Investigation into modelling power output for MEMS energy harvesting ...

Investigation into Modelling Power Output for MEMS Energy Harvesting Devices using COMSOL R Multiphysics l, Alan Mathewson!

Rosemary O'Keeffe!, Nathan Jackson!, Finbarr Waldron!, Mike O'Niele, Kevin McCarth 1.

Tyndall Nationallnstitute, University College Cork, Dyke Parade, Cork, Ireland 2.

3.

Analog Devices Inc. , Limerick, Ireland

Department of Electrical and Electronic Engineering, University College Cork, College Rd. , Cork, Ireland R

Abstract-A COMSOL Multiphysics model was created which

transducers produce an electric charge when mechanically

provides accurate information on the resonant frequency,

stressed. This mechanism has been widely explored in the

stress and power output of an ALN piezoelectric device.

literature because it has been proven that these transducers

The

maximum error in the resonant frequency was found to be 4%.

are smaller and lighter than electrostatic or electromagnetic

The models accurately predicted the trend of the output power

transducers.

for external impedances as well as the matched impedance for maximum

energy harvesting.

The

expected voltage

and

or electromagnetic transducers[3]. This means that

current output for Ig acceleration was also be modeled.

Keywords-energy harvesting, piezoelectric, AlN, I.

Furthermore, piezoelectric transducers exhibit

an energy density which is three times that of electrostatic piezoelectric transducers are the best choice for vibrational energy harvesting. Piezoelectric devices can also be used in

COMSOL

areas of low light intensity and areas where magnetic energy

INTRODUCTION

harvesting could interfere with the system.

Wireless Sensor Networks (WSNs) are becoming more In this paper, MEMS piezoelectric devices for energy

prevalent in our lives. These devices are often used in

harvesting have been modelled for resonant frequency and

remote and inaccessible areas and, the issue of provision of power to wireless nodes is becoming more and more

voltage output data. Modelling of MEMS devices for

important. Batteries have a limited lifespan, e. g. for a 3V

energy harvesting can be an important tool to help optimise

battery approximately 1 - 2 years of operation is possible

structural design. The devices will be used to harvest

[1] and changing batteries could become costly in many of

energy through vibration and the important factors to be

the locations that these sensors need to be deployed into.

considered are resonant frequency, power output and

Furthermore, there is also the environmental impact caused

bandwidth. A model has been created using COMSOL

by disposing of batteries. Batteries are bulky and in

Multiphysics and MATLAB which provides information on

Wireless Body Area Networks (WBANs) very strict size

the expected resonant frequency, voltage and power output

limitations are imposed on all system components and they

of MEMS piezoelectric energy harvesters.

all need to become less obtrusive to gain further acceptance.

IT.

It is therefore important to investigate alternative methods for powering WSN devices and creating autonomous sensor systems.

A. Theory

For these reasons energy harvesting is a major

Piezoelectric devices respond to an applied force by

research area particularly for wireless sensor networks.

generating an electric potential. This is an AC signal which can be used to power devices. The designs discussed here

Solar power is a well developed form of energy

are for use with in-vivo energy harvesting and so the

harvesting, but for energy to be obtained it is essential that

material choice was very important. The material needed to

the device has sufficient exposure to sunlight[2]. This is not

be biocompatible as well as piezoelectric. Another concern

always possible when dealing with WSNs because the

was that it needs to be compatible with CMOS processing

environments where these devices are employed are often in low light areas.

for incorporation into a fully integrated energy harvesting

Energy harvesting systems often require

system and it also needs to provide high conversion

small footprints so it is important that any harvesting device

efficiency because the physical device geometry is

also have a small footprint. For this reason MEMS based

significantly limited when dealing with in-vivo systems.

energy harvesting devices are of particular interest.

Most piezoelectric cantilever devices are designed for use in a vacuum, and for these devices the excitation comes from

Kinetic energy harvesting can be achieved through the

vibrations at the resonant frequency of the device. The

use of transduction mechanisms such as piezoelectric,

resonant frequency is the frequency at which the device will

electromagnetic or electrostatic [2]. Piezoelectric

978-1-4673-6139-2/13/$31.00 ©2013 IEEE

THEORY AND MODELLING

vibrate in a vacuum (undamped) which makes it an

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important factor for most piezoelectric energy harvesting

AI. The mass consists of the layers of the beam and a 1 /lm

devices.

SiOz layer and 425 /lm Si layer below the beam layers. The beam and mass width and height, as well as the layer thickness, are parameterised. This means that the model can

The internal impedance of the energy harvester is a very

be used for structures of varying width, thickness and length.

important factor. The maximum point of energy harvesting

The beam and mass dimensions were changed to obtain

is determined by the matching of the internal and external

different resonant frequencies and frequency response. The

impedance. The expected impedance is calculated by first

base of the devices, i.e. furthest point from the mass, was set

determining the capacitance created between the two plates,

as a fixed point and the rest of the device was allowed to

the Ti and Al plates, of the piezoelectric device using

move freely as shown in figure 1. The load to provide an z excitation of Ig (9.81m/s ) was applied to the tip of the mass

equation (1).

and allowed to propagate through the device to simulate the excitation experienced by the fabricated devices The

(1)

damping could be considered to be negligible due to the size of the devices. . The assumption that the damping would be

where C is the capacitance, the AIN,

cO

Cr

negligible was confirmed by comparing models which

is the relative permittivity of

included damping to those without and it was found that the

is the relative permittivity of a vacuum, A is the

resonant frequency and voltage out was the same for both

surface area of the plates and d is the thickness of the AIN.

models.

The resonant frequency (f) of the device, measured or

Mass Width

modelled, is then used to determine the impedance using equation (2).

1

2nfC

Mass Length

(2)

To calculate the the power this information is inputted into the MATLAB file along with the values of the load

Beam length

resistances used in the shaker experiments. These

Beam Width Top

resistances were chosen to determine the optimum load resistance for maximum power output. The values vary from device to device and these need to be inputted into the MATLAB file for each of the current set of device geometries. This was done as the measurements were taken previous to the model being created so the values used in the measured data was known and using the same impedance values made comparison easier. The MATLAB file can be altered to use different impedance values. Tf the values are not known then a large range of resistance values with small

Anchored

step sizes can be imputted into the MATLAB file and this will give the maximum point of energy harvesting. These

Figure I: Triangular Beam showing Anchor at Base.

results were used to determine the current and the power expected from the piezoelectric devices and these were

The models were evaluated using the piezoelectric

compared to the values achieved through the measurement

devices interface which is an interface offered by COMSOL.

data obtained from the physical devices. To extract

This is interface provides the voltage output from the devices

maximum power from these energy harvesting devices the

when they are stressed. This information is then used with

load impedance needs to be matched to the internal

MATLAB via LiveLink to calculate the output power. The

impedance of the device.

model is very complex due to the large number of thin layers and so can take a long time to solve. To reduce the time to solve an eigenfrequency study can be used. The

B. Modelling of Piezoelectric Structures

eigenfrequency analysis is another interface in COMSOL.

The models were created using COMSOL Multiphysics.

This interface solves the model for resonant frequency and

The structures consist of 5 layers on the beam and 7 layers

stress experienced by the device. Using the eigenfrequency

on the mass of the structure. The piezoelectric element is

analysis the models can be reduced to purely silicon devices.

aluminium nitride (AIN) and the metal layers are titanium

The resonant frequency is a good metric for determining if

(Ti) and aluminium (AI). The beam is 50/lm silicon (Si),

the models are accurate compared to the fabricated devices

l/lm silicon dioxide (SiOz), 200nm Ti, 500nm AIN and I /lm

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but for information on the power output then more complex

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models using the piezoelectric interface most be used. The

120

models were checked for accuracy using the eigenfrequency study.

100

The models are then updated so that the piezoelectric

...

::c

study can be done. Using the piezoelectric interface requires

>. u c CIl :::s c:r CIl .. ....

the addition of all the device layers to the model. The Ti layer is set to ground and the Al layer is a floating potential. This allows for the voltage of the device to be calculated. A stationary study using the piezoelectric interfaceprovides information on the voltage. The results from these models

80 60 40

•

Measured

•

Modelled

20

were then sent to MATLAB using LiveLink from the COMSOL toolkit to calculate the power using the same resistances used for to calculate the power of the fabricated

0

devices. The shaker is excited at the resonant frequency of the devices at 1g acceleration and the output from the devices is

0

5

Devices

10

Figure 2: Comparison of Modelled and Measured Resonant

fed through a series of resisters to give varying output

Frequencies

resistance. The resulting voltage is measured and the current and power results are calculated using these measurements. m.

RESULTS

The models were created to be flexible so that different device geometries could be accounted for by updating the values in the parameters list. These results were then compared to the results from the fabricated devices and the results are shown in figure 2. What is clear from figure 1 is that the resonant frequency can be modelled very accurately using the COMSOL model alone. The maximum difference between the modelled and experimental results is 4%. This error was reduced from previous generations of models, which are discussed by Rivadeneyra et al . [4]. This reduction was achieved due to an increase in the piezoelectric constant of the fabricated material by

Figure 3: Cantilever Device

improving the deposition process. This meant that the material properties were closer to the model parameters. The measured frequencies for the fabricated devices were obtained through the use of laser Doppler Vibrometer (LDV). Tn these experiments a periodic chirp was used to sweep through the frequencies and excite the devices at the resonant frequency. Cantilever displacement was then measured by the laser and the resonant frequency was obtained.

Figure 4: Triangular Beam Device

The cantilever devices, an example of which shown in figure 3, have the same beam width throughout the length. The results for this cantilever device family are shown for 2 wafers, known here as wafer 2 and 3. Three wafers were fabricated; however there was a difference in the film

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quality of wafer Idue to issues with the fabrication

Cantilever Wafer 3

processes. The measured harvestable energy was less than expected as the piezoelectric constant was reduced. This

0.6 0.5 0.4 §' 0.3 ";:' 0.2 ;: 0.1 rf 0

problem was corrected for the second and third wafer batches but due to the fabrication issues the results for wafer 1 are not shown here. Figure 4 shows the triangular beam. This was only fabricated on 1 wafer and the results are shown in figure 6. To update the model to compensate for

1--1-'----

�Measured Data

__----------

-COMSOL

:::s

the change in the beam width over its length, the width at

CII

the base and the tip of the beam were parameterised. This means that the beam is stiffer due to the extra width at the

500000

o

base and also there is a wider surface area for energy harvesting. This means that the energy harvested is

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Resistance (Ohms)

approximately the same for both device families because the stress is lower but the area is larger in the triangular device.

Figure 6: Power Measurement for Cantilever Device Wafer 3

. The results from the cantilever and the triangle beam devices are shown in figures 5 to 7 confirm this assertion

Triangular Beam

Figures 5 to 7 show the power results for the measured

0.7 0.6 §'0.5 .,2.0.4 ; 0.3 rf 0.2 0.1

and modelled devices. The important things to note here are the trend of the results and the point of maximum power. What is evident in all 3 figures is that the measured and modelled results follow the same trend. The resistance

�COMSOL

..

value for maximum energy harvesting is also accurately predicted in all 3 cases. These results show that the models give a good approximation of the expected output results for the devices.

� o

500000

-

Measured Data

1000000

Resistance (Ohms)

Cantilever Wafer 2 0.5 0.4 §' .,2.0.3 ;: 0.2 0.1

��_............

__

o

Figure 7: Power Measurement for Triangular Beam Device

The voltage output from the models was used to determine the current and the power achievable from a

�Measured Data

.. CII o

given device geometry. The voltage was obtained from the stationary study and was modelled to provide the expected voltage from the physical devices. The modelled voltage

CI.

for the cantilever devices was found to be 1. 59V and the

o o

measured voltages were 1.7V and 1.74V respectively. The

2000000 4000000 6000000

difference in the voltage was due to the quality of the AIN

Resistance (Ohms)

deposition. These results show that the model can provide good information on the voltage, however to improve this result a time dependent solution should be completed. This

Figure 5: Power Measurement for Cantilever Device Wafer 2

increases the time to solve significantly and, as is seen from the power results, accurate results can be obtained without this increase in complexity. The results describing current generated are shown in figure 8. Due to the smaller voltage result the result for current is also smaller than expected compared to the measured results. However the trend of the results was accurately modelled and if the time dependent study was used instead of a stationary study, the results describing current would also be increased. The results shown here are for the current created in the cantilever device and this is compared to the current for wafer 2 of the fabricated

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cantilever device. This is a good measure of the accuracy of the models.

Current Measurements 6.00E-Ol 5.00E-Ol � 4.00E-Ol �� COMSOL i 3.00E-Ol 5 2.00E-Ol 1.00E-Ol �----=����..�- Measured Data O.OOE+OO o 500000 1000000 :::s -

__________

..

C,,)

Resistance (Ohms) Figure 2: Current Measurements

IV.

CONCLUSIONS

It has been shown that accurate models for piezoelectric energy harvesters can be created using COMSOL multiphysics and the results used to develop better devices for future generations of device.

The results

show that the resonant frequency, power output, voltage output, current output trend, and optimum load impedance for maximum power output can be modelled using COMSOL multiphysics and MATLAB through LiveLink. These results were compared to results achieved through testing of fabricated devices via LDV and magnetic shaker experiments. This is very promising for future MEMS modelling as it shows that device viability can be confirmed prior to fabrication. The simulation results were compared to fabricated devices tested on a vibrational shaker and it was found that the COMSOL models could accurately predict the power output of the devices. The resulting models gave accurate information on the resonant frequency, the voltage and the power available from devices with varying geometries as well as Si thicknesses. Future enhancements to the model would also allow for optimisation of the impedance by varying the thickness of the piezomaterial and the size of the metal layers. These models could then be used to design energy harvesters which provide maximum power density and operate at the desired resonant frequencies or with a broad Q-factor. V.

ACKNOWLEDGEMENT

This work was funded by the Collaborative Centre for Applied Nanotechnology (CCAN) as part of the Government's Strategy for Science Technology and Innovation through Enterprise Ireland and the International Centre for Graduate Education in Micro- and Nano­ Engineering (TCGEE).

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VI. l.

REFERENCES

Chen, Y.-Y., et aI. , Self-powered Piezoelectric Energy Harvesting Device using Velocity control Synchronized Switching Technique, in IECON 2010 36th Annual Conference on IEEE Industrial Electronics Society 2010, IEEE Conferences: -

Phoenix, Arizona, USA. p. 1785-1790. 2.

Beeby, S. P. , MJ. Tudor, and N. M. White, Energy

Harvesting Vibration Sources for Microsystems Applications. Science and Measurement Technology, 2006. 17(12): p. 175-195. 3.

Priya, S. , Advances in Energy Harvesting using

Low Profile Piezoelectric Transducers. Journal of Electroceramics, 2007. 19(1): p. 167-184. 4.

Rivadeneyra, A. , et al. Frequency response variants of a cantilever beam. in The International Conference on Synthesis, Modeling, Analysis and Simulation Methods and Applications to Circuit Design. 2012. Seville, Spain.

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