A MEMS Electrostatic Vibration-to-Electricity Energy Converter
Yu-Shan Chu, Chiung-Ting Kuo and Yi Chiu
Department of Electrical and Control Engineering, National Chiao Tung University
1001 Ta Hsueh Road, Hsinchu, Taiwan, R.O.C.
Tel: +886-3-573-1838, Fax: +886-3-571-5998, Email: yichiu@mail.nctu.edu.tw
Abstract
This paper presents an electrostatic vibration-to-electric energy converter based on the micro-electro-mechanical systems
(MEMS). For the 3.3 V supply voltage and 1cm2 chip area constraints, optimal design parameters were found from theoretical
calculation and Simulink simulation. In the current design, the calculated output power is 32.4 µW/cm2. The device was
fabricated in a silicon-on-insulator (SOI) wafer with a 200-µm-thick device layer. Measurements are being conducted.
Keywords: energy conversion, energy scavenging, electrostatic, variable capacitor, SOI wafer
1.
INTRODUCTION
y
Cmin
Due to the advance of CMOS VLSI technology, the power
consumption of electronic devices has been reduced
considerably. This technology advance can be used in
applications such as wireless sensor networks [1] or personal
health monitoring [2], where remote or independent power
supply is critical, to build more compact or longer-life-time
modules. In particular, energy scavenging from ambient
natural sources, such as vibration [3], radioisotope [4] and
ambient heat [5], is attracting many recent interests. Among
various approaches, electrostatic vibration-to-electric energy
conversion using the micro-electro-mechanical systems
(MEMS) technology is chosen in this study due to its
compatibility to IC processes and the ubiquity of the energy
source in nature.
displacement due
to vibration
z
y
Cmax
displacement due
to vibration
z
Figure 1 Variable capacitor schematic
2. DESIGN
SW1
A variable capacitor formed by an in-plane gap closing
comb structure is the main component in the electrostatic
energy converter [3,6], as shown in Fig. 1. The energy stored
in the capacitor is increased when the capacitance is changed
from Cmin to Cmax due to the external vibration. Fig. 2
shows a circuit that can be used to extract the converted
energy. The variable capacitor Cv is charged by an external
voltage source Vin through the switch SW1 when the Cv is at
its maximum Cmax. When Cv is charged to Vin, SW1 is open
and then the capacitance is changed form Cmax to Cmin due to
the electrode displacement caused by vibration. In this
process, the charge Q on the capacitor remains constant
(SW1 and SW2 both open). Therefore, the terminal voltage
on the capacitor is increased and the vibration energy is
converted to the energy stored in the capacitor. When the
capacitance reaches Cmin (Vmax), SW2 is closed and the
charge is transferred to a storage capacitor or load. If
complete discharge is assumed, the net output energy per
cycle can be expressed as
Vin
Cv
SW2
Cstor
Figure 2 Operation of the electrostatic energy converter
C
1
E= Vin 2 (Cmax -Cmin )( max )
2
Cmin
1
= Vmax Vin (Cmax -Cmin )
2
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(1)
The energy output is proportional to the difference or ratio
of the variable capacitance. The output power is equal to
the energy output multiplied by the vibration frequency.
Therefore, the characteristics of the vibration source must be
known in order to estimate the generated power. The
vibration spectrum of several household appliances was
measured. A typical vibration source has a peak acceleration
of about 2.25 m/s2 at about 120 Hz (Fig. 3). These values
will be used in the following static and dynamic analysis of
the converter to find out the optimal device design and
output power.
Figure 4 Output power and number of finger gaps vs. initial
finger gap
analyzed so that the maximum allowable displacement can
be achieved by the target vibration source. The
electro-mechanical dynamics of the conversion process can
be modeled as a spring-damper-mass system as shown in Fig.
5. The dynamic equation is
&& e (z)+bm (z,z)+kz=
&
&&
mz+b
- my
(2)
where b m (z,z)
& is the equivalent mechanical damping
representing energy loss caused mainly by the squeezed film
effect, and be(z) is the equivalent electrical damping
representing the energy converted into electricity. Notice
that the mechanical damping force, b m (z,z),
& is a function of
both the displacement z of the shuttle mass and its velocity
z& [3]. The b e (z) term is the electrostaitc force induced on
Figure 3 Typical vibration spectrum of a household
appliance
2.1 Static Analysis
In the in-plane gap closing variable capacitor, the number of
finger gaps should be maximized to obtain large capacitance
change. However, for limited chip area, the increased
number of gaps will result in the decrease of initial finger
distance and hence the capacitance variation and output
power. Therefore, an optimal number of fingers, and thus
the corresponding initial finger gaps, exists to produce
maximum output power for the limited chip dimension.
From Eq. (1) and with a typical input voltage source of 3.3
V, vibration frequency of 120 Hz, and chip area size of 1
cm2, Fig. 4 shows the calculated power output and number
of finger gaps as a function of the initial gap distance,
assuming the finger thickness, length, and width are 200 µm,
1200 µm and 10 µm, repsectively. The minimum gap
distance is assumed to be 0.5 µm, which is controled by
mechanical stops. The dimension of the fingers are
choosen based on the available deep etching process
capability. It can be seen that the initial finger gap has an
optimal value of 25 µm for a max power output of 32.4 µW.
the MEMS structure.
k
bm
z(t)
be
y(t)
Figure 5 Conversion dynamic model
A Simulink model (Fig. 6) was built to simulate the system
behavior based on Fig. 2 and Eq. (2). The charge
redistribution box calculates the charge transfer process
when the capacitance reaches Cmin and SW2 is open. This
process represents the energy output. Due to the limited
shuttle mass that can be achieved in a MEMS process, and
external attached mass m was considered to increase the
displacement of the variable capacitor and the energy
2.2 Dynamic analysis
After the dimension of the variable capacitor was
determined, the dynamics of the micro structure was
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conversion efficiency. Fig. 7 shows the maximum
displacement of the movable plates with various mass
attached. The corresponding spring constant k which
generates the maximum displacement zmax is also showed.
With a larger mass, it is easier to reach the maximum
displacement; however, under the size constraint of 1cm3,
mass more than 19 gram is impractical even if tungsten is
used. Actually, mass larger than 7 gram is hardly available.
Thus, from the calculation shown in Fig. 7, the optimal
design is obtained and listed in Table 1 with m = 5.7 gram
and k = 2.8 kN/m. The output power for a 3.3 V input is
32.34 µW, which is higher than the current results in
literatures.
Table 1 Optimal design of the first generation device
Description
Width of shuttle mass
Length of shuttle mass
Length of finger
Width of finger
Shuttle mass
Initial finger gap
Spring constant
Output power
W
L
Lf
Wf
m
D
k
Pout
a)
c)
b)
d)
Figure 6 Dynamic simulation model
Si
Optimal value
10 mm
8 mm
1200 µm
10 µm
5.7 gram
25 µm
2.8 kN/m
32.34 µW
Al
Figure 8 Fabrication process: (a) define structure by Deep
RIE, (b) etch oxide by HF solution, and (c) apply Al by
thermal evaporation, (e) attach external mass
resonant frequency to match the vibration source and
improve the conversion efficiency.
The fabricated device is shown in Fig. 9. The width of the
finger is reduced to 6.8 µm due to the tolerance in
photolithography and RIE processes. These deviations will
affect the resonant frequency and other characteristics of the
converter.
a)
Figure 7 Max displacement zmax and spring constant k for
various attached mass m
3.
FABRICATION
A SOI wafer with a 200-µm-thick device layer was used for
large capacitance change. The oxide layer and the handle
wafer are 2 µm and 500 µm thick, respectively. The variable
capacitor structure was first defined by deep reactive ion
etching (Deep RIE) (Fig. 8(a)). After the sacrificial oxide
layer was removed using the HF solution (Fig. 8(b)),
aluminum was evaporated for contact (Fig. 8(c)). A steel
sphere was then attached to the central plate to adjust the
Center
plate
Mechanical
stop
Variable
capacitor
Spring
Figure 9 Fabricated device: (a) SEM top view
b)
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4.2 Electrical measurement
The electrical measurement was conducted using an
INSTEK-LCR-816 LCR meter and a HP-4192A impedance
analyzer. The measured capacitance without vibration was
about 500 ~ 600 pF, while the calculated capacitance Cmin is
about 50pf. A major contribution of the large measured
capacitance is the parasitic capacitance Cpar between the
center plate and the substrate beneath it.
Width ~
6.8µm
c)
Besides the parasitic capacitance, there is also a parallel
parasitic conductance. The measured conductance varies
from die to die with an average resistance of 2.5 kΩ. It is
suspected to be caused by the residual particles left in the
device after the release step. The presence of the parasitic
capacitance and conductance has hindered the measurement
of output power. New devices are being fabricated with the
substrate underneath the combs removed to prevent residual
particles.
Figure 9 Fabricated device (cont’d): (b) cross section of
comb fingers, and (c) overview of the fabricated converter
with the attached mass
5. CONCLUSION
The design and analysis of a micro vibration-to- electricity
converter were accomplished. The device was fabricated in a
SOI wafer. The reduced feature size of the fabricated device
resulted in the decrease of spring constants. Mechanical and
electrical measurement of the fabricated device was
conducted. Impedance measurements showed an unwanted
parasitic conductance which resulted in the failure of output
power measurement. Improvement of the design and
fabrication processes is being conducted.
4. MEASUREMENT
4.1 Mechanical measurement
The displacement of the device without the attached mass
was measured using a PROWAVE JZK-1 shaker. The
measured response is shown in Fig. 10. Since the mass was
not attached, the vibration acceleration was increased to 40
m/s2 for easy observation. The maximum displacement is
about 10 µm at 800Hz, and the quality factor Q= ω0 ∆ω is
This project is supported in part by the National Science
Council, Taiwan, ROC, under the Grant No. NSC
93-2215-E-009-066.
about 9.6, where ω0 is the resonant frequency and ∆ω is
the resonant bandwidth shown in Fig. 10. The mass of the
center plate is approximately 0.038 gram, thus the spring
constant can be calculated as k=ω 2 m=960N/m . The
measured spring constant is different from the calculation.
The major factor of the discrepancy is the feature size shrink
in the fabrication process, as shown in Fig 9.
REFERENCES
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(use of a resonant phenomenon)”, JSME International
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[3] S. Roundy, et al., “Micro-electrostatic vibration-toelectricity converters,” Proc. IMECE 39309, 2002.
[4] R. Duggirala, et al., “Radioisotope micropower generator
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PowerMEMS, pp. 133-136, 2004.
[5] T. Douseki, et al., “A batteryless wireless system uses
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[6] C.B. William, et al., “Analysis of a micro-electric
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pp. 8-11, 1996.
Figure 10 Frequency response of the device
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