INFLUENCE OF PARASITIC CAPACITANCE ON OUTPUT VOLTAGE OF
SERIES-CONNECTED PZT ELEMENTS
1
K. Kanda1*, Y. Iga2, T. Fujita1,2, K. Higuchi1, and K. Maenaka1,2
Maenaka Human-Sensing Fusion Project, Japan Science and Technology Agency, Himeji, Japan
2
Electrical Engineering and Computer Sciences, University of Hyogo, Japan
Abstract: Electrically series-connected PZT (Pb[Zr,Ti]O3) generates high output voltage when the elements are
subjected to stress. For the application of series-connected PZT elements to power harvesters, the influence of
parasitic capacitances on the output voltage and the generating output power are investigated numerically and
experimentally. Numerical calculations using a circuit simulator, SPICE validated that the output voltage is
multiplied for the series-connected PZT elements. The investigations about the influence of parasitic capacitance
indicate that the there is an optimum number of series-connection. From measurements of the output voltage of
the series-connected PZT, it is verified that a proper choice of electric resistance generates the best output power.
We conclude that a proper design of the SC-PZT and the peripheral circuit realize a power harvester with high
output power using SC-PZT.
Keywords: PZT thin film, series-connected PZT, high output voltage
INTRODUCTION
parasitic
capacitances
are
experimentally investigated.
For sensor networks and integrated sensing
systems, various types of power harvesters have been
reported for this decade [1]. Piezoelectric power
harvesters have great potential for their high
responsibility and applicability to MEMS [2].
However, integration and miniaturization of the
device result in small voltage output. In addition, the
obtained voltage needs to be rectified, and a voltage
larger than the voltage drop for rectifying is required.
For the integration of power harvesters to an electric
circuit system, not only high power generation but
also high voltage generation is significantly important.
An enhancement in the output voltage makes the
circuit design simple and flexible. Itoh et al. reported
digital output accelerometer using series-conncetion
of PZT elements [3]. The authors reported a concept
of series-connection of PZT elements (SC-PZT) for
sensor applications that provides the generation of
higher output voltage [4]. A well-established
fabrication technique of PZT realized SC-PZT and it
was verified that the output voltage from vibrating
cantilever with SC-PZT is multiplied with the number
of series-connection. Figure 1 shows a conceptual
diagram of SC-PZT. Electrically series-connected
PZT elements generate a high output voltage when the
structure deforms.
The objective in this work is the application of
SC-PZT to energy harvester device. The output
voltage multiplication for SC-PZT is validated using
numerical simulation. In addition, the influence of the
parasitic capacitance is evaluated. Furthermore, a
generating power from SC-PZT and the effects of
0-9743611-5-1/PMEMS2009/$20©2009TRF
numerically
and
Fig. 1: Conceptual illustration of SC-PZT.
OUTPUT VOLTAGE MULTIPLICATION
Validation of Output Voltage Multiplication
For the SC-PZT with ten series connection, the
equivalent circuit is expressed as Fig.2. PZT elements
are modeled as simple capacitors with the capacitance
Cn. The parasitic capacitances Cpn are SiO2 layers
between substrates and lower electrodes of PZT. Cb
and Cm are parasitic capacitances under bonding pads
and the load capacitance, respectively. Although the
output voltage of the equivalent circuit can be
obtained analytically, it becomes more difficult when
there is numerous number of series-connection with
capacitances, Cn designed to have different values.
We used transient analyses in a circuit simulator,
SPICE to estimate the output voltage of SC-PZT
device. The nodal point voltages in the equivalent
circuit in Fig. 2 are analyzed. The electrons generated
from PZT deformation are modeled as “initial
597
PowerMEMS 2009, Washington DC, USA, December 1-4, 2009
Cpn : parasitic capacitance
C n : capacitance of PZT
5
6
7 8
0.08
Output voltage [V]
Node number
0 1 2 3 4
SPICE calculation
measurement: series-connection
measurement: single element
sum total of single element
0.1
9 10
GND
0.06
0.04
0.02
0
1
2
3
4
5
6
7
8
Number of elements
Cb : capacitance for bonding pad
Fig. 4: Comparison between measurements and
calculations. They agree well each other.
Cm : capacitance for measurement
10
Cpn/Cn
0.001
0.002
0.005
0.01
0.02
0.05
0.1
0.2
out
Multiplying factor (V / V
initial
)
Fig. 2: Equivalent circuit of SC-PZT.
8
6
4
2
0
Fig. 3: Fabricated SC-PZT on a Si cantilever.
voltage” at the PZT capacitors. The electric potential
on each PZT capacitor immediately decreases because
of the parasitic capacitances. Parasitic capacitance
decreases the voltage on the PZT capacitor and the
resultant output is the equilibrium voltage. The
equilibrium potentials obtained from the transient
analysis at the nodes indicate the output voltage
between ground and the corresponding node numbers
of PZT element.
For a SC-PZT device illustrated in Fig. 3, the
output voltage is calculated. The details of the
fabrication have been reported in Ref. [3]. In the
calculation, the parasitic capacitances are estimated
from actual dimensions and material properties.
Output voltages measured from each element are
employed as initial voltages of the PZT elements. The
calculated values clearly correspond to the measured
ones as indicated in Fig. 4. The line in Fig. 4 indicates
the total summation of output voltage obtained from
single element. This result demonstrates that the
0
2
4
6
8
Number of elements
10
Fig. 5: Influence of parasitic capacitances. Large
ratio of Cpn/Cn degrades output voltage.
difference between the summation voltage and
measured voltage from series-connected PZT is due to
the parasitic capacitance.
Influence of Parasitic Capacitances
To investigate the affects of parasitic capacitances,
the output voltages for SC-PZT devices with various
ratio of Cpn/Cn are calculated. The ratio of Cpn/Cn
depends on the thicknesses, the areas and the
dielectric constants of PZT and SiO2 located under the
electrodes. Therefore an intended ratio can be
obtained by controlling the process rules and device
designs. For the analyses, the capacitance values for
PZT, SiO2, bonding pad, and wiring are based on an
actual device [3]. The initial voltages are set to 1 V to
evaluate the multiplying factor which defined as the
598
ratio of an initial voltage to net output voltage. Figure
5 shows the relationship between the multiplying
factor of output voltages and number of PZT elements
for the ratio of the parasitic capacitance to the PZT
capacitance. The net output voltage significantly
decreases with the increase of the capacitance ratio.
The voltage drops to almost half values expected
when the value of parasitic capacitance is 20% of SCPZT.
The reduction in the parasitic capacitance
prevents from voltage drops. The reduction of the
parasitic capacitance is realized from the utilization of
the material with a low dielectric coefficient or from
the thickening of the SiO2 layer. We focused on the
thickness of the SiO2 layer and estimated the output
voltages. The parasitic capacitance for the same
model as used in Fig. 4 is altered to various values
that correspond to SiO2 thicknesses. Figure 6 presents
the calculation result. The output voltage for the SiO2
thickness of 0.2 µm reduced, while that for 1.0 µm is
proportional to the series-connection. The reduction in
the parasitic capacitance is crucially important for the
multiplication of the output voltage.
0.1
Output voltage [V]
0.08
€
0.04
0
1
2
3
4
5
6
7
8
Number of elements
Fig. 6: The output voltages when the SiO2
thickness is changed.
8
20
7
6
15
5
4
10
3
2
Multiplying factor
J]
-10
Net energy [x10
For the power harvester application of SC-PZT,
the output power is estimated using SPICE. A load
resistance is connected in parallel to the system shown
in Fig. 2. The potential difference at both ends of the
resistance is output voltage. The PZT elements are
modeled as ideal capacitors, although the each PZT
elements should be modeled as equivalent circuits
composed of resistances and capacitances in actual
case. In the transient analyses, the initial voltages on
PZT capacitances decrease with time because of a
transfer of electrons to parasitic capacitances. The
generated power is consumed in the resistance,
resulting in zero equilibrium voltages. The net energy,
E generated from the initial voltage can be calculated
from
2
∞

∫ 0 V (t) R dt ,
0.06
0.02
ESTIMATION OF OUTPUT POWER
E=
SiO2 thickness [µm]
0.2
0.8
0.4
1.0
0.6
5
1
0
1
10
Number of series-connection
0
100
Fig. 7: The net energy and multiplying factor of
output voltage vs. number of series-connection.
elements. The parasitic capacitances are calculated
from the area and the material properties. The initial
voltages are 1 V to evaluate the multiplying factor
which is the ratio between an initial voltage to net
output voltage. The load resistance is set to 1 kΩ.
Figure 7 indicates the multiplying factor and net
energy obtained from the calculations. There is a clear
peak for the output voltage. However, monotone
decreasing of the output energy indicates that seriesconnection of PZT elements results in a degradation
of output power. The output power and output voltage
is in a trade-off relationship. This result implies that
the optimum number of series-connection depends on
(1)
where V(t) and R are the voltage at the time t and
resistance, respectively.
To investigate a proper number of seriesconnection of PZT elements, a generated net energy
and multiplying factor, defined as the ratio of an
initial voltage to net output voltage, are calculated
when the number of series-connection is changed. The
calculations are conducted for the SC-PZT with
various number of series-connection under the
condition of the same summation area of the PZT
599
MEASUREMENTS
The output power for SC-PZT with nine seriesconnections on a cantilever (wth the dimensions of
length: 13 mm, width: 10 mm, substrate thickness:
500 µm, and PZT thickness: 3 µm is measured. The
output voltages of the PZT elements when the
cantilever is oscillated with a peak-to-peak
amplification of 50 µm at the resonant frequency of
4.2 kHz using a bulk PZT are measured. A resistance
is connected to PZT element in parallel and the output
voltage is measured using an oscilloscope. The output
power is obtained from the square of root-meansquare voltage divided by the resistance. Figure 8
indicates the results. The output power has a peak
around 10 kΩ of the resistance, while the output
voltage decreases with the resistance. The net
impedance of SC-PZT measured with a LCZ meter
was about 27 kΩ at the same frequency. In this work,
the output-voltage measurements at 27 kΩ of the
resistance were not conducted. However, this result
demonstrates that the impedance matching provides a
maximum power for SC-PZT.
In this work, the net peak-to-peak output voltage
was less than 160 mV and the output power was about
50 nW. However, thinning the cantilever enlarges the
output voltages. An optimum design of SC-PZT and
the structure by eliminating parasitic capacitance and
considering the peripheral circuit realizes the energy
harvester with a high output voltage.
60
60
50
50
40
40
30
30
20
20
10
10
0
2
10
Power [nW]
Root-mean-square output voltage [mV]
other conditions, such as the peripheral circuits and
the systems.
The best number of series-connection about the
output voltage for SC-PZT was discussed in this
chapter. Although the PZT elements are modeled as
ideal capacitors, actually they should be modeled as
equivalent circuits composed of resistances and
capacitances due to leak currents. For the further
discussion about the net energy, the leak currents
should be taken into consideration. The internal
impedance of the SC-PZT can be measured and
modeled.
0
10
3
4
10
10
Resistance [Ω]
5
10
6
Fig. 8: Measured output voltage and power.
the degradation of output voltage due to parasitic
capacitances is avoidable by thickening the SiO2 layer.
The output power of the SC-PZT is also investigated
numerically
and
experimentally.
Numerical
calculations indicate that there is an optimum number
of the series-connection for the output voltage and
that the output power decreases with the number of
series-connection. Measurements of the output power
for a vibrating cantilever with SC-PZT clarified that
the proper resistance of the peripheral circuit
maximize the output power. We concludes that a
proper design of the SC-PZT and the peripheral
circuit realize a power harvester with high output
voltage using SC-PZT.
REFERENCES
[1] Mitcheson D P, Yeatman M E, Rao K G,
Holmes S A, Green C T 2008 Energy harvesting
from human and machine motion for wireless
electric devices Proc. IEEE 96 1457-1486.
[2] Choi J W, Jeon Y, Jeong J-H, Sood R, Kim G S
2006 Energy harvesting MEMS device based on
thin
film
piezoelectric
cantilevers
J.
Electroceram 17 543-548
[3] Itoh T, Kobayashi T, Okada H, Masuda T, Suga
T, A digital output accelerometer for ultra-low
power wireless sensor node, Proc. IEEE Sensors
2008 Conf., Lecce, Italy, 26-29 October 2008,
542-545
[4] Kanda K, Iga Y, Hashimoto T, Fujita T, Higuchi
K, Maenaka K 2009 Microfabrication and
CONCLUSIONS
The influence of the parasitic capacitance on the
output voltage is investigated for the application of
the series-connection of PZT elements to energy
harvester. The numerical calculations using a circuit
simulator, SPICE validated the output voltage is
multiplied when the PZT elements are serially
connected. The numerical indications for the parasitic
capacitances of SiO2 layers between the substrates and
the lower electrodes of PZT elements demonstrate that
Application of Series-Connected PZT Elements
Procedia
chemistry
(Proceedings
of
Eurosensors XXIII Lausanne, Switzerland, 6-9
September 2009) 1 808-811
600