: LADDER DESIGN, SECOND STABLE STATE .......................................................... 6
FIGURE 9: LADDER DESIGN TRAJECTORY FOR STATE CHANGE............................................ 7
FIGURE 10: IMPLEMENTATION OF OUR BISTABLE SWITCH IN CADENCE SOFTWARE ............ 8
FIGURE 11: DIMENSIONS OF THE BISTABLE SWITCH ............................................................ 9
FIGURE 12: DYNAMIC MODEL OF CANTILEVER BEAM ....................................................... 10
FIGURE 13: DISPLACEMENT (W) VERSUS LENGTH (L) ........................................................ 11
FIGURE 14: SLOPE (θ) VERSUS LENGTH (L)........................................................................ 11
FIGURE 15: A.) BISTABLE SWITCH DESIGN ACTUATED BY EXTERNAL PROBE HOOKED ONTO
A RING B.) BISTABLE SWITCH DESIGN ACTUATED BY STEPPER MOTORS..................... 14
List of Tables
TABLE 1: LIST OF DIMENSIONS (MEASURED IN MICRONS, ΜM) .......................................... 10
TABLE 2: CONSTANTS USED TO CALCULATE THE LENGTH OF THE CANTILEVER BEAMS...... 11
TABLE 3: VARIATIONS OF THE BISTABLE SWITCH DESIGN (ALL MEASURED IN ΜM) .......... 13
iii
Abstract
The efficiency of many Micro-Electro Mechanical Systems (MEMS) devices can be
increased with the implementation of a bistable switch. A bistable switch has two stable
states that can both be reached through a single actuation or pulse of energy. Such a
switch can be used to change the direction of gears, flip or rotate mirrors, engage or
disengage motors, etc. Its applications are universal. Presently the substitute for a
bistable switch is a monostable switch, which has only one stable state and an unstable
state that requires constant energy to sustain. An effective bistable switch would allow
for a dramatic decrease in the energy used in MEMS devices and as a result, increase in
their efficiency. In this report, you will find the detailed design of a MEMS bistable
switch, including how the solution originated, how the bistable switch was implemented,
and a discussion on its underlying issues.
iv
1. Introduction
1.1 Definition of a Bistable Switch
A bistable switch has two stable states that can both be reached through a single
actuation. Figure 1 is a state diagram illustrating the operation of a bistable switch. The
switch starts out in one of the stable states and when power is applied to the actuators the
switch switches to the other stable state. Power no longer needs to be applied to maintain
the new state of the switch. Re-applying power to the actuators again will return the
switch to its original state and the process can begin again.
Actuation
State 1
State 2
Actuation
Figure 1: Bistable Switch State Diagram
1.2 The Need for a BiStable Switch
In many Micro-Electro Mechanical Systems (MEMS) applications, such as the optical
routers in a fiber-optics communication network, switches with two stable states are often
required. The present solution is to use a monostable switch, which rests at one stable
state when no power is applied and a second unstable state that requires a constant input
of power to be maintained due to its instability. The use of such a switch has the
disadvantages of high power consumption and increased heat dissipation. A more
convenient and economically beneficial design would be a switch that has two stable
states, which can change from state to state via a single actuation. Hence the motivation
for designing a bistable switch as a micro-machined device.
1.3 Description of MUMPs Technology
The technology used to design and implement this bistable switch is termed “Multi-User
MEMS Processes (MUMPs),” which is defined by Cronos Integrated Microsystems as “a
commercial program that provides the international industrial, governmental and
academic communities with cost-effective, proof-of-concept surface micromachining
fabrication. MUMPs is designed for general-purpose micromachining by outside users
who would like to fabricate MEMS devices.”1 MUMPS technology is a powerful design
tool, but it limits the user to only two layers of polysilicon on top of a silicon substrate,
which inhibits the creation of highly sophisticated structures. In addition, since the two
1
Koester D. A., Mahadevan R., Shishkoff A., Markus K. W.. MUMPs Design Handbook 4.0. Cronos
Integrated Microsystems. 3021 Cornwallis Road Research Triangle Park NC 27709. May 1999
1
layers of polysilicon are so incredibly thin (2 microns thick), most structures cannot be
physically pushed without causing any folding, bending or buckling, so any movement of
the structures should be achieved by pulling them. MUMPs technology also comes with
a set of design rules pertaining to the actual dimensions and spacing of the structures
allowable for successful fabrication. The design of our bistable switch was created with
all these constraints in mind.
2. Design Evolution
2.1 Proposed Solutions
In order to find the best solution for a MEMS bistable switch, we first investigated a
variety of bistable switches that are found in simple existing mechanical systems. The
following are descriptions of the 3 possible bistable switch designs we investigated.
2.1.1 Pull-Crown Design
This design, which we entitled “the pull-crown design”, originated from the internal
structure of a certain mechanical pen. Within the mechanical pen resided a crown-shaped
piece that was free to move up and down the pen and swivel side to side. When the user
pushed down on the end of the pen, the crown-shaped piece would be forced downward
and would be lodged in a position that held the pen tip in its extended position. When the
user pushed the end of the pen again, the crown-shaped piece would swivel and be free to
slide up the pen again, thus allowing the pen tip to retract. Figure 2 and Figure 3 show
how we attempted to modify the pen’s design into two stable states under the MUMPs
constraints.
Top bar
Crownshaped
piece
spring
Two locking
mechanisms
Figure 2: Pull-Crown Design, First Stable State
2
Figure 3: Pull-Crown Design, Second Stable State
The idea behind this design is that the crown-shaped piece at the middle pinned down,
but is free to rotate left and right depending on the state of the two locking mechanisms at
the bottom. When the top bar is pulled upward, the crown-shaped piece rotates to a
different state because of the two locking mechanisms and the two springs attached to
them. The top bar then returns downward to a relaxed state and locks the crown in that
state. As a result, a single pull of the top bar will alternate the state of the crown-shaped
piece, resulting in two stable states.
The major drawback with the latch design is the difficulty of designing the proper locking
and unlocking mechanisms that would allow this design to work.
2.1.2 Push-Crown Design
The push-crown design is also derived from the internal structure of the same mechanical
pen described in 2.1.1, but in this design, the crown-shaped piece moves up and down
(using a “push”) while everything around it stays still. Figure 4, Figure 5 and Figure 6
illustrate the operation of the push-crown design.
3
Top bar
Figure 4: Push-Crown Design, First Stable State
Top bar
Figure 5: Push-Crown Design, Transition State
4
Top bar
Figure 6: Push-Crown Design, Second Stable State
In this design, no adjustable locking mechanism is required and the crown-shaped piece,
while allowed to pivot, is not directly anchored to the substrate. The crown-shaped piece
is attached to two springs at the middle (underneath a suspended single layer) and at the
bottom. Whenever the top bar is pulled downward, the bar will push against the crown
piece and move the crown piece along one of the two sides of the channel formed by the
objects colored in purple (Figure 4). Due to its geometry, the crown-shape will be
pushed towards to the other side of the channel from the first stable state and moved into
the transition state (Figure 5). When the top bar is retracted, the spring at the top will
pull the crown-shape upward until it is locked into the second stable state (Figure 6). In
reverse order, another single actuation will move the crown piece from the second stable
state back to the first stable state.
The crown-shaped design was proven to work on a wooden model, but after consulting
the details of the MUMPs technology, we found that there are serious fabrication
difficulties related to this design. First of all, a compressive force between the top bar
and the crown-shaped piece is necessary for this design to work, but has a high risk of
bending or warping the crown piece due to the thickness of the structure in relation to its
other dimensions. Secondly, the attachment of the spring at the middle of the crownshaped requires a suspended silicon layer above the spring. In MUMPs technology, a
suspended layer will conform in shape to the structures below it, which would result in a
kinked spring that would not be functional.
2.1.3 Ladder Design, the Best Solution
The first two designs derived from the mechanical pen were not suitable to be implement
as desired with the MUMPs technology. The design we chose to implement instead was
5
based not on a mechanical pen but on the locking mechanism of an extension ladder.
Figure 7 and Figure 8 show the two stable states of the Ladder Design.
Rail
Guide
Step
Hook
Actuator
Rod
Cantilever
Beams
Pull
Figure 7: Ladder Design, First Stable State
Figure 8: Ladder Design, Second Stable State
In Figure 7, we can see that the ladder design is composed of two cantilever beams on the
left (acting like springs), a hook in the middle, and a “step” attached to the actuator rod
that is freely to move up and down, vertically. The top cantilever beam is anchored at the
top and pivots from that anchor, whereas the bottom cantilever beam is anchored at the
6
bottom and pivots around that anchor. Not shown in Figure 7 or Figure 8 is a box spring
attached to the top of the actuator rod, acting to return the step to its original state after
each downward pull.
To aid in visualization of the switch’s movement, Figure 9 illustrates the movement of
the switch from state 1 to state 2 and back to state 1 again.
a.)
d.)
b.)
e.)
c.)
f.)
Figure 9: Ladder Design Trajectory for State Change
a.) All the components rest at their relaxed state in the first stable state. All the
cantilevers are relaxed, and so is the unseen box spring above the actuator rod.
b.) With the introduction of a pulling force, the actuator rod is pulled downward until
the “step” slips into the “hook.”
c.) When the pulling force is removed, the actuator rod is wishes to be restored
upward by the unseen box spring but is unable to move due to the interlocking of
the hook and step. This locked state is in the second stable state.
d.) A second downward pull moves the step past the hook.
e.) When the applied force is removed, the actuator rod will be forced upward again
by the box spring, pulling the step to bypass the hook
f.) Just before returning to the first stable state, the two cantilevers operate separately
to manipulate the hook and return it to its original position.
The design of the ladder switch is simple, which increases the chance that it can be
reliably fabricated and operated. This design does not require any complex locking
mechanisms, nor does it have the problem of pushing two thin sheets of silicon against
one another, thus satisfying the MUMPs constraints.
7
3. Implementation of the Ladder Design
3.1 List of Components
Figure 10 was generated from a Cadence2 layout and shows the actual implementation of
our bistable switch in MUMPs.
Rail
Guide
Step
Hook
Actuator
Rod
Direction
of
Pull
Cantilever
Beams
Rail
Guide
Figure 10: Implementation of Our Bistable Switch in Cadence Software
As shown in Figure 10, the main components of our bistable switch are the cantilever
beams, hook, pushing rod, and actuator rod. Moreover, although not shown in the
picture, the actuator rod is attached to a box spring at the top that acts to restore the
actuator rod to its original state. At the bottom of the actuator rod, two linear stepper
motors are used to insert the pulling force.
2
Software package used to design our bistable switch
8
All the components that come into contact with each other are designed with a double
layer of polysilicon to ensure a larger contact area. These components include: the step,
the hook, the ends of the cantilever beams and the rail guides. All the other components
are single layers of polysilicon.
3.2 Description of Dimensions
The physical size of our entire design was constrained by the required size of the
rotational joint in the middle of the hook. We would have liked to make the dimensions
smaller but the limitations of the MUMPs technology dictated the size of our switch. Part
of our future work on our switch will be to find a way around these limitations so that the
switch can be made even smaller. Figure 11 provides the labeling for the dimensions
listed in Table 1.
A
B
C
D
K
F
E
H
G
I
J
M
L
Figure 11: Dimensions of the Bistable Switch
9
Table 1: List of Dimensions (measured in microns, µm)
A
12.00
B
36.00
C
50.00
D
82.00
E
120.00
F
2.00
H
49.00
I
30.00
J
80.00
K
86.00
L
120.00
M
2.00
G
75.00
We produced different permutations of this design wherein we varied the lengths of L
and E to account for different pulling forces. The dimension of L and E vary from 85 to
170 microns. The unseen box spring has a length of 250 microns.
3.3 Constraints and Calculations
3.3.1 Cantilever Beams
The lengths and widths of the two cantilever beams and the box spring were calculated to
best accommodate the pulling forces that would be exerted on them. These dimensions
determined the spring constant of both the cantilever and box springs.
To calculate the desired dimensions of the beams, we approximated the dynamics of a
single beam as end load cantilever beam, as shown in Figure 12.
Figure 12: Dynamic Model of Cantilever Beam
We used the equations listed on the www.efunda.com web site3. Given a specific beam
loading case and the dimensions of the beam, the web site provided an online calculator
to determine the maximum displacements, slopes, moments, stresses, and shear forces for
this beam problem. We mainly used the equations shown in Equation 1 through Equation
4, which allowed us to the approximate the beam’s maximum deflection angle (slope)
and maximum displacement before breaking. The values used in Equation 1 through
Equation 4 are shown in Table 2.
3
The exact web address that present the formulas is:
http://www.efunda.com/formulae/solid_mechanics/beams/casestudy_display.cfm?case=cantilever_endload
10
Displacement Calculations:
Figure 13: Displacement (w) versus length (L)
Equation 1
Equation 2
Slope Calculations:
Figure 14: Slope (θ
θ) versus length (L)
Equation 3
Equation 4
Table 2: Constants used to calculate the length of the cantilever beams.
Length of beam, L
Load on end of beam, P
Young’s Modulus, E
Moment of Inertia, I
Varied; we estimated lengths from 85 to 170 µm
30E-6 N
160 GPa
1.6E-23 m
11
To find our spring lengths we fixed our width at 2 microns and the force at half our
expected output from the stepper motors (30 µN) and iterated through lengths until we
found an appropriate deflection angle of 30°.
3.3.2 Box Spring
Similarly, in order to determine the dimensions of the box spring, we used the formulas
presented on the web site www.sfu.ca/adm. These formulas are as follows:
w ⋅ h3
12
Equation 5
96 ⋅ E ⋅ I
N ⋅ L3
Equation 6
I=
K=
where:
I = moment of inertia
w = width of individual beam
h = height of individual beam (thickness)
L = length of individual beam
K = spring constant
E = Young’s Modulus = 160 x 109 Pa
N = number of beams.
Rearranging Equation 6, we can then solve for the length of the individual beam inside
the box spring given the value of the spring constant K, which generates the formula
shown in Equation 7.
96 ⋅ E ⋅ I
L3 =
N ⋅K
Equation 7
12
3.4 Description of Different Design Variations
To ensure that calculation errors and uncertainties were taken into account, we created
several permutations of our original design by selecting different lengths for the
cantilever beams and different sizes for the box spring. Table 3 lists the 9 different
permutations of our design.
Table 3: Variations of the Bistable Switch Design (all measured in µm)
Top Cantilever Length
Bottom Cantilever Length
85
100
120
100
120
150
120
150
170
85
100
120
100
120
150
120
150
170
# of Beams in the Box
Spring
10
10
10
20
20
20
30
30
30
Each permutation in our design submission has two numbers beside it: the first number
indicated the number of beams in the box spring; the second number indicates the length
of the cantilever beams.
We also permutated the cantilever and box spring dimensions with two different types of
actuators. Some designs include a stepper motor to actuate the switch. Others include a
ring to be pulled manually by hooking with an external probe. These two design
variations are shown in Figure 15.
13
a.)
b.)
Box springs
Stepper
motor
ring
Figure 15: a.) Bistable Switch design actuated by external probe hooked onto a ring
b.) Bistable Switch design actuated by stepper motors
14
3.5 Design Issues
Since we have approximated the force exerted by the stepper motors, the actual
dimensions of the cantilevers and box springs may not be optimal, which is why we
included different variations and permutations. We are inexperienced with the
mechanical properties of polysilicon. Only after careful testing will we know if our
calculations are correct and which dimensions work best.
We have designed all components that come in contact with each other with double
layers of polysilicon for larger contact areas, but we are inexperienced with the frictional
forces that occur between structures of such microscopic dimensions. Therefore, we are
unsure as to whether structures will stick or become lodged against one another due to
these frictional forces. We designed the corners of the cantilevers to be rounded to guard
against such an event. We are also unfamiliar with potential stresses and strains that
could occur in various parts of the device, and with the potential problems that could
arise due to the fabrication process. But again, only after careful testing of the fabricated
switches will we know the effectiveness of our design.
4. Future Research
One of the main disadvantages about our current design is its size. Due to the technology
constraints our design requires a stroke length in excess of 160 microns. The main
constraint leading to this size factor is the design of the hub on which the hook pivots.
Our next major goal in terms of research is to shrink the size of the hook so that the entire
device can be minimized. Because the hook doesn’t need to turn in a complete circle, we
are currently considering the replacement of the hub with a torsional spring.
Other improvements we are considering include designing a single input actuator that can
provide a larger stroke length and look into other implementation technologies to see if
one would be a better fit for our design.
15
5. Conclusion
Successful development of a MEMS bistable switch would greatly improve the efficiency
and reduce the cost of many MEMS devices. Based on simple mechanical bistable
switches like the mechanisms found in ballpoint pens and extension ladders, we proposed
several possible solutions for the MEMS bistable switch. After analyzing our designs
with respect to the MUMPs technology we decided that our ladder design best fit the
MUMPs technology. For each component in the ladder design, a series of calculations
were performed to select the optimal dimensions that would best approximate the ideal
performance of the switch. To ensure that calculation errors and uncertainties were taken
into account, we created several permutations of our original design using different
dimensions for certain components like the cantilever beams and box spring. We also
created some permutations that would be actuated by stepper motors, and others by
manual force. Our design uncertainties stem from our inexperience with fabrication
issues and with the material properties of polysilicon. But based on the simplicity of the
mechanism behind this design, we feel confident that this bistable switch will work to at
least some degree. The success of our switch now lies only in the future testing and
refining of the device.
16