International Conference on Computer and Communication Engineering (ICCCE 2010), 11-13 May 2010, Kuala Lumpur, Malaysia

978-1-4244-6235-3/10/$26.00 ©2010 IEEE

Theoretical Modeling and Simulation of MEMS Piezoelectric Energy Harvester

Aliza Aini Md Ralib, Anis Nurashikin Nordin Department of Electrical and Computer Engineering

Kulliyyah of Engineering International Islamic University Malaysia

aliza.aini@gmail.com anis.nordin@gmail.com

Hanim Salleh Department of Mechanical Engineering

College of Engineering Universiti Tenaga Nasional Malaysia

hanim@uniten.edu.my

Abstract— Energy harvesting devices, capable of converting wasted ambient energy to electrical power are rapidly gaining popularity as a source of green and renewable energy. This work presents the design and simulation of MEMS based piezoelectric cantilever beam which can both harvest energy as well as monitor critical vibration frequencies in power plant gas turbines. The design of the energy harvesters consists of a cantilever beam structure with the interdigitated electrodes on the zinc oxide piezoelectric layer with nickel proof mass at the end of the beam. A mechanical finite element simulation was conducted using CoventorWare©. This paper illustrates the proposed theoretical modeling and simulation of piezoelectric energy harvesters.

Keywords: piezoelectric, energy harvesting, cantilever beam.

I. INTRODUCTION Wireless sensor networks have gained tremendous attention

and popularity in commercial applications. A critical issue today is how to power these ubiquitous wireless sensor networks. The conventional batteries have become impractical due to their limited lifetimes, expensive replacement cost and the depleting source of lead. Energy harvesting provides the most promising solution, whereby wasted ambient energy such as light and vibration can be converted to useful electrical power and becoming an attractive alternative to the conventional battery. The increasing interest in piezoelectric devices can be seen in the proliferation of recently designed energy harvesting devices. One such MEMS device is a thin film piezoelectric power generator which employs the d33 mode (longitudinal effect) and has resonant frequency of 13.9 kHz with measured output performance of 1μW [2]. Another prototype of piezoelectric cantilever is capable of generating 270nW when operating at the resonance frequency of 229Hz [3]. To improve the power output and to provide frequency flexibility, an array of MEMS piezoelectric power generation has been designed. This device array has measured performance of 3.98μW effective electrical power and 3.93 volts DC output voltages with bandwidth of 226 – 234Hz [4].

There are five main components of fabrication on MEMS piezoelectric micro generator that is thin film composition and

deposition technique, device design, fabrication process, electrical connections and packaging [5]. The main focus is to design a piezoelectric energy harvester that is able to harvest mechanical energy (mechanical vibrations) as electrical energy. The energy harvesters will generate power at the critical vibration to activate the condition monitoring sensor meant for maintenance and condition monitoring.

This paper emphasizes on the design and simulation of a piezoelectric energy harvesting device used to power a wireless sensor for condition monitoring at power plants. The prototype consists of a cantilever beam structure with interdigitated electrodes on top of the piezoelectric layer. The piezoelectric material used is zinc oxide (ZnO). The proof mass made from nickel is attached at the tip of the beam. The device is designed to operate at the resonance frequency to get maximum electrical power output.

This paper is organized as follows. Section II explains on the piezoelectric principle and design of the energy harvesters. Section III presents the theoretical modeling of piezoelectric energy harvester. Section IV presents the simulation, results and the discussion. Finally, the conclusion is given in Section IV.

II. PIEZOELECTRIC PRINCIPLE AND DESIGN

A. Basic Design Configuration Piezoelectric material deforms in the presence of electric

field and vice-versa, it produces electrical charge when mechanically deformed [6].The piezoelectric constitutive equations is defined as follows:

(1)

(2) Where

= mechanical strain (μm/μm) = mechanical stress (μN/μm2)

Y = modulus of elasticity (Young Modulus) (μm2/μN) d = piezoelectric strain coefficient

E= electric field D= electrical displacement (charge density)

= dielectric constant Piezoelectric material selection is based on coupling

coefficient (k) which indicates the material’s ability to convert mechanical energy to electrical energy or vice versa as shown in Equation 3.

(3)

Materials which have larger coupling coefficients have higher energy conversion efficiency [6].The modulus of elasticity (Y) affects the stiffness of the bender. While, a high dielectric constant ( ) lowers the source impedance and is preferable for energy harvesters.

B. Device structure The cantilever structure with proof mass at the end has

been identified as the most suitable structure for maximum energy conversion design [5]. Researchers have extensively applied this configuration for piezoelectric energy harvesting device. The source of vibration is shown with an arrow as shown in Fig. 1 [5]. The natural frequency of spring mass system, ωn can be written as in Equation 5.

(5) The model of the power output of the system at resonance is where m is the seismic mass, Y is the amplitude vibration ω is the system resonance frequency and ζ is the relative damping ratio.

(6)

From Equation 6, the output power is directly proportional to mass which means that the converter size directly impacts the power output produced. Power is inversely proportional to the damping ratio, which is directly related to selection of materials and design. Output power of the system will be optimized if the piezoelectric system is operating at the resonance frequency [5].

Fig 1. Cantilever beam with tip mass [5]

Mechanical electrical

Fig 2. Circuit representation of piezoelectric cantilever beam

Fig 3. Operating modes of piezoelectric transducer [5]

C. Circuit Representation of Piezoelectric An analytical model can be developed based on Equation 1

and 2. One of the methods is to model both mechanical and electrical portions of the piezoelectric system as circuit elements as shown in Figure 2.

D. Operating mode of piezoelectric conversion With reference to the Fig. 3, two frequent modes that are

applied for energy harvesting devices are d33 mode (longitudinal effect) and d31 mode (transversal effect) [5]. In d31 mode, the stress is applied in axial direction but the voltage is obtained in perpendicular direction. In contrast, for d33

mode, the applied stress has the same direction as the generated voltage [5]. The d31 mode has separate top and bottom electrodes while the d33 mode employs only the interdigitated top electrode [1].

III. THEORETICAL MODELING OF PIEZOELECTRIC ENERGY HARVESTER

In Coventorware© simulation, there are two types of dielectric properties needed for piezoelectric analysis:

A. Piezoelectric Strain (strain charge constitutive relation) The constants are in C/N and the coupling matrix would be

d as shown in Equation 7 and 8. Equation 7 and 8 are the matrix representation of Equation 1 and 2 respectively.

(7)

(8)

Where [ε] = strain matrix [σ] = stress matrix [E]= electric field vector [d]= piezoelectric strain coupling matrix (coefficient) [e]= piezoelectric stress coupling matrix

= material compliance matrix when E=0

= dielectric constant matrix when there is no stress

B. Piezoelectric Stress (stress-charge constitutive relation). The constants are in C/m2 (which translates into C/m2

=pC/μm2 in CoventorWare© units and the coupling matrix would be e [9] as shown in Equation 9 and 10.

(9)

(10) Where [e] = PZE stress coupling matrix

= material stiffness matrix when E=0

= dielectric constant matrix when there is no strain. The relationship between PZE strain coupling matrix and PZE stress coupling matrix is given in Equation 11.

(11) The right side of Equation 7 and 9 are governed by the user specified material stress strain constitutive relationship as shown below. The second part is governed by piezoelectric coefficients [9].

C. Elastic Constant The elastic constant material property specifies linear elastic behavior. Elastic constant relationship between stress and strain is shown as below [9].

(12) Where [σ] = stress matrix [ε] = strain matrix [D]= stiffness matrix For zinc oxide, the elastic constant is shown as below

D. Piezoelectric strain coupling matrix coefficient, [d] Piezoelectric material gives the coefficient for the strain charge form as shown in Equation 13. The equation is in the form of matrix.

S = d t • E (13) Where S= strain matrix dt = piezoelectric strain coupling matrix (coefficient) E=electric field

(15) Where [ε] = strain matrix [d]t=PZE strain coupling matrix ( coefficient) [E]= electric field vector For zinc oxide the piezoelectric strain coefficient matrix is shown as below

(17) The Dielectric entries shown are relative values to vacuum permittivity ε0 = 8.85 x 10-12 c/(v·m) [9].

IV. SIMULATION MODELING OF PIEZOELECTRIC ENERGY HARVESTER

The prototype cantilever structure consists of four layers namely: Si/ PZT/Pt interdigitated electrodes / Ni proof mass. It will be fabricated using four photo mask steps. Silicon acts as the substrate for controlling the bow of the structure. BPSG acts as the sacrificial layer. The chosen piezoelectric layer is Zinc oxide (ZnO) while top intedigitated electrode was deposited on top of zinc oxide piezoelectric layer. An optional proof mass was deposited and patterned. Finally, the sacrificial layer was released to have a free standing structure of the cantilever beam. The fabrication steps are shown in Figure 5. Top view 2D layout was designed as shown in Figure 6. The size of the cantilever beam is 23μm x 71 μm with thickness 37 μm. 3D view of piezoelectric cantilever beam was shown in Figure 7.

TABLE I. FABRICATION STEPS OF PIEZOELECTRIC ENERGY HARVESTER

Nu. Step Name Action Layer name Material Name

Thickness Mask Name

Photoresist

0 Substrate Substrate Substrate SILICON 20 GND 1 Planar Fill Planar Fill Sacrifice BPSG 10 2 Straight Cut Straight Cut Sacrifice + 3 Conformal Shell Conformal Shell Piezo ZnO 5 4 Straight Cut Straight Cut PZT + 5 Conformal Shell Conformal Shell IDT PLATINUM 4 6 Straight Cut Straight Cut IDT + 7 Delete Delete BPSG 8 Conformal Shell Conformal Shell Proofmass NICKEL 8 9 Straight Cut Straight Cut mass +

Fig.6 Top view of piezoelectric cantilever beam for energy harvesting

The aim of the simulation analysis is to simulate the resonance frequency since the resonance frequency provides has the maximum displacement of vibration and therefore maximum output will be produced. A mechanical finite element simulation was conducted using CoventorWare©.

The model must now be meshed so the geometry of the structure can be reduced to a group of simpler finite element bricks and presented to the solver for finite element analysis [9] as shown in Fig. 7. Manhattan Bricks is used for meshing because the structure have Manhattan geometry.

Fig. 7 3D view of piezoelectric cantilever beam for energy harvesting

A. Harmonic piezoelectric analysis simulation

Harmonic analysis computes a displacement solution based on a user range of input harmonic frequencies to find the best resonance frequency which has maximum displacement. Figure 8 shows the graph for displacement versus frequency applied. The graph shows the expected sharp change in displacement as the frequency approaches the Mode 1 value that is 55MHz which shows the highest displacement.

B. Mechanical Modal Analysis Simulation Based on harmonic piezoelectric analysis simulation result, mechanical modal analysis was done by placing 24 Pa pressure at the end of the cantilever beam. The result shows that the highest displacement occurs at z direction as shown in Figure 9. Mode 1 again provides the highest displacement with frequency of 53.7 MHz as shown in Figure 10.

Fig. 8 Graph for displacement vs Frequency for piezoelectric

harmonic analysis

Fig. 9 Result for mechanical modal analysis

Fig. 10 Result for mechanical modal analysis

CONCLUSIONS

We presented in this paper the mechanical finite element simulation of a novel MEMS piezoelectric energy harvesters focusing on low frequencies. Cantilever structure with proof mass at the end has been identified as the most suitable structure for maximum energy conversion design. Zinc oxide was chosen as piezoelectric layer. A nickel proof mass was attached at the end of the beam to obtain maximum power output. This design can be categorized as operating in the d33 mode (longitudinal effect) since only the top Pt interdigitated electrode was utilized. Simulation analysis was done to simulate the resonance frequency since the

resonance frequency provides has the maximum displacement of vibration and therefore maximum output will be produced. From the modal mechanical analysis, the fundamental mode 1 provides the highest displacement with frequency of 53.7MHz.This work presents the design and simulation of MEMS based piezoelectric energy harvester.

ACKNOWLEDGMENT The research was supported by the R&D grant from

Tenaga Nasional Berhad Malaysia and collaboration between Universiti Tenaga Nasional Malaysia and International Islamic University Malaysia.

REFERENCES

[1] Paradiso, J. A. and Starner, T. (2005) “Energy Scavenging for mobile

and wireless electronics. Pervasive Computing.” IEEE CS and IEEE ComSoc. Volume 4, Issue 1:18-27 .January 2005.

[2] W.J. Choi · Y. Jeon · J.-H. Jeong · R. Sood · S.G. Kim (2006) “Energy Harvesting MEMS device based on thin film piezoelectric cantilevers”, Electroceramics Journal 2006, Volume 17, Numbers 2-4, December 2006.

[3] Kok, Swee L. White, Neil M. Harris, Nick R. (2008) “A Free Standing Thick Film Piezoelectric Energy Harvester”, IEEE Sensors 2008 Conference.

[4] Jing-Quan Liu, Hua-Bin Fang, Zheng-Yi Xu, Xin-Hui Mao, Xiu-Cheng Shen, Di Chen, Hang Liao and Bing-Chu Cai, (2008) “A MEMS-based piezoelectric power generator array for vibration energy harvesting “, Microelectronics Journal 2008 (p. 802-806).

[5] Priya, Shashank, Inman, Daniel J. (2009). Energy Harvesting Technologies.

[6] Shad Roundy, Jan M.Rabaey and Paul Kenneth Wright (2003). Energy Scavenging for Wireless Sensor Networks. Kluwer Academic Publishers.

[7] B. S. Lee, W. J. Wu, W. P.Shih, d.Vasic and F.Costa (2007) “Power harvesting using piezoelectric MEMS generator with interdigital electrodes”, IEEE Ultrasonics Symposium 2007.

[8] Hua Bin Fang, Jing- Quan Liu, Zheng- Yi Xu, Lu Dong, Li Wang, Di Chen, Bing-Chu Cai, Yue Liu (2006) “Fabrication and performance of MEMS based piezoelectric power generator for vibration energy harvesting”, Microelectronics Journal 2006 (p.1280 – 1284).

[9] Coventerware Version 2006. MEMS Design and Analysis Tutorials, Volume 1