ADVANCED SENSING TECHNOLOGIES: FROM VANADIUM DIOXIDE MEMS

RESONATORS TO POLYPROPYLENE FERROELECTRET NANOGENERATORS

By

Yunqi Cao

A DISSERTATION

Submitted to

Michigan State University

in partial fulfillment of the requirements

for the degree of

Electrical Engineering – Doctor of Philosophy

2019

ABSTRACT

ADVANCED SENSING TECHNOLOGIES: FROM VANADIUM DIOXIDE MEMS

RESONATORS TO POLYPROPYLENE FERROELECTRET NANOGENERATORS

By

Yunqi Cao

This thesis presents fundamental and applied research studies designed to enable smart

material-based advanced sensing technologies including the use of vanadium dioxide (VO2)

thin films in resonant frequency tuning methods, and the self-powering/energy harvesting

capabilities of polypropylene ferroelectret (PPFE) polymers. The large compressive stress

generated from VO2 thin films during its insulator-to- metal transition (IMT) has been in-

vestigated in recent years for thermally actuated MEMS actuators. This same mechanism

can be used to generate axial stress that produces large shifts in resonant frequencies. Nev-

ertheless, taking full advantage of all benefits of this technique for tunable devices requires

a fundamental understanding of the mechanisms involved and the influences of different

parameters; such as structural aspect ratios, boundary conditions, buckling status, and ac-

tuation methods.

In this work, VO2-based MEMS bridge and cantilever resonators were

developed, and their resonant frequency shifts were characterized with respect to these pa-

rameters. It is found that residual thermal stress during the fabrication process is responsible

for different buckling states in bridge structures. Bi-directional tuning for a monotonic input

is observed in pre-buckled structures, which is related to bending moments and actuation

methods. A ferroelectret nanogenerator is also introduced in this work as a new tuning

technique to provide a programming current that allows fast switching between different

resonant frequency states. This demonstrates the potential use of self-powered tuning actu-

ation of MEMS resonators. Studies of VO2-based resonators on the power consumption and

the device time constant also pave the way for integrating MEMS devices with piezoelectric

energy harvesters as impact sensors.

With the goal of enabling self-powered sensing technologies, a series of studies designed

to understand the parameters that determine the electromechanical coupling in ferroelec-

tret nanogenerators are presented. The electromechanical response of the active material is

analyzed based on fundamental working principles of dipole moments. A lumped model is

proposed, which is developed from constitutive equations and validated with experiments.

The robustness of the device is verified through a series of tests including mechanical re-

peatability, thermal stability, and humidity resistance. The energy conversion efficiency and

maximum power transfer condition are determined under periodic mechanical input, and

a complete energy harvesting system with a fully integrated power management circuit is

proposed for providing DC power output to effectively charge lithium-ion batteries or power

small electronics.

To those who always support, encourage, and trust me.

iv

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

CHAPTER 1

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Problem Description and Motivation . . . . . . . . . . . . . . . . . . . . . .
1.2 Thesis Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Overview of Research Contributions . . . . . . . . . . . . . . . . . . . . . . .
1.4 Dissertation Outline
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1 MEMS Resonators
2.2 Frequency Tuning Technologies

CHAPTER 2 BACKGROUND . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Post Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Electrical Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Electrostatic Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.4 Electrothermal Tuning . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.5 Photothermal Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.6 Piezoelectric Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . .
Stress Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.7
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Insulator-to-Metal Transition . . . . . . . . . . . . . . . . . . . . . .
2.3.1
2.3.2
Structural Phase Transition . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Vanadium Dioxide Synthesis . . . . . . . . . . . . . . . . . . . . . . .
2.4 Flexible Physical Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Resistive Physical Sensors . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 Capacitive Physical Sensors
. . . . . . . . . . . . . . . . . . . . . . .
Self-Powered Physical Sensors . . . . . . . . . . . . . . . . . . . . . .
2.4.3
2.5 Nanogenerator-based Energy Harvesters
. . . . . . . . . . . . . . . . . . . .
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.3 Vanadium Dioxide

CHAPTER 3 DESIGN, FABRICATION OF VANADIUM DIOXIDE MEMS RES-

ONATORS AND FERROELECTRET NANOGENERATORS . . . .
3.1 Fabrication of VO2 based MEMS Resonators . . . . . . . . . . . . . . . . . .
3.1.1 Fabrication Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Buckling States in VO2 MEMS Resonators with Bridge Structures . .
3.1.3 Effect of Residual Axial Stress . . . . . . . . . . . . . . . . . . . . . .
3.2 Fabrication of Ferroelectrect Nanogenerators . . . . . . . . . . . . . . . . . .
3.2.1 Fabrication of Polypropylene Ferroelectrect Films . . . . . . . . . . .
3.2.2 Piezoelectric Effect and Multilayer Devices . . . . . . . . . . . . . . .

v

1
8
11
11
12

14
14
16
17
19
20
21
22
23
23
25
26
27
27
29
30
31
32
34
36

38
38
38
42
45
50
50
52

3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

CHAPTER 4

58
59
60
61
62
64
65
65
68
70
71
74
77
78
81
81
82
87
88
91

4.3 Stress Interfaces in Bridge Structure

INFLUENCE OF VO2 THIN FILM COATINGS ON THE PER-
FORMANCE OF MEMS RESONATORS . . . . . . . . . . . . . . .
4.1 Experimental Setups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . .
4.2 Comparison of Different Structures
4.2.1 Observations of Different Frequency Shifts . . . . . . . . . . . . . . .
4.2.2
Stress Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3 FEM Simulation of Two Ends . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . .
4.3.1 Bending moment in the up-buckled beam . . . . . . . . . . . . . . . .
4.3.2 Bending moment in the down-buckled and bell-shaped beam . . . . .
4.4 Power Consumption of Programming Resonant Frequency . . . . . . . . . .
4.4.1 Determining Device Time Constant . . . . . . . . . . . . . . . . . . .
4.4.2 Frequency Programmability In Cantilevers . . . . . . . . . . . . . . .
4.4.3 Frequency Programmability in Bridges . . . . . . . . . . . . . . . . .
4.4.4 Monitoring Brain Injury in Contact Sports . . . . . . . . . . . . . . .
. . . . . . . . . . . . .
4.5.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.2 Bandwidth Tunability for Bridges . . . . . . . . . . . . . . . . . . . .
4.5.3 Bandwidth Tunability for Cantilevers . . . . . . . . . . . . . . . . . .
4.5.4 Bandwidth Tunability Comparison . . . . . . . . . . . . . . . . . . .
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.5 Enabling Tunable Micromechanical Bandpass Filters

CHAPTER 5 UNDERSTANDING DYNAMIC RESPONSES IN FERROELEC-

96
TRET NANOGENERATORS . . . . . . . . . . . . . . . . . . . . .
96
5.1 Electromechanical Response of Ferroelectret Nanogenerator . . . . . . . . . .
97
5.1.1 Derivation of Electric Output
. . . . . . . . . . . . . . . . . . . . . .
99
5.1.2 Characterization of Electric Output under Sinusoidal Pressure Input .
5.1.3 Characterization of Electric Output under Linear Pressure Input . . . 102
5.1.4 Lumped Parameter Model for Electric Responses
. . . . . . . . . . . 104
5.1.5
Instruments with Different Internal Resistances and Sampling Rates . 106
5.1.6 FENG-based Tactile Sensor
. . . . . . . . . . . . . . . . . . . . . . . 109
5.1.7 FENG-based Micro Robot Arm Controller . . . . . . . . . . . . . . . 112
5.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

CHAPTER 6 FERROELECTRET NANOGENERATOR BASED SELF-POWERED

BENDING SENSOR . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.1 Analysis of Piezoelectricity Under Bending Test . . . . . . . . . . . . . . . . 116
6.1.1 Current Output Under Bending Test . . . . . . . . . . . . . . . . . . 117
. . . . . . . . . . . . . . . . . . 120
6.1.2 Voltage Output Under Bending Test
6.2 Characterization of Piezoelectricity Under Bending Test . . . . . . . . . . . . 120
121
6.2.1 Open Circuit Voltage and Short Circuit Current Under Bending Test
6.2.2 Different Evaluation Methods Under Bending Test . . . . . . . . . . . 127
. . . . . . . . . . . . . . . . . . 130

6.3 Application of PPFE-based Bending Sensor

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6.3.1 Device Robustness
6.3.2 Athletic Assessment

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
. . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

CHAPTER 7 FERROELECTRET NANOGENERATORS FOR SELF-POWERING

SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.1 Power Output of FENG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.1.1 Materials and Experimental Procedures . . . . . . . . . . . . . . . . . 136
7.1.2 Characterization of Electric Output . . . . . . . . . . . . . . . . . . . 138
7.1.3 Energy Conversion Efficiency . . . . . . . . . . . . . . . . . . . . . . 143
7.2 Power Management System . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
7.2.1
Integrated Energy Harvesting System . . . . . . . . . . . . . . . . . . 145
7.2.2 Operation of Energy Harvesting Module . . . . . . . . . . . . . . . . 147
7.2.3 Demonstration of Powering Commercial Electronics . . . . . . . . . . 150
7.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

CHAPTER 8 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
8.1 Summary of Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
8.2 List of Problems Solved in This Thesis . . . . . . . . . . . . . . . . . . . . . 154

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

vii

LIST OF TABLES

Table 2.1 A comparison of quartz crystal and SiTime’s silicon MEMS resonators[28].

16

Table 3.1 Properties of the materials used in FEM simulation, properties of SiO2
and Pt are taken from COMSOL, and the property of VO2 is taken from
the literature[118, 119].

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

Table 4.1 Relative frequency change for coated and uncoated cantilever beams with

different lengths. The phase transition region is from 65◦C to 85◦C.

. . .

62

Table 4.2 Relative frequency change for coated and uncoated bridge beams with
different lengths. The Phase transition region is from 62◦C to 85◦C for
the 300 µm and 65◦C to 85◦C for the others.

. . . . . . . . . . . . . . . .

Table 4.3 Evaluation of the impact

. . . . . . . . . . . . . . . . . . . . . . . . . . .

Table 4.4 Bandwidth tunability for bridges . . . . . . . . . . . . . . . . . . . . . . .

Table 4.5 Bandwidth tunability for cantilevers . . . . . . . . . . . . . . . . . . . . .

62

80

86

87

Table 7.1 Power delivery under different loads . . . . . . . . . . . . . . . . . . . . . 142

viii

LIST OF FIGURES

Figure 1.1 Resistance of continuous VO2 film as a function of temperature during

a full heating and cooling cycle [1].

. . . . . . . . . . . . . . . . . . . . .

Figure 1.2 Crystal structure of VO2 in rutile phase (left) and monoclinic phase

(right). [3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 1.3 The resonant frequency of a 250 µm VO2-based MEMS bridge as a

function of temperature during a full heating and cooling cycle.

. . . . .

Figure 1.4 The resonant frequency of a 300 µm VO2-based MEMS bridge as a
function of temperature during a full heating and cooling cycle, where
a turning point is observed at around 75 ◦C. . . . . . . . . . . . . . . . .

Figure 1.5 Programming resonant frequency of VO2-based MEMS resonator through

electric pulse generated by FENG [20].

. . . . . . . . . . . . . . . . . . .

Figure 1.6 Piezoelectricity of FENG. Working principle of ferroelectric nanogen-
erator: (a) no external stress is applied. (b) when external boundary
load is applied, the polarization field due to internal dipoles decreases
and free induction charges is accumulated on metal electrodes. (c) FEM
results of changes in electrode potential at the polymer-metal boundary
and open circuit voltage arise from accumulated charges.

. . . . . . . . .

Figure 1.7

(a) A complete energy harvesting system for converting random me-
chanical energy to DC electric output for battery charging.
(b) AC
electric output generated from FENG device. (c) DC electric output
delivered from the power management system to system load.

. . . . . .

1

2

4

5

6

7

9

Figure 2.1 Timeline of growing f · Q product, a common figure of merit of res-

onators, from 1990 to 2010 [26].

. . . . . . . . . . . . . . . . . . . . . . .

15

Figure 2.2 Examples of post-fabrication techniques:

(a) Selective deposition of
polysilicon on a comb-drive resonator[34]. (b) Two big PLD gold pieces
from two-layer shots deposited on the surface of a microresonator[35].
(c) Device after FIB machining operation[36]. (d) Three-dimensional
shape control of various device structures.[37]

. . . . . . . . . . . . . . .

Figure 2.3 Examples of circuit-level active electrical tuning: (a) Cross-sectional
view of the disk resonator with an inside tuning element and the diagram
of the tuning circuit [41]. (b) Schematic diagram of a tuning feedback
loop [42].

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

17

19

Figure 2.4 Examples of electrostatic tuning: (a) Schematic drawing of a MEMS
embedded SRR unit cell, where two cantilever arrays are located in the
gap regions of the inner and outer rings [43]. (b) Schematic view of a
tunable comb resonator [44]. . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.5 Examples of electrothermal tuning [48]: (a) Schematic diagram of a
comb resonator with the straight beam for actively thermal tuning via
localized heating.
(b) Frequency changes by different electrothermal
tuning methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.6 Example of photothermal tuning [49]: (a) Schematic diagram of the
resonator structure and the laser deflection method used to measure the
resonant frequency. (b) SEM image of the resonator. (c) The resonant
frequency spectrum of the cantilever resonator with the first four modes.
(d) Relative resonant frequency shift as a function of laser intensity. (e)
Relative resonant frequency shift as a function of temperature. . . . . . .

Figure 2.7 Example of piezoelectric tuning [50]: (a) Resonant response of piezo-
electric beams with clamped-clamped structure. (b) Resonant response
of piezoelectric beams with clamped-free structure. (c) Frequency shift
results for doubly clamped beams. (d) Frequency shift results for can-
tilever beams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.8 Examples of stress tuning: (a) Changes in the resonant frequency of
a buckled beam, the hygrometric polymer coating expands in propor-
tion to relative humidity [51]. (b) Schematic diagram of the bending
apparatus and the measurement setup [52]. . . . . . . . . . . . . . . . . .

20

21

22

24

25

Figure 2.9 Schematic electronic band diagram of VO2 in both rutile phase (left)

and monoclinic phase (right) [53]. . . . . . . . . . . . . . . . . . . . . . .

26

Figure 2.10 XRD scans of VO2 thin film deposited on Si substrate with temperatures

below and above transition temperature [54]. . . . . . . . . . . . . . . . .

28

Figure 2.11 Example of resistive bending sensor and pressure sensor: (a) Structure

of a strain gauge [59]. (b) Structure of a tactile pressure sensor [60]. . . .

30

Figure 2.12 Example of gold nanofilm-based resistive bending gauge [65]: (a) Fabri-
cation of Au nanofilm bending sensor on paper substrate. (b) Model of
the sensor. (c) SEM image of Au nanoparticles film. (d) Photograph of
the flexible bending sensor. (e) Top view of bending sensors on different
substrates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

Figure 2.13 Example of capacitive-based physical sensors for bending and pressure

monitoring [76]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32

x

Figure 2.14 Examples of piezoelectric-based physical sensors [78, 79]: (a) SEM image
of aligned ZnO NWs grown on Al2O3 substrate. (b) The TEM image
of ZnO NWs. (c) Working principle of ZnO NW-based nanogenerator,
the electric output is generated by NWs sliding against each other. (d)
Photograph of NaNbO3 nanowires. (e) Schematic image of m, NaNbO3
- PDMS composite-based nanogenerator.
(f) OM and SEM view of
the device shown in (e). (g) Energy generation mechanism of NaNbO3
NWs-based nanogenerator. . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.15 Illustrations of triboelectric self-powered physical sensors [81]: (a) Series
of materials in TENG family. (b) Working principle of TENG device.
(c) Comparisons between power consumption in commercial electronics
and power output in TENG devices.

. . . . . . . . . . . . . . . . . . . .

Figure 2.16 Road-map of improvements on the power output of nanogenerators [103].

Figure 3.1 Fabrication flow of VO2-based cantilever.

(a) PECVD deposition of
SiO2 layer on Si substrate. (b) Thermal evaporation of Ti/Pt heater
trace, patterned by lift-off. (c) PECVD of second layer SiO2. (d) The
structure defined by dry etching. (e) MEMS structure released by XeF2.
(f) PLD deposition of VO2 coating. . . . . . . . . . . . . . . . . . . . . .

33

34

35

38

Figure 3.2 The PLD equipment for VO2 deposition, the inset shows the plasma

plume coming off of the vanadium target. . . . . . . . . . . . . . . . . . .

39

Figure 3.3

(a) Schematic diagram of the released cantilever structure. Contacts
”1” and ”4” complete the heater loop around the cantilever structure,
contacts ”2” and ”3” are used to measure the resistance of theVO2 film.
(b) Measured resistance of the patterned VO2 film as the temperature
is increased and decreased by Peltier heating.

. . . . . . . . . . . . . . .

Figure 3.4 SEM images for the test structures. Top: cantilever of 550 µm long.
Bottom: bridge of 300 µm. The electrodes for resistive heating actuation
are artificially colored for clarity.

. . . . . . . . . . . . . . . . . . . . . .

Figure 3.5 Fabrication processes of VO2-based bridge resonators. (a) Deposition
of 1 µm SiO2 layer on Si substrate by PECVD. (b) Metalization of
200 nm Pt/Ti thin film by sputtering coating and the heater traces are
patterned by the lift-off method. (c) PECVD Deposition of the second
SiO2 layer of 1 µm. (d) Resonator beam structure defined by plasma
dry etching of SiO2. (e) MEMS structure released by isotropic etching
with XeF2. (f) Deposition of 100 nm VO2 thin film by PLD deposition. .

Figure 3.6 Statistic of buckling preference after the MEMS structure release.

. . . .

40

41

43

43

xi

Figure 3.7 SEM images of VO2-based bridge resonators used in this work. (a) A
300 µm VO2-based bridge resonator with up-buckled profile, scale bar:
50 µm. (b) A 300 µm VO2-based bridge resonator with down-buckled
profile, scale bar: 50 µm. (c) A 300 µm VO2-based bridge resonator
with bell-shape buckling profile, scale bar: 50 µm. (d) Beam center,
scale bar: 10 µm.
(f) A cross
section view of the stacked layers, scale bar: 1 µm. (g) A cross section
view of the VO2 thin film coating, scale bar: 100 nm. . . . . . . . . . . .

(e) Beam anchor, scale bar: 10 µm.

Figure 3.8

Images of the uncoated bridges. (a) Top view optical microscope image
of uncoated microbridge, the over-etching edge is highlighted in the red
circle, where the Si substrate underneath the transparent SiO2 layer
is etched away, scale bar: 100 µm.
(b) Top view optical microscope
image of uncoated microbridge with top SiO2 layer scratched off, the side
undercut and anchor are highlighted, the effective length is measured to
be 377 µm, scale bar: 100 µm. (c) SEM side view of upward sinusoidal
uncoated microbridge, scale bar: 50 µm. (d) SEM side view of downward
sinusoidal uncoated microbridge, scale bar: 50 µm. (e) SEM side view
of downward wavy uncoated microbridge, scale bar: 50 µm. . . . . . . . .

Figure 3.9 Dimensions of VO2 coated bridge.

(a) SEM top view of VO2-based
microbridge, the width is 43 µm and the length is 319 µm, scale bar: 50
µm. (b) SEM cross section view of stacked film layout, the thickness of
the beam body is 2.15 µm, the first SiO2 layer is 0.89 µm, the second
SiO2 layer is 1.04 µm and the Pt heater is 0.22 the second SiO2 layer is
1.04 µm, scale bar: 1 µm. (c) SEM cross section view of VO2 thin film
coating, the thickness is 117 nm, scale bar: 100 nm. . . . . . . . . . . . .

Figure 3.10 FEM simulation of first mode resonant frequency (f1) at room temper-
ature from COMSOL, the scale bars show the lateral deflection at room
temperature. (a) First mode resonant frequency of a pure SiO2 micro-
bridge, f1 = 160.1kHz. (b) First mode resonant frequency of a SiO2
microbridge with embedded Pt metal heater, f1 = 137.3kHz. (c) First
mode resonant frequency of a VO2 coated microbridge without consider-
ing the thermal mismatch between VO2 and SiO2 layer, f1 = 70.2kHz.
(d) First mode resonant frequency of a VO2 coated microbridge consid-
ering the thermal mismatch between VO2 and SiO2 layer, f1 = 258.8kHz.

Figure 3.11 Fabrication process. (a) Polypropylene (PP) film filled with inorganic
silicate particles. (b) Biaxial in-plane stretching of the PP film to create
the air ellipsoids. (c) Diffusion of N2 gas. (d) Ellipsoids expansion by
a sudden decrease in pressure. (e) Plasma discharging. (f) Electrodes
metalization.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

46

47

48

51

xii

Figure 3.12 Sputtering coater used for depositing silver electrodes on PPFE film. (a)
Overview of the sputtering coater (Hummer X, Anatech Inc.). (b) The
silver target mounted on top of the vacuum chamber. (c) The sample
holder at the bottom of the chamber where PPFE is placed for metalization. 53

Figure 3.13 Signal profile compare of Voc and Isc.

output in compression and releasing cycle.
output in compression and releasing cycle.

(a) Triangular waveform Voc
(b) Square waveform Isc

. . . . . . . . . . . . . . . . .

54

Figure 3.14 Changing polarity test of electric output. (a) Open circuit voltage (Voc)
measurement in the forward bias connection. (b) Open circuit voltage
(Voc) measurement in the reverse bias connection.
(c) Short circuit
current (Isc) measurement in the forward bias connection. (d) Short
circuit current (Isc) measurement in the reverse bias connection. . . . . .

Figure 3.15 Schematic demonstration of stacking multilayer structure.

. . . . . . . .

Figure 4.1 Schematic diagram of the laser deflection method used to measure the
resonant frequency of a 300 µm VO2-based bridge resonator, the VO2
phase transition can be induced either by electro-thermal (i.e. resistive,
or Joule) heating or substrate heating. Mechanical vibration input is
provided by the piezoelectric disk. . . . . . . . . . . . . . . . . . . . . . .

55

56

59

Figure 4.2 Resonant frequency change for VO2 coated cantilever beams of different

lengths through full heating and cooling loop.

. . . . . . . . . . . . . . .

60

Figure 4.3 Resonant frequency change for VO2 coated bridge beams of different

lengths through full heating and cooling loop.

. . . . . . . . . . . . . . .

61

Figure 4.4 Resonant frequency change for uncoated cantilever beams of different

lengths as a function of temperature.

. . . . . . . . . . . . . . . . . . . .

63

Figure 4.5 Resonant frequency change for uncoated bridge beams of different lengths

as a function of temperature.

. . . . . . . . . . . . . . . . . . . . . . . .

64

Figure 4.6 The resonant frequency shift of a 300 µm VO2-based microbridge in the
up-buckled state. (a) Resonant frequency shift through a complete heat-
ing and cooling cycle by using integrated resistive heaters. (b) Resonant
frequency shift through a complete heating and cooling cycle using sub-
strate conduction heating. (c) 3D reconstruction of the device showing
the buckling amplitude in +z direction. (d) Normalized buckling am-
plitude change as a function of substrate heating along the beam axial
length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

xiii

Figure 4.7 Schematic illustration of geometric distortion and axial stress upon dif-
ferent bending moments. (a) The initial state of an upward buckled
microbridge with a sinusoidal profile under a positive bending moment.
(b) The lateral deflection in the structure reduces the buckling ampli-
tude, the rotational force on the pinned boundaries leads to a relative
movement of edges B and B(cid:48) towards each other. Compressive axial
stress is therefore induced, which causes an increase in resonant fre-
quency after the turning point shown in Figure 4.6b. (c) The initial
state of a downward buckled microbridge with a sinusoidal profile un-
der a negative bending moment. (d) The lateral deflection in the struc-
ture reduces the buckling amplitude, the rotational force on the pinned
boundaries leads to a relative movement of edges D and D(cid:48) against each
other. Tensile axial stress is therefore induced, which causes a decrease
in resonant frequency after the turning point shown in Figure 4.8b. . . .

Figure 4.8 The resonant frequency shift of a 300 µm VO2-based microbridge in the
down-buckled state. (a) Resonant frequency shift through a complete
heating and cooling cycle by Joule heating. (b) Resonant frequency shift
through a complete heating and cooling cycle by substrate heating. (c)
3D reconstruction of the device showing the buckling amplitude in −z
direction. (d) Normalized buckling amplitude change as a function of
substrate heating along the beam axial length. . . . . . . . . . . . . . . .

Figure 4.9 The resonant frequency shift of a 300 µm VO2-based microbridge with
bell-shape buckle state. (a) Resonant frequency shift through a complete
heating and cooling cycle by Joule heating. (b) Resonant frequency shift
through a complete heating and cooling cycle by substrate heating. (c)
3D reconstruction of the device showing the buckling amplitude in −z
direction. (d) Normalized buckling amplitude change as a function of
substrate heating along the beam axial length. . . . . . . . . . . . . . . .

Figure 4.10 (a) Circuit of resonant frequency programmability by combing VO2-
based resonator and FENG device. C is the capacitor of 1µF, R1 is the
resistance of the heater (252 and 228 Ω for the cantilever and bridge,
respectively), Ip is the pre-heating current (1 and 1.22 mA for the can-
tilever and bridge structures, respectively). (b) Voltage profile of the
discharge current across the heater. (c) The circuit used for measuring
the time constant. A wave-function generator (WG) is connected to
the heater R1. The VO2 film (RV )is connected to a resistor (R2), a
pre-heating voltage source (Vp), and an oscilloscope (DSO). (d) Ther-
mal time constant of the VO2-based cantilever. (e) Schematic of the
rectangular pulse supplied by the WG for time-constant and energy cal-
culation experiments. (f) Frequency shift as the function of the pulse
width.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

68

69

71

72

xiv

Figure 4.11 Tuning and programming frequency states in cantilever structures. (a)
Hysteretic major resonant frequency loops for cantilever structure as a
function of the current. (b) Frequency shift as a function of the voltage
in the capacitor before the discharge pulse. (c) Frequency shift as a
function of pulse amplitude for three different pulse widths (PW). (d)
Frequency shift as a function of energy delivered by the pulse.

. . . . . .

Figure 4.12 (a) Hysteretic major resonant frequency loops for bridge structure as a
function of the current. (b) Frequency shift as a function of the voltage
in the capacitor before discharge. (c) Frequency shift as a function of
pulse amplitude for three different pulse widths (PW). (d) Frequency
shift as a function of energy delivered by the pulse.

. . . . . . . . . . . .

Figure 4.13 (a) Representative impact profile, jerk = (FA-FB)/(m∆A−B), where
FA and FB are the force at point A and B respectively, m is the mass of
the head and ∆A−B is the time from point A and B. The acceleration
is calculated by using an average human head mass of 3.6 kg. (b) The
force exerted on the head, F1, F2, F3, and F4 represent the peak force
of around 1800 N applied at different locations, Arx is the rotational
axis of the head, the size of the head is selected to be the value at 50th
percentile of male adults. . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.14 Experimental setup. The active sample is the resonator (cantilever or
bridge) actuated by Joule heating, while the static sample is the res-
onator (cantilever or bridge) that is not actuated. Two identical piezo-
disks were placed underneath the static sample and the active sample
respectively and they are sharing one driving AC source signal provided
by the network analyzer. The output of the photodetector is connected
to the input of the network analyzer. The laser beams passing through
the beam splitters are not contributing to the measurement and there-
fore are not shown for clarity.

. . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.15 Left: Resonant frequency versus actuation current through a full heating
and cooling cycle for the active bridge. Right: Resonant frequency
signal for the static bridge at room temperature. The measured (f0)
(cid:48)
(cid:48)
0) resonant frequencies are shown. The value for f
and calculated (f
0
was obtained from Equation (3.1), and it does not take residual thermal
stress into account.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.16 The sequence of different stages for the VO2-based tunable band-pass
filter using bridge resonators during a heating/cooling cycle. Plots show
selected stages with pairs of similar output for each cycle. The resonant
peaks for the static and active bridges are represented by the black and
red/blue curves, respectively. Iact is the actuation current applied to
the active bridge.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74

78

79

83

84

93

xv

Figure 4.17 The sequence of different stages for the VO2-based tunable band-pass
filter using cantilever resonators during a heating/cooling cycle. Plots
show selected stages with pairs of similar output for each cycle. The
resonant peaks for the static and active bridges are represented by the
black and red/blue curves, respectively. Iact is the actuation current
applied to the active bridge.

. . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.18 Left: Resonant frequency versus actuation current through a full heating
and cooling cycle for the active cantilever. Right: Resonant frequency
signal for the static bridge at room temperature. The measured (f0)
(cid:48)
(cid:48)
and calculated (f
0) resonant frequencies are shown. The value for f
0
was obtained from Equation (3.2), and it does not take residual thermal
stress into account.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 5.1 Working principle of ferroelectric nanogenerator: (a) No external stress
is applied. (b) When external boundary load is applied, the polarization
field due to internal dipoles decreases and free induction charges are ac-
cumulated on metal electrodes. (c) FEM results of changes in electrode
potential at the polymer-metal boundary and open circuit voltage arise
from accumulated charges. . . . . . . . . . . . . . . . . . . . . . . . . . .

94

95

98

Figure 5.2 Schematic experimental setup. (a) Linear pressure input generated from
a stepper motor. (b) Sinusoidal pressure input provided by the vibration
exciter and the stacking layout of FENG and pressure sensor is shown
in the inset.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Figure 5.3 Electromechanical characterization of FENG under sinusoidal pressure
input. (a) Forward and reverse Voc of FENG under sinusoidal pressure
input. (b) Forward and reverse Isc of FENG under sinusoidal pressure
input. (c) Amplification of Voc and Isc of FENG by a symmetric folding
process under sinusoidal pressure input. (d) Electric output, voltage,
and current, under sinusoidal pressure input with increasing resistive
load. (e) Voc of FENG under sinusoidal pressure input with variable
pressure amplitudes and frequencies. (f) Isc of FENG under sinusoidal
pressure input with various pressure amplitudes and frequencies. . . . . . 101

Figure 5.4 Electromechanical characterization of FENG under linear pressure in-
put. (a) Forward and reverse Voc of FENG under low-frequency linear
pressure. (b) Forward and reverse Isc of FENG under low-frequency
linear pressure. (c) Amplification of Voc and Isc of FENG by a sym-
metric folding process under low-frequency linear pressure. (d) Forward
and reverse Voc of FENG under high-frequency linear pressure. (e) For-
ward and reverse Isc of FENG under high-frequency linear pressure. (f)
Amplification of Voc and Isc of FENG by a symmetric folding process
under high-frequency linear pressure.

. . . . . . . . . . . . . . . . . . . . 103

xvi

Figure 5.5

Illustration of the lumped model. (a) Lumped electromechanical model
of FENG. (b) Equivalent electrical circuit model of FENG. (c) Impact
profile of a sinusoidal pressure input. (d) Isc under a sinusoidal pressure
input. (e) Experimental electromechanical response with different load
resistances. (f) Simulated electromechanical response with different load
resistances.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Figure 5.6 FENG voltage output measurement with different instruments:

(a)
Keithley 2450 and Voc. (b) Keithley 2182 and Voc. (c) Measured volt-
age output when using a Keithley 2450 and a 1 MΩ load resistor. (d)
Measured voltage output when using a Keithley 2182 and a 1 MΩ load
resistor. (e) Tektronix TDS2004C and measured Voc. (f) National In-
struments 9201 and measured Voc.

. . . . . . . . . . . . . . . . . . . . . 107

Figure 5.7 FENG-based matrix pressure sensor. (a)The voltage output of a 15 mm
× 15 mm single layer FENG as a function of input pressure amplitudes
and frequencies. (b) 3D surface fitting of the single-pixel electromechan-
ical response, R2 = 0.93. (c) 16-pixel FENG-based matrix sensor and
3D contour maps of the pressure distribution over the sensor upon an
impact from the user. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Figure 5.8 The fabrication process of a single layer FENG-based matrix sensor
with 16 individual positive electrodes and 1 common negative electrode.
(a) Deposition of the common negative silver electrode on PPFE film.
(b) Deposition of 16 positive silver electrodes.
(c) Wire connection
by conductive copper tape. (d) Spin coating of PDMS substrate and
partially cured. (e) Spin coating of another PDMS layer to encapsulate
the device and the two layers are completely cured.

. . . . . . . . . . . . 110

Figure 5.9 Contour map of the pressure distribution over the sensor with different

impacts applied to different locations. . . . . . . . . . . . . . . . . . . . . 111

Figure 5.10 Deflection of VO2-based actuator at different actuation currents. (a)
Deflection of VO2-based actuator at room temperature in the heating
cycle. (b) Deflection of VO2-based actuator at 3.30 mA in the heating
cycle. (c) The maximum deflection of VO2-based actuator at 4.45 mA
in the heating cycle. (d) Deflection of VO2-based actuator at 5.50 mA
in the heating cycle.
(e) Deflection of VO2-based actuator at room
temperature in the cooling cycle. (f) Deflection of VO2-based actuator
at 3.30 mA in the cooling cycle. (g) The maximum deflection of VO2-
based actuator at 3.95 mA in the cooling cycle. (h) Deflection of VO2-
based actuator at 5.50 mA in the cooling cycle.

. . . . . . . . . . . . . . 112

xvii

Figure 5.11 FENG-based micro robotic arm controller.

(a) Stress applied to the
FENG device. (b) VO2-based MEMS actuator without applying actua-
tion current. (c) Stress released from the FENG device. (d) VO2-based
MEMS actuator with a maximum deflection at actuation current of 4.45
mA. (e) The gate voltage of the p-channel MOSFET controlled by the
output of FENG, the voltage change tracks the motion of the finger. . . . 113

Figure 6.1 Comparison of voltage measurements Voc and V by different instru-
ments. (a) Voc measurement by high impedance voltmeter (Keithley
2450). (b)V measurement by low impedance voltmeter (Keithley 2182),
where R = 10 M Ω is the instrument’s internal resistance. . . . . . . . . . 121

Figure 6.2 Bending configuration of PPFE thin film mounted on the flexible PI sub-
strate. (a) 3D schematic drawing of silver coated PPFE film mounted
on a PI substrate, inset shows the SEM image of the cross-sectional view
of PPFE film. (b) 2D Schematic diagram of a sinusoidal shape buckling
profile under a horizontal axial compression displacement.

. . . . . . . . 122

Figure 6.3 Measured electrical response due to axial displacement ∆L and film
strain 
11. (a) Profile of linear axial compression displacement ∆L as a
function of time. (b) Theoretical normalized film strain 
11 from Eq.(1)
as a function of time. (c) Measured Voc as a function of time. (d) Peak
Voc value as a function of ∆Lmax for a given compression velocity of 14
mm/s.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

Figure 6.4 Characterization of electrical output under bending test. (a,b,c) Short
circuit current Isc under the same ∆Lmax = 3 mm and different v.
From top to bottom: 3.5 mm/s, 7mm/s, and 14 mm/s. (d,e,f) Voltage
measurement under the same ∆Lmax = 3 mm and different v, from top
to bottom: 3.5 mm/s, 7 mm/s, and 14 mm/s.

. . . . . . . . . . . . . . . 126

Figure 6.5 Characterization of Isc−max and Isc−ave under bending test. (a) Isc−max
as a function of ∆Lmax under different v. (b) Isc−ave as a function of
v under different ∆Lmax. (c) Isc−ave as a function of ∆Lmax under
different v. (d) Isc−ave as a function of w(cid:48)(cid:48) under different v. The fit
curves are obtained from Eq.(7) by using proportional constants that
best fit the measured data. . . . . . . . . . . . . . . . . . . . . . . . . . . 128

Figure 6.6 Characterization of Vmax and Vave under bending test. (a) Vmax as a
function of ∆Lmax under different v. (b) Vave as a function of v under
different ∆Lmax. (c) Vave as a function of ∆Lmax under different v.
(d) Vave as a function of w(cid:48)(cid:48) under different v.

. . . . . . . . . . . . . . . 129

xviii

Figure 6.7 Demonstration of performance degradation under different testing con-
ditions. (a) Test of mechanical robustness under repeated bending cy-
cling up to 10000 bending and releasing operation. (b) Test of humidity
resistance by immersion into water for up to 12 hours. (c) Test of ther-
mal stability under different baking temperatures. . . . . . . . . . . . . . 131

Figure 6.8 Demonstration of application in the athletic assessment. (a) Photog-
raphy of showing bending of the wrist during throwing a baseball. (b)
Voltage output signal from the coach throwing the baseball. (c) Voltage
output signal from the learner throwing the baseball.

. . . . . . . . . . . 133

Figure 7.1

(a) Working principle of ferroelectric nanogenerator. (b) Photography
of a 20 mm × 40 mm PPFE film.
(c) Photography of final device
with PI protective layer (20 mm × 40 mm).
(d) Cross-section view
SEM image of PPFE film with cellular structure. (e) Top-view SEM
image (backscattered electrons) of PPFE film, where darker regions are
observed where voids are present. (f) Photography of the experimental
setup for characterizing the electric output under various mechanical
loads. (g) A close-up view of (f).

. . . . . . . . . . . . . . . . . . . . . . 137

Figure 7.2 Electrical output for single layer device. (a) Experimental measurement
of open circuit voltage (Voc). (b) Transferred charge output (Qsc). (c)
Experimental measurement of short circuit current (Isc).
(d) Isc for
multiple-layered devices.

. . . . . . . . . . . . . . . . . . . . . . . . . . . 140

Figure 7.3 Electrical response of single-layer device for different mechanical input.
(a) Forces with different amplitudes and velocities used for electrome-
chanical characterization. (b) Voltage and current output with various
resistive loads under F1. (c) The maximum instantaneous power with
various loads under different force inputs described in (a). (d) Aver-
age power delivery from a single press and release cycle with various
loads. (e) Output voltage and current under F1 with a 600 MΩ load.
(f) Output power under F1 with a 600 MΩ load. . . . . . . . . . . . . . . 141

Figure 7.4 Comparison of energy output under different forces. (a) Energy output
under forces with same peak amplitude and different frequencies. (b)
Energy output under forces with the same frequency and different peak
amplitudes.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

xix

Figure 7.5 Energy harvesting module. (a) A comprehensive energy harvesting sys-
tem, C1 = 1 µF , C2 = 4.7 µF , COU T = 47 µF , L1 = 22 µH and
CF LY = 0.1 µF . (b) Direct charge of capacitors with different capac-
itances. (c) Voltage regulation of nanopower energy harvesting power
supply LTC3588-1. (d) Charging profile of rechargeable solid state bat-
tery CBC012. (e) Discharging profile of rechargeable solid state battery
CBC012. (f) Voltage regulation of integrated power management chip
CBC3112. (g) Discharging profile of integrated energy storage unit in
CBC3112.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

Figure 7.6 Energy harvesting system. (a) Schematic diagram of energy harvest-
ing through direct charge. (b) Schematic diagram of energy harvesting
through LTC3588-1 to power electronic device. (c) Schematic diagram
of energy harvesting through LTC3588-1 to charge CBC012 recharge-
able chip battery.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

Figure 7.7 Energy harvesting demonstration of powering electronic devices and
charging a battery. (a) Powering LCD screen by combing a two-stage
energy harvesting system. (b) Charging rechargeable solid-state battery
CBC012, the stored energy is used for powering three blue LED lights.
(c) Powering humidity sensor by a one-stage energy harvesting system.
(d) Powering temperature sensor by a one-stage energy harvesting sys-
tem. (e) Powering LCD screen by a one-stage energy harvesting system.

150

xx

CHAPTER 1

INTRODUCTION

Figure 1.1 Resistance of continuous VO2 film as a function of temperature during a full
heating and cooling cycle [1].

Vanadium dioxide (VO2) undergoes a fully reversible hysteretic first order solid-to-solid

phase transition in which the crystallographic structure changes from monoclinic (M) phase

to rutile (R) phase. This structural phase transition comes hand-in-hand with an electronic

phase transition, in which the electrical resistance changes drastically. Thus, the phase

transition is commonly referred to as a Mott-Peierls transition, where both an insulator-

to-metal transition (IMT) and a structural phase transition (SPT) begin to occur almost
simultaneously at a temperature of ∼ 68 ◦C [2] upon heating, and typically spans between

1

5-15 ◦C as shown in Figure 1.1,

depending on the microstructural properties of the film and its composition. The phase

transition has been demonstrated to be induced in multiple ways including heat conduction

[4], external electric field [5], optical radiation [6], etc. More recently, VO2-based system-on-

chip micrometer-sized devices have been developed, including electrical switches [7], smart

windows[8] and optical modulators [9, 10], MEMS mirrors [11, 12], and RF resonators [13, 14].

Correlated with the IMT, a structural phase transition (SPT) is also observed at the same

time due to the crystal structural rearrangement. The change in average spacing of vanadium

ions from M-phase to R-phase [15] induces a large strain energy density, which enables large

deflection [16, 11] and fast responsivity in VO2-based bimorph MEMS actuators.

Figure 1.2 shows the crystal structure of VO2 in different phases. In the low-temperature

monoclinic phase, the separations between two adjacent vanadium atoms along with the

Figure 1.2 Crystal structure of VO2 in rutile phase (left) and monoclinic phase (right). [3]

2

aM 1=2cR axis alternate with 2.65˚A and 3.12˚A, thus the VO2 is in a distorted structure

with the doubling of the unit cell. On the other hand, the rutile phase, or the tetragonal

phase, occupies a highly ordered body-centered cubic (BCC) structure with vanadium atoms

equally spaced at a distance of 2.86˚A.

Therefore, the SPT of VO2 leads to a crystal volume contraction of about 1.7% [17]

along the cR axis. The consequently induced compressive stress can be implemented into

active, fully reversible resonant frequency tuning techniques, which could be used to com-

pensate frequency shifts due to performance degradation or random structural variations.

Depending on the resonator structure, the resonant frequency shift can be induced by geo-

metric distortion or residual axial stress [18]. The inherent hysteretic behavior also enables

the programmability within multiple memory states [19, 20, 21]. Figure 1.3 shows the

resonant frequency of a VO2-based MEMS bridge as a function of temperature, where the

separation between heating and cooling loops enables the programmability of multiple me-

chanical states. However, most of the efforts are focused on demonstrating larger frequency

reconfigurability using simpler structures or methods, but little attention has been paid to

the influence of these stress levels when added to already existing large residual stress with

different distributions.

In the first part of this work, the influence of the SPT in VO2 thin film coatings has been

studied on MEMS resonators with both cantilever and bridge structures. During the phase

transition, the resonant frequency shift is induced by the compressive stress generated by

the thermal expansion coefficient mismatch between VO2 and SiO2 films. By comparing the

relative resonant frequency shift of cantilevers and bridges with different aspect ratios, it has

been found that a more stress sensitive structure (bridge) leads to a larger tuning range due

to a high level residual axial stress, while the smaller frequency tuning range in cantilever

is determined by the large geometric change. For bridge structures, small variations in the

device manufacturing process produced three different buckling profiles: upward, downward

and bell-shaped. The resonant frequency tuning direction is found to be heavily dependent

3

Figure 1.3 The resonant frequency of a 250 µm VO2-based MEMS bridge as a function of
temperature during a full heating and cooling cycle.

on the buckling orientations, which is associated with different stress interfaces between VO2

and SiO2 layers. Different actuation methods (electrical resistive heating and substrate heat-

ing) are used and the results showed very different tuning behavior. The actuation dependent

frequency tunability can be attributed to the different boundary conditions, where a turning

point in the frequency curve (see Figure 1.4) occurs when a large deflection transitions the

boundary condition from “fixed-fixed” to “fixed-pinned” during the VO2 phase change. In

order to understand the energy requirements for actuation and explore the possibility of

integrating MEMS resonators with piezoelectric impact sensors for the application of Head

Impact Telemetry System (HITS); we introduced polypropylene ferroelectret nanogenerator

4

(FENG) as the transducer to convert the mechanical energy to electrical energy. A pro-

gramming current pulse generated by the FENG device is sent through a monolithically

integrated resistive heater, which increases the temperature of the device and induces the

phase transition of the VO2 thin film as shown in Figure 1.5. The pulse could come from

a charged capacitor or from the FENG device directly. Next, based on the understanding

of single resonator device, the potential application of VO2-based MEMS devices as second-

order bandpass filters (kHz band) with tunable band selectivity and adjustable bandwidth

has also been demonstrated by using two identical on-chip microresonators excited and mea-

sured at the same time.

This work continues with the exploration of the sensing and energy harvesting capabili-

ties of FENG. FENG is a flexible multilayer structure device with the ability of converting

Figure 1.4 The resonant frequency of a 300 µm VO2-based MEMS bridge as a function of
temperature during a full heating and cooling cycle, where a turning point is observed at
around 75 ◦C.

5

mechanical energy to or from electrical energy. The active material that exhibits the direct

and inverse piezoelectric effect is a dielectric and elastic film with full-of-cell type struc-

ture. Despite that the FENG has the similar electro-mechanical response as piezoelectric

nanogenerator (PENG), the fundamental working principles between these two devices are

different. By applying an external mechanical force, the thickness of the porous midsec-

tion region of the polypropylene ferroelectret (PPFE) film decreases. The piezoelectricity

of FENG mainly arises from the relative movement of positive charge surface to negative

charge surface within each individual ellipsoid void. Figure 1.6 shows the working principle

of FENG under an external mechanical load, the induced free charges at metal electrodes

Figure 1.5 Programming resonant frequency of VO2-based MEMS resonator through electric
pulse generated by FENG [20].

6

produce an open circuit voltage across the device. This work presents a comprehensive study

that uses the fundamental working principles of dipole moments in ferroelectret polymers

to describe the energy conversion mechanism. The study addresses discrepancies in voltage

measurement caused by instruments with different internal resistance and sampling rate. A

lumped parameter model is also proposed and validated to explain the impedance mismatch

at the device-machine interface. Based on the flexibility of the device, FENG-based bending

sensors for human motion and structural distortion monitoring are also investigated. The-

oretical analysis based on constitutive electro-mechanical equations and bi-layer bending

mechanics provide a detailed understanding of the sensing mechanism and its applicabil-

ity. Measured responses are evaluated in terms of instantaneous and average voltage, which

reveal a more comprehensive understanding of the bending dynamics and show great agree-

ment with theoretical predictions. The robustness of the material is also investigated in

Figure 1.6 Piezoelectricity of FENG. Working principle of ferroelectric nanogenerator: (a)
no external stress is applied. (b) when external boundary load is applied, the polarization
field due to internal dipoles decreases and free induction charges is accumulated on metal
electrodes. (c) FEM results of changes in electrode potential at the polymer-metal boundary
and open circuit voltage arise from accumulated charges.

7

terms of mechanical repeatability, thermal stability, and humidity resistance. A new sensor

configuration based on the polarity of piezoelectric materials is also proposed for detecting

the structure deformation with 2D directional information.

Applying flexible materials for energy scavenging from ambient mechanical vibrations is

a clean energy solution that can help alleviate electrical power demands in portable devices

and wearable electronics. A fundamental study on FENG and its interface with self-powered

and energy storage systems is also presented in this work. A single-layered FENG device

has been used for characterizing the device’s output voltage, current, transferred charge,

and energy conversion efficiency. The potential capability of harvesting mechanical energy

and delivering to system load is demonstrated by integrating the device into a fully inte-

grated power management system. The theory for determining the harvested energy that is

ultimately delivered to external electronic loads (or stored in a battery) is also discussed.

1.1 Problem Description and Motivation

There has been plenty of research progress in increasing resonant frequency tuning range, f
· Q product, and decreasing power consumption in MEMS resonators. However, fundamen-

tal research on understanding stress-induced frequency shifts in bimorph MEMS resonators

with different structures has not been as intensive. Due to different structural boundary

conditions, the SPT of VO2 film can induce either a large amount of residual axial stress in

clamped-clamped bridges or a large deflection in clamped-free cantilevers with stress only

concentrated in the vicinity of the anchor. Due to the high stress sensitivity in bridge

structures, small variations in the manufacturing process –which leads to different buckling

profiles and orientations– plays a major role in frequency shifts and tunability. Addressing

this issue requires understanding resonant frequency shifts in a buckled structure; which is

also obtained in this work. The work is extended to explore the possibility of combining

VO2 MEMS resonators with piezoelectric sensors for an integrated HITS system. The en-

8

Figure 1.7 (a) A complete energy harvesting system for converting random mechanical energy
to DC electric output for battery charging. (b) AC electric output generated from FENG
device. (c) DC electric output delivered from the power management system to system load.

ergy consumption of VO2-based MEMS resonators and the impedance match between FENG

device and resistive load becomes essential in this application. We further exploited the self-

powered sensing and the energy harvesting capabilities of FENG. Since the piezoelectricity

FENG comes from engineered macro dipoles –which are different from traditional atomic

level dipoles–, theoretical explanations are needed for determining the direct and transverse

electromechanical response under external mechanical inputs. From the high piezoelectric

9

coefficient of FENG, we describe the energy harvesting capability of converting ambient me-

chanical energy to electric energy. Practical applications require a complete power manage-

ment system for delivering a DC power to rechargeable batteries or commercial electronics,

which is also discussed in this work.

To summarize, the contributions of this work include:

• Determination of the dominating effect of resonant frequency tuning for VO2-based

MEMS resonators with different structures

• Evaluation of the discrepancies in the first mode resonant frequencies caused by thermal

stress in VO2-based MEMS resonators with fully integrated metal heaters

• Illustration of the influence on resonant frequency tuning in terms of different buckling

orientations and profiles as well as the actuation method dependency

• Comparison of using different thermal actuation methods (conductive and resistive (i.e.

Joule) heating), in resonant frequency tuning of pre-buckled bridge resonators

• Studies of the power consumption of programming resonant frequency status in VO2-

based MEMS resonators and the device thermal time constant

• Demonstration of a new frequency tuning method in VO2-based MEMS resonators by

using a piezoelectric transducer

• Demonstration of the potential application of VO2-based bandpass filter; Proposal
of a new HITS system by combining VO2-based MEMS resonators and ferroelectret

nanogenerators

• characterization of FENG in terms of short circuit current, open circuit voltage, output

charge, and energy conversion efficiency

10

• Design of a platform for developing self-powered tactile sensors, and development of

the lumped parameter model for predicting electromechanical behavior under different

resistive loads

• Influence of testing instrumentation on the measurement of the electric output of FENG

• Studies on the potential use of PPFE as a bending sensor, including the comparison of

different evaluation methods for a better understanding of the transverse piezoelectric

effect

• Development of a complete energy harvesting system for collecting ambient random

mechanical energy and charging solid-state batteries

1.2 Thesis Statement

This work presents studies on resonant frequency tuning of VO2-based bimorph MEMS

resonators with different structures; and the development of nanogenerator based tactile

sensors, bending gauges, and energy harvesters. The contributions mentioned above can be

circumscribed within the fields of sensing technologies based on VO2 and FENG devices.

Thesis Statement: Understanding the tuning and programmability of different VO2-

based MEMS resonator structures in terms of beam mechanics, device time constant, band-

width tunability, power consumption, and actuation methods allows for an optimal integra-

tion with self-powering sensing technologies; thus enabling new approaches for the design of

impact and tactile sensors, bending gauges, and energy harvesters.

1.3 Overview of Research Contributions

In this thesis, the contributions listed in Section 1.1 will be presented. As an overview of

the work done, two different structures of VO2-based MEMS resonators have been success-

11

fully designed, fabricated and tested. The bridge structure has been proven to be more stress

sensitive and therefore results in a larger frequency tuning range compared to a cantilever

structure. The resonant frequency tuning behavior is also found to be heavily dependent on

the prebuckled state of bridge resonators. Comparison between different actuation methods

are also carried out and the discrepancy of frequency tunability is found to be related to

a transition of the boundary condition caused by different actuation methods. The power

consumption of programming resonant frequency states of a VO2-based resonator is analyzed

by integrating with FENG as a HITS system. The potential application of implementing

VO2-based MEMS resonators into bandpass filters has been demonstrated and the theoret-

ical maximum tuning range of bandwidth, Q-factor, and selectivity have also been carried

out. The electromechanical responses of FENG under different external mechanical inputs

are modeled based on the working principle of dipole moments and the constitutive equa-

tions of piezoelectric materials. FENG-based tactile sensor arrays and bending gauges are

developed and modeled for impact force distribution and deflection monitoring respectively.

Characterizations of FENG have been carried out in order to determine the output power

and energy conversion efficiency. A FENG-based energy harvester is successfully developed

with an integrated universally adapted power management system, which can be used for

battery charging or powering electronics.

1.4 Dissertation Outline

The following chapters of this thesis are organized as following: Chapter 2 presents a com-

prehensive background on active tuning techniques of MEMS resonators, flexible physical

sensors, and energy harvesters. Chapter 3 introduces the design, simulation, and fabrica-

tion of VO2-based MEMS resonators with different structures as well as the manufacturing

process of FENG device. In Chapter 4, The influence of VO2 thin film on resonators of

different structures are first presented, the influence of different buckling profiles and orien-

12

tations on the resonant frequency shifts are also addressed in the following section, different

actuation methods have been found to result in different tuning patterns as well. Next,

the programmability of MEMS resonators through FENG and VO2 is discussed. The stud-

ies on the device time constant, energy consumption and impact activation threshold are

performed throughout the following sections. Based on a comprehensive study of single

resonator devices, a prototype of VO2-based MEMS bandpass filter is proposed in the last

section. Chapter 5 reports the comprehensive study on the working principle of FENG and

explains the discrepancies in voltage measurements caused by instruments, the dynamic and

static force sensing are also discussed in this chapter. Chapter 6 presents a self-powered

bending sensor using the transverse piezoelectric effect of FENG, the theoretical analysis is

also carried out based on constitutive questions of piezoelectric materials. A fully integrated

complete energy harvesting system is proposed in Chapter 7, where the FENG has been

used to collect random mechanical energy and output regulated DC voltage by a power

management system. Finally, Chapter 8 summarizes the contributions of this work.

13

CHAPTER 2

BACKGROUND

2.1 MEMS Resonators

Performance of electronic devices is often determined by the stability and accuracy of their

internal clocks and frequency reference circuits. For example, the navigation speed and

precision of a global positioning system (GPS) significantly depends on its internal syn-

chronous clock[22]. However, to implement this technology into our portable devices such

as mobile phones or smartwatches, quartz crystal-based resonators are too large and energy-

consuming for this application [23]. Besides clocking applications, RF communications also

benefit from component miniaturization down to the micro-scale. In modern signal process-

ing and transceiver technologies, electromechanical resonators have been widely implemented

in RF circuits (e.g. oscillators, mixers, and filters) and sensing (e.g. temperature, mass, and

humidity) applications [24, 25]. Their small size is a key advantage, which enables scaling
for transceiver miniaturization with ultra-high f · Q product as shown in Figure 2.1. Sen-
sitivities as high as 7 × 10−21 g and 13.89 pmK−1 have also been demonstrated for MEMS

resonators used as mass and temperature sensors, respectively [24, 25]. In order to improve

the quality and reliability of the latest developed wireless communication standards (e.g.

code division multiple access (CDMA), global system for mobile communication (GSM), 3rd

generation (3G), and currently using 5G [27], the performance requirements for resonators

become more and more rigorous. Although quartz crystal-based resonators provide high res-

onant frequencies and Q-factor, the footprint and energy consumption limitations mentioned

earlier still exist. Bulk acoustic wave (BAW) mode of vibration is usually preferred than a

surface acoustic wave (SAW) mode, but the miniaturization technologies for incorporating

a bulk quartz resonator for on-chip systems is not trivial, expensive, and still not capable

14

Figure 2.1 Timeline of growing f · Q product, a common figure of merit of resonators, from
1990 to 2010 [26].

of reducing board size implementation and power consumption to the levels that can be

obtained using RF MEMS. The compatibility of quartz resonators with integrated circuit

(IC) packages and the degradation in device performance (i.e. lowering Q-factor with device

aging) are also major concerns. In addition, the poor shock-proof capability [28] and low

energy efficiency of quartz resonators limits their applications in portable devices.

The number of applications for MEMS resonators has expanded as the technology has

matured. Progress in micro-fabrication processes, design, and materials synthesis has made

possible the cost-effective integration of micro-electro-mechanical resonators into electronic

circuits. MEMS resonator technologies are commonly preferred over their predecessor tech-

nologies which are based on the quartz crystal-based oscillators [29]. Main advantages of

MEMS include (i) small size, (ii) feasibility for on-chip integration of IC active or processing

circuitry, (iii) accurate timing synchronization with external devices, and (iv) low power

consumption. Table 2.1 provides a comparison between quartz crystal and SiTime’s silicon-

15

Table 2.1 A comparison of quartz crystal and SiTime’s silicon MEMS resonators[28].

Quartz crystal resonator MEMS resonator

Features

size

Frequency

Resonant Q (×103)
COMS integration

Packaging

Aging in first year

Compensated temperature stability

Shock immunity
Fabrication cost

based MEMS resonator.

2-5 mm
1-80 MHz
100-200

No

Ceramic or metal

3-5 ppm
1-10 ppm

Poor
High

400µm
1-50 MHz

75-150

Yes

Plastic
3 ppm

1-10 ppm

Good
Low

2.2 Frequency Tuning Technologies

With the progress achieved in micro-fabrication technologies, MEMS resonators with com-

plex structures and different degrees of freedom have been successfully designed and fabri-

cated for applications with ultra-high resolutions. However, MEMS resonators still suffer

from manufacturing defects and device degradation; and face particular application-specific

challenges such as channel switching and frequency selection. Resonant frequencies in MEMS

resonators is determined by many factors, such as geometry, material property, stress and

strain, surface roughness, etc. Multiple efforts have been made to stabilize the resonant fre-

quency throughout the lifetime of MEMS resonators in order to compensate for the frequency

shift caused by fabrication flaws or aging. Hermetic packaging has helped in solving these

issues but at the expense of significantly increasing the production cost of MEMS resonators

[30]. Thus, frequency tunability becomes an alternative way for compensating frequency

shifts in these devices, and to allow multiple channel operation for a single device [31]. The

tuning technologies can be generally categorized into two types: passive tuning and active

tuning. Passive tuning is usually an irreversible method since it usually relies on the use of

focused ion beam (FIB) and pulsed laser deposition (PLD) techniques, which permanently

16

Figure 2.2 Examples of post-fabrication techniques: (a) Selective deposition of polysilicon
on a comb-drive resonator[34]. (b) Two big PLD gold pieces from two-layer shots deposited
on the surface of a microresonator[35]. (c) Device after FIB machining operation[36]. (d)
Three-dimensional shape control of various device structures.[37]

shifts the resonant frequency towards the desired value. On the other hand, active tuning

methods allow for frequency shifts in a fully controllable way. Some of these tuning methods

involve the implementation of MEMS switches or varactor devices with electro-thermal [32]

and electrostatic [33] tunings.

2.2.1 Post Fabrication

Post-fabrication tuning is considered to be a passive tuning method.

It is often used to

compensate for the resonant frequency shift caused by manufacturing defects. They perma-

nently alter the resonant frequency and therefore no further energy is required for resonant

17

frequency tuning during the lifetime of the device. However, they are not able to perform

real-time tuning. Daphne Joachim, et al developed a set of tunable comb-drive resonators

by selectively depositing polysilicon to their rotors [34]. The deposition was done through

electrically heating the resonator in a silane ambient. The newly deposited material suc-

cessfully increased the resonant frequency of each individual device from 0.7 to 2%. Figure

2.2a shows an SEM image of selective deposition of polysilicon on a comb-drive resonator.

The resonant frequency shift for the sample presented is 1.96%. In addition, PLD technique

is also introduced for tuning the resonant frequency by adding extra mass. Figure 2.2b

shows two gold pieces deposited on the microresonator surface, this fine-tuning method can

offer a tuning resolution of 0.5% per laser shot. R.R.A. Syms et al developed a strategy for

permanently tuning the resonant frequency of a comb-drive electrostatic resonator [36]. The

resonant frequency is altered by tuning the suspension stiffness and resonant mass through

a focus ion beam (FIB) micromachining process (see Figure 2.2c). The resonant frequency

tuning can also be achieved by three-dimensional shape control. D Vick et al. reported

a frequency tuning method based on the FIB milling process. The ion impingement com-

ing from multiple directions enables sculpting the shape of the device, such as notching and

tapering. Figure 2.2d shows the three-dimensional control of device structures. The reshap-

ing tuning technique can also be achieved by selective etching [38], local thermally-assisted

chemical reaction [39], and localized annealing [40], etc. However, such tuning process has

certain limitations. Firstly, passive tuning is an irreversible process and can only provide a

onetime permanent tuning. Secondly, the tuning range is limited since either the reshaping

process or the deposition/etching process can only provide a fine-tuning. For stress-sensitive

resonators, the off-targeted resonant frequencies are often induced by the non-uniformity of

the stress level during the fabrication process, in which passive tuning method may not be

able to compensate that. Thirdly, the passive tuning method cannot provide real time tun-

ing for applications such as wireless communication which requires a fast channel switching

capability. Moreover, complicated post-fabrication processes inevitably increase the cost.

18

2.2.2 Electrical Tuning

The electrical tuning mechanism is a circuit-level active tuning method. It tunes the resonant

frequency by manipulating different electrical loads. Figure 2.3a shows an example electrical

tuning method based on MEMS technology [41]. The tuning circuit consists of three segments

of conductors with different lengths. By changing the bias voltage on the MEMS switches,

the effective length of the conductive segment can be switched from one length to another.

For this design, three distinct resonant frequency states can be achieved. The circuit-level

tuning can also be realized by creating a feedback loop, see Figure 2.3b. This tuning

method utilizes the output current to generate a displacement or acceleration signal [42]. The

generated signal is then transformed into a tuning signal which is applied to the resonator

through an additional feedback signal port in order to modify the mechanical stiffness of

the resonator. This tuning method provides a tuning range of 22 kHz in both positive and

negative direction with a central frequency of 14.2 MHz. The active electrical tuning method

is straightforward and easy to implement.

Figure 2.3 Examples of circuit-level active electrical tuning: (a) Cross-sectional view of the
disk resonator with an inside tuning element and the diagram of the tuning circuit [41]. (b)
Schematic diagram of a tuning feedback loop [42].

19

2.2.3 Electrostatic Tuning

As an active tuning mechanism, electrostatic tuning is one of the most attractive methods for

resonant frequency tuning. Figure 2.4a shows split-ring resonator (SRR) with electrostatic

tunability.

Two cantilever arrays each consisted of five beams are placed in both the inner and outer
rings. The length of the cantilevers varies from 300 to 400 µm, with each beam adding

about 2 pF capacitance. For each SRR, only one of the cantilevers will be actuated at the

same time. The MEMS embedded SRR is able to continuously shift the higher frequency

from 14.2 to 12.6 GHz by actuating the cantilever on the outer SRR [43].

In order to

achieve a wider frequency tuning range with higher energy efficiency, MEMS resonators with

comb structures have been extensively studied [45, 46, 47]. A variety of electrostatic tuning

methods such as varactor and parallel plate have been proposed and designed. Figure
2.4b shows a tunable comb structure resonator with a tuning range of ∼ -3.3%, which is

Figure 2.4 Examples of electrostatic tuning: (a) Schematic drawing of a MEMS embedded
SRR unit cell, where two cantilever arrays are located in the gap regions of the inner and
outer rings [43]. (b) Schematic view of a tunable comb resonator [44].

20

achieved by using the capacitive softening effect [44]. By applying different DC voltages

across the gaps between the sensing and driving electrodes, the electrostatic force applied

on the resonant mass changes with different DC voltages, leading to a shift in the stiffness

of the material and the resonant frequency.

2.2.4 Electrothermal Tuning

The resonant frequency in MEMS can also be tuned by thermally inducing an expansion or

contraction of the resonator structure. This technology significantly reduces the complexity

of the system. Localized heating, such as Joule heating, is often used to induce thermal stress

and strain. Figure 2.5a shows an electrothermally tuned comb resonator that consists of

a straight mechanical beam which can be resistively heated to generate thermal stress. For

this device, the relative resonant frequency change is around 6.5% with a central frequency

at around 31 kHz. Electrothermal tuning can also be induced by external heating, which

heats up both the resonator structure and the substrate.

In this scenario, however, the

thermal mismatch becomes less significant due to a lower thermal gradient. The resonant

Figure 2.5 Examples of electrothermal tuning [48]: (a) Schematic diagram of a comb res-
onator with the straight beam for actively thermal tuning via localized heating. (b) Fre-
quency changes by different electrothermal tuning methods.

21

frequency change is therefore mainly attributed to the change in Young’s modulus, which

generally reduces the resonant frequency shift [48]. Figure 2.5b shows a comparison of

external heating method and Joule heating method for the same device presented in Figure

2.5a.

2.2.5 Photothermal Tuning

The thermal stress used to tune the resonant frequency not only can be generated electrically

but also can be optically induced. Optical tuning methods introduce a remote control of the

resonant frequency and provide higher resolution since localized heating can be achieved by

focusing light at different places in the structure. The influence on the resonant frequency

is based on the photo-thermal stress generated by the absorbed light from the laser spot

Figure 2.6 Example of photothermal tuning [49]: (a) Schematic diagram of the resonator
structure and the laser deflection method used to measure the resonant frequency. (b) SEM
image of the resonator. (c) The resonant frequency spectrum of the cantilever resonator with
the first four modes. (d) Relative resonant frequency shift as a function of laser intensity.
(e) Relative resonant frequency shift as a function of temperature.

22

on the structure. Figure 2.6 shows a resonant frequency shift induced by the laser beam

heating up the cantilever. The thermally induced axial stress shifts the resonant frequencies

in a nonlinear pattern.

2.2.6 Piezoelectric Tuning

Piezoelectric tuning method utilizes piezoelectricity, which directly converts an electric in-

put to a mechanical stress/strain that shifts the device’s resonant frequency. Figure 2.7

shows the resonant response of piezoelectric beams with different geometries and the res-

onant frequency shift as a function of DC voltage applied to the piezoelectric layer. The

influence of surface stress on the stiffness of the resonator beam leads to a shift in the reso-

nant frequency. Based on different beam structures with different boundary conditions and

constraints, cantilevers and bridges tend to present different response in frequency shifts.

The relative frequency shift for the cantilevers shows to be independent on the structure’s

length. On the contrary, bridges present different relative frequency shift with varying beam

lengths.

2.2.7 Stress Tuning

Resonant frequency largely depends on the structure’s tensile stress. Many technologies have

been developed and implemented to change the structure’s stress and tune the resonant

frequency. The sensitivity of frequency shift per added stress is largest near the Euler

buckling limit. Buckling occurs when a clamped-clamped beam has a compressive axial

pre-stress level higher than the critical buckling stress limit. As the added stress becomes

closer to this point, the resonant frequency shift becomes more sensitive to a change in axial,

tensile, or compressive stress. D.R. Southworth et al. demonstrated a vapor sensor with

high sensitivity based on a buckled silicon-polymer composite microbridge[51]. The beam is

pre-stressed into a buckled configuration and the volumetric changes in the reactive polymer

23

layer induce a large tension force in the bridge which leads to a large and fast change in

the resonant frequency. The resonant frequency shift as a function of stress in the operation

region is presented in Figure 2.8a. Stress frequency tuning can also be realized in a more

straightforward way. Scott S. Verbridge et al. employed a direct chip-bending method to

Figure 2.7 Example of piezoelectric tuning [50]:
(a) Resonant response of piezoelectric
beams with clamped-clamped structure. (b) Resonant response of piezoelectric beams with
clamped-free structure. (c) Frequency shift results for doubly clamped beams. (d) Frequency
shift results for cantilever beams.

24

realize a fully reversible stress control over a clamped-clamped NEMS resonator. Figure

2.8b shows the schematic diagram of the bending apparatus and the measurement setup.

The external tension force is shown to have the ability to efficiently increase the resonant

frequency and Q-factor of both silicon nitride and single-crystal silicon resonators.

2.3 Vanadium Dioxide

Most of the advances in MEMS have been made along the lines of using silicon and other

common CMOS standard compatible materials. This trend for technological improvement

has been exploited through the use of strategic and complicated geometries, which provides

excellent performance for well-defined applications. However, the improvement achieved by

using complex structures is ultimately limited by the underlying physical capabilities of the

materials used. To improve the tunability and to reduce the complexity of the system, smart

materials have been widely investigated and exploited in MEMS resonators techniques. As a

smart material with high strain energy density and near room temperature phase transition,

Figure 2.8 Examples of stress tuning: (a) Changes in the resonant frequency of a buckled
beam, the hygrometric polymer coating expands in proportion to relative humidity [51]. (b)
Schematic diagram of the bending apparatus and the measurement setup [52].

25

VO2-based MEMS resonators provide a wide tuning range.

2.3.1

Insulator-to-Metal Transition

The underlying physics in the phase change region of VO2 has drawn the attention of both

the physics and the materials science community for more than five decades. The extreme

sensitivity and the characteristic hysteresis are resulted from VO2 being a strongly corre-

lated electron system with narrow d-electron bands. Within the phase transition region,

complex interactions occur between the dynamics of spin, orbital and lattice degrees of free-

dom, resulting in the association of the change in band diagram with the rearrangement of

the atoms [53]. Figure 2.9 shows the schematic electronic band diagram of VO2 in both

the monoclinic phase and rutile phase. Each vanadium cation in VO2 accommodates one

electron in its 3d orbital and is surrounded by the oxygen anions located at the vertices of an

octahedron. The degenerate five 3d orbitals are split into a double degenerate eg state with

higher energy and lower energy t2g state with degeneracy in three degrees under the crystal

Figure 2.9 Schematic electronic band diagram of VO2 in both rutile phase (left) and mono-
clinic phase (right) [53].

26

field of a regular octahedron. Under the crystal field of the tetragonal structure, the t2g

orbital is further split into an a1g state with two degrees of degeneracy and a lower energy eg

state which interacts with the 2p orbital of the oxygen anion to form the molecular orbital.

In the monoclinic phase, the dimerization of the vanadium cation pairs splits the a1g state

into a higher energy antibonding state and a lower energy bonding state, leaving a bandgap

of around 0.7 eV between the valance band and the conduction band.

2.3.2 Structural Phase Transition
VO2 undergoes a first-order solid-to-solid phase transition around the temperature of 68◦C
where its hysteretic behavior spans about 15◦C. During the SPT, the crystal structure

changes from its low-temperature monoclinic phase to its high-temperature rutile phase,

leading to volume shrink along the cR axis about 0.6%. The material’s electrical, optical,

and mechanical properties change drastically during the IMT and show hysteretic behavior.

When VO2 is used as a thin film coating over a micro-mechanical structure, the changes in

the mechanical properties generate large stress that has been exploited to demonstrate high-

performance MEMS actuators with programmable capability. These large stress levels could

also be used to shift the resonant frequency of a micro-mechanical structure. The tuning

mechanism for VO2-based MEMS resonator belongs to electrothermal tuning technology,

the mismatch in thermal stress between VO2 layer and substrate such as amorphous VO2 or

single crystal silicon (SCS) is induced during the SPT to shift the resonant frequency. Thus,

the deposition of VO2 tends to align its (011) plane in the monoclinic phase and (110) plane

in the rutile phase parallel to the substrate [?].

2.3.3 Vanadium Dioxide Synthesis

The synthesis of VO2 thin film can be achieved in multiple ways, such as chemical vapor

deposition (CVD)[55], sol-gel technique[56], and physical vapor deposition (PVD)[57], etc.

27

Figure 2.10 XRD scans of VO2 thin film deposited on Si substrate with temperatures below
and above transition temperature [54].

CVD is the first deposition technology used for VO2 synthesis and has been extensively

used for about half a century. In 1966, Koide and Takei successfully synthesized bulk single

crystal VO2 by introducing vanadium oxychloride (VOCl3) carried by nitrogen gas into the

chamber[58]. VO2 thin film was also synthesized by the same group in the following year.

Other precursors such as vanadium acetylacetonate ((C5H7O2)4V), vanadyl tri-isopropoxide

(VO(OC3H7)3) and vanadium chloride (VCl4) have also been widely implemented to deposit

VO2 thin film coatings.

Sol-gel technique is also one of the most commonly used deposition methods for VO2

thin film synthesis. It has many advantages such as low cost, ease of doping, and better

28

uniformity. The sol-gel process starts with the conversion of monomers into a chemical

solution (sol) which acts as precursors. Then the sol gradually forms an integrated network

(gel) of discrete particles and polymer networks, the gel contains both a liquid phase and

solid phase. The formation of metal oxides involves connecting the metal centers with oxo

(M-O-M) or hydroxo (M-OH-M) bridges and hence generating metal-oxo or metal-hydroxo

polymers in solution. The chemical solution used for VO2 synthesis includes vanadium

isopropoxide (C15H40O5V), diluted VO(OC3H7)3 in ethanol, hydrolysis of vanadium oxo-

alkoxides (VO(OR3)), and sodium metavanadate (NaVO3), etc.

Sputtering is one of the most common PVD processes for depositing high-quality thin

films. VO2 thin films can be grown by reactive ion beam sputtering of a vanadium target in

an argon-oxygen atmosphere. The bombardment of argon (Ar) ions transfers kinetic energy

to the target material, resulting in vanadium ions ejected from the surface of the target. DC

and RF power supplies are often used to enhance the bombardment, DC sputtering is often

favored when a high deposition rate is required. However, for depositing insulating oxides,

DC sputtering causes an accumulation of charges on the surface of the sample, leading to a

lower deposition rate and a poor film quality. Thus, RF sputtering is more preferred in VO2

deposition. PLD, as another PVD technique, possess a similar function as RF sputtering.

Instead of using ion bombardment to knock out target ions, PLD uses high energy pulsed

laser to enable the kinetic energy transfer process. PLD provides an accurate control of the

newly deposited film and is able to perform deposition on a variety of substrates, including

silicon, quartz, sapphire, etc.

In this work, all the samples are fabricated by the PLD

technique.

2.4 Flexible Physical Sensors

Flexible physical sensors have demonstrated to have promising applications in sensing net-

works where the complex environmental stimulus is considered. Bio-compatible soft elec-

29

Figure 2.11 Example of resistive bending sensor and pressure sensor: (a) Structure of a strain
gauge [59]. (b) Structure of a tactile pressure sensor [60].

tronic skins that are capable of force distribution visualization have been exploited exten-

sively in the field of soft robotics [61] and human motion monitoring [62, 63]. Despite the

different approaches in integrating each individual sensing element, the functionality of each

sensing unit can be classified into several groups according to its working principles. Gen-

erally, resistive, capacitive and piezoelectric mechanisms are often considered for various

applications [64]. For example, bending strain gauges can play a major role in motion mon-

itoring wearable gadgets, which can be used for detecting large deflections. Progresses in

flexible electronics of making deformable, stretchable and biocompatible bending sensors also

extends their integration in IoT systems.

2.4.1 Resistive Physical Sensors

Resistive pressure sensors are most widely used in real applications due to their simple device

structure, high signal-to-noise (S/N) ratio, and easy readout features [66]. Conventional

resistive sensors are usually based on metal foils and semiconductor coatings which utilize

the resistance change due to geometrical effect. Limited by the low mechanical compliance,
metal foil sensors only provide a detection range of 2% ∼ 5%. Higher sensitivity can be

30

achieved by utilizing microstructural disconnection mechanism in metallic nanomaterials,

such as nanoparticle (AgNP) [67], gold nanofilm [65], and gold nanowire (AuNW) [68],

coated on polymer substrates. Figure 2.12 shows an example of Au nanoparticle film-based

flexible bending sensor. Recent progresses have also demonstrated fully elastomer-based

resistive strain sensors based on carbon nanotube (CNT) [69, 70], graphene [71], and laser

scribing technique [72], etc. However, those passive sensors still require external power

supported sensing elements which are problematic during their integration in IoT systems

with sustainability requirements.

2.4.2 Capacitive Physical Sensors

Capacitive pressure sensors measure different forces by monitoring the capacitance variations,

caused by the change in separation between parallel plates[73, 74]. By optimizing micro-

Figure 2.12 Example of gold nanofilm-based resistive bending gauge [65]: (a) Fabrication of
Au nanofilm bending sensor on paper substrate. (b) Model of the sensor. (c) SEM image
of Au nanoparticles film. (d) Photograph of the flexible bending sensor. (e) Top view of
bending sensors on different substrates.

31

Figure 2.13 Example of capacitive-based physical sensors for bending and pressure monitor-
ing [76].

structures within each sensing element and the material’s dielectric constant [75], capacitive

sensors with high spatial resolution and large dynamic range have been developed [76, 77].

However, the rather complicated evaluation system and the inherent hysteresis error still

remain a problem. Figure 2.13 shows a capacitive type of flexible sensor for pressure sensing

and bending radius monitoring. The sensor has an address line configuration, where each

sensing element consists of a sandwiched structure as shown in Figure 2.13(right).

2.4.3 Self-Powered Physical Sensors

Although the choice of physical sensing technology is determined by specific applications,

battery-based resistive and capacitive pressure sensors are not considered to be optimal

approaches for the Internet of Things (IoT) devices, which impose sensor network with

lightweight, miniature size, and energy sustainability requirements. Therefore, a direct en-

ergy conversion between mechanical input and electrical sensing output becomes imperative.

Nanogenerator-based self-powered pressure sensors using piezoelectric or triboelectric effect

have been demonstrated as emerging technologies in flexible electronics [80, 81]. Inorganic

piezoelectric nanostructures are introduced by micro-fabrication techniques to improve the

detecting sensitivity and sensing resolution. Nanowires (NWs) such as ZnO [78], CdS [79],

32

and NaNbO3 [82] with high electric output are often used as piezoelectric sensors. Me-

chanical energy from the bending motion of nanowires is converted to an electric output.

Composite nanoparticles (NPs), e.g. BaTiO3 [83, 84], are also often used to improve the

piezoelectric effect by increasing the total dipole moment. To overcome the low flexibility of

inorganic piezoelectric nanogenerators (PENGs) sensors, foldable and stretchable substrates

such as polydimethylsiloxane (PDMS), polyethylene terephthalate (PET), or polyethylene

(PEN) can be used [85]. Figure 2.14 shows a summary of the triboelectric series wearable

electronics for different applications. Triboelectric sensors convert the mechanical energy by

utilizing the internal friction of the material, the selection of the active materials are there-

fore broadened from NWs/NPs to polymers [86] and soft fabrics [87], which significantly

improve flexibility. Their high performance has also been demonstrated by optimization of

the microstructure such as surface etching [88], topology casting [89], injection molding, etc.

The compatibility with micro-fabrication techniques also makes it more adaptable to the

Figure 2.14 Examples of piezoelectric-based physical sensors [78, 79]: (a) SEM image of
aligned ZnO NWs grown on Al2O3 substrate.
(c)
Working principle of ZnO NW-based nanogenerator, the electric output is generated by NWs
sliding against each other. (d) Photograph of NaNbO3 nanowires. (e) Schematic image of
m, NaNbO3 - PDMS composite-based nanogenerator. (f) OM and SEM view of the device
shown in (e). (g) Energy generation mechanism of NaNbO3 NWs-based nanogenerator.

(b) The TEM image of ZnO NWs.

33

Figure 2.15 Illustrations of triboelectric self-powered physical sensors [81]: (a) Series of
materials in TENG family. (b) Working principle of TENG device. (c) Comparisons between
power consumption in commercial electronics and power output in TENG devices.

high spatial resolution requirements [90, 91].

2.5 Nanogenerator-based Energy Harvesters

With the incredible growth of the internet over the past few decades, the world’s economic

structure has been rapidly shifted to rely heavily on information technology. Not long ago,

it was enough for a mobile phone to be able to make calls and send texts. Nowadays, mobile

phones are essentially terminals of all kinds of information and utilities. Internet of Things

(IoT) and big data enable data exchange among health monitor apps, wireless sensor sys-

34

Figure 2.16 Road-map of improvements on the power output of nanogenerators [103].

tem, and smart automation in order to create a more robust and direct way to integrate

real-world decision-making processes into artificial intelligence (AI) networks. Hence, mul-

tifunctionalities have been imposed on personal electronic devices such as smartphones and

even bracelets. However, the future progress of all these technological advances is tied to the

energy budget that comes with all these tools. Self-powering technologies [92, 93, 94, 95] that

converts ambient energy sources from multiple forms (e.g. solar [96, 97], thermal [98, 99]

and mechanical [100, 101, 102]) to electricity have become potential energy solutions for the

smart, multifunctional phones and wearable electronics.

However, the path for a solution to the increasing energy demands needs to be compre-

hensive and inclusive. Approaches should consider scavenging, storing, and using as many

different forms and magnitudes of energy. Unlike solar energy, the energy produced by

35

random mechanical vibrations can be obtained nearly at any time from multiple sources.

Energy harvesting devices such as piezoelectric (PENG) [104, 105], triboelectric (TENG)

[106, 107, 108, 109] and ferroelectric (FENG) [110, 111] nanogenerators that are capable

of converting kinetic energy to electrical energy are considered to be the most promising

devices for integrated self-powered systems [112]. Even though those nanogenerators exhibit

the piezoelectric effect, the origins of the piezoelectricity are quite different. PENG usually

uses inorganic nano piezoelectric materials such as ZnO nanoparticles and nanowires; and

their flexibility can be achieved by their integration with soft substrates such as polyimide

(PI), polyurethane acrylate (PUA), etc. TENG makes use of the triboelectric effect, and

are often considered at the device level for high-efficiency energy harvesting. Their power

densities can be as high as 313 W/m2 [103].

2.6 Summary

In this chapter, a comprehensive review of the background of MEMS resonator, tuning tech-

nology, vanadium dioxide, flexible physical sensors, and energy harvester is presented. First

of all, the motivation for replacing quartz resonators with MEMS resonators is illustrated

in this section. Then, the tuning technologies of both passive tuning mechanism and active

tuning mechanism are discussed in the following section. Passive tuning methods, such as

post-fabrication tuning and post-packaging tuning, are one-time permanent tuning methods

which have less tuning flexibility. Active tuning, on the other hand, provides a real time

tuning configuration, the tuning is fully reversible and covers a wide tuning range. The

active tuning methods discussed in this section include: electrostatic tuning, electrothermal

tuning, photothermal tuning, piezoelectric tuning, and tensile or compressive tuning. Next,

the properties of VO2 thin film are introduced including the insulator-to-metal transition,

spatial phase transition, and synthesis methods of the material. In the second half of this

chapter, flexible physical sensors are introduced. Based on different operating mechanisms,

36

such devices can be categorized into three groups: resistive, capacitive, and piezoelectric.

Advantages and disadvantages of each type of sensor are discussed and compared. To meet

the sustainability requirement imposed by IoT devices, piezoelectric sensors are often pre-

ferred due to their lightweight, high flexibility, and self-powering capability. The high d33

value also enables potential applications in energy harvesting systems.

37

CHAPTER 3

DESIGN, FABRICATION OF VANADIUM DIOXIDE MEMS RESONATORS

AND FERROELECTRET NANOGENERATORS

3.1 Fabrication of VO2 based MEMS Resonators

3.1.1 Fabrication Flow

The VO2-based resonators (cantilevers and bridges) reported in this paper are all within the

same chip. The fabrication processes of VO2-based cantilevers are schematically described

in Figure 3.1. Uncoated MEMS resonators (before VO2 deposition) used in this paper
are 2 µm thick, with a 200 nm layer of titanium/platinum (50 nm Ti / 150 nm Pt) heater
electrode placed in between two 1 µm SiO2 layers. This symmetric stack of layers is designed

Figure 3.1 Fabrication flow of VO2-based cantilever. (a) PECVD deposition of SiO2 layer
on Si substrate. (b) Thermal evaporation of Ti/Pt heater trace, patterned by lift-off. (c)
PECVD of second layer SiO2. (d) The structure defined by dry etching. (e) MEMS structure
released by XeF2. (f) PLD deposition of VO2 coating.

38

to reduce the extrinsic thermal stress during the deposition of the VO2 thin film, which can

produce bending of the structure in the process and an uneven VO2 thin film deposition. In

summary, a SiO2 layer is deposited on a Si wafer using Plasma Enhanced Chemical Vapor

Deposition (PECVD) method, followed by deposition and patterning of Ti/Pt (Ti only used
for adhesion purposes), deposition of a second 1 µm layer of SiO2 (again, using PECVD),

and patterning of the resonator structures through both SiO2 layers. The wafers are then

diced, and released, which is done by isotropic etching of the silicon substrate using xenon

difluoride (XeF2) gas. VO2 thin film is deposited using PLD (see Figure 3.2). During the
deposition process, the chamber is first pumped down to a vacuum level below 10−6 Torr by

using a turbomolecular pump connected with a mechanical scroll pump. Then the oxygen is

Figure 3.2 The PLD equipment for VO2 deposition, the inset shows the plasma plume coming
off of the vanadium target.

39

Figure 3.3 (a) Schematic diagram of the released cantilever structure. Contacts ”1” and ”4”
complete the heater loop around the cantilever structure, contacts ”2” and ”3” are used to
measure the resistance of theVO2 film. (b) Measured resistance of the patterned VO2 film
as the temperature is increased and decreased by Peltier heating.

introduced into the chamber at a flow rate of 20 sccm and a butterfly valve is controlled to

keep the chamber oxygen atmosphere pressure at 15 mTorr. A heater located approximately
2 inches behind the sample is preheated to 595 ◦C. After reaching this temperature, a

metallic vanadium target is ablated by a Krypton Fluoride (KrF) excimer laser with 560 mJ

in energy and 10 Hz in frequency for 10 min. After VO2 deposition, a 30 min annealing step

is performed under the same deposition conditions.

After the deposition is completed, a resistance measurement is performed as the tem-

perature is varied across the phase transition of VO2. The measured drop in resistance of

approximately 3 orders and the hysteretic behavior observed verified the quality of the VO2
thin film. The measurement is performed on the VO2 thin film coated on a 550 µm long

cantilever, which is shown in Figure 3.3. At this point, the devices are ready to be mounted

on an IC package, wire-bonded and tested. The fabricated and tested resonators, shown in

Figure 3.4, include microcantilevers and micro bridges with different lengths.

For the VO2 coated micro-bridges, the initial first mode resonant frequency can be esti-

40

Figure 3.4 SEM images for the test structures. Top: cantilever of 550 µm long. Bottom:
bridge of 300 µm. The electrodes for resistive heating actuation are artificially colored for
clarity.

mated by the following equation [21]:

f 2
b = 1.06

[E2

1 h4

1 + E2

2 + E1E2h1h2(4h2

1 + 4h2
2 h4
(ρ1h1 + ρ2h2)(E1h1 + E2h2)l4

2 + 6h1h2)]

(3.1)

where E1, h1, ρ1 and E2, h2, ρ2 are the Young’s modulus, thickness and density of the SiO2

and the VO2 layer, respectively, and l is the length of the bridge. On the other hand, the

initial first mode resonant frequency of the VO2 coated cantilever can be given by [113]:

f 2
c =

0.26h2
π2l4 ×
1

E1wh1 + 12E2h2[(w + 2h2)( 1

2 +

h2
h1

+

h2
2
2h2
1

) +

h1
6 ]

ρ1h1w + 2ρ2h2(w + h1 + 2h2)

(3.2)

41

With the same variables used for equation (3.1) and w is the width of the cantilever. The

equations above determine the initial resonant frequencies of the two resonator structures

used in this work in the static state (i.e. un-actuated at room temperature). It should be

noted that the equations do not take into account the thin metal layer used for Joule heating

and tuning, but they do provide a good approximation that can be used for initial device
design. The calculated resonant frequencies for a 300 µm bridge and a 550 µm cantilever

are shown in Figure ?? along with the experimental value. Here, a 9% under-etching effect

is assessed for the bridges and 4.5% for the cantilevers. Thus, the effective length of the
bridges and cantilevers are estimated to be 328 µm and 576 µm respectively. The resonant

frequency of the bridges determined by equation (3.1) is about 102.3 kHz, which is far

from the measured frequency. This is due to the strong influence of stress in the resonant

frequency of a bridge structure. To match the experimental curve, the initial residual stress

in the bridge was estimated to be 38.9 MPa— which is within the value found for similar

structures. Thus, considering the stress effect, the resonant frequency for the bridge is

found to be 237.6 kHz. It should be noted that this thermal residual stress does not play

such a strong influence on the resonant frequency of cantilever structures, since the stress

is partially released, producing an initial bending. Thus, the estimated resonant frequency

of the cantilevers determined by equation (3.2) is 5.49 kHz, which is not that far from the

measured resonant frequency (5.09 kHz).

3.1.2 Buckling States in VO2 MEMS Resonators with Bridge Structures

The residual axial stress that causes the large discrepancy in resonant frequency for bridge

structures comes from the residual thermal stress among different materials in the mi-
crobeam. After the SiO2 deposition at 300 ◦C, there is residual thermal stress induces
compressive axial stress (σl) on the beam, which is larger than the critical Euler buckling

42

load σc[114]:

σc = −π2Eef f h2

3L2

,

(3.3)

Figure 3.5 Fabrication processes of VO2-based bridge resonators. (a) Deposition of 1 µm SiO2
layer on Si substrate by PECVD. (b) Metalization of 200 nm Pt/Ti thin film by sputtering
coating and the heater traces are patterned by the lift-off method. (c) PECVD Deposition of
the second SiO2 layer of 1 µm. (d) Resonator beam structure defined by plasma dry etching
of SiO2. (e) MEMS structure released by isotropic etching with XeF2. (f) Deposition of 100
nm VO2 thin film by PLD deposition.

Figure 3.6 Statistic of buckling preference after the MEMS structure release.

43

where Eef f is the effective Young’s modulus of the beam material, h is the thickness, L

is the beam length and the negative sign represents the compressive load.

In this case,

the microbridge will deform into a buckled state with a sinusoidal shape by minimization

of the total energy[115]. For an ideal bridge, the beam has no preference in the buckling

orientations which leads to an equal probability of buckling down or up. However, structural

imperfections cause concave anchor boundary conditions due to diagonal beam configuration

and gradient in film stress; which makes the buckling orientation highly related to L and

h[116]. In this work, the buckling orientation preference of the devices used is statistically

demonstrated by reviewing 400 microbridges in the same fabrication condition before VO2

deposition (i.e. until Figure 3.5e). Figure 3.6 shows the buckling distribution for these

devices: 32% of the devices have an up buckling state while 53% are buckled down. The

remaining structures (15%) show a downward bell-shaped buckling state.

After the VO2 deposition, the device is cooled down from 595 ◦C to 85 ◦C while an
axial tensile stress induced by the contraction of the VO2 film[21]. This tensile stress would

alleviate the buckling state by decreasing the buckling amplitude but is not large enough

to overcome the Euler buckling limit and flatten the beam structure. As the device is
further cooled down from 85 ◦C to room temperature, the VO2 thin film goes through its
phase transition from R-phase to M-phase, and the crystal planes parallel to the surface

increase their areas, which leads to additional stress that consolidates the buckled state.

Thus, the VO2 deposition condition does not change the initial buckling orientation for the

bridge structure. Figure 3.7a-c show SEM images of three VO2-based microbridges with
different buckling profiles from a 75◦ side view. The SEM images for three different types of

microbridges without VO2 coating are shown in Figure 3.8. Magnified views of the beam

center and anchor are presented in Figure 3.7d and Figure 3.7e, respectively, where the

metal resistor lines can be seen clearly. Figure 3.7f shows the cross-sectional view of the

film layout and Figure 3.7g shows a closer look at the VO2 thin film coating.

44

3.1.3 Effect of Residual Axial Stress

Three VO2-based microbridges with same dimensions but different buckling profiles are

tested and analyzed. Because of the diagonal arrangement of the beam, the under-etching

effect results in a concave boundary condition which causes a minimum elongation of the

effective beam length of Lef f = L + 1
2 W , where W is the beam width[116]. From the
SEM images, the L, W and h are measured to be 316 µm, 42 µm and 2.27 µm, respectively
(see Figure 3.9), thus the minimum value of Lef f is estimated to be 337 µm. However,
the actual effective length could be much longer than this value depending on the isotropic

Figure 3.7 SEM images of VO2-based bridge resonators used in this work. (a) A 300 µm
VO2-based bridge resonator with up-buckled profile, scale bar: 50 µm. (b) A 300 µm VO2-
based bridge resonator with down-buckled profile, scale bar: 50 µm. (c) A 300 µm VO2-based
bridge resonator with bell-shape buckling profile, scale bar: 50 µm. (d) Beam center, scale
bar: 10 µm. (e) Beam anchor, scale bar: 10 µm. (f) A cross section view of the stacked
layers, scale bar: 1 µm. (g) A cross section view of the VO2 thin film coating, scale bar: 100
nm.

45

etching time. After scratching out the suspended structure, the actual Lef f is revealed to
be 377 µm as shown in Figure 3.8. Given that the beam body is made of 91.9% SiO2,

3.3% Pt, and 5% VO2, Eef f is approximated as 76.6 GPa, where the Young’s modulus of

each individual material can be found in Table 3.1. Thus, the σc is estimated from equation

(3.3) to be - 9.14 MPa for the coated device and - 7.84 MPa for the uncoated beam. For an

uncoated beam, the residual axial stress (σl) can be calculated by considering the difference

Figure 3.8 Images of the uncoated bridges. (a) Top view optical microscope image of uncoated
microbridge, the over-etching edge is highlighted in the red circle, where the Si substrate
underneath the transparent SiO2 layer is etched away, scale bar: 100 µm. (b) Top view
optical microscope image of uncoated microbridge with top SiO2 layer scratched off, the side
undercut and anchor are highlighted, the effective length is measured to be 377 µm, scale
bar: 100 µm. (c) SEM side view of upward sinusoidal uncoated microbridge, scale bar: 50
µm. (d) SEM side view of downward sinusoidal uncoated microbridge, scale bar: 50 µm. (e)
SEM side view of downward wavy uncoated microbridge, scale bar: 50 µm.

46

in thermal expansion coefficients in SiO2 layer and Si substrate as[117]:

σl =

ESiO2
1 − νSiO2

(αSiO2

− αSi)∆T

(3.4)

where ESiO2
= 70 GP a and νSiO2
= 0.7 × 10−6 K−1 and αSi = 2.8 × 10−6 K−1 are the thermal expansion
of SiO2, αSiO2
coefficients of SiO2 and Si, respectively, and ∆T represents the temperature difference be-

= 0.17 are the Young’s modulus and Poisson’s ratio

tween room temperature and SiO2 deposition temperature. It should be noted that here

the influence of Pt is not considered since it is deposited while the sample remains at room

temperature. The estimated residual axial stress for the uncoated beam is estimated (from

equation (3.4)) to be - 49.6 MPa at room temperature. This value indicates compressive

stress much larger than σc and therefore the devices exhibit buckled state as shown in Figure

3.8.

For a VO2 coated microbridge, the Finite Element Method (FEM) (see Figure 3.10)

Figure 3.9 Dimensions of VO2 coated bridge. (a) SEM top view of VO2-based microbridge,
the width is 43 µm and the length is 319 µm, scale bar: 50 µm. (b) SEM cross section view
of stacked film layout, the thickness of the beam body is 2.15 µm, the first SiO2 layer is 0.89
µm, the second SiO2 layer is 1.04 µm and the Pt heater is 0.22 the second SiO2 layer is 1.04
µm, scale bar: 1 µm. (c) SEM cross section view of VO2 thin film coating, the thickness is
117 nm, scale bar: 100 nm.

47

shows a first mode resonant frequency of 70.2 kHz, and the parameters used for the simula-

tion are summarized in Table 3.1. However, the resonant frequencies of the three devices are

Figure 3.10 FEM simulation of first mode resonant frequency (f1) at room temperature from
COMSOL, the scale bars show the lateral deflection at room temperature. (a) First mode
resonant frequency of a pure SiO2 microbridge, f1 = 160.1kHz. (b) First mode resonant
frequency of a SiO2 microbridge with embedded Pt metal heater, f1 = 137.3kHz. (c) First
mode resonant frequency of a VO2 coated microbridge without considering the thermal
mismatch between VO2 and SiO2 layer, f1 = 70.2kHz. (d) First mode resonant frequency
of a VO2 coated microbridge considering the thermal mismatch between VO2 and SiO2 layer,
f1 = 258.8kHz.

48

measured to be 236.5 kHz, 247.6 kHz, and 266.7 kHz for down-buckled beam, up-buckled

beam, and “bell-shape”-buckled beam, respectively. The large discrepancy between the sim-

ulation and experimental results is attributed to the mismatch of the thermal expansion

coefficient between the VO2 and SiO2 layers. Given that all materials are deposited at dif-

ferent temperatures, the mismatch in the thermal coefficients leads to a large residual film

stress at room temperature. With this taken into account, the FEM simulation gives an

estimation of the first mode resonant frequency to be 258.8 kHz, which is close to the exper-

imental measurements. According to Euler-Bernoulli beam theory, the first mode resonant

frequency of a buckled microbridge increases when the beam body undergoes compressive

axial stress and decreases when the axial load is tensile. The relation between resonant

frequency and residual axial stress can be expressed as:

(cid:115)

f =

2

ρef f Lef f

2 (|σl| − |σc|)

(3.5)

where ρef f = 2920 kg/m3 is the effective density of the beam. Equation (3.5) indicates that

when σl equals to σc, the resonant frequency is not measurable, which is the Euler buckling

limit condition. Any deviation of the σl from σc, by either adding compressive or tensile

stress, would lead to a rapid increase in the resonant frequency. The σl is estimated to be

-20.7 MPa for the up-buckled beam, -21.9 MPa for the down-buckled beam, and -23.9 MPa

for the bell-shaped beam. It can be seen that the compressive residual stress in the beam

after VO2 deposition becomes smaller, (compared to the estimated value of - 49.6 MPa before

deposition), but it is still larger than σc of the coated beam. This is also consistent with

the observations by comparing Figure 3.7 and Figure 3.8 that the buckling amplitudes are

reduced after VO2 deposition.

When VO2 is thermally actuated, the material undergoes an SPT from M-phase to R-

phase.

In the low-temperature region before the phase transition, the vanadium atoms

are alternatively spaced at distances of 2.65 ˚A and 3.12 ˚A. During the phase transition, the

crystalline structure is rearranged into a more organized phase with vanadium atoms equally

49

spaced at 2.87 ˚A [120]. This distortion in the structure leads to a 0.7% contraction of the

film along the c-axis direction[121]. Thus, high strain energy is induced into the beam body

with a significant amount of stress and strain[15]. The added compressive stress in the VO2

thin film will induce tensile stress in the SiO2 beam body –note that no external force is

added to the beam during the SPT. Thus, a bending moment is generated to distort the

beam structure into a curved shape with the film of a larger thermal expansion coefficient on

the convex side. For a C-C bridge structure, the two fixed anchors restrict the large lateral

deflection and lead to a high residual stress level along the beam longitudinal direction. This

residual tensile stress in the SiO2 beam body causes a resonant frequency increase in an

unbuckled microbridge[21] and a resonant frequency decrease in a buckled microbridge[122].

3.2 Fabrication of Ferroelectrect Nanogenerators

3.2.1 Fabrication of Polypropylene Ferroelectrect Films

PPFE exhibits a strong piezoelectric effect where its ”piezoelectricity” originates from the
distortion of the µm-sized charged air ellipsoids inside the PPFE. Those engineered macro-

scaled dipoles change dipole moments upon compression and releasing operation. In this

section, the fabrication process is briefly described and schematically shown in Figure 3.11.

First, the fabrication process starts with the polypropylene (PP) film filled with inorganic sil-

icate particles as stress concentrator [123, 124]. When the material undergoes a bi-directional

Table 3.1 Properties of the materials used in FEM simulation, properties of SiO2 and Pt are
taken from COMSOL, and the property of VO2 is taken from the literature[118, 119].

Materials

Thermal expansion coefficient (1/K)

Density (kg/m−3)

Young’s modulus (GPa)

Poisson’s ratio

Strain reference temperature (K)

SiO2

0.7 × 10−6

Pt

8.8 × 10−6

VO2

5.7 × 10−6

2200
70
0.17
573.15

21450
169
0.38
293.15

4670
140
0.33
743.15

50

Figure 3.11 Fabrication process. (a) Polypropylene (PP) film filled with inorganic silicate
particles.
(c)
Diffusion of N2 gas. (d) Ellipsoids expansion by a sudden decrease in pressure. (e) Plasma
discharging. (f) Electrodes metalization.

(b) Biaxial in-plane stretching of the PP film to create the air ellipsoids.

stretching process, the stress starts to accumulate at the silicate location. When the mate-

rial’s cohesive strength is reached, the PP film fails and micro-cracks propagate along the

stretching axis with the help of stress concentrator [125]. Next, the PP film is introduced

in a high-pressure nitrogen (N2) environment of above 5 MPa where the N2 gas is able to

51

diffuse into the micro cracks through the PP film. Then, the high-pressure ambient is sud-

denly removed and the air ellipsoids are expanded rapidly creating ellipsoid structure [126].
A heat treatment at ∼ 100 ◦C follows in order to increase the strength of the void structure

[127, 128]. After that, the high electric field is applied to the PP film and plasma discharging

occurs in the air ellipsoid resulting in two opposite surfaces of the voids are charged with

different polarities. Finally, silver thin films are sputtered on both sides of the PPFE film as

metal electrodes by using sputtering coater (Hummer X, Anatech Inc.) as shown in Figure

3.12. The PPFE film is placed in a vacuum chamber beneath the silver target at the distance

of 30 mm. During the deposition, the base vacuum level of 20 mTorr is reached and N2 gas

is introduced to the chamber until the pressure is stabilized at 65 mTorr. A high voltage

of 1.5 kV is then applied to generate a large electric field inside the chamber to create N2

plasma bombardment on the silver target, leading to a thin film of silver deposited on PPFE

surface. The above setting would give an approximately 500 nm thick silver thin film for a

30 min deposition.

3.2.2 Piezoelectric Effect and Multilayer Devices

This section discusses the linear coupling between the electrical and mechanical domain

of the PPFE and justifies the piezoelectric effect for the electromechanical response. Al-

though the fundamental working principle of PPFE differs from the piezoelectric material,

the electromechanical response shares very similar behavior. For piezoelectric material, the

fundamental equations establish a linear coupling between electric polarization field and

mechanical force by:

P = d33

F
A

,

(3.6)

where P is the polarization field, d33 is the piezoelectric coefficient, F is the mechanical

input force and A is the contact area. Charges accumulated at the boundaries due to this

induced P and surface charge density σ can be determined as σ = P . By using a capacitive

52

(a)
Figure 3.12 Sputtering coater used for depositing silver electrodes on PPFE film.
Overview of the sputtering coater (Hummer X, Anatech Inc.). (b) The silver target mounted
on top of the vacuum chamber. (c) The sample holder at the bottom of the chamber where
PPFE is placed for metalization.

model, the accumulated charges Qsc and open circuit voltage Voc can be expressed as:

and

Qsc = σA = d33 · F,

Voc =

Qsc
C

=

d33g

A

· F,

(3.7)

(3.8)

where C is the equivalent capacitance of the device. Equations (3.7) and (3.8) show that

both Qsc and Voc have linear relation with F . When output terminals of the device are short

connected, Qsc is released as short-circuit current (Isc) and can be described as:

Isc =

dQsc

dt

=

d33g

A

· dF
dt

,

(3.9)

which takes the derivative form of F (and also Voc) as shown in Figure 3.13. Figure 3.13a

shows the Voc output in a compression and releasing cycle, the triangular waveform follows

the same profile as the mechanical input F1. The Isc which takes the derivative form of Voc

53

exhibits a square waveform as shown in Figure 3.13b. The measured signal waveform is in

accordance with equation (3.8) and equation (3.9) and verifies the piezoelectric effect.

Changing polarity test is also carried out to justify that the output signal comes from the

device. Figure 3.14a and Figure 3.14c show the Voc and Isc output in a forward connection

- i.e. connecting the device and testing instrument through terminals with the same polarity.

Switching the connecting terminals produces the results shown in Figure 3.14b and Figure

3.14d.

Since the device can be modeled as a capacitive model. Therefore, the output should

follow the corresponding behavior. For a single layer device with a fixed thickness under

a given mechanical force, the output in terms of voltage and current can be magnified by

increasing the contact area. Thus, by connecting N pieces of single-layer devices in parallel,

both Voc and Isc can be increased by N times. This can be easily done by stacking N layers

as shown in Figure 3.15, where all the positive and negative electrodes are respectively

connected with each other. In this configuration, Voc and Isc can be expressed as:

Voc = N · d33g

A

· F

(3.10)

Figure 3.13 Signal profile compare of Voc and Isc.
in compression and releasing cycle.
releasing cycle.

(a) Triangular waveform Voc output
(b) Square waveform Isc output in compression and

54

Figure 3.14 Changing polarity test of electric output. (a) Open circuit voltage (Voc) mea-
surement in the forward bias connection. (b) Open circuit voltage (Voc) measurement in
the reverse bias connection. (c) Short circuit current (Isc) measurement in the forward bias
connection. (d) Short circuit current (Isc) measurement in the reverse bias connection.

and

3.3 Summary

Isc = N · d33g

A

· dF
dt

(3.11)

This chapter presents the design and fabrication of VO2-based MEMS resonators and the

development of ferroelectret nanogenerators. The resonators used throughout this work are

55

Figure 3.15 Schematic demonstration of stacking multilayer structure.

three bridges with the lengths of 200, 250 and 300 µm as well as three cantilevers of 350,
450 and 550 µm. The resistance measurement is performed after the VO2 deposition to

confirm the film quality. First mode resonant frequencies of both structures are measured

and compared to simulated values. The discrepancy in the experimental and simulated data

can be attributed to the residual thermal stress and the under etching effect. Moreover,

microbridges with different buckling profiles are observed even when the same fabrication

conditions are used. The buckling amplitude and orientation preference are found to be

56

related to boundary conditions, geometric dimensions, and residual thermal stress. FEM

simulation, as well as analytical methods, are used to estimate the residual thermal stress.

The fabrication process of ferroelectret nanogenerator (FENG) is also introduced in this

chapter. The strong piezoelectric effect of the material comes from the engineered macro

dipoles upon external mechanical load occurs. The working principle of the device is ex-

plained in the point of view of changing dipole moment and a capacitive model. Changing

polarity test is also carried out to confirm the success of the device fabrication.

57

CHAPTER 4

INFLUENCE OF VO2 THIN FILM COATINGS ON THE PERFORMANCE

OF MEMS RESONATORS

This chapter discusses the performance of VO2 based MEMS resonators with both cantilever

and bridge structures. The study first focuses on the resonant frequency tuning behavior at

the two ends of the phase transition region where VO2 is either in its monoclinic or rutile

phase. Opposite trends have been found before and after the phase transition region. By

comparing the relative resonant frequency shifts in both structures, it has been found that

the bridge structure is more stress-sensitive while the cantilever structure is dominated by

the geometric effect. The large residual thermal stress in bridge structures would also lead to

different types of buckling profiles and amplitudes. Thermal actuation is achieved by apply-

ing an electrical current to integrated heaters, or by uniform substrate heating. Bidirectional

tunability is found when substrate heating is used, while Joule heating shows a monotonic

change in frequency. This phenomenon can be attributed to the transition in boundary

conditions, where the turning points are indicated by the prominent changes in buckling

amplitude. The devices’ power consumption, response time constant are also discussed in

this chapter. A pulse width modulation (PWM) method is used to find out the underly-

ing mechanisms for programming the resonant frequency states within the phase transition

region. By combining VO2-based MEMS resonators with ferroelectret nanogenerators, a

new type of head injury telemetry system is developed for compact sports injury evaluation.

Finally, a prototype of second-order MEMS bandpass filter is inspired by the tunability and

the programmability of the VO2-based resonators. In a specific measuring configuration ana-

log to laser interferometer, the bandwidth tunability and Q-factor enhancement have been

demonstrated.

58

Figure 4.1 Schematic diagram of the laser deflection method used to measure the resonant
frequency of a 300 µm VO2-based bridge resonator, the VO2 phase transition can be induced
either by electro-thermal (i.e. resistive, or Joule) heating or substrate heating. Mechanical
vibration input is provided by the piezoelectric disk.

4.1 Experimental Setups

The first mode resonant frequency of the VO2-based MEMS resonator is measured by the

laser deflection method which is briefly described as a schematic diagram shown in Figure

4.1. The device is first attached on the thermal conductive IC package, which is also fixed

onto a Peltier heater, by thermally conductive silver paste. A thermocouple is then placed

onto the IC package close to the device in order to monitor the temperature. A piezoelectric

actuation disk is also placed beneath the Peltier heater which provides the AC sweeping

mechanical force in order to determine the resonant frequency. Then the whole package is

placed into a vacuum chamber and pumped down to below 10 mTorr. An AC electrical

sweeping signal is provided by a network analyzer (HP-3589A) and drives the piezoelectric

59

Figure 4.2 Resonant frequency change for VO2 coated cantilever beams of different lengths
through full heating and cooling loop.

actuator into vibration. The VO2 resonator exhibits strong vibration at its natural resonant

frequency and deflects away the laser beam focused onto the beam center. This difference

in the light intensity is captured by a photodiode detector, which is also connected with

the network analyzer. To avoid any undesirable heating effect caused by the laser beam,

especially in the phase transition window of VO2, a neutral density filter (ND = 1) is used

to reduce the laser power shine on the device while still providing a detectable optical signal.

4.2 Comparison of Different Structures

Measurement of the first mode resonant frequency has been performed for VO2 coated can-

tilevers and bridges through the full heating and cooling curves. Different lengths of each

type of beams were used to analyze the structure dependence of the resonant frequency shift.
The geometries used for the three cantilevers are 2 µm thickness and 50 µm width for all
and 350/450/550 µm length for each, while the geometries used for the other three bridges
are 2 µm thickness and 40 µm width and 200/250/300 µm length for each. The thickness of

60

the VO2 coating is approximately 0.2 µm for all the beams.

4.2.1 Observations of Different Frequency Shifts

The resonant frequencies increase rapidly during the IMT phase transition region for both the

C-C (unbuckled) structures and the C-F structures. This behavior is due to a large amount

of stress generated by the VO2 thin film. However, in order to completely understand the

behavior of VO2-based MEMS resonators, the slopes at the two ends of the frequency-

temperature curves should also be given attention. By comparing the frequency curves

between the cantilevers (Figure 4.2) and the bridges (Figure 4.3) both with the VO2

coatings, we found that the frequencies of the cantilevers always decrease before the phase

transition and become almost flat after the transition has been completed. However, the

trend for bridges is different. The resonant frequency will increase in the low-temperature

region and then decrease after the phase transition.
If we further compare coated and
uncoated beams (In Figure 4.2, 4.3, 4.4, and 4.5, only the 350 and 550 µm cantilevers and

Figure 4.3 Resonant frequency change for VO2 coated bridge beams of different lengths
through full heating and cooling loop.

61

200 and 300 µm bridges have been plotted but the data is also listed in Table 4.1 and Table

4.2), we find that at the higher temperature region, they share the same trend (not the

slope). Thus, the discrepancy in frequency shift pattern between the coated and uncoated

beams with the same structure can be explained by the difference in stress levels.

Table 4.1 Relative frequency change for coated and uncoated cantilever beams with different
lengths. The phase transition region is from 65◦C to 85◦C.

Cantilever length (µm) Before transition Phase transition After transition

350
450
550

-0.39%
-0.40%
-0.43%

6.91%
7.26%
6.94%

0.08%
0.09%
0.04%

SiO2
0.53%
0.57%
0.53%

Table 4.2 Relative frequency change for coated and uncoated bridge beams with different
lengths. The Phase transition region is from 62◦C to 85◦C for the 300 µm and 65◦C to 85◦C
for the others.

Bridge length (µm) Before transition Phase transition After transition

200
250
300

2.21%
1.21%
3.47%

25.20%
30.46%
37.19%

-0.18%
-0.30%
-0.38%

SiO2
-0.24%
-0.48%
-0.51%

4.2.2 Stress Effect

For a certain beam structure, the factors in determining the frequency shift involve Young’s

modulus and stress. However, Young’s modulus of the SiO2 increases very slowly as a
function of temperature at a rate of 178 ppm/◦C[129], which cannot be the main factor in

determining the frequency change in Figure 4.4 and Figure 4.5. So Young’s modulus can be

taken as a constant value and thus the frequency change can be taken as stress-induced. For

instance, the uncoated bridge will undergo compressive stress as the temperature increases

due to the constraint of the thermal expansion. This induced negative stress will lead to a

decrease in the resonant frequency[130]. On the other hand, for the VO2 coated beams, the

62

Figure 4.4 Resonant frequency change for uncoated cantilever beams of different lengths as
a function of temperature.

large difference in the thermal expansion coefficient between VO2[21] and SiO2 will apply a

tensile force to the bridge which will increase the frequency. It is also important to note that

before the phase transition, where VO2 is in its monoclinic phase, the thermal coefficient

is larger than that of in the rutile phase (The thermal expansion coefficient of VO2 in the
monoclinic phase is about 5.7 × 10−6 K−1[21, 118]).

So, before the phase transition, the surface stress generated by the VO2 film and applied

to the SiO2 beam dominates in determining the frequency shift pattern. As for the rutile

phase, the thermal coefficient of VO2 is smaller so that the surface stress generated by

VO2 can no longer suppress the thermal stress and thus the frequency shift follows the

same trend of the uncoated beams. One thing that needs to be clarified here is that unlike

the bridges, applying surface stress to a cantilever will induce axial stress in the opposite

direction within the beam[131, 132, 133]. Based on this, we can predict that the relative

frequency change of the VO2 coated cantilevers will be independent of the beam length

because the increase of the resonant frequency for a cantilever under a compressive surface

stress indicates that the geometric effect dominates in the frequency shift[130], and this is

63

Figure 4.5 Resonant frequency change for uncoated bridge beams of different lengths as a
function of temperature.

also confirmed by the data listed in Table 4.1. Although the external stress dominates at

the lower temperature while the thermal stress dominates at the higher temperature, the

increase of the frequency for the cantilevers at higher temperature is very small but the

frequency drop for the bridges within the same temperature region is lager and comparable

to that of the uncoated beams. The reason is that the resonant frequency is much more

sensitive to the stress for a C-C structure than a C-F structure according to the prediction

of Euler-Bernoulli beam theory[131, 132, 133].

4.2.3 FEM Simulation of Two Ends

A finite element method (FEM) simulation has been done on the 550 µm cantilever and the
300 µm bridge to analyze the thermal expansion effect on the frequency shift. The simulation

is simplified by applying mixing rule to the density and Young’s modulus since the beams

we used contains a small portion of Pt. Initial stress and strain, as well as the under etching

effect, should also be taken into consideration for the simulation to meet the measurement.

64

The simulation for the bridge is not as straightforward and requires a deeper understanding

of the system. For the bridge, we cannot apply a fixed constraint at the two ends in the

longitudinal direction because in this case, the generated thermal force is calculated by

applying the thermal strain generated under the free thermal expansion condition. Any

object that undergoes thermal expansion will induce the thermal stress below that value.

However, the exact stress magnitude cannot be calculated[134]. The fundamental principle

here is to reduce the physical constraints in the simulation. This can be done by simply

applying a fixed constraint at one end of the silicon substrate and a roller constraint at the

other.

4.3 Stress Interfaces in Bridge Structure

It is well known that the resonant frequency of an unbuckled microbridge structure increases

with increasing axial tensile stress, while the opposite is true for a buckled microbridge. How-

ever, microbridge resonator structures usually deviate from ideal C-C structures in terms

of the flexibility of the anchor, which changes the fixed-fixed boundary condition into a

pinned-pinned or fixed-pinned condition. This section addresses the influence of different

buckling profiles and amplitudes in bridge structures on the performance of resonant fre-

quency tuning[135]. The microbridges that used for this study have the same dimensions

with different buckling states, the fabrication process is introduced in detail in chapter 2.

4.3.1 Bending moment in the up-buckled beam

For an up-buckled microbridge with profile as shown in Figure 4.6, the VO2 thin film

deposited on the SiO2 surface is under tension at room temperature[136]. When the VO2

is thermally actuated, compressive surface stress is induced to the convex side of the beam

surface due to the SPT. This leads to a decrease in the surface tensile stress and consequently,
a positive bending moment is generated on the pinned axis A and A(cid:48) (see Figure 4.7). On the

65

other hand, the upper edges B and B(cid:48) of the beam (see Figure 4.7) tend to move toward the

beam center. When Joule heating is used for the electrothermal actuation method, the heat

is mainly concentrated along the suspended beam (not the substrate). Unlike the uniform

heating that occurs during conduction heating, a large thermal gradient is expected between

the suspended beam and its anchor; which results in ”cold anchors” that remain in fixed-

fixed condition. In this case, the lateral deflection and the relative movement of edges B and
B(cid:48) are significantly lower, and axial tensile stress is induced at the beam boundaries AB and
A(cid:48)B(cid:48). As the temperature increases and the SPT proceeds, this residual axial tensile stress

accumulates and results in a monotonically decrease in the resonant frequency as shown in

Figure 4.6a (as expected for a buckled C-C beam).

The resonant frequency tunability is also found to be correlated with the actuation

method. As shown in Figure 4.6b, when the substrate heating is used to induce the VO2

SPT, the resonant frequency shift behaves in a very different way compared to the Joule

heating method shown in Figure 4.6a. During the heating loop, the resonant frequency

decreases at the onset of the SPT, similarly to the case for Joule heating. When the tem-
perature reaches about 76◦C, the resonant frequency approaches its minimum value (∼ 235

kHz) and then start to increase as the heating loop continues.

It should be noted that

this turning point, which leads to a bidirectional tunability, happens in the middle of the

SPT –from the cooling curve, this value of temperature remains within the hysteresis region.

Thus, the microbridge is still subjected to a positive bending moment. Figure 4.6c shows

the 3D reconstruction image of this up-buckled bridge with its height distribution informa-

tion, taken by using the bottom of the etched cavity as the reference plane. The normalized

buckling amplitude with respect to the fixed top surface is plotted along the beam longitu-

dinal direction and shown as a function of substrate heating temperature in Figure 4.6d. It
can be seen that the buckling amplitude decreases by ∼ 5% between 70 to 90◦C, and the first
noticeable change occurs between 70 and 80◦C, which includes the turning point shown in

Figure 4.6b. Thus, for substrate heating, the lateral deflection is no longer restricted by the

66

Figure 4.6 The resonant frequency shift of a 300 µm VO2-based microbridge in the up-
buckled state. (a) Resonant frequency shift through a complete heating and cooling cycle by
using integrated resistive heaters. (b) Resonant frequency shift through a complete heating
and cooling cycle using substrate conduction heating. (c) 3D reconstruction of the device
showing the buckling amplitude in +z direction. (d) Normalized buckling amplitude change
as a function of substrate heating along the beam axial length.

fixed-fixed boundary condition that exists when using Joule heating. The relative movement
of edges B and B(cid:48), therefore, induces compressive axial stress and results in an increase in the

resonant frequency. This transition from a fixed-fixed boundary condition to a fixed-pinned

boundary condition can be attributed to different thermal distribution profiles upon the

actuation methods used. Unlike the Joule heating method, the substrate heating provides

a more uniform thermal distribution, with a much lower temperature gradient between the

suspended beam and the two anchors.

67

Figure 4.7 Schematic illustration of geometric distortion and axial stress upon different bend-
ing moments. (a) The initial state of an upward buckled microbridge with a sinusoidal profile
under a positive bending moment. (b) The lateral deflection in the structure reduces the
buckling amplitude, the rotational force on the pinned boundaries leads to a relative move-
ment of edges B and B(cid:48) towards each other. Compressive axial stress is therefore induced,
which causes an increase in resonant frequency after the turning point shown in Figure 4.6b.
(c) The initial state of a downward buckled microbridge with a sinusoidal profile under a
negative bending moment. (d) The lateral deflection in the structure reduces the buckling
amplitude, the rotational force on the pinned boundaries leads to a relative movement of
edges D and D(cid:48) against each other. Tensile axial stress is therefore induced, which causes a
decrease in resonant frequency after the turning point shown in Figure 4.8b.

4.3.2 Bending moment in the down-buckled and bell-shaped beam

When considering a down-buckled beam, the VO2 thin film is coated on the concave side of

the beam. During the SPT, compressive stress is added to this side of the beam body, which
causes a negative bending moment exerted on the bridge. The boundary interfaces D and D(cid:48)

tend to move against each other. Figure 4.8a shows the resonant frequency measurement

as a function of Joule heating for a full heating and cooling cycle. The fixed-fixed boundary

condition, in this case, results in compressive axial stress, which increases the resonant

frequency in the heating loop. Similar to what happened in the up-bucked beam, at the
onset of critical lateral deflection (between 70 and 80 ◦C –see Figure 4.8d), the fixed-fixed

boundary condition transitions into a fixed-pinned condition where the rotational force on

68

Figure 4.8 The resonant frequency shift of a 300 µm VO2-based microbridge in the down-
buckled state. (a) Resonant frequency shift through a complete heating and cooling cycle by
Joule heating. (b) Resonant frequency shift through a complete heating and cooling cycle
by substrate heating. (c) 3D reconstruction of the device showing the buckling amplitude in
−z direction. (d) Normalized buckling amplitude change as a function of substrate heating
along the beam axial length.

the anchor pushes the edges D and D(cid:48) (in Figure 4.7d) against each other, leading to a tensile

stress along the beam axis. As shown in Figure 4.8b, the sign of the change in frequency
with temperature turns at a similar temperature (∼ 76 ◦C) to that observed for up-state

buckled bridges (Figure 4.6b). It should be noted that the change in frequency for these

cases have opposite signs (i.e. up-state buckled beam turns from increasing to decreasing

frequency; while the opposite is true for the down-state buckled beams). The change in

buckling amplitude along the beam length is shown in Figure 4.8d. This bidirectional

resonant frequency tunability observed for VO2 buckled bridges under substrate heating

69

also explains the unclear phenomena observed in a previous work, where a bump is observed

in the frequency-temperature curve[122].

As indicated in Figure 3.6, down-buckled microbridges with the downward bell-shaped

profile are also observed. The buckling amplitude for these devices is plotted in Figure 4.9d

along the beam length with respect to different substrate heating temperatures. It can be

seen that the buckling plots for this type of bridges are in a bell-shaped profile, which is

different from the sinusoidal profiles observed for up- and down-state buckled bridges. In

the bell-shaped buckled bridges, the resonant frequency tunability exhibits more complicated

patterns as demonstrated in Figure 4.9a-b. However, both actuation methods (i.e. Joule

heating and substrate heating), show similar resonant frequency shift patterns across the

SPT region, since the general trend of the geometric distortion in this type of beam is also

reducing the buckling amplitude upon a negative bending moment.

4.4 Power Consumption of Programming Resonant Frequency

Programming resonant frequency states in a mechanical structure allow for the operation

of a single device in multiple frequency channels. This not only broadens the spectrum of

applications for the device, but also reduces interference, noise, and enables anti-jamming

in communication systems.

In this section, the study on the power consumption of pro-

gramming resonant frequencies in VO2 MEMS resonators is presented by means of pulse

width modulation (PWM) methods. It is found that the tuning of the frequency states is

determined by the supplied energy, and the programming is more efficient for larger, shorter

pulses –even if the duration of the pulse is shorter than the system’s thermal time constant.

We explore two different mechanical structures, bridge, and cantilever. A wider tuning range

is found for the bridge structure (22%), which is due to the larger frequency sensitivity with

stress for this configuration. The tuning/programming action uses harvested mechanical

energy, which could come from the user. The potential use of the developed system as an

70

Figure 4.9 The resonant frequency shift of a 300 µm VO2-based microbridge with bell-shape
buckle state. (a) Resonant frequency shift through a complete heating and cooling cycle by
Joule heating. (b) Resonant frequency shift through a complete heating and cooling cycle
by substrate heating. (c) 3D reconstruction of the device showing the buckling amplitude in
−z direction. (d) Normalized buckling amplitude change as a function of substrate heating
along the beam axial length.

accelerometer or impact sensor for monitoring brain injuries in contact-sports is discussed.

4.4.1 Determining Device Time Constant

The testing configuration consisted of connecting the device’s metal heater to a DC current

source which provided a pre-heating current to the VO2-based resonator (see Figure 4.10a).

The pre-heating level was selected at the point where the resonant frequencies between the

heating and cooling major hysteretic curves have the largest difference. A capacitor was then

charged by the FENG device through a rectifier. A single-pole-single-throw switch was used

71

Figure 4.10 (a) Circuit of resonant frequency programmability by combing VO2-based res-
onator and FENG device. C is the capacitor of 1µF, R1 is the resistance of the heater (252
and 228 Ω for the cantilever and bridge, respectively), Ip is the pre-heating current (1 and
1.22 mA for the cantilever and bridge structures, respectively). (b) Voltage profile of the
discharge current across the heater. (c) The circuit used for measuring the time constant.
A wave-function generator (WG) is connected to the heater R1. The VO2 film (RV )is con-
nected to a resistor (R2), a pre-heating voltage source (Vp), and an oscilloscope (DSO). (d)
Thermal time constant of the VO2-based cantilever. (e) Schematic of the rectangular pulse
supplied by the WG for time-constant and energy calculation experiments. (f) Frequency
shift as the function of the pulse width.

to avoid capacitor leakage after charging. Once the capacitor was charged, the discharge

current pulse was added to the pre-heating current. The temperature increase due to the

current pulse was large enough to heat the structure across the phase transition. When the

pulse ended, the temperature of the sample returned to the pre-heating value, but this time

72

following the cooling curve of the hysteresis curve. Thus, the resonant frequency before and

after the pulse corresponding to the values in the heating and cooling curves, respectively.

In order to find the conditions of the tuning current pulse for increasing the sample’s

temperature across the phase transition, it is necessary to know the system’s response time.

The dynamics of the system is governed by two main processes (thermal and mechanical),

and each one has a corresponding time constant. The thermal process is the mechanism

by which the current pulse increases the temperature of the sample, while the mechanical

process is the mechanism by which the system responds to the phase change of the VO2

film. The relation between the thermal time constant and the mechanical time constant can

be described as follows:

(cid:48)

τ

= τT + τM ,

where τM is the mechanical time constant, τT is the thermal time constant and τ

(4.1)

(cid:48)

, is the

response time of the device to the new thermal equilibrium. The thermal time constant is

mainly determined by how fast the external heat can be distributed in the device[137, 138].

The thermal process is the slowest of the two [139] and thus, it will determine the time

response of the entire system.

Since the changes in the structural and electrical properties of VO2 across the phase

transition have similar time constants [140, 141, 142, 143], the thermal time constant of the

system can be obtained by simply applying a current pulse and monitoring the change in

resistance of the VO2 film. The measurement setup is shown schematically in Figure 4.10c.

In this experiment, the thermal time constant was defined as the time required for the device

to respond when the current was increased from the preheated level of 1 mA to 1.7 mA. The
measured thermal time constant of this 450 µm long VO2-based cantilever was 20.3 ms, (see

Figure 4.10d). To validate the measured time constant for the electro-mechanical system,

rectangular pulses of the same amplitude but varying width were applied, while the resonant

frequency shift was measured. As the pulse width was increased, the frequency shift also

increased until the frequency shift reached a maximum value. Thus, the minimum width of

73

Figure 4.11 Tuning and programming frequency states in cantilever structures. (a) Hysteretic
major resonant frequency loops for cantilever structure as a function of the current. (b)
Frequency shift as a function of the voltage in the capacitor before the discharge pulse. (c)
Frequency shift as a function of pulse amplitude for three different pulse widths (PW). (d)
Frequency shift as a function of energy delivered by the pulse.

the pulse that was able to obtain the maximum frequency shift should be approximately the

value of the time constant. The frequency shift as a function of the pulse width is plotted

in Figure 4.10f. The thermal time constant in this case was estimated to be 21 ms, which

is very close to the value determined in Figure 4.10d.

4.4.2 Frequency Programmability In Cantilevers

The resonant frequency of the cantilever as a function of the current is plotted in Figure

4.11a. The programmability of the resonant frequency was achieved by first apply a DC

74

current to a pre-heated level where the heating curve and the cooling curve have the max-

imum separation[144, 145, 146]. A transient current pulse was then induced in order to

complete the phase transition in the VO2 film and switch the resonant frequency from the

heating curve to the cooling curve. Even though the single layer FENG device is able to

generate large open circuit voltage, the short circuit current is still on the scale of µA. Thus,

directly connecting a single layer FENG device to the resonator does not produce enough

temperature increase to cross the phase transition completely. Therefore, the single-layer

FENG device was stacked to 7 layers, which amplified the output to 7 times larger than

the single-layer device. Second, a capacitor was previously charged by the FENG device

through a rectifier to a level high enough to go through the phase transition completely.

Then, the stored energy was released in the form of discharge current for tuning action by

using a push-button switch. The current pulse used for the tuning can be determined by the

following equation:

I =

V0
R

e

− t

RC + Ip,

(4.2)

where V0 is the voltage charged to the capacitor, R is the resistance of the heater in the

cantilever, C is the capacitance of the capacitor and Ip is the pre-heating current. In this ex-

periment, the pre-heated current level was chosen to be 1 mA where the resonant frequency

separation between the heating curve and the cooling curve is 30 Hz. The capacitor was pre-

viously charged to different voltage levels, and then the discharge current was induced for the

tuning. This results in pulses of different amplitude, but the same duration, since the time

constant remained unchanged. As shown in Figure 4.11b, the resonant frequency shift in-

creases with the voltage stored in the capacitor. This suggests that the tuning/programming

of the resonant frequency in the devices is determined by the supplied energy. The maximum

frequency shift was obtained when the capacitor was charged to 2.9 V.

As discussed earlier, the thermal time constant of the cantilever is approximately 20.3

ms. This means that in order to get the maximum frequency shift, the applied current pulse

should be at least 20 ms. However, the discharge current pulse used for the tuning in this

75

experiment has the decay time constant of around 0.27 ms and the transient current only

lasts about 1.3 ms. Although the pulse width (PW) was much shorter than the time constant

of the device, the transient current still provided enough energy for the resonant frequency

to completely across the phase transition region. This finding is crucial for the use of a single

strike on a FENG device for programming action. The energy released from the capacitor

to the heater can be determined by:

∆E =

2 − V1

2),

C(V0

1
2

(4.3)

where V1 is the voltage of the capacitor after discharging. To confirm that the tuning

mechanism is determined by the supplied energy –independently on how fast was the energy

delivered– the following experiment was performed. Instead of applying the RC discharge

current, three rectangular pulses of different widths were applied from a waveform generator.

The frequency shift as a function of the pulse amplitude was measured (see Figure 4.11c).

The maximum frequency shift was achieved by the different rectangular pulses respectively

at different amplitudes. The energy delivered by the rectangular pulses can be calculated by

using the parameters shown in Figure 4.10e:

∆E =

(Vh

2 − Vl
R

2)t

,

(4.4)

where R is the resistance of the heater, Vh is the high voltage, Vl is the low voltage, and t is

the width of the pulse. Figure 4.11d shows the resonant frequency shift as a function of the

energy delivered by three different pulses, and by the discharge current from the capacitor.

All four curves show very similar behavior. This confirms that the tuning mechanism is
dominated by the supplied energy. The energy required for tuning this 450 µm VO2-based

cantilever is about 5.1 µJ. Moreover, if the cantilever was applied a rectangular pulse of

Vh=578 mV and Vl=280 mV (considering the TCR of the heater is around 33.5 Ω/mA2),

the duration of the pulse should be at least 20 ms. In this case, the energy consumed by the

cantilever is about 18.2 µJ. This larger energy consumption is probably due to the larger

76

heat dissipation during a longer tuning process. Thus, it is more energy-efficient to apply a

shorter pulse with higher amplitude.

4.4.3 Frequency Programmability in Bridges

The resonant frequency programmability was also demonstrated for a 300 µm long VO2-

-based micro-electro-mechanical bridge structure. The resonant frequency as a function of

current was plotted in Figure 4.12a. The current step here was chosen to be 0.01 mA

since the bridge structure is more sensitive to the stress, which also translates into a much

larger tuning frequency than the cantilever structure (32% for the bridge, and 4% for the

cantilever). For the bridge structure, the pre-heating current was 1.22 mA. The resonant

frequency tuning based on the RC discharge current is illustrated in Figure 4.12b. The

frequency shift increases with the voltage in the capacitor, and saturates at around 1.6

V. The maximum resonant frequency shift was measured to be around 42 kHz, which is

consistent with the value estimated from Figure 4.12a. This indicates that a voltage of 1.6

V in the capacitor provided enough energy to completely cross the phase transition region

(for a pre-heating current of 1.22 mA). The thermal time constant was also measured for

the bridge using the same method used for the cantilever. The value was determined to

be around 9 ms, which is much shorter than the cantilever. This is due to two reasons:

(i) the bridge has one more anchor than the cantilever, which represents a more uniform

temperature distribution and one more heat sink that helps dissipate temperature; and (ii)

the bridge is shorter than the cantilever, which means the bridge has less thermal mass and

therefore the response time is shorter.

The energy was also found to be the tuning parameter for the bridge structures. Figure

4.12c-d show the frequency shift as a function of rectangular pulse amplitude and energy,

respectively. The same pattern shown in Figure 4.11c-d was observed, and the minimum

energy required for inducing a frequency shift of around 30 Hz was 5.11 µJ. In Figure 4.12d,

there is a small discrepancy between the discharge current and the rectangular pulse. This

77

Figure 4.12 (a) Hysteretic major resonant frequency loops for bridge structure as a function
of the current.
(b) Frequency shift as a function of the voltage in the capacitor before
discharge.
(c) Frequency shift as a function of pulse amplitude for three different pulse
widths (PW). (d) Frequency shift as a function of energy delivered by the pulse.

can be attributed to the high sensitivity to stress. The rectangular pulses were provided by

the waveform generator as a voltage signal. The energy consumption for programming (i.e.

dynamic power consumption) required by the bridge was estimated to be 2.07 µJ.

4.4.4 Monitoring Brain Injury in Contact Sports

As discussed above, the tuning/programming of multiple frequency states can be achieved

by very short pulses, as long as the delivered energy is enough. Thus, practical applications

could include impact sensors, such as those needed for monitoring injuries in high-contact

78

Figure 4.13 (a) Representative impact profile, jerk = (FA-FB)/(m∆A−B), where FA and
FB are the force at point A and B respectively, m is the mass of the head and ∆A−B is the
time from point A and B. The acceleration is calculated by using an average human head
mass of 3.6 kg. (b) The force exerted on the head, F1, F2, F3, and F4 represent the peak
force of around 1800 N applied at different locations, Arx is the rotational axis of the head,
the size of the head is selected to be the value at 50th percentile of male adults.

sports, where a single, quick (but intense) impact generates enough energy to program a

different frequency state. The flexibility of the FENG device and the size of the resonator

structure enables the required flexibility for the integration of this system in wearables or even

textiles. This subsection includes the discussion of an application note for monitoring head

injuries and shows how a single impact can transition the VO2-based resonator completely,

and program a frequency state about 40 kHz different than the pre-heated state.

To evaluate the severity of the impact, several criteria are used in the biomechanics.

For example, the threshold for concussion under the acceleration is estimated to be 70-

75 g[147, 148] (where g is the gravitational acceleration. An angular acceleration of 7900

radian/s2 applied to the head will cause an 80% probability of Mild Traumatic Brain Injury

(MTBI)[149]. A Head Injury Criteria (HIC) of more than 1000 relates to an 18% risk of

severe head injury, a 55% risk of serious injury and a 90% risk of moderate head injury[150].

However, different evaluation methods (e.g. MTBI and HIC) use different criteria. The

acceleration threshold for the concussion and MTBI focuses on the peak force and how fast

is the force applied. On the other hand, the HIC value emphasizes on the impulse of the

79

impact, which includes the real time force and the duration of the impact, the value can be

determined by the following expression[151, 152]:

(cid:90) t2

t1

HIC = {[

1

t2 − t1

a(t)dt]2.5(t2 − t1)}max

(4.5)

where t1 and t2 are the initial and final times of the impact interval which gives the maximum

HIC value, a(t) is the acceleration measured in the number of gravitational acceleration (i.e.

the number of gs). However, the HIC value may not reflect the real significance of the

impact. A quick inspection tells us that, for a profile like this, Equation (4.5) can give

low HIC values for short duration pulses, even if the force amplitude is relatively large. For

example, an impact with a long duration and a small force magnitude can lead to a large HIC

value while a large force magnitude with short duration would give low HIC values. Thus,

the criteria here is selected to be the acceleration threshold for causing a concussion or an

MTBI. The impact used to induce the maximum frequency shift from the pre-heating level

of 1.22 mA for the bridge described in the previous subsection is shown in Figure 4.13a. In

this experiment, the FENG was directly connected to the VO2 resonator without charging a

capacitor and the output of the FENG from a single impact from a human punch was used

to induce the frequency shift. The real-time force is plotted as a function of time. The peak

force was measured to be around 1800 N and the acceleration was determined based on the

average head mass of about 3.6 kg[153]. The maximum acceleration is therefore calculated

to be 51 gs. The severity of applying this force to the head of a human being will depend on

the location of the point-of-contact. The severity of the head injury in terms of the rotational

acceleration is summarized in Table 4.3. Even though the calculation does not include the

Table 4.3 Evaluation of the impact

Location
Force (N)
Jerk (m/s3)

Linear Acceleration (gs)

Rotational Acceleration (radian/s2)

F1
1800
13883

51
5067

F2
1800
13883

51
2467

F3
1800
13883

51
NA

F4
1800
13883

51
7333

80

resistance of the neck and may enlarge the real rotational acceleration, the combination of

the VO2 and the FENG still provides the potential of sensing the threshold acceleration

which causes the brain injury.

4.5 Enabling Tunable Micromechanical Bandpass Filters

In this section, we demonstrate the potential use of VO2-based MEMS devices as second-

order kilohertz (kHz) bandpass filters with tunable band selectivity and adjustable band-

width. Two identical on-chip microresonators are actuated using mechanical excitation and

measured using optical detection. One of the resonators is not actuated while the other is

tuned by applying electric currents across an integrated resistive heater, which induces the

phase transition of the VO2, and consequently a large stress to the mechanical structure. The

responses of both MEMS resonators are combined, resulting in a resonant peak of tunable

bandwidth controlled by the input current. The bandwidth can be extended to 2.62 times

by using two bridges or 2.39 times by implementing one pair of cantilevers. The results for

both devices are discussed.

4.5.1 Experimental Setup

The experimental setup for measuring resonant frequencies of both resonators is shown in

Figure 4.14. After the first mirror and beam splitter, the beam was split and focused

on both samples using two long working distance objectives (10X Mitutoyo MY10X-803

Objective lens). Each sample represented a chip that contained resonator structures that

were fabricated simultaneously. A piezoelectric transducer was attached to the back of each

sample, and both transducers were driven into mechanical vibration by the output signal

of a network analyzer (HP3589A). The laser was focused on identical resonator structures,

and the reflected beam was directed to a photodetector through another beam splitter. The

output of the photodetector was connected to the input of the network analyzer. In this

81

configuration, the network analyzer would display the voltage output of the photodetector as

a function of frequency. The network analyzer drove the piezoelectric transducers at different

frequencies, inducing the resonator’s largest vibration amplitude at a frequency close to

their natural frequency. Vibrations from the resonator structure produced oscillations in

the reflected laser beam (of magnitude proportional to the vibration amplitudes), which

were converted to a voltage by the photodetector and sent back to the network analyzer.

It should be noticed that in this measurement setup, the input/output characteristics of

the system does not require coupling of electrical and mechanical signals. The input signal

applied to the filter system was a time-dependent electrical signal, but the actuation signal

was the mechanical vibration provided by the piezoelectric transducer. The tuning signal is

the current applied to the heater of the active element, which is an electrical signal, but the

output is a mechanical vibration detected optically. This method is an adaptation of laser

deflection and interferometer techniques commonly used to characterize MEMS –in fact, it

also allows for the testing of a single resonator structure by simply blocking the optical path

to one of the structures.

In the reported experiments, the temperature for one of the samples (active sample) was

increased by applying a current to the integrated resistive heater (i.e. by Joule heating);

while the other sample (static sample) remained at room temperature. The current supplied

to the active sample was computer-controlled and provided through wire bonding connections

to pads at the border of the chip. Both samples were mounted on two individual three-axis

moving stages to facilitate alignment of the laser beam on the resonator structure.

4.5.2 Bandwidth Tunability for Bridges

Two different structures of microbeam resonators (cantilevers and bridges) were tested in this

experiment and the bandwidth tunability of each structure was demonstrated and compared.

The maximum bandwidth amplification, Q-factor, and bandwidth tuning window will be

discussed in the following sections. The bandwidth was calculated using the 3dB of the

82

Figure 4.14 Experimental setup. The active sample is the resonator (cantilever or bridge)
actuated by Joule heating, while the static sample is the resonator (cantilever or bridge) that
is not actuated. Two identical piezo-disks were placed underneath the static sample and the
active sample respectively and they are sharing one driving AC source signal provided by the
network analyzer. The output of the photodetector is connected to the input of the network
analyzer. The laser beams passing through the beam splitters are not contributing to the
measurement and therefore are not shown for clarity.

resonant peak method using the following equation:

BW = f2 − f1,

(4.6)

where BW stands for the bandwidth. f1 and f2 are the two frequencies on each side of the

√
resonant frequency (fr) where the amplitude of the signal is 1/

2 of its maximum value.

The Q-factor (Q) is then calculated based on the bandwidth value using the equation as

below[154]:

Q = fr/BW.

(4.7)

First, two identical bridges were used to create the bandpass filter. The active bridge was

activated by Joule heating, and the resonant frequency was measured through the whole

heating and cooling cycle (Figure 4.15-left) by blocking the laser beam coming from the

83

Figure 4.15 Left: Resonant frequency versus actuation current through a full heating and
cooling cycle for the active bridge. Right: Resonant frequency signal for the static bridge at
(cid:48)
room temperature. The measured (f0) and calculated (f
0) resonant frequencies are shown.
(cid:48)
0 was obtained from Equation (3.1), and it does not take residual thermal
The value for f
stress into account.

static sample. The frequency shift comes as the result of a large amount of stress generated

by the VO2 thin film coating during its phase transition region. When the laser beam coming

from the static sample was unblocked, we were able to get two resonant signals, one from the

static bridge and the other from the active bridge. These optical signals were routed to the

photodetector, and its output to the network analyzer, which showed the resonant peaks for

both devices. The top-left plot in Figure 4.16 (Stage “a”) shows the output of the spectrum

analyzer for both bridges at room temperature i.e. while the active bridge was not actuated

(Iact = 0 mA). The current step is 0.01 mA within the bandwidth tuning window and 0.1

mA for the outside region. It should be noted that, although both bridges are geometrically

identical, their resonant frequencies at room temperature are not the same. This could be

due to any slight difference between the fabrication processes of both devices; we believe

that the most likely cause was a difference in ”effective length” for the two structures, which

could have occurred during isotropic release step.

When a current was applied to the active bridge (Iact), its resonant frequency would

shift to a certain value according to the hysteresis curve shown in Figure 4.15. Figure

84

4.16 shows a sequence of over-imposed resonant frequency peaks for the static and active

bridges for different Iact values. The sequence starts at room temperature (Stage “a”), goes

through a heating cycle (increasing Iact), until the transition of VO2 is completed (Stage

e in Figure 4.16). At this point, the cooling cycle begins (reducing Iact), until we reach

room temperature again (Stage “j” in Figure 4.16). Starting at room temperature, the

combination of both resonant peaks resembles the behavior of a band-pass filter; and its

width is tuned by current steps of increasing magnitude that induce the phase transition

of VO2. As the actuation current increases from room temperature, the active peak moves

towards the static peak, reducing the filter’s bandwidth. When Iact = 2.89 mA (b Stage),

the active and static peaks show very similar resonant frequencies, and both responses are

merged into one signal peak. As Iact is further increased, the resonant frequency of the

active bridge keeps increasing, and the active peak continues starts moving to the right of

the static peak. At Iact = 2.92 mA (Stage “d”), the resonant frequency of the active bridge

begins to separate, and by Iact = 3.00 mA, the two fr curves clearly become two separate

peaks. The largest measured bandwidth during the heating cycle was around 1.85 kHz (at

Iact = 2.92 mA). The cooling cycle (Stage “f ” through “j”) was performed to demonstrate

the reversibility of the system. As the actuation current decreases, the active peak moves
towards the static peak and the peaks begin to merge at Iact ∼ 2.57 mA. The maximum
bandwidth of the cooling cycle is around 2.06 kHz (at Iact = 2.57 mA), which is 2.62 times

larger than a single device. As the current further decreases, the difference in the resonant

frequencies become smaller. At Iact = 2.52 mA (Stage “i”) the two peaks become one, and

the system goes back to its initial condition when Iact is turned off. The stages included

in Figure 4.16 are displayed for similar frequency measurements between the heating and

cooling cycle i.e. the two plots in a single row show similar output. However, the Iact values

are different between these similar stages. This is due to the hysteresis of VO2 which does

not show a linear correspondence between the two cycles (see Figure 4.15).

It can be noticed that at the stages where the signal snaps into two individual peaks

85

Table 4.4 Bandwidth tunability for bridges

Bandwidth (Hz)

Q-factor

Stage

a

Bandwidth (Hz) Snap
NA
0.00

Q-factor
Iact (mA)

Stage

f

Static bridge

787
306

c

Active heating
b
d
1849 Snap
732
NA
131
330
2.89
2.92
3.00
Active cooling
g
i

1391
174
2.91

h

e

j

Bandwidth (Hz) Snap 2062
117
2.57

Q-factor
Iact (mA)

NA
2.70

1607
151
2.55

666
362
2.52

Snap
NA
0.00

(Stages “a”,“e”,“f ”,“j”), the signal level for each individual peak is of equal amplitude to

the signal of a single bridge (Figure 4.15-right). However, for the stages which have extended

bandwidth (Stages “b”,“c”,“d”,“g”,“h”,“i”), the signal level is higher than the one generated

by the single bridge resonator. This is due to the additive effect of the two individual signals

generated by the static resonator and the active resonator, which occurs only during stages

with band-pass filter behavior. Also, at Stages “b” and “i”, the bandwidths are smaller and

therefore, a higher Q-factor is achieved (see Table 4.4).

The resonant peak of the single static bridge used in this system has a bandwidth of 787

Hz (see Figure 4.15). Thus, a tunable bandwidth amplification up to 2.62 was achieved

by using one pair of identical bridges.

It should be noted that, in this particular case,

the shift in fr for the active bridge ”crossed” the fr of the static bridge. Therefore, the

tunable bandwidth could include a different range of frequencies by increasing or reducing

the separation between the two peaks at room temperature. It is important to clarify that the

applied current Iact is the tuning parameter but not the input to the system that generates

oscillation. During the entire heating-cooling cycle, the input is the frequency of the AC

signal applied to the piezo-disks (supplied by the network analyzer). The measured output

is the combined resonant peaks. The data for actuation current, bandwidth and Q-factor

86

Table 4.5 Bandwidth tunability for cantilevers

Bandwidth (Hz)

Q-factor

Stage

Bandwidth (Hz)

Q-factor
Iact (mA)

A
155
33
3.0

Static cantilever

135
38

Active heating

E

C
279
18
4.2

D
B
332 Snap
212
NA
16
24
3.4
5.4
6.2
Active cooling

Stage

F

G
Bandwidth (Hz) Snap 331
16
5.2

Q-factor
Iact (mA)

NA
6.0

H
284
18
4.0

I

228
22
3.2

J
174
29
2.8

are summarized in Table 4.4.

4.5.3 Bandwidth Tunability for Cantilevers

The VO2-based bandpass filter could also be achieved by using a pair of identical cantilever

structures. The measurement method and the tuning method are the same as those used

for bridges. The bandwidth tunability is shown in Figure 4.17 and all the related data is

summarized in Table 4.5. The resonant frequency of the active peak follows the hysteresis

curve shown in Figure 4.18-left. The resonant frequency signal for the single static cantilever

was measured (Figure 4.18-right) and the bandwidth was calculated to be 135 Hz. The

starting stage here is chosen to be the one with an Iact = 3.0 mA rather than 0 mA. The

reason is that the initial bending of this active cantilever cannot produce a signal comparable

to that of the static cantilever. Nevertheless, this difference does not affect significantly the

results obtained and drawn conclusions, since the difference between the resonant frequency

at Iact = 0.0 mA and at 3.0 mA was found to be only 12 Hz. The maximum bandwidth for

this system is reached at Iact = 5.4 mA and at Iact = 5.2 mA for the heating and cooling

cycles, respectively. The maximum bandwidth obtained by this system is about 322 Hz,

which is 2.39 times the bandwidth of a single cantilever.

87

4.5.4 Bandwidth Tunability Comparison

The room temperature measurement in Figure 4.17 (Stage “a”) shows that the fr for

both cantilevers (active and static) are much closer than the fr for both bridges at room

temperature. When both devices were measured independently, the difference in fr between

the active and static devices was found to be about 8% and 1% for the bridges and cantilevers,

respectively. This supports the claim that different effective lengths due to irregular under-

etching during isotropic release play a major role in the different fr for the two bridges at

room temperature. A bridge structure has two anchors, and therefore, a difference in the

effective length due to under-etching difference will have a stronger influence in a bridge

structure than in a cantilever structure. Due to the much smaller difference in the fr for the

cantilevers, the measurement at room temperature for both cantilevers (active and static) is

simply a slightly broader peak than the single cantilever, shown in Figure 4.18. Unlike the

case for the bridges, as the tuning actuation begins for the active cantilever (by increasing

Iact), the bandwidth begins to increase monotonically during the heating cycle. There is no

“crossing” between resonant peaks for the cantilevers. This monotonic bandwidth tuning

behavior for the cantilever also holds during the cooling cycle. Another striking difference

between both results is the required “tuning energy”. Starting at the onset of the phase

transition, crossing the entire phase-change to generate maximum deflection in cantilevers
requires Iact ∼ 3.5 mA (Figure 4.18-left), while the bridges require less than 0.75 mA
(Figure 4.15-left).

The actuation current required to reach the maximum bandwidth for the cantilevers and

the bridges (from stage “A” to stage “D” for the cantilevers and from stage “b” to stage “d”

for the bridges) is 2.4 and 0.03 mA, respectively. Considering the resistance of the heater

traces of the cantilevers and bridges (285 and 245 Ω, respectively), the power consumption

for maximum bandwidth tuning is calculated to be 5.75 mW for the cantilever, and 0.04

mW for the bridge structures.

88

The main reason for this larger energy requirement for the cantilever relates to two

main differences between the device structures: (i) thermal mass, and (ii) heat distribution.

Notice that the bridge structures are almost half as long as the cantilever structures. A larger

length translates to a larger thermal mass, which means that a larger amount of energy will

be required to increase temperature. Thus, it is more energy demanding to induce the phase

transition of VO2 in the cantilever structure than in the bridge structure. Also, note that

the heater design for the bridge covers a larger surface of the bridge structure, which allows

for a more uniform. Finally, there is a significant difference between the change in frequency

for the active device per unit current (i.e., sensitivity); and the total tuning range between

bridges and cantilevers. The explanation for the different sensitivities and tuning ranges

share the thermal mass issue described above – larger energy is required in a cantilever

structure to induce the same temperature increase, but this mechanism does not play a

major role. The dominant mechanism (for both larger sensitivity and tuning range) relates

to the stronger dependence of resonant frequency with stress for the bridge structure. In

fact, this higher sensitivity of the resonant frequency of a bridge structure to stress is the

reason why the pairs of equivalent stages in the heating and cooling cycle look more similar

for the cantilevers than for the bridges. The tuning experiments for the cantilevers involved

current steps of 0.1 mA, while the bridges required steps 10 times smaller.

The relation between the resonant frequency and the stress for both structures is now

qualitatively discussed. During the VO2 IMT phase transition region, the VO2 crystal struc-

ture changes from its low-temperature monoclinic phase to its high-temperature rutile phase

with a contraction in the c-axis. Essentially, the area of the crystal planes parallel to the

surface of the substrate is reduced during the phase transition (heating cycle). This gener-

ates compressive stress at the surface of the beam material, which in turn will induce elastic

deformation and changes in the geometry of the beam. The deformation will then change the

dimensions and the density of the beam, which will further shift the resonant frequency of

either the bridge or the cantilever. Thus, the influence of the stress on the resonant frequency

89

is not only due to the induced stress (stress effect) but also caused by geometric variations

(geometric effect). However, different beam structures have different responses to the same

type of axial stress. For the case of a cantilever (clamped-free structure), the deformation

along the longitudinal direction is not constrained and the axial stress is released. This

results in a zero net axial stress along the longitudinal direction and a net in-plane stress in

the clamped end. For the cantilevers used in this paper, where the width is about 30 times

larger than the thickness, the resonant frequency shift is then dominated by the geometric

effect and can be described by the following expression[155]:

∆f /fr = {(1 + 2ν)/(1 − ν)} σ

(4.8)

where ∆f stands for the relative resonant frequency change, ν is the Poisson’s ratio, and

σ is the applied surface stress. The bridges, on the other hand, have more net axial stress

than the cantilevers due to their clamped-clamped structure. The resonant frequency shift is

mainly dominated by the stress effect and can be estimated by the following expression[155]:

∆f /fr = 0.1475(L/h)2σ

(4.9)

where L and h are the length and thickness of the bridge. Given that the Poisson’s of

SiO2 (which makes up for about 90% of the resonator’s structure) is 0.2; and the (L/h)2
for the bridges and cantilevers is in the order of 104, the frequency shift per stress unit is

much larger for the bridges. Furthermore, unlike in the case of a cantilever, the added stress

during the phase transition in a clamped-clamped structure is not “released” in the form of

structural bending – unless it reaches the Euler stress limit, which was not the case for the

present structures. The resonant frequencies shift for the cantilevers and bridges reported

in this work when transitioned across the entire phase transition were about 3.1% and 7.3%,

respectively.

90

4.6 Summary

In this chapter, the first mode resonant frequency has been measured for the cantilevers and

bridges both with and without VO2 to analyze the influence of VO2 thin film coating on

VO2-based MEMS resonators. For the structures we used in this experiment, the geometric

effect dominates in the frequency change for the cantilevers and the stress effect dominates

for the bridge frequency behavior.

The influence of VO2 thin film on pre-buckled bridge resonators is also studied in this

work. Due to the mismatch in the thermal expansion coefficients between layers, the mi-

crobridges exhibit buckling status with various buckling profiles which can be classified into

three groups: up, down, and bell-shape. The resonant frequency is measured throughout the

full heating and cooling cycles. The tunability shows a strong dependency on the actuation

methods and the buckling profile of the bridge. This phenomenon is attributed to a tran-

sition in the boundary condition from a fixed-fixed constraint to a fixed-pinned constraint.

Resistive (or Joule) heating shows a monotonic change in frequency, whereas the substrate

heating exhibits a bi-directional change in frequency. When a lateral deflection happens in

the beam structure, the magnitude of the present axial stress is released, and the resonant

frequency starts to shift in the opposite direction. A significant difference in the frequency

tunability is also observed for those microbridges with different buckling profiles. By de-

positing the VO2 thin film on either the concave or convex side of the beam (corresponding

to up- and down-buckled bridges, respectively), different bending moments are induced and

exerted on the microbridges. This results in opposite trends in the frequency tunability

across the SPT.

The programmability of frequency states in electro-mechanical resonators was demon-

strated by combing VO2-based resonators with a stacked FENG device. The tuning action

was achieved by first applying a DC current to a pre-heated level where the frequency separa-

tion between the heating curve and the cooling curve is the maximum. Then, a short energy

91

pulse was applied to program a different resonant frequency state in the structure. It was

found that shorter pulses with larger amplitudes are more energy-efficient than longer pulses

of smaller amplitudes. The pulse could also come from a capacitor charged by multiple small

impacts - as long as the supplied energy is above the minimum threshold for actuation. This

threshold will depend mainly on the type of structure and pre-heating level. The maximum

tuning range for the cantilever was around 30 Hz (0.38%) while it was about 40 kHz (22%)

for the bridge since the resonant frequency of the bridge is more stress sensitive.

Finally, a prototype of VO2-based tunable MEMS bandpass filter is presented. The

resonant frequency curves of two MEMS structures were measured simultaneously. One of

the devices was actuated by current pulses sent through an integrated resistive heater, while

the other structure was not actuated. Each current pulse increased the temperature of the

mechanical structure, inducing the phase transition of the VO2 film in the actuated sample.

The generated stress during the phase-change of VO2 induces resonant frequency shifts.

Two different resonator structures, cantilevers and bridges, were used to demonstrate fully

reversible bandwidth tunability action. The bandwidth was increased 2.39 and 2.62 times the

value of a single resonator for the cantilever and bridge system, respectively. The required

power for inducing full tuning action in both systems is much larger for the cantilever system

(approximately 5.75 mW) than for the bridge system (approximately 0.04 mW). This is due

to the much larger sensitivity of the bridge structures to added stress.

92

Figure 4.16 The sequence of different stages for the VO2-based tunable band-pass filter using
bridge resonators during a heating/cooling cycle. Plots show selected stages with pairs of
similar output for each cycle. The resonant peaks for the static and active bridges are
represented by the black and red/blue curves, respectively. Iact is the actuation current
applied to the active bridge.

93

Figure 4.17 The sequence of different stages for the VO2-based tunable band-pass filter using
cantilever resonators during a heating/cooling cycle. Plots show selected stages with pairs
of similar output for each cycle. The resonant peaks for the static and active bridges are
represented by the black and red/blue curves, respectively. Iact is the actuation current
applied to the active bridge.

94

Figure 4.18 Left: Resonant frequency versus actuation current through a full heating and
cooling cycle for the active cantilever. Right: Resonant frequency signal for the static bridge
(cid:48)
0) resonant frequencies are shown.
at room temperature. The measured (f0) and calculated (f
(cid:48)
The value for f
0 was obtained from Equation (3.2), and it does not take residual thermal
stress into account.

95

CHAPTER 5

UNDERSTANDING DYNAMIC RESPONSES IN FERROELECTRET

NANOGENERATORS

Self-powered pressure sensors are critical devices in IoT sensing networks. Continuous efforts

have been made in the community to improve the device performances by optimizing the

materials selection and structural configurations. Therefore, a design platform for under-

standing the device-machine interface is imperative. This chapter presents a comprehensive

study that uses the fundamental working principles of dipole moments in ferroelectret poly-

mers to describe the energy conversion mechanism. The study addresses discrepancies in

voltage measurements caused by instruments with different internal resistances and sampling

rates. A lumped parameter model is also proposed and validated to explain the impedance

mismatch at the device-machine interface. Applications including control of MEMS microac-

tuator through static response and dynamic pressure sensor array for impact distribution

sensing have also been demonstrated.

5.1 Electromechanical Response of Ferroelectret Nanogenerator

This section addresses the development of the electromechanical behavior of the ferroelectret

polymer in terms of open circuit voltage (Voc) and short circuit current (Isc). The derivation

starts with the fundamental physics in the point of view of dipole moments and is supported

by FEM simulation. The electric output is characterized by different resistive loads with

various mechanical inputs. The influences of instruments’ internal resistance and sampling

rate on the measurements of electric output are also demonstrated in section.

96

5.1.1 Derivation of Electric Output

FENG is a flexible multilayer structure device with the ability of converting mechanical en-

ergy to or from electrical energy. The active material that exhibits the direct and inverse

piezoelectric effect is a dielectric and elastic film with full-of-cell type structure. Despite

that the FENG has a similar electrical-mechanical response as piezoelectric nanogenerator,

the fundamental working principles are different. By applying external mechanical pres-

sure (F/A), the thickness of the porous midsection region of the polypropylene ferroelectret

(PPFE) film decreases. The piezoelectricity of FENG mainly arises from the relative move-

ment of positive charge surface to negative charge surface within each individual ellipsoid

void. Each ellipsoid has a permanent dipole moment pi which can be expressed as pi = qili,

where qi is the trapped charges and li is the initial separation. For a FENG device of vol-

ume V and consisting of N ellipsoids, the initial permanent polarization field is therefore

i=1pi/V . When external mechanical load is applied, the structure

determined to be P0 = ΣN
distortion causes a change in the void separation from li to l(cid:48)
needs to be modified as P(cid:48) = ΣN
field induces free charges on metal electrodes and can be expressed as: Q = ΣN

i/V = ΣN

i=1qil(cid:48)

i=1p(cid:48)

i and the polarization field

i/V . Thus, the change in polarization

i=1qi(li−l(cid:48)

i)/h,

where h is the thickness of the FENG. This expression for Q can be further rewritten as

Q = (F/EV )ΣN

i=1pi, where F , E, and A are the applied force, Young’s modulus of PPFE,

and area, respectively. Since the FENG device shares a capacitive model[112, 156], Voc under

F can be described as:

Voc =

hP0

EA

F,

(5.1)

where 
 is the relative dielectric constant of PPFE. It can be seen from Equation (5.1)

that there is a linear coupling between Voc and P (or F ). As shown in Figure 5.1a-b, the
decrease in distance between the charged surfaces, from li to l(cid:48)

i, produces a relative movement

of charges with different types. This change in dipole moments generates a displacement

current and is accounted for the Isc output under a short circuit condition, which can be

97

Figure 5.1 Working principle of ferroelectric nanogenerator: (a) No external stress is applied.
(b) When external boundary load is applied, the polarization field due to internal dipoles
decreases and free induction charges are accumulated on metal electrodes. (c) FEM results
of changes in electrode potential at the polymer-metal boundary and open circuit voltage
arise from accumulated charges.

expressed as:

Isc =

P0
E

· ∂F
∂t

.

(5.2)

The derived expressions for Voc and Isc of a FENG (Equations (5.1) and (5.2)) indicate

that the open circuit voltage and short circuit current produced by FENG increase with

compression load and rate of change in dipole moments, respectively. From this derivation,

it follows that the electric output is frequency-dependent; but only in the Isc term –not

Voc. This is explained and demonstrated experimentally in the next section. Some of the

previously reported observations on frequency-dependent Voc could be due to the use of

low-input impedance instruments. Figure 5.1c shows the electromechanical behavior of the
PPFE film based on a 250 µm × 90 µm 2-D finite element method (FEM) model. At the

initial state, the permanent polarization field induced boundary charges lead to an electric

potential at the polymer-metal interface. When the compression load occurs, the polarization

98

field is reduced due to the decrease in dipole moments. This results in a lower electric

potential and therefore free charges accumulate on metal electrodes. Because the device

shares a capacitive electrical model, the accumulated charges give rise to an open circuit

voltage, which is dependent on the mechanical input.

5.1.2 Characterization of Electric Output under Sinusoidal Pressure Input

The experimental demonstration of the parameters that determine the Voc and Isc of a

FENG follows. The electric outputs of a FENG in terms of: (i) Voc, (ii) Isc, and (iii) voltage

with resistive load (Vload) are measured during repetitive external mechanical inputs, which

consist of both: pressing and releasing stages in each pulse. Since the open circuit voltage and

short circuit current outputs will be different from those with a load, the input impedance of

the equipment used to measure these two parameters (Voc and Isc) has an influence on the

measurements. When measuring Isc, an ammeter usually directly converts the input current

to a reading through a galvanometer. Therefore the measurement is less dependent on the

instrument’s internal circuit and should be an accurate reading of the current when a short

circuit is connected to the FENG. However, a voltmeter consists of a galvanometer with a

large internal resistor connected in series. The obtained voltage reading is the input current

flowing through the galvanometer times the internal resistance. Therefore using voltmeters

with different internal resistances will result in different measurements. Specifically, using

a voltmeter with lower internal resistance will show Voc with two peaks during a single

mechanical pulse input (one peak with positive magnitude in the pressing stage and one

peak with negative magnitude in the releasing stage). According to Equation (5.1), these

two peaks of opposite signs do not correctly represent the physics of the process, since the

releasing step also represents a pressure of positive magnitude - which should produce a

positive Voc output. In other words, the instant of peak pressure (i.e. the instant where

pressing stops and releasing begins) should also represent a peak in the Voc output (not

Voc = 0V ). Considering the high impedance of the PPFE film in the low-frequency range, a

99

Figure 5.2 Schematic experimental setup. (a) Linear pressure input generated from a stepper
motor.
(b) Sinusoidal pressure input provided by the vibration exciter and the stacking
layout of FENG and pressure sensor is shown in the inset.

testing instrument with much higher internal impedance is required for getting an accurate

Voc measurement. In this experiment, Voc is measured by Keithley 2450 Source Measure

Unit. The internal impedance of the voltmeter is in the trillion Ohm (TΩ) range which

provides more accurate results.

The electric outputs under periodic nonlinear pressure inputs generated by a vibration

exciter (Figure 5.2) are shown in Figure 5.3. The changing polarity test is also carried

out to confirm that the electric signal comes from the FENG. As shown in Figure 5.3a

and Figure 5.3b, the electromechanical response of FENG exhibits similar behavior as the

piezoelectric effect. The Voc follows the change of the external mechanical input while the

Isc is proportional to the derivative of the input according to Equations (5.1) and (5.2). An

oscillation of exponentially decaying amplitude is observed at the rising edge of the signal

(See Figure 5.3b, Figure 5.3c). And the nearly infinite peak at the rising edge is related to

the derivative of the sinusoidal pressure input at P = 0 N . The observed oscillation can be

related to the mechanical properties of the PPFE film and the electrical impedance match

which reveals the electromechanical model of FENG. Also, it can be seen from Figure 5.3c
that folding a 30 mm × 15 mm patch of FENG along a symmetry axis into a smaller patch

100

Figure 5.3 Electromechanical characterization of FENG under sinusoidal pressure input. (a)
Forward and reverse Voc of FENG under sinusoidal pressure input. (b) Forward and reverse
Isc of FENG under sinusoidal pressure input. (c) Amplification of Voc and Isc of FENG by
a symmetric folding process under sinusoidal pressure input. (d) Electric output, voltage,
and current, under sinusoidal pressure input with increasing resistive load. (e) Voc of FENG
under sinusoidal pressure input with variable pressure amplitudes and frequencies. (f) Isc of
FENG under sinusoidal pressure input with various pressure amplitudes and frequencies.

of 15 mm × 15 mm can double both the Voc and Isc for a given mechanical input.

The electric outputs under different resistive loads are also investigated and results are

shown in Figure 5.3d. A mechanical input with a pressure amplitude of 110 kPa and

101

frequency of 1.7 Hz shows a voltage output that increases with resistive load, approaching

Voc. Figure 5.3e and 5.3f show Voc and Isc as a function of pressure amplitude and frequency.

Voc increases with pressure amplitude but remains constant for different frequencies from a

given pressure amplitude as indicated by Equation (5.1). Isc, on the other hand, increases

with the changing rate of the mechanical input, which is related to pressure amplitude and

frequency, as shown in Figure 5.3f. These experimental results are consistent with the

theoretical and conceptual rationale explained above.

5.1.3 Characterization of Electric Output under Linear Pressure Input

The electric output under a periodic linear pressure input is shown in Figure 5.4. The

changing polarity test is also carried out to confirm that the electric signal comes from the

FENG. As we can see in Figure 5.4a and Figure 5.4b, the electromechanical response of

FENG exhibits similar behavior as the piezoelectric effect. The Voc follows the change of

the external mechanical input while the Isc is proportional to the derivative of the input. A

similar linear pressure input of the same amplitude but the higher frequency is also used to

study the electromechanical response of FENG with different frequencies (See Figure 5.4d,

e, and f). The Voc shown in Figure 5.4d shows the same peak value as in Figure 5.4a due

to the same amplitude of the pressure input. Figure 5.4b and Figure 5.4e show how the

magnitude of Isc increases with frequency. Since the stepper motor applies a continuous

linear input by accumulating the mechanical step inputs through the control of the duty

cycle of the electric driving signal, the linear electromechanical behavior is, in fact, a static

state response. Strong oscillations can be observed at the rising edge of the signal even

when a linear mechanical input posses a lower acceleration than the sinusoidal input. The

observed oscillation can be related to the mechanical properties of the PPFE film and the

electrical impedance match which reveals the electromechanical model of FENG.

By comparing Figure 5.4a with Figure 5.3a, although the pressure inputs have the

same amplitude and frequency, different Voc outputs are measured due to different pressure

102

Figure 5.4 Electromechanical characterization of FENG under linear pressure input.
(a)
Forward and reverse Voc of FENG under low-frequency linear pressure. (b) Forward and
reverse Isc of FENG under low-frequency linear pressure. (c) Amplification of Voc and Isc
of FENG by a symmetric folding process under low-frequency linear pressure. (d) Forward
and reverse Voc of FENG under high-frequency linear pressure. (e) Forward and reverse Isc
of FENG under high-frequency linear pressure. (f) Amplification of Voc and Isc of FENG
by a symmetric folding process under high-frequency linear pressure.

input profiles (linear and sinusoidal). The different Isc amplitudes shown in Figure 5.4b

and Figure 5.3b under the same pressure input further validate this result. The oscillation

is also observed at the rising edge of the signal (See Figure 5.3b and Figure 5.3c). And

the nearly infinite oscillation peak at the very beginning of the rising edge is related to the

103

derivative of the sinusoidal pressure at P = 0 N point (higher acceleration than the linear

pressure).

5.1.4 Lumped Parameter Model for Electric Responses

Many lumped parameter models have been developed for different types of piezoelectric film

materials in different operating frequency regions. In the low-frequency region, a simple RC

model can be effectively used for modeling the electrical behavior[157]. For piezoelectric

polymer, the internal resistance is nearly infinite, thus the electrical model is purely ca-

pacitive. Multiple electromechanical lumped models for piezoelectrics have been proposed,

which consider the underlying physics and specific applications [158, 159, 160]. However, a

lumped model for describing the electromechanical response of nanogenerators is still needed

to analyze the electric output under different impact pressure profiles and resistive loads.

The overshoot presented in the Isc at the rising edge of the pressure input shown in Figure

5.4b suggests a second-order system model. When external mechanical stress is applied, a

change in dipole moments of the mid-section layer is induced in terms of the charge separa-

tion. This produces a displacement current that is proportional to the changing rate of the

dipole moment. Hence, a second-order system is used to describe the electrical domain. The

electromechanical lumped parameter model and its equivalent electrical circuit are shown in

Figure 5.5a and Figure 5.5b respectively. The variable ϕ represents the transduction from

the mechanical domain to the electrical domain.

The derived lumped model can be used to compare the outputs due to sinusoidal inputs

used in Figure 5.5a. Figure 5.5c shows the pressure due to a sinusoidal input. Figure

5.5d shows the Isc under this sinusoidal pressure input. The transduction to the electrical

domain involves differentiating the mechanical input with respect to time. When the load

(R2) equals zero (i.e. short circuit condition), the system presents an underdamped response

with the strongest oscillation as shown in Figure 5.5d. Based on the derived model, it is

possible to predict the electric output under different resistive loads. When the resistance

104

Figure 5.5 Illustration of the lumped model. (a) Lumped electromechanical model of FENG.
(b) Equivalent electrical circuit model of FENG. (c) Impact profile of a sinusoidal pressure
input. (d) Isc under a sinusoidal pressure input. (e) Experimental electromechanical response
with different load resistances. (f) Simulated electromechanical response with different load
resistances.

of the load increases, the system evolves from an underdamped system to an overdamped

system. The oscillation will decrease with increasing load resistance and the output voltage

(Vload) changes its profile from an Isc-like signal to a Voc-like signal. Figure 5.5e shows

the measured electromechanical response under different resistive loads. The large transient

oscillation only occurs with low resistive loads. It should also be noted how the measured

output voltage profile keeps approaching the open circuit voltage and input pressure profiles

shown in Figure 5.3a. This means that the profile (and value) of the measured open circuit

105

voltage will be highly dependent on the internal resistance of the instrument used. Figure

5.5f shows the simulated response based on the model shown in Figure 5.5b, where the

parameter C1 is 32 pF (which is the capacitance of the PPFE film), C2 and L are chosen

to be 0.15 nF and 2000 H in order to fit the experimental data. The system exhibits

an underdamped response for low resistive loads and an overdamped response for higher

resistance loads.

5.1.5

Instruments with Different Internal Resistances and Sampling Rates

This subsection studies the influence of testing instruments with different input resistances

on the open circuit voltage (Voc) of FENG. As discussed in previous subsections, the exper-

imentally measured Voc heavily depends on the internal resistance of the voltmeter. Hence,

four instruments with different internal resistive impedances are used to measure the Voc

and the results are compared. Figure 5.6 shows the measured data of testing instruments:

Keithley 2450, Keithley 2182, Tektronix TDS2004C and National Instruments 9201. The

internal impedances for those testing instruments are measured to be 0.41 TΩ, 10 MΩ, 1

MΩ, and 1 MΩ respectively. All the measurements are made under the same pressure input

of 110 N and 1.7 Hz. As can be seen in Figure 5.6a, the Keithley 2450 (which has the

highest internal resistance and sampling rate) shows results that follow the pressure profile.

This is expected since the instant of peak pressure (i.e. the instant where pressing stops

and releasing begins) should also represent a peak in the Voc output. Figure 5.6b shows the

results for Keithley 2182, which offers intermediate internal resistance but very low sampling

rate. Therefore the Voc plots behave like the short current (Isc) pattern with much lower

amplitude than the Voc measured with the Keithley 2450. Figure 5.6e and Figure 5.6f

show the data obtained from Tektronix TDS2004C and National Instruments 9201. These

two instruments have the lowest internal resistance of around 1 MΩ but high sampling rate.

The readings for both instruments have the same amplitude for Voc with some ripple ob-

served due to the under-damped response in the low load condition. As discussed, the FENG

106

Figure 5.6 FENG voltage output measurement with different instruments: (a) Keithley 2450
and Voc. (b) Keithley 2182 and Voc. (c) Measured voltage output when using a Keithley
2450 and a 1 MΩ load resistor. (d) Measured voltage output when using a Keithley 2182 and
a 1 MΩ load resistor. (e) Tektronix TDS2004C and measured Voc. (f) National Instruments
9201 and measured Voc.

can be modeled as a second-order system, therefore the electromechanical response can be

determined by the damping ratio ξ from the following expression:

ξ =

α
ω0

,

(5.3)

where α is the attenuation factor and ω0 is nature resonant frequency. Those factors can be

determined by the lumped parameters as:

107

and

α =

R
2L

ω0 =

1√
LC

,

(5.4)

(5.5)

where R and L are the lumped resistance and inductance, while C is the effective capacitance

of C1 and C2 in Figure 5.5. When a small resistive load, e.g. R = 1 M Ω, the damping

ratio ξ is calculated to be 0.057, which indicates an underdamped response for the system

and therefore a strong oscillation is observed. As the resistive load increases to beyond 17.4

MΩ, the system presents an overdamped response where the decay of the transient current

does not exhibit an oscillation behavior.

In order to further validate the influence of internal resistance on the measurement out-

come, the voltage output of FENG under 1MΩ load is measured with Keithley 2450 and

Keithley 2182. Figure 5.6c and Figure 5.6d shows the results. Since the 1 MΩ load is

much smaller than the internal resistance of both instruments (Keithley 2450 and Keithley

2182), most of the generated current will flow through the load resistor (and not into the

instrument), thus providing an accurate reading of the voltage drop at the load. By com-

paring the voltage measurements in Figure 5.6e and Figure 5.6f with those in Figure 5.6c

and Figure 5.6d, we can see that the Voc measured by an instrument with 1 MΩ internal

resistance matches the voltage under a 1 MΩ load. Moreover, because the Keithley 2182 has

a very low sampling rate, some of the ripple oscillations are not captured in the measure-

ment, and the nature of the second-order response of FENG may also be neglected. This

demonstrates that the internal resistance of the voltmeter can have a significant influence on

the Voc measurement of the FENG as well as other nanogenerators with high impedance.

108

Figure 5.7 FENG-based matrix pressure sensor. (a)The voltage output of a 15 mm × 15 mm
single layer FENG as a function of input pressure amplitudes and frequencies. (b) 3D surface
fitting of the single-pixel electromechanical response, R2 = 0.93. (c) 16-pixel FENG-based
matrix sensor and 3D contour maps of the pressure distribution over the sensor upon an
impact from the user.

5.1.6 FENG-based Tactile Sensor

As discussed above, the Voc is proportional to the input mechanical pressure amplitude and

is independent of its rate of change with time. However, most of the commercial voltmeters
have internal resistances in the range of 1 ∼ 10 MΩ. When using such low-impedance

instruments to measure Voc, the measurement is misleading, since it is actually the voltage

drop across a resistive load Vload, which can be approximated by Isc times the internal

resistance Rin of the voltmeter. Thus, Vload changes with both: pressure amplitude and its

109

Figure 5.8 The fabrication process of a single layer FENG-based matrix sensor with 16 indi-
vidual positive electrodes and 1 common negative electrode. (a) Deposition of the common
negative silver electrode on PPFE film. (b) Deposition of 16 positive silver electrodes. (c)
Wire connection by conductive copper tape. (d) Spin coating of PDMS substrate and par-
tially cured. (e) Spin coating of another PDMS layer to encapsulate the device and the two
layers are completely cured.

rate of change with time. Because the FENG is able to output voltage signal which depends

on the input pressure profile, no external power supply is required for device operation as a

pressure sensor (i.e. FENG can be implemented as a self-powered flexible dynamic pressure
sensor). In this work, the electromechanical response is characterized for a 15 mm × 15 mm

single layer FENG device and the Vload is measured by using a voltmeter with 1 MΩ resistive

internal resistance (NI9201, National Instruments). Given that the sinusoidal pressure input

can be expressed by P = Pmaxsin(2πf t), where Pmax is the peak pressure amplitude, f is

the frequency; Vload can be expressed as:

Vload = αPmaxf cos(2πf t)

(5.6)

where α = 2πAP0Rin/E. The maximum value Vpeak is therefore found to be at Vpeak =

Vload(t = 0) and is linearly related to Pmaxf . Figure 5.7a and Figure 5.7b show the 3D

surface plot of the Vpeak as a function of the input pressure amplitude and frequency. By

fitting the data into a polynomial function, the relation between Vpeak, Pmax, and f can be
given by: Vpeak = 3.1 × 10−7P 1.1f 0.85, which is expected from Equation (5.6).

A single FENG-based pressure sensor can be easily integrated into an N × N array of

pressure sensor by a specific arrangement of the positive electrodes. Figure 5.7c shows an
array of 16 individual FENG devices, each with an area of 15 mm × 15 mm. All the elements

110

Figure 5.9 Contour map of the pressure distribution over the sensor with different impacts
applied to different locations.

in the array are equally spaced in both the X and Y directions. A common negative electrode

is patterned on the backside of the PPFE film. To protect the silver electrodes from wearing

during repeated use and humidity, the device is encapsulated into a polydimethylsiloxane

(PDMS) protective layer (See detailed fabrication process in Figure 5.8). Since the positive

electrodes are electrically insulated from each other, each electrode can be taken as an
independent pixel pressure sensor. Hence, this 4 × 4 matrix pressure sensor with a resolution

of 16 pixels can be implemented to map the distribution of an impact. Figure 5.7c shows the

3D contour map of the pressure distribution upon an external impact from the user’s hand

press. The different magnitudes of pressures are labeled and presented in different colors

(see Figure 5.9 for 2D contour map of pressure distributions). The pressure distribution

under different impacts is also presented.

111

Figure 5.10 Deflection of VO2-based actuator at different actuation currents. (a) Deflection
of VO2-based actuator at room temperature in the heating cycle. (b) Deflection of VO2-
based actuator at 3.30 mA in the heating cycle. (c) The maximum deflection of VO2-based
actuator at 4.45 mA in the heating cycle.
(d) Deflection of VO2-based actuator at 5.50
mA in the heating cycle. (e) Deflection of VO2-based actuator at room temperature in the
cooling cycle. (f) Deflection of VO2-based actuator at 3.30 mA in the cooling cycle. (g) The
maximum deflection of VO2-based actuator at 3.95 mA in the cooling cycle. (h) Deflection
of VO2-based actuator at 5.50 mA in the cooling cycle.

5.1.7 FENG-based Micro Robot Arm Controller

Due to FENG’s large internal impedance, almost any commonly used voltmeters could cause

a discharge of the self-charged electrical energy in the device and results in transient signal

output. Thus, the application is limited to dynamic pressure monitoring. When static

response needs to be addressed, an electronic switch can be induced where the FENG can

112

(b) VO2-based MEMS actuator without applying actuation current.

(a) Stress applied to the FENG
Figure 5.11 FENG-based micro robotic arm controller.
device.
(c) Stress
released from the FENG device. (d) VO2-based MEMS actuator with a maximum deflection
at actuation current of 4.45 mA. (e) The gate voltage of the p-channel MOSFET controlled
by the output of FENG, the voltage change tracks the motion of the finger.

be used to control the gate voltage. Here we demonstrate this application by using a micro-

robotic arm controlled through the movement of the human body (e.g. movement of a

finger) by combining the FENG and a VO2-based bimorph microelectromechanical systems

(MEMS) actuator. The VO2-based actuator can be thermally actuated by utilizing the large

difference in the thermal expansion coefficient of the VO2 coating and SiO2 substrate in the

113

bimorph beam structure. Therefore the beam structure bends up towards the out of plane

direction (see Figure 5.10). In this work, the VO2-based MEMS actuator has dimensions
of 550 µm in length, 50 µm in width and 2.3 µm in thickness. The actuation is induced by

applying a current to the resistive metal heater which is embedded into the beam material.

To enable the control of the deflection of the VO2 actuator, a single layer FENG device of
15 mm × 35 mm is fabricated and encapsulated into a PDMS ring structure and then put

onto the user’s finger. As shown in Figure 5.11, the FENG senses the stress coming from

the flexing of the finger, and the voltage output is used to control the actuation current

through the gate terminal of a p-channel metal-oxide-semiconductor field-effect transistor

(MOSFET), which in turn controls the current through the VO2-based MEMS actuator.

5.2 Summary

In this chapter, a polypropylene ferroelectret polymer thin film with the large piezoelectric

effect is presented. The discussion is mainly focused on the design platform for implementing

the PPFE film as a flexible pressure sensor. Both static and dynamic pressure responses are

studied when different device-machine interfaces are considered. The characterizations in
terms of Voc and Isc are performed on a 15 mm × 15 mm single layer FENG thin patch
under different mechanical impacts provided by a vibration exciter. The results show that

the energy conversion process from mechanical to electrical domain could be significantly

affected by the internal impedance of instruments. Measurement results can also be affected

by the instrument sampling rate since the transient oscillation signal occurs at the starting

edge within a short time window. A lumped parameter model is also proposed to explain

the load-dependent voltage measurement variations and the results are validated by the

experiment. Applications in terms of the pixelated sensor array and the human-robotic

control interface are also demonstrated at the end. This paper provides useful information

on the design of sensor/machine interface, especially when polymer-based sensor with high

114

internal impedance is used, and in troubleshooting the variations caused by instruments.

115

CHAPTER 6

FERROELECTRET NANOGENERATOR BASED SELF-POWERED

BENDING SENSOR

The significant growth of wearable electronics is in constant search for optimizing systems

with high flexibility and self-powering capacity. In this chapter, we utilize flexible polypropy-

lene ferroelectret (PPFE) thin film polymer with the large transverse piezoelectric coefficient

for bending curvature self-powered sensing. The electric energy comes from the geometry

distortion of the built-in macro dipoles with initial surface charge distributions. Theoretical

analysis based on constitutive electromechanical equations and bi-layer bending mechanics

provide a detailed understanding of the sensing mechanism and its applicability. Different

evaluation methods are used to have a more comprehensive understanding of the electrome-

chanical responses under different bending conditions. It has been found that the velocity and

magnitude of the mechanical input influence the average voltage output, while instantaneous

voltage is not dependent on the latter. The robustness of the material is also investigated,

where the device shows no performance degradation by immersion into the water up to 12

hours and under 10k bending cycles. Thermal stability tests reveal degradation starting
at ∼ 75◦C and an immediate failure of the device at ∼ 150◦C. Finally, an application is

demonstrated by showing the potential use of the characterized system as a self-powered

sensor for athletic assessment[161].

6.1 Analysis of Piezoelectricity Under Bending Test

In this section, we present the theoretical analysis of the piezoelectricity of ferroelectret

polypropylene (PP) polymer under a bending condition. This piezoelectric effect is origi-

nated from the transverse piezoelectric coefficient which leads to a decrease in the dipole

separation distance under an axial compression. The analysis starts with the fundamen-

116

tal constitutive equations for piezoelectric materials, which addresses the linear coupling

between electrical and mechanical domain. Expressions for electrical outputs (current and

voltage) are deducted as a function of mechanical input.

6.1.1 Current Output Under Bending Test

The constitutive equations of a typical piezoelectric material among stress σij, strain 
ij,

electric field Ei and displacement field Di can be described as below:






11


22


33

2
23

2
31

2
12



0

0

0

0

0

d15

−

0

0

0

d15

0

0



k11

0

0

+



0

k22

0

0

0

k33



E1

E2

E3





σ11

σ22

σ33

σ23

σ32

σ12

=


 =

and



D1

D2

D3

c11

c12

c13

0

0

0

c12

c13

c11

c13

c13

c33

0

0

0

0

0

0

0

0

0

c44

0

0

0

0

0

0

c44

0

0

0

0

0

0

(c11 − c12)/2



0

0

0

0

0

0

d31 d31 d33



0

0

d15 0

0

d15

0

0

0




11


22


33

2
23

2
31

2
12




d31

d31

d33

0

0

0


 ,



E1

E2

E3

 ,

(6.1)

(6.2)

where cij is the elastic constant, dij is the piezoelectric constant, and kij is the dielectric

constant. Given σ22 = 0 under a perfect bending condition and 
22 = 0 due to the symmetric

structure, the relation between Ei and 
ij can be revealed as:

0 = c12
11 + c13
33 − d31E3.

(6.3)

117

Equation (6.2) also gives the relation between Di and 
ij, which results in the transverse

piezoelectric effect:

D3 = d31
11 + d33
33 + k33E3.

Combining Equation (6.3) and Equation (6.4) yields:

kE3 = d
11 + D3,

(6.4)

(6.5)

where k = k33 + d33d31/c13 and d = d33c12/c13 − d31 and the longitudinal strain 
11 can be
given by[162]:


11 = −w(cid:48)(cid:48)(x)(hP P F E + hP I )/2,

(6.6)
where w(cid:48)(cid:48)(x) is the second derivative of buckling amplitude w(x) = A[1 + cos(2πx/L0)]/2
√
L0∆L is the maximum buckling amplitude solved by minimization of the
and A = (2/π)

total energy[115]. Therefore, 
11 can be described as:
√
2π(hP P F E + hP I )

∆L


11 =

√

L0

∆L

cos(

2πx
L0

).

(6.7)

Considering the PPFE sample is located at the middle of the PI substrate, 
11 can be

approximated by taking the maximum value[163]:


11 ≈ 2π(hP P F E + hP I )

√
L0

L0

√
∆L

.

(6.8)

Given that Voc = E3hP P F E and D3 = 0 for open circuit voltage Voc measurement, Equation

(6.5) yields:

Voc =

dhP P F E

k


11 =

2π(hP P F E + hP I )dhP P F E

√
L0

kL0

√
∆L.

(6.9)

Equation (6.9) indicates that Voc is proportional to 
11 and

When measuring the short circuit current, the device is connected to an ammeter and no

voltage drop is expected across the instrument. Solving Equation (6.5) for D3 results in:

√

∆L.

√
∆L

D3 = −d
11 = −2πd(hP P F E + hP I )

√

L0

L0

118

.

(6.10)

Therefore, the short circuit current can be determined by Isc = −SP P F E(∂D3/∂t), which
can be further expressed as:

Isc =

πdSP P F E(hP P F E + hP I )

√

√

L0

L0

∆L

d∆L

dt

.

(6.11)

For the linear axial compression displacement used in this work, ∆L can be expressed as:

vt

∆L =

v(T − t)

if t < T /2

if T /2 < t < T,

(6.12)



Isc =

where v is the constant axial compression velocity and T is the time period of a full com-

pressing and releasing cycle. Thus, Equation (6.11) can be rewritten as:

√
πdSP P F E (hP P F E +hP I )

− 1
v
t
2
√
− πdSP P F E (hP P F E +hP I )

√
L0
√

L0

L0

L0

v

(T − t)

− 1
2

if t < T /2

if T /2 < t < T.

(6.13)

It can be seen from Equation (6.13) that the maximum short circuit current Isc−max can

be found at t = 0 and t = T which leads to an infinite value. However, in real materials,

this value is limited to a finite value by the different loss mechanisms within the process,

which are partly determined by the material’s properties. Nevertheless, it can be deduced
from Equation (6.12) and Equation (6.13) that Isc−max is independent of the maximum

compression displacement ∆Lmax = vT . The dependency can be found when the average
short circuit current Isc−ave is considered for a given compression stage. Given that Isc−ave

can be expressed as:

Isc−ave =

(cid:82) T

2
0 Iscdt
T /2

The expression of Isc−ave can be found by combining Equation (6.13) and Equation (6.14):

.

(6.14)

√
2

Isc−ave =

2πdSP P F E(hP P F E + hP I )v

√
L0∆Lmax

L0

.

(6.15)

119

6.1.2 Voltage Output Under Bending Test

Measuring voltage output V , or open circuit voltage Voc using a voltmeter with small internal

resistance is considered. Figure 6.1a and b show the schematic configurations for measuring

Voc and V , respectively. When measuring V , the voltage reading is given by Ohm’s law as
V = I(cid:48)R, where R is the internal resistance of the instrument and I(cid:48), which is the current

flowing through R, is also affected by R.

In this case, the expression for D3 shown in

Equation (6.5) can be combined with E3hP P F E = V to result in:

(cid:48) =

D3

k

hP P F E

V − d
11.

(6.16)

Thus, the current passing through the instrument internal resistance is given by I(cid:48) =
(cid:48)/∂t) and the measured voltage V can be determined by solving the following
−SP P F E(∂D3
differential equation:

V = −SP P F EkR
hP P F E
= −SP P F EkR
hP P F E

dV
dt
dV
dt

+

d
11
dt

+ SP P F EdR

√
πdR SP P F E(hP P F E + hP I )

√
L0t

L0

(6.17)

v

.

The maximum instantaneous voltage (Vmax) can be found at dV /dt = 0 and expressed as:

Vmax =

πdR SP P F E(hP P F E + hP I )

√

L0

L0t

v

.

(6.18)

√

When small internal resistance of voltmeter is selected, R (cid:28) RP P F E, where RP P F E is the
internal resistance of PPFE film, I(cid:48) can be approximated as I(cid:48) ≈ Isc and Equation (6.17)
can be simplified as V ≈ IscR. Therefore the voltage measured by a voltmeter with small
internal resistance shows similar dynamic behavior as expected from Isc.

6.2 Characterization of Piezoelectricity Under Bending Test

In this section, we focus on the distortion of the macro dipoles and the consequent electric

output under a bending operation caused by an axial displacement. As shown in Figure

120

Figure 6.1 Comparison of voltage measurements Voc and V by different instruments. (a)
Voc measurement by high impedance voltmeter (Keithley 2450).
(b)V measurement by
low impedance voltmeter (Keithley 2182), where R = 10 M Ω is the instrument’s internal
resistance.

6.2a, the PPFE film is attached to a flexible PI substrate. In this configuration, the elec-

tromechanical response can be described by characterizing the output voltage/current to

the generated deflection due to an axial load that results in a buckled bridge shape shown

in Figure 6.2b. The experiment is assisted by using a computer-controlled stepper motor

as the linear actuator to provide the horizontal compressive axial stress that causes axial

displacement ∆L and vertical displacement w. In order to compare different electromechan-

ical responses under different bending conditions, ∆L and the compression velocity v were

programmed by pulse width modulation (PWM) of DC voltages applied to the motor.

6.2.1 Open Circuit Voltage and Short Circuit Current Under Bending Test

Assuming the initial length of the PI substrate is L0, the flexible sample buckles into

a sinusoidal shape with w described as a function of horizontal axial parameter x as:

w(x) = A[1 + cos(2πx/L0)]/2, where the origin of x is at the center and A is the max-

√
L0∆L[115]. The in-plane x-axial strain

imum buckling amplitude given by A = (2/π)

(
11) within the PPFE can be estimated by using the curvature of the buckled shape as:

11 = −w(cid:48)(cid:48)(x)(hP P F E + hP I )/2, where w(cid:48)(cid:48)(x) is the bending curvature, hP P F E is the thick-

121

Figure 6.2 Bending configuration of PPFE thin film mounted on the flexible PI substrate.
(a) 3D schematic drawing of silver coated PPFE film mounted on a PI substrate, inset shows
the SEM image of the cross-sectional view of PPFE film. (b) 2D Schematic diagram of a
sinusoidal shape buckling profile under a horizontal axial compression displacement.

ness of PPFE film and hP I is the thickness of the PI substrate. Given that the PPFE film

is located at the center of the PI substrate where maximum longitudinal strain occurs, 
11

122

can be approximated as:


11 =

√
2π(hP P F E + hP I )

√
L0

L0

∆L

,

(6.19)

from which we can use the fundamental equations that relate strain to the electric field in

piezoelectric materials to obtain:

√

2π(hP P F E + hP I )dhP P F E

√

Voc =

(6.20)
where d = d33c12/c13 − d31 and k = k33 + d33d31/c13, d33, c12, c13, d31 and k33 come from
piezoelectric matrix and stress/strain transformation matrix. Thus, Voc is proportional to

∆L,

kL0

L0

the strain in PPFE film which is exactly the linear coupling relation between mechanical

and electrical properties in piezoelectric materials.

However, Voc measurements are often taken by connecting a voltmeter across the open

circuit terminals at the output of the device[164]. Therefore, the profile of the measured

Voc will be dependent on the instrument’s internal resistance; and its proximity to a real

open-circuit scenario will increase with this internal resistance value. In this work, a Keithley
2450 is used to measure Voc, which has an internal resistance ≥ 10 GΩ. Figure 6.3 shows
the relation between ∆L, 
11, and Voc. The bidirectional linear axial displacement provided

by stepper motor as shown in Figure 6.3a gives a normalized strain profile determined by

Equation (6.19) as shown in Figure 6.3b. The measured Voc also shows a similar profile as


11 which is also indicated by Equation (6.20). Figure 6.3d shows the measured peak value

of Voc (scattered points) as a function of different maximum axial displacement ∆Lmax, and

the theoretical curve for these Voc maximum points, taken from evaluating Equation (6.20)

at ∆L=∆Lmax.

For short circuit current measurements, the device is connected to an ammeter, where the

voltage drop across is minimal. This results in a simple linear relation between displacement
field D3 and 
11. Given that Isc = −SP P F E(∂D3/∂t), (where Isc is the short circuit current
and SP P F E is the area of PPFE film), Isc can be further expressed as:

Isc =

πdSP P F E(hP P F E + hP I )

√

√

L0

L0

∆L

d∆L

dt

.

(6.21)

123

Figure 6.3 Measured electrical response due to axial displacement ∆L and film strain 
11.
(a) Profile of linear axial compression displacement ∆L as a function of time. (b) Theoretical
normalized film strain 
11 from Eq.(1) as a function of time. (c) Measured Voc as a function
of time. (d) Peak Voc value as a function of ∆Lmax for a given compression velocity of 14
mm/s.

124

Equation (6.21) shows that Isc is proportional to the changing rate of compressive load
( d∆L

dt ), and its magnitude increases with PPFE film area; which can be achieved by stacking
multiple layers or connecting them in parallel. For linear axial compression, the compression

velocity v (input parameter), is given by:

vt

∆L =

v(T − t)

if t < T /2

if T /2 < t < T,

(6.22)

where T is the time period for a complete compressing and releasing cycle. Thus, Isc(t) can

be determined as:

Isc(t) =

πdSP P F E(hP P F E + hP I )

√

L0

L0

√
v

− 1
2 ,
t

(6.23)

for the compression stage and its negative value can be used for the releasing stage. Equation

(6.23) indicates that the short circuit current increases with increasing v, which is also

shown in Figure 6.4a-c. The PPFE acts as a current transducer, which translates energy

from mechanical to the electrical domain. Therefore, the internal resistance R of the voltage

measuring instrument must be taken into consideration. To distinguish the voltage measured

by a voltmeter with low input impedance from the Voc measured by an instrument with high

input impedance, the symbol V is used for the clarity.

In this case, the current flowing

through the device-instrument circuit loop is also affected by R through the induction of an

electric field. Thus, the measured voltage V can be determined by solving the differential

equation. When the internal resistance of the voltmeter is much lower than the impedance

of PPFE, V can be approximated to:

V ≈ IscR,

(6.24)

where R = 10 M Ω for the voltmeter Keithley 2182A used in this work. Therefore, voltage

measurements (Figure 6.4d-f) have the same curve profile as Isc (Figure 6.4a-c).

The characterization is performed for a PPFE film mounted on a PI substrate under axial

stress that generates buckling (and bending), while the current and voltage are measured

125

Figure 6.4 Characterization of electrical output under bending test. (a,b,c) Short circuit
current Isc under the same ∆Lmax = 3 mm and different v. From top to bottom: 3.5 mm/s,
7mm/s, and 14 mm/s. (d,e,f) Voltage measurement under the same ∆Lmax = 3 mm and
different v, from top to bottom: 3.5 mm/s, 7 mm/s, and 14 mm/s.

across the device. The axial compressive displacement is provided by a stepper motor with

bi-dimensional displacement. The PPFE used for the bending test is 15 mm wide, 50 mm
long, and 80 µm thick. Two 500 nm silver thin films are sputtered on both sides of the PPFE
as electrodes. The device is mounted on a 25 mm × 60 mm PI substrate with a thickness

of 0.8 mm. The ∆Lmax and v are programmed and controlled through the FPGA interface.

Figure 6.4a-c show the measured Isc under different compression velocities with the same
maximum compression displacement of 3 mm, which is converted to curvature of 46.8 m−1.

As predicted by Equation (6.23), the current output increases with increasing compression

velocity. Figure 6.4d-f show the measured output voltage V under the same conditions used

126

for measuring Isc. The voltage output follows a similar relation with compression velocity

to the one observed in Isc measurements; which agrees with the described theory.

6.2.2 Different Evaluation Methods Under Bending Test

Characterizing self-powered sensors is often done in terms of peak short circuit current
(Isc−max) and measured peak voltage (Vmax) values [162]. However, since Isc is proportional
2 , the Isc−max and Vmax are found at t = 0 for any applied axial stress. This means

− 1

to t

that the largest generated electrical output occurs at the moment an axial displacement
begins to occur; and therefore, Isc−max and Vmax should be independent of the maximum

range of axial displacement, ∆Lmax. This usually goes unnoticed, because for a commonly

used bending condition, the ∆Lmax is always coupled with a faster compression velocity v;

e.g. when ∆Lmax is increased, the compression time period T /2 is kept the same, leading

to a higher v.

The relation between the maximum instantaneous current and voltage output is further

characterized by using different compression velocities and axial displacements (or curva-
tures). Figure 6.5a shows the Isc−max under different axial displacement velocities ranging

from 3.5 mm/s to 14 mm/s with different maximum axial displacements from 1.2 mm to
6 mm, which converts to a bending curvature range of 29.6 m−1 to 66.2 m−1. No obvious

changes in Isc and Voc are observed for different ∆Lmax under the same compression ve-

locity, indicating that the compression velocity is the dominant factor in determining the

peak electrical outputs under the bending operation. An estimation of the peak value can

be made from Equation (6.21) by giving a certain small (nonzero) time –usually determined

by the instrument’s sampling rate– and assuming the traveled distances in this time are
comparable for different velocities. Then, the Isc−max can be approximated to be linearly

proportional to v, which is also indicated in Figure 6.5a.

As indicated by Equation (6.23) and Figure 6.5, the Isc−max and Vmax values are found
− 1
2 .

at the beginning of each compression and releasing cycle, then decaying as a function of t

127

Figure 6.5 Characterization of Isc−max and Isc−ave under bending test. (a) Isc−max as a
function of ∆Lmax under different v. (b) Isc−ave as a function of v under different ∆Lmax.
(c) Isc−ave as a function of ∆Lmax under different v. (d) Isc−ave as a function of w(cid:48)(cid:48) under
different v. The fit curves are obtained from Eq.(7) by using proportional constants that
best fit the measured data.

For a compression stage, the average current output, Isc−ave, can be calculated by averaging

Isc over the compression time period T /2, leading to:

(cid:82) T

Isc−ave =

=

2
0 Iscdt
√
T /2
2πdSP P F E(hP P F E + hP I )v
2

√
L0∆Lmax

L0

(6.25)

.

Equation (6.25) gives the relation among Isc−ave, v, and ∆Lmax. Figure 6.5b shows that
Isc−ave is linearly proportional to v for each given ∆Lmax, which is in agreement with the
theory. Figure 6.5c shows measurements of Isc−ave as a function of ∆Lmax for different

128

Figure 6.6 Characterization of Vmax and Vave under bending test. (a) Vmax as a function of
∆Lmax under different v. (b) Vave as a function of v under different ∆Lmax. (c) Vave as a
function of ∆Lmax under different v. (d) Vave as a function of w(cid:48)(cid:48) under different v.

values of v, where the data follows the square-root dependence on ∆Lmax predicted by

theory. For real application and bending sensing purposes, it is important to know the
relation between the measured electric signal (Isc−ave in this case) and bending curvature.
Given that w(cid:48)(cid:48) is linearly proportional to 
11, which is also linearly proportional to
Isc−ave also exhibits an inverse dependence on w(cid:48)(cid:48), as shown in Figure 6.5d.

∆L,

√

Given that most of the data acquisition and readout circuits are designed to respond

to voltage signals, it is more desirable to have sensors that generate voltage output signals

(instead of current signals). Typical commercial voltmeters have internal resistances between

1 MΩ to 10 MΩ, which are much lower than the impedance of PPFE. Therefore, in the

129

interest of completing a study that makes the proposed bending sensor more compatible

with typical measuring instruments, the rest of the work is focused on the measured voltage

V , instead of the ideal Voc value. As discussed above, V can be approximated as IscR, and

it is expected to exhibit similar dynamic profile as Isc; which is observed experimentally

(Figure 6.6). It should be noted that Voc (Figure 6.3c) shows a different dynamic profile

than V (Figure 6.4d-f); and the relationship between Isc and V through the instrument’s

internal resistance (V = IscR) is validated in the experimental results shown in Figure 6.5

and Figure 6.6.

6.3 Application of PPFE-based Bending Sensor

In this section, a study on the degradation of PPFE films in terms of mechanical robust-

ness, resistance to humidity and thermal stability is performed next. The acquired models

discussed above are implemented in an athletic monitoring system, based on the comparison

of generated electric waveforms.

6.3.1 Device Robustness

Figure 6.7 shows the performance of PPFE as a function of bending cycles for an axial com-
pression velocity of 14 mm/s and maximum bending curvature of 46.8 m−1. This experiment

was carried out using the same setup described for all the previous bending experiments. No

significant degradation is observed during the repeated cycling test, indicating the PPFE

film as a bending sensor exhibits long term mechanical stability. Wearable sensors can be

implemented in systems that allow for the assessment of an athlete’s performance in sports.

However, there are several factors that can deteriorate the device’s reliability. For example,

resistance to humidity is a key parameter which could significantly reduce the performance

of the sensor, especially for those have the capacitive impedance. Triboelectric sensors with

an air gap will experience a change in their performance due to the absorption of the ambient

130

Figure 6.7 Demonstration of performance degradation under different testing conditions. (a)
Test of mechanical robustness under repeated bending cycling up to 10000 bending and
releasing operation. (b) Test of humidity resistance by immersion into water for up to 12
hours. (c) Test of thermal stability under different baking temperatures.

water and therefore require additional packaging methods[165, 166, 167]. Even tough PPFE

has a porous structure, it is sandwiched in between two continuous PPFE films, which pre-

vent the swelling of the voids due to water absorption. Thus, it proves to be water-resistant

as demonstrated in Figure 6.7b. When using polymer as the base material for piezoelectric

applications, the flexibility of the polymer may experience poor thermal stability. Figure

6.7c shows the thermal degradation percentage under different baking temperatures as a
function of time. No degradation is observed for baking temperature of 50◦C. As the tem-

131

perature increases, the material starts to degrade. When baked at 75◦C, no degradation is

measured until baking for 60 min, the performance saturates at the level of around 65%.
Significant degradation appears at the temperature of 125◦C and above. For a short time

and low-temperature processes such as encapsulating PPFE into PDMS and PI layers, it is

acceptable to sacrifice some of the performance. However, higher temperatures should be
avoided, since a temperature of 150◦C would destroy the quasi-piezoelectric property of the

material due to the collapsing of the voided structure.

6.3.2 Athletic Assessment

Based on the analysis above, it can be seen that Vmax and Vave exhibit different behaviors

under the same bending condition. This suggests that by monitoring these two parameters,

information about the bending curvature and speed can be extracted. A potential appli-

cation for this can be found in monitoring the bending curvature and speed of an athlete’s

wrist during a baseball throw or a basketball shoot. Hence, this flexible self-powered PPFE

bending sensor can be attached to the player’s wrist to monitor the posture and movement

profile when participating in those sports. In the present application, we suggest a way to

compare the bending profile of an athlete with what can be considered an ”ideal movement

behavior”; perhaps coming from a coach or a database that holds a history of “good throws”.

Figure 6.8a shows a demonstration of throwing a baseball from the player. Figure 6.8b

and Figure 6.8c show the measured voltage waveforms from a coach and the athlete, re-

spectively. By comparing the Vmax and Vave values obtained by the coach and the athlete,

a learning score can be generated from the algorithm described above. This way, the athlete

can monitor his/her athletic performance and even have a database with a history of the

progress made.

The score used for determining the learner’s athletic performance is described below.

First, the performance of throwing a baseball is assumed to be equally determined by two

factors with the same weights (50%): speed and curvature of wrist bending. As indicated

132

Figure 6.8 Demonstration of application in the athletic assessment.
(a) Photography of
showing bending of the wrist during throwing a baseball. (b) Voltage output signal from
the coach throwing the baseball. (c) Voltage output signal from the learner throwing the
baseball.

by Equation (6.21), (6.24), and (6.25), Vmax is proportional to v and Vave is proportional
−1. Therefore, comparing the Vmax value obtained by the coach with the Vmax
obtained for the learner yields a ”performance score” in terms of velocity parameter v. Then,

to v∆Lmax

the value of Vave for the coach is compared to the Vave value obtained for the learner. The

ratio of these two Vave values is proportional to v and inversely proportional to the bending

curvature. Since the comparison for v was obtained from the Vmax values, the comparison

between Vave values can be used to obtain a ”performance score” in terms of the radius

of curvature. In Figure 6.8, the Vmax is 0.48 V and 0.16 V for the coach and the learner

respectively while Vave is 0.167 V and 0.066 V. By defining the score of the coach is 100, the

score of the learner is about 52.

133

6.4 Summary

The porous flexible polypropylene ferroelectret (PPFE) thin film is introduced in this work

as a bending sensor. The bending operation is provided by an axial displacement and the

bending profile follows the fundamental mechanical analysis. The output of PPFE film in

terms of open circuit voltage, short circuit current, and measured voltage is characterized

under different bending conditions. Given that the PPFE can be considered as a current

source with large internal impedance, its open circuit voltage is heavily dependent on the in-

ternal resistance of the voltage measurement instrument. To clarify the bending dependency
of an electric output, Isc−ave and Vave are used instead of Isc−max and Vmax. The average

electric output values are found to have a similar behavior due to the approximation under

a condition of using low internal resistance voltmeter. Both outputs show linear dependency

on v and inverse square-root dependency on ∆Lmax. The robustness of the material in terms

of bending repeatability, resistance to humidity, and thermal stability are also presented for

considerations in real applications, such as the sports assessment application demonstrated

in this chapter.

134

CHAPTER 7

FERROELECTRET NANOGENERATORS FOR SELF-POWERING

SYSTEMS

Applying flexible materials for energy scavenging from ambient mechanical vibrations is a

clean energy solution that can help alleviate electrical power demands in portable devices and

wearable electronics. This chapter presents fundamental studies on a flexible ferroelectret

polymer with a strong piezoelectric effect and its interface with self-powered and energy
storage systems. A single-layered device with a thickness of 80 µm was used for characterizing

the device’s output voltage, current, transferred charge, and energy conversion efficiency.

The potential capability of harvesting mechanical energy and delivering to system load is

demonstrated by integrating the device into a fully integrated power management system.

The theory for determining the harvested energy that is ultimately delivered to external

electronic loads (or stored in a battery) is discussed. The maximum power delivery is found
to be for a 600 MΩ load, which results in a device power density of 14.0 Wm−3 for input

mechanical forces with frequency around 2 Hz[168].

7.1 Power Output of FENG

In the section, we fully describe the corresponding, applicable theory for characterizing the

generated and stored power; as well as the system’s energy efficiency. The device physics is

briefly explained, followed by a study where the effects of the force amplitude and frequency

variations in the mechanical input on the generated output are described. Characterization

experiments are carried out in terms of open circuit voltage (Voc), short circuit current (Isc)
and output charges (Qsc) on a 20 mm × 40 mm single layer device. The maximum power
is measured under different loads with various input mechanical forces and the maximum

surface energy density is determined.

135

7.1.1 Materials and Experimental Procedures

The device used in this work is a thin film flexible multilayer structural device with an 80
µm PPFE film sandwiched in between two 500 nm thin film metal electrodes. The device
is then encapsulated in between two 20 µm thick PI protective layers. The PPFE film is

the active material of the device that contributes to the conversion of mechanical energy

to electrical energy, and it consists of continuously distributed ellipsoid air voids, each with

two oppositely charged surfaces (see Figure 7.1a). Each giant engineered void forms a

permanent macro-scale dipole moment and constitutes a polarization field across the PPFE

film thickness. When an external mechanical load is applied that generates compression of

the film along the thickness direction, the size of the dipoles changes, generating a change

in the polarization field and a time-varying electric field. This time-varying electric field

(and the generated displacement current) can be applied to an external load by the metal

electrodes on each surface of the film. Given the capacitive nature of the material, the

accumulated free charges generate an open circuit voltage (Voc) across the film and can be

expressed as:

Voc(t) =

Q(t)g(t)


A

,

(7.1)

where Q is the accumulated charge at electrodes, g is the thickness of the PPFE film, 


is the dielectric constant of PPFE and A is the contact area of the device. This Voc(t) is

the generated electric field to compensate for the change in the polarization field during

mechanical pressing. The direct proportionality between Voc(t) and Q(t) indicates that both

quantities follow the same dynamic behavior and are in phase –since g(t) and Q(t) are both

synchronized with the applied force. Generated charges (i.e. Q(t)) can be collected and sent

to external circuits or loads. When the external load is a short circuit, the short circuit

current (Isc) is given by:

Isc(t) =

dQ(t)

dg

Uin,

(7.2)

where Uin is the compression velocity due to mechanical input. It is shown in Equation

136

Figure 7.1 (a) Working principle of ferroelectric nanogenerator. (b) Photography of a 20 mm
× 40 mm PPFE film. (c) Photography of final device with PI protective layer (20 mm × 40
mm). (d) Cross-section view SEM image of PPFE film with cellular structure. (e) Top-view
SEM image (backscattered electrons) of PPFE film, where darker regions are observed where
voids are present. (f) Photography of the experimental setup for characterizing the electric
output under various mechanical loads. (g) A close-up view of (f).

(7.1) and Equation (7.2) that, although the fundamental operation mechanism is different

from piezoelectric materials (piezoelectricity is at the atomic scale, while PPFE films are

based on macro-scale dipoles), it still exhibits a piezoelectric electromechanical response -

i.e. it generates a voltage signal of increasing magnitude upon compressive mechanical load

until maximum compression is achieved; followed by a voltage signal of decreasing magnitude
when released. Figure 7.1b and Figure 7.1c show photographs of a 20 mm × 40 mm PPFE

film and a single layer device of the same size with protective polyimide (PI) coatings and

connection wires, respectively. Figure 7.1d and e provide scanning electron microscopy

(SEM) images of PPFE films. Since the inorganic silica stress concentrators (particles in

Figure 7.1d) are randomly distributed, ellipsoid shape voids with very different sizes are

created upon the bidirectional stretching process. The top SEM image shown in Figure

7.1e shows darker regions where ellipsoids are present.

137

The following describes the experiments that were completed to characterize the electrical

signals and maximum power output generated by a single-layer device due to mechanical

input. As shown in Figure 7.1f, a stepper motor is used as a linear actuator, which pushes a
rubber piston towards a single layer device (surface area of 20 mm × 40 mm) mounted on the

back scaffold. A trailer is used to transfer the rotation of the motor to a linear displacement

of the piston and the linear mechanical load is realized by using four mechanical springs

connected in parallel. The applied force amplitude and its velocity are computer-controlled

by programming the duty cycle and number of pulses applied to the stepper motor. A force

sensor (A502, Tekscan, Inc) is placed behind the device to monitor the real time force applied

to the device (Figure 7.1g shows a close-up view for clarity).

7.1.2 Characterization of Electric Output

For the single-layer device used in this experiment, a linear external mechanical load is

applied periodically to the device, where each cycle contains a pressing stage, followed by

a releasing stage with a symmetric profile. The electrical outputs in terms of Voc, Isc, and

transferred charges Qsc –which in the ideal case would be equal to the accumulated charge

at the electrodes [156] are measured and presented in Figure 7.2. Figure 7.2a shows Voc

for a periodic force with the profile shown in Figure 7.3a corresponding to F1. For this

cyclic load with peak force of 78 N and frequency of 2 Hz (period of 0.5 s), a single layer

(cid:82) T

o Voc

device outputs a maximum Voc of around 56 V, given that the root mean square voltage
2(t)dt, thus VRM S is calculated to be 29 V.
VRM S can be expressed as V 2

RM S = 1
T

It should be noted how the Voc profile follows an increasing/decreasing profile that follows

the compression/release profile of the applied force (F1). This is the expected behavior for

linear coupling between mechanical domain and electrical domain of piezoelectric material

but is different from the one observed for the same type of device, or in other reports of

nanogenerators that operate under similar phenomena based on displacement current. The

rationale for these differences lies in the mismatch of the internal impedance of FENG and

138

the voltmeter for Voc measurement. When Voc is being measured, there should be no current

flowing through the device-voltmeter circuit loop. Voc should be proportional to the strain

(relative change in film thickness), which is also linearly related to the applied mechanical

stress. Therefore, profiles for Voc (see Figure 7.2a) and force F1 (Figure 7.3a) follow a

similar pattern. However, unlike Voc, Isc is originated from the displacement current, which

is proportional to the derivative of polarization charge (or accumulated charge Qsc, in this

case). Therefore, Isc shows a bipolar square wave profile as the derivative form of a triangular

wave. When a voltmeter with much lower internal resistance R, (note that the capacitance
of FENG is ∼ 17 - 30 pF · cm−2[169]) is connected for obtaining Voc, the measured voltage
V is determined by V = IR; where I is the non-zero current flowing through the device-

voltmeter loop. During each pressing and releasing time period T , the transferred charge

can be determined by taking the integral of Isc as Q(t) =(cid:82) T

0 | Isc(t) | dt, which is equal to
11.5 nC (see Figure 7.2b), which also follows the same profile as Voc and Equation (7.1).

However, Isc comes from the change in that charge (Q(t)) per unit change in thickness (g(t)),

and therefore presents a bi-polar profile for every Voc cycle.

Instruments with relatively

low internal resistance will dissipate the generated displacement current in their internal

resistance and display a voltage profile that follows the product of the displacement current

and the internal resistance. The profiles for Voc(t) and the applied force F1 become closer to

each other and more synchronized in time as this internal resistance increases[163]. In this
case, the device supplies a peak current Isc of 0.1 µA, which corresponds to a root mean

square current IRM S of 73 nA. Here, the same method of determining VRM S is used for

calculating IRM S by substituting Voc with Isc (see Figure 7.2c), with a cyclic profile that

crosses Isc = 0 nA at the time of peak voltage in Voc(t). To increase the output current,

the simplest way is to increase the capacitance of the device by increasing the area. This

can be easily achieved by folding a larger device multiple times into a smaller size or by

stacking the several single-layer devices into a multi-layer structure. Figure 7.2d shows the

relation between Isc output and stacking layers; where an increasing current peak is found

139

Figure 7.2 Electrical output for single layer device. (a) Experimental measurement of open
circuit voltage (Voc). (b) Transferred charge output (Qsc). (c) Experimental measurement
of short circuit current (Isc). (d) Isc for multiple-layered devices.

to be proportional to the number of layers.

To obtain optimal power delivery, it is necessary to look at both electric output pa-

rameters: voltage and current, produced by mechanical forces with different profiles. For

this characterization, linear forces with different amplitudes and velocities are introduced

(see Figure 7.3a) and the electromechanical responses due to various resistive loads are

measured. F1, F2, and F3 have the same pressing and releasing cycle but different force

amplitudes: A1 > A2 > A3; where Ai is the force amplitude of force Fi. On the other hand,

F4 and F5 have the same force amplitude as F1 but longer cycles: T5 > T4 > T1, where Ti

140

Figure 7.3 Electrical response of single-layer device for different mechanical input. (a) Forces
with different amplitudes and velocities used for electromechanical characterization.
(b)
Voltage and current output with various resistive loads under F1. (c) The maximum instan-
taneous power with various loads under different force inputs described in (a). (d) Average
power delivery from a single press and release cycle with various loads. (e) Output voltage
and current under F1 with a 600 MΩ load. (f) Output power under F1 with a 600 MΩ load.

is the duration of a single pressing/releasing cycle of force Fi. Since Voc(t) is proportional

to the compression distance and Isc(t) is proportional to the compression velocity, the force

with greater amplitude and shorter pressing/releasing cycle should deliver higher voltage

and current output, therefore higher power to the external loads.

This would correspond to F1 from the applied forces (see Figure 7.3a). Figure 7.3b

141

shows the voltage and current output under F1, for a wide range of load resistances. The

instantaneous peak power delivered to the load is also measured for all forces and plotted as

a function of load resistance as shown in Figure 7.3c. Table 7.1 summarizes the amplitude

and cycle of each force with related output instantaneous peak power. The maximum power

delivery is found to be at around 600 MΩ. It is noted that the power output is more sensitive

to force amplitude than to speed or frequency. Doubling the force amplitude produces a 4X

increase in power output while decreasing the cycle by a half produces a 2X increase in that

same parameter. This measurement is in agreement with theory, since increasing the force

amplitude has an effect on Voc(t) (force amplitude is directly proportional to g(t)) and Isc(t)

(force amplitude is directly proportional to the generated displacement current); while the

compression/releasing velocity only affects Isc(t) (see Equation (7.1) and Equation (7.2)).

Therefore, the device is more suitable for harvesting energy from environments involving

large, slow-motion mechanical energy sources, such as human footstep [170], ocean waves

[171], and wind blow [172, 173], etc. Figure 7.3d shows the average power output delivered

(cid:82) T
by each pressing and releasing cycle with various loads. The maximum average power Pave =
0 I(t) · V (t) dt is estimated to be around 0.902 µW with a 600 MΩ load, with a device
power density (Pv) of ∼ 14.09 Wm−3, for input force F1, which has a frequency of 2.13
Hz. The voltage and current output for this load are also plotted in Figure 7.3e, and the

1
T

instantaneous power as a function of time during a single cycle is shown in Figure 7.3f.

Table 7.1 Power delivery under different loads

Force: Fi

Amplitude: Ai(N )

Cycle: Ti(s)

Peak power: Pmax(µW )

F1
78
0.47
2.38

F2
33
0.47
0.56

F3
16
0.47
0.17

F4
78
0.89
1.28

F5
78
1.76
0.61

142

7.1.3 Energy Conversion Efficiency

This subsection provides a detailed calculation of the energy conversion efficiency. The

linear coupling between the mechanical domain and electrical domain considering the full

spring-mass-dashpot model can be expressed as the following equation [174]:

where δV , δF , δQ, and δg represent the variations in output voltage, input force amplitude,

output charges, and input compression velocity, respectively. Variable g is the thickness of

the PPFE film, 
 is the dielectric constant, A is the area, and k is the spring constant. By

using the Laplace transform, we obtain the expression for δQ and δg as:

(7.3)

(7.4)

(7.5)

(7.6)

(7.7)



δV

δF

 =







 ,

δQ

δg

g

A

Q

A

Q

A k

(cid:90)

δQ =

(cid:90)

δIdt =

δI
s

,

δg =

δUindt =

δUin

s

.

δF =

Q
s
A

δI +

k
s

δUin,

δg =

δF
k

− QδQ
k
A

.

and

Therefore, we have

and

The second term on the right side of Equation (7.7) represents the spring-softening effect

due to electrostatic forces generated by the accumulated charges. Considering Q = 45.5t nC
and 
 = 10 × 10−12F · m−1 [175], the second term becomes three orders smaller than the

first term; which simplifies Equation (7.7) to:

δF ≈ kδg,

(7.8)

which indicates a simple spring model operating in the linear region of the elastic material.

Therefore the energy conversion efficiency is defined as:

143

Figure 7.4 Comparison of energy output under different forces. (a) Energy output under
forces with same peak amplitude and different frequencies. (b) Energy output under forces
with the same frequency and different peak amplitudes.

(cid:82) V · Idt
2k [(cid:82) F(cid:48)dt]2 = 0.14%.

1

ηS =

Wout
Win

=

(7.9)

It is also necessary to discuss the energy output behavior under forces with different

amplitudes and frequencies. Since the output charges are proportional to the change in

thickness, the same force amplitude should result in the same energy output. On the other

hand, increasing compression velocity (or input mechanical frequency) results in higher out-

put current. Figure 7.4 validates this statement by showing the energy output from the

forces F1, F2, F3, F4, and F5 reported in previous subsections.

7.2 Power Management System

This section introduces a fully integrated power management circuit for energy harvesting

devices with ultra-high impedance; which is a major current bottleneck in nanogenerator

technologies. With either periodic or random mechanical force input, the circuit can deliver

a regulated direct current (DC) power. Finally, the complete system is characterized and

integrated into multiple real applications; which include charging a lithium battery; and

144

powering an LCD screen, thermometer, and humidity sensor.

7.2.1

Integrated Energy Harvesting System

The simplest energy harvesting system can be achieved by direct charging[176] through a

bridge rectifying diode circuit. However, the unregulated voltage output has been proven

to deliver very low efficiencies and will significantly reduce the life-span of a rechargeable

battery or electric device which often requires a constant DC input. To effectively harvest

the energy from ambient energy sources for consumer electronics, a comprehensive power

management system is necessary [177, 178]. To meet the DC power supply requirement of

most electronic devices, the AC electric output from piezoelectric material is first converted

to DC signal by using a rectifying bridge [179, 180]. Then, a DC-DC buck converter is often

used for impedance adaption and voltage regulation [181]. In this work, the comprehensive

energy harvesting system uses an energy harvesting module based on a nanopower energy

harvesting power supply (LTC3588-1, Linear Technology Corp.) to harvest the mechanical

energy as shown in Figure 7.5a. The FENG generates random electric pulses that are

managed by LTC3588-1 as the first stage, which produces a DC output. As long as a

continuous mechanical energy source is present, the harvested and regulated energy can be

used to power electronic devices or to charge a rechargeable battery (CBC012, a cutoff voltage

of 3 V) for energy storage. Here, we present a method for powering an electronic device,

while charging a backup battery by implementing an integrated power management chip

(CBC3112) as a second stage. CBC3112 is able to supply a constant DC voltage, typically

of 3.3 V, which can be connected to the electronic device to be powered. Meanwhile, it

sends any excessive energy to an internal secondary battery (cutoff voltage of 2.75 V) for

energy storage. As shown in Figure 7.5a, VDD is internally applied to a charge pump

VCHG, which contains a flying capacitor CF LY in its voltage doubler circuit for charging

the internal integrated backup battery VBAT . When EN terminal asserts high (i.e. when

CBC3112 senses a voltage generated by the device), the charge pump is activated and VBAT

145

Figure 7.5 Energy harvesting module. (a) A comprehensive energy harvesting system, C1 =
1 µF , C2 = 4.7 µF , COU T = 47 µF , L1 = 22 µH and CF LY = 0.1 µF . (b) Direct charge of
capacitors with different capacitances. (c) Voltage regulation of nanopower energy harvesting
power supply LTC3588-1. (d) Charging profile of rechargeable solid state battery CBC012.
(e) Discharging profile of rechargeable solid state battery CBC012. (f) Voltage regulation of
integrated power management chip CBC3112. (g) Discharging profile of integrated energy
storage unit in CBC3112.

is being charged by VDD. The output voltage VOU T can either be supplied from VDD or

VBAT depending on the switchover voltage threshold determined by VM ODE.

Figure 7.5b shows unregulated direct charging profiles for capacitors with different ca-

146

pacitances, where the voltage across the capacitor continuously increases with the charging

operation. The voltage output regulation realized by LTC3588-1 is shown in Figure 7.5c,

where the output voltage is regulated at a constant voltage of 3.6 V. After the system enters

the regulation mode, the excessive energy is stored in CST ORAGE with increasing voltage

measured across the capacitor. By further comparing the voltage drop at CST ORAGE and in-

crease in COU T , the energy transfer efficiency of this energy harvesting module is estimated

to be 38.5%. The output DC power can be directly used for powering electronic devices

(load) or charging a battery (energy storage). Figure 7.5d shows the charging profile of a

rechargeable solid-state chip battery CBC012. The battery is being charged at a constant

voltage of 3.6 V, and is partially-charged after 15 min of a mechanical force of amplitude

78 N and frequency 4.26 Hz applied to the device. The discharging profile is presented in

Figure 7.5e to demonstrate the energy stored in the battery. When a second stage power

management chip CBC3112 is connected to the output terminal of LTC3588-1, the combined

system is able to simultaneously output a constant DC power and transfer the excessive en-

ergy from CST ORAGE to an embedded integrated battery. Figure 7.5f shows the input and

output voltage of CBC3112 as a second stage. Since CBC3112 sends part of the energy to

the internal battery as energy storage, fluctuations are observed in the voltage, which is not

observed when charging battery chip CBC012 as shown in Figure 7.5d. Figure 7.5g shows

the discharging profile of the internal battery. More details on the operation of the energy

harvesting module are found in the next subsection.

7.2.2 Operation of Energy Harvesting Module

This subsection provides a brief introduction of the operation mechanism of the energy

harvesting module and the energy storage system. The complete two-stage energy harvesting

system shown in Figure 7.5a contains a first stage energy management module LTC3588-1

and a second stage integrated energy chip CBC3112. The LTC3588-1 chip includes a full-

wave rectify bridge in its first stage which converts the AC input voltage from PZ1 and

147

Figure 7.6 Energy harvesting system. (a) Schematic diagram of energy harvesting through
direct charge. (b) Schematic diagram of energy harvesting through LTC3588-1 to power
electronic device. (c) Schematic diagram of energy harvesting through LTC3588-1 to charge
CBC012 rechargeable chip battery.

PZ2 to a DC voltage. Two output voltage selectors D0 and D1 are used to program the

output voltage VOU T by assigning different combinations of high and low voltages. The

harvested energy is first stored in an input capacitor CST ORAGE and transferred to the

output capacitor COU T through a buck converter. Two bypass capacitors C1 and C2 are

148

connected to terminals VIN 2 and CAP as energy reservoirs to drive the buck switches. When

the voltage across Cstorage is above the regulation point of around 4.5 V, the buck converter

is enabled, and the stored energy is delivered to COU T through an inductor. To minimize

the energy loss in the energy transfer process, the buck converter first ramps the inductor

current up to 260 mA through an internal P-MOS switch and then ramps it down to 0 mA

through an N-MOS switch. When the voltage across COU T reaches the setpoint determined

by D0 and D1, the system is in a regulation mode and the buck converter is forced into

a sleep state with the ultra-low quiescent current. In this case, the harvested charges are

continuously accumulated in the CST ORAGE and the voltage across CST ORAGE increases

until it reaches the limit.

The second stage CBC3112 chip is able to provide a constant DC output at 3.3 V while
charging the internal backup Lithium-ion battery with the excessive energy. A 0.1 µF flying

capacitor CF LY is used in the voltage doubler circuit for the charge pump. With the EN

pin is asserted high, the charge pump is enabled and the internal energy storage unit is

being charged from the power supply (VDD) through the charge pump. VOU T can either be

supplied from VDD or internal backup battery VBAT . Figure 7.6 shows designs of different

energy harvesting systems. Figure 7.6a shows the schematic circuit for direct charging,

where the AC output signal is converted into a DC signal by a rectifying bridge. The

unregulated output pulses cannot be directly supplied to an electronic device or battery

and can only be stored in a capacitor. This configuration is also considered as the first

stage AC-DC converter in an energy harvesting module. To obtain a regulated constant

DC voltage, an integrated system with a buck converter or buck-boost converter is required.

Figure 7.6b shows the energy harvesting system by only using the first stage LTC3588-1

energy management module. This configuration is able to provide a constant DC output

for powering the electronic devices or charging a battery by the regulation of the energy

output from Cstorage. Even though the system is able to harvest and store the energy, the

long-time energy storage is still limited by the leakage current of the capacitor. Thus, as

149

Figure 7.7 Energy harvesting demonstration of powering electronic devices and charging a
battery. (a) Powering LCD screen by combing a two-stage energy harvesting system. (b)
Charging rechargeable solid-state battery CBC012, the stored energy is used for powering
three blue LED lights. (c) Powering humidity sensor by a one-stage energy harvesting system.
(d) Powering temperature sensor by a one-stage energy harvesting system. (e) Powering LCD
screen by a one-stage energy harvesting system.

shown in Figure 7.6c, a rechargeable lithium-ion chip battery is connected to the output

terminal of LTC3588-1, which can be used for energy storage.

7.2.3 Demonstration of Powering Commercial Electronics

By utilizing ambient mechanical energy, electronic devices can be powered solely by the

energy harvesting modules like the ones described earlier. Figure 7.7a shows the demon-

stration of powering a commercial 3V LCD screen by combining an 8-layer FENG device

150

with a two-stage energy harvesting system. This system is capable of delivering a constant

DC power while storing the excessive energy to an integrated chip battery. During the nor-

mal operation, the word ”FENG” is displayed on the screen, while storing the energy shown

in Figure 7.5g. Figure 7.7b shows the implementation of the energy harvesting system

(one-stage) for the application of charging a rechargeable solid-state battery. The charged

battery is used to power three LED lights. Figure 7.7c and Figure 7.7d demonstrate uti-

lizing harvested energy to power commercial 1.8 V humidity sensor and temperature sensor,

respectively. The same LCD screen which is shown in Figure 7.7a can also be self-powered

by this one-stage energy harvesting module as shown in Figure 7.7e.

7.3 Summary

In summary, this chapter shows a comprehensive approach that describes the use of PPFE

films as nanogenerators and their integration into systems that can convert mechanical energy

to electrical energy for either energy storage or powering of electronic devices. The generated

electric output and its dynamic behavior is characterized in terms of open circuit voltage,

short circuit current, transferred charge, the efficiency of the complete system and delivered

power. The output current and voltage are found to be related to the input mechanical loads

and velocities. Various resistive loads have been used to find the maximum power output,
which is around 0.902 µW under a linear F1 with 600 MΩ. Therefore the energy conversion

efficiency is calculated to be 0.14% for the performed experiment. To effectively harvest

the energy from ambient mechanical sources, a comprehensive energy harvesting module

with a corresponding power management circuitry has been proposed; which can be used for

powering electronic devices, charging a solid-state chip battery, or both.

151

CHAPTER 8

SUMMARY

8.1 Summary of Contributions

In this work, VO2 thin films are combined with polypropylene ferroelectret films to develop

self-powered tunable cantilever and bridge MEMS resonator devices. The phase change

across the VO2 thin film is responsible for the frequency tuning capability, while the piezo-
electric properties of the PPFE film (with a strong piezoelectric coefficient of ∼ 300 pC/N)

enables self-powering. The analysis of the film residual thermal stress is performed in order

to explain the different buckling orientations and amplitudes in bridge structures. FEM

simulations are carried out for the first mode natural resonant frequencies estimation, taking

into consideration the residual thermal stress. Bridge and cantilever resonators with various

aspect ratios are used to study the influence of VO2 thin coatings on resonant frequency

shifts. It is found that the cantilever structure presents a smaller relative frequency change
(∼ 7%), dominated by geometric modifications during actuation, and the change is inde-

pendent of the beam length. On the other hand, due to a large residual axial stress, bridge

resonators exhibit a structure-dependent relative frequency shift with a significantly larger

tuning range of up to 37%. The resonant frequency tuning was demonstrated on three bridge

resonators with different buckling states. Peltier and Joule heating are used as actuation

methods, and the results are compared. A bi-directional tuning behavior is observed in the

Peltier heating method for all three bridges while the same monotonic change in frequency

is shown when Joule heating is used. This phenomenon is attributed to a transition in the

boundary condition, which only occurs when substrate heating is used. Besides the studies

on frequency tunability, resonant frequency programmability is also demonstrated in both

structures. Here, FENG is introduced as a transducer to provide the programming current

152

pulse.

In order to effectively program a frequency state, the device power consumption

and time constant are determined first by using the PWM method. Experimental results

reveal that sending a short current pulse with a much higher amplitude could reduce the
power consumption from mW to µW range. This demonstrates the potential application

of integrated VO2-based resonators and FENG devices into HITS systems. A prototype of

VO2-based MEMS bandpass filter is demonstrated by exciting and measuring two identical

on-chip resonators. The bandwidth can be extended to 2.62X by using two bridges or 2.39X

by one pair of cantilevers.

Further studies were designed to demonstrate self-powering, sensing, and energy harvest-

ing capabilities of FENG. The electromechanical response is first characterized by applying

a periodic external mechanical input. Electric output in terms of open circuit voltage, short

circuit current, and transfer charges are analyzed; and the electromechanical coupling is

described. The discrepancies in voltage measurements caused by different instruments’ in-

ternal resistance are discussed in detail and a lumped parameter model has been proposed

to explain the mismatch at the device-machine interface. The lumped model is validated

with experimental data for both dynamic and static electromechanical responses. A de-

sign platform for implementing FENG-based devices into self-powered tactile systems and

a human-controlled micro-robotic controller has been demonstrated. Furthermore, based

on the excellent flexibility of PPFE, a FENG-based bending sensor is also developed using

the large transverse piezoelectric effect. The electromechanical responses are well charac-

terized and predicted by the constitutive equations. Extra attention has been paid to the

evaluation methods where the average value of voltage reveals a correlation between both

the bending velocity and the bending curvature while the peak value is only related to the

velocity. The robustness of the device is also demonstrated in terms of thermal stability,

humidity resistance, and mechanical repeatability. In the last chapter, a complete energy

harvesting system is developed by integrating FENG with a power management circuit. The

system is capable of effectively converting random ambient mechanical energy to regulated

153

DC electrical power with an efficiency of ∼ 38%. The developed technology is able to power

commercially available electronic devices or charge a lithium-ion battery.

8.2 List of Problems Solved in This Thesis

This work addresses the following:

1. Designed and fabricated VO2-based MEMS resonators with fully integrated metal

heaters. Different structures including clamped-clamped and clamped-free beams have

been developed and the first mode resonant frequencies are estimated by FEM simu-

lation.

2. Developed ferroelectret nanogenerators based on flexible polypropylene ferroelectret

polymer films with a high d33 value of ∼ 300 pC/N.

3. Performed Characterizations of VO2-based tunable MEMS resonators, demonstrated

resonant frequency tunability as high as 37.2%, studied the influence of VO2 coatings

on different structures with various aspect ratios.

4. Studied the buckling effect of VO2-based bridge resonators, analyzed the effect of

buckling directions and amplitudes on the resonant frequency tunability.

5. Studied the influence of applying different electro-thermal actuation methods on pre-

buckled bridge resonators. Explained the bi-directional tunability observed in the

substrate heating.

6. Studied the power consumption of programming resonant frequency status in VO2-

-based MEMS resonators, developed a new type of HITS by combining VO2-based

resonators with FENG.

154

7. Proposed the prototype of VO2-based tunable MEMS bandpass filters with off-chip
connection configuration, demonstrated ∼ 7.3% tunability of the central frequency
and ∼ 262% tunability of the bandwidth.

8. Designed, fabricated FENG-based self-powered flexible sensors with a pixelated con-

figuration, the sensor is able to map the force distribution of an impact.

9. Studied the influence of measuring instruments on the electric output of FENG, mod-

eled the material as a second-order system and explained the measuring discrepancies

with different instruments.

10. Demonstrated FENG as bending strain gauges, characterized electric output under dif-

ferent bending conditions, validated the device robustness in terms of thermal stability,

humidity resistance and mechanical repeatability.

11. Designed and developed a power management system for converting random AC elec-

tric current from nanogenerator to regulated DC voltage, the system has an energy
delivery efficiency of ∼ 38% and is able to effectively charge a rechargeable Lithium-

ion battery.

155

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