OPTIMIZED GEOMETRIC DESIGN OF PARALLELIZED ELECTRODES IN A
ELECTROSTATIC ENERGY HARVESTER
Y. Hamate1∗ , E. Schaler2 , H. Okamoto3 , H. Kuwano1
1 Department of Nanomechanics, Tohoku University, Sendai, 980-8579 JAPAN
2 Deparment of Mechanical Engineering, University of Maryland, USA
3 Department of Electronics and Information Systems, Akita Prefectural University, JAPAN
∗ Presenting Author: hamate@nanosys.mech.tohoku.ac.jp
Abstract: This paper presents design optimization for increasing power output of in-plane vibrating electrostatic
energy harvesters. With a fixed gap length between charged stripes and counter electrodes, g, an optimal degree of
parallelization for a unit harvester exists. With a freestanding electret configuration, the maximum performance can
be obtained with the optimum ratio of L/g = 5.84, where L is the periodicity of parallelized electret stripes.
Keywords: Electret, Design optimization, vibration harvester
INTRODUCTION
There has been a growing interest in environmental
energy harvesting, where low density energy sources,
such as light, vibration, thermal gradient, etc., are utilized to generate electricity, especially in the field of socalled sensor network societies [1]. In sensor networks,
a large quantity of small sensor nodes are distributed,
and often communicate with each other, to enhance the
quality of the information network. A key example is a
health monitoring system for large structures, including
buildings and bridges. In such a system, powering each
node would be problematic, considering its distributed
nature. Using batteries is not practical, since replacing
or recharging batteries in each of the distributed sensor
nodes is unacceptable due to both economical and environmental concerns. Thus, self-powering sensor nodes
is a key technology to achieve a sensor network system.
Vibrations are a ubiquitously available energy source.
While numerous research approaches have been dedicated to this area, electrostatic harvesters have some advantages in micro-scale applications, mainly because of
greater flexibility via the ability to design mechanical
and electrical features separately [2].
Electrets, which can hold electric charge quasi-
permanently, are often used in electrostatic energy harvesters. Figure 1 shows the schematic of an electretbased vibration energy harvester. The electret generates
an electric field, which induces charges in the surrounding electrodes. Introducing relative movement between
the electret and counter-electrodes by utilizing external
vibrations causes the amounts of induced charge in the
electrodes to change. This charge variation can be converted into electricity by connecting the harvester electrodes to an external circuit with loads. The relative
displacement can be either perpendicular or parallel to
the surface of the electret, which corresponds to capacitance changes due to gap length or overlapping surface
area, respectively. The latter case is further explained in
Fig. 2, and often called in-plane type electret harvesters.
There are several strategies to increase the output
power of electret-based vibration energy harvesters. The
basic idea is simple: increase the induced charges in the
work electrodes. The simplest method is to reduce the
gap length between electret and counter electrodes [3].
Fig. 2: Operation principles of an in-plane type electrostatic vibration energy harvester.
Fig. 1: Schematic of an electret-based vibration energy
harvester.
Fig. 3: Schematic of a parallelized in-plane energy harvester.
Fig. 4: Experimental setup of a macro-model to verify
the analytical solutions.
(a)
(b)
Fig. 5: Electrodes configurations, (a) upper electrodes
simulating freestanding electret stripes, and (b) bottom
work electrodes connected to external circuit for measuring output power. A piezoelectric actuator was used
to apply external vibration.
0.7
Normalized output power (nA2mm4)
In the case of in-plane type harvesters, the use of a freestanding electret film, in which the electret film is removed from its backing plate so that the electric field
generated by the electret is efficiently used to induce
countercharges in a work electrode rather than in a backing plate, is reported to also enhance output power [4].
In this report, we use this freestanding configuration.
The other approach in in-plane harvesters is parallelization. In MEMS applications, size (volume or mass)
is always a consideration, so output power is usually
evaluated in power density. In-plane harvesters exploit
capacitance change due to variation of overlapping area.
Thus, if the effective electret area is too large compared
to the area change driven by external vibrations, the vast
majority of electret charge does not contribute to countercharge induction. Parallelizing an electret/electrodes
unit, as shown in Fig. 3, is often used to increase output
power density by effectively utilizing the available area.
However, too much parallelization of electret stripes, in
other words a striping period L that is too small compared to g, results in smoothing out the electric field
near the counter electrodes. Consequently, given the gap
length, there exists an optimum degree of paralleliztion,
or optimum L/g. Similar optimization research has been
reported [5], but it dealt with the optimization of harvesters with a unit of one work electrode for one charged
stripe, while this study addresses the optimized geometry of a unit of two work electrodes for one charged
stripe.
Theoretical analysis predicts that the optimum ratio of
L/g is 5.84 for a freestanding configuration. The details
of the theoretical calculation will be reported elsewhere.
0.6
0.5
0.4
0.3
0.2
0.1
0
0
EXPERIMENTAL VERIFICATION
A macro model was developed to verify the theoretically obtained optimum ratio, as shown in Fig. 4.
Since experiments using electret may involve uncertainties in reproducibility, we use voltage-biased metallic
electrodes backed by an glass epoxy substrate to simulate a freestanding electret film. Figure 5 shows (a) upper electrodes simulating electret stripes, and (b) work
electrodes. L is fixed at 10 mm throughout the experiments, and L/g is varied by changing g. Thus, output
needs to be evaluated in normalized values: a normal-
2
4
6
8
10
12
14
L/g
Fig. 6: Normalized output power for different L/g ratio.
ized current in Ig2 , and a normalized power in I 2 g4 . The
bottom work electrodes were oscillated by a piezoelectric actuator at its resonat frequency of 647 Hz, with an
amplitude of 3 µ m. Only the middle two out of four
output electrodes were connected to an external circuit
to ensure that the periodic boundary condition was satisfied.
Figure 6 shows measured normalized output as a
function of L/g. The dotted line indicates a theoretical prediction. The measured value peaks at L/g = 7.14,
which is 20% larger than the theoretical value. Reasons
for the discrepancy are twofold. In the large g region,
which corresponds to a small L/g, the actuall output
was very small, and a deteriorated signal-to-noise ratio
ended up with larger error bars in Fig. 6. The other reason is that upper electret-simulated electrodes and bottom electrodes were not perfectly in parallel. This resulted in both smaller g regions and larger g regions than
the prescribed value. Since the normalized output power
is proportional to g4 , output increases due to a smaller g
region are more dominant than output decreases due to
a larger g region.
Fig. 7: Design of a micromachined device.
Fig. 8: Process chart for electret wafer fabrication.
MICRO MODEL PROTOTYPE
Prototypes of a micromachined device were also fabricated, and consist of two parallel wafers: an electrode
wafer containing patterned Al and an electret wafer with
patterened CYTOP, as shown in Fig. 7. Electrode wafers
were fabricated via deposition of Al (∼225nm) onto
glass wafers and patterning of the Al using photolithography, with wet-etching (NMD-3) of the Al / exposed
photoresist (OFPR-800). The fabrication process for the
CYTOP wafers is depicted in Fig. 8. First, CYTOP was
spin-coated on silicon wafers up to ∼ 8µ m. Then, patterning of the CYTOP was performed using photolithography (development of Al masks) / plasma-etching (O2 )
of the CYTOP. Finally, positive ions were implanted in
the CYTOP using corona discharge to complete the electret wafer fabrication.
The device size was 20 mm × 20 mm. We examined
four different configurations for L as summarized in Table 1.
The device was oscillated with a shaker, as shown in
Fig. 9. The external vibration applied was sinusoidal
wave of 2 mm peak-to-peak at 75 Hz. Output power was
measured on a 1 MΩ external load. Red lines in Fig. 10
show measured output for three different gap lengths,
0.2, 0.3, and 0.6 mm. In contrast to the macro model
experiments shown in Fig. 6, L/g values were varied by
changing L as shown in Table 1.
In this case, the measured power does not peak at
the predicted value of L/g of 5.84, and rather shows
monotonous increase with increasing L/g. This result
can be attributed to non-uniform surface potential for
different wafers. Table 1 shows surface potentials for
each wafer with different L, measured at 0.5 mm above
the surface. Although, available surface area for charge
implantation is same for all four patterned wafers, the
measured surface potential decreased with decreasing L.
The reason for this is not clear, though increasing corners and side edges on striped electret surfaces is likely
to reduce implanted charges when corona discharge conditions are the same. Genda et.al. [6] reported that
micropatterned electrets show lower surface potential
and lower charge stability with smaller striped patterns.
They developed a new technique using contact elec-
Fig. 9: Experimental setup of a micro-scale device.
Table 1: Electret surface potential measured at 0.5 mm
above substrates.
L (mm)
Surface Potential (V) % of Max.
Potential
0.5
7.29
2.49
1.0
9.27
3.16
2.0
20.6
7.04
4.0
65.7
22.4
No Pattern
293
100
0.003
average power
normalized power
Power (nW)
0.4
g = 0.2 mm
0.3
0.2
0.3 mm
0.1
0.6 mm
0.002
0.001
Normalized power (nW/V2)
0.5
0
0
2
4
6
8
10 12 14 16 18 20
L/g
Fig. 10: Generated power against L/g for three different
gap lengths. Red lines are output power, and blue lines
are normalized power.
trification to implant charges into micropatterned electrets [6]. Other approaches for charge implantation into
micromachined electret, like separating the electret from
a micro striped structure, reported by Sterken et.al. [7],
would also address this problem.
To eleminate the effect of non-uniform surface potential, we calculated the normalized output power, and
plotted it in blue lines in Fig. 10. The normalized power
is defined as the measured power divided by square of
surface potential, because the output power is proportional to the square of current which is then proportional
to induced charge, and hence surface potential. The normalized power shows a clear peak at L/g = 5 with the g
= 0.2 mm case. Other cases shows similar trends despite
lack of data points near the predicted peak.
We verified the theoretically obtained optimum L/g
ratio of 5.84, by both macro and micro scale experiments. However, Fig. 10 still shows importance of reducing g to increase output. Thus, as a design strategy for in-plane type electret energy harvesters, one may
first want to design g as small as possible, then set optimized L as L = 5.84 g. Note that one should be aware
of the difficulties in implanting charges into finely patterned electret, which could spoil the above mentioned
optimized configurations.
CONCLUSION
We present an optimized geometry for electret based
in-plane vibration harvesters. The theoretical calculation predicts the optimum value of L/g = 5.84 for a freestanding electret configuration. A series of experiments
using both macro and micro scale devices verified the
theoretical prediction. It is also shown that, however, L
optimization is valid when other parameters, such as g
and surface potential, are fixed. Thus, as a design strategy, L/g optimization should be considered in conjunction with other design optimizations.
ACKNOWLEDGEMENT
This work was supported by a grant (No. 18GS0203)
funded by the Ministry of Education, Culture, Sports,
Science and Technology, Japan.
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