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

  • Vasudha HegdeEmail author
  • Siva S. Yellampalli
  • H. M. Ravikumar
Open Access
Technical Paper
  • 53 Downloads

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.

The range of the frequency from the day to day application is as listed in Table 1. From the table it is clear that the SPL that can be targeted are in the range 70–140 db. It has been also mentioned that the operating in resonant frequency can also damp the noise pollution (Choi et al. 2019).
Table 1

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).

The important parameters of energy harvesting in order to get maximum output voltage are maximum deflection, optimized value of stress/strain and maximum value of piezoelectric coefficient d31. The voltage generated is given by the Eq. (1).
$$ V = \frac{{Ed_{33} \varepsilon_{11} dA}}{c} $$
(1)
where E is Young’s modulus or Modulus of elasticity of the material in Pa. d33 is the piezoelectric charge coefficient. ε11 is the applied strain. dA is the area of the electrodes in µm2. 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.

Thus the structure designed has a silicon circular diaphragm on which ZnO layer is sandwiched between two Aluminium electrodes is positioned. The Silicon diaphragm converts the acoustic pressure into the mechanical parameters like deflection, stress and strain. Further, ZnO layer converts the deflection into charge which is collected by the electrodes as voltage. The physical dimensions of the silicon diaphragm and the ZnO layer decide the natural frequency of the sensor as represented in (2).
$$ f = \frac{0.469t}{{R_{0}^{2} }}\sqrt {\frac{E}{{\rho (1 - v^{2} )}}} $$
(2)
where 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. R0 is the radius of the diaphragm in µm. ρ density of the material in kg/m3 (Tang et al. 2013).
Acoustic pressure is applied from the bottom of the structure and in order to stabilise the applied pressure, a cavity is formed at the bottom of the structure. The structural design of the acoustic sensor is as shown in Fig. 1.
Fig. 1

Schematic view of the device. a Cut section of layers with dimensions, b Top view of the device with contact pad

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

  1. (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.
    Fig. 2

    Simulated square shaped diaphragm a natural frequency, b displacement, c stress, d strain

     
  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.
    Fig. 3

    Simulated circular shaped diaphragm, a natural frequency, b displacement, c stress, d Strain

     
  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.
    Fig. 4

    Simulated rectangular shaped diaphragm, a natural frequency, b displacement, c stress, d strain

    After the above analysis on the shape of the diaphragm, circular structure has been selected for fabrication due to the following reasons.
    1. (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.

       
    2. (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).

       
     

3.1.2 Diameter of the diaphragm

The simulation of the circular diaphragm of thickness 30 micron is considered for simulation under structural mechanics physics and Eigen frequency study. It is found from the simulation as shown in Fig. 5 that 3000 micron radius gives the frequency in the acoustic range 10.809 kHz. The diaphragm of radius 4000 micron is not considered due to fabrication difficulty which may result into stiction during back etching.
Fig. 5

Simulated Eigen frequency study of circular diaphragm with radius, a 500 micron, b 1000 micron, c 2000 micron, d 3000 micron, e 4000 micron

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

The structure has the cavity formed at the back of the diaphragm and the cavity has a hole of 1500 micron diameter to stabilize the acoustic pressure applied. The structure is simulated using Structural mechanics physics and Eigen frequency study. The simulated structure, frequency response with two modal frequencies and displacement of the diaphragm at second modal frequency is as shown in Fig. 6. From the simulation of the structure, it is clear that the first natural frequency of the structure is occurring at 11,076 Hz.
Fig. 6

Comsol simulation of the structure, a Eigen frequency of entire structure with cavity, b frequency response with two modal frequencies, c displacement at second modal frequency

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).

The analogous terms in the acoustic domain and electric domain used to represent the system is as shown in Table 2. When the equivalent circuit representation is done, application of analysis techniques like Kirchoff’s laws can be carried out for further analysis (Horowitz 2005).
Table 2

Equivalent lumped models in acoustic and electrical domains

 

Kinetic energy storage

Potential energy storage

Energy dissipation

Acoustical

Acoustic mass (kg/m4)

Acoustic compliance (m3/Pa)

Acoustic resistance (m4 S)

Electrical

Inductance (H)

Capacitance (F)

Resistance (Ω)

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

Pin is the total acoustic pressure applied on the diaphragm. Pd is the pressure across the other end of the diaphragm. Mad is acoustic mass in kg/m4. Cad is acoustic compliance in m3/Pa.

For the acoustic structure as shown in Fig. 1, the lumped element model has been derived as shown in Fig. 7. The applied acoustic pressure (Pin) 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 (Rad) of the channel is assumed to be negligible. The acoustic energy is stored in the acoustic mass (Mad) and the acoustic compliance (Cad) 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.
Fig. 7

Lumped element model of acoustic sensor

In order to evaluate the equivalent circuit parameters of Fig. 6 and natural frequency of the represented acoustic structure, the diaphragm is assumed to be circular plate attached to a piston and having mass Mad and acoustic compliance of Cad. Assuming the acoustic pressure on plate is uniform and the deflection is equal to maximum deflection at the centre, mass of the diaphragm (Mad) and acoustic compliance (Cad) are calculated as shown below.
  1. 1.

    Mass of the diaphragm (Mad) = density × volume

    $$ = \, \rho \, \times {\text{ A }} \times {\text{ h}} $$
    (3)
    where A is the area of the diaphragm = π × r2 m2. ρ is the density of the diaphragm = 2320 kg/m3. Mad = 1.967893 μ kg.
     
  2. 2.

    Acoustic compliance of diaphragm (Cad)

    The calculation of acoustic compliance of diaphragm (Cad) has the following steps.
    1. (a)

      Effective diameter:

      The diaphragm is hinged at the periphery and the effective diameter is calculated as shown in Fig. 8.
      Fig. 8

      Calculation of effective diameter

      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

      $$ ({\text{b}}) \, \;{\text{Moment }}\;{\text{of }}\;{\text{Inertia }}\left( {\text{I}} \right)\,{\text{I}} = \frac{1}{2}{\text{M}}_{\text{ad}} \left( {{{r^{\prime}}}} \right)^{2} $$
      (5)
      where Mad is the Mass of the diaphragm in kg. d′ is the Effective radius in m. I = 3.957 kg m2.
      1. (c)

        Flexural rigidity (D)

        The flexural rigidity is calculated using (6)

        $$ {\text{D}} = {\text{ E }} \times {\text{ I}} $$
        (6)
        where E is the Young’s modulus of elasticity for silicon = 160 × 109 Pa. I is the Moment of Inertia in kg m2

        D = 0.6297 N kg

        Thus acoustic compliance of the diaphragm, Cad is given by (7)

        $$ {\text{C}}_{{\text{ad}}} = \frac{{{\text{A}}}}{{{\text{D}}}} $$
        (7)
        where A is the area of the diaphragm in m2. D is the Flexural rigidity in N kg.
         
       
     
  3. 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 Mad and Cad,

    $$ {\text{f}}_{0} = 1 1. 9 3 {\text{ KHz}} $$
     

From Fig. 7 it is clear that the pressure across diaphragm (Pd) 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 GDS-II file is generated using CleWin tool. The final design is as shown in Fig. 9.
Fig. 9

The GDS of final layout design of sample with demarcation lines for dicing

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.

Step 3: Deposition of Aluminum layer as bottom electrode on Silicon Oxide of 0.3 µm thickness and 1500 µm radius by RF sputtering. The structure after deposition of Silicon oxide and Aluminum layer is as shown in Fig. 10.
Fig. 10

The structure after Silicon oxide and bottom layer aluminum deposition

Step 4: Deposition of key layer ZnO piezoelectric material of 1 µm thickness and 1700 µm Radius by Sputtering. The structure is as shown in Fig. 11.
Fig. 11

The structure after deposition of ZnO layer

Step 5: Deposition of Aluminium Film layer as top electrode of 0.3 µm thickness and 1500 µm radius by RF sputtering by RF sputtering. Figure 12 shows the structure after top aluminium electrode deposition.
Fig. 12

The structure after top layer aluminum deposition

Step 6: Formation of diaphragm of thickness 30 µm and radius 3000 µm by back etching of the substrate by Deep Reactive Ion Etching (DRIE). The resulting structure is as shown in Fig. 13.
Fig. 13

The structure formed after back etching with open cavity

The devices after fabrication are diced along the dicing line. The devices are ready for characterization and testing after basic packaging. The devices before packaging are as shown in Fig. 14. Further the devices are packaged on a special purpose SMD adapter PCB as shown in Fig. 15. The terminals are brought out for external connection. The bottom layer of the PCB is drilled with a 1500 micron diameter hole to make a cavity through which the acoustic signal may be guided. The cavity ensures the acoustic pressure stability.
Fig. 14

Devices after fabrication and dicing

Fig. 15

The top and bottom view of the packaged device for practical applications

6 Characterization and testing of acoustic sensor

6.1 Characterization

In line characterization of the device is done during the device fabrication using the inline characterization facility of National Nanofabrication Centre (NNFC), CeNSE, IISc, Bengaluru. The major characterization done is the thickness measurement after deposition of all the layers using DeKTak and AFM method to measure the piezoelectric coefficient D33 after deposition of ZnO layer. The thickness of the layers after every deposition by sputtering is measured by DeKTak profilometer. After the last process of back etched silicon wafer by DRIE to form the diaphragm, the depth measurement is done and the DeKTak measurement is as shown in Fig. 16. The structure including the sandwiched Piezoelectric layer, SiO2 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 d33 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).
Fig. 16

The thickness of the etch depth by DRIE measured by DeKTaK Profilometer

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

The testing of the fabricated device is done by the DC probe station to obtain dc voltage (in the range − 10 to + 10 mV) vs Current and Frequency (in the range 1–60 kHz and 30 mV(p–p) vs Conductance of the device. The experimental setup is as shown in Fig. 17. The V–I dc characteristics is as shown in Fig. 18. From the graph, it is clear that applied voltage and current are in linear relationship and the resistance of the device is constant and has the value ~ 145 kΩ.
Fig. 17

DC probe station to analyze the V–I and circuit parameters

Fig. 18

DC voltage applied vs current

The Conductance of the device as a function of frequency is represented as shown in Fig. 19. Figure 19 represented as frequency vs Conductance confirms the occurrence of first natural frequency in the range of 11–12 kHz as the conductance is highest in this range.
Fig. 19

Frequency vs conductance

6.2.2 Microsystem analyser (MSA)

Microsystem analyser or laser vibrometer works on the principle of Doppler principle. It has been used to understand the displacement and modal frequencies. MSA has been used to understand the displacement and modal frequencies. In this experimental setup, a device under testing (device 3 × 2) has been used as an actuator by applying 3 V AC–500 mV dc offset across the electrodes. The corresponding vibration displacement and modal frequencies when the device has been working as actuator are noted as shown in Fig. 20.
Fig. 20

MSA experimental set up

From the results as represented in Fig. 21 it is clear that the device is behaving as expected as an actuator and the inverse piezoelectric properties of the device were proven as shown. The first peak occurring at 13.2 Hz and deflection of 4.5 nm.
Fig. 21

Device in actuator mode to determine deflection and first modal frequency

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.

The experimental setup is as shown in Fig. 22. The acoustic pressure of different pressure levels (SPL 120–140 db) are applied at frequencies varying from 31.5 Hz to 8 kHz.
Fig. 22

Experimental setup for acoustic calibrator for linearity test by NAL acoustic calibrator

The linearity range as tested by NAL calibrator is as represented in Fig. 23. From the graph, it is clear that, the device is in linear range of operation till 140 dB.
Fig. 23

Linearity of operation of the device in 120 dB to 140 dB

The frequency response of the device as frequency vs output voltage is obtained by the experimental set up a show in Fig. 24. Since the acoustic calibrator has the frequency range limitation only up to 8 kHz, in order to get the frequency response of the device over a wide range of frequency, the device is coupled to a 5v(p–p) at piezoelectric crystal of specification 20 nf, 10 kHz at the bottom of the device as shown in Fig. 24, so that the acoustic pressure is directly guided to the cavity. The piezoelectric crystal (speaker) is connected to signal generator so that a signal of varied range frequency and fixed AC voltage is applied.
Fig. 24

Experimental setup for frequency vs generated voltage

From the above experiments it is clear that the device frequency response is good in the acoustic frequency range. The frequency sweep is as shown in Fig. 25. It indicates that the output voltage is increasing in 11–12 kHz range confirming g the occurrence of resonance which is also justified by the frequency response graph as shown in Fig. 26.
Fig. 25

Frequency sweep in the range 2 kHz to 12 kHz

Fig. 26

Frequency vs output voltage

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 (D33).

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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© The Author(s) 2019

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Electrical and Electronics Engineering, Nitte Meenakshi Institute of TechnologyBangaloreIndia
  2. 2.School of Engineering and Applied SciencesSRM UniversityAmaravatiIndia
  3. 3.Electrical Power and Control Engineering, School of Electrical Engineering and ComputingAdama University of Science and TechnologyAdamaEthiopia

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