Harvesting energy from ambient vibration is proposed as an alternative to
storage based power supplies for autonomous systems. The system presented
converts the mechanical energy of a vibration into electrical energy by means
of a variable capacitor, which is polarized by an electret. A lumped element
model is used to study the generator and design a prototype. The device has
been micromachined in silicon, based on a two-wafer process. The prototype was
successfully tested, both using an external polarization source and an
electret.Comment: Submitted on behalf of EDA Publishing Association
  (http://irevues.inist.fr/EDA-Publishing

Altena, Geert

Fiorini, P.

Puers, R.

Sterken, T.

English

arXiv

Harvesting energy from ambient vibration is proposed as an alternative to storage based power supplies for autonomous systems. The system presented converts the mechanical energy of a vibration into electrical energy by means of a variable capacitor, which is polarized by an electret. A lumped element model is used to study the generator and design a prototype. The device has been micromachined in silicon, based on a two-wafer process. The prototype was successfully tested, both using an external polarization source and an electret

Sterchen, T. M.

Altena, G.

Puers, R

I-Revues

 Stresa, Italy, 25-27 April 2007 
 
CHARACTERISATION OF AN ELECTROSTATIC VIBRATION HARVESTER 
 
T. Sterken
1,2, G. Altena
3, P.Fiorini
1, R. Puers
2 
 
1 IMEC, Leuven, Belgium,  
2 K.U.Leuven, Leuven, Belgium 
3 IMEC – NL/Holst Centre, Eindhoven, The Netherlands 
Tom.Sterken@imec.be 
 
ABSTRACT 
 
Harvesting energy from ambient vibration is proposed as 
an alternative to storage based power supplies for 
autonomous systems. The system presented converts the 
mechanical energy of a vibration into electrical energy by 
means of a variable capacitor, which is polarized by an 
electret. A lumped element model is used to study the 
generator and design a prototype. The device has been 
micromachined in silicon, based on a two-wafer process. 
The prototype was successfully tested, both using an 
external polarization source and an electret. 
 
1. INTRODUCTION 
 
Autonomy, mobility and lifetime are important 
characteristics of state-of-the-art electronic systems. The 
autonomy of these systems is assured by the use of 
primary or secondary batteries; the lifetime of storage 
based energy supplies depends on the ratio between the 
amount of energy stored in the battery to the power 
consumption of the electronic device. As the storage 
capacity is limited by the size (and weight) of the device, 
designers of electronic circuits make strong efforts to 
decrease the power consumption of the device.  
An alternative approach is presented by ambient energy 
harvesters. These devices extract and convert energy from 
the environment. In this way the theoretical lifetime of 
autonomous systems is not limited by the size of the 
device, but depends on the availability of the ambient 
energy source. Low power design is still a key parameter 
in the autonomy of the system, as the power level of 
ambient energy supplies tends to vary in the lower 
microwatt ranges.  
The feasibility of vibration powered systems depends on 
the ambient conditions, the envisioned application and 
boundary conditions such as maximum size, maximum 
weight and cost issues [1].  
The generator presented in this contribution extracts 
energy from vibrations to which the autonomous device is 
subjected. The vibrations are characterised by small 
amplitudes of displacement in the micrometer scale and 
by relatively large frequencies, in the 100 - 3000 Hz 
range. These vibrations can be found in industrial 
environments. The generator design as presented is not 
suited for large amplitude motion scavenging, 
characterised by lower frequency vibrations. These are 
often related to human activities. 
Vibration harvesting generators consist of a seismic mass 
whose motion is coupled either to an electromagnetic, a 
piezoelectric or an electrostatic transducer. The inertia of 
the mass acts as an artificial reference to the vibration.  
The mass is often suspended to reduce unwanted damping 
losses. At the same time the suspension can be designed 
to allow resonance at the main working frequency of the 
vibration. This approach is favourable for vibrations at 
higher frequencies with lower amplitudes: resonance 
converts the small amplitude of the package into an 
internal motion with a larger amplitude. 
 The work produced by the relative motion between the 
package of the device and the mass is converted to 
electrical energy by a transducer. In this work an 
electrostatic transducer is designed and fabricated using 
micromachining technology (Fig. 1). The transducer 
consists of a variable capacitor that is polarised. As the 
capacitance changes, a current is forced between the 
electrodes of the capacitance, through a load circuit. The 
current performs work in the electrical system, while the 
mechanical motion is damped by the associated 
electromechanical forces. The polarisation source can 
either be an external voltage source or a built-in electret.  
 
Suspension
Damping
Mass
Internal 
Motion
Input 
Vibration
load
----
Polarisation 
Source
Suspension
Damping
Mass
Internal 
Motion
Input 
Vibration
load
---- ---- ----
Polarisation 
Source
 
Figure 1.   Schematic overview of an electrostatic 
harvester for vibrations. 
 
©EDA Publishing/DTIP 2007 ISBN: 978-2-35500-000-3               T. Sterken  et al.
Characterisation of an Electrostatic Vibration Harvester
 
2. DESIGN 
 
The design of the prototype is based on the analysis of a 
lumped element model of the generator. This type of 
modeling converts the mechanical behavior to an 
electrical circuit, based on the equivalences between the 
behavior of masses, springs and dampers to inductances, 
capacitors and resistors respectively. The transducer then 
connects the mechanical equivalent circuit to the 
electrical load circuit. The equivalent model for the 
transducer is based on the relations between the forces, 
voltages, charges and geometry of the capacitance. As 
these relations are non-linear, a linearised small-signal 
model is used. The equivalent model consists of a 
transformer which is shunted by a capacitor (Fig. 2). The 
value of the capacitance corresponds to the value of the 
variable capacitor at equilibrium: C0. The transformer is 
characterized by the ratio n between the generated current  
i  and the velocity ż at the mechanical poles of the 
generator: 
()
pol V
dz
z dC
z
i
n = =
&
             (1) 
The analysis of this system leads to the following 
conclusions concerning design and optimization of a 
vibration harvester.  
  As a first rule the mass that is used as a reference 
should be maximized within the constraints of the 
application. A better reference will allow the use of a 
higher electromechanical damping. Furthermore the 
suspensions can be tuned to allow resonance at the 
dominant frequency of the vibration. At resonance the 
small input amplitude is converted to a larger amplitude, 
which is specifically useful at higher frequencies where 
the amplitude of the vibration is smaller than the system 
dimensions.  
  Although the use of resonance allows increasing the 
power that is generated, it also has a drawback: as the size 
of the system is minimized, resonance will result in 
impact of the mass onto the package. Besides reliability 
issues this impact also limits the output power of the 
system over a span of frequencies around the resonance 
frequency. The bandwidth depends on the ratio between 
the amplitude of the vibration and the maximum allowed 
displacement. The higher the maximum allowed 
displacement, the smaller the bandwidth will be. The 
optimum power will thus be reached when the mass and 
maximum displacement are tuned to the size constraints 
and energy spectrum of the application. 
  The design of the transducer allows tuning the output 
voltage and output impedance to the available vibration 
and mechanical design. In order to allow a maximum 
power transfer in a given maximum displacement, the 
power factor across the transducer should be optimized.  
At the same time the electromechanical impedance should 
be as large as possible. These conditions are met when the 
load resistance equals the impedance of the capacitance. 
The electromechanical impedance is then given by: 
() 0
2
2
2
0
2
2
1
2
1
1 C
n
R n
RC
R n
ZEM ω ω
= =
+
=       (2) 
Optimal power is reached by maximizing equation 2. The 
design of the capacitance must allow a high capacitance 
change per micrometer of displacement.  
The design consists of multiple variable overlap 
capacitors that are electrically connected  in parallel. 
Scaling down the width and pitch of the electrodes will 
result  in    a higher transformation factor n without 
influencing the total capacitance. This capacitance 
depends on the surface that is used (Figure 3c).  
Note that the use of multiple capacitors in parallel 
increases the frequency of the generated electrical signal: 
once the motion of the mass exceeds the pitch of the 
capacitors, the electrical signal is reproduced. This effect 
partly counteracts the advantage on n versus C0 of the 
structure: at higher electrical frequency the capacitance 
will shunt the load circuit. 
 
3. FABRICATION 
 
The variable capacitor is fabricated using a stack of two 
bonded wafers. The fixed electrode is created on a Pyrex 
wafer by sputtering and patterning an aluminum layer.   
Then photosensitive BCB (Benzo-Cyclo-Butene) by the 
Dow Chemical Company is spun and patterned (Figure 
3a). Both the thickness of the aluminum layer (200 nm) 
and the BCB layer (1.2  µm) determine the distance d 
between the fixed electrode and the moving electrode. 
The use of Pyrex allows reducing parasitic capacitances 
shunting the generator, while the thermal expansion 
coefficient remains tuned to the one of silicon. This 
requirement is a necessity as BCB bonding occurs at 
250°C.  
The moveable electrode of the capacitor is bulk 
micromachined together with the mass and the suspension 
springs in a 6” silicon <100>-wafer. First, the capacitor, 
the mass and the springs are patterned and then etched 
into the silicon by deep reactive ion etching (DRIE) using  
Package
Mass
Input
Vibration 
Load
Damping
Suspension
Generator
AC    DC
Turn Ratio
n : 1
C0
Package
Mass
Input
Vibration 
Load
Damping
Suspension
Generator
AC    DC
Turn Ratio
n : 1
Package
Mass
Input
Vibration 
Load
Damping
Suspension
Generator
AC    DC AC    DC
Turn Ratio
n : 1
C0
 
Figure 2. Equivalent electrical circuit  
 
©EDA Publishing/DTIP 2007 ISBN: 978-2-35500-000-3                
a STS ASE etcher to a depth of 100 µm. Next, a 500 nm 
thick SiO2 layer is grown using thermal oxidation.  
A 150 nm thick Si3N4 layer is used on the back side of the 
wafer as a hard mask for wet anisotropic etching (Figure 
3b). The two wafers are then combined using aligned 
wafer-to-wafer bonding where the BCB layer acts as an 
adhesive [3]. This two-wafer stack is anisotropically 
etched in KOH. A layer of approximately 30 µm is left to 
prevent leakage of KOH into the cavity between the Si 
wafer and the glass wafer (Figure 3c). This 30 µm thick 
Si layer is removed with a DRIE process. The variable 
capacitor is finally released by removing the SiO2 which 
served as an etch stop. SEM micrographs of the mass and 
suspension are shown in Figure 4. 
  
3. CHARACTERISATION 
 
During a first test the variable capacitance was measured 
as a function of displacement (Figure 5). A small 
discrepancy can be noticed in the capacitance change per 
micrometer. From these curves the capacitance change 
per micrometer is calculated and given in figure 5.The 
second test in the characterisation of the prototype 
consists in displacing the mass over a 40 μm 
displacement at a frequency of 40 Hz.  
Capacitance versus displacement
0
2
4
6
8
10
12
14
-20 -15 -10 -5 0 5 10 15 20
Displacement (μm)
C
a
p
a
c
i
t
a
n
c
e
 
(
p
F
)
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
Measured Capacitance Simulated Capacitance
Measured Capacitance Change Simulated Capacitance Change
C
a
p
a
c
i
t
a
n
c
e
 
C
h
a
n
g
e
 
(
p
F
/
μ
m
)
 
Figure 5. Capacitance and capacitance change per unit of 
displacement, as measured and simulated. 
 
Generated Voltage on 1 MOhm Load
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
01234567
Time (ms)
O
u
t
p
u
t
 
V
o
l
t
a
g
e
 
(
V
)
-80
-60
-40
-20
0
20
40
60
D
i
s
p
l
a
c
e
m
e
n
t
 
(
m
i
c
r
o
m
e
t
e
r
)
Output Voltage (V)
Input displacement (micrometer)
 
Figure 6. Voltage generated as a function of displacement 
over  a 1 MΩ load resistor. 
 
In this way the mass moves across multiple capacitances 
per cycle. The shape of the signal corresponds to the 
simulated and measured changes of capacitance versus 
displacement. During this test the polarisation voltage 
was limited to 10V, as higher voltages resulted in a pull-
in of the mass. In figure 6 the generated signal is 
illustrated as a function of time, as well as the 
displacement of the probe. The signal is symmetric 
towards the maximum displacement point. Peak voltages 
up to 200mV are generated over a 1 MΩ load, while the 
velocity of the mass has a maximum of 0.03 m/s. 
A final test applied to the device consists in charging the 
SiO2 layer between the two electrodes of the variable 
capacitor. The electret is charged by electrostatically 
pulling down the movable electrode until the electret 
layer touches the aluminum electrode. The electret is 
charged up to the pull-in voltage, which was 15V. 
Unfortunately this test does not allow checking the 
electret voltage after charging without destroying the 
device.  
   
Figure 4. SEM photographs of the released device (left) 
and a close-up of the suspension (right). 
 
Pyrex
BCB Fixed Electrode (Al)
SiO2
(A)
Si3N4
(B)
(C)
Pyrex
BCB Fixed Electrode (Al)
Pyrex
BCB Fixed Electrode (Al)
SiO2
(A)
Si3N4
(B)
Si3N4
(B)
(C)
 
Figure 3. The variable capacitor consists of two wafers 
(A+B), which are next bonded and released (C).
T. Sterken  et al.
Characterisation of an Electrostatic Vibration Harvester
©EDA Publishing/DTIP 2007 ISBN: 978-2-35500-000-3                
As the mass of the generator was displaced by the probe, 
a similar voltage pattern was generated as given in Figure 
6.  
The device was next mounted on an industrial tool with a 
strong vibration of 1g at 2.6 kHz (Figure 7). As the 
displacement of the mass does not exceed the pitch of the 
electrodes, the signal is sinusoidal at the frequency of the 
vibration. Due to a small misalignment of the two 
electrodes, the shape of the generated voltage on the 
positive half of the cycle differs from the shape on the 
negative half of the cycle. A power of 90 nW is generated 
on a 1 MΩ load resistor. 
 
4. CONCLUSIONS 
An electrostatic generator based on ambient vibrations 
was studied and designed according to the conclusions of 
the analysis. A process flow is developed based on a 
stack of two bonded wafers, each bearing an electrode of 
the variable capacitor. After fabrication the generator is 
tested, first by displacing the mass, next by subjecting the 
device to industrial vibrations. The capacitor proved to 
extract energy, both when polarised by an external 
voltage source as well as by means of an electret. 
 
 
 
 
5. REFERENCES 
 
[1] P.D. Mitcheson, T.C. Green, E.M. Yeatman and A.S. 
Holmes, “Architectures for Vibration-Driven Micro-
Power Generators”, Journal of Microelectromechanical 
Systems, Vol. 13, pp. 429-440, 2004. 
[2] S. Roundy et al., “Improving Power Output for 
Vibration-Based Energy Scavengers”, IEEE Pervasive 
Computing, Vol. 4, pp. 28-36, 2005. 
[3] T. Sterken, P. Fiorini and B. Puers, “Combining BCB 
with KOH : wet bulk micromachining vs. wafer 
bonding.” In 16th MicroMechanics Europe Workshop - 
MME, pages 80 – 83, Goteborg, Sweden, September 
2005. 
 
Generated Voltage at 2.6 kHz
-0.2
-0.2
-0.1
-0.1
0.0
0.1
0.1
0.2
0.2
0.3
0.3
-1.0 -0.5 0.0 0.5 1.0
Time (ms)
V
o
l
t
a
g
e
 
(
V
)
 
Figure 7. A voltage of 300mV is generated across a 1 MΩ 
resistor when subjected to a 2.6kHz vibration at 1g. 
T. Sterken  et al.
Characterisation of an Electrostatic Vibration Harvester
©EDA Publishing/DTIP 2007 ISBN: 978-2-35500-000-3               

Characterisation of an Electrostatic Vibration Harvester

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