Piezoelectric Micro Power Generator (PMPG):
A MEMS-Based Energy Scavenger
by
Rajendra K. Sood
Submitted to the Department of Electrical Engineering and Computer Science
in Partial Fulfillment of the Requirements for the Degrees of
Bachelor of Science in Electrical [Computer] Science and Engineering
and Master of Engineering in Electrical Engineering and Computer Science
at the Massachusetts Institute of Technology
September 2003
©2003 Massachusetts Institute of Technology. All rights reserved.
The author hereby grants to M.I.T. permission to reproduce and
distribute publicly paper and electronic copies of this thesis
and to grant others the right to do so.
X
De artment of Electrical Engineering and Computer Science
September 8, 2003
Author
Certified by
Sang-Gook Kim
Thesis Supervisor
Accepted by
Arthur C. Smith
Chairman, Department Committee on Graduate Theses
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
JUL 2 0 2004
LIBRARIES
BARKER
Piezoelectric Micro Power Generator (PMPG):
A MEMS-Based Energy Scavenger
by
Rajendra K. Sood
Submitted to the
Department of Electrical Engineering and Computer Science
September 8, 2003
In Partial Fulfillment of the Requirements for the Degree of
Bachelor of Science in Computer [Electrical] Science and Engineering
and Master of Engineering in Electrical Engineering and Computer Science
ABSTRACT
As MEMS and smart material technologies begin to mature, their applications, such as
medical implants and wireless communications are becoming more attractive.
Traditionally, remote devices have used chemical batteries to supply their energy.
However, batteries are no longer suitable for many of these remote applications due to
their relatively large bulk and weight, limited lifetime and high cost. The commercially
sponsored Auto ID tag has demonstrated the need for a power source with the
characteristics of our Piezoelectric Micro Power Generator (PMPG). The PMPG is a
MEMS-based energy scavenging device which converts ambient, vibrational energy into
electrical energy. It consists of a composite micro-cantilever beam with a PZT
piezoelectric thin film layer and a top, interdigitated electrode structure which exploits
the d33 mode of the piezoelectric. When excited into mechanical resonance, the PMPG
acts as a current generator whose charge can be stored by an electrical charge storage
system. A single PMPG device delivered more than 1 siW of DC power at 2.36 V DC to
an electrical load from an ambient, vibrational energy source. The corresponding energy
density is approximately 0.74 mW-h/cm 2, which compares favorably to competing
lithium ion battery solutions for the Auto ID tag. The PMPG power system has an
electrical efficiency greater than 99%. In the near future the PMPG power system will
serve as the power source for the Auto ID tag and has benefits over its competitors.
Namely, the PMPG has a potentially infinite lifetime, is a cheaper, less bulky power
solution versus competing lithium ion batteries, and should prove to have a better
packaging scheme.
Thesis Supervisor: Sang-Gook Kim
Title: Edgerton Associate Professor of Mechanical Engineering
3
Table of Contents
1. Introduction ...............................................................................
1.1 M otivation ..........................................................................
1.2
1.3
1.4
1.5
PMPG Power System Description .................................................
9
Competing Power Solutions .....................................................
10
PMPG Power Source as Applied to Auto ID Tag .............................
11
P urpose ..........................................................................
... 13
2. Mechanical Design .....................................................................
2.1 Background Design and Considerations ........................................
2.2 Approximations in the Mechanical Modeling .................................
2.3 PMPG Resonance Frequency Calculations ......................................
2.4 Seismically, Excited Spring-Mass Damper ....................................
15
15
17
18
20
3. Piezoelectricity and PZT ..............................................................
3.1 Definitions and Principles of Piezoelectricity ................................
3.2 Poling Process .......................................................................
3.3 Basic Description of Device Operation ...........................................
3.4 Piezoelectric Characterization of PMPG Type-1 Device ....................
23
23
25
28
28
4. Electro-Mechanical and Electrical Equivalent Models ........................
4.1 Higher d33 Mode Open Circuit Voltage vs. d31 Mode ..........................
4.2 PZT Poling and Electrical Resistance and Capacitance ......................
4.3 Electro-Mechanical Model and Equivalent Electrical Circuit ................
4.4 Resonance Frequency Condition ................................................
4.5 PMPG Voltage Amplitude Requirement ........................................
32
32
33
34
39
40
5. Fabrication ..............................................................................
5.1 Fabrication Process Steps ..........................................................
5.2 Process C onsiderations ..............................................................
5.3 PM PG M ask Layout .................................................................
42
42
44
45
6. Experimental Setup ...................................................................
6.1 PMPG Packaging and Poling ......................................................
6.2 Polytec© PSV-300H Laser Vibrometer System ..............................
6.3 Optical Positioning/Base Shaking System .......................................
6.4 Base Shaking and Acoustic Excitation Experimental Setups ................
6.5 Electrical Data Measurements: Kistler© 5010B Dual Mode Amplifier and
Power Storage System ..........................................................
49
49
51
53
55
58
7. Tests and Results .........................................................................
61
7.1
7.2
4
7
.7
PMPG Direct Excitation (Actuation Mode) Results ..........................
Laser Vibrometer Surface Scans ...................................................
61
64
7.3 PMPG Base Shaking (Sensor Mode) Results .................................
66
7.4
7.5
7.6
7.7
Load Varying Experiments ...........................................................
Charging/Discharging of Power Storage Capacitor ..........................
Electrical Efficiency Calculations ..............................................
Acoustic Excitation Results .....................................................
70
74
79
83
8. Conclusions ..............................................................................
85
8.1 Performance Specifications of the PMPG Power System .................... 85
8.2 Improving Upon the Current Technology ...................................... 86
8.3 Application Driven Questions Regarding the PMPG ......................... 87
8.3.1 Can the PMPG be used to power an active Auto ID tag (i.e. to power
the RF communication)? ................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
8.3.2 Although acoustic energy harvesting could not be demonstrated in
our experiments, is this type of energy harvesting possible? . . . . . ... 90
8.4 Overview of Lithium Ion Battery Technology and Comparison to PMPG
Power System .....................................................................
93
8.5 Research Summary ................................................................
97
Bibliography ..................................................................................
99
Appendix A.1 ................................................................................
101
Appendix A.2 ................................................................................
109
5
Acknowledgements
I would first like to thank Professor Sang-Gook Kim for supporting my research
and pushing me to achieve my goals. I valued his technical advice, and especially his
ability to keep me focused on the big picture of what I was trying to achieve. I would
like to thank Professor Sanjay Sarma and the Auto ID Center whose funding made this
research possible. Special thanks must be given to Dr. Yongbae Jeon whose help on this
project was immeasurable. Dr. Jeon was responsible for most of the fabrication of the
PMPG devices in addition to several other contributions. Without Dr. Jeon's
contributions, this research simply would not have been possible. Special thanks must
also be given to Lodewyk Steyn, whose help made the laser vibrometer experimentation
possible. With Lodewyk's help I was able to gather the pertinent data and results for my
research. I would like to thank Nicholas Conway for his extensive technical advice and
help with Matlab@ simulations. Stan Jurga helped me immensely with my laboratory
setup, specifically in machining the parts for the optical positioning/base shaking system.
Thanks must also be given to my office mates, Yong Shi and Chee Wei Wong for their
advice and support. Micah O'Halloran was very gracious, lending me his time and
giving me important insight into the workings of the electrical equivalent model of the
PMPG power system. Thanks to Dan Opila and Dr. Jeung-Hyun Jeong for mechanical
characterizations of the PMPG device. Professors Steve Senturia, Jeffrey Lang and
Michael Perrot for their insights pertaining to the electro-mechanical modeling of the
device. My friends here at MIT, especially Erik Deutsch and Jay Bardhan- will always
remember those late nights at MTL. Finally, I would like to thank my family for giving
me the support I needed throughout my years at MIT.
6
Chapter 1: Introduction
1.1
Motivation
One of the most promising new fields in engineering is Microelectromechanical
systems, or MEMS, in which silicon chip fabrication technology is used to create
extremely small (on the order of a micron) electromechanical devices. Examples include
MEMS-based optical display technologies, extremely accurate measurement systems and
DNA amplification systems, to name a few. Ambient energy exists within the
environment of the system and is not stored explicitly, for example in a battery. The
most familiar ambient energy source is solar power. Other examples include
electromagnetic fields (used in RF powered ID tags, inductively powered smart cards,
etc.), thermal gradients, fluid flow, energy produced by the human body, and the action
of gravitational fields. Finally, vibrational energy can be used as an ambient source. A
power generator based on transducing mechanical vibrations can be enclosed to protect it
from a harsh environment and it functions in a constant temperature field, among other
benefits.
A comparison of potential ambient sources for energy harvesting is given in
Figure 1.1. Vibrational energy harvesting via piezoelectric conversion has a high power
density compared to most of the available energy sources. When taking into account cost
of manufacturing and applications such as powering low cost devices (e.g. small sensors
and/or low power integrated circuits), then solar, hydrocarbon fuel and fuel cells are too
extravagant and expensive for these applications. Solar power is similarly impractical.
Piezoelectric energy harvesting becomes a more attractive option. The challenge is to
prove that the piezoelectric energy harvesting device can outperform batteries from a
cost/performance perspective. MIEMS-based energy harvesting devices have been
created and are a part of on-going research in the MIEMS field [1, 2, 3, 4, 5].
7
Power density (10 year lifetime)
(W/cm 3)
Energy Source
Solar (outdoor)
15,000
Solar (indoor)
6
Vibration (piezoelectric)
Vibration (electrostatic)
Temperature gradient
Batteries (non-rechargeable)
250
50
15(at 10 0 C gradient)
3.5
Batteries (rechargeable)
7*
Hydrocarbon fuel (micro heat engine)
Fuel cells (methanol)
33
28
Figure 1.1: Comparison of Ambient Energy Sources [4]
* one year lifetime
There are many advantages of using an ambient vibrational energy source: (1)
The energy source has an infinite lifetime, which means the device can have an infinite
shelf time. (2) No physical links to the outside of the system are needed. (3) The device
can be enclosed and protected from the harsh environment. (4) Ambient acoustical
energy (either acoustical noise or artificially generated acoustical energy) can be used as
an on-demand energy source, so long as the mechanical structure can couple external
acoustic waves.
Portable systems that depend on batteries have a limited operating life and can fail
at inconvenient times, while a circuit powered by an ambient energy source has a
potentially infinite lifetime. In systems with long lifetimes where battery replacement is
difficult, ambient energy harvesting is actually necessary. Examples include medical
implants, wireless sensors and smart structures where sensors are embedded in bulk
structural members. Such devices, at best, provide limited access to the embedded
electronics. "In the future, the dominant systems that require their own power source
may be imbedded systems." [6] Aggressive power scaling trends over the last decade
have resulted in power consumption in only the 10's to 100's of ytW for low to medium
throughput DSP circuits and other digital VLSI circuits. This scaling will allow for
8
energy harvesting solutions for powering the kinds of imbedded systems and low power
circuits previously mentioned.
100 mW
TI 1V DSP [21
10 mW
C
Video
a.
o
Medical
D6comPrO$OnMonitoring,
1R
[3]
Acquisition,
1Detection
[4][5]
101W
'10 liW
Fig. 1.
.........
ptIM
Programmable
DSP
Trends i~n power
cxnspt
Custom
DSP
n for
Sensors
low to medium
thrOLuhput DSP.
Figure 1.2: DSP Power Consumption Trends [6]
1.2
PMPG Power System Description
The PMPG is a unique, MEMS-based energy scavenging device. It consists of a
composite micro-cantilever beam with a top, interdigitated electrode and optional proof
mass (Figure 1.3). The interdigitated electrode is used to exploit the d33 excitation mode
of the piezoelectric material, lead zirconate titanate (also known as PZT). This allows for
a higher open circuit voltage versus a d31 electrode structure constrained to the same
beam geometry. Single devices can be lumped together with a single proof mass and/or
arrayed on a single chip to increase the total power output. Devices can be mechanically
tuned to resonate at different frequencies by varying the dimensions of the cantilever
beam. A rectifying circuit and electrical storage device (capacitor) are required for
rectifying and storing the electrical energy for each device (Figure 1.4).
9
Interdigitated Electrode
PZT layer
ZrO2 layer
Membrane layer
Figure 1.3: Device schematic of d33 mode piezoelectric device (PMPG). The left side of
the diagram is a cross-sectional view. Alternating plus and minus potentials exist on
adjacent mini-electrodes (which together make up the interdigitated electrode) when the
PMPG device is bent during mechanical resonance. The right side of the diagram is a top
view of the inter-digitated electrode.
Rectifying bridge
D4 D1
IPMph
CO
dq/dt
Total PI\A P
I
Current tource
L Cr -ourceI
I
D2
D3
IRLoad
16
G
ZP
Ic
C
Power
torage
Capacitor
R Load
PMPGT
Figure 1.4: PMIPG Power System: PMPG with Rectifier, Storage Cap and RLoad
1.3
Competing Power Solutions
There have been several patents (e.g. International Publication Number WO
01/20760 Al [7], United States Patent 5,835,996 [8] and Remon Technologies patents
(6,239,724 and 6,198,965 and 6,140,740 and pending patent 20010026111) [9], etc.)
which describe micro power generators. They describe micro fabricated generators with
infinite shelf and duty lifetimes that can be integrated as part of a monolithic device on a
chip. These patents, however, do not describe how to achieve the generated high voltage
sufficient for processing in a rectification, or how to fabricate the devices using MEMS
fabrication technology. International Publication Number WO 01/20760 Al is too
obscure because it does not describe how to fabricate the cantilever structure or the
10
shapes of the piezoelectric and electrode layers. Patent 6,140,740 uses a diaphragm
structure rather than a cantilever structure that is used in the present invention. Both of
these patents use the d31 piezoelectric mode instead of the d33 mode which is used by the
PMPG.
The dry cell is the most commonly used form of chemical battery, widely used in
flash lights, portable consumer electronics, etc. "Embedded or wearable sensor
electronics require relatively small battery form factors and long lifetime, so lithium
button cells are the most desirable solution." [6] This is why the lithium ion battery is the
Auto ID Consortium's preferred battery solution for the Auto ID tag. However, the
Piezoelectric Micro Power Generator (PMPG) can be a better power source for the Auto
ID tag than conventional lithium ion battery technology.
1.4
PMPG Power Source as Applied to Auto ID Tag
The Auto ID tag is a cheap, RF-based identification tag which will be used in
consumable applications such as grocery product identification. The tag would
effectively replace bar codes with a tiny chip that can be identified from a distance via the
RF. Any Auto ID tag which would employ the PMPG as a power source would
automatically be categorized as either "active" or "semi-passive"/"semi-active",
depending on the type of tag in which it is used. Active tags have a power source which
is used to power both the microchip's (ID) circuitry and the RF communication signal
being sent to the reader (communication beacon). Active tags usually require large
batteries for powering the RF communication. These batteries are larger in size than the
PMPG. They are also very expensive. Semi-active tags use the battery to power the ID
circuitry and use the RF power from the reader for communication. This allows the semiactive tag to increase its communication range to the 10's of meters versus just 5 meters
for the completely passive tag.
The PMPG power source is ideal for the semi-active tag, although the possibility
of using the PMPG for the active tag remains a possibility. According to Klaus
Finkenzeller from his book RFID Handbook: "Using current low power semiconductor
technology, transponder chips can be produced with a power consumption of no more
11
than 5 LW." [10] In the case of the current, semi-active Auto ID technology, EEPROM
running at I microwatt READ and 3 microwatt WRITE is being used. These read/write
power requirements are built into the total 5 micro-Watt power specification of the semiactive Auto ID circuitry. This, therefore, defines the present power requirement of the
PMPG system: The PMPG must be able to provide power to the ID circuitry within a
semi-active tag system. This is an achievable goal.
The Auto ID tag requires a power source that can supply approximately 5
sW of
DC power to its on-board digital identification circuitry (which can be modeled as an
electrical load input). The power source must be small in size- on the order of 500stm X
500 tim total device area, and self-sustaining with no physical links to the outside world.
This corresponds to a power density of 5 ttW/(500pm X 500 pm) = 2 mW/cm 2 . The
Auto ID team is currently using an expensive lithium ion battery to power its semi-active
RF Auto ID tag. This lithium, printed battery is expected to have a lifetime of about 3
years. [11] A cheaper, less bulky power-MEMS device that uses an external, vibrational
energy source could provide the needed power in this range. The PMPG is therefore a
good fit for the Auto ID Project and an ideal replacement for the current battery
technology being used.
Active and semi-active tags are more expensive (about $1) than "passive" tags
which use only the RF power supplied by the reader to power the ID circuitry and RF
communication. The Auto ID consortium is targeting passive RFID tags as the solution
for mass market product identification because these tags cost much less (The goal is to
create a 5 cent tag.). If the PMPG can prove to be a cheaper power solution to the other
battery alternatives (lithium ion battery is the most common), then it would still fall in the
semi-active tag category, but could potentially bring the cost down from the $1 tag.
According to the Auto ID Consortium: "Active and semi-passive tags are useful
for tracking high-value goods that need to be scanned over long ranges, such as railway
cars on a track, but they cost a dollar or more, making them too expensive to put on lowcost items. The Auto-ID Center is focusing on passive tags, which cost under a dollar
today. Their read range isn't as far - less than ten feet vs. 100 feet or more for active tags but they are far less expensive than active tags and require no maintenance." [12]
12
This means that semi-active tags have a narrower range of applications in the real
world due to their higher cost. If the PMPG can bring down the cost, then more
applications will be possible. Possible applications for semi-active tags which employ
the PMPG as their power source: 1.) ID tags for the automotive industry where products
cost more, and can thus afford the higher cost of the semi-active tags. The external
vibration (shaker) source of the car parts makes PMPG-type energy harvesting possible.
A MIEMS-based tire pressure monitoring system (TPMS) which employs the PMPG as its
power source is one possibility. 2.) Contactless smart cards for public transportation.
This application needs to be explored further. 3.) Container transport identification.
Current international containers use an RFID system which carries a small, chemical
battery for supplying power to the electronic data carrier in the transponder. The PMPG
might prove a cheaper battery solution provided it can withstand the large variation in
container temperatures (-40'C to +120 C).
Therefore, the benefit of the PMPG over other power sources must be proven in at
least four major categories: 1.) Power generation specifications versus other isolated
power sources (batteries). 2.) Cost. For example, the PMPG chip could be fabricated on
the same chip as the Auto ID circuitry, making it cheaper than a separately packaged
battery solution. 3.) Lifetime (infinite for PMPG versus a few years for chemical
batteries). The PMPG power system would also require no maintenance. 4.) Simpler and
more reliable packaging scheme.
1.5
Purpose
The purpose of my research is to create a MEMS device capable of converting
vibrational energy from the environment into electrical energy via the piezoelectric
effect, and subsequently storing the generated, electrical charge in a power storage
system for use as an on-demand, electrical power source. Ultimately, such a device
would use acoustic waves as its ambient, vibrational energy source and would fulfill the
power density requirement of the Auto ID tag. The initial mechanical design of the
PMPG cantilevers targeted an acoustic frequency range between 20 kHz to 40kHz. In
this way, "proof-of-concept" experiments would be conducted whereby an artificial
13
acoustic noise source from an acoustic speaker would resonate the cantilever structures
above the audible. The reason for targeting a frequency range above the audible (greater
than 20 kHz) was to avoid any violations of federal communications laws and still be a
viable power source for the Auto ID tag.
My work on this project involved design, fabrication and testing of the PMPG
device, with the majority of the fabrication work having been done by Dr. Yongbae Jeon.
My research can be summed up as a "proof of concept": To prove that a single PMPG, or
array of such devices, can be externally vibrated and produce the power density
specification given by the Auto ID Project.
14
Chapter 2: Mechanical Design
2.1
Background Design and Considerations
The primary reason for choosing the cantilever structure for our piezoelectric
transducer is because, among the common MEMS support structures (cantilever, doubly
supported beam, diaphragm, etc.) it is the most compliant structure for a given input
force. Initially, it was thought that direct acoustic excitation of the PMPG devices by
means of an artificial acoustic source would be the best way to prove the piezoelectric
micro power generation concept. In order to meet federal, FCC regulations, an artificial
acoustic noise source would have to remain above the audible. For this reason, the initial
resonance frequency of the PMPG device was designed to be 20 kHz or above. Devices
were originally designed to have a resonance frequency of either 20 kHz or 40 kHz
depending on their length.
However, the fabrication process was changed when it was determined that a
bottom platinum (Pt) layer would not be suitable as a diffusion barrier for proper d33
piezoelectric mode operation. ZrO 2 was chosen as its replacement. The choice of ZrO 2
further required that the membrane layer be changed from SiNX to SiO 2 in order to
provide good matching between ZrO 2 and the Si substrate. Thicknesses of the material
layers were also changed. This meant that the stiffness, and ultimately, the resonance
frequency, of the composite cantilever beam were changed from the initial design.
The fabrication process was constantly being varied to produce a good composite
structure which matched the materials well and provided a good thin film PZT layer with
good perovskite structure. All of these fabrication changes meant that the resonance
frequency calculations took a back seat to the fabrication issues. This explains, in part,
why the final resonance frequency of the tested Type-I PMPG device was measured at
13.7 kHZ instead of 20 kHz as intended. The final material order (from bottom) and
thicknesses for the Type-1 PMPG device are: 1st layer is 0.4 ttm of PECVD oxide;
layer is 50 nm of ZrO2 ; 3'd layer is 0.48
stm of PZT (4 sol-gel
spin-ons);
4 th
2 nd
layer is the
top, interdigitated electrode consisting of Pt (200 nm)/Ti (20 nm); SU-8 Proof Mass is
15
located at the end of the cantilever beam and is 50 ,Im tall, 20 ,Im long and 261 ,im wide
(same width as beam).
A cantilever beam can be designed with a certain length, width and thickness (I'm
assuming a uniform cross-section.) such that it resonates at a chosen, first-mode
resonance frequency. A composite cantilever beam, which consists of multiple layers,
can be designed in much the same manner. First of all, the resonance frequency of the
cantilever beam is targeted at the same frequency as the vibration/noise source in order to
couple the most possible ambient energy into the mechanical structure. There are
multiple resonance frequencies/modes of the beam, but we will use the first mode
because the beam shape at maximum deflection is analogous to a simple static beam
deflection under a uniformly distributed force or pressure. This type of beam deflection,
along with one other condition, will allow for the stress through the thickness of the PZT
layer to be of uniform polarity (either completely tensile or completely compressive)
during bending.
It is important to have uniform stress through the PZT thickness during bending
because otherwise the charge will not be of the same polarity thereby causing charge
cancellation. The polarity of the stress will be the same through the thickness of the PZT
thin film only if the composite beam's neutral axis remains below the PZT layer. If the
neutral axis, exists somewhere in the middle of the PZT layer, then when the beam is bent
up, the PZT material located above the neutral axis will be in compression and the PZT
material below will be in tension.
The microfabricated PMPG cantilever devices do exhibit some out of plane
bending or warpage due to residual stress effects. As long as the released beam is not
bent up or down too much (perhaps, no more than ±100 from the neutral position), the
apparent stiffness and natural frequency of the beam should remain unchanged for the
curled beam [13]. Most importantly, the power production in the PZT depends only on
the change in strain, regardless of the initial stress/strain state of the PZT. Given residual
stresses in the material, the strain in the PZT will still oscillate.
The thinking behind the Type-I PMPG device was that in making it wider than it
is long (261 ym wide and 170 [tm long after the XeF 2 etch step), we would be increasing
the active surface area of the device, thereby allowing more charge to be collected by the
16
wider electrode structure. The other part of the thinking was purely mechanical: If the
beam is wider than it is long, then it will be stiffer in the lateral direction, forcing the
movement to be primarily up-and-down during resonance rather than side-to-side.
2.2
Approximations in the Mechanical Modeling
1.) Beam thickness and mass is at least an order of magnitude smaller than that of
the proof mass for the Type-1 PMPG device. Therefore, the mass of the beam
is dominated by the proof mass Mproof.
2.) The effect of the top, interdigitated electrode on the total stiffness is neglected
because its cross-sectional area is only a fraction (approx. 12%) of the area of
the other composite layers. The top electrode will only serve to further stiffen
the beam, so the natural frequency would increase slightly if it is taken into
account. The calculations to account for the electrode geometry are difficult
and introduce needless complexity into the analysis.
3.) The composite cantilever beam is idealized as a structure made up of N
separate layers perfectly bonded together with no slipping. Figure 2.1 is a
cross-sectional view of a composite beam made up of three layers: SiO 2 , ZrO 2
and PZT.
17
-~~~
F YSiO
ZO
exlAxis
noa
2
Dimensions:
Y1-height of centroid of area of SiO 2
Y2-height of centroid of area of ZrO 2
Y3-height of centroid of area of PZT
Y -height of neutral axis of beam from bottom
Figure 2.1: Cross Section of the Type-1 PMIPG Composite Beam.
Picture taken from [13].
2.3
PMPG Resonance Frequency Calculations
The first task in determining the stiffness of the beam is finding the neutral axis of
the beam. The neutral axis is the location in the beam that experiences no normal strain
when the beam bends. This is a trivial problem in a symmetric beam of uniform material;
the neutral axis is the middle of the beam. However, in a composite beam the effects of
the different moduli of each layer must be summed up to find the neutral axis:
-
(Y
A E
ZYL= L(2.1)
where Y is the height of the centroid for composite layer i with corresponding
area Ai and Young's modulus E.
Calculation of the neutral axis for the Type-i PM.PG device reveals that Y =
4.5075e-007 m, or less than 0.451 ,Im. Given that the height to the top of the ZrO 2 layer
(immediately below the PZT layer) is 0.45 Itm, this means that the neutral axis only
creeps in less than 1 nm into the bottom of the PZT layer. This is insignificant, and so we
18
can expect to be getting the maximum possible charge out of the device during uniform
bending.
Once the neutral axis is known, the stiffness k of the beam can be calculated. The
moment of inertia of a beam with a rectangular cross section is given by equation 2.2.
b. * h3
I 2 '
(2.2)
12
where hi is the height of the cross section and b is the width of the beam.
The parallel axis theorem describes the stiffness of a cross section that is not
being bent about its centroid, which is the case for each of the composite layers which
make up the composite cantilever beam. Therefore, the moment of inertia needs to be
adjusted for each material layer according to equation 2.3:
2
Ii = Ii+ A * h
(2.3)
where h iis defined as Yi - Y .
The total stiffness of a beam is normally expressed as the product of a beam's
moment of inertia and the material's modulus of elasticity. To get the total equivalent
stiffness
"EITotal"
for the composite beam, you must sum up the contributions from each
individual layer:
EITotal =E
Once
ELTotaI
1
* I+E
2
* 12+E
3
*
3
(2.4)
is known, the k stiffness of the beam can be directly calculated. In
the case of a cantilever beam which is being driven by a uniformly distributed load force
(given in Newtons) over its top surface area, the k stiffness term is given by:
k
8 * El
"Total
(2.5)
where L is the effective length of the cantilever beam (to be measured after the
XeF 2 etch step). This k stiffness term will be applied for both the base shaking and
acoustic excitation methods.
19
Finally, the resonance frequency for a PMPG device with proof mass Mpfoof can
be expressed as:
k
6
(2.6)
MMprooff
where Mproof is the mass of the proof mass in kg and o is given in rad/sec.
Resonance frequency f in Hertz is given by f = o/(27r).
Using this method to derive the resonance frequency for the Type-I PMPG
device, we arrive at f = 9.109 kHz which is comparable to the actual, measured resonance
frequency of 13.7 kHz. According to Dan Opila's analysis in [13], the resonance
frequency for a PMPG cantilever device without a proof mass can also be computed:
*(1.
E_=__""
EI
beam
1875 1)2
(2.7)
3
where mbeam is the total mass of the cantilever beam in kg.
2.4
Seismically, Excited Spring-Mass Damper
In order to understand the mechanical dynamics of the base shaking experiments,
a suitable model must be used. Base shaking of the PMPG micro cantilever device can
be modeled as a seismically, excited spring-mass damper as shown in Figure 2.2. In this
diagram the base is labeled "Moving Part". This is the same as the moving Si substrate to
which the cantilever is attached. The mass "M" is the lumped mass and is analogous to
the lumped mass of the PMPG device. In the case of the Type-1 device, this is
approximated by Mproof. The cantilever has stiffness K and damping coefficient B. Input
base displacement is xi and output displacement is the cantilever tip displacement xO. The
differential equation which balances the forces in the system is given as equation 2.8
[14]. The same equation can be rewritten as equation 2.9 where the resonance frequency
oz and the damping ratio
20
are used as variables.
S'ensor CLsLe
arnsdiicer
Figure 2.2: Base Shaking Experiment can be Modeled by Seismically, Excited SpringMass Damper System. PMPG cantilever device is represented by mass M with input
base displacement xi and output cantilever tip displacement x0 . Picture taken from [14].
MN, +Bi 0 +Kx0 =Kx,+Bkc
(2.8 )
X2, 2wak + w 2 x
02x, + 2to)ic
1
Mof
where4%=-and Q= B
(2.9)
2Q
Theoretically, for a fixed base shaking frequency (in this case, resonance) a linear
increase in base shaking displacement should result in a linear increase in the cantilever
tip displacement. In the special case where the system is shaking at resonance, the
increase should be proportional to the
Q of the system.
We know this from the following
standard equation which solves equation 2.9 through the use of the Laplacian:
0
x
where s =jw,
= w/(2Q),
(2.10)
s- + 2(a -s +wf
o
first mode resonance frequency and
Q
mechanical quality factor of the system.
The mechanical
Q
of the system can be calculated according to equation 2.9 if the
lumped mass M, resonance frequency
o and damping coefficient B are known.
However, it is not always easy to get good estimates of all three of these values.
21
Therefore, it is recommended that the
Q be measured experimentally
and then used to
calculate the damping coefficient B with equation 2.9. This is done in Chapter 7.
Mechanical calculations for the Type-I PMPG device are performed in Appendix A. 1
22
Chapter 3: Piezoelectricity and PZT
3.1
Definitions and Principles of Piezoelectricity
The piezoelectric effect couples electric fields to elastic deformation or strain.
The energy conversion process works in either the forward or reverse direction: 1.) A
mechanical strain within the piezoelectric material establishes an electric field in the
material. A piezoelectric transducer that works in this mode is working in the sensor
mode. 2.) The application of a voltage across the material will induce a mechanical
strain. This is the actuation mode. In the case of the Piezoelectric Micro Power
Generator, it is best to look at the piezoelectric effect from the point of view of charge
generation in the sensor mode.
The axial stress within the PZT thin film layer can be calculated directly from the
created strain which arises when the cantilever beam is bent upwards or downwards. GXX
is the axial stress in the longitudinal direction of the piezoelectric layer and is calculated
according to equation 3.1. The longitudinal direction is labeled as the x-direction. In the
case of the PMPG this is referred to as the "3" direction of the applied strain. The
piezoelectric coefficients are written with two numerical subscripts (i.e. d3 1 ). In the case
of the sensor mode, the first number represents the direction of the applied strain and the
second number represents the direction of the generated electric field. d31 couples an
applied strain in the "3" direction to a generated electric field in the "1" direction. d33
couples an applied strain in the "3" direction to a generated electric field in the same "3"
direction.
XXEzT
*a
(3.1)
where EpzT is the Young's modulus of PZT and a is the internal PZT strain
generated when the cantilever beam is in uniform bending.
The PMPG interdigitated electrode structure exploits the d33 piezoelectric mode.
It was chosen because it allows for a higher open circuit voltage to be created across the
positive and negative terminals of the electrode versus a same sized d31 cantilever beam.
This comparison is described in more detail in Chapter 4. A simple comparison of the
23
two electrode types (d31 vs. d33) and their generated charge expressions is shown in
Figure 3.1. Note that the positive "3" direction is in the "right" direction and the positive
"1" direction is in the "up" direction. The two charge generation equations in Figure 3.1
use different cross-sectional areas. These areas are defined by their respective electrode
geometries.
Ignoring fringing effects,
ApzT(31)
and
APzT(33)
are the areas through which the
produced electric fields pierce (perpendicularly) for the d31 and d33 devices, respectively:
APZT (31)
APZT
=W*L
(33) =npairs
(3.2)
tPZT
overlap
where W is the width and L the length of the top and bottom d3 1 electrode, tPzT is
the thickness of the PZT thin film layer, nfpairs is the number of mini-electrodes which
make up a single interdigitated electrode structure and loverlap is the overlap length
between adjacent mini-electrode pairs as indicated in Figure 3.2. From now on AWzT(33)
will be referred to simply as APZT.
A compressive stress (which is negative in sign) will create a positive charge
within the piezoelectric material. This generated charge will be gathered by the electrode
which is in direct contact with the piezoelectric layer. The charge generation equation for
the d33 piezoelectric mode is shown once again as equation 3.3 along with an explicit
definition of the d3 3 coefficient.
24
d. 1 mode
d., mode
I
2
3 :-00'3"T
+IT
1
d31
xx*
A PZT(3 1)
Q33
33
*yxx
APZT(33)
Figure 3.1: d31 vs. d33 Electrode Geometry and Charge Generation Comparison. Width
W for the d31 mode is in and out of the page. loverlap for the d33 mode is in and out of the
page.
Q33 = -d33 UXXAPzT
whered3
OR
3.2
d 33
short circuit charge density Coulombs
~(.)
applied mechanical stress
Newton
strain development
meters
applied electric field
Volt
(33)
Poling Process
Charge generation would not be possible if the PZT were not poled prior to device
operation. Poling is done by applying a high, DC voltage directly to the positive and
negative terminals of the interdigitated electrode at a raised temperature for a fixed
amount of time. This process is described in Chapter 6. Note: In this paper, the word
"electrode" is often used to describe the combined positive (+) and negative (-) electrodes
for a d33 PMPG device. Poling of the PMPG device sets up an alternating, remnant
polarization vector P between successive pairs of mini electrodes (See Figure 3.2.).
Maxwell's Equations require that the following boundary condition must hold across the
Pt-PZT boundary for each mini-electrode pair:
25
D =-*E+P =0
((3.4)
where D is the electric displacement, E is the dielectric constant of the PZT, E is
the electric field and P the polarization vector established between the mini-electrode
pairs (fingers) of the interdigitated electrode.
Interdigitated Electrode
L
A k L 5 1Z
PZT
layer
r 02
aye r
lo verap
Membrane layer
Figure 3.2: Alternating Polarization Vectors Created Between Mini Electrode Pairs
During Poling. When the device is operated in sensor mode, the generated E field is in
the opposite direction as the remnant polarization vector. Mini-electrode overlap length
is indicated as loverlap.
What the poling actually does is create a surface of mirror charges or dipoles at
each of the two Pt-PZT boundaries for each pair of mini electrodes. One of the
boundaries will have + charges on the PZT side of its boundary matched by - charges on
the Pt side. The other boundary will have - charges on the PZT side of its boundary
matched by + charges on the Pt side. The mirror charges at both boundaries cancel each
other out perfectly (the definition of dipoles), such that there is no net, free charge inside
the PZT. A schematic diagram of this charge distribution is shown in Figure 3.3:
26
Current
RLeakage
Flow
Au
y
AP
AE-
__JWWWA
AQ
_
+
+
-+pT-
-Q -+
+
-++Q
+=10-
+
Figure 3.3: Charge Distribution During Poling. When an external force generates an
axial stress within the PZT layer, charge will flow through the RLakage resistance due to
the above set of events.
Ignoring fringing effects, the electric field that is produced during device
operation, cuts through the full thickness of the PZT and is restricted by the overlap
length of the mini-electrodes. Referring again to Figure 3.3: If a step of positive stress
(tensile) +AG is introduced into a section of PZT below a pair of mini electrodes, +AP
polarization is created via the piezoelectric effect. With +AP must come an equal, but
opposite -A(a-E). There is now an E-field formed inside the PZT, between each pair of
mini-electrodes. This E-field alternates back and forth as you go along the length of the
beam (Again, see Figure 3.1.). It exists because there is net, free charge AQ introduced
onto the PZT side of each of the Pt-PZT boundaries: net, free negative charges on the
PZT side of one of the boundaries and net, free positive charges on the PZT side of the
other boundary (These extra charges are not shown in Figure 3.3.). Without the remnant
polarization vectors, the created E-field would not be directed in any particular direction.
It would be random, and therefore, no charge would build up on the electrode during
device operation. This is why poling is critical. The created, net free charge is the basis
for the piezoelectric, charge generation equation.
However, this charge will not remain there forever. It will leak off through the
intrinsic, electrical resistance
RLeakage
(also referred to as Ro) of the PZT and back to the
opposite boundaries in order to reestablish charge equilibrium (complete dipole
formation). This leakage is indicated by the "current flow" in Figure 3.3. The time it
27
takes for the created AQ to leak off of the electrode is determined by its effective "RC"
time constant where "R" is RLeakage or Ro and "C" is the total electrode capacitance, yet to
be determined. These calculations are performed in Chapter 4.
3.3
Basic Description of Device Operation
In the case of the Piezoelectric Micro Power Generator, a uniform strain polarity
on the top of the beam (where the PZT thin film exists) is desired. In other words, the
strain should be of the same polarity throughout the entire thickness of the PZT. One
way to ensure this is to make sure that the mechanical neutral axis of the composite beam
is below the PZT layer. During compression, the PZT thin film will then generate a
positive voltage on the electrode, and during tension it will generate a negative voltage.
The resonating cantilever beam will be changing its tip displacement as a sinusoidal
funtion of time at resonance frequency, o. The PZT layer will therefore exhibit a
sinusoidally, time-varying change in strain at the same resonance frequency, o. This
leads to a corresponding generated charge, which is similarly time-varying. The largest
amount of generated charge (positive or negative) will be generated when the tip
displacement of the cantilever beam is at either maximum.
3.4
Piezoelectric Characterization of PMPG Type-1 Device
The microstructure and crystal orientation of the PZT film were determined by
using field emission type scanning of an electron microscope and an X-ray diffractometer
(XRD). The microstructures and typical XRD pattern of the PZT film on ZrO 2 /SiO2/Si
(as is used in the Type-1 PMPG Device) are shown in Figures 3.4 and 3.5, respectively.
The PZT film is dense, consisting of a random perovskite phase structure with an
approximate 100 nm diameter grain size.
In order to ensure that the Type-I PMPG device was properly poled, a P-V
hysteresis curve needed to be determined. Figure 3.6 shows the P-V hysteresis curve of
the device. This data was measured using the Radiant Technologies® RT-66A High
Voltage Interface with Trek@ Model 601C. The spontaneous polarization (Ps), remanent
2
2
polarization (Pr), and coercive field are 50 ftC/cm , 20 Wi/cm2 and 38 KV/cm,
28
respectively. The dielectric constant and dielectric loss of the PZT thin film were also
measured as a function of frequency. The data is plotted in Figure 3.7. As you can see,
our PZT thin film can be operated across a wide frequency range while the dielectric
constant (1200o) and dielectric loss remain relatively constant.
Figure 3.4: Top View SEM Picture of PZT Thin Film used in Type-I PMPG Device
Courtesy of Y.B. Jeon [15]
29
PZT/Pt/SiO2 /Si
Pt(111)
Pt(002)
PZT(011)
PZT(111.
Do
PZT(001)
PZT(112)
Wt.
CUnO
PZT(002)
PZT(102)
I
20
*
I
30
*
I
40
*
I
50
20
Figure 3.5: XRD Pattern of PZT on ZrO 2/SiO 2/Si [15]
30
60
60
d3type P MPG (#1)
PZT thickness: 0.5pm
Inter-digited electrode dista hce: 4pm
40
0
U
U
U
a-20
udu
-
Er
-60
-160
-200
-100
0
-60
50
100
200
150
Applied voltage (Volt)
Figure 3.6: P-V Hysteresis Curve of PMPG Type-I Device. Remant polarization
magnitude is 20 gC/cm 2 . [15]
dielectric constant
1200
dielectric loss
1 .2
typi cal thin -film
m
PZT dielectric
1000-
"
0.8
800-
0.4
600-
--
0.0
1
10
100
f req u en cy (k(Hz)
Figure 3.7: Dielectric Constant and Dielectric Loss of PZT Thin Film as a Function of
Frequency [15]
31
Chapter 4: Electro-Mechanical and Electrical Equivalent
Models
4.1
Higher d33 Mode Open Circuit Voltage vs. d3 Mode
The d33 mode piezoelectric cantilever will allow for a much higher open circuit
voltage (OCV) compared to a similary sized d31 mode cantilever. In order to compare
these two structures, we will first assume the same PZT thickness,
tPZT.
The separation
distance, d between positive and negative electrodes is equal to tPzT for the d31 mode.
The d31 piezoelectric cantilever employs a top and bottom electrode structure. However,
for the d33 mode, d is the distance between the interdigitated fingers (mini-electrodes) and
can be defined independent of the PZT thickness. The d33 coefficient is also at least two
times greater in magnitude than the d 31 coefficient. In the case of our PZT, d3 3 is
estimated to equal 200 pC/N, while d3 1 is approximately -100 pC/N. The d33 and d31
coefficients are linearly proportional to their g33 and g31 counterparts in the following
way:
933 -:
3
(4.1)
g31-
3
F
where F is the dielectric constant of the PZT.
Since these two sets of coefficients are linearly proportional to one another, the
comparison of open circuit voltages can be made using either the g or d coefficient types.
Referring to Figure 4.1, we see that two piezoelectric cantilevers of the same size are
compared to one another using the g33 and g31 coefficients. The classic piezoelectric
equation relating input strain to generated, open-circuit voltage is shown for both the d31
(g31) and d33 (g33) modes. In this example, the separation distance d between mini
electrode pairs in the d 33 device is 10 times greater than tPZT. Note: For our tested Type-I
PMPG device,
32
tWzT
= 0.48
sm and
d = 4 Am. Therefore, dl/tPzT = 8.33. We quickly see
that the OCV of the d33 mode device in Figure 4.1 will be at least 20 times greater than its
d3 l counterpart. For the tested Type-I Device, we expect the d33 open circuit voltage to
be at least 16 times greater than a similarly sized d3 l cantilever beam.
d3 1 mode
d., mode
1
-A
-
E
V31
Cy
XX
-r
I
F
V33
t p.zt a %1
V3
?
= 2d / t,.
e V3 1 = 20 * V3
(i933 >2g ,1
d-
yxad*g:
1
10 ty)
Figure 4.1: Open Circuit Voltage Comparison of g33 vs. g3] Modes for Same Cantilever
Beam Geometry. Picture part of figure taken from [16].
4.2
Electrical Resistance and Capacitance
As discussed in Chapter 3, when an external force generates an axial stress within
the PZT layer, generated charge will build up on the electrode. However, this charge will
not remain there forever. It will leak off through the intrinsic, electrical resistance
RLeakage
(also referred to as Ro) of the PZT and back to the opposite boundaries in order to
reestablish charge equilibrium (complete dipole formation). This leakage is indicated by
the "current flow" in Figure 3.3. The time it takes for the created AQ to leak off of the
electrode is determined by its effective "RC" time constant where "R" is effectively
RLeakage
or Ro and "C" is the total electrode capacitance, yet to be determined. The total
33
electrode capacitance consists of an intrinsic, electrical term and an electro-mechanical
term due to the piezoelectric response.
RLeakage
is given by:
p*d
RLeakage =R 0
(4.5)
APZT
where p is the resistivity of PZT.
Reakage
has units of Ohms (Q).
The intrinsic, electrical capacitance Co (units of Farads) between the two mini
electrodes is found by using the classic definition of electrical capacitance:
Co = E*APZT
d
(4.6)
Equations 4.5 and 4.6 concern the Ro and Co for one mini-electrode pair.
However, there are several such pairs for a single, interdigitated electrode structure of the
PMPG device. If there are
"npairs"
number of pairs, then each of these pairs run in
parallelwith one another. This results in equations 4.7 and 4.8:
R
(4.7)
p*d
pairs
Co = npair *
PZT
E *APZT
d
(4.8)
For the lab tested Type-I PMPG device, Ro was calculated to be 2.37E10 Q and
Co is 4.48 pF.
4.3
Electro-Mechanical Model and Equivalent Electrical Circuit
In designing a MEMS device, it is necessary to understand the electro-mechanical
modeling of the device. Proper understanding of the electro-mechanical modeling will
result in an equivalent electri-cal circuit for the device. This work provides an equivalent
electrical circuit model of the PMPG power system which consists of the MEMS device
(PMPG) along with the additional rectification bridge and charge storage system that is
necessary for delivering constant, DC power to an external load.
34
The electro-mechanical model that I have chosen is the model described by
Professor Stephen Senturia in his book Microsystem Design [17]. Professor Senturia
describes the piezoelectric actuator mode through a piezoelectric rate gyroscope example.
In this example, an externally applied voltage in the electrical domain results in a tip
displacement wo of a tine structure (tuning fork) in the mechanical domain. A
transformer is used to couple the electrical and mechanical domains:
"A transformer with turns ratio n couples the electrical domain, in which the
voltage V is the voltage applied to the electrode pair, to the mechanical domain, in which
the tine displacement wo is the displacement coordinate and F is the effective force
causing this displacement." [17]
The transformer relations are:
F
n*V
xe
(4.9)
n
where xn is the tip velocity and le is the generated current in the electrical
domain due to the tip velocity which is a mechanical input.
If Ym is an admittance in the mechanical domain, such that Nii
0
= Y, * F , then
using the above transformer relations we arrive at an equivalent admittance Ye in the
electrical domain:
Y, = n 2* yI
(4.10)
This means that in order to convert an admittance from the mechanical domain to
an equivalent admittance in the electrical domain, you simply multiply by n2 . In order to
convert between impedances, divide by n2
Of course the same model can be used for the sensor mode where an externally
applied force in the mechanical domain will result in an electrical response in the
electrical domain. The PMPG is operated in the sensor mode. Figure 4.4 illustrates the
electro-mechanical model and resulting equivalent electrical circuit. The displacement
coordinate for the PMPG is just the tip displacement wo of the cantilever beam. The tip
velocity Nxo is the first time derivative of wo. I is the total current. In the case of the
PMPG, I= Ie since the only input is the time varying mechanical force F.
35
The general expression for the electro-mechanical capacitance Ce is derived from
an input axial strain and the resulting charge developed on the electrode. For our
interdigitated electrode structure where npairs is the number of mini-electrode pairs, the
equivalent electrical capacitance Ce has the following expression:
Ce =
where
EPZT is
n pairs *E PZT *dd 33 *A PZT
d
(4.11)
the Young's modulus of PZT.
The mechanical capacitance Cm is represented by 1/k where k is the stiffness
coefficient of the composite cantilever beam. Therefore, from equation 4.10, we have:
2
C,
(4.12)
=n
k
By equating equation 4.12 with equation 4.11, we arrive at the equation for the
turns ratio n:
n
*d 2 *A
*E
Ik * pd
33
PZT
PZT
(4.13)
d
-~
Knowing the turns ratio allows us to complete the equivalent electrical circuit:
Le
= m2
n
(4.14)
-b
Ax
--
n2
where Le is the equivalent electrical inductance in Henries, m is the lumped mass
from the mechanical model, Re is the equivalent electrical resistance and b is the
mechanical damping coefficient.
Now that we know Ce, the total electrode capacitance CTotai can be calculated as:
CTotal
CO + C
(4.15)
Ce for the Type-I PMPG device is calculated to be 1.06 pF. Therefore, CTotaI =
4.48 pF + 1.06 pF = 5.54 pF. The capacitance of the Type-I PMPG was measured as 7
36
pF at 13.7 kHz resonance. Therefore, the calculated and measured values compare
favorably. Re is calculated to be 0.013 MQ for the Type-I PMPG device and the
equivalent inductor impedance Le has a magnitude of 0.61 MQ at 13.7 kHz. Ce has an
impedance magnitude of 10.95 MQ at 13.7 kHz.
The current I is created by an AC current source. Essentially, the PMPG device
acts as an AC current generator in parallel with the output impedance. While the PMPG
is mechanically resonating, the PZT thin film is experiencing an alternating stress:
tensile, compressive, tensile, compressive, etc.. This time varying change in stress results
in a time varying change in charge produced on the electrode. Taking the first time
derivative of the charge function Q(t) gives the AC current source IPMPG. This concept is
clearly diagramed in Figure 4.5.
Senturia's model does not include Ro as part of the output impedance in the
equivalent electrical circuit. It is critical to include Ro because this value (2.37E10 Q =
23,700 MQ) dominates the output impedance. I have included Ro in the equivalent
electrical circuit in Figure 4.4. Although, the calculated value for Ro may sound too high,
it is actually reasonable. According to Kistler Instrument Corporation: Piezoelectric,
"charge-mode transducers exhibit a high impedance output in the range of 10' to 1011
Ohms". [18] My calculated value is right in the middle of this range. Because Ro is
several orders of magnitude bigger than the other output impedance terms, it effectively
dominates the total output impedance:
ZPMPG
= s*L +
+ b +,R,
~ Ro
(4.16)
where s =j*(o and o = 2t*13.7kHz. Figure 4.5 shows the final equivalent
electrical circuit of the PMPG including the AC current source.
37
Transformer
.
1:n
+
+
C0
F/k
Electrical
Domain
Mechanical
Domain
b/n
+
I
b
C1T
V
n2/k
VOD
2
-
n2lk
Equivalent
Electrical Circuit
Ow
wx
0
Figure 4.4: Electro-Mechanical Model and Resulting Equivalent Electrical Circuit of the
PMPG. Transformer principle links the electrical and mechanical domains. Left side
drawing taken from [17].
Tip Displacement (wO)
-t
Z(t) = Zo cos ((t)
t
Strain (x)
x(t) =
t
Charge (Q)
-xO cos (0Ot)
~V
Q(t)
= d33 ((t) APZT
+
t
/""
Stress (
IPMPG(t) -
a(t) = X(t)EPzr
t
Current (1)
dQ(t)
dt
Figure 4.5: Changing Tip Displacement during Resonance Results in AC Current Source
IPMPG(t).
38
I
V
IPMPG(t)
'PMPG
K
Figure 4.6: Final Equivalent Electrical Circuit of the PMPG Including AC Current
Source IPMPG(t).
4.4
Resonance Frequency Condition
As mentioned in section 4.2, an external force (vibrational shaker source in the
case of the base shaking experiments) on the cantilever beam will cause the beam to
bend, introducing an axial stress within the PZT. The axial stress will result in created
charge, AQ which develops on the electrode. The time it takes for the created AQ to leak
off of the electrode is determined by its effective "RC" time constant where "R" is
effectively
RLeakage or
RO and "C" is
CTotal.
The PMPG must, at the very least, resonate at a frequency that satisfies the
following condition:
ar >>1
(4.17)
where co is the cantilever beam resonance frequency in Hertz and T=R*CTota-II
1For the case of the
lab tested Type-I PMPG device, the capacitance was measured as 7 pF. RO was
calculated to be 2.37E10 Q. Therefore, T is estimated to be 0.166. At 13.7 kHz resonance, we easily
satisfy the resonance condition because 13.7E3*0.166 = 2270 >> 1. Another way to know that we've
satisfied the resonance frequency condition is to check whether we're actually getting charge out of the
device at resonance. This was verified in the laboratory experiments, which is discussed in more detail in
Chapter 7.
39
4.5
PMPG Voltage Amplitude Requirement
VF
is the forward voltage level of a single diode. You must drop this amount of
voltage across the diode in order for current to flow through it. For a full rectification
bridge, such as the one used by the PMPG power system, the full voltage drop during
rectification is
2*VF.
The required PMPG voltage amplitude VPMPG out of the MIEMS
device (assuming no voltage doublers are used) can be calculated by knowing the
required load/cap voltage VR and the forward voltage drop VF.
VF
is calculated by knowing the current flowing through the diode. The current
flowing through the diode will be determined by the PMPG AC current source, which is
best determined through measurement. Looking ahead and taking the current flowing
through the load resistance during DC steady state, we find that the current level is 0.44
tA. The equation for the current flowing through a diode for a given voltage applied
across it is:
VF
Idioe=
s
1
(e *A -1)
(4.18)
where Is = 5.1 nA, Dt = 25.88 mV and r = 2 for the 1N5711 small signal Schottky
diode during device operation.
Using equation 4.18 to calculate VF given
'diode =0.44
tA, we find that VF should
equal 0.23 V. The DC load voltage level VR is application specific, and in this case
would need to be given by the Auto ID team. A required load voltage was not given to us
by the Auto ID team, although 2 V DC should probably be enough given today's digital
IC technology. Therefore, the following condition must be met in order to drive the Auto
ID circuitry with the required load voltage:
VPMPG
VC ±2*VF
(4.19)
Specifically, VPMPG > 2.46 V. We will find in Chapter 7 that the calculated VPMPG
amplitude is 2.62 V, so the condition is met. This is exactly why we're using the d33
piezoelectric mode and the interdigitated electrode structure. The generated voltage
VPMPG
will have to be large (on the order of 3 V) if it is to exceed the value of VR + 2*VF.
The d33 mode allows us to produce this high voltage, whereas the d31 mode would not.
40
Finally, determination of the required storage capacitor value is also application specific.
It is dependent on a number of electrical specifications governed by the dynamics of the
digital Auto ID circuitry. These specifics were not given. However, the power storage
capacitance value can be easily changed to suit the needs of the Auto ID tag, and is
therefore easily achievable. Electro-mechanical model and equivalent electrical circuit
calculations were performed in Matlab@ and are shown in Appendix A. 1. We arrive at
the equivalent electrical circuit for the total PMPG power system which is shown in
Figure 4.7.
Rectifying bridge
---- -0
IPMPGlt)
Total P\AP
Current source
L
G
ZP
CO
D4 D1
dq/dt
I
D2
D3
Ic
C
---
IRLOad
G
Power
torage
Capacitor
RLoad
PMPGT
Figure 4.7: Equivalent Electrical Model of PMPG Power System: PMPG with Bridge
Rectifier, Storage Cap and RLad
41
Chapter 5: Fabrication
5.1
Fabrication Process Steps
We fabricated a thin film lead zirconate titanate, Pb(Zr,Ti)0
3
[PZT], MEMS-
based cantilever device of d33 mode using a simple fabrication process with only three
photo masks. The Type-1 PMPG device that was tested in the laser vibrometer
experiments has the following composite layer composition: PZT(0.48tm)/
Zr0 2(0.05ptm)/ PECVD oxide(0.4ptm). Figure 5.1 shows the device schematic of the d33
mode piezoelectric device. The basic design of the multilayer structure is as follows:
Layer 1: Membrane layer (SiO 2 and/or SiNx) for controlling stress and bow of the
cantilever structure; Layer 2: Diffusion barrier/buffer layer (ZrO 2) for preventing
electrical charge diffusion from the piezoelectric layer above it; Layer 3: PZT
piezoelectric layer; Layer 4: Top interdigitated electrode (Pt/Ti); Layer 5: Optional Proof
Mass (SU-8).
First, the membrane layer (PECVD oxide for the Type-i Device) is deposited on
the Si wafer. The PECVD oxide layer is annealed at 750'C for 30 minutes. The 50 nm
thick ZrO 2 layer is deposited via a sol-gel spin-on process. It acts as a buffer layer on top
of the various membrane layers and is dried at 350'C for 1 minute, then annealed at
700'C for 15 minutes. The composition of the PZT solution (Mitsubishi Materials
Corporation) is 52/48 as Zr/Ti ratio, Pb content, meaning that Pb/(Zr+Ti) is 118/100. The
solution is subsequently spun-on the substrate at 500 rpm for 3 seconds and 1500 rpm for
30 seconds. The precursor gel film is pyrolyzed at 350'C for 5 minutes on a hot plate in
several repeated cycles to create a final PZT layer with 0.48 um thickness. In this case,
four cycles of 0.12 Ixm thick PZT were used.
The PZT film is annealed at 700'C for 15 minutes in a box furnace. The PZT
layer and membrane layers are patterned via RIE with BCl 3 :C12 (30:10) for 70 min with
the l't mask. The interdigitated top electrode requires the 2 "d mask and is deposited using
an e-beam evaporation and lift-off procedure with 20nm Ti and 200nm Pt. The SU-8 is
spin coated on top of the existing layers and patterned with the 3'd mask to create the
proof mass. In the case of the Type-1 PMPG device, the proof mass is 50 yIm thick. SU-
42
8 allows for very high aspect ratio structures. The cantilever membrane is then released
with the XeF 2 vapor etcher. No mask is required because XeF 2 has a high etch selectivity
between Si and the other layers. Table 5.1 contains the general PMPG fabrication
process for a Type-1 Device. Figure 5.2 shows the changing side profile of the PMPG
device as it goes through the full fabrication process.
Interdigitated Electrode
PZT layer
ZrO2 layer
Membrane layer
Figure 5.1: Device schematic of d33 mode piezoelectric device (PMPG). The left side of
the diagram is a cross-sectional view. It shows the alternating plus and minus potentials
that are imposed on the adjacent mini-electrodes (which together make up the interdigitated electrode) when the PMPG device is poled. The right side of the diagram is a
top view of the inter-digitated electrode.
Table 5.1: General PMPG Fabrication Process for Type-1 Device
Step
1
Process
PECVD Oxide membrane layer
Description
Deposit 0.4 pm of PECVD Oxide
2
ZrO 2 diffusion barrier layer
3
PZT piezoelectric layer
4
RIE to define beam geometry
One sol-gel spin-on of ZrO 2 (50
nm). Dried and then annealed.
PZT precursor film followed by
four sol-gel spin-on's of PZT
(0.48 fim). PZT film is dried and
annealed for each spin-on cycle.
BCl 3:C12 (30:10) for 70 min with
the
5
Pt/Ti interdigitated electrode
6
SU-8 Proof Mass
7
8
XeF 2 to release cantilever beam
PMPG Si chips
1 st
mask.
E-beam evaporation and lift-off of
top, interdigitated Pt (200 nm)/Ti
(20 nm) electrode using 2 nd mask.
Spin coating of SU-8 (50 lim).
Patterned with 3rd mask.
Isotropic etch release.
Create PMPG chip dies by cutting
Si wafer with sharp razor
43
Proof mass
ZrO2
Me mb rane
(a) Films deposition (CVD, spinning)
Igntg
i
(d) Proof mass (SU-8, spinning)
electrode
Prxmms
ZrO2
(b) Top electrode deposition & lift-off
(c) Films patterning (RIE)
e) Cantilever release (XeF 2)
f) Packaging & poling
Figure 5.2: Cross-sectional Profile of PMPG Device During Fabrication Process Steps
5.2
Process Considerations
The initial process used a bottom platinum layer as the diffusion barrier layer
instead of zirconium oxide. It also used a silicon nitride membrane layer instead of the
PECVD oxide layer that was ultimately used. It was found through [19] that if an
interdigitated, top electrode structure was used on top of the PZT, then a metal layer such
as platinum could not be used as the diffusion barrier under the PZT. The reason for this
is that the bottom platinum layer would act as an electrical plane, directing the generated
E-field down into the platinum layer, rather than across between the mini-electrode
fingers. Therefore, "...PZT films have to be deposited on an insulating buffer layer with
a low dielectric constant instead of the conventional platinum buffer layer." [19]
Specifically, a ZrO 2 thin film layer can work as an effective buffer layer to prevent the
reaction and interdiffusion between the PZT film and silicon substrate.
Upon choosing ZrO 2 , it was found not to match well with the silicon nitride
membrane layer we were using. A different membrane layer had to therefore be used.
44
Trial spin-on's of ZrO 2 on SiO 2 proved successful for interfacing ZrO 2 to the silicon
substrate. Another consideration that must be made is that the XeF 2 isotropic etch step
effectively lengths the mechanical length of the beam due to undercutting of the base
region during etching. For example, the Type-I Device has an original length of 146 yIm
after RIE (Mask #1), but this lengthens to approximately 170 ptm after the XeF 2 etch step.
As a side note, the final, tested device turned out to have a resonance frequency of 13.7
kHz- not the initially designed frequency of 20 kHz. This is because the fabrication
process was changed after the initial mechanical design had been done (i.e. the composite
layers and thicknesses were changed as mentioned above.). A recalculation of the
resonance frequency for the new fabrication process results in a theoretical resonance
frequency of 11.45 kHz which corresponds well with the measured value of 13.7 kHz.
5.3
PMPG Mask Layout
Figure 5.3 shows the AutoCAD@ layout of a single PMPG die containing both
the RIE etch mask (Mask #1) and top, interdigitated electrode (Mask #2). Mask #2 also
includes alpha-neumeric numbering in Pt/Ti for identifying specific PMPG device types.
Each device type has its own set of beam dimensions, electrode dimensions, proof
mass/no proof mass, etc. which distinguishes it from other device types. For example,
two Type-I Devices are found towards the upper right hand corner of the die in Figure
5.3. The Type-I Device RIE trench and beam areas are both indicated by white arrows.
A zoomed in picture of the same Type-i Device is shown in Figure 5.4. The layout is
image reversed for purposes of mask fabrication. SEM photo graphs of released PMPG
cantilever devices are shown in Figure 5.5.
45
Figure 5.3: AutoCAD@ Layout of Masks #1 and #2 (Image Reversed)
46
Figure 5.4: Zoomed in Picture of Type-I Device from Figure 5.3
47
Figure 5.5: Top: PMPG Device; Bottom Left: Multiple Cantilever Device; Bottom
Right: Type-I Device w/ Proof Mass. Some out of plane warpage is apparent in these
devices.
48
Chapter 6: Experimental Setup
6.1
PMPG Packaging and Poling
The MEMS chip with multiple PMPG devices was super glued to a multiple pin,
ceramic package. Each MEMS device has two bond pads: One for the positive potential
and one for the negative. The chip was packaged using wire bonding. Two package pins
are required for each MEMS device (plus and minus). Therefore, two wire bonds are
made from each MEMS device on the chip to metal contacts on the front side of the
package. These metal contacts are electrically connected to the package pins on the back
side of the ceramic package. Electrical wire was then stripped and soldered directly to
the exposed pins on the back of the package in order to interface with the measurement
electronics (charge amplifier) and proto board containing the external rectification
circuitry and load. The packaging was covered with a glass lid to prevent environmental
contamination.
A fully packaged PMPG MEMS chip is shown in Figure 6.1.
The
package used in the base shaking experiments is smaller than the one in Figure 6.1, but
the packaging process is the same.
After packaging, the devices were poled using a hot plate and high voltage DC
power supply (Agilent 6614C). The packaged MEMS chip was heated to 100 'C and
poled at 90V DC for 30 minutes.
The temperature was then cooled down to room
temperature while maintaining the 90 V applied voltage.
Once the chip is at room
temperature, the applied field can be removed. The station for doing the poling of the
PMPG devices is shown in Figure 6.2.
49
Figure 6.1: Packaged PMPG MEMS Chip with Soldered Electrical Wiring to Pins.
Individual MIEMS devices are nearly visible. (Pins on the backside are not shown.)
50
Figure 6.2: Experimental Setup for Poling PMPG Devices. Packaged MEMS device,
such as the one shown in Figure 6.1, is heated on hot plate to 100 'C and poled at 90V
DC for 30 minutes.
6.2
Polytec© PSV-300H Laser Vibrometer System
Lodewyk Steyn supervised my laser vibrometer experimentation in the Laser
Vibrometer Room at the Gas Turbine Laboratory at MIT and was responsible for running
the laser vibrometer system. The Polytec© PSV-300H scanning laser vibrometer is a
versatile measurement system. The minimum displacement that the system can measure
is governed by the frequency at which one measures. For our operating frequency, the
laser vibrometer system can detect sub-nanometer displacement.
positioning accuracy is approximately ±10
sm, perhaps
The laser beam
a little better. The laser beam
spot size is 7 Am.
The optical zoom of the PSV-300H camera system was good enough to visualize
the proof mass of our Type-1 PMPG device and place the laser beam roughly in the
center of it (See Figure 6.3).
Ideally, the laser beam should be positioned at the
cantilever tip (end of the proof mass), to get the true tip displacement of the cantilever.
However, during resonance of the PMPG micro cantilever, tip displacement magnitude
data seemed to fluctuate when the laser beam was placed at the end of the proof mass.
"Center of proof mass" displacement was therefore used.
51
Placement of the laser beam at a specific location on the MEMS device is made
possible by the computer interface of the laser vibrometer system.
The live video
captured by the camera system is displayed on the computer screen. The user can see the
red laser beam reflecting off of the device surface and then place it in a specific location.
The PSV-300H can scan the surface area of an object while gathering displacement data.
This was done during resonance to capture .avi movie files of the moving micro
cantilever beam at 13.7 kHz. Hundreds of surface area data points were collected for
each surface area scan. Surface area scanning results are shown in Chapter 7. Surface
scan information such as the desired surface area and number of surface area scan points
are defined through the computer interface.
The frequency response or static
displacement data is plotted in the lower half of the computer screen, below the camera
system video capture.
The laser vibrometer is pictured in Figure 6.9. A picture of the
computer interface is shown in Figure 6.4.
Figure 6.3: Approximate Location of Laser Beam for Type-I PMPG Experiments
52
Figure 6.4: Polytec© Laser Vibrometer Computer Interface. The laser vibrometer
system's camera captures live video which can be seen towards the top of the computer
interface. Here a video capture of the PMPG device is shown. The laser beam is located
to the lower right of the PMPG. Frequency scan data would be shown in the data plot
section of the computer interface (lower half of the screen)
6.3
Optical Positioning/Base Shaking System
In order to properly position and shake the MEMS package in front of the laser
beam, an optical positioning/base shaking system needed to be created and adapted to the
optics table in the Laser Vibrometer Room.
Referring to Figure 6.5, the optical
positioning/base shaking system consists of: 1.) An aluminum block used to raise the rest
of the positioning system to the level of the laser beam. This part was machined from
aluminum stock and adapted to the optics table and X-Z translation stage.
2.) X-Z
Translation stage: Newport@ Model 461-XYZ-M translation stage for X-Z positioning of
the MIEMS package. X-axis is in and out of the paper; Z-axis is in the up/down direction.
3.) "Adapter Plate 1" (not shown in Figure 6.5) between X-Z translation stage and Tip
53
Tilt stage- also machined from aluminum stock. 4.) Tip Tilt stage: Newport© Model 485
Tilt/Rotation Platform provides two independent tilt adjustments. 5.) "Adapter Plate 2"
(not shown in Figure 6.5) is super glued between Tip Tilt stage and Piezoelectric Shaker.
6.) Piezoelectric Shaker: NEC/Tokin@ AE0505D08 resin coated type multilayer
piezoelectric actuator.
7.) "Adapter Plate 3" is super glued to the other side of the
Piezoelectric Shaker and then mechanically screwed into "Adapter Plate 4". 8.) One
"Adapter Plate 4" plate is necessary for each PMPG package that is tested. The plate is
permanently super glued to the PMPG package. These plates are "hot swappable", which
means they are meant to be swapped in and out together with each new PMPG package
for testing. 9.) PMPG package: Consists of PMPG MIEMS chip super glued to ceramic
packaging.
Figure 6.6 shows the packaged PMPG chip attached to the optical
positioning/base shaking system.
Figure 6.5: Schematic Diagram of Laboratory Setup. Power Storage System voltage
data is measured by the Tektronix© TDS 2024 oscilloscope (not shown) and saved on the
computer. Adapter Plates 1 and 2 not shown.
54
Figure 6.6: Packaged PMPG Chip Adapted to Piezoelectric Shaker. Laser beam is
shining at the lower left end of the PMPG chip. Electrical wiring is soldered to the
package pins and extends out to either the charge amplifier or Power Storage System.
6.4
Base Shaking and Acoustic Excitation Experimental Setups
Again, referring to Figure 6.5, the base shaking setup consists of the laser
vibrometer sytem, voltage amplifier with waveform generator, optical positioning/base
shaking system, charge amplifier, Power Storage System, oscilloscope and computer
interface. The waveform generator signal was set at 1 Vpp at 13.7 kHz and then sent to
the voltage amplifier for amplification. The voltage amplifier was tuned in order to vary
the final drive signal for driving the piezoelectric shaker. A 20 Vpp drive signal was
determined for driving the piezoelectric shaker.
This drive signal resulted in the
measured 14 nm base displacement during resonance. Pictures of the waveform signal
generator and voltage amplifier system are shown in Figures 6.7 and 6.8, respectively.
Once the piezoelectric shaker is shaking at the proper frequency, and the base
55
displacement is measured by the laser vibrometer, then the electrical data can be
measured. A photograph of the base shaking laboratory setup is shown in Figure 6.9.
Figure 6.7: Waveform Signal Generator
Figure 6.8: Voltage Amplifier
56
Figure 6.9: Base Shaking Experimental Setup. Laser vibrometer sytem, optical
positioning/base shaking system, Power Storage System and oscilloscope. Computer
interface, voltage amplifier and charge amplifier are not shown. The oscilloscope is used
to measure the load voltage data as a function of time, which is then sent to a computer
for data file saving.
The waveform generator, Onkyo@ TX-SR500 audio amplifier and Sony© Model
SS-CN495H front speaker were used to generate the acoustic waves during acoustic
excitation experiments. The waveform generator signal is sent to the audio amplifier,
which then drives the speaker. The speaker's tweeter is placed directly in line with the
exposed MEMS devices. This makes laser vibrometer scanning impossible. Therefore,
during acoustic excitation, the electrical properties of the MEMS device can be directly
analyzed, but the mechanical deformation cannot be. Electrical data is measured with the
same methods as used in the base shaking experiments.
The acoustic excitation
laboratory setup is shown in Figure 6.10.
57
Figure 6.10: Acoustic Excitation Setup. The speaker is the black box located behind the
laser vibrometer. The tweeter of the speaker is placed directly in line with the exposed
MEMS devices. Audio amplifier not shown.
6.5
Electrical Data Measurements: Kistler@ 5010B Dual Mode
Amplifier and Power Storage System
The Kistler@ 5010B Dual Mode Amplifier can be used as either a closed-circuit
charge measurement system or an open circuit voltage measurement system. In the case
of the base shaking experiments, it was used in the charge measurement mode for
measuring the generated charge, Q out of the Type-1 PMPG device. It is a very user
friendly system. The output from the PMPG was connected to the input of a simple, RC
high pass filter circuit (completely passive) to remove 60 Hz electrical noise from the
PMPG signal.
The output from the RC filter was then sent to the "Charge Input"
connection on the back side of the charge amplifier.
A voltage output signal is produced by the charge amplifier at the "Output"
connection, also on the back side of the amplifier. Two settings on the front panel
determine the charge measurement resolution in pC/V, where V is the peak-to-peak (pp)
"Output" voltage. The two settings are the "Transducer Sensitivity" and "Scale". Setting
these to 10 and 1, respectively, maximizes the charge resolution such that 1 Vpp output
voltage represents 10 pC peak-to-peak generated, closed-circuit charge. The "Output"
58
voltage signal is measured and displayed on the Tektronix@ TDS 2024 oscilloscope.
This data can be saved by connecting the oscilloscope to a computer.
The Power Storage System is needed for doing charging/discharging experiments
of a storage capacitor and for measuring the delivered power to a resistive load. It
consists of the rectification bridge circuit (made up of four STMicroelectronics@ 1N5711
small signal Schottky diodes), a power storage capacitor and a resistive load connected
together on a proto board according to Figure 3.1. These diodes were chosen specifically
because, compared to most discreet components, they have the smallest forward voltage
drop, VF. For example, VF is approximately 0.2V at the steady state, forward current
level of 0.44 ItA.
In addition, the 1N5711 has a low reverse diode current during PMPG device
operation because the reverse bias voltage peaks at only 2.62V (Discussed in more detail
in Chapter 7.).
The reverse current peaks out at approximately 5 nA during device
operation, so very little current will leak away during reverse biasing of the diodes.
These two important electrical characteristics of the 1N5711 allow for the largest possible
DC voltage to develop across the cap/load. In the same respect, the 10 nF mylar cap was
chosen because it does not leak currently easily. The resistors are discreet components,
able to be placed on the proto board. The value of the resistor was varied and placed in
parallel with the storage cap. An up-close picture of the Power Storage System is shown
in Figure 6.11.
During acoustic excitation, the electrical wire leads from the PMPG package were
again attached to the Kistler© charge amplifier and Power Storage System for electrical
measurements.
However, the measured electrical response was very weak.
More
importantly, it was proved that the electrical measurements were a result of electronic
noise coming from the audio system, not from the PMPG device. Electrical wire was
attached to the charge input of the Kistler@ amplifier, but not connected to the PMPG
package wiring. The resulting voltage output signal from the amplifier was the same as
when it was attached to the PMPG. Therefore, the electrical response must be due to
noise. The noise strength far outweighed the electrical response from the PMPG. The
possible reasons for this are discussed in Chapter 7.
59
Figure 6.11: Power Storage System Residing on Proto Board. Four small-signal
Schottky diodes are shown along with the 10 nF mylar storage capacitor to the left. Red
and black wires from left come from the PMPG package and are connected to the
rectification circuitry. Two black wires in the middle of the picture connect storage
capacitor in parallel with the load resistance to the right.
60
Chapter 7: Tests and Results
7.1
PMPG Direct Excitation (Actuation Mode) Results
Extensive experimentation was performed on a Type-I PMPG device because it
exhibited the best piezoelectric properties (best hysteresis curve) among the devices that
were poled on the MEMS chip. The "Type" number designates a specific beam
geometry. In this case, the Type-1 beam is actually more like a plate than a cantilever,
where the width (261 Itm) is bigger than the length (170 /tm). 170 ttm is the length of the
structure after taking into account XeF 2 undercutting. 146 yim is the original length as
found on the photo mask for the device fabrication process. Other PMPG devices on the
MEMS chip are actually cantilever beams with the length being longer than the width.
Figures 7.1 through 7.3 are plots based on measurement data taken from the laser
vibrometer system (Polytec@ PSV-300H Scanning Laser Vibrometer) in the Laser
Vibrometer Room at the Gas Turbine Laboratory at MIT. Figure 7.1 shows the
frequency response of cantilever tip deflection due to 3V amplitude (±3V) direct,
electrical excitation of the Type-I PMPG device. In other words, the PMPG was used as
an actuator in Figures 7.1 through 7.3, not as a sensor. The "white noise excitation"
method used to excite the PMPG device in Figure 7.1 means that the device was excited
very quickly through the frequency spectrum, so that all frequencies are excited "at
once", just like white noise.
You can see three distinct resonance peaks. These correspond to the first three
mechanical resonance modes of the structure. The first resonance peak was measured at
13.91 kHz with a maximum tip deflection of 4 Itim, the second at 21.88 kHz with 0.2 yIm
deflection, and the third at 48.5 kHz with 2 ytm deflection. The first mode is the desired
operating mode for the PMPG device. Not only does it have the largest deflection, but it
also has the desired, uniform bending motion of the device during resonance. If the
device is not uniformly bent, then part of the beam, along the length, will be in tension
while the other part is in compression. The generated charge will not be of uniform
polarity along the length of the beam, and therefore, you will not get the maximum
possible charge out of the device.
61
The first resonance peak shifted slightly when the excitation frequency spectrum
was narrowed around it and the frequency was scanned more slowly, as was done in
Figures 7.2 and 7.3. The applied voltage was also changed from ±3V in Figure 7.1 to
±1V and ±5V in Figures 7.2 and 7.3 respectively. This change in applied voltage could
cause a change in the overall stiffness of the structure, which explains the peak shift from
13.75 kHz in Figure 7.2 to 13.57 kHz in Figure 7.3. Lastly, as was expected, the
maximum cantilever tip deflection increased as the applied voltage increased. The tip
deflection was 0.7 ,Im, 4 itm and 4.66 ftm for the 1V, 3V and 5V amplitude voltages
respectively. The laser vibrometer system was very versatile in allowing for increased
scanning resolution and narrowing or expanding of the frequency range around some
desired frequency value.
13.91kHz
Frequency Response of Cantilever Tip
(Off-Center) from 3V Amplitude White
Noise Excitation
4.03.5-
21.88kHz
3.0(D
E
2.5-
48.5kHz
2.0-
-1.51.0
oD
005
-0.5-
0
50000
100000
150000
200000
Frequency (Hz)
Figure 7.1: Frequency Response of Cantilever Tip Displacement for 3V Amplitude
Applied Voltage Signal. First three resonant peaks are visible.
62
Frequency Response of Cantilever Tip
Displacement for 1V Amplitude (+-1V)
Applied Voltage Signal to PMPG
0.70.6-
0.5-
0.40.3O
0.20.1
0.010000
12000
14000
16000
18000
20000
Frequency (Hz)
Tip displacement is 0.696 um at resonance (13.75kHz)
Figure 7.2: Frequency Response of Tip Displacement Around Resonance for IV
Amplitude Applied Voltage Signal
Frequency Response of Cantilever Tip
Displacement for 5V Amplitude (+-5V)
Applied Voltage Signal to PMPG
4-
E
E3-
E
T.)
0
CL)
2-a,
'
0-
10000
12000
I
14000
'
16000
i
18000
'
20000
Frequency (Hz)
Tip displacement is 4.66 um at resonance (13.565kHz)
Note: resonance freq. has decreased
Figure 7.3: Frequency Response of Tip Displacement Around Resonance for 5V
Amplitude Applied Voltage Signal
63
7.2
Laser Vibrometer Surface Scans
Figures 7.4 through 7.6 are based on data taken from the white noise excitation
experiment shown in Figure 7.1. Not only can the laser vibrometer system "scan" across
the frequency spectrum, but it can also physically scan the laser beam across the surface
of the PMPG device. Computer .avi files were generated using the laser vibrometer
system, which demonstrate deflection of the plate structure at the three resonance
frequencies. Still pictures, as shown in Figures 7.4 through 7.6, of these .avi movies give
an indication of the deformation during resonance.
As can be seen in Figure 7.4, the first resonance mode has an "up and down" or
uniform bending type motion whereby the support structure at the back end of the device
(left side of the picture) remains stationary while the tip bends up and down. The second
mode in Figure 7.5 is a "torsional" mode where the left, front end bends up at the same
time that the right, front end is bent down, and vice versa. This kind of motion is not
desired for proper device operation. The third mode shown in Figure 7.6 is a "snake
mode" where the device has two bending points along its length. The first bending point
is towards the back end of the structure, allowing for primary up and down bending of the
plate structure. The second bending point is towards the tip end, so that when the plate is
bent primarily down, its tip is bent up, like a coiled snake. Again, this type of bending is
not desired for generating the maximum possible charge out of the device.
64
Figure 7.4: First Mode Resonance ("up and down"/uniform bending motion) at 13.91
kHz due to Direct Excitation of the PMPG Device. Maximum deflection is 4 microns.
Figure 7.5: Second Mode Resonance ("torsional mode") at 21.88 kHz due to Direct
Excitation of the PMPG Device. Maximum deflection is 0.2 microns.
65
Figure 7.6: Third Mode Resonance ("snake mode") at 48.50 kHz due to Direct
Excitation of the PMPG Device. Maximum deflection is 2 microns.
7.3
PMPG Base Shaking (Sensor Mode) Results
Figures 7.7 and 7.8 show data that was taken during base shaking experiments of
the Type-1 PMPG device in which the device is used as a sensor. The entire packaged
MEMS chip was shaken by the piezoelectric shaker at the first mode resonance frequency
of 13.7 kHz. By changing the voltage amplitude sent to the shaker, the resulting "base
displacement" magnitude will change. "Base displacement" is simply defined as the
displacement of the silicon substrate to which the micro cantilever is attached. Increasing
the applied shaker voltage increases the base displacement, and therefore results in a
larger cantilever tip displacement. The larger cantilever tip displacement creates a larger
closed-circuit charge, which is measured by the Kistler charge amplifier. The 13.7 kHz
shaking frequency (resonance) is kept constant for these base shaking experiments.
In these base shaking experiments, the largest measured cantilever tip
displacement magnitude was 2.56 pm at the center of the proof mass. This corresponds
with a 33 nm base displacement magnitude at 13.7 kHz shaking frequency. The
measured tip displacement was larger at the end of the proof mass- approximately 3.4
gm, or 33% larger than the 2.56 pim "center of proof mass" displacement. However, the
laser vibrometer data would fluctuate quite a bit when the laser beam was placed at the
end of the proof mass during resonance. Most likely, the laser beam could not maintain
coherence when placed too close to the end of the cantilever. Therefore, the 3.4 ttm tip
66
displacement is an estimate based on the most "stable" value. Again, the tip
displacement data in Figure 7.7 is based on the center of proof mass displacement, not the
end of the proof mass.
Theoretically, for a fixed base shaking frequency (in this case, resonance) a linear
increase in base shaking displacement should result in a linear increase in the cantilever
tip displacement. In the special case where the system is shaking at resonance, the
increase should be proportional to the Q of the system. We know this from the following
standard equation:
x
x
+ 2JCO -s
s +2+2) -s +
0)
-
S=.j()
nn
s=jO),,
where xo output cantilever tip displacement, xi input base displacement, s =
jw, { = 1/(2Q), on=a first mode resonance frequency and Q quality factor of the
system.
Although I did not save the frequency response data for the sensor mode (base
shaking experiments), I can still try to extract the Q from the actuation mode and see how
it applies to the sensor mode. The Q from the actuation mode can be found by taking the
ratio of the tip displacement at resonance to the tip displacement far outside the resonance
peak. Looking back at Figure 7.3, we see that at resonance, the tip displacement is 4.66
pm and far to the left in the frequency spectrum, the displacement is approximately 0.1
,Im. Therefore, the Q is approximately 47. The damping coefficient b can now be
calculated according to equation 2.9. This is done in Appendix A.1.
If the x and y axes of Figure 7.7 were both measured in the same length units (for
example, microns), then a linear fit of the figure, which includes the origin as a
constrained data point, would result in the equation:
Y = 85.5X
(7.2)
This would imply that the Q of the sensor mode is approximately 85. Comparing
this to the estimated Q value of 47 for the actuation mode, we can see that they are on the
same order. Moreover, it makes sense that the Q of the sensor mode would be less than
the Q of the actuation mode. We know that Q = m*On/b. The damping coefficient, b for
67
the sensor mode should be less than the damping coefficient for the actuation mode
where the cantilever tip velocity is higher. This means the
be greater than 47, which means
Q = 85
Q for the
sensing mode should
is likely a reasonable value.
Figure 7.8 shows the amount of generated, closed-circuit charge as measured by
the Kistler@ Type 5010B charge amplifier for the base shaking experiments. In order to
reduce low frequency (60 Hz), electrical noise on the Kistler@ charge amp signal, a
simple, high-pass RC filter was created on a protoboard and placed in-between the wires
leading from the PMPG packaging and the input to the charge amplifier. As the
magnitude of the cantilever tip displacement increases, the axial stress in the PZT layer
increases, thereby increasing the charge collected on the interdigitated electrode of the
Type-1 device. This should also follow a linear relationship, where a linear increase in
the tip displacement results in a linear increase in the generated closed-circuit charge.
The largest, achieved closed-circuit charge amplitude was 13.2 pC for the 2.56 /tm tip
displacement. The theoretical charge amplitude for a 2.56 Itm tip displacement was
28.38 pC (Again, please refer to Appendix A. 1.). Given a measured electrode
capacitance of 7 pF and the large output impedance ZPMPG, this would imply that the open
circuit voltage amplitude generated by the PMPG device is 13.2 pC/7 pF = 1.89 V.
68
C
o 2.5-
U
a
E
o
2.0-
E
()
E
0
0
CO
0
1.5-
0
U
0
E
0.0-
1ITITl
Due to Base Shaking at
FTip Displacement
I
. Maximum
I
I
Cantilever
7.7: Resulting,
Figure
0
5
10
15
20
*
25
30
35
Maximum Base Displacement (nm)
Figure 7.7: Resulting, Maximum Cantilever Tip Displacement Due to Base Shaking at
13.7 kHz Resonance (no electrical loading)
14 1
12
-
0
0
N
0
Q
8U
6
-
.
0
E
Cd 0 0
U
0
4
U
0
0
0
-2
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Maximum Cantilever Tip Displacement(microns)
Figure 7.8: Generated, Closed-Circuit (no electrical loading) Charge Amplitude Due to
Maximum Cantilever Tip Displacement at 13.7 kHz Resonance
69
7.4
Load Varying Experiments
Figure 7.9 shows the voltage measured across the load resistance. For these
resistive loading experiments, the PMPG device was attached to the power storage
system which consists of the bridge rectifier (four STMicroelectronics@ 1N5711 small
signal Schottky diodes), 10 nF mylar storage capacitor and the variable load resistance.
The MEMS device was shaken by the piezoelectric shaker at 13.7 kHz resonance with a
measured base displacement magnitude of 14 nm. Note: Previously measured base
displacement data would indicate that 14 nm is a bit small. The applied voltage to the
shaker was 20V peak-to-peak and should have resulted in a base displacement magnitude
closer to 30 nm. The electrical equivalent model for the total system (PMPG + power
storage system) is shown in Figure 7.15. Since the load resistance is in parallel with the
storage capacitor, the voltage across the storage cap and load resistance is exactly the
same. The voltage measurements were taken using the oscilloscope.
The sensing circuit that was used for doing the voltage measurements is shown in
Figure 7.10. The 100k "sensing" resistor is placed in series with the variable load resistor
("RLoad") on the same proto board where the high pass filter resides. The sensing resistor
prevents the 1Mn scope probe resistance from interfering with the variable resistor. A
formula for calculating the total load resistance is as follows:
RTotal = RLoad + (1OOkQ |1M
) = Road + 90.9kQ
(7.3)
As expected, the load voltage in Figure 7.9 increases with increased load
resistance. The highest DC cap voltage of 3V was measured for the 10.1 MQ (10 Mn +
90.9 kM) total load resistance. The DC cap voltage for the 5.2 MQ load resistance was
2.36V. 10 MK2 was the highest variable resistor used in the resistive loading experiments.
The highest load voltage does not necessarily translate to the highest amount of
electrical power delivered. The power transferred to the load resistance is a function of
both the load voltage across it and the load resistance itself. Specifically, it is calculated
according to:
70
Load
-Load
(7.4)
2
RLoad
where PLoad is the electrical power transferred to the load resistance,
load voltage and RLoad is the load resistance.
V"oad
is the
Figure 7.11 plots the electrical power delivered to the load as a function of the
load resistance. The data in this figure is based on the measured load voltage data from
Figure 7.9 and is calculated using equation 7.4. The maximum, transferred, electrical
power occurs for the 5.2 MQ load resistance. At this value of the load, the transferred
power was 1.01 yW. Increasing the load resistance to 10.1 MQ increases the load
voltage to 3V, but the transferred electrical power actually decreases to 0.89 pLW. This
result is not unexpected. The transferred power will increase with load voltage until
some peak point based on the load resistance, after which it will drop. The ideal load
resistance for transferring the maximum electrical power, should therefore be somewhere
between 5.2 MQ and 10.1 MQ. Time did not permit for testing other load resistance
values.
71
3.0
0
-
2.5-
2.0 0
CO
S1.5-
0
0
<
1.0-
0)
c,
75
0.5-
0.0 0
2
4
6
8
10
Resistive Load (M-Ohms)
Figure 7.9: Voltage Across Load Resistor vs. Load Resistance at 13.7 kHz Resonance.
Maximum base displacement was measured at 14 nm during base shaking. Generated,
closed-circuit charge was measured at 24.4 pC peak-to-peak prior to electrical loading.
RLoad
(variable load resistor)
10 nF, 100 nF
100k
1M
/ /"-
sense resistor
scope probe
resistance
Figure 7.10: Sensing Circuit for Load Voltage Measurements
72
1.04-
0
-
0.
-8-
E
-
0.60-
(U
0
0
-
_0
0.4-
(D 0.2-
a)
0
I
0
I
2
I
I
4
6
I
I
8
10
Resistive Load (M-Ohms)
Figure 7.11: Power Delivered to Load Resistor vs. Load Resistance at 13.7 kHz
Resonance. Same experimental variables as in Figure 7.9.
Figure 7.12 has one odd data point which is difficult to explain. For no electrical
load (RLoad = 0) the cantilever tip displacement was actually measured at its smallest
value of 1.85 microns. Intuitively, the tip displacement would be the largest for no
electrical load, because there is no extra loading that can dampen the mechanical system
via electro-mechanically coupling. I don't have a reasonable explanation for this
anomalous data point. The rest of the plot makes sense: As the resistive loading
increases, the maximum tip displacement (for the same base shaking magnitude and
frequency) decreases.
73
CD,
3.0-
C
2
E
2.8-
2.6-
()
0.
.C/)
o
2.4-
0.
Fo 2.22.0 -
E
E 1.8
0
2
4
6
8
10
Resistive Load (M-Ohms)
Figure 7.12: Cantilever Tip Displacement as a Function of Load Resistance at 13.7 kHz
Resonance. Same experimental variables as in Figure 7.9. Unloaded cantilever tip
displacement data point is circled.
7.5
Charging/Discharging of Power Storage Capacitor
What is happening in Figures 7.13 and 7.14 is the charging and discharging of a
10 nF mylar storage cap with a 5.2 MC load resistance across it. The two figures share
the same time axis. Again, the PMPG was shaken at resonance with approximately the
same 20V peak to peak AC voltage signal driving the piezoelectric shaker. Figure 7.13
shows the DC cap voltage vs. time, and Figure 7.14 shows the source current into the RC
parallel circuit (storage cap plus 5.2 MQ load resistance) vs. time. The source current
into the RC circuit is labeled as "dq/dt" in Figure 7.15.
Figure 7.14 is not measured data, rather it is a plot that is derived from the data in
Figure 7.13. Referring to Figure 7.15, by KCL we know that the PMPG source current,
dq/dt = Ic + IRLoad. The current through the storage capacitor and load resistor are given
by Ic = C-(dVc(t)/dt) and IRLoad = VC(t)/RLoad, respectively. Therefore, the PMPG source
current can ultimately be derived and plotted in Figure 7.14 from the cap voltage data,
Vc(t) shown in Figure 7.13:
74
dq= C-
dt
+
dt
(7.5)
RLoad
The PMPG device was shaken for approximately 0.8 seconds at 13.7 kHz by the
piezoelectric shaker and then the shaking was stopped. While the shaking was going on,
the storage cap was being charged up to a 2.28V DC (a little less than the 2.36V achieved
in the previous base shaking experiments), steady-state voltage. The charging happened
over a time period of approximately 0.2 seconds as measured between times ti = 4.75 sec
and t2 = 4.95 sec in Figure 7.13. As expected, the cap voltage rose exponentially during
this time, exactly as an RC circuit being driven by an AC current source should behave.
The PMPG source current initially spikes to a level of approximately 0.85 PA because it
is sourcing both the storage cap and the resistive load.
The 0.85 ptA current level should correspond to the PMPG AC current amplitude.
Two theoretical PMPG AC current amplitude values were calculated and are shown in
Appendix A. 1. The first is the current amplitude based on Stephen Senturia's current
equation for le. This gives a value of 0.0745 pA, which is roughly an order of magnitude
smaller than the measured value. The second theoretical value for the current amplitude
is derived using my expression for the current, which is the first time derivative of the
charge expression, Q(t). This gives a value of 0.389 /tA which is on the same order as
the measured current level. The current quickly drops to approximately 0.4 pIA by time t2
since the source current is only feeding the resistive load. 0.4 ItA is a reasonable value
given that the current flowing through the resistive load should be (2.28V/5.2MQ) = 0.44
pA based on the achieved DC voltage level.
Between times t 2 = 4.95 sec and t3 = 5.55 sec, the shaker was still shaking, and the
PMPG current source, as shown to the far left of Figure 7.15, was therefore still active.
However, no additional charge was accumulating on the storage capacitor during this
time period because the capacitor was full. The DC voltage level in Figure 7.14 stays
constant during this time period, as expected. At the same time, all the current that was
being sourced by the PMPG was delivered to the resistor and none of it was going to the
cap. The 0.4 pA current level in Figure 7.14 still holds.
75
Between times
t3 =
5.55 sec and t4 = 5.85 sec, the base shaking was stopped, and
therefore the PMPG was no longer sourcing the current. This explains why the DC cap
voltage in Figure 7.13 begins to decay after time t3 = 5.55 sec. The theoretical decay time
of an RC circuit is approximately equal to 5, where
-
RLoad*C.
Doing this calculation
gives 5r = 5*5.2MQ*10nF= 0.26 seconds. The measured decay time was approximately
0.3 seconds, so this checks. The source current in Figure 7.14 drops to zero almost
instantly- much faster than the decay time of 0.3 seconds. Of course, this is expected.
Since the PMPG is no longer shaking, there can be no current coming from it.
Lastly, to prove that a larger amount of electrical charge can be stored by the
PMPG power system, a 100 ItF storage capacitor was used instead of the 10 nF cap. A
1.08 MQ load resistance (1 MQ + 83.3 k sense resistance) was placed in parallel with
the storage cap. The capacitor was charged for 6 minutes (360 seconds) during base
shaking as shown in Figure 7.16. The charging time was approximately 350 seconds.
Charging and discharging times of an RC circuit should be the same. The reason
why the charging time of the 5.2 M92/10 nF RC circuit was 0.2 seconds, and the
discharge time 0.3 seconds is because there is a resistance introduced by the rectifying
bridge circuitry which is seen during charging, but not during discharging. This
resistance runs in parallel with the 5.2 MQ load and therefore reduces the overall
resistance. The RC time constant is reduced proportionally, and so, the charging time is
smaller compared to the discharging time. The same affect can be seen in the large
capacitor (100 [tF) charging experiment. Expected charging time is 5=
5*1.08MQ*100ptF = 542 seconds. However, the measured charging time in attaining the
1.05V steady-state DC voltage was only 350 seconds. We know that the capacitance did
not change during the experiment. Therefore, the effective resistance value must be
lower than 1.08 MQ.
Steady-state DC load/cap voltage is 1.05V in this large capacitor base shaking
experiment. The maximum power output to the load is therefore (1.05V) 2/1.08MQ =
1.02
stW.
The 1.093 Mn load with the 10 nF storage cap resulted in a steady state
voltage of 0.93V. As you can see, these two voltages are nearly the same. This should
be the case because the load resistances are approximately equal. Large charge storage
has now been proved.
76
Figure 7.13: Charging and Discharging of 1OnF Capacitor with 5.2 MQ Total Load (5.1
MQ + 90.9 kf Sense Resistance). Charging time and decay time are approximately 0.2
seconds and 0.3 seconds, respectively. Steady-state DC load/cap voltage is 2.28V in this
base shaking experiment.
77
X 10-7 PMPG Source Current Based on Averaged Cap Voltage Data
87 --
E
0
CL4-
0
I
I
I
4.4
4.6
4.8
5
5.2,
5.4
5.6
5.8
6
Time (s)
Figure 7.14: PMPG Source Current into RC Circuit During Charging and Discharging.
Steady-state current is approximately 0.4 jtA which makes sense given 2.28V/5.2MQ
0.44 ItA.
Rectifying bridge
D4 D1
ZP
CO
Im
Total PM\PO
Current tource
L --
-U--
dq/dt
G
1
D2 D3
IRLoad
*
Ic
Power 4
C
torage
Capacitor
R
PMPG
Figure 7.15: Electrical Equivalent Model of PMPG Power System: (PMPG + Power
Storage System)
78
Load
Figure 7.16: Charging of large 100 jtF Capacitor with 1.08 MC Total Load (1 MQ +
83.3 kQ Sense Resistance). Charging time is approximately 350 seconds. Steady-state
DC load/cap voltage is 1.05V in this base shaking experiment. The 1.093 MQ load with
the 10 nF storage cap resulted in a steady state voltage of 0.93V. These two voltages
should be approximately the same because the loads are almost the same.
7.6
Electrical Efficiency Calculations
One practical measure of the electrical efficiency of the PMPG Power System is
to calculate the ratio of generated charge that flows through the load versus all other
leakage charge in the system at DC steady state during mechanical resonance of the
PMPG device. In order to do this, we need to use some actual experimental data. The
steady state charging/discharging data from Figures 7.13 and 7.14 is chosen because both
the current flowing through the load resistance and the DC cap voltage during steady
state are known- 0.44 ytA and 2.28 V, respectively. These two values are enough to
calculate the PMPG output voltage amplitude (VPMPG), as measured across ZPMPG in
Figure 7.15.
The PMPG output voltage is simply:
79
VPMPG (t)
VPMPG
(7.6)
sin(2;T * 13.7kHz * t)
One time period at resonance is simply T = 1/f = 1/13.7 kHz = 7.3E-5 seconds.
Therefore, the generated charge flowing through the load resistance (in this case, 5.2
MQ) over one time period is:
Q = 0.44 ItA*7.3E-5
= 32 pC. We know that in order for
charge to flow through the load, current had to flow through Schottky diodes. And, in
order for current to flow through the Schottky diodes, they must be forward biased such
that:
VPMPG
> 2.28V. The question then becomes: What PMPG voltage amplitude,
VPMPG
is required in order to create 32 pC of charge through the load over one time period?
Please refer to Figure 7.17. Essentially, for each value of
set of values
t2
VDiff(t)
which is the difference between
VPMPG(t)
VPMPG,
there is a unique
and 2.28 V from time t1 to
as shown in Figure 7.17. VDiff(t) biases two Schottky diodes during each time period,
causing current to flow through them and into the load. Therefore, plugging VDiff(t) into
the diode current equation will give the current flowing through the two Schottky diodes
for each value of
VDiff
from time t1 to
t2 .
The current flowing through a diode for a given
bias voltage (in this case, VDiff) across it, is as follows:
VDiJf
Idiode =
(7.7)
Is (e 1 4 -1)
where Is = 5.1 nA, PDt = 25.88 mV and i = 2 for the 1N5711 small signal Schottky
diode during device operation.
Numerically integrating the diode current from ti to
you the generated charge,
integration.
Q. The two hatch marked
t2
and multiplying by 2 gives
areas in Figure 7.17 represent the
Q is calculated for each different value of VPMPG until the value
of Q
matches 32 pC and, thus, the corresponding value of VPMPG is found. A Matlab@ script
was created to do this and is found in Appendix A.2. A plot of VPMPG versus generated Q
was created in Matlab@ and the resulting plot is shown in Figure 7.18. The result is that
for the cap charging/discharging experiment in Figures 7.13 and 7.14, a PMPG voltage
amplitude of VPMPG = 2.624 V was needed to create the 32 pC of charge that flowed
through the resistive load in the DC steady state over one time period during resonance.
Comparing this value to the estimated open circuit voltage value of 1.89 V in
section 7.3, creates somewhat of a mystery. Clearly, the open circuit voltage must be
80
greater than or equal to 2.624 V in order to deliver the 2.28 V to the load. Yet, based on
the measured, closed-circuit charge amplitude of 13.2 pC, the implied open circuit
voltage level is 1.89 V. This probably means that the closed-circuit charge measurement
is not very accurate.
Now that we know
VPMPG,
the electrical efficiency of the PMPG Power System
can be calculated directly. The desired charge through the resistive load during one time
period at resonance is 32 pC. The charge lost to the PMPG output impedance, ZPMPG
over one time period is less than:
QzPMPG
The charge lost to
ZPMPG
-
VPMPG
ZPMPG
(7.8)
*T
is less than the equation above, because the voltage
across the output impedance is only equal to VPMPG twice during the period (once during
the positive part of the sinusoid, and once during the negative part), and less than that at
all other time.
ZPMPG
was estimated to be 2.38E10 Q in the Chapter 4 calculations. This
means that the peak current flowing through the ZPMPG Output impedance is
2.624V/2.38E10
= 0.11 nA. If even we keep this current constant and multiply by the
entire time period, we only get QZPMPG
=
(0.11 nA)*(7.3E-5 sec) = 8E-3 pC << 32 pC. If
even ZPMPG were as low as 1E9 Q, the peak current would still only reach 2.62 nA <<
440 nA (constant current flowing through load).
The only other place where charge is lost is during rectification, where there is
reverse current flow when the Schottky diodes are back biased. Referring to the
STMicroelectronics© 1N5711 data sheet (not shown here), we find that the reverse
current flow at a back bias voltage of 2.62V would be, at most, 5 nA. Because two
diodes are back biased at any one time, this translates to 10 nA of reverse current. Of
course, this is the peak current flow- the diodes are back biased at a voltage less than
2.62V for most of the time. Again, 10 nA << 440 nA. Therefore, in the very worst case
scenario, the electrical efficiency of the PMPG power system is:
.
Efficiency
.
440nA
440nA + 10nA + 2.62nA
=97%
(7.9)
81
In fact, the electrical efficiency is almost surely greater than 99%.
VL=V
IToe=1
(e 77I0 -1)
t2
Q= 2* J
( do)dt
ti
228
L
.
V5
0%
V.
- VDA ,
VP
o v-----2.2
V
-
G
I- -----
-------
-------
/
ti
t2
Figure 7.17: VPMPG(t) and Resulting Charge Over One Time Period at Resonance.
82
1.2-
0
0.
-/
0.
0r)
DA
0.4/
32pC- ----
0.2-
0/
225
2.3
2.35
2.4
2.45
2.5
2.55
2.6
2.65
2.7
2.75
PMPG Voltage Amplitude, VPMPG 2.624 V
Figure 7.18: PMPG Voltage Amplitude vs. Generated Charge Through Load Resistance
During One Charging Time Period (7.3E-5 seconds)
7.7
Acoustic Excitation Results
As discussed in Chapter 6, the acoustic excitation results were not as successful as
the base shaking results, although there are probable reasons for this. As shown in Figure
6.9 of Chapter 6, the optical positioning/base shaking system was positioned directly in
front of the speaker tweeter while the speaker was turned on. Therefore, the idea was for
the acoustic waves to act as a uniform pressure wave, forcing the top side of the
cantilever beam in an up and down motion. The reasons why this did not occur are the
following:
1.) With the air gap and trench existing around the cantilever beam, the cantilever
beam senses a pressure on both the top and bottom surfaces. Therefore, the
net driving force from one side is not achieved.
83
2.) Considering that the acoustic waves are traveling at the speed of sound (333
m/sec) and at a frequency of 13.7 kHz, the wavelength of the waves are
simply 333/13,700 m = 2.43 cm. The Type-i PMPG device that I was trying
to actuate is only 261 pm wide and 170 ttm long. The acoustic waves are
more than ten times bigger than the MEMS structure and are therefore passing
it without any interaction.
3.) There is no focusing or coupling of the acoustic waves into the MEMS
structure. For example, an acoustic resonator could serve this purpose. Still,
one must address the point that the cantilever is receiving pressure from both
sides (top and bottom).
84
Chapter 8: Conclusions
8.1
Performance Specifications of the PMPG Power System
The Piezoelectric Micro Power Generator (PMPG) power system has
demonstrated that it can generate the required power for the semi-active Auto ID tag.
That is, when a single Type-1 PMPG micro-cantilever structure is in Ist mode resonance
(13.7 kHz), over 1 tW of power is delivered to the load (5.2 Me). The corresponding
base displacement at this frequency was measured at 14 nm. The interdigitated electrode
structure exploits the d33 mode of the piezoelectric and allows for a DC voltage of 2.36 V
to develop across the load at 1 tW power level. 2.36 V is suitable for many, if not most
low power digital circuits. A 3 V DC voltage was achieved for a larger load (10.1 MQ)
at a lower power level of 0.89 yIW. If necessary, a higher DC voltage is possible by using
a simple voltage doubler circuit (completely passive) in conjunction with the PMPG
power system. The maximum, closed-circuit charge amplitude is 13.2 pC at 13.7 kHz,
which corresponds to a maximum cantilever tip displacement ("center of proof mass") of
2.56 itm during base shaking experiments. A 5V amplitude drive signal at resonance
resulted in a 4.66 ym tip displacement during actuation mode.
The total area of the PMPG MEMS device is smaller than 3001tm X 300 ytm. Of
that area, 100ptm X 100 Itm is estimated for each of the two bond pads (20,000 ttm 2 total
bond pad area per single device). Rectification and power storage electronics are
expected to take up minimal area compared to the actual MEMS device. Still, we've
allowed for a generous 50% increase in the area due to electronics and any other
miscellaneous space needs. This brings the estimated PMPG power system area to
135,000 im2 per single device, which translates to a power density of (1 AW)/(135,000
2)
/WM2
M
C2.
/m2) = 7.41 _W/mm = 0.741 mW/cm.
Based on the calculated power density value, the current PMPG power system is
capable of generating 2 1kW (two PMPG devices) within the prescribed area of 500
stm X
500 Am. If the targeted power is 5 yW, then the required area becomes 5 x 135,000 tm 2
2
= 675,000 yIm . This is roughly 8001km X 800 /tm. I think this is a conservative estimate
for the area. It can, in all likelihood, be reduced. One should also consider that this is a
85
first generation device. Performance is sure to improve with subsequent generations. A
power density greater than or equal to 2 mW/cm2 should be achievable from our
technology. The PMPG power system has an electrical efficiency in excess of 99%.
This means that the real design challenges remain in the mechanical domain:
Mechanically Coupling the most possible ambient vibrational energy (whether acoustic
or seismic) directly into the MEMS structures.
8.2
Improving Upon the Current Technology
A multiple beam device, in which multiple micro-cantilever beams are joined
together via a joining proof mass, could greatly increase the power density and would
require only one rectifying circuit/storage capacitor. Also, it would require only one pair
of bond pads. For example, if five beams were used, then only 20,000 tm2 of area would
be needed for the bond pads instead of 100,000 ttm 2 . This, of course, is based on the
assumption that the individual beams resonate in-phase with one another, which should
occur since they are attached to one another by the proof mass. If not, then the generated
electrical signal cannot be rectified. However, excessive out-of-plane warpage still
remains a concern for cantilever type structures. Some other suggested improvements:
1.)
Optimize the electrode design. Design the electrode (optimize) over the
highest stress region and not over the low stress region. Design the
interdigitated fingers to have the optimal width and spacing to maximize
charge collection ability.
2.)
Use better piezoelectric thin film with a higher d33 coefficient, if possible.
3.)
For the same mechanical force/energy source, reduce the mechanical damping
coefficient so that the tip velocity is increased.
4.)
Create a "flat bridge" structured PMPG device with optional, central proof
mass. A concept drawing for this device is shown in Figure 8.1. Current
PMPG cantilever structures are prone to out-of-plane bending due to residual
stresses in the thin films which make up the composite beam structure. The
doubly supported, flat bridge design would avoid this excessive warpage of
86
the piezoelectric thin film device. However, it will be less compliant than a
similarly sized cantilever structure.
5.)
Tune the resonance frequency of the MEMS structures to better match the
ambient energy spectrum. For example, seismic (base shaking) energy from
the environment exists in higher levels at lower frequencies, such as around
120 Hz. [4]
Figure 8.1: Flat Bridge Design to Avoid Excessive Warpage of the Piezoelectric Thin
Film Device.
8.3
Application-Driven Questions Regarding the PMPG
8.3.1
Can the PMPG be used to power an active Auto ID tag (i.e. to power the RF
communication)?
Two types of tags were discussed with Roger Stewart [11]: 1.) Class-3 tag uses
the IF back scatter sent from the reader to partially power the ID circuitry. Local power
source (battery) is still used, in part, to power the ID circuitry. Communication
frequency is in the "100's of kHz" [11]. 2.) Class-4 tag is fully active. Communicates at
915 MHz frequency.
87
If a Class-3 tag communication frequency in the 100's of kHz is employed, then it
might be possible for the PMPG power source to power the RF communication circuitry
which is governed by the following equation:
P=f -C-V
2
(8.1)
This RF circuitry spec is the real limiting factor for power, not the
electromagnetic (EM) radiated power over the communication distance.
The reader can read an EM signal with a power of only "a few nanoWatts" [11].
According to Klaus Finkenzeller in his "RFID Handbook", an electromagnetic RF signal
at 915 MHz will experience a free space path loss of 29.5 dB over a distance of 1 meter.
This translates to a factor loss of 102.95 = 891 ~ 900. Let's say that "a few nanoWatts"
means 2 nW. In that case, the tag needs to generate an RF signal with an EIRP (effective
isotropic radiated power) power of approximately 2nW*900 = 1.8 ytW in order for the
reader to read it at a distance of 1 meter. The PMPG is perfectly capable of generating
1.8 ttW, so the radiated power from the tag is not the major issue.
Roger Stewart cited a power spec in the "1 to 10's of milliWatts" [11] in order to
power the RF communication circuitry on the chip at the 915 MHz communication
frequency for a Class-4 tag. The RF circuitry is responsible for generating the RF signal
that will be radiated from the tag. Let's say 10 milliWatts of required power. Using the
RF circuitry power equation from above:
10mW = 915Mhz -C -(3V)
2
(8.2)
where I assumed a 3V DC operating voltage for the circuitry and the 915 MHz
operating frequency. Solving for the circuit switching capacitance C, we get 1.2 pF,
which is a reasonable value. If we choose, instead, a communication frequency in the
"100's of kHz" of 500 kHz for example, then the required power becomes 5.4 /LW, which
is achievable by the PMPG power source. It is clear that the required RF circuitry power
is greater than the required, radiated power. The RF circuitry power is therefore the
power spec of concern. These are back-of-the-envelope calculations, but it leaves the
possibility open for the PMPG to power the RF communication for the Auto ID tag or
other autonomous sensing devices.
88
2.) The other power spec that Roger Stewart cited was a 1 milliWatt burst of
power for approximately 1 millisecond. This specification is for transmitting a quick
burst of data over the RF for the Class-4 tag. This would require 1 micro Joule of
available energy from the power source. The PMPG power system is perfectly suited for
delivering instantaneous power to a load because the electrical energy is available on the
storage capacitor.
As an example, we achieved a 2.36V DC storage cap voltage in our power
measurements when the PMPG MEMS device was in resonance and attached to the
power storage system (bridge rectifier circuit plus 10 nF storage capacitor) with a 5.2 MQ
load in parallel with the storage cap. The rise time for charging up the cap to 2.28 V was
0.2 seconds in our storage capacitor charging/discharging experiment.
The electrical energy stored on a capacitor of capacitance C with voltage V across
it is:
F
ECaa
1
I=CV
(8.3)
89
Therefore, in order to store 1 microJoule of energy on the cap, the required
capacitance at 2.28 V DC would have to be 380 nF. Charging the 10 nF cap in our
experiment required 0.2 seconds with a single PMPG device. Charging a 380 nF cap can
therefore be done in approximately 7.5 seconds. However, given the allocated space on
the Auto ID tag, I would expect at least five PMPG devices working in series to charge
the storage capacitor. This would reduce the charging time to 1.5 seconds or less.
Therefore, if one can afford to wait approximately 1 second between data bursts, then
active, RF data transmission is possible via the PMPG power system for a Class-4 Auto
ID tag. Note: The DC voltage on the cap will decrease as the charge is bled away to
drive the load. Therefore, the initial charge stored on the cap may have to be greater than
2.28V*380nF = 866 nC in order to ensure the load is driven above a certain, minimum
load voltage which will be application specific. This implies a somewhat larger storage
capacitance, and therefore, a longer charging time than previously mentioned.
8.3.2
Although acoustic energy harvesting could not be demonstrated in our
experiments, is this type of energy harvesting possible?
One significant problem with trying to actuate the PMPG cantilever devices
directly with acoustic waves is that the pressure source is not only created on the top
surface of the cantilever beam, but also on the bottom surface. Therefore, there is no unidirectional pressure force acting on the beam to force it in one direction. One solution to
this problem is to place the PMPG chip on top of a diaphragm-type structure where the
top surface is completely exposed to the incoming acoustic wave, but the bottom surface
exists within the closed cavity of the diaphragm (See Figure 8.2). If the frequency of the
acoustic waves is known, then a suitable diaphragm structure can be constructed which
will resonate at the same frequency and couple the acoustic energy. The energy
harvesting problem has now been converted from one of acoustic energy harvesting to a
problem of mechanical vibration energy harvesting or base shaking, which has already
been shown to work in the lab. In this case, the resonating diaphragm is the resonating
base.
90
In order to ensure that a uniform pressure is received across the surface of the
diaphragm structure, the acoustic waves have to act like plane waves at the surface.
However, the goal is to couple the most acoustic energy into the diaphragm structure.
These two ideas do not exactly work together. In order to ensure a uniform pressure, k
>> L. But, if that condition is imposed, then most of the acoustic waves will pass the
diaphragm structure and not couple the energy into the diaphragm structure. This is a
design issue that needs to be further researched. Still, we assume:
A ~L
(8.4)
where X is the wavelength of the acoustic waves and L is the diameter of the
diaphragm structure.
It is also desirable that the diaphragm structure can couple omni-directional
acoustic waves. By "omni-directional", I mean that you don't have to worry which
direction the acoustic waves are coming from. Therefore, the position of the acoustic
source relative to the diaphragm is not critical. This is difficult if k z L. The next set of
geometrical conditions ensures that the acoustic waves are in the far-field and that
acoustic plane waves reach the diaphragm surface:
r >> A
1!
r >>-A
(8.5)
where r is the distance from the acoustic sound source to the diaphragm.
Since the plane waves are really pressure waves of moving air particles, they are
governed by the two following equations:
c=
U =
-f
P. C
(8.6)
(8.7)
where c is the speed of sound (333 m/sec), U is the velocity of the moving air
particles, P is the pressure magnitude at the surface of the diaphragm and p is the density
of air (1.21 kg/M3 ).
91
Equation (8.7) is the "Ohm's Law" of acoustics where the particle velocity U is
the "current", pressure P is the "voltage" and the term p-c represents the acoustic
impedance. The needed base velocity (velocity of the moving diaphragm) can be
calculated by knowing the required base displacement Xo for piezoelectric energy
harvesting (The maximum base displacement will correspond to a maximum cantilever
tip displacement at resonance.) and the resonance frequency f. This base velocity is set
equal to the velocity of the moving air particles. The required pressure P at the surface of
the diaphragm can then be calculated from equation 8.7. We know that the pressure from
the sound source dies off as l/r, so we can finally calculate the needed air pressure
intensity from the sound source at a distance r.
In order to use an artificial acoustic noise source, the frequency would have to be
above the audible (above 20 kHz), so let's use 40 kHz as an example. This, of course,
means the diaphragm structure would have to resonate at 40 kHz, as would the PMPG
cantilever devices. If f = 40 kHz, then k = 333/40,000 = 0.83 cm. The diaphragm
diameter should therefore be on the order of a centimeter, or perhaps a bit smaller. The
distance away from the sound source, r would have to be on the order of 1 meter since r
>> k. By using a reasonable value for L as indicated, the thickness and ultimate stiffness
of the diaphragm structure can be determined based on the resonance frequency value,
which in this case is 40 kHz.
Ideally, one would wish to make the diaphragm structure as compliant (less stiff)
as possible, so that the force produced by the acoustic waves at the surface will result in
maximum displacement of the diaphragm, and therefore, maximum tip displacement of
the PMPG cantilevers- bigger charge generation amplitude. Other improvements that
could be made: 1.) Create an acoustic resonator structure (e.g. a tube resonator or
Helmholtz resonator) on top of the diaphragm structure to better couple the acoustic
waves into the diaphragm. Geometry of the resonator would be determined by the
wavelength of the acoustic sound waves. 2.) Use material which matches well
acoustically with air (not easy to do because air is so light).
92
Compliant diaphragm
structure
r
Artificial acoustic noise
source with wavelength A and
frequency f which matches
resonance frequency of
=L
PMPG chip with
multiple PMPG
devices
Ideal diaphragm
support structure
diaphragm structure as well as
PMPG cantilever devices.
Figure 8.2: Acoustic plane waves impinging on diaphragm structure with PMPG chip
8.4
Overview of Lithium Ion Battery Technology and Comparison to
PMPG Power System
"Energy harvesting techniques can result in infinite lifetime, but the output power
available is in general less than stored energy solutions." [6] For a given volume, stored
energy techniques (i.e chemical batteries) usually result in greater power generation
versus ambient energy harvesting devices. One attractive asset of the PMPG power
system is that the power is essentially generated from the surface of the silicon chip. In
other words, PMPG power density is better defined as the generated power per unit area
or Watts/m2, mW/cm2 , etc. As long as the PMPG power system can deliver the required
power as specified by the application, and do it within a reasonable amount of area, then
the power density advantage of the chemical battery is moot.
Active and semi-active RFID tags currently use primary (nonrechargeable)
chemical batteries. Primary battery types can be classified according to their chemistry
system. "The major classes are LeClanche (the traditional zinc/carbon/ammonium
93
chloride "dry cell" type), alkaline (widely used in consumer applications), zinc-air (for
hearing aids and similar applications) and lithium." [20] Power generation specs are
normally broken down into the following categories: I.) Specific energy (amount of
energy available per unit mass, expressed in watt-hours per kilogram) II.) Energy density
(energy per unit volume, expressed in watt-hours per cubic centimeter) III.) Open-circuit
voltage (the voltage available at the battery terminals when the battery is at full capacity
and not supplying current, expressed in volts); Most electronic components used in RFID
tags require a minimum operating voltage of 3V. IV.) Service lifetime (the time, in
months or years, that the battery can be expected to perform as specified) V.) Operating
temperature range.
"Lithium is an ideal material for battery anodes because of its high intrinsic
negative potential, the greatest of all metals. Lithium is also the lightest nongaseous
metal... Batteries based on lithium chemistries have the highest specific energy and
energy density of all types." [20]
"Lithium cells, all of which use a nonaqueous electrolyte, have nominal open
circuit voltages (OCVs) of between 2.7 and 3.6 volts. Lithium batteries also have
extended operating temperature ranges, enabled by the absence of water and the chemical
and physical stability of the materials. Some lithium-based systems.. .can operate at
temperatures as low as -55C and as high as +150C." [20]
There are three lithium battery chemistries which are suitable for use in RFID
systems: 1.) lithium/manganese dioxide or Li/MnO 2 and 2.) lithium/thionyl chloride or
Li/SOC 2. 3.) lithium/cobalt dioxide or Li/CoO 2 . Lithium/manganese dioxide cells have
an OCV of 3.1V and a "moderately high energy density... They are best suited to
applications having relatively high continuous or pulse current requirements." [20]
However, to ensure a reliable 3V DC operating voltage for the RFID electronics, at least
two lithium/manganese dioxide cells must be connected in series. This adds extra weight
and cost. If each battery costs 5 cents, then the cost of the tag will be greater than 10
cents.
Lithium/thionyl chloride cells have the highest energy density of all lithium types.
They also have the highest OCV at 3.6V. This means that, usually, only one battery of
this type needs to be used to ensure proper operating voltage so long as one cell is
94
sufficient to supply the current necessary for the required operating lifetime.
"Lithium/thionyl chloride cells are best suited for applications having a very low
continuous current and moderate pulse current requirements- a description that fits most
RFID tag applications." [20] These two lithium battery types also differ in the cylindrical
shape description. Lithium/manganese dioxide cells are manufactured with a spiralshaped cathode ("jelly roll" construction) and "crimped, nonhermetic elastomer seals...
Lithium/thionyl chloride cells are manufactured in welded, hermetically-sealed cases
using a 'bobbin' construction, in which the electrodes are a central rod and a surrounding
'can'." [20]
For the PMPG, the silicon chip itself is a good, solid substrate and there are no
liquids or aqueous solutions involved with the PMPG system. Chemical batteries, on the
other hand, must deal with hermeticity issues; for example, avoiding the leakage of
electrolytes under various temperatures and pressures. Packaging of the PMPG power
system should therefore be easier and more reliable versus chemical batteries. Another
one of the PMPG's main advantages resides is in its cheap manufacturability. The
PMPG could ultimately be microfabricated on the same silicon chip as the Auto ID
electronics, for example. This integration would save the added cost of having both a
separately packaged power solution (as exists now with the lithium ion battery) and
separately packaged electronics. Finally, the PMPG power delivery would be reliable
and would certainly last at least through the application lifetime, if not longer.
A comparison of the PMPG power system traits versus lithium battery solutions
can be found in Table 8.1 below. The PMPG power system exceeds the lithium ion
battery technology in nearly every category. Note: the lifetime for the current, printed,
lithium ion battery being used in the semi-active RFID tags is approximately 3 years.
The cited 10 year lifetime for Li/MnO 2 and Li/SOC 2 battery technology in Table 8.1 is
probably because these are large batteries for more expensive RFID applications. The 3
year lifetime should be considered.
95
Table 8.1: Lithium Battery Types Versus PMPG For RFID Tag
Applications [20]
Characteristic
Nominal OCV
Li/MnO 2
Internal construction
Hermeticity
Hermeticity after temperature cycling
Flammability of electrolyte
Energy density
Specific energy
Operating temperature range
+85C(1)
Shelf life under manufacturer-specified
storage conditions
More than one source
(1) Standard -
Li/SOC1 2
3.6 V
3.1 V
Bobbin
Spiral
Hermetic
Nonhermetic
Potential leakage Excellent
Nonflammable
Flammable
1080 Wh/L
637 Wh/L
430 Wh/Kg
319 Wh/Kg
-20C TO +60C
-55C to
10 years
Yes
10 years
Yes
High temperature version to +125C
Characteristic
PMPG
3 V (Can use
Nominal OCV
Li/CoO 2
4V
voltage doubler
Internal construction
Hermeticity
Hermeticity after temperature cycling
Flammability of electrolyte
Energy density
(per unit area)
to increase voltage)
thin film
MEMS packaging
Nonhermetic
Excellent
potential
leakage
Excellent
**unknown
N/A
0.74 mW-h/cm
2
2
0.8 mW-h/cm
not given
Specific energy
**N/A
Operating temperature range
-20C TO +80C
Shelf life under manufacturer-specified
storage conditions
Infinite
More than one source
Yes
unknown
*Cost
*Cheap
Expensive
-50C TO +180C
60,000 cycles
(c harge/discharge)
PMPG energy density is better defined as the available electrical energy per unit area
since the PMPG devices are all formed on the upper surface area of the silicon die.
**
N/A
96
Not Applicable
8.5
Research Summary
A novel MEMS-based, piezoelectric, micro cantilever was fabricated and tested
for its ambient energy harvesting abilities. The micro cantilever, called the Piezoelectric
Micro Power Generator (PMPG), consists of a bottom membrane layer (SiO 2 or
SiO 2/SiNx) followed by an electrical diffusion barrier layer (ZrO2), an active piezoelectric
layer (PZT), a top, interdigitated electrode (Pt/Ti) and optional SU-8 proof mass. The
device is surface micromachined using a XeF 2 etch release step for creating the released
cantilever structure. The fabricated device demonstrated a well-formed, thin film PZT
layer with a random perovskite structure of 100 nm grain size. The spontaneous
polarization (Ps), remanent polarization (Pr), and coercive field are 50 tC/cm 2, 20 pC/cm2
and 38 KV/cm, respectively.
The interdigitated electrode structure exploits the d33 mode of the piezoelectric
thin film. This allows for a higher open circuit voltage versus a d31 cantilever of the same
beam dimensions. Powering of digital IC circuits such as that used on the Auto ID tag
now becomes possible. The PMPG power system consists of the PMPG MEMS device, a
four diode rectification bridge, power storage capacitor and resistive load. A set of base
shaking experiments were performed where the PMPG MEMS device was first packaged
and poled and then mechanically excited by a piezoelectric base shaker. The MEMS
package was hooked up to the power storage system and the output power was measured.
Our 170 /im long, 261
sim wide Type-1
PMPG device achieved a measured,
closed-circuit charge amplitude of 13.2 pC at 13.7 kHz first mode resonance frequency
during base shaking experiments. The corresponding base and tip displacements were 14
nm and 2.56 ptm, respectively as measured by the Polytec@ PSV-300H Laser Vibrometer
System. The PMPG delivered 1 yIW of continuous DC power at 2.36 V to the resistive
load. Given an estimated PMPG power system area of 0.135 mm2,2 the power density is
0.741 mW/cm2. The corresponding energy density is 0.74 mW-h/cm2, which compares
favorably to competing lithium ion battery solutions for the Auto ID tag. The PMPG
power system has an electrical efficiency greater than 99% and should be able to supply 5
ttW of DC power within an 800 pm X 800 tm. Power density is expected to increase
with future technology improvements.
97
The PMPG power system technology has proven that it can supply the needed
power for the semi-active RFID tag. The benefits of the PMPG power system over
conventional lithium ion battery technology are that it should be cheaper to manufacture,
has a more dependable packaging solution, is less bulky and has a potentially infinite
lifetime. Our results show that a d33 mode, thin film piezoelectric cantilever device could
be useful not only as a piezoelectric micro power generator, but also for micro-actuators
and sensors. The mechanical resonance frequency of the cantilever can be tuned to target
specific frequencies within the ambient energy spectrum. This is done by altering the
cantilever dimensions (i.e. layer thicknesses, length of the beam and the inclusion of a
proof mass, if necessary). The fact that powering of the RF communication may be
possible makes for some interesting applications such as wireless monitoring systems for
rotating machinery, monitoring of gas lines and other remote sensing applications.
Acoustic energy harvesting should also be possible provided that the packaging is better
adapted for acoustic coupling.
98
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http://www.rapidttp.com/transponder/tadiran.html
100
Appendix A.1
Calculations of Mechanical and Electro-Mechanical Models of the
Type-1 Device:
%MECHANICAL MODEL CALCULATIONS:
t=[0.4, 0.05, 0.12, 0.12, 0.12, 0.12]/1000000; % From bottom layer
E1=[69, 244, 63, 63, 63, 63]; % Young's Moduli (in GPa) of composite layers
v=[0.15, 0.27, 0.3, 0.3, 0.3, 0.3]; % Poisson Ratios of composite layers
sigma=[-20, 400, 620, -110, 70, 110]/1000; % Residual Stresses of composite layers
L=170E-6; % Length of composite beam
W=261E-6; %Width of composite beam
E=E1.*1E9;
t_PZT=0.48E-6; %Thickness of total PZT layer (4 sol-gel spin-ons)
1_overlap=195E-6; % Overlap length between adjacent mini-electrodes for Type-I
% PMPG Device
A_PZT=tPZT*l_overlap; %cross-sectional area of PZT
d=4E-6; % separation distance between adjacent mini-electrodes for Type-I PMPG
% Device
densitySU8=2200; % density of SU8 proof mass in kg/mA3
[m,n]=size(t); % n is the number of layers
z=cumsum(t)-t/2; % Distance of each layer's neutral plane from bottom surface
yn=(z*diag(t)*E')/(t*E'); % Neutral Axis
e=(sigma*t')/(t*E'); % Contraction Strain
sigma n=sigma-e*E; % New stress as a result of contraction
M=sum(sigma n*diag(t)*z'); % Moment
EI=sum(E*((diag(t)A3)/12+diag(t)*diag(z-yn)A2));
EI_W = EI*W;
cur=M/EI; % Beam Curvature due to residual stress effects
%Theoretical k stiffness:
% k=8*EI_W/(LA3); % k stiffness term based on uniformly distributed input force:
% Perscribed load must be given in Newtons.
m_proof= (20E-6*50E-6*261E-6)*densitySU8; % Proof mass in kg
m=mproof;
%Theoretical Resonance Frequency (rad/sec):
% w=sqrt(k/m);
% f=w/(2*pi); % Resonance frequency measured in Hertz
101
% Mechanical Calculations Based on Lab Results (Measured 13.7 kHz resonance):
w=2*pi*13.7E3; % Lab resonance frequency
k=wA2*m; % Approximate k from lab data
f=w/(2*pi); % Resonance frequency measured in Hertz
% Proof that Viscous Damping is not an issue in our system:
% Viscous damping constant, bviscous is taken from "Design and Analysis
% of a Piezoelectric Vibration Powered MicroGenerator System" by
% Masoud Agah, et al:
A_surface=L*W;
viscosity-air=1.73E-5; % Measured in Pascal-sec
g=0.5*W; % Gap underneath the plate is roughly one half the width due to
% XeF2 isotropic etch process
b_viscous=0.42*(A-surface)A2*(viscosityair)/(gA3);
% ELECTRO-MECHANICAL MODEL CALCULATIONS:
EPZT=63E9; % Young's modulus of PZT in Pascals (N/mA2)
d33=200E-12; % d33 piezoelectric coefficient of PZT in Coulombs/Newton
epsilon_0=8.854E-12; % Permittivity of free space in Farads/meter
epsilonPZT=1200*epsilon_; % Based on measured dielectric properties of PZT thin
%film.
n-pairs=18; % number of mini-electrode pairs which make up full interdigitated
%electrode in Type-i Device
C_9=n-pairs*epsilonPZT*APZT/d; %electric capacitance
C-e=n-pairs*EPZT*(d33)A2*APZT/d; % Capacitance due to piezoelectric response
% (electro-mechanical capacitance)
C_total=CO+C-e;
k-p=sqrt(C-e/C_0); %electromechanical coupling coefficient
% Turns ratio, n can be derived from Ce = nA2/k relationship:
n=sqrt(k*Ce); % Transformer turns ratio n
% Final electrical circuit consists of C_0 dielectric capacitance in parallel with
% m/n^A2 equivalent inductance, nA2/k equivalent capacitance, b/nA2 equivalent
% resistance and R_0 electrical resistance, which are all four in series.
Le=m/(nA2)/npairs; % Inductance due to piezoelectric response
Q-mech=47; %Mechanical Quality factor: Measured from laser vibrometer experiments
b=m*w/Q-mech; % Mechanical damping coefficient in kg/sec (N-sec/m)
R-e=b/(nA2)/n-pairs; % Resistance due to piezoelectric response
roePZT=1E7; % Resistivity of PZT in Ohm-m
102
R_O=roePZT*d/A_PZT/n-pairs; % Electrical resistance
R_total=R_0 + R_e; % Total output resistance
%Admittance, Y is the reciprocal of the output impedance:
s=j*w;
Y=s*C_0 + 1/(s*L-e + Rtotal + (1/(s*Ce))); % PMPG complex output admittance
Z=1I/Y; % PMPG complex output impedance
Y_mag=abs(Y); % Magnitude of output admittance
Z_mag=1/Ymag; % Magnitude of output impedance
% --------------------------------------------------------------------
%LAB DATA:
X_0=1E-6*[2.56 2.3 1.97 1.71 1.64 1.2 0.76 0.52 0.2];
% Max tip deflection measured in base shaking experiment at resonance
% as shown in Figures 7.7 and 7.8
% -----------------------------------------------------------------
v_0=X_0*f; % Tip velocity at resonance frequency, f- based on lab data
%Current Source can be derived from transformer relation in electro-mechanical model:
I_e=v_0*n % Magnitude of PMPG AC current source
C_0_mag=abs(l/(CO*s)) % Magnitude of C_0 capacitance at 13.7 kHz resonance
C_emag=abs(1/(C-e*s)) % Magnitude of C-e capacitance
"..
L_mag=abs(s*L e) % Magnitude of Le inductance
RLCseries=Lmag+C-e-mag+Rtotal
Z_PMPG = RLCseries;
V=X_0*k/n; %AC voltage source amplitude at resonance
Q=Ctotal*V; % Created Charge on Electrode
I_PMPG=f*Q; %Alternative AC current source calculation
103
THEORETICAL MECHANICAL VALUE CALCULATIONS:
yn =
4.5075e-007
This value is good because the neutral axis remains below the PZT thin film layer.
EI=
4.4256e-009
k=
1.8808
f=
9.109 kHz
Note: This compares pretty well to the experimental resonance frequency of the Type- 1
Device which was measured at 13.7 kHz.
b_viscous =
6.4364e-009
b=
6.992 1e-007
104
CALCULATED ELECTRO-MECHANICAL VALUES BASED ON THE
FOLLOWING LAB DATA: TIP DISPLACEMENT, QMECH, 13.7 kHz
RESONANCE FREQUENCY (Note: Capacitance and resistance values are independent
of tip displacement):
% Max tip displacement measured in base shaking experiment at resonance as shown in
Figures 7.7 and 7.8:
X_0=1E-6*[2.56 2.3 1.97 1.71 1.64 1.2 0.76 0.52 0.2];
Qmech
=
47
f=
13700
k=
4.2547
b_viscous
=
6.4364e-009
b
=
1.0516e-006
As you can see, the viscous damping of the cantilever beam is almost three orders of
magnitude smaller than the damping coefficient b. Therefore, viscous damping is not an
issue in our system.
%Electrical capacitance, C_0:
C_0 =
4.4752e-012
% Electro-mechanical capacitance, C_e:
105
C-e =
1.0614e-012
%Total capacitance (C_0 + C-e):
C_total =
5.5366e-012
%Electrical resistance, R_0 dominates output impedance, "Z_PMPG":
R_0 =
2.3742e+010
%Equivalent electrical resistance, R_e:
R-e =
1.2937e+004
% Equivalent electrical Inductance (in Henries), L_e:
L-e =
7.0638
% Inductor impedance magnitude at 13.7 kHz resonance:
L-mag =
6.0805e+005
% Ce impedance magnitude at 13.7 kHz resonance:
C-e-mag =
1.0945e+007
106
% C_0 impedance magnitude at 13.7 kHz resonance:
C_0_mag =
2.5959e+006
%Z_PMPG:
Z_PMPG =
2.3753e+010
% Open Circuit Voltage, V (also known as VPMPG):
5.1254
4.6048
3.9442
3.4236
3.2835
2.4025
1.5216
1.0411
0.1330
0.0842
0.0576
0.4004
% Closed-circuit charge,
Q
Q = CV
= Ctotal*V:
=
1.0e-010 *
0.2838
0.2550
0.2184
0.1896
0.1818
0.0222
% AC Current Source Amplitude as calculated with Stephen Senturia's Model:
I_e =
1.0e-007 *
0.7453
0.6696
0.5735
0.4978
0.4775
0.3494
0.2213
0.1514
0.0582
107
% AC Current Source Amplitude as calculated with my definition of IPMPG = dQ/dt:
I_PMPG =
l.Oe-006
0.3888
108
*
0.3493
0.2992
0.2597
0.2491
0.1822
0.1154
0.0790
0.0304
Appendix A.2
Matlab Script Used to Generate Figure 7.18:
fraj.m:
function y = fraj(t)
global Acurr Is C f phi;
Vdiff = Acurr*sin(2*pi*f*t)-C;
y = Is*(exp(Vdiff/phi)-1);
rajfile.m:
clear all; close all;
global Acurr Is C f phi;
tol = 0.5e-12;
C = 2.28;
Is = 5.le-9;
f = 13.7e3;
Qreal = 3.2e-11;
A = 2.3:.001:2.7;
phi = 2*25.88e-3;
A_match = 0;
for i = 1:length(A)
Acurr = A(i);
t 1 = asin(C/A-curr)/2/pi/f;
t2 = (pi-asin(C/Acurr))/2/pi/f;;
Q(i) = 2*quadl(@fraj,t1,t2,tol);
end
j = find(abs(Q-Qreal) < tol)
A_match = A(j)
disp('doggg!')
plot(A,Q)
title(")
xlabel('PMPG Voltage Amplitude')
ylabel('Generated Charge')
109