# Simulation, mathematical modeling, fabrication and experimental analysis of piezoelectric acoustic sensor for energy harvesting applications

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## Abstract

In this paper, an acoustic sensor having ZnO based circular diaphragm sandwiched between two aluminum electrodes as the key element that can find applications in energy harvesting from acoustic sources has been designed, modeled, simulated, fabricated and tested. The ZnO layer is RF sputtered on Silicon substrate and a cavity has been formed by back etching the substrate. The dimensions of the structure are chosen such that the natural frequency of the structure closely matches with that of source frequency to get maximum output voltage due to resonance. The structure is mathematically modeled by Lumped Element Model method and simulated with Finite Element Model method. The experimental results indicate approximately 40 mV output voltage (Open circuit) at 140 db and the natural frequency in the range 11–12 kHz which is in close approximation with the results in mathematical model and simulated structure.

## 1 Introduction

The increase in demand of self-sustaining low power electronic devices has accelerated the demand for energy harvesting from locally available sources. The micro energy harvesting devices using vibration signal, acoustic signal, etc., can replace the conventional batteries as they have limitation due to limited lifetime and hazardous chemicals. Different methods of energy harvesting along with the concept, methodology of implementation have been published making the relevance of focused research in this field (Choi et al. 2019). Energy harvesting from acoustic sources through piezoelectric transduction can be a good alternative for self-sustaining of very low power devices. The acoustic sources available abundantly in nature make this method more adaptable. The miniaturization of the acoustic sensors makes it portable and compact as they can be easily embedded inside the application. Their natural frequency can be matched with different frequency ranges to get maximum displacement due to resonance. This implementation is supported by very well-established MEMS fabrication processes (Choi et al. 2019).

Energy harvesting by acoustic or vibration sources can be efficiently done by piezoelectric materials because of their scalability, repeatability and ease of integration with CMOs technology. Scaling down of the devices is preferred (Li et al. 2016).

Further, the selection of the suitable material for fabrication is done by Ash by approach with the value of figure of merit (Pratap and Arunkumar 2007). For biomedical applications and also for the applications having environmental concerns, piezoelectric materials like ZnO, AlN and lead free materials are preferred over Lead Zirconate Titanate (PZT) (Li et al. 2016). This selection also justifies the clean room compatibility during fabrication.

Sound pressure level (SPL) of various sound sources

Sound energy source | Sound pressure level (db) |
---|---|

Jet engine at 1 m | 150 |

Stun grenade | 158–172 |

Simple open ended thermoacoustic device | 176 |

Car air conditioning system | 71.9 |

Inside airplane | 86 |

Auditory threshold at 1 kHz | 0 |

Normal conversation | 40–60 |

Threshold of pain | 130–140 |

Rustling of leaves | 20 |

Quiet room | 40 |

Sonic boom | 110 |

Traffic on a busy roadway at 10 m | 80–90 |

Jack Hammer | 100 |

The range of frequencies applied from ambient acoustic sources is harvested in Horowotz resonator has design of a micro machined piezoelectric diaphragm microphone with a circular diaphragm. The fabrication steps and ranges of operation and experimental results are discussed (Horowitz 2005; Ahmad 2006).The steel substrate based ZnO acoustic sensor was designed and tested for range of frequency and linearity in SPL range (Garg and Rajanna 2005).

The mathematical model of acoustic piezoelectric energy harvester modeled as a circular composite piezoelectric circular plate by lumped element model (LEM) for the acoustic sensor structure with cavity on Silicon substrate matched with simulated structure with simulation done by FEM tool like Ansys (Mahopatra 2011).

However, the major drawback of the acoustic energy harvester is that any small deviation in the acoustic source frequency will result into drastic reduction in the deflection of the diaphragm resulting into decreased output voltage. The ambient acoustic sources invariably have variation in frequency. The literature on broad band energy harvesting also suggested the different methods to increase the bandwidth of the designed structure (Mahopatra 2011). This work makes an attempt to simulate the better efficient acoustic sensor structure by designing and fabricating to test the output voltage and frequency response of the same. The characterization methods are discussed in (Mika 2007)

The paper is organized as follows. Section 2 discusses the theoretical aspects of piezoelectricity and basic design of the structure. Section 3 explains the simulation of the structure with shapes of diaphragm and structure with cavity. Section 4 presents mathematical model of the structure using lumped element model (LEM). Section 5 presents the fabrication steps and inline characterization of the structure. Section 6 presents the experimental results and the conclusion with future scope.

## 2 Theoretical design of piezoelectric acoustic sensor

Piezoelectricity provides the conversion interface between electrical and mechanical domains. When mechanical pressure is applied on piezoelectric materials, the electric polarization takes place resulting into accumulation of charge which results into potential difference. This phenomenon is called direct piezoelectric effect. Conversely the reverse piezoelectric effect phenomenon is exhibited when stress or strain is developed due to application of electric field (Choi et al. 2019).

Acoustic sensing and energy harvesting applications make use of direct piezoelectric effect where acoustic energy in the form of vibration of particular frequency is converted into electrical energy. The applications with more range of frequencies prefer diaphragm based structure due to inherent advantages like uniform distribution of the stress and strain across the key element, more stabilized output voltage and longer life (Choi et al. 2019). Further the circular shape of the diaphragm is preferred due to the following advantages. First one is the largest centre deflection is observed in circular diaphragm. However the stress at the edges is the least in circular diaphragm. The maximum range of unidirectional stress and strain is available for circular diaphragm. The natural frequency being one of the important factors in diaphragm design for acoustic applications, the second advantage is circular diaphragm has least value of first mode of vibration frequency (Li et al. 2016).

_{31}. The voltage generated is given by the Eq. (1).

*E*is Young’s modulus or Modulus of elasticity of the material in Pa.

*d*

_{33}is the piezoelectric charge coefficient.

*ε*

_{11}is the applied strain.

*dA*is the area of the electrodes in µm

^{2}.

*c*is the capacitance of the structure in farad.

The maximum value of deflection is obtained by designing the dimension of the sensor structure so that the natural frequency of the structure is same as the source frequency (Tang et al. 2013). The piezoelectric coefficient of the material chosen should be of highest value which depends on the material, the orientation and also the fabrication process. The material chosen should be environmental friendly so that it can find applications in biomedical devices and it should be clean room friendly so that it can be fabricated easily on silicon substrate. Thus the piezoelectric material chosen for the device key element is ZnO.

*t*is the thickness of the diaphragm in µm.

*E*is the Young’s Modulus or Modulus of elasticity of the material in Pa.

*v*is the Poison’s ratio.

*R*

_{0}is the radius of the diaphragm in µm.

*ρ*density of the material in kg/m

^{3}(Tang et al. 2013).

## 3 Structure simulation using FEM

The structure has been simulated using Comsol Multiphysics which is a finite element method (FEM) based tool. This simulation tool has been used to compare the shape and dimensions like radius, thickness of the diaphragm. The important parameters like stress, strain, displacement, natural frequency and voltage induced are analysed using the tool.

The initial simulation was done to identify the shape of the structure which gives better stress/strain and displacement and natural frequency in the range of source frequency. Further the entire structure including the sandwiched ZnO layer between aluminum electrodes deposited on the Silicon diaphragm with cavity at the back has been simulated to calculate the natural frequency and voltage generated due to application of acoustic pressure. The modal frequency analysis is also done to ensure the contribution of the modal frequencies for the displacement and voltage.

### 3.1 Diaphragm design

The diaphragm design has been studied from the point of view of shape, diameter and type of the material (Piezoelectric coefficient) of the diaphragm. For the convenience of the fabrication facility, the thickness of the diaphragm is fixed at 30 micron. The simulation study has been carried out using structural mechanics physics and stationary and Eigen frequency study.

#### 3.1.1 Diaphragm shape

- (a)
Square shape

For comparison of various shapes of the diaphragm, the side length of √*πa*has been assumed, where*a*is 3000 micron. The natural frequency, displacement, stress and strain graph is as shown in Fig. 2. - (b)
Circular shape

For the simulation of circular diaphragm, the diameter is assumed to be*2a,*where*a*is 3000 micron. The natural frequency, displacement, stress and strain graph is as shown in Fig. 3. - (c)
Rectangular shape

For simulating rectangular shaped diaphragm, the width π/2 and length 2a has been considered. The displacement, stress and strain along the length are analyzed as shown in Fig. 4.After the above analysis on the shape of the diaphragm, circular structure has been selected for fabrication due to the following reasons.- (i)
The maximum centre deflection is observed in circular diaphragm. However the stress at the edges is the least in circular diaphragm. The maximum range of unidirectional stress and strain is available for circular diaphragm. This factor greatly affects the voltage generated as the piezoelectric layer can be coated in this region to get maximum voltage.

- (ii)
Another important factor for acoustic energy harvesting is natural frequency and circular diaphragm has least value of first mode of vibration frequency (Khakpour 2010).

- (i)

#### 3.1.2 Diameter of the diaphragm

From the above simulation analysis, the size of the circular shaped silicon diaphragm with thickness 30 micron, 3000 micron radius has been decided for the acoustic range of frequency. Further due to the unidirectional stress and strain, the piezoelectric layer of thickness 1 micron and diameter 1700 micron sandwiched between two Aluminum electrode layers of thickness 300 nm and radius 1500 micron has been the decided structure for fabrication.

### 3.2 Structure design simulation

## 4 Mathematical modeling of the structure

When the dimension of the structure is a close match with the incident acoustic signal wavelength, the lumped element mathematical model can be done (in μm). In this case, the variation of energy as a function of space is very less. Mathematically, for this condition, the spatial and temporal components can be decoupled, allowing the use of ordinary differential equations for finding the solution (Horowitz 2005).

Equivalent lumped models in acoustic and electrical domains

Kinetic energy storage | Potential energy storage | Energy dissipation | |
---|---|---|---|

Acoustical | Acoustic mass (kg/m | Acoustic compliance (m | Acoustic resistance (m |

Electrical | Inductance (H) | Capacitance (F) | Resistance (Ω) |

The representation of the terms to form the lumped element equivalent network is as shown.

P_{in} is the total acoustic pressure applied on the diaphragm. P_{d} is the pressure across the other end of the diaphragm. M_{ad} is acoustic mass in kg/m^{4}. C_{ad} is acoustic compliance in m^{3}/Pa.

_{in}) from the top of the diaphragm is assumed to be equal to the pressure applied by the diaphragm in the downward direction towards the cavity and the acoustic resistance (R

_{ad}) of the channel is assumed to be negligible. The acoustic energy is stored in the acoustic mass (M

_{ad}) and the acoustic compliance (C

_{ad}) of the diaphragm. The conversion from acoustic energy to electrical energy is majorly due to the energy stored in acoustic mass and acoustic compliance of the diaphragm which converts acoustic vibration into the diaphragm deflection. The stress and strain due to the deflection of the diaphragm acts on the piezoelectric material and converts it into electric charge. Hence this conversion or transduction is represented in the form of a transduction transformer (n:1 ratio) in the LEM equivalent circuit. The equivalent circuit is as shown in Fig. 7. Further the charge which is stored in the capacitance of the sandwiched piezoelectric material between two electrodes is represented by the capacitance Cp.

_{ad}and acoustic compliance of C

_{ad}. Assuming the acoustic pressure on plate is uniform and the deflection is equal to maximum deflection at the centre, mass of the diaphragm (M

_{ad}) and acoustic compliance (C

_{ad}) are calculated as shown below.

- 1.
Mass of the diaphragm (M

_{ad}) = density × volumewhere A is the area of the diaphragm = π × r$$ = \, \rho \, \times {\text{ A }} \times {\text{ h}} $$(3)^{2}m^{2}. ρ is the density of the diaphragm = 2320 kg/m^{3}. M_{ad}= 1.967893 μ kg. - 2.
Acoustic compliance of diaphragm (C

_{ad})The calculation of acoustic compliance of diaphragm (C_{ad}) has the following steps.- (a)
Effective diameter:

The diaphragm is hinged at the periphery and the effective diameter is calculated as shown in Fig. 8.The effective diameter is the actual diameter considered for pressure application on the circular diameter. From Fig. 3, minimum stress occurs at a distance 20% of length (McAfee 2006), it is assumed that the hinge of the diaphragm at the periphery opposes the deflection and hence \( \frac{d}{6} \) is subtracted both the sides, resulting into the effective diameter to be \( \frac{2d}{3} \) as shown in Fig. 8.

From the Fig. 8,

$$ {{d^{\prime}}} = d - \frac{d}{3} = \frac{2d}{3} $$(4)Effective diameter d′ = 4000 μm

where M$$ ({\text{b}}) \, \;{\text{Moment }}\;{\text{of }}\;{\text{Inertia }}\left( {\text{I}} \right)\,{\text{I}} = \frac{1}{2}{\text{M}}_{\text{ad}} \left( {{{r^{\prime}}}} \right)^{2} $$(5)_{ad}is the Mass of the diaphragm in kg. d′ is the Effective radius in m. I = 3.957 kg m^{2}.- (c)
Flexural rigidity (D)

The flexural rigidity is calculated using (6)

where E is the Young’s modulus of elasticity for silicon = 160 × 10$$ {\text{D}} = {\text{ E }} \times {\text{ I}} $$(6)^{9}Pa. I is the Moment of Inertia in kg m^{2}D = 0.6297 N kg

Thus acoustic compliance of the diaphragm, C

_{ad}is given by (7)where A is the area of the diaphragm in m$$ {\text{C}}_{{\text{ad}}} = \frac{{{\text{A}}}}{{{\text{D}}}} $$(7)^{2}. D is the Flexural rigidity in N kg.

- (c)

- (a)
- 3.
Natural frequency of the structure

The natural frequency at which the structure resonates is given by the Eq. (8).

$$ \frac{{\text{A}}}{{\text{D}}}{\text{f}}_{{\text{o}}} = \frac{1}{{2\pi \sqrt {{\text{M}}_{{{\text{ad}}}} {\text{C}}_{{{\text{ad}}}} } }} $$(8)Substituting the values of M

_{ad}and C_{ad},$$ {\text{f}}_{0} = 1 1. 9 3 {\text{ KHz}} $$

From Fig. 7 it is clear that the pressure across diaphragm (P_{d}) is converting acoustic pressure to deflection and stress/strain. Further the piezoelectric coating is acting like transformer converting acoustic energy into electric charge electrical energy. The Equivalent circuit representation depicts this transduction between two domains, i.e. acoustic and electric as a transformer having turns ratio ‘n’.

The natural frequency of the structure calculated by lumped element modeling (LEM) method and finite element method (FEM) simulation are in good agreement. The slight disparity in natural frequency and voltage is justified from the approximations considered in the calculations and simulation.

## 5 Fabrication and packaging of piezoelectric acoustic sensor

The devices are fabricated on a 3 inch single side polished, single crystal P type < 100 > oriented silicon wafer. All the fabrication process steps are performed at National Nanofabrication Centre (NNFC), CeNSE, IISc, Bangalore under Indian Nanoelectronics Users Program (INUP).

The fabrication process flow is done in the following steps.

Step 1: Initial Si wafer cleaning (100 Orientation)

Step 2: Deposition of Silicon oxide of 1 µm thickness on Silicon wafer by thermal oxidation.

## 6 Characterization and testing of acoustic sensor

### 6.1 Characterization

_{2}layer and wafer is 330 μm. Hence back etching of unpolished side of the wafer by 300 μm resulted into the diaphragm of thickness 25 μm (approx). The d

_{33}piezoelectric coefficient of ZnO is measured using AFM. It is found to be 26 pm/V which is a close match to the values in literatures (Horowitz 2005).

### 6.2 Testing

The testing of the fabricated devices is carried out at micro nano characterization facility (MNCF) and packaging Lab, CeNSE, IISc, Bengaluru.

#### 6.2.1 DC probe station

#### 6.2.2 Microsystem analyser (MSA)

#### 6.2.3 Linearity and frequency response

Linear operation of the device is an important parameter to be tested to ensure that the performance of the device operation is linear. This property of the device is tested by NAL calibrator.

## 7 Conclusions

Piezoelectric acoustic energy harvesters form a popular method to power lower power electronic devices and make them autonomous because of their inherent advantages like ease of scaling, robustness and better power density. Simulation, mathematical modeling and characterization and testing of piezoelectric acoustic energy harvester with circular diaphragm are presented in this paper. Zinc Oxide (ZnO) has been chosen as piezoelectric material for the application due to the environmental and biomedical compatibility, no polling necessity and better piezoelectric co efficient (D_{33}).

The analysis of the diaphragm and the structure is carried out by finite element tool Comsol Multiphysics to optimize the shape and size of the diaphragm to choose the natural frequency; stress and strain plot to position the piezoelectric layer. The fabrication is done on 3 inch single side polished < 100 > P type silicon wafer. In characterization has been performed for the RF sputtered layers using DeKTak profilometer and the piezoelectric coefficient is measured using AFM. The value of D33 for the deposited ZnO layer of thickness 1 micron by the given recipe is found to be 26 pm/V. The experimental measurements are conducted by DC probe station, Micro system analyzer, NAL calibrator and by customized piezoelectric crystal speaker to analyze the equivalent circuit parameters, deflection value, and linearity and frequency response. The output voltage is linear in the acoustic frequency range and approximately 40 mV (open circuit) has been generated at 140 db. The natural frequency of the device is almost 12 kHz which in close match with the simulated value and that by mathematical modeling.

## Notes

### Acknowledgements

This research (fabrication and characterization) was performed using facilities at CeNSE, funded by Ministry of Electronics and Information Technology (MeitY), Govt. of India and located at the Indian Institute of Science, Bengaluru. The authors would like to thank faculty and staff of CeNSE, IISc, Bengaluru for the support.

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