Non-linear and electret based vibration energy scavenging system Dr. Ghislain Despesse, Researcher, CEA, LETI, Minatec, Grenoble, France Sébastien Boisseau, PhD student, CEA, LETI, Minatec, Grenoble, France Dr. Pierre-Damien Berger, Head of Smart Devices Program, CEA, LETI, Minatec, Grenoble, France Over the past few years, MEMS and smart material technologies improvements have allowed autonomous sensor devices to become more and more widespread. As batteries are not always appropriate to power these systems, energy scavenging solutions from ambient power are currently being developed. Among the potential energy sources, we have focused on mechanical surrounding vibrations. Thanks to measurements and in agreement with recent studies [1], we have observed that most of surrounding mechanical vibrations occurs at frequencies below 100 Hz and are spread on a large frequency band (10 to 100 Hz). Contrary to existing structures tuned on a particular frequency [2, 3], we have investigated conversion structures with a high electrical/mechanical coupling enabling a high electrical damping. We now demonstrate that this global efficiency can be improved with a new type of electrostatic microstructure, which is no more a simple microaccelerometer-inspired microstructure [5] but a microstructure fully designed to meet the constraints of environmental vibration energy scavenging. The sizing procedure of this new type of structure will be discussed in this paper. The study is based on the system design presented on Figure 14. This system combines the use of an electret material to permanently polarize the electrostatic structure and the use of a non-linear spring to enlarge the frequency response. We present in a first step the available energy evaluation process, which start from a temporal acceleration measurement in the location where the scavenger system will be placed and finish with the estimation of the available power in function of the scavenger system resonant frequency and electrical damping. From these results, we determine which resonant frequency and which electrical damping is optimal to maximize the extraction of the available vibration energy. In a second step, the beams that act as non-linear springs between the seismic mass and the casing, are sizing in order to take advantage of the resonant effect on a band of frequency that is in agreement with the frequency band where the energy is preponderant. In a third step we optimize the electrode structuration and the required voltage/field to reach the optimal electrical damping. Finally we present the choose electret material properties, the required electret thickness and the associated process to reach the optimal voltage/field. 1 Available power evaluation process from ambient vibration measurements In order to optimize the scavenger system, we have to take into account the real available vibrations of the environment where the energy will be scavenged. Indeed, the best scavenger system for a specific application will be the system that presents an input mechanical impedance in agreement with the mechanical impedance of the vibration source, it is to say a system able to absorb the maximum of the available

energy. Then, the most appropriate conversion principle to use is mainly dependant of the vibration characteristics. In our case, we focus our work in scavenging the vibrations that occur in transportation systems where the vibrations are spread in frequency as shown on Figure 1. m.s-2

a(t)

m.s-2 0.25 0.2 0.15 0.1 t(s) 0.05

6 4 2 -2

2

4

6

8

A(f)

10

20

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f(Hz)

Figure 1: Acceleration measurement on a car (temporal and spectral)

In order to evaluate the available energy we use the classical linear viscous damping model [6]. In function of the input displacement Y and its pulsation ω, the moving mass m, the resonant pulsation ωn of the structure and the mechanical and electrical damping ζm and ζe, the maximum mechanical available power P is given by: 6 P(f) for fr=50 Hz µW ζe 2 3 ω  1 mY ζ eω n   0.015 1/10  ωn  0.01 P= 1/100 2 2 2 0.005  ω    ω   f(Hz)  2(ζ e + ζ m )  + 1 −    60 80 20 40 8 ω n    ω n      0 Figure 2: Available power expression and calculation in function of the spectral frequency for a given resonant frequency and for different electrical damping values

By applying the available power expression on the acceleration spectrum we can deduce the available power spectrum. The Figure 2 presents the power spectrum for a given resonant frequency and for different electrical damping and for a low mechanical damping (compare to the electrical damping value). To deduce the global available power Pg(fr) for one resonant frequency, we have to integrate the spectral energy over the full spectral frequencies. Then, we can make the same operation for different resonant frequencies values and deduce the global available power per gram of seismic mass in function of the resonant frequency and for different electrical damping as shown on Figure 3. µW Pg(fr ) ζe 20 15 10 5

1 1/10 1/100 20

40

60

80

f r (Hz)

Figure 3: Global available power per gram of seismic mass in function of the resonant frequency and for different electrical damping

From these calculations we can deduce the resonant frequency and the electrical damping that maximize the output power. But, in order to limit the system size, we have also to take into account the associate displacement amplitude. The maximal displacement calculation process is similar to the available power calculation

process. Starting from the acceleration spectrum we can deduce the spectral displacement Z(f) by using the displacement expression Z (see Figure 4) calculated from the viscous damping model [6]. Then, by making an inverse Fourier transform, we calculate, for a given resonant frequency value and for different electrical damping, the temporal relative displacement z(t). Finally, to find the maximum relative displacement, we look for the maximum absolute value reached during the measurement time. By making this operation for different resonant frequencies, we can draw the maximal displacement amplitude zmax(fr) in function of the resonant frequency (see Figure 4). A

Z=

ω

2 n

4 (ζ e + ζ m )

2

2 2 ω   ω     + 1 −     ωn    ωn  

2

µm 7 5 3 1

ζe

Z(f) fr=50Hz Hz Z(f) pour for fr=50

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ζe µm 75 25 -25 -75

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Figure 4: Maximal relative displacement calculation process

If to maximize the output power it is interesting to have a very low resonant frequency, about 5 Hz in the studied case (see Figure 3), it induces a very high relative displacement, about few millimeters (see Figure 4). Then, in order to limit the system size, it could be interesting to take a higher resonant frequency even if the scavenged power is reduced. On the other part, by choosing a high electrical damping, the scavenged power for a same displacement amplitude can be significantly higher than for a low electrical damping and in this case the output power is less dependent of the input frequency variation. 2 Use of a non-linear beam to enlarge the frequency response As shown on Figure 4 results, in the case of car vibrations, the relative displacement amplitude is quite high in low frequency and quite low in high frequency. Then, to improve the scavenger system, it could be interesting to limit the low frequencies amplification and to highly amplify the high frequencies. To reach that, we propose to introduce a non-linear effect in the system spring by using a geometrical non-linear beam.

Beam that acts as a nonlinear spring

Seismic mass 1g L z(t)

y(t)

e

Thickness h=500 µm

h

Figure 5: Mechanical system part with non-linear clamped-clamped beams

To introduce a highly non-linear effect, we chose to use a clamped-clamped beam as spring witch have a force(Fk)/relative-displacement(z) relation that is expressed as:  z2  Fk = k 0 1 + 2  z  e  where K0 represents the spring constant in small displacement and e the beam thickness The non-linear effect becomes significant when the relative displacement amplitude reaches the beam thickness e in the displacement direction. The equivalent spring constant increases with the increase of the relative displacement amplitude and induces an increase of the resonant frequency. To estimate the system equivalent resonant frequency freq we calculate the stored mechanical energy in the non-linear spring and look-for the linear spring constant klin that gives the same energy for the same relative-displacement value zref, and then, we deduce the equivalent resonant frequency in function of the relative-displacement amplitude zref : yref

yref

 z2  ∫0 klin z dz = ∫0 k0 z1 + e 2  dz k 4 2 2 ⇔ 12 klin z ref = 12 k0 z ref + 14 02 zref e 2 2 e 2 + z ref 2e 2 klin ⇔ k0 = 2 ⇒ f req = f 0 2 2 e + z ref 2e 2 The Figure 6 presents the equivalent resonant frequency in function of the relative displacement amplitude for a beam of 10 µm in thickness e and inducing, for the global system, a resonant frequency of 30 Hz in small displacement.

Figure 6: Equivalent resonant frequency in function of the relative displacement amplitude

The Figure 6 shows that the resonant frequency is quite constant until the relative displacement amplitude reach the beam thickness e of 10 µm and then the resonant frequency increases quickly with the displacement amplitude. In order to optimize the energy extraction, we want to reach an equivalent resonant frequency of 50 Hz for 50 µm relative-displacement amplitude. The Figure 7 shows the beam length/thickness relation that gives an equivalent resonant frequency of 50 Hz for 50 µm.

Figure 7: Beam length L in function of its thickness e to ensure freq=50 Hz at 50 µm

The length/thickness ratio that gives freq=50 Hz at 50 µm is quite high and makes the beam too soft in the vertical direction h to efficiently maintain the 1g seismic mass. In our case, to ensure a good working of the converter part, we want to limit the vertical displacement in the h direction to less than 0.1 µm when the structure is placed on the 1G gravity acceleration. But, as shown on Figure 8 representing the vertical displacement in function of the beam length keeping freq=50 Hz at 50 µm, it is impossible.

Figure 8: Vertical displacement due to the gravity in function of the beam length keeping freq=50 Hz at 50 µm

To overcome this limitation, we propose to reduce the non-linear effect. In fact, the non-linear effect is due to the beam tautness witch is negligible in low displacement. Then, to reduce the non-linear effect, we propose to limit this tautness by introducing a spring that act in serial with the beam elasticity in its length direction. We name α the ratio between the additional spring constant and the beam spring constant in its length direction. By assuming a vertical displacement lower than 0.1 µm and an

equivalent resonant frequency of 50 Hz at 50 µm, we find an α value of 0.16, a beam length L of 2097 µm and a beam thickness e of 9.88 µm (see Figure 9). 903 µm 2097 µm

61 µm

250 µm

Additional spring (α parameter)

9.9 µm 15 µm

Mechanical anchor 4000 µm Beam that acts as a non-linear spring

150 µm

m=1g 8*9 mm²

10 mm 325 µm

150 µm 10 mm

Figure 9: Mechanical structure design

Starting from the same resonant frequency as on the Figure 6, the Figure 10 shows that, by introducing the α parameter, the resonant frequency increases more slowly with the displacement amplitude. freqα(zref)

Figure 10: Equivalent resonant frequency in function of the relative displacement amplitude including the α parameter

The Figure 11 presents the relative displacement amplitude response in function of the input normalized vibration frequency and for different acceleration level. Its shows that the relative displacement is quite constant until the small displacement resonant frequency f0 and then it is amplified on more or less one frequency decade depending of the acceleration level.

Figure 11 : Relative displacement amplitude in function of the normalized input vibration frequency and for different input acceleration level

The result corresponds to our objective to make the relative displacement quite constant even if the input vibration amplitude decreases with the frequency, the system amplifying the higher frequency vibration on around one decade. Let’s now go to the converter part that converts the available input energy in electrical energy. 3

Electrets based electrostatic converter

3.1 Electrets definition Electrets are, in electrostatics, the equivalent to magnets in magnetostatics. They are based on dielectrics able to keep an electric field through time thanks to charge trapping (Figure 12). Electrets can be obtained from different ways but the easiest way is the corona discharge. The principle of Corona discharge is to create ions thanks to a high voltage and a point effect (see Figure 13). A grid is used to control the surface voltage of the sample during its charging.

Figure 12: electret (surface charges on a dielectric film)

Figure 13: Corona discharge

3.2 Global system Actually, the global system is composed of two wafers in front of each other. Electrodes and electrets are on the upper wafer and counter-electrodes are on the upper wafer. When a vibration occurs, the upper plate moves respectively to the lower one thanks to springs (see part 2). This generates a variation of the electret charge influence in electrodes and a charge circulation if the electrodes are connected to a load.

Side view

Non linear spring and guidance

Reported seismic mass

m (1g)

Packaging

500 µm Glue and spacer to obtain a 1 µm gap

Insulator

Wire ≤ 50 Ω ≤ 25 pF

Etching ≥ 10 GΩ

Electroded surfaces

1 µm protective layer

electret

Figure 14 : structure design

3.3 Sizing of the structure By using Comsol Multiphysics to compute the capacitance of the system and Simulink to simulate the global system, the geometry of the system has been optimized. It has been proven that to get the maximum output power, the electret

should be taken as thin as possible (typically 500 nm). By choosing a gap of 5 µm for technical reason, we can deduce that to maximize the power density, the bump width must be around 40 µm and the distance between bumps must be around 60 µm. 3.4 Electrets material choice and characterization We chose to use SiO2 as electret dielectric material because it can keep a large charge (up to 10mC/m²) on thin layers (< 500 nm). After different measurements and treatments we show that with a good heat treatment and by using a judicious protective layer, up to 97% of the initial charge can be kept after more than 100 days on thermal SiO2 electrets (surface voltage of 100 V). These results were obtained on a full wafer, we actually work to reach the same results on structured electrodes but only 10 V of charge surface are sufficient to convert the available mechanical power for our structure size.

SiO2+Si3N4 Al

Fabrication results

Figure 15: Electret structure on silicon wafer

3.5 Expectable energy We show that up to 15 µW can be harvested from ambient vibrations (50µmpp@50Hz) and the main limitation doesn’t come any more from the converter part but from the available mechanical power. 4

Conclusions Starting from the real vibration that occurs in a car, we estimated the available power in function of the system resonant frequency and in function of the electrical damping and we showed that in the best case the available power is around 15 µW. We estimated the associated relative displacement amplitude and showed that in order to limit this one it is interesting to have a high electrical damping and to use a non linear spring. Finally we designed and did some measurements on electret materials and showed that only 10% of full electret voltage capability is sufficient to convert all the available power. References [1] “A study of low level vibrations as a power source for wireless sensor nodes”, S. Roundy, P. K. Wright and J. Rabaey, Computer Communications, vol. 26, 2003. [2] “Integrated power harvesting system including a MEMS generator and a power management circuit”, M. Marzencki, Y. Ammar, S. Basrour, The 14th International Conférence on Solid-State Sensors, Lyon, France, June 10-14, 2007, pp 863-872 [3] “Energy harvesting MEMS device based on thin film piezoelectric cantilevers”, W.J. Choi, Y. Jeon, J.-H. Jeong, R. Sood, S.G. Kim, Jnal of Electroceramics, 2006. [5] Paul D. Mitcheson, Tim C. Green, Eric M. Yeatman, Andrew S. Holmes, “Architectures for Vibration-Driven Micropower Generators”, Journal of microelectromechanical systems, vol. 13, No. 3, JUNE 2004, pp. 429-440. [6] C. B. Williams and R.B Yates, "Analysis of a micro-electric generator for microsystems", Proceedings of the Transducers 95/Eurosensors IX, 369-372, 1995.