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A Picowatt Energy Harvester.
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2010 MRS Fall Meeting
Draft
Symposium S
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Evans, Joseph; Radiant Technologies, Inc
Smits, Johannes; Scladix
Montross, Carl; Radiant Technologies, Inc
Salazar, Gerald; Radiant Technologies, Inc.
piezoelectric, microelectro-mechanical (MEMS), energy generation
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A Picowatt Energy Harvester
Joe Evans1, Johannes Smits2, Carl Montross1, and Gerald Salazar1
Radiant Technologies, Inc., 2835D Pan American Fwy NE, Albuquerque, NM 87107 USA
2
Scaldix B V Stationsstraat 13 4331 JA Middelburg, The Netherlands
1
ABSTRACT
The authors describe an energy harvester circuit fabricated with integrated thin
ferroelectric film capacitors on a silicon substrate. The harvesting mechanism is a folded
double-beam cantilever with proof masses at both end points. Interdigitated electrode
capacitors are located at the three points on the folded cantilever that are expected to
experience maximum bending moment and should produce up to 5V as a function of external
vibration. The die has the dimensions of 1.6mm on a side and is designed to be mounted in a
TO-18 package transistor-style package. Due to its small size, the self-contained
piezoelectric MEMs device should produce at least 50 picowatts in a 1g vibration
environment while occupying little space.
INTRODUCTION
We have designed and are fabricating a picowatt energy harvester using piezoelectric
MEMs technology. The first devices have been fabricated up to but not including the final
release etch steps. A photomicrograph of a device prior to release is in Figure 1.
Figure 1. Photomicrograph of energy scavenging device in fabrication.
A complete die with dicing lanes appears in Figure 1. A portion of a second die appears
to the left of the complete die. The “U” shaped structure in middle of the die will be etched
through the wafer from the backside resulting in a folded cantilever structure. The two
outside arms, containing the interdigitated electrodes (IDEs), form the primary cantilever set
and will bend together. A bridge joins the two primary cantilevers at the top of the figure. A
secondary cantilever extends from that bridge back towards the base of the die exactly in the
center of the die. This cantilever has its own IDE set at the point of maximum bending. The
substrate underneath the three cantilevers will be removed by a two part etch process, making
the cantilevers thin and flexible. The etch process will also release each die from the
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substrate. Blocks of the original substrate will be left at the ends of the primary and
secondary cantilevers to act as inertial masses to increase the amplitude of cantilever tip
motion. The gaps between the fingers of the IDE electrodes are 10 microns. The IDEs rest
on the top surface of 0.8 micron-thick 4/20/80 PNZT film. They will require 190 volts to
pole each capacitor. Connected in series, the three IDE capacitors should generate as much
as 5 volts at maximum bending. Were the same capacitors to be fabricated as parallel plate
capacitors, they might generate at most 100mV at maximum bending, not nearly enough to
power control circuitry to collect and control energy coming from the device. The hysteresis
loop for the device in Figure 1 is shown in Figure 2 below.
IDE Hysteresis
[ 180V 2ms ]
Polarization (µC/cm2)
50
40
30
20
10
0
-10
-150
-100
-50
0
Voltage
50
100
150
Figure 2. 180V 2 millisecond hysteresis loop of the interdigitated electrodes of Figure 1.
The die has the dimensions of 1.6mm on a side and will fit inside a four-pin TO-18
package. The TO-18 package is the traditional metal transistor can in use since the 1960s. A
side view of the energy harvesting die is shown in Figure 3 to provide a visual interpretation
of the interconnected bending moments of the primary and secondary cantilevers. Note that
the die will have to be mounted on a pedestal on the package header to keep the inertial
masses from hitting the header surface during vibration.
Pedestal
TO-18 Header
Figure 3. Side view of the energy scavenger mounted on a pedestal on the TO-18 header. The increased
height of the pedestal is necessary to allow full motion of the substrate-thick end-point masses.
THEORY
We calculate the voltage developing at the electrodes of a piezoelectric bimorph
vibrating with amplitude a0 at the clamping point in a direction perpendicular to the length.
One of the boundary conditions for the solution of the differential equation is that the
clamping point undergoes a sinusoidal motion with an amplitude a0. All other boundary
conditions are those of free bimorphs [1].
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The solution of the Euler Bernoulli equation gives the local deflection in the x direction
along the length of the cantilever as:
(1)
We use here the conventions c=cos kL, s=sin kL, ch= cosh kL, sh= sinh kL as described in
[1]. The shape of the vibrated bimorph near resonance is shown in Figure 4.
Figure 4. The deflection profile of the cantilever.
Note that the cantilever has a higher radius of curvature near the clamping point and is nearly
straight at the free end. The piezoelectric capacitor used as the scavenging engine will gain
capacitance linearly with its length but will receive minimal piezoelectric distortion near the
free end of the cantilever. Consequently, the authors elected to restrict the length of the
piezoelectric capacitors to the region of maximum bending so that each cantilever will
operate a higher energy to capacitance ratio.
To find the charge induced between the electrodes we use the piezoelectric constitutive
equations in the form given by Berlincourt, Curran and Jaffe [2]:
(2)
S is the elastic deformation, or strain, T the elastic stress, D is the dielectric displacement, and
E the electric field. The elastic stiffness modulus at constant electric field is cE, the
piezoelectric constant is e, and the dielectric constant at constant strain is εS. The charge Q
under short circuit conditions, (E=0) in the electrodes becomes:
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(3)
w = width of the bimorph
h = thickness of the single piezoelectric element of the bimorph
k = wave number
Voltage and charge are related by Q=CV, where C is the capacitance. For the
capacitance we have [3]:
(4)
L = length of the bimorph
Combining equation (3) and (4) we arrive at
(5)
The total electrical energy Ue inside the bimorph is now Ue = { QV/ 2}
(6)
The Q-factor of the cantilever will be quite high near resonance.
Mechanical energy is introduced into the bimorph by the clamping fixture that is
vibrated. In each place we can cut the beam into two pieces, and represent the forces on the
cut planes which the two pieces exert on each other with forces in the cut planes. The force
Fs in the planes is equal to Fs = -EIz''', so the force at the clamping point: -EI z'''(0). The
mechanical energy put into the beam is { Fs(0) a0/2 }. For the mechanical energy Um we find:
(7)
With the electrical and mechanical energies, we can calculate the energy conversion
efficiency ηe:
(8)
For a bender operating in a d{33} mode the factor k{31} should be replaced by k{33}.
The internal energy, mechanical and electrical, must reach steady state before the
electrical part can be removed. The steady state total internal energy is equal to the total
amount of energy that has been put in Ui = Ue + Um. At most the electrical energy can be
taken out as output energy Uo. We define power conversion efficiency as
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(9)
Because the energy conversion efficiency reaches very high values near resonance, the power
conversion efficiency approaches the value of unity at resonance and it becomes
advantageous to design the energy harvester with more than one resonance frequency, as in a
folded bender.
DEVICE FABRICATION
The fabrication process for the energy scavenger combines a well-established thin PZT
film capacitor process with known micro-electromechanical machine (MEMs) process steps.
Both process types use integrated circuit techniques which, when combined, allow the
definition of structures geometrically on CAD system software and the transference of the
design to a substrate surface with micron tolerances. The conversion of a piezoelectric
MEMs concept to real machine simplifies in this situation to integration of the plan forms of
PZT capacitors with those of the micro machinery. The concept of a geometric approach to
micro-scale devices was introduced to VLSI integrated circuit design (Very Large Scale
Integration) in 1980 by Mead and Conway [4], an advance which resulted in an explosion of
commercial IC circuits, computers, and automated circuit layout tools. The authors hope that
this same philosophy will benefit piezoelectric MEMs technology the same way.
Capacitor Process:
The capacitor process in use for the fabrication of the piezoelectric elements uses
capacitors having thin 4% niobium-doped 20/80 PZT (PNZT) films and platinum electrodes.
The interdigitated electrodes of Figure 1 require only one level of platinum in the process
flow. The electrodes for this device were executed on top of the thin PNZT.
The process uses a commercial lift-off step to pattern the platinum electrodes. The top
platinum is 1000Å in thickness, making it possible to achieve one micron features and gaps
with the lift-off process. Despite the presence of platinum electrodes with the PNZT, fatigue
is not a factor because the polarization is never switched after the first poling. Imprint may
over time affect the energy generation efficiency. The niobium doping of the 20/80 PZT
significantly reduces the imprint rate of the domains for temperatures below the industrial
standard of 85ºC.
Standard industrial procedures such as etching, sawing, soldering, and packaging after
the capacitors have been completed have an impact on film performance. Passivation is
critical to protect capacitor performance during the MEMs etch processes. The passivation
for these capacitors places a stack of titanium dioxide and silicon dioxide on their top
surfaces, essentially adding 2,700Å of glass atop the piezoelectric elements.
MEMs Process:
The energy scavenger has three thicknesses in its mechanical design. The first is the
substrate thickness itself, an etch depth of zero from the backside of the substrate. The
substrate is necessary to 1) provide structural strength to the micromachine, 2) provide a
foundation to mount the device in packaging, and 3) create inertial masses. The second
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thickness is that of the cantilevers. The final thickness is that of the full substrate so the
device can be self-diced from the substrate after the last etch.
Two deep RIE steps and a buried oxide layer in the substrate (SOI) are used to create the
MEMs structure. The depth of the buried oxide determines the thickness of the cantilevers.
After completion of the capacitors, a trench pattern is placed on the top surface of the
substrate in photoresist. A DRIE etch is executed to the buried oxide. This pattern defines
the geometry of the cantilevers as well as the dicing lanes. The substrate is flipped over, a
backside pattern is placed on the backside of the substrate, and a second DRIE etch is
executed to the buried oxide. The backside pattern is not the same as the trench pattern from
the front side. Where the backside and trench patterns align, the substrate will be etched
through to the surface to form the dicing lanes and the lateral dimensions of the cantilevers.
Where the backside and trench patterns do not align, the substrate is removed from
underneath a cantilever, a membrane, or bridge structure. Once the two DRIE process steps
have been completed a short plasma etch or wet buffered oxide etch will remove the exposed
buried oxide layer to free the dice and the cantilever structures.
PREDICTION OF PERFORMANCE
The primary cantilevers of the energy scavenger of Figure 1 have the dimensions of
1060µ long, 465µ wide, and 40µ thick. The secondary cantilever has the same thickness and
is 880µ long and 470µ wide. The cross bar connecting the two primary cantilevers is 550µ
thick, 140µ wide, and 1600µ long. It is the inertial mass for the primary cantilevers. The
inertial mass for the secondary cantilever is 550µ thick, 470µ wide, and 130µ long. Given
that the IDEs have 10µ gaps and 5µ fingers on 0.8µ-thick 4/20/80 PNZT with a d33 value of
60pm/v, we predict that resonance will occur at approximately 50 Hz. A 1g sine wave
stimulation at resonance should generate 50 picowatts of power and 200mV across the IDE
electrodes. The 1g stimulation reference is a small signal. The voltage generated by the
scavenger will increase linearly with the amplitude of the stimulation ( Eq (5) ). The power
generation will increase with the square of the driving amplitude ( Eq(6) ).
CONCLUSION
The authors have designed and are fabricating a picowatt energy scavenger using
piezoelectric MEMs process technology. The scavenger should approach 100% energy
conversion efficiency near mechanical resonance and should be able to generate 50 picowatts
of power at 50 Hz/1g.
REFERENCES
1.
2.
3.
4.
J. G. Smits and A. Ballato, J Micro ElectroMechanical Systems 3, 105-112 (1994)
A. Berlincourt, D. R. Curran, and H. Jaffe, Physical Acoustics D 1 (A), Edited by W. P.
Mason (Academic Press, New York, 1964) 188
J. G. Smits, S. I. Dalke, and T. K Cooney, Sensors and Actuators 28, 41-61 (1991)
C. Mead and L. Conway, Introduction to VLSI Systems (Addison-Wesley, California,
1980)