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Magnetic spring in electromagnetic vibration energy harvester and applications of focused ultrasonic transducer

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Magnetic spring in electromagnetic vibration energy harvester and applications of focused ultrasonic transducer

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MAGNETIC SPRING IN ELECTROMAGNETIC VIBRATION ENERGY HARVESTER
AND APPLICATIONS OF FOCUSED ULTRASONIC TRANSDUCER

by

Lurui Zhao

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)

May 2021

Copyright 2021 Lurui Zhao
ii
Acknowledgements
I would like to express my sincere appreciation for and deepest gratitude to my advisor,
Professor Eun Sok Kim. His navigation, encouragement, advice, and insight has been essential in my
pursuit of a doctorate degree and my development as a researcher and an engineer. Professor Kim has
provided me with many life-changing opportunities and opened my eyes to view this world differently.
With Professor Kim’s support, I’m able to work on fascinating research projects across MEMS fields,
gain interdisciplinary experience, present at international conferences and communicates with world-
leading researchers and colleagues. This work would not be here without Professor Kim’s guidance.
I would like to thank Professor Wei Wu and Professor Andrea Armani who have been valuable
members of my dissertation committee and who have provided insightful discussions and advice
toward improving this thesis.
I would also like to thank Dr. Martin Han and Dr. Le Trinh who have been the collaborators
in my research projects. They have taught me fundamentals of discipline which are out of my current
knowledge scope and made it possible for me to progress on integrative work.
I am grateful to the former members of the USC MEMS group, including Dr. Lingtao Wang,
Dr. Qian Zhang and Dr. Yufeng Wang who have provided the foundation for my research, lab training,
and mentorship. I would like to thank my current group members including Dr. Anton Shkel, Hai Liu
and Jaehoon Lee for their thoughtful discussion and friendship. I would express my special
appreciation to Yongkui Tang and Dr. Yunqi Cao for their support in experiments and inspirations. I
would never forget the time etching Si dome with Yongkui (using HNA) in the cleanroom at 4 am
here at Los Angeles, and the time in 419 when Yunqi and I brainstorm and exchange ideas while
experimenting with thermal conduction of sodium chloride.
iii
My sincere thanks go to Dr. Donghai Zhu and Alfonso Jimenez for their continued support
at the clean-room facilities at USC. Their efforts have been essential in completing this work.
I am also very thankful to all my friends, Dr. Yifei Wang, Dr. Boxiang Song, Dr. Yuhan Yao,
Hao Yang, Dr. Yuanrui Li, Dr. He Liu and all others here at California or around the world for their
emotional support and encouragement.
Finally, I want to express my eternal love to my family, who provides me with the best
environment, humanity education and correct value, enabling me to make this far and continue.

iv
Table of Contents

Acknowledgements ............................................................................................................................................ ii
List of Tables .................................................................................................................................................... vii
List of Figures .................................................................................................................................................. viii
Abstract ............................................................................................................................................................ xvi
Chapter 1 : Introduction ................................................................................................................................... 1
1.1 Motivation ....................................................................................................................................... 1
1.1.1 Magnetic spring based vibrational electromagnetic energy harvester ......................... 1
1.1.2 Focused ultrasonic transducer without phased array .................................................... 3
1.2 Review on Vibration/Force Energy Harvesters ....................................................................... 4
1.2.1 Electrostatic Energy Harvester ......................................................................................... 5
1.2.2 Piezoelectric Energy Harvester......................................................................................... 6
1.2.3 Triboelectric Energy Harvester ........................................................................................ 8
1.2.4 Ferroelectret Energy Harvester ...................................................................................... 10
1.2.5 Electromagnetics Energy Harvester .............................................................................. 12
1.3 Review on Acoustic Tweezers ................................................................................................... 14
1.3.1 Standing-wave tweezers. .................................................................................................. 15
1.3.2 Travelling-wave tweezers ................................................................................................. 16
1.3.3 Acoustic-streaming tweezers ........................................................................................... 17
1.4 Overview of Chapters ................................................................................................................. 18
1.5 References ..................................................................................................................................... 21
Chapter 2 : Analytical Model Based on Surface Charge for Magnet ........................................................ 34
2.1 Background ................................................................................................................................... 34
2.2 Theory and Modeling .................................................................................................................. 35
2.2.1 Model of the Permeant Magnet ...................................................................................... 36
2.2.2 Magnetic Force ................................................................................................................. 40
2.3 Model Validation and Discussion .............................................................................................. 43
2.3.1 Validation with Experimental and Simulation Data .................................................... 43
2.3.2 Comparison to Existing Models ..................................................................................... 48
2.3.3 Effective Spring Constant ............................................................................................... 52
2.4 Summary ........................................................................................................................................ 55
2.5 References ..................................................................................................................................... 57
Chapter 3 : Magnetic Spring for Electromagnetic Vibration Energy Harvesters ................................... 60
3.1 Background ................................................................................................................................... 60
3.2 Theory ........................................................................................................................................... 61
3.2.1 Lossless System ................................................................................................................. 62
3.2.2 Vibration with Damping.................................................................................................. 72
v
3.2.3 Forced Vibration............................................................................................................... 76
3.3 Experimental Results ................................................................................................................... 77
3.3.1 Testing Setup ..................................................................................................................... 77
3.3.2 Ring-down ......................................................................................................................... 79
3.3.3 Forced Oscillation ............................................................................................................ 80
3.4 Application .................................................................................................................................... 83
3.5 Summary ........................................................................................................................................ 86
3.6 References ..................................................................................................................................... 87
Chapter 4 : Focused Ultrasonic Transducer with Controllability on Focal Length ............................... 89
4.1 Background ................................................................................................................................... 89
4.2 Device Design .............................................................................................................................. 89
4.3 Simulation ..................................................................................................................................... 92
4.4 Fabrication .................................................................................................................................... 93
4.5 Measurement ................................................................................................................................ 94
4.6 Results ............................................................................................................................................ 96
4.7 Summary ........................................................................................................................................ 97
4.8 References ..................................................................................................................................... 98
Chapter 5 : Focused Ultrasonic Transducer with Controllability on Focal Location ......................... 101
5.1 Background ................................................................................................................................ 101
5.2 Device Design ........................................................................................................................... 102
5.3 Fabrication ................................................................................................................................. 104
5.4 Measurement and Results ........................................................................................................ 105
5.5 Summary ..................................................................................................................................... 107
5.6 References .................................................................................................................................. 108
Chapter 6 : Immersive Acoustic Tweezers................................................................................................ 109
6.1 Background ................................................................................................................................ 109
6.2 Device Design ........................................................................................................................... 111
6.3 Fabrication ................................................................................................................................. 114
6.4 Measurement and Results ........................................................................................................ 115
6.5 Summary ..................................................................................................................................... 117
6.6 References .................................................................................................................................. 118
Chapter 7 : Zebra Fish Embryo Trapping with Acoustic Tweezers ..................................................... 119
7.1 Background ................................................................................................................................ 119
7.2 Device Design ........................................................................................................................... 120
7.3 Fabrication ................................................................................................................................. 123
7.4 Experiment setup ...................................................................................................................... 125
7.5 Results ......................................................................................................................................... 126
7.6 Summary ..................................................................................................................................... 130
7.7 References .................................................................................................................................. 131
Chapter 8 : Rotational Manipulation on Trapped Particle with Acoustic Tweezers........................... 132
8.1 Background ................................................................................................................................ 132
8.2 Design and Simulations ............................................................................................................ 133
8.2.1 Design of Single Acoustic Transducer ....................................................................... 133
vi
8.2.2 Design of the Acoustic Tweezers ................................................................................ 136
8.3 Fabrication ................................................................................................................................. 139
8.4 Experiment and Result ............................................................................................................. 141
8.4.1 Experiment Setup .......................................................................................................... 141
8.4.2 Polyethylene Particles .................................................................................................... 141
8.4.3 Zebrafish Embryo ......................................................................................................... 143
8.5 Summary ..................................................................................................................................... 143
8.6 References .................................................................................................................................. 145
Chapter 9 : Immersive Micro-propeller ..................................................................................................... 146
9.1 Background ................................................................................................................................ 146
9.2 Design ......................................................................................................................................... 146
9.3 Fabrication ................................................................................................................................. 147
9.4 Measurement ............................................................................................................................. 149
9.5 Results ......................................................................................................................................... 150
9.6 Summary ..................................................................................................................................... 151
Chapter 10 : Conclusions and Future Directions ..................................................................................... 152
References ...................................................................................................................................................... 154

vii
List of Tables
Table 1.1 Acoustic tweezers summary [83] .............................................................................................. 15
Table 2.1 Grade, coercive force and geometry of rare earth neodymium magnets used in model
validation shown in Figure 2.6 and Figure 2.7. The top movable and bottom
anchored magnets are of same type and size except for the polarity arranged. ................ 45
Table 2.2 RMSD of FEM simulation and DCS model compared to experimentally measured
value over separation distance from 0mm to 50.8mm. ........................................................ 48
Table 2.3 The 3rd order polynomial curve fitting for the experimentally measured force (in N)
vs separation distance (in mm). ................................................................................................ 50
Table 2.4 RMSDs of the point charge model, the dipole model, the 3rd order polynomial curve
fitting over the separation distance from 1.27 to 50.8mm. .................................................. 52
Table 3.1 Grade and geometry of rare earth neodymium magnets used in magnetic springs
plotted in Figure 3.2. The levitated and anchored magnets are of same type and size
except for the polarity arranged. .............................................................................................. 63
Table 3.2 Summary for the magnets used in the designed energy harvester. ..................................... 84

viii
List of Figures
Figure 1.1 Schematic illustrations [32] of electrostatic energy harvester that bias voltage is
provided by electret materials. .................................................................................................... 6
Figure 1.2 Various configurations of piezoelectric cantilevers [33, 37]: (a) unimorph; (b)
bimorph; (c) a piezoelectric cantilever with interdigitated electrodes; (d) a
piezoelectric cantilever with proof mass at its free end. ......................................................... 8
Figure 1.3 Schematic illustration of the structure and working principle of the triboelectric
generator [38]. (a) The structure of an integrated generator in bending and releasing
process and related electrical measurement tests. Photographic images of a flexible
TEG and mechanical bending equipment. (b) Proposed mechanism of a TEG (see
text for details): charges are generated by fractioning two polymer films, which
results in the creation of a triboelectric potential layer at the interfacial region
(indicated by dashed lines);a mechanical compression results in a change in the
distance between the two electrodes (from D to d), thus, under the driving of the
triboelectric potential, a change in system capacitance leads to the flow of current in
the external load which drives the flow of the free electrons across the electrodes to
minimize the total energy of the system. ................................................................................ 10
Figure 1.4 Energy conversion mechanisms of FENG [40]: (a) Charge distribution and giant
dipoles of FENG after micro plasma discharging, showing that the upper and lower
surfaces of voids are oppositely charged. (b) and (c) Direct electromechanical
interaction effect. (b) Pressed by human hand on the surface of FENG. (c) Pressure
released and giant dipoles restore original sizes. (d) and (e) Reverse electromechanical
interaction effect. (d) Giant dipoles further expand as positive potential is applied.
(e) Giant dipoles shrink as negative potential is applied. ..................................................... 12
Figure 1.5 Illustrations of various acoustic-tweezer technologies [83]. (a) A typical BAW-based
standing-wave tweezer device. The number of pressure nodes and antinodes inside
the channel is determined by adjusting the applied acoustic wave frequency with
respect to the distance between the matching layer and the reflection layer; (b) SAW-
based standing-wave tweezers use IDTs to generate mechanical waves. Four sets of
IDTs are used to generate a 2D pressure node field that traps and patterns particles;
(c) Active traveling-wave tweezers with a transducer array to manipulate particles. By
controlling the relative phase of the acoustic wave from each transducer, flexible
pressure nodes can be formed to achieve dynamic patterning; (d) Passive traveling-
wave tweezers with a single transducer to achieve complex acoustic distributions and
control over particles; (e) Acoustic-streaming tweezers use oscillating microbubbles
inside a microfluidic channel to generate out-of-plane acoustic microstreaming flows;
(f) Solid-structure-based acoustic-streaming tweezers generate a directional fluid
flow under acoustic excitation. ................................................................................................. 18

ix
Figure 2.1 Laterally configured single magnetic springs with (a) cuboid magnets and (b) disk
magnets. (c) A vertical magnetic spring with two coupled magnetic springs
composed of two anchored magnets and one moveable magnet. Equivalent springs
are modeled along the central axis between the two magnets forming the spring. .......... 36
Figure 2.2 The dual-charged-surfaces (DCS) model for (a) a vertically magnetized block magnet:
(b) zero net magnetic charge and (c) surface magnetic charge being proportional to
the body magnetization. ............................................................................................................ 38
Figure 2.3 Magnetic field established by uniformly charged rectangular plate P1, on reference
plane. ............................................................................................................................................ 38
Figure 2.4 Schematic (left) and the DCS model (right) of a vertically configured magnetic spring
with mass load: in the model, the two magnets are represented by four magnetically
charged plates (P1 - P4), so that the resultant force between the two magnets is the
combination of the repulsive forces (between P1 and P4 as well as between P2 and
P3) and the attractive forces (between P1 andP3 as well as between P2 and P4). ........... 41
Figure 2.5 FEM simulation results for magnetic flux density (arrows) and magnetic scalar
potential (color bar). The magnetic force is numerically calculated from the
simulation results and shown in Figure 2.6 and Figure 2.7. ................................................. 46
Figure 2.6 Experimentally-measured, FEM-simulated, and analytically-calculated (based on the
DCS model) magnetic forces vs separation distance in a magnetic spring for four
different pairs of N52 grade Neodymium magnets (listed in Table 2.1). The analytical
solution from the DCS model compares well with the measured and FEM simulation
results. .......................................................................................................................................... 47
Figure 2.7 Comparison among DCS model, point charge model, dipole model and 3
rd
order
polynomial curve fitting with experimentally measured data for four magnet pairs.
The magnets detail can be found in Table 2.1 and curve fitting coefficients are shown
in Table 2.3. ................................................................................................................................. 51
Figure 2.8 Calculated restoring forces of the vertically configured magnetic springs vs
separation distance between the two magnets. The two magnets used in a magnet
spring are of same geometry and type (Table 2.1), and the proof mass attached to
the movable magnet is varied between 300 g and 500 g. ..................................................... 54
Figure 2.9 Calculated effective spring constant vs vibration amplitude in vertical direction z
(where z = 0 is the equilibrium position), as a function of the proof mass attached
on the movable magnet. ............................................................................................................ 55

x
Figure 3.1 A magnetic spring composed of two magnets arranged vertically, one magnet
anchored and the other levitated (by the magnetic repulsive force). On the levitated
magnet is a proof mass, so that the displacement of the levitated magnet may be
enhanced for a given externally applied acceleration or force (for larger power
generation from vibration energy). An equivalent spring also is indicated between
the two magnets. ........................................................................................................................ 62
Figure 3.2 Calculated restoring forces (based on DCS model for same types of the levitated and
anchored magnets) showing (a) mostly non-linear spring constant except when the
vibration is small around the equilibrium position, (b) higher restoring force for the
magnet with higher grade (with N52 being a higher grade than N42) and thus higher
coercive force, (c) the proof mass determining the maximum negative restoring force,
(d) higher restoring force for wider magnets, and (e) higher force for taller magnets.
...................................................................................................................................................... 64
Figure 3.3 Calculated responses of a lossless or damping-free magnetic spring (composed of
two cuboidal N52 grade neodymium magnets with 25.4 mm side length, along with
300 gram proof mass on the movable magnet of the magnetic spring): (a) free
vibrations vs time as a function of the initial displacement between 10 and 550 mm
and (b) spectrum of the time-domain displacement () xt for various initial
displacements (same color coding as in Figure 3.2). ............................................................. 67
Figure 3.4 Calculated vibration amplitude and frequency vs the initial displacement. ....................... 68
Figure 3.5 Calculated vibration amplitude and frequency vs (a)-(b) proof mass, (c) coercive
force, (d) side length of the magnet, and (e) height of the magnet. .................................... 72
Figure 3.6 Model of a magnetic spring with proof mass including two types of damping. ............... 73
Figure 3.7 Natural vibration with damping: (a) and (b) ring down vs time as a function of
various damping conditions; (c) and (d) frequency spectra of the time-domain ring-
down signals in (a) and (b). ....................................................................................................... 75
Figure 3.8 Forced vibrations of a magnetic spring vs time under externally applied accelerations
with varying amplitudes
2
0
2, 3, and 4 / a m s = and frequencies f = 1.32, 1.68, 2.52,
and 2.88 Hz. In about 4 seconds, the system reaches a steady state forced vibration
at the frequency of external drive. ........................................................................................... 77
Figure 3.9 Photo of the testing setup along with a magnetic spring composed of a levitated
magnet (on which a proof mass is mounted) and an anchored magnet inside a plastic
housing......................................................................................................................................... 79
Figure 3.10 Measurement of free vibration of the magnetic spring: (a) ring-down vs time, with
both the shape and the period changing due to the spring’s non-linearity, as the
amplitude rings down due to damping and (b) the period of the non-sinusoidal ring-
down curve vs time. ................................................................................................................... 80
xi
Figure 3.11 Vibration amplitude of the fundamental resonance of the magnetic spring vs
frequency of externally applied sinusoidal acceleration; (a) as a function of applied
amplitude (showing the decreasing resonant frequency as the amplitude increases)
and (b) as a function of the proof mass (showing the increasing resonant frequency
as the mass increases). ............................................................................................................... 83
Figure 3.12 (a) Schematic of the electromagnetic vibration energy harvester based on a magnetic
spring and (b) photo of the fabricated harvester. .................................................................. 85
Figure 3.13 Measured power (into a matched load of 256 ) from the electromagnetic vibration
energy harvester: (a) power vs frequency as a function of the applied acceleration at
0.1, 0.15 and 0.2g and (b) power vs applied acceleration at 2Hz. ....................................... 86
Figure 4.1 Top-view and cross-sectional view schematics of a 4-bit resolution transducer. Four
equal-width concentric ring electrodes are patterned on PZT. Each electrode can be
actuated individually. By varying the selection of the electrodes to be actuated, the
focal length can be varied. ........................................................................................................ 90
Figure 4.2 The radius of the circular center electrode r 0 determines lower bound of the focal
length approximately. The n
th
radius r n is used to determine if the n
th
ring electrode
needs to be actuated of a particular focal length. .................................................................. 91
Figure 4.3 A plan for selecting the actuation group of the electrodes for a 32-bit resolution
transducer. The red blocks mean the corresponding n
th
electrode rings are selected
for actuation, while the blue ones mean unselected.............................................................. 91
Figure 4.4 Simulation results showing the focal effect and focal length of 5, 7, 10 and 12 mm....... 92
Figure 4.5 Fabrication process of the transducer. .................................................................................... 93
Figure 4.6 Photos of the fabricated transducer. The top photo shows the transducer after
releasing sacrificial photoresist layer for air reflector region which shelters the
asymmetric electrode part. The O 2 plasma etched releasing hole can be clearly seen.
The bottom photos show the close-up views of the patterned electrodes........................ 94
Figure 4.7 Measurement setup schematics for droplet ejection experiment. Droplet ejection can
be observed by CCD camera, while the focal length can be measured with the
micropositioner. ......................................................................................................................... 95
Figure 4.8 Cross-sectional-view photos of the water ejections obtained at the water heights of
5 mm (a), 7 mm (b), 10 mm (c), and 12 mm (d). ................................................................... 96
Figure 4.9 Measured focal lengths vs designed focal lengths. ................................................................ 96
Figure 4.10 Ejected droplet size vs designed focal length (both measured and simulated data). ....... 97
xii
Figure 5.1 Example of a piezoelectric transducer with Fresnel zone-plate lens. For un-sectored
full ring lens, the focal point is located along the central line above the ring centers
due to the symmetricity [134]. ............................................................................................... 102
Figure 5.2 A single sector is consisted of 3 sub-regions: inner pie-shape sector, middle torus,
and outer torus. The Fresnel ring pattern within each sub-region is arranged to offset
the focal point with a desired distance on the focal plane. (a) relative position of the
central line and one sector; (b) the inner pie-shape sector corresponding to focal
point 1 which is furthest from the central line on the focal plane; (c) the middle torus
corresponding to focal point 2 and (d) the outer torus corresponding to focal point
3 which is closest to the central line; (e) and (f) the cross-sectional views of the
Fresnel rings within different sub-regions that are designed to have different lateral
offset for the focal point on the focal plane. ...................................................................... 103
Figure 5.3 Top view of the design of a single sector. Three sectors are individually accessible. ... 104
Figure 5.4 Brief fabrication steps. ............................................................................................................ 105
Figure 5.5 Measurement setup. The hydrophone is mounted on the 3-axis positioner and
connected to the oscilloscope for readout. ......................................................................... 106
Figure 5.6 Actual measurement setup and fabricated device. One sector is actuated during
measurement. ........................................................................................................................... 106
Figure 5.7 Measured normalized acoustic field in each sub-region. ................................................... 106
Figure 6.1 Conceptual diagrams of the transducer consisting of three sets of Fresnel lens (i.e.,
multi-foci Fresnel lens). A symmetric lens in circumferential direction is needed to
generate a focused beam, and a pair of two sectors is chosen for a specific focal
length, as illustrated in this diagram. Our fabricated device has 3 pairs of the lens
sectors for three focal lengths. In a) - c), the red pair denotes the sectors that are
actuated for a particular focal length. By driving different pairs, acoustic waves can
be focused at different focal lengths (as indicated with the perspective-view diagrams
with liquid over the transducer, at the upper row). ............................................................ 110
Figure 6.2 Top view diagram of a multi-foci Fresnel lens design with 18 evenly distributed
(circumferentially) sectors. ..................................................................................................... 111
Figure 6.3 Cross-sectional schematic of a multi-foci Fresnel lens. Two sectors from different
Fresnel lenses are conceptually shown on right and left side of the transducer. The
two Fresnel lenses focus at different distance along the center line perpendicular to
the lens surface. The Bessel beam zone is developed due to the interference of the
two focused acoustic beams. For each Fresnel lens, the Fresnel band design is
determined by the Equation (1). ........................................................................................... 112

xiii
Figure 6.4 Brief fabrication process for the tweezers. .......................................................................... 113
Figure 6.5 Photos of a) Fresnel lens with 18 sectors before forming the air cavities; b) the lens
at close-up after forming the air cavities through the etch holes and c) the tweezers
packaged with laser-cut acrylic reservoir (on top of the tweezers) and 18 wires for
electrical connections to the 18 sectors. .............................................................................. 114
Figure 6.6 Transducer packaged with resavior. Instead of accessing all 18 sectors, we use only
one wire-out on the front side, in this design, to provide concise electrical connection.
................................................................................................................................................... 114
Figure 6.7 Schematics of the measurement setup for testing the acoustic tweezers with
microspheres dispersed in water within the acrylic reservoir. The transducer is driven
by an amplified pulsed-sinusoidal signal, and the video of the particle trapping by the
acoustic tweezers is captured through a CCD camera. ..................................................... 116
Figure 6.8 Photos taken at different times with polyethylene microspheres (0.5 mm in diameter)
in the reservoir over the tweezers. When the tweezers is actuated (right after 0 ms),
all the microspheres except one trapped microsphere at the center are pushed to the
edges of the reservoir, and remain there, while the tweezers holds exactly one
microsphere at the trapping zone at the center (see the photos from 207ms to
1897ms). When we stop the electrical actuation of the tweezers, the trapped
microparticle is released. ........................................................................................................ 116
Figure 7.1 Full ring Fresnel lens transducer: (Top) Top view of full-ring Fresnel half-wave-band
electrodes (dark rings) on piezoelectric substrate (light square) and (Bottom) Cross-
sectional view showing how focusing effect occurs. Acoustic wave from the rings of
the patterned electrodes interfere constructively at a focal point leading to an
intensified acoustic pressure. ................................................................................................. 120
Figure 7.2 Top and cross-sectional schematics of a tweezers consisting of three sets of Fresnel
zone plate sectors for three different focal lengths: (top two figures) when one pair
of the sectored Fresnel is actuated and (bottom) when two such pairs are actuated at
the same time. Trapping zone is developed due to the interference of the two (or
more) focused acoustic beams. ............................................................................................. 121
Figure 7.3 Mask pattern of the top electrode of the acoustic tweezers with 3 sets of 6 sectored
electrodes for a total of 18 sectors of Fresnel-lens-patterned electrodes: one set of
sectored Fresnel lens covers a total of 120º, as each sector occupies 20º angular space.
................................................................................................................................................... 122
Figure 7.4 Cross-sectional view of a Fresnel lens based on air cavity showing that due to
acoustic impedance mismatch, the acoustic waves are reflected at the air/liquid
interface. Acoustic waves are generated where there are electrodes, and propagate
only through the regions where there is not air cavity. ..................................................... 123

xiv
Figure 7.5 Brief fabrication steps for the acoustic tweezers. ............................................................... 124
Figure 7.6 Photo of a fabricated acoustic tweezers............................................................................... 124
Figure 7.7 Experimental setups for (Top) Horizontal operation and (Bottom) vertical operation.
................................................................................................................................................... 125
Figure 7.8 Possible resonances in the liquid reservoir: (Left) A horizontally placed tweezers may
introduce resonance between the device surface and liquid surface, while (Right) a
vertically placed tweezers may introduce resonance between the device surface and
solid sidewall of the reservoir, making the optimum operating frequency shifted. ...... 126
Figure 7.9 (Top) Trapping and (Bottom) releasing a zebrafish embryo with the tweezers placed
horizontally............................................................................................................................... 128
Figure 7.10 (Top) Trapping and (Bottom) releasing of a zebrafish embryo with the tweezer
placed vertically. ...................................................................................................................... 129
Figure 8.1 Full ring Fresnel lens transducer: (Left) Top view of full-ring Fresnel half-wave-band
electrodes (dark rings) on piezoelectric substrate (light square) and (Right) Cross-
sectional view showing how focusing effect occurs. Acoustic waves from the rings
of the patterned electrodes interfere constructively at a focal point leading to an
intensified acoustic pressure [134]. ....................................................................................... 134
Figure 8.2 Top and cross-sectional schematics demonstrating the generation of multi focal
points from sectored Fresnel lens (for three different focal lengths): a) and b) when
one pair of the sectored Fresnel is actuated; c) when two such pairs are actuated at
the same time. Multi focal points and Bessel beam zone are developed due to the
interference of the two (or more) focused acoustic beams. ............................................. 135
Figure 8.3 Pattern of the active ultrasoice source after filtered by Fresnel lens. A total 18 sectors
are arranged in 3 sets of 6 pi-shaped sectore: one set of sectored Fresnel lens covers
a total of 120º, as each sector occupies 20º angular space. Three sets are featuring at
17.0, 18.5 and 20.0 mm focal lengths seperately. ............................................................... 135
Figure 8.4 Simulated normalized absolute pressure produced by a single transducer shown in
Figure 8.3. (a) on cross-sectional plane along the central vertical line (with the
transducer placed at the bottom) and (b) on the focal plane at 18.0 mm. ...................... 136
Figure 8.5 Schematics showing the formation of paired transducers as acoustic tweezers, placed
in parallel to each other. a) a pair of two sectored transducers aligned at the central
line, with Fresnel lens facing each other; b) two transducers with 0º rotation offset
on the central line and c) two transducers with 30º rotation offset on the central line.
................................................................................................................................................... 137

xv
Figure 8.6 Simulation result of normalized absolute pressure distribution of the acoustic
tweezers formed by the two transducers placed as depicted in Figure 8.5 (c) with a
separation distance of 36 mm and a rotation offset of 30º. a) and b) show the pressure
distribution on major trapping zone plane at 18.4 mm above bottom transducer (17.6
mm to the top transducer), when the transducers are driven at 1.070 and 1.072MHz,
respectively. c) and d) show the pressure distribution on the cross-sectional plane
along the central line, when the transducers are driven at 1.070 and 1.072MHz,
respectively ............................................................................................................................... 138
Figure 8.7 Simulated normalized pressure along the central line from the one transducer surface
to the other. Top figure shows the pressure when both transducers are driven at 1.07
MHz. and bottom figure shows the pressure when driven at 1.072 MHz. The slight
change on the trapping zone when frequency shifts leads to the manipulation of the
trapped particle. ....................................................................................................................... 139
Figure 8.8 Brief fabrication flow. ............................................................................................................. 140
Figure 8.9 Photo of the fabricated transducer. ...................................................................................... 140
Figure 8.10 Setup for the rotation control experiment. Two transducers are vertically placed in
the water. .................................................................................................................................. 141
Figure 8.11 Photos showing the rotational manipulation on a half-colored (half green and half
red) polyethylene sphere of 1 mm in diameter: a) the sphere is released and soon
trapped in a trapping zone of the acoustic tweezers; b)-e) by changing the frequency
(applied to the tweezers) from 1.1689 MHz to 1.1691 MHz, the trapped sphere rotate
around 90 degree, as the red half rotates from left side to down side; f)-i) by changing
the frequency from 1.1691 MHz to 1.1693 MHz, the sphere rotate additional 90
degree, as the red half rotates from down side to right side. ............................................ 142
Figure 8.12 The trapped half-colored sphere rotates back when frequency is reversed from
1.1693 MHz back to 1.1689 MHz. ....................................................................................... 142
Figure 8.13 Rotational manipulation on a 24-36 hours-post-fertilization zebrafish embryo.
Rotation is observed when the frequency (applied to the acoustic tweezers) is slightly
lowered from 1.1730 to 1.1726 MHz. .................................................................................. 143
Figure 9.1 Brief fabrication steps. ............................................................................................................ 148
Figure 9.2 Photo of a finished transducer. ............................................................................................. 149
Figure 9.3 Photos of the propeller (suspended with a wire) being propelled. From the
measurement, the direction of the propulsion can be measured. .................................... 150
Figure 9.4 Photos showing the propeller turning to the right or left due to the directional thrust.
................................................................................................................................................... 150
xvi
Abstract
This thesis presents two separate topics. Chapter 2 and 3 discuss the modeling and
optimization of magnetic spring which is used in electromagnetic vibration energy harvester that
enables ultra-low resonant frequency of several hertz to the harvester. Chapter 4 to 9 cover several
types of ultrasonic-transducer-based devices including acoustic tweezers, micro-propellers, and
focused ultrasonic transducer with controllability on its focal length and location.
For magnet modeling, this thesis presents a new analytical model for a permanent magnet that
is particularly useful for calculating magnetic force between two permanent magnets in a magnetic
spring. The new model treats a single magnet as a pair of parallel magnetically charged surfaces, which
we call dual charged surfaces (DCS). With the model, the force between two magnets is treated as
interaction of four charged surfaces, which can be calculated analytically as a function of magnets’
geometry and magnetization. This new model overcomes a major problem of other commonly used
analytical models (dipole and point charge models) which predict infinitely large repulsive force when
the separation distance between two magnets approaches zero, and allows accurate calculation of the
repulsive force in both near and far fields. The model is validated with experiments and finite element
method (FEM) simulations, through demonstrating correct prediction on the magnetic force vs
separation over a wide range of the separation distance. With the root-mean-square deviation (RMSD)
as a measure of the model accuracy, the DCS model is shown to have better accuracy over the Gilbert
model (based on a pair of point charges), the Ampere model (based on a pair of dipoles) and the fitted
power series method.
For magnetic spring modeling, this thesis analyzes non-linear vibratory behavior of magnetic
springs designed to have resonant frequencies at an extremely low frequency of several Hz associated
with human’s walking motion. First, a simple vertically configured magnetic spring with one stationary
xvii
magnet and one movable magnet is studied with an analytical duel-charged-surface (DCS) model for
a permanent magnet. In a lossless (or damping-free) magnetic spring, the apparent resonant
frequencies for natural vibration depend on the initial distance between the two magnets (which
determines the total energy in the spring), proof mass, magnet’s coercive force and magnet geometry.
How the resonant frequencies depend on those parameters are presented, as the parameters are varied.
Then damping through friction, air viscosity and electromagnetic induction is added to the lossless
model, and ring-down characteristics as well as forced vibration characteristics under an externally
applied acceleration are analyzed. As a validation of the theoretical model, a magnetic spring is built
and shown to have resonant frequencies at 3- 6 Hz with a tunable range (3 Hz) of the resonant
frequency. In addition, a vibration energy harvester from human’s walking motion is designed and
demonstrated to have an extremely low resonant frequency of about 3 Hz. The harvester (occupying
3
3 1 15 cm  volume and weighing 200 gram) is measured to produce about 10mW power from a
person’s normal walking.
For acoustic tweezers, this thesis reports our recent design of an immersive acoustic tweezers
capable of trapping and holding large and heavy particles such as micro-particles up to 1 mm in
diameter, as well as zebrafish embryos at their 24 - 36 hours post fertilization, by developing a 3-
dimensional energy well in the bulk of liquid medium. The acoustic tweezer is built on a 2.03 mm
thick lead zirconate titanate (PZT) substrate and operated at its thickness mode, with 18 symmetric
beamforming sectors (pie shaped when viewed from top) arranged for 3 focal lengths (17.0, 18.5 and
20 mm). For a single focal length, the six beamforming sectors (with air-cavity-reflectors for
eliminating out-of-phase wave interference) work together as a sectored Fresnel lens. The acoustic
waves aiming at different focal lengths interfere with each other such that they produce a Bessel beam
zone (with negative axial radiation force) along the center line perpendicular to the transducer surface,
which works as the energy well for trapping and holding particles. The tweezers using 1.17 MHz
xviii
ultrasound shows strong trapping capability and large trapping zone and is capable of trapping and
holding late-stage zebrafish embryos (0.7 - 1mm in diameter and 1.3 – 1.5 mg in weight). The
fabricated acoustic tweezers has been shown to trap 24hours-post-fertilization zebrafish embryos
when it is placed either horizontally or vertically.
This thesis also describes an electrically controllable acoustic tweezers capable of holding and
rotating mm-sized particles through varying the frequency of the electrical voltage applied to the
tweezers. The tweezers is composed of a pair of vertically placed acoustic tweezers, in parallel and
center aligned, so that the trapping zone of each of the tweezers set overlaps with each other’s. Each
single transducer is built on a 2.03 mm thick lead zirconate titanate (PZT) substrate with 18 symmetric
beamforming sectors (pie shaped when viewed from top) arranged for 3 focal lengths (17.0, 18.5 and
20.0 mm) defined by air-cavity acoustic lens. Acoustic waves generated from the pair of the two
tweezers produce Bessel beam zone with acoustic energy well, where a particle gets trapped and held.
Once a particle is captured, rotational manipulation is achieved by fine tuning the tweezers’ driving
frequency, which impacts the trapping zone quite slightly, enabling gravity to provide an asymmetric
force that rotates the trapped particle. Our experiments show that a trapping of mm-sized particle is
achieved at 1.17 MHz driving frequency for both transducers, and tuning of the frequency by about
100 Hz generates rotation of the trapped particle. The on-demand rotational manipulation is shown
to be effective in rotating mm-size polyethylene particles and 24 - 36 hours-post-fertilization zebrafish
embryos that are 1.3 - 1.5 mg in weight.
For focal point controllability, this thesis reports a novel acoustic transducer capable of
delivering focused acoustic beam with electrically tunable focal length over 7 mm. Constructed on a
1.02 mm thick lead zirconate titanate (PZT) substrate, the transducer uses a collection of equal-width-
equal-spacing concentric ring electrodes (and a circular electrode at the center) on one side of the
xix
substrate. With each electrode individually addressable, a desired focal length is mapped to a set of the
electrodes generating the acoustic waves that arrive at the focal point in-phase for constructive
interference. We have demonstrated a device capable of electrically tuning the focal length (of a focal
spot of sub-mm in diameter) from 5 to 12 mm, with the electrical tunability confirmed through droplet
ejection from liquid surface (that is at the focal plane), as the liquid level is varied. Meanwhile, this
thesis describes the modeling, design, fabrication and measurement of a focused ultrasonic transducer
with electrically controllability over the focal point location. Built on a 1.02 mm thick lead zirconate
titanate (PZT) substrate, the transducer consists of 6 pie-shape sectors of nickel deposited electrodes,
with each sector divided into 3 sub-regions along its radius (inner, middle and outer). Partial Fresnel
lenses made of 20μm-thick Parylene-sealed air-cavities are built on the top of electrode sub-regions,
which are designed to be offset along the sector radius to deliver an off-centered focal point position
for each sub-region. With the electrical addressability to each sub-region electrode, the transducer can
be configured to deliver focused ultrasound to different focal points on its focal plane. We have
fabricated a transducer capable of delivering multiple focal points over its focal plane through
actuating different sets of the electrodes and demonstrated its functionality by measuring the acoustic
pressure with a point hydrophone.
For micro-propeller, this thesis introduces a novel ultrasonic propeller with electrically
controllability over its propulsion direction. Built on a 1.02 mm thick nickel-coated lead zirconate
titanate (PZT) substrate, the propeller consists of 18 sectors of individually accessible Fresnel lens that
are composed of Parylene air-cavity-reflectors on top of the front-side nickel electrode. A backside
air-reflector is added to prevent any propulsion from the backside that may cancel the propulsion
from the front side. A fabricated propeller weighing 4.9 grams is measured to have (1) a maximum
perpendicular thrust of 13.8mN in water when driven by 80Vpp applied to all the sectors and (2) a
maximum lateral thrust of 2.1mN under 80V pp applied to a single sector.
1
Chapter 1 :
Introduction
The work presented in thesis consists of two separate topics in electrical engineering:
electromagnetic vibration energy harvester and focused ultrasonic transducer. In electromagnetic
vibration energy harvester topic, this thesis presents analytical model for permanent magnet (chapter
2) and study of magnetic spring that is used in the electromagnetic vibration energy harvester (chapter
3). In the focused ultrasonic transducer topic, this thesis presents work on controllability improvement
of the transducer (chapter 4 and chapter 5), as well as several devices that makes use of the core
mechanism of focused ultrasonic transducer, including acoustic tweezers (chapter 6, chapter 7 and
chapter 8) and immersive micro-propellers (chapter 9).
Motivation is firstly introduced in this chapter. Then general reviews of relates areas are
covered. Finally, an overview of each following chapters is outlined. Detailed theory discussion, device
design, fabrication process and experimental results are shown in following chapters.
1.1 Motivation
1.1.1 Magnetic spring based vibrational electromagnetic energy harvester
The advancement in consumer electronics in recent years has revolutionized our daily life, but
it also raises another problem for us: power. If you are not sitting next to a power outlet, or if you are
working in the field, how to maintain the electronics alive when the battery sign is red? The emergence
of Internet-of-Things (IoT), wearable and implanted health monitoring devices, location service, and
many other applications ask for communication between devices more frequently than ever, draining
the battery draining even faster. The need of a carryon renewable energy source is increasing, and thus
draws the attention of many researches on this topic.
2
Energy can be harvested from many ambient sources such as solar, vibration or thermal.
Different harvesting mechanism and techniques are behind each source respectively. The application
scenario (user specs) determines the source to use. Even when using same source, the mechanism may
be different for distinct application condition. Take the vibration energy as an example, when the
frequency and amplitude vary, we need to use different methods to collect and convert the energy.
Piezoelectrical harvester may be used for kHz or MHz vibration but electromagnetics harvester may
be used for sub-50Hz vibration.
There’re a wide range of application scenarios for the researchers to choose and work on with
respective harvesting approach. The work in this thesis focus on electromagnetics energy harvester
that scavenges power from vibrational energy. Under the following scenarios the user can potentially
benefit from the energy harvester developed in this thesis:
• Soldiers on the battlefield. Soldiers need to carry substantial amount of equipment when on the
battlefield, which are all powered by and relied on batteries. Less battery means less load on the
soldier, hence a better mobility. When the battery is drained, the soldiers may not have access to
power supply at all time due to the complex battlefield condition. A vibrational energy harvester
can be much useful in this scenario to keep the soldier enabled without losing combat
effectiveness, since the vibration from the soldier and environment is of great power source.
• Engineers in the field. Sharing certain level of similarity as the soldier, field engineers need to
power on their carry-on equipment outdoor. Even though the environmental condition could be
less harsh than the battlefield, a sustainable power supply is in need to enable their work un-
interrupted from any battery issue.
3
• Geologists, wild rescue responder or wrangler. They have more opportunity to travel to remote
locations beyond modern society, and power outlet. When they travel on foot, a vibrational
energy harvester can supply their electronics and equipment in the wild to continue their work.
• Hiker, mountaineer. Even for recreational purpose, a good power source could be helpful to
keep people away from unknown risks. When hikers are on the trail, they can power their GPS
out of the energy harvested from their walking. Keeping an communication tool powered on
could be life-saving if extreme weather hits or any emergency happens.
1.1.2 Focused ultrasonic transducer without phased array
Ultrasonic transducer is a powerful tool in medicine and other industry. Applications of
ultrasonic transducer can be found everywhere in daily life: non-invasive health screening with
ultrasonic imaging, nondestructive testing for construction and pipeline, or even fingerprint sensing
on the hand-held consumer electronics. In most of those applications the beamforming is done to
deliver focused ultrasound by using phased array. Higher intensity focused ultrasound has been used
as means of medical treatment, for cosmetic purpose, weight losing or potentially tumor treatment.
The phased array approach of ultrasound generation and beamforming makes use of many
small ultrasonic transducers, where each single element can be pulsed and controlled independently.
By varying the firing timing of those elements, a constructive interference pattern is set up that results
in radiating ultrasonic beam at a set angle, or focused at certain location away from the transducers,
depending on the timing. As a result, the control part of the phase array usually asks for a complex
design, cumbersome equipment and multiple channel high power input supplies.
The work in this thesis, on the other hand, explore the possibility of designing focused
ultrasonic transducer without phased array, thus minimizing the control part of the system, to provide
4
convenient use of focused ultrasonic transducer with focal point controllability and other focused
ultrasonic transducer based applications such acoustic tweezers and propeller.
1.2 Review on Vibration/Force Energy Harvesters
Efforts have been put into research in multiple disciplines in energy harvesting over the past
decades, not only to solve the growing environmental problems caused by greenhouse gas emission
from fossil fuels, but also to catch up with the development of energy scavenging smart and
distributive electronics that ranges from portable/wearable/implanted device to wireless IoT sensors
[1-5]. The advancement of modern electronics accompanies with the need of consuming power
anywhere and anytime, so a ubiquitous energy source is much preferred for energy harvesting.
Considering the energy form presented in daily life, mechanical energy is the most common and easy-
to-find one, in large, tiny or even unnoticeable forms, and can be accumulated from low energy density
environments. The omnipresence of mechanical energy in wind [6-10], waves [11-14], shaking from
machine [15-18], motion of animal [19-24] or even biological process [25-29] makes it a good candidate
in the renewable energy sources.
Electrostatic [14, 30-34], piezoelectric [5, 25, 27-29, 33, 35-37], triboelectric [1, 2, 6-8, 11, 12,
17, 19-21, 23, 24, 26, 38, 39], ferroelectret [40-45] and electromagnetic [33, 46-52] transductions are
most widely used mechanisms to scavenge mechanical energy. Electrostatic energy harvester typically
makes use of parallel-plate capacitor with a movable plate and has good compatibility with integrated
circuit (IC) fabrication process. However, the requirement of using pre-charged electret membrane or
external voltage bias adds the application complexity and the small output current limits its powering
capability. Piezoelectric energy harvester is typically built on a cantilever unimorph or bimorph with
piezo material and resonant structures to tune the frequency. High voltage can be generated by piezo
energy harvester, but limited output current and huge impedance matching are still challenging for
5
application. Triboelectric and ferroelectret nanogenerator have similar low output current capability
and loading matching issue. Compared to them, electromagnetic energy harvester can drive low
impedance load with high current benefit from the low internal impedance of the harvester.
1.2.1 Electrostatic Energy Harvester
Electrostatic energy harvester work on the capacitance charge of a variable capacitor under a
constant bias voltage. There are two categories of electrostatic energy harvester, based on the bias
voltage source: (1) electret-free energy harvesters, where the bias voltage is supplied by an external
power source, and (2) electret-based harvesters, where the bias voltage is provided by electret materials,
as shown in Figure 1.1. The electret-free electrostatic harvesters generate power by the relative
movement between two components with different potentials, often a movable mass and a set of
fixed electrodes. The different potential is commonly generated by two energy conversion schemes: a
charge-constrained energy conversion cycle, and a voltage-constrained energy conversion cycle [31].
In the charge-constrained scheme, the charge is kept constant by a switch and the voltage voltage-
contained scheme is vice versa. CMOS-compatible processes and high output voltage are two
outstanding advantages of the electrostatic energy harvester, which is beneficial for external power
circuit management [53].
Illustrated in Figure 1.1 is one of general schemes of the electrostatic energy harvester with
electret materials mainly contains a variable capacitor on the basis of out-of-the-plane gap closing [32].
The top plate forms a spring-mass resonant system by consisting of a proof mass suspending to outer
frame through four beams (spring structure). Both two parallel plates are fabricated on silicon
substrate with SiO2 insulation layer on the surfaces. Metal layers are deposited on each plate as the
electrodes of the capacitor. CYTOP polymer is coated on the bottom electrode as an electret material,
and it can also function as the adhesive layer in low temperature bonding. Bump stoppers are designed
6
on the proof mass to avoid the “pull-in” effect of electrostatic force when the proof mass moves close
to the bottom electrode at high vibration acceleration. When driven by an ambient vibration source,
the capacitance of the harvester changes as the gap distance between the two electrodes varies. Hence,
a current between the two electrodes is generated from the movement of induced charges by the pre-
charged electret. Tuning the overlapping area between two electrodes by the in-plane vibration of the
proof mass can also achieve the same goal for another scheme of electrostatic energy harvester [34,
54].

Figure 1.1 Schematic illustrations [32] of electrostatic energy harvester that bias voltage is provided by
electret materials.
1.2.2 Piezoelectric Energy Harvester
Piezoelectric Energy Harvesters generate power by stretching or compressing piezoelectric
materials, which have the unique feature of direct electromechanical coupling of converting
mechanical strain to electrical energy [55]. The piezoelectric materials play an important role in the
performance of this energy converting. Generally, piezoelectric materials can be categorized into two
groups [33]: first, ferroelectric ceramics or polymers, such as lead zirconate titanate (PZT), barium
titanate, microfiber composites (MFCs), polyvinylidene fluoride (PVDF), or lead magnesium
niobate/lead titanate; and, second, non-ferroelectric crystalline materials, such as zinc oxide (ZnO) or
7
aluminum nitride (AlN). For energy harvesting applications, PZTs and MFCs are currently the most
widely used piezoelectric materials since they exhibit a relatively high piezoelectric coefficient and have
a mature fabrication process. When going to micro/nano scale or for embedded applications, MEMS-
compatible lead-free piezoelectric thin films, such as AlN or ZnO, have a brighter future.
Cantilever-based devices are the most common form of the piezoelectric energy harvester [33].
The cantilever piezoelectric energy harvester usually consists of a piezoelectric cantilever with a proof
mass attached at the free end. When external vibration is applied, the piezoelectric cantilever is bent
by the inertial force of the proof mass, generating electrical potential across the piezoelectric material.
The harvester can be implemented in the configuration of a single piezoelectric material layer
(unimorph) or of two piezoelectric material layers (bimorph)[56]. In a unimorph configuration, a single
layer of piezoelectric material is sandwiched between two metal electrodes (Figure 1.2 (a)). The
external vibration bends the unimorph cantilever and introduces the displacement of the piezo
material. The voltage is then generated and picked up by the two electrodes. In a bimorph
configuration (Figure 1.2 (b)), the cantilever is formed with two piezoelectric layers between two
electrodes, with a structural non-piezo layer separating two piezo active layers. When the external
vibration deforms the cantilever, tension is generated on the top layer and compression is generated
on the bottom layer. The two piezoelectric layers can be poled in the same or the opposite directions,
and they can be connected in series or in parallel.
In a piezoelectric cantilever, the poled directions of the piezoelectric layers are usually
perpendicular to the planar direction of the piezoelectric layers because it is the most convenient way
to polarize piezoelectric sheets when they are fabricated. Piezoelectric cantilevers operating in the
above manner are said to be operating in the “d31 mode,” where “3” denotes the polarization direction
of the piezoelectric layer and “1” denotes the direction of the stress, which is primarily in the planar
8
direction of the cantilever. The d31 mode utilizes the d31 piezoelectric charge constant, the induced
polarization in the poled direction (direction “3”) of the piezoelectric per unit stress applied in
direction “1.” For a given piezoelectric material, d31 is always smaller than d33 because in the 31 mode
the stress is not applied along the polar axis of the piezoelectric material. Therefore, in order to utilize
a piezoelectric sheet in the “d33” mode for higher energy output, an interdigitated electrode design
can be used (Figure 1.2 (c)) [37]. In this electrode design, an array of narrow positive and negative
electrodes is placed alternately on the surface of a piezoelectric sheet when it is fabricated. During
poling treatment of the sheet, the interdigitated electrodes direct the electric field to apply laterally
within the sheet so that the sheet is polarized in the lateral direction instead of the conventional vertical
direction. This way, when the sheet is subjected to bending, the stress direction is parallel to the poled
direction of the piezoelectric, enabling the utilization of the primary piezoelectric charge constant, d33.

Figure 1.2 Various configurations of piezoelectric cantilevers [33, 37]: (a) unimorph; (b) bimorph; (c)
a piezoelectric cantilever with interdigitated electrodes; (d) a piezoelectric cantilever with proof mass
at its free end.
1.2.3 Triboelectric Energy Harvester
Figure 1.3 (a) demonstrates the schematics of the typical structure of a polymer based
triboelectric energy harvester, or triboelectric generator (TEG) [38]. Two different polymer sheets are
stacked in the TEG: one rectangular Kapton film and one flexible PET substrate, with one placed
onto the other. The two short edges of the device were sealed with ordinary adhesive tape and to
9
ensure an adequate contact between two polymer sheets. Both the top and bottom surfaces of the
structure were covered with a thin layer of Au alloy film from sputter coating. The metal films are
implemented for two main reasons: (1) producing equal but opposite sign mobile charges via the
electrostatic induction of the tribology generated potential at the interfacial region; (2) served as
common electrodes for directly connecting the device with an external circuit.
When the external force is applied to the device during the deformation process, two insulating
polymeric materials are touched and rubbed with each other. The surfaces of the two polymer films
are non-uniform with a different roughness of hundreds of nanometers. Mechanical compression
between the two layers of polymers leads to a relative sliding. As a result of small degree of friction,
electrostatic charges with opposite signs are generated and distributed on the two surfaces of the
polymer films due to the presence of the nanometer scale roughness, with the PET film positively
charged and Kapton film negatively charged, and forming an interface dipole layer, which is called
a triboelectric potential layer. Such a dipole layer forms an inner potential layer between the planar
metal electrodes. The induced charges will not be quickly conducted away or neutralized owing to the
insulative nature of the polymer films. To minimize the energy created by the triboelectric potential,
electrostatically induced free charges will flow across the external load between the two electrodes.
Simultaneously, mechanical compression between the two layers of polymers leads to a small
reduction in the interplanar distance (from D to d). Step by step mechanism of TEG is demonstrated
in Figure 1.3.

10

Figure 1.3 Schematic illustration of the structure and working principle of the triboelectric generator
[38]. (a) The structure of an integrated generator in bending and releasing process and related electrical
measurement tests. Photographic images of a flexible TEG and mechanical bending equipment. (b)
Proposed mechanism of a TEG (see text for details): charges are generated by fractioning two polymer
films, which results in the creation of a triboelectric potential layer at the interfacial region (indicated
by dashed lines);a mechanical compression results in a change in the distance between the two
electrodes (from D to d), thus, under the driving of the triboelectric potential, a change in system
capacitance leads to the flow of current in the external load which drives the flow of the free electrons
across the electrodes to minimize the total energy of the system.
1.2.4 Ferroelectret Energy Harvester
Ferroelectret Energy Harvester, or ferroelectret nano generator (FENG), makes use of
polypropylene ferroelectret to harvest mechanical energy from human motion. Polypropylene (PP) is
11
a type of commodity plastic [57, 58]. Once the PP film experiences stretching in two perpendicular
directions, the inorganic particles serve as stress concentrators or microcracks, allowing the film to be
filled with lens-shaped voids with diameters ranging from 1 to 100 μm. During this process, high
pressure (for example, 5 MPa) nitrogen or carbon dioxide gas is diffused into the PP film, so that the
internal pressure within the voids becomes equal to the external pressure. Next, the external gas
pressure is suddenly released, resulting in dramatically swell of those voids in PP film. By applying a
large electric field to the treated film, Paschen breakdown occurs inside the voids. The current within
the air gap transfers a sheet charge density across the air gap. During microplasma discharge, charges
separated by the ionization of the gas transportation under the charging field and light flashes can be
observed with the naked eye, forming a ‘microstorm’. After microplasma discharging, two thin layers
of silver (500 nm) were deposited on both top and bottom side of PP film (80 μm) by sputtering [40].
By using micro-plasma discharging in the fabricated foam structure in PP film, opposite
charges accumulate on the upper and lower surfaces of the artificial voids that in turn form numerous
highly oriented giant dipoles, as shown in Figure 1.4 (a). Once two layers of silver are sputtered on
both outer surfaces of PP film, the giant dipoles in the PP film induce charges of opposite polarity in
each silver film. Unlike piezoelectric material that have spontaneous electric polarization, micro-
discharging treatment turns the PP film from completely nonpolar materials into artificial intelligent
material that mimics both the microscopic molecular structure and macroscopic electromechanical
behavior of the piezoelectric material. Furthermore, in comparison with traditional piezoelectric
materials, FENG features with flexibility and internally charged cellular structures, making them highly
efficient in charge storage and more sensitive to mechanical stress. The direct electromechanical
interaction effect of FENG is illustrated in Figure 1.4 (b) and (c). When the FENG experiences
compression or expansion in the thickness direction, the internal dipole moments simultaneously
change in magnitude according to the applied pressure. Consequently, the change of dipole moments
12
drive the compensation electrons from the electrode with negative charge to the electrode with
positive charge, creating a potential between the two electrodes under open-circuit condition, or a
flow of charges under closed-circuit condition.

Figure 1.4 Energy conversion mechanisms of FENG [40]: (a) Charge distribution and giant dipoles of
FENG after micro plasma discharging, showing that the upper and lower surfaces of voids are
oppositely charged. (b) and (c) Direct electromechanical interaction effect. (b) Pressed by human hand
on the surface of FENG. (c) Pressure released and giant dipoles restore original sizes. (d) and (e)
Reverse electromechanical interaction effect. (d) Giant dipoles further expand as positive potential is
applied. (e) Giant dipoles shrink as negative potential is applied.
1.2.5 Electromagnetics Energy Harvester
For the electromagnetic energy harvester, the basic working principle is Faraday’s law of
electromagnetic induction. The induction electromotive force is generated in the circuit when the
magnetic flux passing through the closed loop changes. When the vibration presents in the ambient
environment, the magnet or coil is driven to vibrate against each other, making the magnetic flux
passing through the coil to vary with time. Induced voltage will then be generated in the coil. If a load
is hooked in the closed loop, the induced current will flow in the circuit.
13
Looking at the history of the research progress on the electromagnetic energy harvester, three
main directions of efforts are made to improve the output performance: (1) reducing the resonant
frequency, (2) broadening the frequency band and (3) improving the compatibility with the MEMS
system.
Due to a large number of low frequency vibrations in the environment, the harvesters with
low resonance frequency are easy to collect them and much desired. However, if natural frequency of
the harvester is very low (<10Hz) its volume is usually large. The effort to lower the resonant
frequency lies in the direction that renovates the suspension system [59-64].
Frequency mismatch can easily happen during the harvester operation. If the environmental
vibration frequency deviates a little from the designed frequency, which is most of the time the
resonance frequency of the device, the generated power decreases rapidly. Frequency mismatch is
inevitable since most of the real environmental vibrations are either varying or random in nature. Thus,
broadening the frequency band of vibration is another main approach to improve the harvester’s
efficiency. Several solutions have been proposed to solve this problem: (1) parameters of the harvester
are altered such as the mass or the stiffness, so that the resonance frequency is tuned to match the
environmental frequency [65-67]; (2) an array of harvester units can be integrated with various spring
or mass dimensions [68-71]; (3) harvesters can be designed with multiple vibration modes, while each
mode represents one resonant frequency [72-77]; (4) nonlinear energy harvesting that through
modulation of spring stiffness, nonlinearity can be introduced in electromagnetic vibration energy
harvesters [53, 78-80]; and (5) try to eliminate the spring structure in the device and the vibration is
completely free so that the output can be effectively generated in a range of frequency [81, 82].
Finally, if the harvester adopted micro machining and the manual bulk magnet assembly, it
inevitably leads to difficulties in precise control and adjustment of the mass dimension, distribution
14
and location during the micro assembly process. Therefore, this traditional method increases the cost
of assembled and is not conducive to large-scale production and manufacture. Researchers processed
the spring, coil and other vibration structures by MEMS technology, and then assembled the bulk
magnet together. In recent years, with the continuous development of magnet electroplating
technology, some researchers began to try to integrate magnets in the harvester using MEMS process,
which tuned the device fully into the sheet structure, reduces the volume of the device, greatly
improves the compatibility with MEMS system [52].
1.3 Review on Acoustic Tweezers
Acoustic tweezers are an emerging platform for the precise manipulation of bioparticles across
a broad size range. By using the interaction of sound waves with solids, liquids, and gases, acoustic
tweezers spatially and temporally manipulate matter. It is a versatile tool that can address many of the
limitations of other particle-manipulation techniques. Because acoustic waves with frequencies in the
kilohertz-to-megahertz range can be easily generated, acoustic tweezers can directly manipulate
particles across a length scale spanning more than five orders of magnitude (10−7 to 10−2 m). In
addition, the applied acoustic power (10−2–10 W/cm2) and frequencies (1 kHz to 500 MHz) are
similar to those used in ultrasonic imaging (2–18 MHz, less than 1 W/cm2), which has been safely
used in diagnostic applications.
Standing-wave tweezers, traveling-wave tweezers, and acoustic-streaming tweezers are the
three main types of acoustic tweezers. Both standing-wave and traveling-wave tweezers manipulate
particles or fluids directly via an applied acoustic radiation force, whereas acoustic-streaming tweezers
indirectly manipulate particles via acoustically induced fluid flows. The characteristics of each type of
acoustic tweezers, including pros, cons, and suitable applications, are listed in Table 1.1.

15
Table 1.1 Acoustic tweezers summary [83]
Type Subtype Pros Cons Application
Standing
wave
Surface
wave
[84]
Precision Low throughput; simple,
compact, inexpensive
devices and accessories
Limited acoustic-field
pattern
Nanoparticle
manipulation, cell
separation, cell
patterning, cell
concentration, 3D
translation and rotation
Bulk
wave
[85]
High throughput Limited precision; heat
generation; high power
Cell separation, sample
preparation, levitation of
cells and small organisms
Traveling
wave
Active
[86]
Flexibility (i.e.,
the ability to
rewrite
the acoustic field
in real time)
Typically, multiple
transducers and
multiplexed transmission
system are needed
Cell sorting, real-time
cell patterning for
bioprinting and tissue
engineering, 3D
translation and rotation
of cells and droplets
Passive
[87]
Simple, easily
fabricated
structures;
simple electronic
control scheme
Generation of only a few
acoustic-field patterns with
one structure; complex
simulation and calculations
needed
Cell patterning, levitation
of droplets, high-
resolution ultrasonic
imaging
Acoustic
streaming
Bubble
based
[88-90]
Selective
frequency
actuation
Unstable bubble size;
limited reproducibility
Fluid mixing and
pumping,
3D rotation of cells and
small organisms, neural
stimulation
Solid
structure
[91, 92]
Stability and
reproducibility;
ability to handle
highly viscous
fluids (for
example, blood
and sputum)
Limited vibration patterns Fluid mixing and
pumping,
3D rotation of cells and
small organisms

1.3.1 Standing-wave tweezers.
According to the source of acoustic wave generation, standing-wave acoustic tweezers can be
further divided in to BAWs and SAWs two subtype.
BAWs tweezers use piezoelectric transducers to convert an electrical signal into mechanical
waves. They are widely used for particle and cell manipulation by forming resonance patterns inside
16
channels [93], as shown in Figure 1.5 (a). Acoustic waves reflected from the reflection layer form
standing waves and establish a pressure distribution in the fluid. Through adjustment of the frequency
with respect to the dimensions of the channel geometry, the number of pressure nodes and antinodes
in the channel can be tailored [94]. The periodic distribution of pressure nodes produces acoustic
radiation forces that determine the trajectories and positions of particles inside these resonators.
SAWs, in contrast, are commonly generated by interdigitated transducers (IDTs) patterned on
a piezoelectric surface [95]. 1D and 2D interference patterns can be achieved by using sets of two and
four IDTs, respectively [84, 95] (Figure 1.5 (b)). Suspended particles in a standing SAW field move to
pressure nodes or antinodes according to their physical properties [96]. In addition to 2D in-plane
manipulation, standing SAWs are used to achieve 3D manipulation by exploiting the modulation of
acoustic parameters (for example, phase shifts and amplitude modulation), thus enabling the trapping
position to be changed in real time [97]. Owing to their compact size, SAW-based tweezers can be
conveniently integrated with microfluidic systems enabling versatile lab-on-a-chip tools [84].
Standing-wave tweezers are mainly used for separating and patterning different types of
particles and cells. Whereas BAW-based standing-wave tweezers have the advantage of handling
higher volumes of fluids in a shorter time, as is desirable for blood processing in transfusion
applications, SAW-based tweezers have higher precision, owing to the higher frequencies used [98],
thus rendering them more suitable for nanoparticle manipulation and tissue-engineering applications.
1.3.2 Travelling-wave tweezers
Travelling-wave tweezers, which consist of two subgroups, active and passive methods, can
form arbitrary pressure nodes in 3D space by controlling the phase patterns of the acoustic waves.
Active traveling-wave tweezers make use of a single acoustic-transducer element or an array of
elements. By selectively controlling each individual element in an array, active methods can produce
17
complex acoustic beams that result in dynamic manipulation capabilities (Figure 1.5 (c)). Passive
methods use structures with features that are smaller than the acoustic wavelength, such as acoustic
metamaterials and photonic crystals, to manipulate the acoustic waves. Passive methods are an
inexpensive approach for modulating acoustic waves and forming complex beam patterns (Figure 1.5
(d)). SAW-based traveling-wave tweezers featuring a single IDT are mainly used for on-chip cell and
particle manipulation in sorting applications. Compared with standing-wave tweezers, traveling-wave
tweezers can more easily be modulated in real time and are better suited for applications requiring
arbitrary patterning or single object handling (e.g., cell printing or single-cell analysis).
1.3.3 Acoustic-streaming tweezers
The steady flow generated by the absorption of acoustic energy by the liquid can also be used
to indirectly manipulate particles in a solution [99, 100]. This flow, termed acoustic streaming, is most
generated via oscillating microbubbles or oscillating solid structures. Oscillating microbubbles can
produce sufficient acoustic radiation forces to trap cells, particles, or small organisms on the bubble
surface [90] (e.g., the magnitude of the acoustic radiation forces to move red blood cells is
approximately 2 pN [101]) (Figure 1.5 (e)). Streaming vortices created by oscillating bubbles can also
rotate particles at a fixed position [88] and enable fluidic actuation by enhancing mass transport across
laminar flows in confined microchannels [90]. Similarly, to microbubbles, acoustically driven sharp-
edge structures or thin membranes oscillate in a liquid (Figure 1.5 (f)), thus resulting in acoustic
streaming, owing to viscous attenuation. These streaming flows generate regions of recirculation or
pressure gradients that can be used in particle manipulation, fluid mixing, and pumping applications
[91, 92]. Acoustic-streaming tweezers tend to be simple devices that are easy to operate; however—in
contrast to traveling-wave tweezers, which can be used in liquids and in air—acoustic-streaming
tweezers can operate only in liquids. In addition, acoustic-streaming tweezers offer a lower degree of
spatial resolution, because microbubble and microstructure-based phenomena are nonlinear. These
18
tweezers are primarily used for fluid handling [102], such as pumping or mixing of highly viscous
fluids, or rotational manipulation applications.

Figure 1.5 Illustrations of various acoustic-tweezer technologies [83]. (a) A typical BAW-based
standing-wave tweezer device. The number of pressure nodes and antinodes inside the channel is
determined by adjusting the applied acoustic wave frequency with respect to the distance between the
matching layer and the reflection layer; (b) SAW-based standing-wave tweezers use IDTs to generate
mechanical waves. Four sets of IDTs are used to generate a 2D pressure node field that traps and
patterns particles; (c) Active traveling-wave tweezers with a transducer array to manipulate particles.
By controlling the relative phase of the acoustic wave from each transducer, flexible pressure nodes
can be formed to achieve dynamic patterning; (d) Passive traveling-wave tweezers with a single
transducer to achieve complex acoustic distributions and control over particles; (e) Acoustic-streaming
tweezers use oscillating microbubbles inside a microfluidic channel to generate out-of-plane acoustic
microstreaming flows; (f) Solid-structure-based acoustic-streaming tweezers generate a directional
fluid flow under acoustic excitation.
1.4 Overview of Chapters
In chapter 1, motivation for the work is introduced, and a high-level background of the thesis
is presented. Key concepts are introduced, and the overall scope is presented with reference to existing
publications in the field.
Chapter 2 introduces the theoretic work on modeling the permanent magnets, which are used
in magnetic spring in vibrational energy harvester to lower the resonant frequency. The analytic model
19
paves the road for further discussion on the performance of the magnetic spring and make it possible
to do optimization work.
Chapter 3 makes use of the analytic model developed in Chapter 2 to analyze the magnetic
spring in lossless system and lossy system. Magnetic spring’s dependencies on various conditions are
studied. Those dependencies help to optimize the design of low frequency electromagnetic vibrational
energy harvester.
Chapter 4 shifts the topic from energy harvester to acoustic transducer. In this chapter a
focused ultrasonic transducer with controllability over its focal length is introduced. The design,
modeling, fabrication, and measurement are discussed.
Chapter 5 introduce another focused ultrasonic transducer design with controllability over its
focal location. Different from the device introduced in previous chapter that the controllability is on
the focal length, the transducer in this chapter has control on the focal point location on its focal plane.
Similarly, the design, modeling, fabrication, and measurement are discussed.
Chapter 6 highlights an immersive acoustic tweezers. Based on the multi-foci ultrasonic
transducer, this device is capable of trapping sub-millimeter size polyethylene microspheres. The
design, fabrication and experimental results are discussed in this chapter.
Chapter 7 provides stronger acoustic tweezers design that is capable of trapping larger zebra
fish embryos. Improved design is introduced, and exciting trapping results are presented, with detail
on design and fabrication.
Chapter 8 presents work that extends the functionality of acoustic tweezers from trapping to
rotational control. Mechanism is discussed along with fabrication and experimental results.
20
Chapter 9 describes work on immersive micro-propeller as another application of focused
ultrasonic transducer. Device design, fabrication and experimental results are presented.
Lastly in chapter 10, the conclusions of this work are discussed, and future research directions
are proposed.

21
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Equation Chapter 2 Section 1
34
Chapter 2 :
Analytical Model Based on Surface Charge for Magnet
2.1 Background
Vibration-energy harvester [46-51, 103-111] typically relies on resonant characteristics of its
mass-spring system, which needs to have very low resonant frequencies to harvest energy from slowly
moving objects such as human motion. For example, harvesting vibration energy associated with
human’s waking motion would provide a way to power wearable devices without battery or with less
dependence on battery [104, 111]. But such vibration energy is concentrated at a very low frequency
of 2 – 4 Hz [112]. For an elastic spring, such a low resonant frequency means a very low spring
constant and/or a very large load mass, which is very difficult in a miniature or micron-sized device.
Also, the structural deformation in an elastic spring often leads to aging and degradation of structural
integrity.
Magnetic spring, on the other hand, offers a very low resonant frequency without any major
concern over structural degradation, and has been used for electromagnetic vibration-energy
harvesters [106-108, 112]. However, the dynamic behavior of magnetic spring has not been well
studied due to lack of an accurate analytical model of a magnet. In most of the reported energy
harvesters with magnetic spring, the magnetic force ()
M
Fx in the spring’s restoring force is either
modeled as the force between a pair of point magnetic charges Q m1 and Q m2 [106-108, 113]

0 1 2
2
( ) ,
4
mm
M
QQ
Fx
x


= (2.1)
or fitted to a summation of low order power series [110, 111, 113] as

3
( ) ,
M
F x kx x  =+ (2.2)
35
where
0
 and x are air permeability and the separation distance between two magnets that form the
magnetic spring, respectively, while k and  are fitting parameters. However, these two methods have
limitations: in the case of Equation (2.1), the non-linear behavior of the spring is poorly estimated
when the distance between the two magnets becomes short. In the case of Equation (2.2), the fitting
parameters are magnet-specific, making the parametric sweeping for optimization and analysis difficult.
Thus, an accurate and simple analytical modeling of magnetic spring is needed.
This chapter presents a new and accurate analytical model (based on surface magnetic charge)
for cuboid magnet. The validation experiments and simulations demonstrate its correctness and
accuracy on estimating the force between permanent magnets used for a magnetic spring. Comparison
with Gilbert model (based on point-charge pair), the Ampère model (based on dipole pair) and the
fitted series method shows the DCS model has better accuracy, with a lowest RMSD.
2.2 Theory and Modeling
A typical magnetic spring consists of two well-shaped permanent magnets, which are aligned
along the central line, in a housing that confines the motion of the movable magnets, as shown in
Figure 2.1 (a) and (b). A pair of coupled magnetic springs (Figure 2.1 (c)) can also be used to form a
vertical magnetic spring. Cuboid and cylinder magnet are commonly used due to their ease in
fabrication and incorporation into a housing structure. The magnetization of the permanent magnet
is perpendicular to the surface, and the magnets are set with same pole facing each other to make the
magnetic force repulsive. As the magnetic force between two magnets increases dramatically when
magnets get closer, it’s easier to gain stable equilibrium state from repulsive magnetic force than from
attractive force.
36
To obtain an equilibrium position for the magnetic spring, the restoring force should have the
sign opposite to the magnetic force of the magnetic spring. Forces such as electrostatic force,
gravitational force, inertia force, other mechanical/structural force or even another magnetic force
can act as the restoring force.

Figure 2.1 Laterally configured single magnetic springs with (a) cuboid magnets and (b) disk magnets.
(c) A vertical magnetic spring with two coupled magnetic springs composed of two anchored magnets
and one moveable magnet. Equivalent springs are modeled along the central axis between the two
magnets forming the spring.
2.2.1 Model of the Permeant Magnet
The magnetization of the magnet depends on the magnetizing field applied to it during the
magnet fabrication. For axial-magnetized cuboid magnet and cylinder magnet, the magnetization of
the whole magnet should be approximately constant, since the field exerted on it doesn’t have
prominent spatial variation. Since there’s no current density in the permanent magnet, the magnetic
field intensity can be conveniently represented in terms of the scalar magnetic potential  as
. = −   H (2.3)
37
The scalar magnetic potential satisfies Poisson’s equation under Ampere·meter convention

2
m
   = − (2.4)
Considering the continuous condition inside permanent magnet body and around the
boundary, the magnetic charge density
m
 and the magnetic surface charge density
sm
 are given as

m
 =−H (2.5)
( ).
ab
sm
 − − = n H H (2.6)
where
a
H and
b
H are the magnetic fields for each side of the interface and n is the surface normal
vector.
For a cuboid magnet illustrated in Figure 2.2 (a), if the block permanent magnet is uniformly
magnetized along the thickness, the magnetization inside the magnet will be constant, and the body
density  will be zero (Figure 2.2 (b)). According to Equation (2.6), the surface charge densities are
given

sm c
H  = (2.7)
where
c
H is the coercive force and could be easily obtained from magnet datasheet.
Thus, the magnet can be modeled as a pair of two magnetically charged planes of a distance
c between the two parallel planes of size a by b , whose surface densities are given by Equation (2.7),
which is the basis for the dual-charged-surface (DCS) model for axis-magnetized permanent magnets.
38

Figure 2.2 The dual-charged-surfaces (DCS) model for (a) a vertically magnetized block magnet: (b)
zero net magnetic charge and (c) surface magnetic charge being proportional to the body
magnetization.
As an equivalent of the electric Coulomb law, magnetic Coulomb law describes the force
between two point magnetic charges (Q 1 and Q 2) being proportional to their charge magnitudes and
inversely proportional to the square of the distance (r) between the charges as follows:

0 12
3
||
.
4
QQ
Fr
r


= (2.8)
The magnetic field from one magnetic charge is:

1
3
.
4 | |
Q
H r
r 
= (2.9)

Figure 2.3 Magnetic field established by uniformly charged rectangular plate P1, on reference plane.
39
Now, for a finite rectangle plane of size 2a x 2b with magnetic charge density
1
 , centered at
0 z = plane as shown in Figure 2.3. The magnetic field () Hr in space is the superposition of the
magnetic fields generated by infinitesimally small charges dxdy  on the plane, which could be written
as

1
1 2 2 2
11
'' 1
| ( , , ) | .
4 ( )
,
( ') '
PP
dx
x y
dy
H x y z
yz
dH
x


 −
=
++
=
−
   
(2.10)
In the magnetic spring described in Figure 2.1, magnets are aligned coaxially with the same
poles facing against each other. The overall lateral force which is perpendicular to the polarity axis will
be close to zero due to the symmetricity at a balanced position. Thus, we are interested in calculating
the z component of the magnetic field which is the dominant factor for. From the geometry
relationship in Figure 2.3, we have
1
1 2 2 2
2 2 2
1
1
1 2 2 2
2 2 2
1
( , , , )
( ')
( ')
.
(,
''
4
, , )
(
(
')
(
'
'
1'
')
( ')
'' 1
4 ( )
( ') )
P
z
P
y
H
dx dy yy
xx
xx
d
x y z
y y z
y y z
H x y z
x
yy
x dy z
xx
x
z
y y z







=

+
+
−
− −
−
+
+−



=

+ − +
− −
−
++



(2.11)
To simplify the lengthy expression of
y
H and
z
H coming from the double integral of
Equation (2.11), two auxiliary functions
1
g and
2
g are introduced here. Let

1
2 2 2
n ( , , ) arcta g
yx
z x y z
x y z



+
=
+

(2.12)
and

2 2 2
2
( , , ) ln[ )]. g x y z x x yz = + + + (2.13)
Then the magnetic field component ( , , )
y
H x y z and ( , , )
z
H x y z can be expressed as
40

1
22
22
[ ( , , ) ( , , )
4
( , , ) ( , , )]
y
H g x a y b z g x a y b z
g x a y b z g x a y b z


= + − − + +
+ − + − − −
(2.14)
and

1
11
11
[ ( , , ) ( , , )
4
( , , ) ( , , )].
z
H g a x b y z g a x b y z
g a x b y z g a x b y z


= + + + + −
+ − + + − −
(2.15)
Both Equation (2.14) and Equation (2.15)can be checked by Gauss’ Law applied at an
infinitely large charged plane case. When Gauss’ Law is applied at the vicinity of a horizontally placed
infinitely large charged plane, the equations show that the perpendicular field (H z) is a constant while
the lateral field (H y) is zero. A quick validation on this could be obtained by extending the dimension
to infinity, namely a → +  and b → +  , in which case the Equation (2.12) yields
1,
( , , )
2
ab
g x y z

→ +
= , and the summation of auxiliary function (2.14) would be canceled to yield 0.
As a result, Equation (2.15) would indicate a constant magnetic field
1
( , , )
2
z
H x y z

= , while
( , , ) 0
y
H x y z = is verified by Gauss’ Law
2.2.2 Magnetic Force
The equivalent model of a vertically configured magnetic spring is shown in Figure 2.4. Cuboid
magnets are represented by reversely magnetically charged parallel plates. The magnetic forces
between two magnets are abstracted as composition of interactions among four charged plates. As
demonstrated in Figure 2.4 (b), four plate-pairs interactions contribute to the resultant force, in which
two are attractive force (between P1-P3 and P2-P4) and two are repulsive force (between P2-P3 and
P1-P4).
41
The force between two charged plates can be determined by integrating the infinitesimal force
on the target plate while treating the other plate merely as field source. For example, for the P1-P3
pair in Figure 2.4 with the magnetic charge density of P1 and P3 being
1

and
3
 , respectively, if we
take P1 as the field source, the force along z-axis on P3 is

3
1 0 3 1
01
3
3
( , , ) , , ,
( , , , ),
()
zz
P
ab
z
ab
F d dS H x y d
dx dyH x y d
    
  
+
−−
=
=


(2.16)
where d is the distance between two plates; dS is an infinitesimal area on P3; and
z
H comes from
Equation (2.15)

Figure 2.4 Schematic (left) and the DCS model (right) of a vertically configured magnetic spring with
mass load: in the model, the two magnets are represented by four magnetically charged plates (P1 -
P4), so that the resultant force between the two magnets is the combination of the repulsive forces
(between P1 and P4 as well as between P2 and P3) and the attractive forces (between P1 andP3 as
well as between P2 and P4).
For P1 and P3 having the same dimension 2a x 2b, due to the symmetricity of ( , , ) g x y z , the
integral on a symmetric interval gives same value for all four functions in Equation (2.14). Equation
42
(2.16) can be rewritten as
22
0
1 3 1 3
00
( , , ) ( , , )
ab
z
F d dx dy g x y z

   

=  

. By properly applying
trigonometric substitutions and partial integration, the final expression of
z
F is

0
1 1 2 1 3 2 3
( , , ) [ ( ) ( ) ( )],
z
F d f d f d f d

   

=  + + (2.17)
where
1
f ,
2
f and
3
f are as follows

2 2 2
1
2 2 2 2 2 2 2
3
2
( ) arctan[ / (
1
( ) ( ) [ln( ) ln( ) ln( )].
2
( ) l
]
) ( n
) f h ab ab a b d
f d a b d a b d a d b d
f h a b
d
dd

=  + +


= +  + + − + − +


=+


 
(2.18)
In general, Equation (2.17) describes the magnetic force between two parallel, uniformly
charged planes of the same size. Equation for a more complex geometry case can be obtained from
Equation (2.16). According to the sign of
1
 and
3
 , the force is attractive when the two planes have
opposite charges and repulsive when those have same charges.
The net magnetic force between the two magnets is the sum of the forces due to the four pairs
of the surface charge planes, and is

, 1 4 , 2 3 , 1 3 , 2 4
.
I z P P z P P z P P z P P
F F F F F
− − − −
= + + + (2.19)
Since P1 and P2 (or P3 and P4) are two poles of a same magnet, their surface charge densities
have only sign difference. With
B
M and
T
M being the magnetization of the bottom and top magnet,
the surface charge densities are
0 BB
M  =− and
0 TT
M  =− . By combining Equations (2.17) and
Equation (2.19), the magnetic force
I
F is
( ) ( ) ( ) ( ) ( ), , , , , 2 , , , ,
I z B T z B T z B T z B T
l l c F l F F F F l c l c         + =− − − + + + ++ − (2.20)
43
where l and c are the distance between two magnets and the thickness of each magnet (which is also
the distance between two equivalent charge plates), as shown in Figure 2.4, respectively.
2.3 Model Validation and Discussion
In this section, the model is validated with experimental measurement and FEM simulation in
COMSOL Multiphysics of the repelling magnetic force between permanent magnets. Also, the
accuracy of the model is compared to other widely used models.
2.3.1 Validation with Experimental and Simulation Data
Experimental data of magnetic force vs separation distance are collected in a setup similar as
shown in Figure 2.4. Two magnets are aligned in a housing co-axially with the same pole facing each
other. The lower magnet is anchored with the housing while the top magnet is set to move freely. The
load on the top magnet is adjustable and an external force is applied on the top magnet. As the load
or external force changes, the top magnet moves in response to the load or external force to change
the separation distance between the two magnets. Thus, the static balance is established among the
gravity, magnetic force and externally applied force. And the repulsive magnetic force at different
separation distance is obtained from the reading of external force
ext
f and gravity
load
Mg :
( ) .
M load ext
F x M g f =− (2.21)
Four different rare earth neodymium magnets (
44
Table 2.1) are used in the experiments that include the measurement of B-H curves of the
magnets. The top movable and bottom anchored magnets are of same type and size except for the
polarity arranged.

45
Table 2.1 Grade, coercive force and geometry of rare earth neodymium magnets used in model
validation shown in Figure 2.6 and Figure 2.7. The top movable and bottom anchored magnets are of
same type and size except for the polarity arranged.
Grade H c (MA/m) Length (mm) Width (mm) Height (mm)
Magnet 1 N52 1.15 25.4 25.4 25.4
Magnet 2 N52 1.15 25.4 12.7 6.35
Magnet 3 N52 1.15 25.4 12.7 12.7
Magnet 4 N52 1.15 12.7 12.7 25.4

Three-dimensional stationary magnetic field FEM simulations are carried out in COMSOL
Multiphysics for each pair (or magnetic spring) of the magnets in
46
Table 2.1, as the separation distance between the two magnets is varied. The measured B-H
curves of cuboid magnets are used as the magnets’ material properties for the simulations. From the
simulation results, the magnetic scalar potential and magnetic flux density are calculated. One
exemplary cross-sectional plane along the center of the magnet pair is plotted in Figure 2.5. Then, the
magnetic force exerted on a magnet is calculated by integrating the simulated magnetic flux density
over the magnet, for a particular separation distance.

Figure 2.5 FEM simulation results for magnetic flux density (arrows) and magnetic scalar potential
(color bar). The magnetic force is numerically calculated from the simulation results and shown in
Figure 2.6 and Figure 2.7.
The analytical solution from the DCS model is compared with the experimentally measured
data and simulation results. Root-mean-square deviation (RMSD) is used as a measure of the
differences between the values predicted by a model (or simulation) and experimentally observed
values. The RMSD, the quadratic mean of the differences between predicted magnetic forces and
observed values, is defined as

( )
,,
2
(
,
( ) )
max
min
M Model M Measured
x
xX
xX
ma min
F x F x
RMSD
XX
=
=
−
=
−

(2.22)
47

Figure 2.6 Experimentally-measured, FEM-simulated, and analytically-calculated (based on the DCS
model) magnetic forces vs separation distance in a magnetic spring for four different pairs of N52
grade Neodymium magnets (listed in
48
Table 2.1). The analytical solution from the DCS model compares well with the measured and FEM
simulation results.
Table 2.2 RMSD of FEM simulation and DCS model compared to experimentally measured value
over separation distance from 0mm to 50.8mm.
Pair
RMSD ( 𝑵 / √ 𝒎𝒎 )
FEM Simulation DCS Model
Magnet 1 – Magnet 1 8.49 15.23
Magnet 2 – Magnet 2 14.66 2.75
Magnet 3 – Magnet 3 11.30 9.92
Magnet 4 – Magnet 4 2.47 2.59

2.3.2 Comparison to Existing Models
Several widely used magnet models for magnetic spring are the Gilbert model, the Ampere
model and the power series with fitting parameters. The Gilbert model assumes that the magnetic
intensity is concentrated at the center of the magnet as a magnetic monopole
m
Q
, and the force
between two magnets is calculated with Equation (2.1) with
C m
Q H A =
where
C
H
and A are the
coercive force and pole surface area, respectively. The Ampere model, however, assumes the permeant
magnet as a dipole
m
p Q d =
with d being the distance between two pole surfaces, and the magnetic
force as a function of the separation distance x is calculated by

0
12 2 2 2 2
1 2 1 2
1 1 1 1
( ) .
4 ( ) ( ) ( )
M m m
F x Q Q
x x d d x d x d



= + − −

+ + + +

(2.23)
The major issue with the point charge model and the dipole model is that as two magnets gets
close to each other (i.e., as x approaches zero), the force approaches infinity, causing serious inaccuracy
in a very important region when the magnets are configured as a magnetic spring.
Other than the analytical Equations (2.1) and Equation (2.23), one can use a power series with
fitting parameters, such as the third order polynomial below
49

3
0
( ) .
n
n
Mn
n
F x a x
=
=
=

(2.24)
Table 2.3 shows the third order polynomial curve fitting for the experimentally measured data
for the four pairs of the magnets in
50
Table 2.1. The polynomial fitting works acceptably for a small range of the separation distance
but may be grossly off when the separation distance varies over a wide range.
Table 2.3 The 3
rd
order polynomial curve fitting for the experimentally measured force (in N) vs
separation distance (in mm).
Pair
3
a
2
a
1
a
0
a
2
R
Magnet 1 – Magnet 1 -0.0120 1.1428 -34.281 360.19 0.9744
Magnet 2 – Magnet 2 -0.0041 0.3697 -9.7161 75.714 0.9164
Magnet 3 – Magnet 3 -0.0063 0.5729 -15.690 133.79 0.9443
Magnet 4 – Magnet 4 -0.0046 0.4182 -11.224 91.57 0.9323

The forces calculated with the DCS model, the point charge model, the dipole model and the
3
rd
order polynomial curve fitting are plotted along with the experimentally measured forces in Figure
2.7. The RMSDs of the three conventional analytical models are shown in Table 2.4 to be much worse
than the RMSDs of the DCS model shown in Table 2.3.
51

Figure 2.7 Comparison among DCS model, point charge model, dipole model and 3
rd
order
polynomial curve fitting with experimentally measured data for four magnet pairs. The magnets detail
can be found in
52
Table 2.1 and curve fitting coefficients are shown in Table 2.3.
Table 2.4 RMSDs of the point charge model, the dipole model, the 3
rd
order polynomial curve fitting
over the separation distance from 1.27 to 50.8mm.
Pair
RMSD ( 𝑵 / √ 𝒎𝒎 )
Point charge Dipole 3
rd
poly fitting
Magnet 1 – Magnet 1 47341.0 47056.9 209.77
Magnet 2 – Magnet 2 11845.9 11070.2 51.39
Magnet 3 – Magnet 3 11820.8 11573.3 86.79
Magnet 4 – Magnet 4 2932.7 2915.0 60.73
2.3.3 Effective Spring Constant
According to the Earnshaw's theorem [114] on magnetic levitation, a movable magnet cannot
maintain a stable stationary equilibrium state solely by magnetostatic interaction with a fixed or
anchored magnet. Thus, a magnetic spring formed with two magnets (one movable and the other non-
movable) needs a mechanical fixture to make the movable magnet travel co-axially with the non-
movable, anchored magnet. In case of a magnetic spring with two magnets arranged vertically with
the bottom one fixed to a housing and the top one levitated (and movable), gravity on the movable
magnet works as the force to bring two magnets together. In this configuration, the restoring force is
a superposition of the repelling force (between the two magnets) and the gravity on the levitated
magnet, if damping due to friction and air viscosity is negligible. In the equilibrium, the magnetic force
equals to the gravity of the levitated magnet (plus any mass load on it, if any).
For an elastic spring which follows Hooke’s Law, the restoring force comes from the elastic
spring itself, and has opposite signs at two sides of the equilibrium position. However, the magnetic
force is unidirectional, and cannot act as a restoring force without a secondary force. In a vertical
magnetic spring, the restoring force F(x) is the resultant force of the magnetic repelling force F m(x)
and the gravity

( ) ( ) ,
M
F x F x mg =−
(2.25)
53
where m and g are proof mass and gravitational acceleration constant, respectively. By setting the
restoring force to be zero (i.e.,
0
( ) 0 Fx =
), the equilibrium position
0
x
can be determined from
Equation (2.25). When the vibration amplitude is small around
0
x
, the magnetic spring’s resonant
frequency can be estimated to be
0
0
|
1
2
xx
k
f
m 
=
= . The calculated restoring forces are plotted in Figure
2.8 for various magnets and masses.
Since () Fx varies non-linearly with respect tox , the effective spring constant ( ) / k dF x dx =
is dependent on the vibration amplitude. The calculated effective spring constants are shown in Figure
2.9 for a magnetic spring composed of two cuboid N52 grade neodymium magnets with side length
of 25.4mm as a function of traveling location and proof mass (i.e., the mass of one of the magnets).
As the proof mass increases, the spring constant becomes greater. The non-linearity of the spring
constant leads to asymmetrical vibration of the magnetic spring in time domain and broadens the
spectrum of the motion of the proof mass.

54
Figure 2.8 Calculated restoring forces of the vertically configured magnetic springs vs separation
distance between the two magnets. The two magnets used in a magnet spring are of same geometry
and type (
55
Table 2.1), and the proof mass attached to the movable magnet is varied between 300 g and 500 g.

Figure 2.9 Calculated effective spring constant vs vibration amplitude in vertical direction z (where
0 z = is the equilibrium position), as a function of the proof mass attached on the movable magnet.
2.4 Summary
This chapter presents a new and accurate analytical model for magnet which is very useful for
calculating the static and dynamic force between permanent magnets (used in a magnetic spring). A
single magnet is modeled as a pair of double-charged-surfaces (DCS), and the magnetic force is
calculated based on the interaction between two DCSs, as a function of geometry parameters and
magnetizations of two permanent magnets. The DCS model, for the first time as an analytical model,
provides accurate estimate on the behavior of a magnet spring when the separation distance between
two magnets approaches zero, and will be very valuable for micro-scale magnetic springs. The model
is validated with experimental and simulation data.
56
This analytical model for magnets leads to easier and simpler design and optimization of a
magnetic spring than FEM based approach. In addition, the non-linear vibration of a magnet spring
can easily be investigated with the model.
57
2.5 References
[46] Y. Wang, Q. Zhang, L. Zhao, A. Shkel, Y. Tang, and E. S. Kim, "Stackable dual-layer coil
based on wafer-level transfer technique for electromagnetic energy harvester." pp. 1264-1267.
[47] Y. Wang, Q. Zhang, L. Zhao, and E. S. Kim, "Non-resonant, broad-band vibration-energy
harvester based on self-assembled liquid bearing." pp. 614-617.
[48] Y. Wang, Q. Zhang, L. Zhao, and E. S. Kim, “Non-resonant electromagnetic broad-band
vibration-energy harvester based on self-assembled ferrofluid liquid bearing,” Journal of
Microelectromechanical Systems, vol. 26, no. 4, pp. 809-819, 2017.
[49] Q. Zhang, Y. Wang, L. Zhao, and E. S. Kim, "Microfabricated thousand-turn coils for mW
power generation from sub-mm vibrations." pp. 606-609.
[50] Q. Zhang, Y. Wang, L. Zhao, and E. S. Kim, “Integration of microfabricated low resistance
and thousand-turn coils for vibration energy harvesting,” Journal of Micromechanics and
Microengineering, vol. 26, no. 2, pp. 025019, 2016.
[51] Y. Wang, Q. Zhang, L. Zhao, and E. S. Kim, "Ferrofluid liquid spring for vibration energy
harvesting." pp. 122-125.
[103] Y. Wang, L. Zhao, A. Shkel, Y. Tang, and E. Kim, "Vibration energy harvester based on
floating magnet for generating power from human movement." pp. 404-407.
[104] Y. Wang, Q. Zhang, L. Zhao, Y. Tang, A. Shkel, and E. Kim, “Vibration energy harvester with
low resonant frequency based on flexible coil and liquid spring,” Applied Physics Letters, vol.
109, no. 20, pp. 203901, 2016.
[105] Q. Zhang, Y. Wang, and E. S. Kim, “Electromagnetic energy harvester with flexible coils and
magnetic spring for 1–10 Hz resonance,” Journal of Microelectromechanical Systems, vol. 24, no. 4,
pp. 1193-1206, 2015.
58
[106] Q. Zhang, Y. Wang, and E. S. Kim, “Power generation from human body motion through
magnet and coil arrays with magnetic spring,” Journal of Applied Physics, vol. 115, no. 6, pp.
064908, 2014.
[107] C. Saha, T. O’donnell, N. Wang, and P. McCloskey, “Electromagnetic generator for harvesting
energy from human motion,” Sensors and Actuators A: Physical, vol. 147, no. 1, pp. 248-253,
2008.
[108] M. Salauddin, M. Halim, and J. Park, “A magnetic-spring-based, low-frequency-vibration
energy harvester comprising a dual Halbach array,” Smart Materials and Structures, vol. 25, no. 9,
pp. 095017, 2016.
[109] M. Masoumi, and Y. Wang, “Repulsive magnetic levitation-based ocean wave energy harvester
with variable resonance: Modeling, simulation and experiment,” Journal of Sound and Vibration,
vol. 381, pp. 192-205, 2016.
[110] B. Mann, and N. Sims, “Energy harvesting from the nonlinear oscillations of magnetic
levitation,” Journal of sound and vibration, vol. 319, no. 1-2, pp. 515-530, 2009.
[111] W. Wang, J. Cao, N. Zhang, J. Lin, and W.-H. Liao, “Magnetic-spring based energy harvesting
from human motions: Design, modeling and experiments,” Energy Conversion and Management,
vol. 132, pp. 189-197, 2017.
[112] J. E. Bertram, and A. Ruina, “Multiple walking speed–frequency relations are predicted by
constrained optimization,” Journal of theoretical Biology, vol. 209, no. 4, pp. 445-453, 2001.
[113] S. Mukhopadhyay, J. Donaldson, G. Sengupta, S. Yamada, C. Chakraborty, and D. Kacprzak,
“Fabrication of a repulsive-type magnetic bearing using a novel arrangement of permanent
magnets for vertical-rotor suspension,” IEEE transactions on magnetics, vol. 39, no. 5, pp. 3220-
3222, 2003.
59
[114] W. Jones, “Earnshaw's theorem and the stability of matter,” European Journal of Physics, vol. 1,
no. 2, pp. 85, 1980.
Equation Chapter (Next) Section 1
60
Chapter 3 :
Magnetic Spring for Electromagnetic Vibration Energy Harvesters
3.1 Background
Wearable devices [22, 41] are typically powered by batteries, which need to be replaced or
recharged, interrupting their operation. Harvesting vibration energy from human’ waking motion [19,
46-51, 63, 105, 106, 112] can provide a way to power wearable devices without battery or with less
dependence on battery. But such vibration energy is concentrated at a very low frequency of 2 – 4 Hz
[112]. Thus, any vibration-energy harvester for generating power from human’s walking motion, if it
relies on resonant characteristics of its mass-spring system, needs to be designed to have a very low
resonant frequency of 2 – 4 Hz, which is extremely difficult with elastic spring.
Magnetic spring, on the other hand, can readily be designed to have a very low resonant
frequency, and we have study magnetic springs with resonant frequencies over 2 – 4 Hz. With such a
low-resonant-frequency magnetic spring, we notice that its non-linear vibration characteristics easily
dominate, and affect the performance of the vibration-energy harvesters based on such magnetic
spring. Interestingly, though, literature is largely mute on the non-linear characteristics.
In most of the reported vibration-energy harvesters with magnetic spring, a point charge
model is used to analyze the system with substantial inaccuracies [105, 106, 108, 111], especially in
estimating the non-linear behavior of the spring when the distance between the two magnets (forming
the magnetic spring) is short. An accurate modeling of magnetic spring is needed to understand the
dependency of the magnetic spring’s properties on various parameters and predict the resonant
behavior for optimizing vibration energy harvesters based on magnetic spring.
61
This chapter presents a theoretic model (for mass magnetic spring) based on the analytical
duel-charged-surface (DCS) model of a permanent magnet. The non-linear vibration dependency on
the magnetic spring’s parameter is investigated through the model and is validated through
experiments. Based on the model, a prototype vibration energy harvester is designed, fabricated, and
demonstrated to have optimized resonant frequencies over the extremely low frequencies (2 – 4 Hz)
associated with human’s walking motion.
3.2 Theory
A typical magnetic spring consists of two well-shaped permanent magnets, which are aligned
along a line, in a housing that confines the motion of the movable magnets. Depending on a housing
structure, cuboid or cylinder/disk magnets are commonly used. The magnetization of a permanent
magnet is perpendicular to the surface. With the same poles facing each other, the magnetic force
between two magnets in a magnetic spring is repulsive, and is balanced by other forces due to gravity,
friction, etc. For example, gravity of a movable magnet keeps it from being repelled by another magnet
that is stationary or anchored, when the magnetic spring is set in a vertical direction. A simple magnetic
spring shown in Figure 2.1 (b) is composed of two magnets arranged vertically with the bottom one
fixed to a housing and the top one unanchored and levitated (and thus movable). According to the
Earnshaw's theorem [114] on magnetic levitation, the top magnet cannot maintain a stable stationary
equilibrium state solely by the magnetostatic interaction with the bottom magnet, thus a mechanical
fixture is needed to confine the motion of the levitated part to travel along one dimension and stay
co-axial with the anchored magnet. In this configuration, the restoring force is the superposition of
the repelling force and the gravity from the levitated part, assuming negligible friction. In equilibrium,
the magnetic force equals to the gravity of the levitated magnet together with the load.
62

Figure 3.1 A magnetic spring composed of two magnets arranged vertically, one magnet anchored and
the other levitated (by the magnetic repulsive force). On the levitated magnet is a proof mass, so that
the displacement of the levitated magnet may be enhanced for a given externally applied acceleration
or force (for larger power generation from vibration energy). An equivalent spring also is indicated
between the two magnets.
3.2.1 Lossless System
For a vertical magnetic spring without damping, with
x
defined to be the distance between
the levitated magnet and the anchored magnet, the restoring force
res
F is
( ) ( )
res M
F x F x mg =− (3.1)
where
M
F is the force between two magnets, while m and g are the total mass of the load (including
the mass of the levitated magnet) and gravitational constant, respectively. With the same poles facing
Confining fixture
Proof
mass
Levitated magnet
Anchored magnet
S
S
N
N
63
each other in the magnet pair,
M
F is positive. The equilibrium position is
0
x when
0
()
M
F x mg = .
When the displacement
0
xx  , the magnetic force between the two magnets is weaker than the
gravitational force mg , and thus ( ) 0
res
Fx  brings the proof mass back to the equilibrium position
0
x . On the other hand, when the displacement
0
xx  , the positive restoring force brings the
displacement x back to
0
x .
With Equation (3.1), the restoring forces of the magnetic springs based on the magnets listed
in Table 3.1 are plotted in Figure 3.2 (a). The equilibrium position
0
x for each spring is where the
restoring force is zero in the figure. Near
0
x , the restoring force is linearly dependent on the separation
distance, if the distance is small, and one spring constant can describe the behavior. When the
displacement is large (
0
xx  ), the restoring force saturates at the gravitational force mg − , while
when the displacement approaches zero, the restoring force is dominated by the rapidly-increasing
repulsive force between the magnets. Due to this non-symmetrical restoring force, the magnetic spring
is mostly non-linear, and the vertical displacement in natural vibration is not sinusoidal.
Table 3.1 Grade and geometry of rare earth neodymium magnets used in magnetic springs plotted in
Figure 3.2. The levitated and anchored magnets are of same type and size except for the polarity
arranged.
Grade Length (mm) Width (mm) Height (mm)
Magnet 1 N52 12.7 12.7 12.7
Magnet 2 N52 12.7 12.7 6.35
Magnet 3 N52 6.35 6.35 12.7
Magnet 4 N52 6.35 12.7 12.7
Magnet 5 N52 6.35 12.7 6.35
Magnet 6 N42 6.35 12.7 6.35

64

Figure 3.2 Calculated restoring forces (based on DCS model for same types of the levitated and
anchored magnets) showing (a) mostly non-linear spring constant except when the vibration is small
around the equilibrium position, (b) higher restoring force for the magnet with higher grade (with N52
being a higher grade than N42) and thus higher coercive force, (c) the proof mass determining the
maximum negative restoring force, (d) higher restoring force for wider magnets, and (e) higher force
for taller magnets.
Approxim
ate linear region
65
As can be seen in Figure 3.2 (b), the higher-grade rare earth neodymium magnet (having higher
coercive force) makes
0
x and the increasing rate of the restoring force (as the separation distance
approaches zero) larger. For a given magnetic spring, the proof mass affects the maximum negative
restoring force ( mg − ) and restoring acceleration with a heavier mass leading to smaller
0
x and less
dynamic range (Figure 3.2 (c)). The geometry of magnets also affects the restoring force with larger
width, length or height of the magnet delivering higher positive restoring force and more dynamic
range (Figure 3.2 (d) and Figure 3.2(e)).
For free vibration of the magnetic spring without damping, the governing equation is

2
2
( ) .
restoring M
dx
m F F x mg
dt
= = − (3.2)
To solve the equation, a duel charged surface (DCS) model is again used for the magnets, which
models the permanent magnet into magnetically charged surfaces. As a result, the magnetic force
()
M
Fx can be presented with an analytical equation, as a function of x , geometry and coercive force
of the magnets. The initial condition of ( 0) xt = and ( 0) vt = defines the total energy in the system, as
the initial displacement x determines the initial potential energy while the initial velocity v determines
the initial kinetic energy.
A. Initial Displacement
For a magnetic spring composed of two cuboidal N52 grade neodymium magnets with 25.4
mm side length and a proof mass of 300 grams, Equation (3.2) is solved as a function of initial
displacement between 16 and 770 mm, and the calculated displacement, velocity and acceleration in
time domain are shown in Figure 3.3. Though the vibration is not sinusoidal in time nor symmetrical
across the equilibrium position, it’s still periodic. Within each cycle, the total energy is divided between
kinetic energy and potential energy, as the displacement varies. Since the initial condition of
66
displacement and velocity together determines the total energy, the initial condition determines the
vibration frequency, spectral distribution, etc.
The movable magnet along with the 300-gram load is released with zero velocity at different
initial displacement (between 16 and 770 mm), and is let to vibrate freely without any damping. For
initial displacement
0 i
xx  , the proof mass is pushed upwards first and then drops, while for initial
displacement
0 i
xx  , the proof mass drops first and then get pushed upward. The time-domain
vibration plotted in Figure 3.3 shows a decrease followed by an increase in the period as the initial
displacement sweeps from 16 to 770 mm with
0
x being 95 mm. The observation corresponds to the
fact that the higher total energy in the system, the longer the vibration period.
67

Figure 3.3 Calculated responses of a lossless or damping-free magnetic spring (composed of two
cuboidal N52 grade neodymium magnets with 25.4 mm side length, along with 300 gram proof mass
on the movable magnet of the magnetic spring): (a) free vibrations vs time as a function of the initial
displacement between 10 and 550 mm and (b) spectrum of the time-domain displacement () xt for
various initial displacements (same color coding as in Figure 3.2).
68
A fast Fourier transform (FFT) is applied on the time-domain displacement () xt , and the
amplitudes at DC and harmonic frequencies are shown in Figure 3.4. As expected, the fundamental
frequency first increases as the initial displacement increases from 0 to
0
x and then drops after
0
x . If
we consider only for
0 i
xx  , the fundamental frequency drops linearly at -2Hz/m, as
i
x increases.
The DC amplitude corresponds to the location of the symmetric axis of the displacement, which is
different from
0
x . The traveling range of a magnetic spring can approximately be estimated by
doubling the DC amplitude.

Figure 3.4 Calculated vibration amplitude and frequency vs the initial displacement.
B. Proof Mass
For a pair of cuboid N52 grade neodymium magnets with 25.4mm side length and for a
150mm initial displacement, the vibration amplitude and frequency are calculated as the proof mass is
69
varied from 10g to 900g at an interval of 10g, and the calculated values are shown in Figure 3.5 (b).
The dependency of the fundamental frequency on the proof mass shows three segments: 1) when the
proof mass is light with the initial displacement around the corresponding equilibrium position
0
x
:
there is a region where the dependency is high; 2) then as the proof mass increases, there is a flat
region where the frequency is approximately independent of the proof mass change; and 3) when the
proof mass continues to increase, a low sensitive linear dependence appears. One special observation
is that in the first high sensitivity segment, the displacement x is within the linear region of
0
x
in
Figure 3.2. Thus, the frequency of the magnetic spring can be estimated with
1
2
eff
k
m
f

= where
0
()
M
eff
xx
dF x
k
dx
=
= . A total of 0.4Hz frequency tunable range is observed over 900g proof mass change
in this magnetic spring.
The magnetic spring in Figure 3.5 (a) is composed of two cuboid N52 grade neodymium
magnets of 12.7mm in width and length and 6.35mm in height. Proof mass is swept from 1g to 80g
at an interval of 1g and initial displacement is set to 80mm. The similar three segments show up on
the curve, with a total 0.6Hz frequency tunable range over 80g proof mass change.
C. Coercive Force
The coercive force determines the magnetic field strength around the permanent magnet, and
a magnet with higher grade has larger coercive force. Figure 3.5 (c) plots the dependency on coercive
force from 0.5 to 1.3MA/m on a magnetic spring composed of two cuboid N52 grade neodymium
magnets of 12.7mm in side length (for a square shape) and 6.35mm in height, along with a proof mass
of 60 gram, released at 80mm initial displacement. The frequency depends on the coercive force
70
linearly with negative slope. However, the change on the frequency is quite small for such a large range
of the coercive force.
D. Magnet Geometry
The magnet geometry also plays a major role in deciding the fundamental frequency of the
magnetic spring. For a magnetic spring with two N52 grade magnets and 60g proof mass and with
80mm initial displacement, Figure 3.5 (d) shows the frequency dependency on the side length when
the magnet height is fixed at 6.35mm while Figure 3.5 (e) shows the frequency dependency on the
height when the side length is fixed at 12.7mm. The frequency shows a linear dependency on the side
length with a -0.04Hz/mm sensitivity, and partially linear dependency over a certain height range with
a -0.06Hz/mm sensitivity.

71

72

Figure 3.5 Calculated vibration amplitude and frequency vs (a)-(b) proof mass, (c) coercive force, (d)
side length of the magnet, and (e) height of the magnet.
3.2.2 Vibration with Damping
Two major damping mechanisms are considered: the sliding/rolling friction and the velocity
damping. The sliding/rolling friction comes from the fact that the moving part (levitated magnet and
load) needs sideway support from the housing to maintain the stability in the motion. Considering no
roller mechanics is employed, the simplest case is the moving part touching the sidewall and
experiencing lateral supporting force N which is proportional to the load’s gravity N mg  . As the
friction force is also proportional to the normal force, we define the sliding friction force as
()
ff
f mg sign v  = −  (3.3)
where
f

is the converted friction damping ratio, while the sign function returns the sign of velocity.
Similarly, the velocity damping force is proportional to the load’s velocity. The velocity damping
73
includes air damping, electro-magnetic damping, etc. The velocity damping force can be represented
as

vv
fv  =− (3.4)
where
v

is the converted velocity damping ratio. These damping mechanisms are illustrated in Figure
3.6.

Figure 3.6 Model of a magnetic spring with proof mass including two types of damping.

Magnetic spring
𝑎 𝑒 𝑥𝑡 ( 𝑡 ሻ
𝑥 ( 𝑡 ሻ
𝑣 ( 𝑡 ሻ , 𝑎 ( 𝑡 ሻ
𝐹 𝑀 ( 𝑥 ( 𝑡 ሻ ሻ 𝑚
𝑚 g
𝑓 𝑣 ( 𝑣 ( 𝑥 ሻ ሻ
𝑓 𝑓 ( 𝑁 ሻ
𝜇 𝑣 𝜇 𝑓
Housing
𝑁
𝑁
74
With damping considered, Equation (3.2) becomes

2
2
( ) ( ) ( ) .
f M v M v f
d x dx
m F x mg f f F x mg sign x mg
dt dt
 = − + + = − −  − (3.5)
A mass magnetic spring system composed of two cuboid N52 grade neodymium magnets with
25.4mm side length with a proof mass of 300 grams is used to calculate the ring down pattern based
on Equation (3.5), with an initial displacement of 40mm. The calculated ring down in time under the
two different damping mechanisms are plotted in Figure 3.7 (a) and Figure 3.7 (b). Unlike the velocity
damping which causes an exponential decay in time, the ring down under the friction damping is
approximately linear in time, as the damping force takes the energy away through heat. As noted earlier,
the vibration frequency and amplitude depend on the overall system energy. The time domain signal
shows the decreasing vibration amplitude and period as the energy in the system is lost due to the
damping. As can be seen in Figure 3.7 (c) and Figure 3.7 (d), the frequency spectra of the time-domain
signals show the bandwidth-broadening effect of damping in addition to multiple peaks.

75

Figure 3.7 Natural vibration with damping: (a) and (b) ring down vs time as a function of various
damping conditions; (c) and (d) frequency spectra of the time-domain ring-down signals in (a) and (b).
76
3.2.3 Forced Vibration
The forced vibration occurs when the magnetic spring is driven by an external force or
acceleration. For a sinusoidal external acceleration drive
0
( ) sin(2 )
ext
a t a ft  = + , the governing
equation becomes:

2
2
( ) ( ) ( ) .
ex M M t v f v f
d x dx
m ma F x mg f f F x mg sign x mg
dt dt
 + = − + + = − −  − (3.6)
For a magnetic spring based on two cuboid N52 grade neodymium magnets with 25.4mm side length
along with a proof mass of 300g and initial displacement of 400mm, with damping added as
0.3
f
 =
and
0.3
v
 =
, the fundamental resonant frequency of the natural vibration of the magnetic spring is
estimated to be 1.68Hz. If an external acceleration
0
sin(2 )
ext
aa ft  =
is applied to the magnetic spring,
with
0
a
= 2, 3, and 4 m/s
2
and f = 1.32, 1.68, 2.52, and 2.88 Hz, the solutions of Equation (3.6) are as
shown in Figure 3.8. As can be seen, when the external acceleration amplitude is small and unable to
compensate the energy loss due to damping, the total energy drops (as the displacement amplitude
drops) with the resonant frequency being shifted higher. This is why the forced vibration has a larger
amplitude at 2.52Hz than 1.68Hz when the external acceleration amplitude is 2 and
2
3 / ms .
77

Figure 3.8 Forced vibrations of a magnetic spring vs time under externally applied accelerations with
varying amplitudes
2
0
2, 3, and 4 / a m s = and frequencies f = 1.32, 1.68, 2.52, and 2.88 Hz. In about
4 seconds, the system reaches a steady state forced vibration at the frequency of external drive.
3.3 Experimental Results
3.3.1 Testing Setup
As shown in Figure 3.9, a linear actuator is used to apply an external vibration force to a
magnetic spring, for testing various magnetic springs. A rectangular acrylic tube structure is employed
to house the magnetic spring and confines the motion to vertical direction (z axis) only. The lower
78
magnet is anchored to the structure, while the top magnet is suspended by the repulsive force from
the bottom magnet and confined by the side walls of the housing. Both magnets are cuboid N52 grade
neodymium magnets with 25.4mm side length. An adjustable mass load is attached on top of the
levitated magnet. The side walls are well polished and coated with dry lubricant (dry film spray with
Polytetrafluoroethylene (PTFE) from WD-40

) to confine the movable magnet and mass load with
minimum friction. The housing is fixed to the linear actuator that can provide accurate external driving
acceleration in one direction. Two analog accelerometers (ADXL 335 with 17.8 ms
-2
/V sensitivity) are
attached; one on the housing structure and the other on the load of the magnetic spring with
tensionless ultra-flexible wires providing electrical connection. The motions of both the housing and
the proof mass are monitored in real time with the accelerator outputs via an oscilloscope. The
operation data of the linear actuator and the oscilloscope data are synchronized on the desktop
computer for digital signal processing.
79

Figure 3.9 Photo of the testing setup along with a magnetic spring composed of a levitated magnet
(on which a proof mass is mounted) and an anchored magnet inside a plastic housing.
3.3.2 Ring-down
The non-linearity of the magnetic spring is observed first through ring-down experiments.
When the proof mass is released from an initial distance, it vibrates down and up, until it comes to a
complete stop. Unlike a linear spring with a single spring constant, the ring-down vibration of the
magnetic spring shows a non-sinusoidal wave and a change on the vibration period (Figure 3.10 (a)),
as plotted in Figure 3.10 (b), as the time passes by and the amplitude drops. Also, the ring-down is
more like linear, rather than exponential, in time due to the fact that the magnetic spring is non-linear.
Consequently, it is not possible to extract Q-factor from the ring down curve.
80

Figure 3.10 Measurement of free vibration of the magnetic spring: (a) ring-down vs time, with both
the shape and the period changing due to the spring’s non-linearity, as the amplitude rings down due
to damping and (b) the period of the non-sinusoidal ring-down curve vs time.
3.3.3 Forced Oscillation
The linear actuator is programmed to output vertical sinusoidal motion to deliver the desired
external acceleration
0
( ) sin(2 )
ext
a t a ft  =
to the housing of the magnetic spring. The frequency of
the external acceleration is swept from 2 to 4Hz with 0.1Hz step. When the external acceleration is
applied, the magnetic spring goes through a transient period for several seconds, and reaches the
steady state vibration at the frequency of the external acceleration. A fast Fourier transform (FFT) is
applied on the measured, steady-state, time-domain vibration to extract the vibration amplitude at the
fundamental resonant frequency and its harmonics. The resonant frequencies are noted to be where
peaking occurs, and there are multiple resonant frequencies near the driving frequency. Figure 3.11 (a)
81
shows the magnetic spring’s vibration amplitude at its fundamental resonant frequency (measured and
confirmed to be the same as the drive frequency) vs frequency as a function of the applied acceleration
amplitude. As the applied acceleration increases, the vibration amplitude also increases, but the
resonant frequency drops from 3.1Hz at
2
0.5 / ms to 2.8Hz at
2
1.5 / ms . This drop is due to the fact
that the higher vibration level means a larger energy sustained in the system, resulting in a lower
resonant frequency.
For a given magnetic spring, the resonant frequency shifts as the proof mass is varied, as
shown in Figure 3.11 (b). When the proof mass is increased from 191.9 to 373.4g, the peaking
frequency increases from 2.9 to 3.3Hz, validating the theory and calculation in Figure 3.5 (b) and
Figure 3.8, with decreasing vibration amplitude.
82

2.8
Hz
2.9
Hz
3.1
Hz
83

Figure 3.11 Vibration amplitude of the fundamental resonance of the magnetic spring vs frequency of
externally applied sinusoidal acceleration; (a) as a function of applied amplitude (showing the
decreasing resonant frequency as the amplitude increases) and (b) as a function of the proof mass
(showing the increasing resonant frequency as the mass increases).
3.4 Application
In designing a mass magnetic spring system for vibration energy harvesting, the above-
developed model and theory can provide the dependencies of the resonant frequency and amplitude
on various parameters including desired working acceleration, proof mass and magnet specification.
2.9H
z
3.1H
z
3.3H
z
84
A resonance well matched to available vibration energy leads to maximizing the vibration amplitude
and thus power generation in the energy harvester.
We have designed a magnetic spring with resonant frequencies over the extremely low
frequencies associated with human’s walking motion and fabricated an electromagnetic vibration
energy harvester based on the magnetic spring.
The energy harvester is composed of a magnetic spring that suspends an array of movable
magnets surrounded by a coil array. The movable magnet array and the coil array generate electrical
power through electro-magnetic induction (Figure 3.12). The power-generating magnets together with
the levitated magnet in the spring make up the proof mass. For targeted frequency (2 to 3Hz) and
external acceleration range (motion from human body), we calculate the needed magnetic spring, and
list the magnets in Table 3.2. N52 grade NdFeB magnets are chosen for their large coercive force and
high surface field capability without adding extra weight. To match up with the optimized design of
the coil, an array of 6 power-generating magnets are used.
Table 3.2 Summary for the magnets used in the designed energy harvester.
Magnets Grade Weight (g) Length (mm) Width (mm) Height (mm)
Power-generating magnets N52 15.37 25.4 12.7 6.35
Levitated magnets N52 38.4 12.7 6.35 15.875
Anchored magnets N52 38.4 12.7 6.35 15.875

Assembled in a 1mm thick laser-machined acrylic housing, the energy harvester occupies a
total volume of
3
3 1 15  cm and a total weight of 200gram. Two 1.5 mm thick printed circuit boards
(PCB) coil are arranged on front and back sides, aligned with power-generating magnet array. On each
PCB, five 6-layer coils are connected in series, which has 20 turns in a single monolayer coil. In total,
1200 turns coil are achieved on two PCBs, with a measured resistance of 256Ω.
85
Between the housing and movable part, six tiny Teflon balls are added in pre-defined groves
(Figure 3.12 (a)) for (1) rolling spacers to minimize the gap between the coil and magnets to 0.3mm
for good utilization of the magnetic field from the power-generating magnets, (2) minimize the friction
(and thus damping) by converting the sliding friction to rolling friction, and (3) automatic alignment
from tilting of the moving part.
The energy harvester is tested on the same vertical linear actuator controlled by the
measurement automation system, as the applied frequency and acceleration amplitude are varied
(Figure 3.13 (a)). Maximum power delivery (into a 256Ω matched load) occurs when the external
acceleration frequency matches the natural resonant frequency of the magnetic spring. As the applied
acceleration increases, the resonant frequency decreases, as validated by our modeling. As a result, for
an applied acceleration of 0.2g, a largest power of 15.4mW is delivered at 3.1Hz, while a largest power
of 9.3mW occurs at 2 Hz for 0.9g, which is the highest external acceleration that the energy harvester
can take for the current package size.

Figure 3.12 (a) Schematic of the electromagnetic vibration energy harvester based on a magnetic spring
and (b) photo of the fabricated harvester.
86

Figure 3.13 Measured power (into a matched load of 256 ) from the electromagnetic vibration energy
harvester: (a) power vs frequency as a function of the applied acceleration at 0.1, 0.15 and 0.2g and (b)
power vs applied acceleration at 2Hz.
3.5 Summary
This chapter presents a theoretical model for permanent magnetic springs that is used for
generating power from human’s walking motion and implement it in Python. The analytical model
predicts accurately the non-linear vibration behavior and offers insight to the dependence of the
vibration frequency on various parameters. The natural resonant frequency of a magnetic spring is
determined by its total energy, magnet geometry, coercive force and proof mass. By using the model,
we study the characteristics of the magnetic spring in order to extract maximum possible power out
of human’s walking.
Based on the model, we have designed a magnetic spring and applied it in an electromagnetic
vibration energy harvester to obtain an extremely low resonant frequency that matches a typical
human’s walking motion. A resonant frequency as low as 3.1Hz is achieved for the fabricated energy
harvester, and 10mW level power is delivered from a person’s normal walking with the harvester
occupying
3
3 1 15  cm volume and weighing 200 gram.

87
3.6 References
[19] T.-C. Hou, Y. Yang, H. Zhang, J. Chen, L.-J. Chen, and Z. L. Wang, “Triboelectric
nanogenerator built inside shoe insole for harvesting walking energy,” Nano Energy, vol. 2, no.
5, pp. 856-862, 2013.
[22] K. C. Pradel, W. Wu, Y. Ding, and Z. L. Wang, “Solution-derived ZnO homojunction
nanowire films on wearable substrates for energy conversion and self-powered gesture
recognition,” Nano letters, vol. 14, no. 12, pp. 6897-6905, 2014.
[41] W. Li, D. Torres, T. Wang, C. Wang, and N. Sepúlveda, “Flexible and biocompatible
polypropylene ferroelectret nanogenerator (FENG): on the path toward wearable devices
powered by human motion,” Nano Energy, vol. 30, pp. 649-657, 2016.
[46] Y. Wang, Q. Zhang, L. Zhao, A. Shkel, Y. Tang, and E. S. Kim, "Stackable dual-layer coil
based on wafer-level transfer technique for electromagnetic energy harvester." pp. 1264-1267.
[47] Y. Wang, Q. Zhang, L. Zhao, and E. S. Kim, "Non-resonant, broad-band vibration-energy
harvester based on self-assembled liquid bearing." pp. 614-617.
[48] Y. Wang, Q. Zhang, L. Zhao, and E. S. Kim, “Non-resonant electromagnetic broad-band
vibration-energy harvester based on self-assembled ferrofluid liquid bearing,” Journal of
Microelectromechanical Systems, vol. 26, no. 4, pp. 809-819, 2017.
[49] Q. Zhang, Y. Wang, L. Zhao, and E. S. Kim, "Microfabricated thousand-turn coils for mW
power generation from sub-mm vibrations." pp. 606-609.
[50] Q. Zhang, Y. Wang, L. Zhao, and E. S. Kim, “Integration of microfabricated low resistance
and thousand-turn coils for vibration energy harvesting,” Journal of Micromechanics and
Microengineering, vol. 26, no. 2, pp. 025019, 2016.
[51] Y. Wang, Q. Zhang, L. Zhao, and E. S. Kim, "Ferrofluid liquid spring for vibration energy
harvesting." pp. 122-125.
88
[63] J. Seo, J.-S. Kim, U.-C. Jeong, Y.-D. Kim, Y.-C. Kim, H. Lee, and J.-E. Oh, “Optimization
and performance improvement of an electromagnetic-type energy harvester with
consideration of human walking vibration,” Journal of the Korean Physical Society, vol. 68, no. 3,
pp. 431-442, 2016.
[105] Q. Zhang, Y. Wang, and E. S. Kim, “Electromagnetic energy harvester with flexible coils and
magnetic spring for 1–10 Hz resonance,” Journal of Microelectromechanical Systems, vol. 24, no. 4,
pp. 1193-1206, 2015.
[106] Q. Zhang, Y. Wang, and E. S. Kim, “Power generation from human body motion through
magnet and coil arrays with magnetic spring,” Journal of Applied Physics, vol. 115, no. 6, pp.
064908, 2014.
[108] M. Salauddin, M. Halim, and J. Park, “A magnetic-spring-based, low-frequency-vibration
energy harvester comprising a dual Halbach array,” Smart Materials and Structures, vol. 25, no. 9,
pp. 095017, 2016.
[111] W. Wang, J. Cao, N. Zhang, J. Lin, and W.-H. Liao, “Magnetic-spring based energy harvesting
from human motions: Design, modeling and experiments,” Energy Conversion and Management,
vol. 132, pp. 189-197, 2017.
[112] J. E. Bertram, and A. Ruina, “Multiple walking speed–frequency relations are predicted by
constrained optimization,” Journal of theoretical Biology, vol. 209, no. 4, pp. 445-453, 2001.
[114] W. Jones, “Earnshaw's theorem and the stability of matter,” European Journal of Physics, vol. 1,
no. 2, pp. 85, 1980.
Equation Chapter (Next) Section 1
89
Chapter 4 :
Focused Ultrasonic Transducer with Controllability on Focal Length
4.1 Background
Focused ultrasound (FUS) has a wide application potential in imaging [115-119], tumor
treatment [120-123], neuron stimulation [124-128], etc. However, the previously designed transducers
[129-131] are of a fixed focal length, with no electrical controllability for the focal length, and are
incapable of dynamically changing the focal spot without physically moving the transducer. The new
device described here offers tremendous degree of operating freedom by enabling the electrical
controllability of the focal length. By using the new design, a real-time, fast-response, on-demand
changing of focal length can be achieved.
4.2 Device Design
The transducer is built on a 1.02 mm thick PZT substrate, whose fundamental thickness-mode
resonant frequency is 2.25 MHz. Two layers of nickel sputtered on both sides which serve as
electrodes. Ultrasonic waves are generated at the areas covered by patterned nickel electrodes due to
the PZT’s piezoelectric effect. The electrode patterns are designed to have one (1) circular center and
thirty-one (31) concentric equal-width annular rings (outside the center electrode), for a total of 32
electrodes. Each and every one of the 32 patterned electrodes is wired out to a pad with individual
accessibility. The radius of the circular center electrode is 2 mm, while the width of each of the annular
ring is 0.2 mm with equal spacing of 0.05 mm between two adjacent electrodes.
Electrical controlling the focal length is achieved by selecting a group of electrodes to actuate
so that the acoustic waves generated from those selected electrodes will arrive at the desired focal
90
length in-phase, interfere constructively, and create a focal spot of high acoustic intensity. As each
electrode can be selected or unselected, the 32 electrodes give a 32-bit resolution of controlling
precision. Figure 4.1 illustrates a 4-bit transducer. Higher bit resolution will give more precise control
over the focal length.

Figure 4.1 Top-view and cross-sectional view schematics of a 4-bit resolution transducer. Four equal-
width concentric ring electrodes are patterned on PZT. Each electrode can be actuated individually.
By varying the selection of the electrodes to be actuated, the focal length can be varied.
The radius of the circular center electrode r 0 approximately defines the lower bound of focal
length, as suggest by:

22
0
/4
min
r
f


+
= (1)
For the n
th
ring electrode, we use its central radius (average of inner and outer radius) to
calculate the contribution to the focal point according to their phase factor (P.F.):

22
. . sin( 2 )
n
P
r f f
F 

=
+−
(2)
91

Figure 4.2 The radius of the circular center electrode r 0 determines lower bound of the focal length
approximately. The n
th
radius r n is used to determine if the n
th
ring electrode needs to be actuated of a
particular focal length.
If the contribution is positive for in-phase constructive interference, we will add this electrode
into the group of the electrodes to be actuated. Otherwise (i.e., out-of-phase destructive interference),
we will not select the ring to actuate. Figure 4.3 demonstrates the actuation selection group based on
our 32-bit transducer design. As we vary the focal length, the actual focal size will change accordingly:
a shorter focal length will result in a smaller focal size, while a longer focal length will induce a larger
focal size.

Figure 4.3 A plan for selecting the actuation group of the electrodes for a 32-bit resolution transducer.
The red blocks mean the corresponding n
th
electrode rings are selected for actuation, while the blue
ones mean unselected.
92
4.3 Simulation
Simulation on particle displacement (that is directly related to acoustic intensity) is carried out
to verify the initial design as well as the capability to control the focal length. A C++ FEM program
has been coded based on the piezoelectricity and acoustics, and data visualization has been achieved
by another Python program. To make a clear demonstration of the electrical controllability of the focal
length, we choose 4 typical focal lengths (5, 7, 10, and 12 mm) to run the simulation. For the four
cases, we simulate on the same electrode patterning (32-bit) but different sets of the actuated
electrodes from Figure 4.3.

Figure 4.4 Simulation results showing the focal effect and focal length of 5, 7, 10 and 12 mm.
The simulated results on the vertical cross-sectional particle displacement are shown in Figure
4.4 for each of the four focal-length actuating selections. Focal effects are significant with an elliptical
focal region at the desired focal length. The particle displacement at the focal spot is about 10 times
larger than the average value of the particle displacements in the rest of the region. As expected, the
focal size is dependent on the focal length.
93

Figure 4.5 Fabrication process of the transducer.
4.4 Fabrication
A brief fabrication process is illustrated in Figure 4.5. We start with a 1.03mm thick PSI-5A4E
PZT sheet with nickel layer sputter-deposited on its both sides. AZ5214 photoresist is coated for both
front and back sides for the electrode pattern delineation. Front-to-back alignment is done by aligning
at the pre-defined dicing edge of PZT sheet. The electrode wiring-outs are patterned on the front side.
After the wet etch of nickel layer, a second layer of photoresist is spin-coated for a sacrifice layer in
forming air cavities which block acoustic waves in the region (and its conjugate region) where annular
rings are disturbed for electrical wiring-outs (so that the acoustic-wave sources may be
circumferentially symmetric). Then, with the protection of the backside electrode, a 6 m thick
Parylene film is deposited, and release holes are defined on the front side where air cavities are needed.
Oxygen reactive ion etch (RIE) is used to etch through the Parylene to form the release holes, and the
94
sacrificial layer is removed by acetone through the release holes. A second layer of Parylene film is,
then, deposited to seal the holes to finish the air-cavity reflectors and provide the transducer with
electrical insulation for liquid immersive operations. The finished transducer is shown in Figure 4.6.
Different packages may be used for different applications. We build an acrylic handler to house
the transducer and position it under water for verifying the focal length through droplet ejection
experiment. Reservoir based package is also adopted for other application and operation.

Figure 4.6 Photos of the fabricated transducer. The top photo shows the transducer after releasing
sacrificial photoresist layer for air reflector region which shelters the asymmetric electrode part. The
O 2 plasma etched releasing hole can be clearly seen. The bottom photos show the close-up views of
the patterned electrodes.
4.5 Measurement
We use water-droplet ejection to verify the focal length, focal size and electrical-focal-length
controllability. When the liquid level is right at the focal plane, the water within the focal spot will
receive an intensified acoustic energy from the focused ultrasound, which leads to ejection of water
95
droplets. By observing the droplet ejection, we can measure the focal length from the water height at
which the droplet ejection occurs (as the focused ultrasound is the one that causes the ejection) and
the lateral focal size (which is closely related to the droplet size).

Figure 4.7 Measurement setup schematics for droplet ejection experiment. Droplet ejection can be
observed by CCD camera, while the focal length can be measured with the micropositioner.
Figure 4.7 illustrates the measurement setup schematics for our transducer. The function
generator outputs the driving waveform of pulsed sinusoidal wave of 2.25 MHz, 200 pulse cycles at a
pulse repetition frequency of 60 Hz, which then is amplified to around 430 V pp by a power amplifier.
A 3-axis positioner holds the acrylic handler to position the transducer within the water. A CCD
camera is attached to a long-range microscope for observing the droplet ejection from the side, with
a synchronized delay-adjustable light strobing with light-emitting-diode (LED) working as a
stroboscope for capturing the ejection process at various points in time.
96

Figure 4.8 Cross-sectional-view photos of the water ejections obtained at the water heights of 5 mm
(a), 7 mm (b), 10 mm (c), and 12 mm (d).
4.6 Results
When our transducer is positioned at the desired focal length under the water surface, the
droplet ejection occurs, and the water height is recorded as the transducer’s focal length. By changing
the delay from the stroboscopic LED to the moment when the droplet ejection starts (after necking
of a water column), we measure the lateral size of the droplet.

Figure 4.9 Measured focal lengths vs designed focal lengths.
97
Each of the photos in Figure 4.8 shows the necking of the water column just before a droplet
is ejected. The diameter of the droplet is measured from the captured video. The water height is read
out from the positioner. The graph in Figure 4.9 shows the relation between the designed focal length
(by the actuation plan) versus the measured focal length. The graph in Figure 4.10 summarizes the
measured lateral dimensions of the droplets in Figure 4.8 with respect to the set focal lengths, as well
as the simulated focal sizes from our C++ program.

Figure 4.10 Ejected droplet size vs designed focal length (both measured and simulated data).
4.7 Summary
This chapter presents the design, fabrication and testing of a 32-bit focus ultrasonic transducer
with electrically controllable focal length from 5 to 12 mm, with a controllable range of 7 mm.
Simulations carried out with a C++/Python program show the cross-sectional views of four typical
focal-lengths (5, 7, 10, and 12 mm), showing that the focal length can be varied via electrical selection
of a proper set of the electrodes.
98
The transducer is tested through liquid droplet ejections to demonstrate the tunability of the
focal length. When the transducer is configured for a particular focal length, we measure to focal
length by finding the water level where the ejection occurs, as we vary the water height. Under various
actuating conditions, the focal lengths are measured, and compared to the designed focal lengths. The
size of the ejected liquid droplet (corresponding to the focal size) is measured (and simulated) to vary
between 400 and 800 μm in diameter, and be dependent on the focal length.
4.8 References
[115] S. Vaezy, X. Shi, R. W. Martin, E. Chi, P. I. Nelson, M. R. Bailey, and L. A. Crum, “Real-time
visualization of high-intensity focused ultrasound treatment using ultrasound imaging,”
Ultrasound in medicine & biology, vol. 27, no. 1, pp. 33-42, 2001.
[116] J. Ye, S. Ito, and N. Toyama, “Computerized ultrasonic imaging inspection: From shallow to
deep learning,” Sensors, vol. 18, no. 11, pp. 3820, 2018.
[117] K. K. Shung, “High frequency ultrasonic imaging,” Journal of medical ultrasound, vol. 17, no. 1,
pp. 25-30, 2009.
[118] L. N. Bohs, and G. E. Trahey, “A novel method for angle independent ultrasonic imaging of
blood flow and tissue motion,” IEEE transactions on biomedical engineering, vol. 38, no. 3, pp. 280-
286, 1991.
[119] S. Lin, S. Shams, H. Choi, and H. Azari, “Ultrasonic imaging of multi-layer concrete structures,”
NDT & E International, vol. 98, pp. 101-109, 2018.
[120] A. Sadeghi-Naini, O. Falou, H. Tadayyon, A. Al-Mahrouki, W. Tran, N. Papanicolau, M. C.
Kolios, and G. J. Czarnota, “Conventional frequency ultrasonic biomarkers of cancer
treatment response in vivo,” Translational oncology, vol. 6, no. 3, pp. 234-IN2, 2013.
99
[121] M. Zhang, L. Zhang, P. C. K. Cheung, and V. E. C. Ooi, “Molecular weight and anti-tumor
activity of the water-soluble polysaccharides isolated by hot water and ultrasonic treatment
from the sclerotia and mycelia of Pleurotus tuber-regium,” Carbohydrate Polymers, vol. 56, no. 2,
pp. 123-128, 2004.
[122] F. L. Lizzi, R. Muratore, C. X. Deng, J. A. Ketterling, S. K. Alam, S. Mikaelian, and A. Kalisz,
“Radiation-force technique to monitor lesions during ultrasonic therapy,” Ultrasound in medicine
& biology, vol. 29, no. 11, pp. 1593-1605, 2003.
[123] G. A. Husseini, and W. G. Pitt, “Ultrasonic-activated micellar drug delivery for cancer
treatment,” Journal of pharmaceutical sciences, vol. 98, no. 3, pp. 795-811, 2009.
[124] M. Plaksin, S. Shoham, and E. Kimmel, “Intramembrane cavitation as a predictive bio-
piezoelectric mechanism for ultrasonic brain stimulation,” Physical review X, vol. 4, no. 1, pp.
011004, 2014.
[125] W. Qiu, J. Zhou, Y. Chen, M. Su, G. Li, H. Zhao, X. Gu, D. Meng, C. Wang, and Y. Xiao, “A
portable ultrasound system for non-invasive ultrasonic neuro-stimulation,” IEEE Transactions
on Neural Systems and Rehabilitation Engineering, vol. 25, no. 12, pp. 2509-2515, 2017.
[126] Y. Hertzberg, O. Naor, A. Volovick, and S. Shoham, “Towards multifocal ultrasonic neural
stimulation: pattern generation algorithms,” Journal of neural engineering, vol. 7, no. 5, pp. 056002,
2010.
[127] M. D. Menz, Ö. Oralkan, P. T. Khuri-Yakub, and S. A. Baccus, “Precise neural stimulation in
the retina using focused ultrasound,” Journal of Neuroscience, vol. 33, no. 10, pp. 4550-4560, 2013.
[128] W. J. Tyler, S. W. Lani, and G. M. Hwang, “Ultrasonic modulation of neural circuit activity,”
Current opinion in neurobiology, vol. 50, pp. 222-231, 2018.
[129] D. Huang, and E. Kim, “Micromachined acoustic-wave liquid ejector,” Journal of
Microelectromechanical Systems, vol. 10, no. 3, pp. 442-449, 2001.
100
[130] C.-Y. Lee, H. Yu, and E. S. Kim, "Acoustic ejector with novel lens employing air-reflectors."
pp. 170-173.
[131] L. Wang, C.-P. Liao, M. Gross, and E. S. Kim, "Self focusing acoustic transducer (SFAT) with
10-mm focal length for cancer-specific localized cytolysis of 3D cell spheroids in 3D Matrigel."
pp. 653-656.

101
Chapter 5 :
Focused Ultrasonic Transducer with Controllability on Focal
Location
5.1 Background
As introduced in last chapter, focused ultrasound (FUS) has been used in imaging, tumor
treatment, neuron stimulation, etc. It has also been shown to be effective in liquid droplet ejection
[132-136] and acoustic tweezing [137]. One type of FUS transducers makes use of the surface
electrodes that are patterned into Fresnel lens to focus ultrasonic waves through constructive wave
interference at the desired focal point. By patterning the electrodes in Fresnel-lens shapes (i.e., annular
rings with varying widths and spacings), the portions of the ultrasonic waves that will cause destructive
interference not generated.
Electrical controllability over the location of focal point is highly desirable for many
applications listed above. A phased array of ultrasonic transducers can be used for such controllability,
but it requires many power amplifiers or high-voltage phase shifters for high intensity application, as
a time-shared phase array with one power amplifier and one phase shifter reduces the focal intensity.
We recently reported a design with electrical controllability over the focal length, and advanced the
transducer technology from fixed focal length [131, 138] to electrically tunable focal length [139]. That
advancement provided the capability of dynamically changing the focal length without any mechanical
motion of the transducer along the z-axis, but not the focal position over a plane. As the supplement
to the focal length controllable device, this thesis describes a novel design that offers electrical control
over the focal point location on a focal plane (x-y plane) without any mechanical motion of the
transducer. By adopting this design, it is possible to deliver FUS with minimal mechanical operation,
102
and on-demand change of focal position is possible with a single-element transducer of a compact
size.
5.2 Device Design
Fresnel zone-plate focuses ultrasound through near-field effect. Since the focal point of a
Fresnel zone-plate is along the line perpendicular to the center of the annular ring (Figure 5.1), we
make the focal points off-centered by offsetting the centers of the ring patterns in different regions of
the transducer, so that the focal points of different regions may be at different locations. By electrically
selecting and actuating the electrodes in each of the regions, the focal position can be electrically
changed.

Figure 5.1 Example of a piezoelectric transducer with Fresnel zone-plate lens. For un-sectored full
ring lens, the focal point is located along the central line above the ring centers due to the symmetricity
[134].
The transducer is fabricated on a 1.02mm thick PZT with nickel electrodes on it both sides.
The front nickel layer is patterned into 6 sectors, with each sector divided into 3 sub-regions along its
radius (i.e., inner pie-shape sector, middle torus, and outer torus) with 0.05 mm spacing between the
regions. Individual accessibility to each electrode is provided by surface routing. On top of the
patterned electrode, off-center Fresnel zone-plate pattern is defined by air-cavities (sealed with 20 m
thick Parylene) that block unwanted acoustic waves (i.e., the waves that contribute to destructive
interference) through impedance mismatching between solid and air. Focal positions of the three
103
lenses are offset from the device center by 3, 2, 1, -1, -2, -3mm, where a total 6mm offset range is
achieved.

Figure 5.2 A single sector is consisted of 3 sub-regions: inner pie-shape sector, middle torus, and outer
torus. The Fresnel ring pattern within each sub-region is arranged to offset the focal point with a
desired distance on the focal plane. (a) relative position of the central line and one sector; (b) the inner
pie-shape sector corresponding to focal point 1 which is furthest from the central line on the focal
plane; (c) the middle torus corresponding to focal point 2 and (d) the outer torus corresponding to
focal point 3 which is closest to the central line; (e) and (f) the cross-sectional views of the Fresnel
rings within different sub-regions that are designed to have different lateral offset for the focal point
on the focal plane.
104

Figure 5.3 Top view of the design of a single sector. Three sectors are individually accessible.
5.3 Fabrication
As illustrated in the brief fabrication process shown in Figure 5.4, we use a 1.03mm thick PSI-
5A4E PZT with nickel layer on its both sides as the substrate to start with. Photoresist is spin-coated
for both the front and back sides for the electrode patterning. Front-to-backside alignment is done by
aligning at a pre-defined dicing edge of the PZT substrate. The sectored electrodes (with its sub-
regions) are patterned on the front side, while the backside electrode is patterned into a full circle.
After wet-etching nickel layer, we coat a second layer of photoresist for a sacrificial layer in forming
air cavities which blocks unwanted acoustic waves and forms a partial Fresnel lens pattern. Then, while
protecting the backside electrode, we deposit 5 m thick Parylene film, and define release holes on the
front side where air cavities are needed. Oxygen reactive ion etch (RIE) is used to etch through the
Parylene to form the release holes, and the sacrificial layer is removed by acetone through the release
holes. Then a second layer of Parylene film is deposited to seal the holes to finish the air-cavity
reflectors as well as to provide the transducer with electrical insulation for experiments with the
transducer immersed in liquid.
105

Figure 5.4 Brief fabrication steps.
5.4 Measurement and Results
We use a hydrophone to measure the acoustic field strength on the designed focal plane along
the bi-sector radius, when the device is immersed in DI water. As shown in Figure 5.5, the hydrophone
is held by a 3-axis positioner and can be adjusted for a linear scan along the bi-sector line. The
transducer is actuated by the signal generated from a function generator and amplified by a power
amplifier. Hydrophone captures the acoustic field in the water and we use an oscilloscope for readout.
106

Figure 5.5 Measurement setup. The hydrophone is mounted on the 3-axis positioner and connected
to the oscilloscope for readout.

Figure 5.6 Actual measurement setup and fabricated device. One sector is actuated during
measurement.

Figure 5.7 Measured normalized acoustic field in each sub-region.
107
By selecting different sub-regions to actuate, which corresponds with different focal point
location, we scanned a hydrophone over bi-sector lines on the designed focal plane. The results of the
normalized acoustic field are shown in Figure 5.7, which confirms the focal effect at different locations.
5.5 Summary
This chapter presents the design, fabrication and testing of a focused ultrasonic transducer
with electrically controllability over the focal point position on its focal plane. The focal point can be
tuned to multiple locations on the focal plane, each focal point being located along the central radius
of the designated sectors, at around 1.0mm away from the central point.
The transducer was immersed in water, and its acoustic pressure field was tested with a point
hydrophone. While electrically selecting an electrode sector for a particular focal position, we
measured the acoustic field, and obtained a focal effect along the bi-sector radius of the actuated sector
(1, 2 and 3mm off-centered from the central point), confirming the effectiveness of the focal point
controllability.

108
5.6 References
[131] L. Wang, C.-P. Liao, M. Gross, and E. S. Kim, "Self focusing acoustic transducer (SFAT) with
10-mm focal length for cancer-specific localized cytolysis of 3D cell spheroids in 3D Matrigel."
pp. 653-656.
[132] Y. Tang, and E. S. Kim, "Acoustic Droplet-Assisted Particle Ejection through and from
Agarose-Gel-Filled Petri Dish." pp. 64-67.
[133] C.-Y. Lee, W. Pang, S. C. Hill, H. Yu, and E. S. Kim, “Airborne particle generation through
acoustic ejection of particles-in-droplets,” Aerosol Science and Technology, vol. 42, no. 10, pp. 832-
841, 2008.
[134] C.-Y. Lee, H. Yu, and E. S. Kim, "Harmonic operation of acoustic transducer for droplet
ejection application." pp. 1283-1286.
[135] C.-Y. Lee, H. Yu, and E. S. Kim, “Nanoliter droplet coalescence in air by directional acoustic
ejection,” Applied physics letters, vol. 89, no. 22, pp. 223902, 2006.
[136] J. W. Kwon, H. Yu, Q. Zou, and E. S. Kim, “Directional droplet ejection by nozzleless
acoustic ejectors built on ZnO and PZT,” Journal of Micromechanics and Microengineering, vol. 16,
no. 12, pp. 2697, 2006.
[137] K. H. Lam, H. S. Hsu, Y. Li, C. Lee, A. Lin, Q. Zhou, E. S. Kim, and K. K. Shung, “Ultrahigh
frequency lensless ultrasonic transducers for acoustic tweezers application,” Biotechnology and
bioengineering, vol. 110, no. 3, pp. 881-886, 2013.
[138] L. Wang, Y.-J. Li, A. Lin, Y. Choe, M. E. Gross, and E. S. Kim, “A self-focusing acoustic
transducer that exploits cytoskeletal differences for selective cytolysis of cancer cells,” Journal
of microelectromechanical systems, vol. 22, no. 3, pp. 542-552, 2012.
[139] L. Zhao, and E. S. Kim, "Focused ultrasound transducer with electrically controllable focal
length." pp. 245-248.
109
Chapter 6 :
Immersive Acoustic Tweezers
6.1 Background
Optical tweezers offers trapping and tweezing of microparticles without any physical contact,
but is not capable of handling heavy and/or large particles without having to raise the light intensity
and consequent heat that damages temperature-sensitive particles such as living cells. On the other
hand, acoustic tweezers is capable of handling heavy and large particles due to the fact that it relies on
mechanical, not optical, waves that carries substantial amount of mechanical pressure or force. But no
acoustic tweezers has been reported to be able to trap and hold sub-mm particles in liquid.
Potential applications of acoustic tweezers include imaging cells or embryos in real time as
they grow, studying biomechanical properties of cells, and sorting cells based on size. The tweezers
can be used to stretch or compress a living cell to study cell deformability, adhesion, locomotion, etc.
For example, tumor or embryonic cells can be studied at individual cell level as to their biomechanical
properties and growth characteristics under controlled mechanical forces. Being able to test a single
living cell or microcluster at a time offers many avenues for furthering the knowledge about living
cells and their interactions with the host and the environment.
Tweezing is also possible with a magnetic tweezers, which requires that magnetic beads be
attached to the particle or cell for tweezing. In contrast, a focused acoustic beam offers superior
tweezing performance, including: (1) a large tweezing force can easily be obtained without appreciable
heating, since acoustic wave is basically a mechanical pressure wave; (2) the tweezers can work in all
kinds of liquid media whether transparent or not; (3) no conjugation, tagging or labeling is needed.
110
These unique properties make acoustic tweezers ideally suited to tweezing biological samples that are
larger than ten microns in diameter, in any kinds of media containing nutrients, reagents, etc.
Exploiting the unique advantages that acoustic tweezers offer, various types of acoustic
tweezers have been explored. Some ultrasonic manipulations of microparticles have relied on
ultrasonic standing waves formed between two solid surfaces [140]. In such cases, one of the two solid
faces transmits ultrasonic waves, while a second surface reflects the waves, producing the needed
standing waves. Such standing-wave-based “tweezers” often create multiple trapping points or
trapping lines, disposed in a periodic grid in 3D; consequently, it is not possible to move a single
particle on demand. One can design standing-wave tweezers such that they capture only one or a few
particles; however, the spacing between the two solid faces becomes very narrow, and the tweezers
must be moved around mechanically to capture a desired particle.

Figure 6.1 Conceptual diagrams of the transducer consisting of three sets of Fresnel lens (i.e., multi-
foci Fresnel lens). A symmetric lens in circumferential direction is needed to generate a focused beam,
and a pair of two sectors is chosen for a specific focal length, as illustrated in this diagram. Our
fabricated device has 3 pairs of the lens sectors for three focal lengths. In a) - c), the red pair denotes
the sectors that are actuated for a particular focal length. By driving different pairs, acoustic waves can
be focused at different focal lengths (as indicated with the perspective-view diagrams with liquid over
the transducer, at the upper row).
111
Another recent approach is to use a highly focused transducer to hold a lipid droplet that is
confined to a Mylar sheet in water [141]. In addition, surface acoustic waves (SAWs) have been used
to manipulate microparticles that are trapped and moved on a liquid surface (i.e., at the interface
between liquid and air), as pressure nodal points are formed by the standing waves confined on the
liquid surface [142]. On the other hand, the acoustic tweezers described in this thesis can tweeze live
cells (without damaging them) in 3D space without any label, a limitation on liquid type, or extra
needed component. It offers unique capability of tweezing live cells in 3D space without optical
tweezers’ force limitation and requirement for transparent media.

Figure 6.2 Top view diagram of a multi-foci Fresnel lens design with 18 evenly distributed
(circumferentially) sectors.
6.2 Device Design
The acoustic tweezers derives from a multi-foci focused acoustic transducer based on Fresnel
lens. As shown in Figure 6.1, the transducer consists three sets of Fresnel lens which are designed to
have focal lengths slightly away from one another (featuring focal lengths of 3.5, 5.0 and 6.5mm).
Three sets of Fresnel lenses are aligned on a PZT substrate to form the three different focal points on
the center line perpendicular to the substrate surface. When acoustic wave passes through the three
sets of Fresnel lens, the wave interferences will create a Bessel beam over a zone spanning the three
focal points. Consequently, negative axial radiation force is developed within the zone along the center
112
line where the three individual focal points are supposed to exist. The negative axial radiation force
establishes an energy well within the Bessel beam zone, where particle(s) can be trapped.

Figure 6.3 Cross-sectional schematic of a multi-foci Fresnel lens. Two sectors from different Fresnel
lenses are conceptually shown on right and left side of the transducer. The two Fresnel lenses focus
at different distance along the center line perpendicular to the lens surface. The Bessel beam zone is
developed due to the interference of the two focused acoustic beams. For each Fresnel lens, the
Fresnel band design is determined by the Equation (1).
To incorporate and align three sets of Fresnel lens, we divide the original full-circle Fresnel
lens into 6 sectors, with each sector occupying a pie shape with 20 degrees, unlike our earlier approach
[142]. The 6 sectors are evenly distributed over 360 degrees, with 40 degrees spacing between two
adjacent sectors (Figure 6.2). In this way, one Fresnel lens covers a total of 120 degrees (=6 x 20
degrees), so that we may be able to accommodate three Fresnel lenses with 20 degrees rotation
between each lens (to fill up the spacing). Both simulations and experiments show that the six groups
of the 18 sectored Fresnel lens need to be designed and operated symmetrically in circumferential
direction. With the same overall occupying area of Fresnel lens, the simulation shows the negative
axial radiation force is established only when the lens spread evenly around the circumference.
The transducer is based on a 1.02 mm thick PZT substrate with nickel layer sputtered on both
sides. Sectors of Fresnel lens are made on the front nickel electrode out of Parylene-sealed air-cavities.
Due to the acoustic-impedance mismatch between solid and air, the acoustic waves (generated by PZT)
113
are reflected where the air-cavities present [130]. The radii of the Fresnel-lens bands are determined
by [129] ( ),
4
n
n
f Rn

+ = where
n
R ,  , and f are the n
th
Fresnel band radius, wavelength, and
focal length, respectively (Figure 6.3).

Figure 6.4 Brief fabrication process for the tweezers.
114

Figure 6.5 Photos of a) Fresnel lens with 18 sectors before forming the air cavities; b) the lens at close-
up after forming the air cavities through the etch holes and c) the tweezers packaged with laser-cut
acrylic reservoir (on top of the tweezers) and 18 wires for electrical connections to the 18 sectors.

Figure 6.6 Transducer packaged with resavior. Instead of accessing all 18 sectors, we use only one
wire-out on the front side, in this design, to provide concise electrical connection.
6.3 Fabrication
A brief fabrication process is illustrated in Figure 6.4. We start with a 1.02mm thick PSI-5A4E
PZT sheet with nickel layer sputtered on both sides. The AZ5214 photoresist is coated for both front
and back sides for delineation of the electrode patterns, followed by patterning of the photoresists
with front-to-back alignment through a pre-defined dicing edge of the PZT sheet. After patterning
the nickel electrode with wet etchant, a second layer of photoresist is coated for a sacrificial layer in
forming air cavities for Fresnel lens. Then while protecting the backside electrode, we deposit a 6 m
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thick Parylene on the front side. Release holes are defined on the front side for forming air cavities
through photolithography, and oxygen reactive ion etch (RIE) is used to etch through the Parylene to
form the release holes. The sacrificial layer is removed by Acetone. A second layer of Parylene film is
deposited to seal the release holes to finish the air-cavity reflectors and also to provide the transducer
with electrical insulation for operating the transducer immersed in liquid. Two types of tweezers (one
with individually accessible sectors and the other with the sectors inaccessible individually) are
fabricated, and the finished transducers are shown in Figure 6.5. A laser-machined acrylic reservoir is
then attached to the tweezers for holding liquid and also providing sidewalls that reflect acoustic waves
(Figure 6.6).
6.4 Measurement and Results
The fabricated transducers with the acrylic reservoir are tested for particle trapping in a setup
shown in Figure 6.7. The reservoir packaged transducer is held by a 3-axis positioner stage which can
provide motion after the microparticle has been trapped. Polyethylene microspheres of 0.3 - 0.5 mm
in diameter and 1.0 g/cc in density are dispensed in water over the tweezers. All the Fresnel lens
sectors are driven with 2.07 MHz, 300 V pp pulsed sinusoidal signal at a pulse repetition frequency of
60 Hz, which is generated by function generator and amplified by power amplifier. A CCD camera is
attached to the stage for top-view videotaping over the transducer. Figure 6.8 shows photos taken at
different microsphere trapping stages with the tweezers being started right at 0 ms. During the
following continuous actuating period of the tweezers (up to 1,897 ms), only one microsphere (0.5
mm in diameter) is captured and firmly held at the trapping zone which is at 5.0 mm from the tweezers
surface, as expected, while other microspheres are dispersed away from the trapping zone. When the
tweezers is turned off, the trapped microsphere is released, and flows freely along with all the other
dispersed microspheres.
116

Figure 6.7 Schematics of the measurement setup for testing the acoustic tweezers with microspheres
dispersed in water within the acrylic reservoir. The transducer is driven by an amplified pulsed-
sinusoidal signal, and the video of the particle trapping by the acoustic tweezers is captured through a
CCD camera.

Figure 6.8 Photos taken at different times with polyethylene microspheres (0.5 mm in diameter) in the
reservoir over the tweezers. When the tweezers is actuated (right after 0 ms), all the microspheres
except one trapped microsphere at the center are pushed to the edges of the reservoir, and remain
there, while the tweezers holds exactly one microsphere at the trapping zone at the center (see the
photos from 207ms to 1897ms). When we stop the electrical actuation of the tweezers, the trapped
microparticle is released.
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6.5 Summary
This chapter describes the design, fabrication and testing of an acoustic tweezers that can trap
microparticles up to 0.5 mm in diameter through a 3-dimensional Bessel beam zone with energy well
formed in a bulk of liquid. The tweezers consists of three sets of Fresnel lens that individually features
a focal length of 3.5, 5.0 and 6.5 mm. A new approach of sectoring Fresnel-lens annular bands is used
to preserve the symmetry of the Fresnel lens while easily aligning the three sets of the lenses in position.

118
6.6 References
[129] D. Huang, and E. Kim, “Micromachined acoustic-wave liquid ejector,” Journal of
Microelectromechanical Systems, vol. 10, no. 3, pp. 442-449, 2001.
[130] C.-Y. Lee, H. Yu, and E. S. Kim, "Acoustic ejector with novel lens employing air-reflectors."
pp. 170-173.
[140] J. Wu, “Acoustical tweezers,” The Journal of the Acoustical Society of America, vol. 89, no. 5, pp.
2140-2143, 1991.
[141] J. Lee, S.-Y. Teh, A. Lee, H. H. Kim, C. Lee, and K. K. Shung, “Single beam acoustic trapping,”
Applied physics letters, vol. 95, no. 7, pp. 073701, 2009.
[142] Y. Choe, J. W. Kim, K. K. Shung, and E. S. Kim, “Microparticle trapping in an ultrasonic
Bessel beam,” Applied physics letters, vol. 99, no. 23, pp. 233704, 2011.

119
Chapter 7 :
Zebra Fish Embryo Trapping with Acoustic Tweezers
7.1 Background
Optical tweezers has been successful in scientific instruments over decades, as it offers
trapping and tweezing of microparticles without any physical contact by using highly focused laser
beams. However, the manipulating force from optical tweezers is on the order of piconewtons and
typically only capable of handling particles in micron-size. To handle heavy and/or large particles
using optical tweezers usually requires raising the laser intensity, which consequently brings heat effect
that possibly damages temperature-sensitive particles such as living cells. Acoustic tweezers, on the
other hand, is capable of handling heavy and large particles up to the order of mm in size, since it
relies on mechanical, instead of optical, waves that carries substantial amount of mechanical pressure
or force.
Tweezing is also possible with a magnetic tweezers, which requires that magnetic beads be
attached to the particle or cell for tweezing. In contrast, an acoustic tweezers offers the following
advantages: (1) a large tweezing force without appreciable heating, as acoustic wave is basically a
mechanical pressure wave; (2) the operability of the tweezers in all kinds of liquid media whether
transparent or not; (3) no conjugation, tagging or labeling needed. These unique properties make
acoustic tweezers ideally suited to tweezing biological samples that are larger than ten microns in
diameter, in any kinds of media containing nutrients, reagents, etc.
Our previously reported acoustic tweezers [143] had shown to be effective in trapping
polyethylene microspheres of 0.3-0.5mm in diameter and 1.0g/cc in density. This thesis describes our
recent acoustic tweezers capable of holding heavier and larger particles such as zebrafish embryos at
120
their 24 – 36 hours-post-fertilization, using our ideas to electrically tune the focal point of the focused
ultrasonic transducers [139, 144, 145].
7.2 Device Design
We reported an acoustic tweezers based on multi-foci self-focused ultrasonic transducer,
using the focusing idea illustrated in Figure 7.1 [145]. Constructive interference of generated ultrasonic
waves occurs at a designed location (along the central line of the Fresnel rings and perpendicular to
the transducer), where the acoustic pressure is magnified.

Figure 7.1 Full ring Fresnel lens transducer: (Top) Top view of full-ring Fresnel half-wave-band
electrodes (dark rings) on piezoelectric substrate (light square) and (Bottom) Cross-sectional view
showing how focusing effect occurs. Acoustic wave from the rings of the patterned electrodes
interfere constructively at a focal point leading to an intensified acoustic pressure.
Here, for a multi-foci self-focusing ultrasonic transducer, we sector Fresnel rings, and make
the sectors contribute to different focal lengths, as illustrated in Figure 7.2. The sectors are arranged
such that when the set of the sectored lens with the same focal length is actuated, the symmetry of

Piezoelectric Substrate
Fresnel Lens
121
acoustic field is preserved. For the acoustic tweezers, three sets of six sectored Fresnel rings are
designed for three different focal lengths along the central line perpendicular to the transducer surface.
When all the three sets are actuated, the acoustic waves interfere with each other to create a Bessel
beam over a zone spanning the three focal points. Consequently, negative axial radiation force is
developed within the zone along the center line where the three individual focal points are supposed
to exist. The negative axial radiation force produces an energy well within the Bessel beam zone, where
particle(s) can be trapped (Figure 7.2).

Figure 7.2 Top and cross-sectional schematics of a tweezers consisting of three sets of Fresnel zone
plate sectors for three different focal lengths: (top two figures) when one pair of the sectored Fresnel
is actuated and (bottom) when two such pairs are actuated at the same time. Trapping zone is
developed due to the interference of the two (or more) focused acoustic beams.

122
For the design of each set of the sectored Fresnel lens, we divide the original full Fresnel lens
into 6 sectors, with each sector occupying a 20º pie shape, unlike our earlier approach which makes
use of full rings [146]. The 6 sectors are evenly distributed over 360º with two adjacent sectors
occupying 40º (Figure 7.3). In this way, one set of sectored Fresnel lens covers a total of 120º (=
6×20º), leading to three sets of six sectored 20º Fresnel rings. For better symmetry of the resulting
acoustic field, one can use more sectors of smaller occupying angular degree for each set of the sectors.

Figure 7.3 Mask pattern of the top electrode of the acoustic tweezers with 3 sets of 6 sectored
electrodes for a total of 18 sectors of Fresnel-lens-patterned electrodes: one set of sectored Fresnel
lens covers a total of 120º, as each sector occupies 20º angular space.
We chose to use six 20º sectors (for each set of the three sets for three different focal lengths)
which were the minimum number needed for good circumferential symmetry according to simulation
and experiment. For a given overall area of Fresnel lens, the simulation shows that the negative axial
radiation force is established only when the lens spread evenly around the circumference.
Built on a 2.03 mm thick PZT substrate with nickel electrode on both sides, the transducer
produces acoustic waves most powerfully at its thickness resonance around 1.17 MHz. Sectors of
Fresnel air-cavity lens (made of Parylene-sealed air-cavities) are added to the top nickel electrode that
is patterned into a large circle (Figure 7.4). The bottom electrode is also patterned into a large circle

123
and aligned to the top electrode, so that when a voltage is applied between the top and bottom
electrodes, acoustic waves may be generated by the PZT. The acoustic impedance mismatch between
air and liquid makes the air-cavities be very effective in preventing the acoustic waves from
propagating from the PZT to liquid medium, as the acoustic waves are reflected where the air-cavities
present (Figure 7.4). For a desired focal length, the radii of the Fresnel-lens bands are designed with
( ),
4
n
n
f Rn

+ = where
n
R ,  , and f are the n
th
Fresnel band radius, wavelength, and focal
length, respectively. We chose the focal lengths for the 3 sets of sectored Fresnel lens to be 17.0, 18.5
and 20.0 mm, much longer than our previous work [142], as the ultrasound frequency is much lower
and provides a large trapping zone.

Figure 7.4 Cross-sectional view of a Fresnel lens based on air cavity showing that due to acoustic
impedance mismatch, the acoustic waves are reflected at the air/liquid interface. Acoustic waves are
generated where there are electrodes, and propagate only through the regions where there is not air
cavity.

7.3 Fabrication
Following a brief fabrication process illustrated in Figure 7.5, we start with a 2.03 mm thick
PSI-5A4E PZT substrate with nickel layer sputtered on both sides. The nickel is patterned into a
circular electrode (on both sides) of which area covers all the sectors, with front-to-back alignment
through a pre-defined dicing edge of the PZT sheet. After patterning the nickel electrode with wet

124
etchant, a thick layer of photoresist is coated and patterned to define the sacrificial layer in forming
air cavities for Fresnel lens. Then a 10 m thick Parylene is deposited on the front side while backside
electrode is protected by the tape. Release holes are then defined on the center of each air cavity torus
on top of the Parylene layer for etching away sacrificial photoresist to form the air cavities, and oxygen
reactive ion etch (RIE) is used to etch through the Parylene to form the release holes. The sacrificial
layer is removed by acetone. A second layer of Parylene film is deposited to seal the release holes and
also to provide the transducer with electrical insulation for operating the transducer immersed in liquid.
Figure 7.6 shows a photo of the fabricated transducer.

Figure 7.5 Brief fabrication steps for the acoustic tweezers.

Figure 7.6 Photo of a fabricated acoustic tweezers.

125
7.4 Experiment setup
The acoustic tweezers has been operated either horizontally or vertically as illustrated in Figure
7.7 with the tweezers immersed in liquid in an open reservoir. As the trapping zone is non-spherical
and extends along the transducer central line, the trapping capability differs as the tweezers is placed
horizontally or vertically.

Figure 7.7 Experimental setups for (Top) Horizontal operation and (Bottom) vertical operation.
The acoustic tweezers is powered by continuous sinusoidal signals generated from a function
generator and amplified by a power amplifier. A CCD camera is positioned to the side of the reservoir

126
for videotaping and image capturing. Microparticles in DI water are first used for tuning the frequency
and amplitude, confirming the location and trapping strength. When the operating parameters are
optimized, we replace the water with a culture solution of 3% methylcellulose and egg water (1:5 ratio),
which provides nutrition to keep the embryos alive.
Wild type zebrafish embryos are used for the trapping experiments. When the embryos are
incubated into desired stage (24 – 36 hours post fertilization), they are picked individually using pipette
and gently released into the reservoir with the culture solution. As the embryo has higher density than
the solution, it falls down due to gravity.
7.5 Results
Both horizontal operation and vertical operation have been carried out with the tweezers
actuated with a continuous sinusoidal signal. It turns out that there are resonances of the acoustic
waves in the liquid reservoir, which lead to a slight shift in the optimum operating frequency. During
the horizontal operation, the resonance occurs between the transducer and the liquid-air interface;
while during the vertical operation, the resonance occurs between the transducer and the solid sidewall
of the reservoir, as illustrated in Fig. 8.

Figure 7.8 Possible resonances in the liquid reservoir: (Left) A horizontally placed tweezers may
introduce resonance between the device surface and liquid surface, while (Right) a vertically placed
tweezers may introduce resonance between the device surface and solid sidewall of the reservoir,
making the optimum operating frequency shifted.

127
For horizontal operation, a continuous 10V pp, 1.169 MHz sinusoidal drive voltage is applied
to the tweezers to obtain trapping of a zebrafish embryo. Figure 7.9 shows photos taken at different
embryo trapping stages when the tweezers is placed horizontally. After releasing the embryo, the
embryo falls and gets trapped at 267 ms and held in the trapping zone firmly until the tweezers is
turned off. After the tweezers is turned off, the embryo falls freely again.
For vertical operation, a continuous 40V pp, 1.172 MHz sinusoidal drive voltage is applied to
the tweezers to obtain the trapping. Figure 7.10 shows photos taken at different embryo trapping
stages when the tweezers is placed vertically. After releasing the embryo, the embryo falls and gets
trapped at 1,836 ms and held in the trapping zone firmly until the tweezers is turned off. After the
tweezers is turned off, the embryo falls freely again.

128

Figure 7.9 (Top) Trapping and (Bottom) releasing a zebrafish embryo with the tweezers placed
horizontally.

129

Figure 7.10 (Top) Trapping and (Bottom) releasing of a zebrafish embryo with the tweezer placed
vertically.

130
7.6 Summary
This chapter describes the design, fabrication and testing of an acoustic tweezers working at
1.17MHz that can trap microparticles up to 1 mm in diameter, as well as late-term zebrafish embryos
at 24 - 36 hours after fertilization. The tweezers consists of three sets of sectored Fresnel lens that
individually have focal lengths of 17.0, 18.5 and 20.0 mm. Both horizontal and vertical operations of
the acoustic tweezers show capture and hold of a late stage zebrafish embryo that is about 1 mm in
diameter and 1.3 - 1.5 mg in weight, and is not spherical, nor homogeneous.

131
7.7 References
[139] L. Zhao, and E. S. Kim, "Focused ultrasound transducer with electrically controllable focal
length." pp. 245-248.
[142] Y. Choe, J. W. Kim, K. K. Shung, and E. S. Kim, “Microparticle trapping in an ultrasonic
Bessel beam,” Applied physics letters, vol. 99, no. 23, pp. 233704, 2011.
[143] L. Zhao, and E. S. Kim, "Acoustic tweezers for sub-MM microparticle manipulation." pp.
1088-1091.
[144] L. Zhao, and E. SokKim, "Focused Ultrasonic Transducer with Electrically Controllable
Focal-Point Location." pp. 1-3.
[145] Y. Tang, and E. S. Kim, "Electrical Tuning of Focal Size with Single Focused Ultrasonic
Transducer." pp. 1-4.
[146] Y. Choe, J. W. Kim, K. K. Shung, and E. S. Kim, "Ultrasonic microparticle trapping by multi-
foci Fresnel lens." pp. 1-4.

132
Chapter 8 :
Rotational Manipulation on Trapped Particle with Acoustic
Tweezers
8.1 Background
As already discussed in last chapter, acoustic tweezers has been developed to extend the
contactless tweezering capability and provide less limitation on heavy particle handling. Recently
reported acoustic tweezers [143, 147, 148] is capable of handling heavy and large particles up to the
order of mm in size, since it relies on mechanical, instead of optical, waves that carries substantial
amount of mechanical pressure or force.
Our previously reported acoustic tweezers [147] had shown to be effective in trapping
polyethylene microspheres up to 1 mm in diameter (1.0g/cc in density), as well as late-term zebrafish
embryos (24 - 36 hours after fertilization), in both horizontal and vertical operations of the acoustic
tweezers [147]. The capturing and holding of a late stage zebrafish embryo (1 mm in diameter and 1.3
- 1.5 mg in weight,) has demonstrated the effectiveness of the acoustic tweezers in handling non-
spherical, non-homogeneous living cells in biomedical application.
Electrically controllable manipulation of the particles or cells trapped by the acoustic tweezers
is highly desirable in many applications. For example, rotational control is one of the powerful
functions that will benefit researchers in cell imaging and/or real-time observation, as it allows the
researcher to orient the trapped particle in any desired way.
This chapter describes an on-demand rotation control with our recent acoustic tweezers
(capable of holding heavy and large particles such as mm-size polyethylene particles and zebrafish
133
embryos at their 24 – 36 hours-post-fertilization) obtained by setting a pair of the tweezers to face
each other and fine-tuning the driving frequency (1.07 MHz) by about 100 Hz.
8.2 Design and Simulations
The tweezers consists of two identical acoustic transducers. The single transducer is designed
to deliver multiple focal points along the center line and thus create Bessel beam zone where the
energy well develops. The radially-inward radiation force around the zone surrounding the multiple
focal points lowers the acoustic potential energy in the zone. Consequently, when a moving particle
passes by the zone, it gets trapped if the kinetic energy of the particle is smaller than the depth of the
potential energy well.
8.2.1 Design of Single Acoustic Transducer
A single acoustic tweezers with multiple focal points is made with Fresnel-zone-plate air-cavity
lens over a 2.03 mm thick lead zirconate titanate (PZT) substrate (sandwiched by a pair of patterned
electrodes to produce acoustic waves through thickness-mode vibration, most powerfully at 1.07
MHz). Air cavities are used to form the Fresnel lens, since the large acoustic impedance mismatch
between air and liquid produces excellent reflection, and consequently, no waves propagate through
the regions that are covered by air cavities[130]. Fresnel zone plate is typically consisted of annular
rings, as a set of full-ring Fresnel-zone-plate air-cavity lens allows passing of only the acoustic waves
that will result in constructive wave interference at a focal point [129]. The focal point of a Fresnel
zone-plate is along the line perpendicular to the center of the annular ring (Figure 8.1).
134

Figure 8.1 Full ring Fresnel lens transducer: (Left) Top view of full-ring Fresnel half-wave-band
electrodes (dark rings) on piezoelectric substrate (light square) and (Right) Cross-sectional view
showing how focusing effect occurs. Acoustic waves from the rings of the patterned electrodes
interfere constructively at a focal point leading to an intensified acoustic pressure [134].
To create multiple focal points along the same central line, annular rings of Fresnel air cavities
are sectored into pie shapes with the different sectors designed for different focal lengths (Figure 8.2).
To preserve the symmetry of the acoustic field, the full ring is sectored and distributed evenly
throughout 360º. For 3 focal points, each focal length is covered by the sectors occupying a total of
120º. For this design, 6 sectors with each sector occupying 20º are used for a focal length, and three
sets of such sectors are used for 17.0, 18.5 and 20.0mm focal lengths.

Piezoelectric Substrate
Fresnel Lens
135

Figure 8.2 Top and cross-sectional schematics demonstrating the generation of multi focal points from
sectored Fresnel lens (for three different focal lengths): a) and b) when one pair of the sectored Fresnel
is actuated; c) when two such pairs are actuated at the same time. Multi focal points and Bessel beam
zones are developed due to the interference of the two (or more) focused acoustic beams.

Figure 8.3 Pattern of the active ultrasonic source after filtered by Fresnel lens. A total 18 sectors are
arranged in 3 sets of 6 pi-shaped sectors: one set of sectored Fresnel lens covers a total of 120º, as
each sector occupies 20º angular space. Three sets are featuring at 17.0, 18.5 and 20.0 mm focal lengths
separately.
FEM simulation has been carried out with COMSOL to study the pressure distribution in the
medium. As shown in Figure 8.4, a major high pressured region is developed along the central vertical
line near the designed 3 focal points at 17.0, 18.5 and 20.0 mm. Satellite high pressure zones around
the major focal zone provide acoustic potential barriers to get particles trapped in the less pressured
region.

136

Figure 8.4 Simulated normalized absolute pressure produced by a single transducer shown in Figure
8.3. (a) on cross-sectional plane along the central vertical line (with the transducer placed at the bottom)
and (b) on the focal plane at 18.0 mm.
8.2.2 Design of the Acoustic Tweezers
A pair of two acoustic transducers (based on the sectored air-cavity Fresnel lens shown in
Figure 8.3, and fabricated in the steps shown in Figure 8.8) is placed in parallel and aligned to the
central line, with the air-cavity lenses facing each other (Figure 8.5). The distance between two
transducers and the rotation angel along the central line is finely tuned for best trapping zone
formation. A resonant chamber is formed between the two transducers which can be used to enhance
the trapping force. The location and size of the trapping zone is defined by the tweezers’ frequency
and the resonant chamber. When the two transducers are aligned with a rotational offset on the sector
designs (such as illustrated in Figure 8.5 (c)), the symmetricity in the resonant chamber breaks, and
consequently, the trapping zone moves to a non-central place. A trapping zone is where a lower
pressure region is developed within a higher-pressure region, as shown in Figure 8.6. The
asymmetricity causes the higher-pressure region (the potential barrier) to appear differently on two
sides of the trapping zone, providing the possibility of creating control over the trapping zone

a) b)
137

Figure 8.5 Schematics showing the formation of paired transducers as acoustic tweezers, placed in
parallel to each other. a) a pair of two sectored transducers aligned at the central line, with Fresnel lens
facing each other; b) two transducers with 0º rotation offset on the central line and c) two transducers
with 30º rotation offset on the central line.
When a fine tuning of the operating frequency is applied on the tweezers, a minute change of
the trapping zone topology is induced, which in turn affects the balanced trapping state. Figure 8.6
and Figure 8.7 show the simulated change of the pressure distribution, and thus the trapping zone
when the frequency is tuned from 1.070 MHz to 1.072 MHz. Both the location and intensity of the
potential barrier respond to the frequency change, as the center of the trapping zone moves up a bit.
During the tuning, the trapping zone goes through a dynamic re-stabilization process, generating a
force to manipulate the trapped particle to move/situate to the re-established trapping zone. If the
trapped particle is not spherical and homogenous, the force is possible to exert a torque to rotate the
particle to maintain a minimum potential energy in the newly developed trapping zone, creating a
repeatable controllability on the rotation of the particle.
When the tweezers is horizontally placed, the gravity of the particle becomes part of the
unbalanced and asymmetric force, creating easier condition to for trapped particle to rotate.

138

Figure 8.6 Simulation result of normalized absolute pressure distribution of the acoustic tweezers
formed by the two transducers placed as depicted in Figure 8.5 (c) with a separation distance of 36
mm and a rotation offset of 30º. a) and b) show the pressure distribution on major trapping zone
plane at 18.4 mm above bottom transducer (17.6 mm to the top transducer), when the transducers are
driven at 1.070 and 1.072MHz, respectively. c) and d) show the pressure distribution on the cross-
sectional plane along the central line, when the transducers are driven at 1.070 and 1.072MHz,
respectively

139

Figure 8.7 Simulated normalized pressure along the central line from the one transducer surface to the
other. Top figure shows the pressure when both transducers are driven at 1.07 MHz. and bottom
figure shows the pressure when driven at 1.072 MHz. The slight change on the trapping zone when
frequency shifts leads to the manipulation of the trapped particle.
8.3 Fabrication
As illustrated in the brief fabrication process shown in Figure 8.8, we use a 1.03mm thick PZT
with nickel layer on its both sides as the substrate to start with. Photoresist is spin-coated for both the
front and back sides for the electrode patterning, followed by a wet-etching nickel layer to form the
actual electrode. A second layer of photoresist is coated as a sacrificial layer in forming air-cavity
reflectors. Then, while protecting the backside electrode, we deposit 5 m thick Parylene film, and
define release holes on the front side where air cavities are needed. Oxygen reactive ion etch (RIE) is
used to etch through the Parylene to form the releasing holes, and the sacrificial layer is removed by
acetone soaking through the holes. Another layer of 5 m thick Parylene film is deposited to seal the

140
releasing holes and provide electrical insulation to the transducer. Figure 8.9 shows the photo of a
packaged single transducer.

Figure 8.8 Brief fabrication flow.

Figure 8.9 Photo of the fabricated transducer.

141
8.4 Experiment and Result
8.4.1 Experiment Setup
The setup for the rotational control experiment is shown in Figure 8.10, as the tweezers is
composed to two transducers placed vertically. One transducer is fixed while the other one can be
positioned manually for precise spacing and central line alignment.

Figure 8.10 Setup for the rotation control experiment. Two transducers are vertically placed in the
water.
8.4.2 Polyethylene Particles
A 3.7 cm separation distance and a 30º rotation offset are arranged between two single
transducers, and both of the transducers are driven at 1.1689 MHz with 38 V pp continuous sinusoidal
wave. A dot-marked (red dot colored on background green as an indicator of rotation) polyethylene
sphere of 1 mm in diameter is first injected to the vicinity of the trapping zone by a pipette. After the
sphere gets captured firmly, we tune the driving frequency of the tweezers up from 1.1689 to 1.1691
MHz, and observe that the sphere moves slightly downward, starting to rotate. After the dynamic

142
rotation process, where the sphere gains its 90-degree rotation, the sphere moves back upward again,
re-captured. When the frequency is increased further to 1.1693 MHz, the sphere is observed to rotate
an additional 90 degree (Figure 8.11). When the frequency is tuned back to 1.1689 MHz from 1.1693
MHz, backward rotations are observed (Figure 8.12).

Figure 8.11 Photos showing the rotational manipulation on a half-colored (half green and half red)
polyethylene sphere of 1 mm in diameter: a) the sphere is released and soon trapped in a trapping
zone of the acoustic tweezers; b)-e) by changing the frequency (applied to the tweezers) from 1.1689
MHz to 1.1691 MHz, the trapped sphere rotate around 90 degree, as the red half rotates from left side
to down side; f)-i) by changing the frequency from 1.1691 MHz to 1.1693 MHz, the sphere rotate
additional 90 degree, as the red half rotates from down side to right side.

Figure 8.12 The trapped half-colored sphere rotates back when frequency is reversed from 1.1693
MHz back to 1.1689 MHz.

143
8.4.3 Zebrafish Embryo
For manipulation of a zebrafish embryo which is much heavier than the polyethylene sphere,
we increase the driving voltage to 40 V pp and tune the frequency to 1.1730 MHz for a better trapping
effect. After the embryo is captured, successful rotational manipulation is observed during a slight
lowering of the driving frequency from 1.1730 to 1.1726 MHz (Figure 8.13).

Figure 8.13 Rotational manipulation on a 24-36 hours-post-fertilization zebrafish embryo. Rotation is
observed when the frequency (applied to the acoustic tweezers) is slightly lowered from 1.1730 to
1.1726 MHz.
8.5 Summary
This chapter shows that we have obtained an electrical control on the rotation of a trapped
particle or cell with a pair of two acoustic transducers that can trap particles up to 1 mm in diameter,
as well as late-term zebrafish embryos at 24 - 36 hours after fertilization, by tuning the frequency
applied to both of the transducers. Each of the transducers consists of three sets of sectored Fresnel
lens that individually have focal lengths of 17.0, 18.5 and 20.0 mm. Our experiments show that a
trapping of mm-sized particle is achieved at around 1.17 MHz driving frequency, while tuning of the

144
frequency by about 100 Hz generates on-demand rotational manipulation. The angular manipulation
has been effective in rotating mm-size polyethylene particles and 24 – 36 hours-post-fertilization
zebrafish embryos that are 1.3 – 1.5 mg in weight.

145
8.6 References
[129] D. Huang, and E. Kim, “Micromachined acoustic-wave liquid ejector,” Journal of
Microelectromechanical Systems, vol. 10, no. 3, pp. 442-449, 2001.
[130] C.-Y. Lee, H. Yu, and E. S. Kim, "Acoustic ejector with novel lens employing air-reflectors."
pp. 170-173.
[134] C.-Y. Lee, H. Yu, and E. S. Kim, "Harmonic operation of acoustic transducer for droplet
ejection application." pp. 1283-1286.
[143] L. Zhao, and E. S. Kim, "Acoustic tweezers for sub-MM microparticle manipulation." pp.
1088-1091.
[147] L. Zhao, and E. S. Kim, "Acoustic tweezers for trapping late-stage zebrafish embryos." pp.
57-60.
[148] Y. Tang, and E. S. Kim, "Acoustic tweezers based on linear fresnel lens with air cavities for
large volume particle trapping." pp. 763-766.

146
Chapter 9 :
Immersive Micro-propeller
9.1 Background
Immersive micro-propeller has potential applications in drug delivery, microfluidics, robotics,
etc. A quasi-static propeller with no moving parts is desired in microfluidic systems and/or in systems
where any mechanical damage as well as wear and tear have to be minimized. Ultrasonic propeller is
based on focused ultrasound capable of producing acoustic streaming and requires no moving parts.
A micro-propeller based on focused ultrasound has been reported to have a thrust ratio of 19:1 (i.e.,
thrust force over the weight). However, it produced a thrust force only in one direction. Electrical
controllability over its propulsion direction is highly desirable for the propeller to navigate around in
liquid. This thesis presents a novel design for highly efficient, immersive, propeller with electrical
controllability of the propulsion direction.
9.2 Design
The transducer is built on a PZT with sectored Fresnel lens on the PZT’s one surface. The
PZT produces longitudinal acoustic waves, which pass through the sectored Fresnel lens designed to
allow only the acoustic waves (that would constructively interfere at the focal point) to pass through.
Acoustic streaming effect from the focused ultrasound pushes the medium where the transducer is
immersed and propels the transducer in the direction opposite to the wave propagation direction.
When the Fresnel lens is made of fully annular rings, the lateral propulsion forces cancel each
other out, leading to a thrust force perpendicular to the lens surface. However, when the annular rings
are sectored into pie shape and the actuation on one sector is weaker or stronger than the other
147
sector(s), there exists unbalanced propulsion force, which thrusts the transducer in a direction that is
not perpendicular to the surface. By controlling the actuation amplitudes on the sectors, the
propulsion direction can be electrically controlled, as the ratio of the lateral and perpendicular thrust
is varied. With sectors of Fresnel lens with different focal lengths, the thrust torque can also be
changed due to the unequal arm, making it possible for the propeller to rotate itself when it is fully
suspended in liquid without any wire hindering the rotation.
We designed a micropropeller to be built on a 1.02 mm thick PZT substrate (having a
fundamental thickness-mode resonance at 2.25 MHz), with 18 sectors of individually accessible
Fresnel lens that are composed of Parylene air-cavity-reflectors. The 18 sectors of Fresnel lens are
designed in 3 symmetric groups with different focal lengths. Upon actuation, intensified acoustic
intensity is delivered at the transducer’s focal point in liquid medium, where acoustic streaming effect
pushes the medium and propels the transducer in the opposite direction of the wave propagation. As
the sectors do not have the circular symmetricity of the Fresnel annular-ring patterns, when the sectors
(or a pair of the sectors) are driven unequal voltages, the lateral propulsion forces do not cancel each
other, resulting in a directional thrust. Thus, the direction of the propulsion can be controlled in either
by selecting different sectors or by varying applied voltage level. A large air-reflector is added on the
backside of the PZT (the side opposite to the front side where the sectors of the Fresnel lens are
formed), in order to prevent any propulsion from the backside that may cancel the propulsion from
the front side.
9.3 Fabrication
As illustrated in the brief fabrication process shown in Figure 9.1, we use a 1.03mm thick PSI-
5A4E PZT with nickel layer sputter-deposited on its both sides as the substrate to start with.
Photoresist is spin-coated for both the front side and backside for electrode patterning. During
148
photolithography, front-to-backside alignment is done by aligning at a pre-defined dicing edge of the
PZT substrate. The sectored electrodes (with its sub-regions) are patterned on the front side. After
wet-etching the nickel layer, a second layer of photoresist is coated for a sacrificial layer in forming air
cavities which block unwanted acoustic waves and form the sectored Fresnel lens pattern. Then, while
protecting the backside electrode, we deposit 5 m thick Parylene film, and pattern release holes on
the front side where air cavities are needed. Oxygen reactive ion etch (RIE) is used to etch the Parylene
to form the releasing holes, and the sacrificial layer is removed by acetone through the release holes.
Then a second layer of Parylene film is deposited to seal the holes to complete the air-cavity reflectors
as well as to provide the transducer with electrical insulation for liquid immersive operations. The
finished transducer is shown in Figure 9.2.

Figure 9.1 Brief fabrication steps.
149

Figure 9.2 Photo of a finished transducer.
9.4 Measurement
The fabricated propeller is tested in water with a flexible wire suspending the device (Figure
9.3). Upon actuation, the propeller is pushed to leave its equilibrium position to reach a new position
with certain angle to the ground. The gravity and the force along the flexible wire will cancel out the
thrust force, so that by measuring the gravity and the angle we can back-calculate the thrust force. In
this way we characterize the thrusts under different driving conditions when the thrust is perpendicular
to the device. Once we know the perpendicular thrust, we change the condition to actuate only one
sector to characterize the lateral thrust for the sector under certain condition.
150

Figure 9.3 Photos of the propeller (suspended with a wire) being propelled. From the measurement,
the direction of the propulsion can be measured.

Figure 9.4 Photos showing the propeller turning to the right or left due to the directional thrust.
9.5 Results
A maximum perpendicular thrust of 13.8mN is measured under 80Vpp driving voltage with
all sectors on, while a maximum lateral thrust of 2.1mN is measured under 80Vpp voltage with a single
sector on. With all the sectors actuated, the net thrust will be perpendicular. By actuating a selected
sector alone, directional thrust is exerted to make the transducer turn left or right (Figure 9.4).
151
9.6 Summary
This chapter presents the design, fabrication and demonstration of a 2.25MHz ultrasonic
underwater propeller with 18 sectors of sectored Fresnel lens. Each sector can be driven individually
so that we may be able to introduce unbalanced lateral thrust in order to create directional propulsion
when only one sector is actuated, or each sector of the many sectors is driven with different voltage.
The fabricated propeller is tested and characterized in water while suspending the propeller
with a wire. A maximum perpendicular thrust of 13.8mN is measured under 80Vpp driving voltage
with all sectors on, while a maximum lateral thrust of 2.1mN is measured under 80Vpp voltage with
a single sector on.

152
Chapter 10 :
Conclusions and Future Directions
This thesis presents studies on magnet modeling and the application of this analytic modeling
in magnetic spring for low frequency optimization in vibrational energy harvester. The proposed
analytical model for permanent magnets has better accuracy over the existing models. By using this
model, we are able to analyze the magnetic spring’s frequency dependencies over several conditions
and optimize the design of magnetic spring in vibrational energy harvester to achieve maximum power
delivery.
Moreover, this thesis shows the demonstrations of several devices and concepts that advances
the focused ultrasonic transducer and extends the application of the focused ultrasonic transducer.
The demonstrated devices included controllability over focused ultrasonic transducer’s focal length
and focal location, the application as acoustic tweezers and the application of micro-propeller. Those
devices were conceptualized, designed, modeled, fabricated, and experimentally verified.
Proposed future directions for vibrational energy harvester that uses the magnetic spring are:
1) since the moving range of the magnets could be considerably large when the energy harvester is
equipped on human body, an optimization of coil and magnets arrangement can be pursued to add
more coil on the magnet traveling path but with less turns (to control the resistance); and 2) a power
management system that has load matching functionality that maximize the delivery of power to
consumer components/subsystems.
Proposed future directions for focused ultrasonic transducer with focal controllability are: 1)
using arrays of current single transducer design to achieve multiple focal points control; 2) employ
153
phased array approach on concentric equal-width ring design to extend focal length controllability or
to use it as acoustic tweezers with motion control.
Finally, proposed work on the micro-propeller is to add a control system to deliver unbalanced
thrusting control signal to the propeller to achieve the smart steering. Next step tasks include: 1)
development of micro-sized power management chip that delivers high voltage power to the propeller;
2) wireless delivery of power and wireless communication; 3) automation system or feedback system
on controlling of motion; 4) packaging technique of the propeller.

154
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Abstract (if available)

Abstract This thesis presents two separate topics. Chapter 2 and 3 discuss the modeling and optimization of magnetic spring which is used in electromagnetic vibration energy harvester that enables ultra-low resonant frequency of several hertz to the harvester. Chapter 4 to 9 cover several types of ultrasonic-transducer-based devices including acoustic tweezers, micro-propellers, and focused ultrasonic transducer with controllability on its focal length and location.

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Asset Metadata

Creator Zhao, Lurui (author)

Core Title Magnetic spring in electromagnetic vibration energy harvester and applications of focused ultrasonic transducer

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 04/19/2021

Defense Date 03/16/2021

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag acoustic tweezers,energy harvester,magnetic spring,micro-propeller,OAI-PMH Harvest,ultrasonic transducer

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Kim, Eun Sok (committee chair), Armani, Andrea (committee member), Wu, Wei (committee member)

Creator Email luruizha@usc.edu,zhaoluruia@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-447197

Unique identifier UC11668578

Identifier etd-ZhaoLurui-9493.pdf (filename),usctheses-c89-447197 (legacy record id)

Legacy Identifier etd-ZhaoLurui-9493.pdf

Dmrecord 447197

Document Type Dissertation

Rights Zhao, Lurui

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA