Design, Modeling, Characterization and Analysis of a MEMS ...

Felipe Augusto Costa de Oliveira

Design, Modeling, Characterization andAnalysis of a MEMS Piezoelectric Micro

Cantilever for Energy Harvesting and VibrationSensing

Belo Horizonte

2019

Felipe Augusto Costa de Oliveira

Design, Modeling, Characterization and Analysis of aMEMS Piezoelectric Micro Cantilever for Energy

Harvesting and Vibration Sensing

Dissertation submitted to the Graduate Pro-gram in Electrical Engineering of Escola deEngenharia at the Universidade Federal deMinas Gerais, in partial fulfillment of the re-quirements for the degree of Master in Elec-trical Engineering.

Universidade Federal de Minas Gerais – UFMG

Escola de Engenharia

Programa de Pós-Graduação em Engenharia Elétrica

Supervisor: Prof. Davies William de Lima Monteiro

Belo Horizonte2019

Dedicated to all people that embrace innovation,in their own lives seeking personal growth,

and for the society in pursuit of a better world.

Acknowledgements

I would like to thank all teachers devoted to the knowledge pursuit, who sharetheir experiences promoting the education of students who might have a positive impactin the society. A very special thanks to professor Davies William de Lima Monteiro, whohas introduced me to the exciting field of microelectronics and micro systems, and whohas always been able to motivate me to keep working on this research. I also thank Prof.Luciana Pedrosa Salles, for all the assistance given in laboratory during the conductionof the experiments.

The help given by Bruno Henrique Guimarães, Rubens Alcântara de Souza andVinícius Vecchia was crucial to obtain the experimental results. They have helped derivingand building the experimental setup and also conducting the measurements. A specialthanks to Rubens, who did a training to operate the machine that performs the wire-bonding process (which is necessary for accessing the studied device terminals) and wasable to prepare the device under test from the naked die. I also thank Antônio de Páduafor granting access to the clean room and providing the training for using the wire-bondingequipment.

The project started as an undergrad research activity at OptMA lab in UFMG,Universidade Federal de Minas Gerais, with a scholarship funded by CNPQ (BrazilianNational Research Council). The fabrication of the studied device chip was only possibledue to the funding provided by FAPEMIG (Research Foundation of the State of MinasGerais). The work was also partially funded by CAPES. Therefore, I would like to thankthe previous government for all the research support given in terms of financial resourcesprovided by these institutes.

Finally, I am very grateful to my mother, who has always supported me in everyendeavor and who raised me with much dedication and affection. I could not have doneanything if it wasn’t for her.

“Look deep into nature,and then you will understand everything better.

(Albert Einstein)

Resumo

Este trabalho apresenta um estudo aprofundado de um micro-cantilever (viga engastadamicrofabricada) piezoelétrico micro-fabricado, que consiste em uma haste com uma massana ponta e um filme fino de material piezoelétrico depositado na base ancorada. O dis-positivo foi fabricado utilizando uma tecnologia MEMS (micro-electromechanical system)disponível comercialmente, sendo projetado para aplicação seja como sensor de vibraçõesou como micro-gerador de energia para a alimentação de circuitos eletrônicos autônomos,como os nós de sensoriamento sem fio. O objetivo deste trabalho é a modelagem e ca-racterização do dispositivo, visando avaliar o potencial para aplicação em sensoriamentode vibrações e em micro-geração de energia. É importante ressaltar que dispositivos co-merciais para a geração de energia a partir de vibrações já existem, no entanto eles sãovolumosos e não são micro-fabricados1, o que aumenta o tamanho e o custo do sistemaeletrônico sendo alimentado por eles.

É feita uma contextualização da tecnologia MEMS (micro-electromechanical systems) euma breve apresentação de conceitos importantes sobre piezoeletricidade e dos materiaispiezoelétricos tipicamente utilizados. O projeto do micro-cantilever é apresentado, salien-tando os aspectos funcionais, construtivos e de design. É realizada uma introdução sobrenós de sensoriamento sem fio, destacando os elementos eletrônicos típicos destes sistemase o estado atual da tecnologia de dispositivos de baixo consumo de potência. A potên-cia mínima necessária para a alimentação de um sistema de baixo consumo moderno étomada como meta energética a ser provida pelo micro-cantilever proposto. É tambémapresentada uma revisão de trabalhos na área, observando a capacidade de geração dedispositivos similares como referência do que se pode esperar deste tipo de dispositivo.Em seguida é apresentado um estudo da intensidade de aceleração e frequência de máximapotência de fontes de vibrações ambientes típicas, obtendo-se valores de base para a fontede energia mecânica primária, da qual a geração depende.

O dispositivo necessita de circuitos eletrônicos de suporte, para fornecer energia com umatensão elétrica de valor e forma apropriada para a alimentação do sistema eletrônico.Deste modo, foi feita uma revisão de circuitos de suporte, incluindo retificadores passi-vos, dobrador de tensão e conversores estáticos para regulação de tensão e casamento deimpedâncias. Duas abordagens diferentes para a modelagem analítica são apresentadas,fornecendo uma base teórica para simular o comportamento do dispositivo de interesse.O primeiro modelo é derivado a partir da aplicação das equações constituintes da piezo-eletricidade em um modelo geométrico simplificado uni-dimensional do micro-cantilever.1 No momento em que este trabalho foi realizado, não foi encontrado um dispositivo comercial micro-

fabricado que gera energia a partir de vibrações.

O outro modelo é baseado em um circuito elétrico equivalente, modelando a estruturamecânica como elementos de circuito. As equações para obtenção dos parâmetros utili-zados pelos modelos, como a frequência de ressonância, o coeficiente de amortecimentomecânico e o coeficiente de acoplamento eletromecânico também são discutidas.

Para a realização dos experimentos de caracterização no dispositivo proposto, foi neces-sário um encapsulamento apropriado para o chip que contém o micro-cantilever. Apósalgumas tentativas de encapsulamento mal sucedidas, um procedimento para a obtençãode uma amostra de teste válida foi alcançado, sendo reportado neste trabalho. Os expe-rimentos requereram uma fonte de vibrações mecânicas controlada, que foi construída apartir de um alto falante de áudio adaptado. Desta maneira, um setup experimental foidesenvolvido e os experimentos desejados foram descritos.

A simulação do comportamento do micro-cantilever foi conduzida, empregando as equa-ções derivadas dos modelos analíticos em um programa em Python para realizar os cálculose gerar os gráficos desejados. O modelo uni-dimensional simplificado foi utilizado para es-timar a potência gerada pelo micro-cantilever sob diferentes valores para a frequência dasvibrações e da carga resistiva conectada ao dispositivo. Os parâmetros do circuito elétricoequivalente foram calculados e a simulação foi realizada utilizando um software específicopara a análise de circuitos, obtendo-se a curva de resposta em frequência e a análise tran-siente. Os resultados obtidos por ambas as estratégias de modelagem foram comparados euma máxima diferença percentual de 20% foi encontrada, para o valor de potência gerada.Apesar da discrepância no valor da potência, os resultados obtidos foram razoavelmenteconsistentes. Alguns dos parâmetros importantes calculados, respectivamente pelo mo-delo uni-dimensional e pelo modelo de circuito, são: a frequência de ressonância, 147 Hze 143 Hz; o valor óptimo de carga resistiva, 7.66 MΩ e 8.03 MΩ; e a máxima potênciagerada para vibrações de 4 m/s2 de intensidade, 364 nW e 445 nW.

A caracterização do dispositivo fabricado foi feita realizando os experimentos propostos,medindo-se a resposta em frequência, o valor de carga resistiva ótima, o coeficiente deamortecimento mecânico e a curva de sensibilidade a vibrações. O valor da frequência deressonância e da carga ótima medidas tiveram uma discrepância pequena relativos aosvalores calculados, no entanto, os valores do coeficiente de amortecimento e da potênciagerada foram muito diferentes do esperado. A potência medida foi cerca de quatro ve-zes menor que a prevista pela modelagem e o coeficiente de amortecimento foi cerca detrês vezes menor. Utilizando os dados de caracterização em conjunto com o modelo uni-dimensional, um modelo semi-empírico mais fidedigno foi proposto, realizando um ajustepolinomial de segunda ordem na variável de intensidade das vibrações e usando os valoresmedidos da frequência de ressonância e do coeficiente de amortecimento. Os resultados

puramente analíticos do modelo semi-empírico e medidos foram comparados por meio dacurva de resposta em frequência. O novo modelo proposto apresentou resultados conside-ravelmente mais precisos no intervalo de operação das medições, predizendo uma potênciade 458 nW, contra os 2332 nW encontrados no modelo original, enquanto o valor medidofoi de 491 nW.

Baseado nos resultados obtidos, uma análise de aplicabilidade foi feita. A conclusão é queo dispositivo proposto pode ser utilizado como micro-gerador para alimentar circuitosautônomos, no entanto, tendo uma aplicação limitada a situações onde condições especí-ficas são atendidas. Em resumo, estas condições são: a presença continuada de vibraçõesambientes contendo um harmônico de alta intensidade na frequência de ressonância dodispositivo; que o sistema alimentado tenha uma demanda de potência muito pequena, naordem de alguns nano-watts; e que um circuito retificador de alta eficiência e baixa cor-rente seja utilizado. Acredita-se que é possível reprojetar o dispositivo para melhorar suaperformance como um micro-gerador de energia. O micro-cantilever atual seria melhorutilizado como um sensor de vibração, tendo uma elevada sensibilidade para a detecçãode uma vibração com um harmônico na sua frequência de ressonância de 162 Hz. Umchip contendo vários micro-cantilevers similares, com comprimentos ligeiramente diferen-tes, poderia ser projetado para a medição precisa da intensidade de várias frequências devibrações.

Palavras-chaves: MEMS. Micro-Sistemas. Micro-Estruturas. Piezoeletricidade. Micro-geração de energia. Sensores.

Abstract

This work provides an in-depth study of a piezoelectric micro-cantilever device, which isa specific kind of microfabricated structure, consisting of a cantilever beam with a proofmass at the tip and a thin film of piezoelectric material deposited on its anchored base.The device was fabricated using a commercially available MEMS (micro-electromechanicalsystem) technology, having an intended application as either a vibration sensor or asan energy harvester for powering autonomous electronic circuits, such as wireless sensornodes. The goal of this work is to model and characterize the device in order to assessits potential applicability for vibration sensing and energy harvesting. It is important tomention that commercial vibration energy harvesters have been available for a while, butthey are bulky and not microfabricated2, which increases the size and cost of the overallelectronic system relying on them.

A brief application overview of the MEMS technology is presented and an introductionto important concepts about piezoelectricity and its typical materials is provided. Theproposed micro-cantilever design is presented, stressing the functional, constructive anddesign aspects of the structure. An introduction to wireless sensors nodes (WSN) is given,pointing out the typical electronic components of these systems and the current state ofthe low-power devices. The minimum power requirements for a modern low-power WSNis taken as a power goal to be provided by the proposed micro-cantilever for the energyharvesting application. A review of papers in the field of vibrational energy harvesters,highlighting the generation capabilities of similar piezoelectric devices, is used for refer-ence of what can be expected of these devices. A study of the acceleration intensity andmaximum power harmonic frequency of typical ambient vibration sources is presented,yielding a baseline for the parameters of the primary mechanical energy source, on whichthe piezoelectric generation relies.

The device depends on auxiliary circuits to provide energy in a voltage range and patternappropriate to the needs of the powered system. For that reason, a review of circuit topolo-gies for the energy harvesting application is presented, including passive rectifiers, voltagemultipliers and static converters for voltage regulation and impedance matching. Two dif-ferent approaches of analytical modeling are discussed, providing a theoretical basis tosimulate the device behavior. The first model is derived applying the piezoelectric char-acteristic equations in a one dimension geometric simplification of the micro-cantilever.The other model uses an equivalent electric circuit, modeling the mechanical structure ascircuit elements. The equations to obtain the necessary parameters to apply the models,2 At the time this work was conducted, a commercial vibration energy harvester built with MEMS

technology was not found.

such as the resonance frequency, the mechanical damping coefficient and electromechani-cal coupling coefficient are also discussed.

In order to perform the characterization experiments in the proposed device, an appropri-ate package for the chip that contains the micro-cantilever was required. After a coupleunsuccessful packaging attempts, a procedure to obtain a valid test sample was accom-plished and reported in this work. The experimentation required a controlled vibrationsource, which was build adapting an audio speaker. In this way, an experimental setupwas developed and the desired experiments were described.

A simulation of the micro-cantilever behavior was done, using the analytical model equa-tions in a Python script to perform the calculations and generate the desired plots. Thesimplified one-dimensional model was used to estimate the power generated by the can-tilever under different values of vibration frequency and resistive load connected to thedevice. The equivalent electrical circuit parameters were calculated and the simulationwas performed using an specific circuit analysis software, deriving the frequency responsecurve and the transitory analysis. The obtained results from both modeling strategieswere compared and a maximum percentage difference of 20% was found, for the gen-erated power value. Despite the discrepancy in the power value, the results from bothmodels were reasonably consistent. Some important parameters calculated, respectivelyby the one-dimension model and the circuit model, are: the resonance frequency, 147 Hzand 143 Hz; the optimal load resistance, 7.66 MΩ and 8.03 MΩ; and the maximum powergenerated for a vibration intensity of 4 m/s2, 364 nW and 445 nW.

The characterization of the fabricated device was done by means of the proposed ex-periments, measuring the frequency response, the optimal resistive load, the mechanicaldamping coefficient and the vibration sensitivity curve. The resonance frequency and op-timal resistive load measured had a rather minor deviation from the calculated values,but the damping coefficient and the power generated were more different. The measuredpower was about four times lower than the modeling predictions and the damping coef-ficient was about three times lower. Using the experimental data and the one-dimensionmodel, a more accurate semi-empirical model was proposed, performing a second orderpolynomial fit in the vibration intensity variable and using the measured values for theresonance frequency and the damping coefficient. The pure analytical, semi-empirical andmeasured results were compared, using the frequency response curve. The new model isconsiderably more accurate in the measured operation range, predicting a power outputof 458 nW, against the 2332 nW found in the original model, when the measured powerwas 491 nW.

Based on the obtained results, an applicability analysis was made. The conclusion is thatthe proposed device could be used as an energy harvester to power autonomous circuits,but with a limited range of application and assuming that specific conditions are met. Insummary, those conditions are: the presence of continuous ambient vibrations with a highintensity harmonic matching the device resonance frequency; the powered system has avery low energy requirement, in the order of a few hundred nano-watts; and that a highlyefficient low-current rectification circuit is used. It is believed that the device could beredesigned to increase its performance as a power source. The current design could bebetter used as a vibration sensor, having a very high sensitivity for detecting a specificvibration harmonic that matches its resonance frequency, of 162 Hz. A chip containing anarray of similar structures, with slightly different lengths, could be designed to accuratelymeasure the specific intensities of several different vibration frequencies.

Key-words: MEMS. Micro-Systems. Micro-Structures. Piezoelectricity. Energy Harvest-ing. Sensors.

List of Figures

Figure 1 – Representation of the two modes of operation in piezoelectric materials.(a) Longitudinal mode, associated with the 𝑑33 coefficient; (b) Transver-sal mode, related to the 𝑑31 coefficient. Figure taken from (HEHN;MANOLI, 2015). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Figure 2 – a) Diagram of a piezoelectric micro-cantilever with inter-digitated elec-trodes; b) Microscope photograph of the device represented in the dia-gram; c) Cross section diagram explaining the longitudinal mode withinter-digitated electrodes. Figures in a) and b) were taken from (DU-TOIT; WARDLE; KIM, 2005). . . . . . . . . . . . . . . . . . . . . . . 39

Figure 3 – Cross-section diagram of the layers in the PiezoMUMPs process, out ofscale. Figure adapted from an image provided in (COWEN et al., 2014). 42

Figure 4 – Simulation of the stress generated by the displacement of the tip massof the cantilever, using the COMSOL Multiphysics software. . . . . . . 44

Figure 5 – Three-dimensional model of the piezoelectric micro-cantilever proposed,with corresponding dimensions in µm. . . . . . . . . . . . . . . . . . . 45

Figure 6 – Autonomous wireless sensor module, with a piezoelectric vibrationalenergy harvester in a vacuum package as the only energy source. Figuretaken from (ELFRINK et al., 2010). . . . . . . . . . . . . . . . . . . . 54

Figure 7 – SEM photography of the micro-cantilever, in the left; cross section dia-gram of the device layers, in the right. Figure taken from (MARZENCKI;AMMAR; BASROUR, 2008). . . . . . . . . . . . . . . . . . . . . . . . 56

Figure 8 – SEM photography of the device as seen from top, in the left, and frombottom, in the right. Figure taken from (SHEN et al., 2008). . . . . . . 56

Figure 9 – Schematic of a diode based full-wave rectifier circuit. . . . . . . . . . . 60Figure 10 – Waveform plot of the voltages in the diode based full-wave rectifier

circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Figure 11 – Schematic of a MOSFET based full-wave rectifier circuit. . . . . . . . . 61Figure 12 – Waveform plot of the voltages in the MOSFET based full-wave rectifier

circuit, without the capacitor in parallel with the load. Comparisonmade with transistors of different threshold voltages. . . . . . . . . . . 62

Figure 13 – Schematic of a Villard cascade voltage multiplier with two stages. . . . 63Figure 14 – Waveform plot of the output voltage of the multiplier circuit, without

load (open circuit) and with a 500 kΩ resistive load. . . . . . . . . . . . 64Figure 15 – Schematic of the Boost and Buck-Boost converters. . . . . . . . . . . . 65Figure 16 – Schematic of the circuit used by Kong for impedance matching. Figure

taken from (KONG et al., 2010). . . . . . . . . . . . . . . . . . . . . . 68

Figure 17 – Diagram of the dimensions of a cantilever with tip mass. . . . . . . . . 71Figure 18 – Equivalent electrical circuit model for a piezoelectric cantilever with tip

mass. Image taken from (ROUNDY; WRIGHT, 2004). . . . . . . . . . 78Figure 19 – Photograph of the sub-die containing the micro-cantilever structure. . . 82Figure 20 – Sub-die glued to the gold plated universal PCB. . . . . . . . . . . . . . 83Figure 21 – Sub-die after the wire-bonding process and with the adhesive coating

protecting the frail gold wire connections. . . . . . . . . . . . . . . . . 84Figure 22 – a) Photograph of the device sample, DUT, ready for testing; b) Front

view cross section diagram of the DUT. . . . . . . . . . . . . . . . . . . 84Figure 23 – Audio speaker adapted for generating controlled vibrations, with the

device under test and an accelerometer placed in its vibration axis. . . 86Figure 24 – Generic damped oscillation signal, with the associated exponential de-

cay curve related to the damping coefficient. . . . . . . . . . . . . . . . 89Figure 25 – Power and voltage versus load resistance plot, according to the one-

dimension power estimation model. . . . . . . . . . . . . . . . . . . . . 93Figure 26 – Optimal load resistance and voltage versus the excitation frequency. . . 95Figure 27 – Frequency response curve, showing the generated power as function of

the excitation frequency. The curve in blue represents the power fora fixed value of resistive load, calculated for the resonance frequency.The curve in green was generated using different values of resistive load,optimized for each frequency value. . . . . . . . . . . . . . . . . . . . . 95

Figure 28 – Electrical circuit schematic used for the simulation in the LTspice soft-ware. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Figure 29 – Frequency response curve. . . . . . . . . . . . . . . . . . . . . . . . . . 98Figure 30 – Output voltage obtained from the transient simulation. . . . . . . . . . 99Figure 31 – Measured power and voltage generated by the micro-cantilever for sev-

eral different values of resistive load connected. . . . . . . . . . . . . . 102Figure 32 – Measured frequency response curve, with the power dissipated in a

8.2 MΩ resistive load, on the left axis, and the associated effectivevoltage, on the right axis. . . . . . . . . . . . . . . . . . . . . . . . . . 103

Figure 33 – Measured voltage decay curve, with the associated voltage amplitudeand exponential fit curve highlighted. A vibration intensity of approx-imately 2.5 m/s2 was used for the measurement. . . . . . . . . . . . . . 105

Figure 34 – Micro-cantilever voltage, in blue, and corresponding signal generatorcontrol voltage, in red, versus the vibration intensity measured by theaccelerometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Figure 35 – Measured and simulated vibration sensitivity, using the polynomial fit-ting parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Figure 36 – Comparison between the frequency response curve, obtained from thepure analytical calculations, the semi-empirical model and the mea-sured results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

List of Tables

Table 1 – Proposed device dimensions . . . . . . . . . . . . . . . . . . . . . . . . . 45Table 2 – Consumption of Low Power Components for WSN . . . . . . . . . . . . 51Table 3 – Data from similar devices published by other authors . . . . . . . . . . 53Table 4 – Intensity and frequency of common ambient vibration sources . . . . . . 58Table 5 – Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Table 6 – Calculated Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Table 7 – Equivalent Circuit Parameters . . . . . . . . . . . . . . . . . . . . . . . 97Table 8 – Summary of the Analytical Results . . . . . . . . . . . . . . . . . . . . . 100

List of abbreviations and acronyms

IC Integrated circuit.

MEMS Micro-electromechanical system.

RF Radio frequency.

IoT Internet of Things.

SAW Surface acoustic wave.

APM Acoustic plate mode.

FPW Flexure plate wave.

FBAR Film bulk acoustic resonator.

PZT Lead zirconate titanate.

AlN Aluminum nitride.

RoHS Restriction of certain hazardous substances.

MPW Multi project wafer.

MUMP Multi user MEMS project.

SOI Silicon on Insulator.

WSN Wireless sensor node.

MCU Microcontroller unit.

CMOS Complementary metal-oxide semicondutor.

SPI Serial peripheral interface.

I2C Inter integrated circuit.

BLE Bluetooth low energy.

ESB Enhanced ShockBurst.

RTC Real time clock.

EPROM Erasable programable only memory.

RAM Random access memory.

I/O Input/output.

ADC Analog to digital converter.

PWM Pulse width modulation.

TI Texas Instruments.

SEM Scanning electron microscopy.

RISC Reduced instruction set computer.

FFT Fast Fourier transfer.

AC Alternated current.

DC Direct current.

MOSFET Metal-oxide semiconductor field effect transistor.

IEEE Institute of electrical and electronics engineers.

SPICE Simulation program with integrated circuit emphasis.

DUT Device under test.

PCB Printed circuit board.

UV Ultra violet.

CSV Comma separated value.

List of symbols

Hz Hertz, frequency unit.

W Watt, power unit.

C Coulomb, electrical charge unit.

N Newton, force unit.

∘C Degree Celsius, temperature unit.

m Meter, length unit.

A Ampere, electrical current unit.

V Volt, electrical voltage unit.

Ω Ohm, electrical resistance unit.

F Farad, electrical capacitance unit.

s Second, time unit.

bps Bits per second, data transmission unit.

Pa Pascal, pressure and mechanical stress unit.

bar Bar, pressure unit. 1 bar is equivalent to 105 Pa.

rad Radian, angular frequency unit.

g Gram, mass unit.

∘ Degree, angle unit.

dB Decibel, unit to express ratio between two quantities in a logarithmicscale.

p = 10−12 Pico, metric prefix, associated with a unit measure.

n = 10−9 Nano, metric prefix, associated with a unit measure.

µ = 10−6 Micro, metric prefix, associated with a unit measure.

m = 10−3 Milli, metric prefix, associated with a unit measure.

c = 10−2 Centi, metric prefix, associated with a unit measure.

k = 103 Kilo, metric prefix, associated with a unit measure.

M = 106 Mega, metric prefix, associated with a unit measure.

G = 109 Giga, metric prefix, associated with a unit measure.

𝑑𝑖𝑗 Piezoelectric coefficient that relates the electrical field in the 𝑖 axis withthe mechanical stress in 𝑗 axis.

𝑑33 Piezoelectric coefficient for the longitudinal mode.

𝑑31 Piezoelectric coefficient for the transversal mode.

𝐿𝑡𝑜𝑡 Total length of the micro-cantilever.

𝐿𝑏 Micro-cantilever beam length.

𝑊𝑏 Width of the micro-cantilever.

𝐿𝑝𝑚 Length and width of micro-cantilever tip mass.

𝐿𝑒 Micro-cantilever top electrode length.

𝑊𝑒 Micro-cantilever top electrode width.

𝑡𝑝𝑚 Substrate thickness, the same thickness of the micro-cantilever tip mass.

𝑡𝑠 Top silicon layer thickness.

𝑡𝑜𝑥 Insulating silicon dioxide layer thickness.

𝑡𝑝 Thickness of the piezoelectric layer.

𝑡𝑚 Thickness of the metal layer.

𝑉𝑡𝑜𝑡 Total volume of the micro-cantilever.

𝑉𝑑 Diode forward polarization voltage.

𝑉𝑔𝑠 Gate to source voltage in a MOSFET transistor.

𝑉𝑑𝑠 Drain to source voltage in a MOSFET transistor.

𝑉𝑡 Threshold voltage in a MOSFET transistor.

𝑑𝑐 Duty cycle.

𝜏𝑜𝑛 Time that a pulse signal stays in the high voltage logical level, in oneperiod.

𝑇𝑠𝑤 Switching period, measured in time units.

𝑉𝐵𝑜𝑢𝑡 and 𝑉𝐵𝐵𝑜𝑢𝑡 Average output voltage of a Boost and Buck-Boost converters,respectively.

𝑉𝑑𝑐 Converter input voltage.

𝑅𝐶1, 𝑅𝐶2 and 𝐶𝐶 Values of the components for the impedance matching circuit.

𝑅𝑙𝑖𝑛 Equivalent input load resistance generated by the impedance matchingcircuit.

𝐿𝐵𝐵𝑖𝑛𝑑 Inductance value for the Buck-Boost converter.

𝑓𝑁 Resonance frequency, in Hertz units.

𝐾 Spring constant.

𝑀 Device mass.

𝐸 Effective Young modulus for a generic material.

𝑊 Width of a generic cantilever beam.

𝑡 Thickness of a generic cantilever beam.

𝐿 Length of a generic cantilever beam.

𝜌𝑠𝑖 Silicon density.

𝐾 ′ Effective spring constant.

𝐸𝑠𝑖 Silicon Young modulus.

𝜔𝑁 Angular resonance frequency, in radians units.

𝜋 Pi constant, approximately equal to 3.1416.

𝑘231 and 𝑘2

33 Electromechanical coupling coefficients for the transversal and longi-tudinal modes, respectively.

𝑠11 First element of the compliance matrix of a piezoelectric material.

𝜀33 Dielectric permittivity of a piezoelectric material.

𝑘2𝑒 Effective electromechanical coupling coefficient.

𝜁𝑚 Mechanical damping coefficient.

𝜁𝑚,𝑑𝑟𝑎𝑔, 𝜁𝑚,𝑠𝑞𝑢𝑒𝑒𝑧𝑒, 𝜁𝑚,𝑎𝑛𝑐ℎ𝑜𝑟 and 𝜁𝑚,𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑎𝑙 Mechanical damping coefficient compo-nents, associated with the four main causes for the damping.

𝜇𝑎𝑖𝑟 Dynamic viscosity of air.

𝜌𝑎𝑖𝑟 Air density.

𝑔0 Minimal gap/distance between the micro-cantilever and other struc-tures.

𝜂𝑏𝑒𝑎𝑚 Structural damping factor of the cantilever beam.

𝑅𝑝 Leakage resistance.

𝜌𝐴𝑙𝑁 Aluminum nitride density.

𝑥𝐵 Mechanical vibration intensity in the base of the micro-cantilever.

𝜔 Mechanical vibration angular frequency.

𝑅𝑙 External load resistance.

𝐶𝑝 Device capacitance.

𝑥 Displacement of the tip mass.

𝑉 Voltage across electrodes.

𝑅𝑒𝑞 Equivalent parallel resistance between the external load and the inter-nal leakage resistance.

𝜀0 Dielectric permittivity of vacuum.

𝜀𝑝 Relative dielectric permittivity of the piezoelectric material.

𝑟 Auxiliary variable, defined as 𝑟 = 𝜔𝑁𝑅𝑒𝑞𝐶𝑝.

Ω Ratio between the vibration frequency and resonance frequency.

𝐾𝑖𝑛𝑣 Auxiliary variable, defined as 𝐾𝑖𝑛𝑣 = 1 − 𝑘2𝑒 .

𝑅𝑙𝑜𝑝𝑡 Optimal load resistance value.

𝜎𝑖𝑛 Voltage source in the equivalent electrical circuit model.

𝐿𝑚 Inductance in the equivalent electrical circuit model.

𝑅𝑏 Resistance in the equivalent electrical circuit model.

𝐶𝑘 Capacitance in the equivalent electrical circuit model.

𝑁 Transformer turn ratio in the equivalent electrical circuit model.

𝑆 Strain in the piezoelectric material.

�̇� Strain rate.

𝑖 Current in the equivalent circuit model.

ℰ Electrical field.

𝑑 Distance between parallel plates.

𝑘1 and 𝑘2 Auxiliary geometrical variables for the equivalent circuit model.

𝑡𝑒𝑞 Effective thickness of the micro-cantilever beam.

𝐼 Second inertia moment.

𝑉𝑜𝑐 Open circuit voltage.

𝑠 Laplace variable.

𝑃 Generic power.

𝑅 Generic resistance.

𝐹𝑝 Performance factor.

𝑘′1 Corrected 𝑘1 variable, accounting for the micro-cantilever center of mass

in the center of the tip mass.

𝐿𝑝 and 𝐿𝑠 Inductances in the primary and secondary of an electrical transformer.

𝑃𝑚𝑎𝑥 Maximum power generated by the micro-cantilever.

𝑉𝑃 𝑚𝑎𝑥 Output voltage of the micro-cantilever in the point of maximum power.

𝑖𝑃 𝑚𝑎𝑥 Output current of the micro-cantilever in the point of maximum power.

𝐴 and 𝐵 Exponential fit parameters.

𝑡 Time variable.

𝑄 Quality factor.

𝑉0 Zero acceleration voltage.

𝜎 Accelerometer sensitivity.

𝑉𝑜𝑢𝑡 Accelerometer output voltage.

𝑉+𝑔 and 𝑉−𝑔 Accelerometer voltage corresponding to the gravity acceleration andminus the gravity acceleration.

𝐴𝑓𝑖𝑡 Acceleration fit variable.

𝑎2, 𝑎1 and 𝑎0 Second order polynomial fit parameters, for the acceleration fit vari-able.

𝑃𝑐𝑜𝑒𝑓𝑓 Baseline power coefficient.

Contents

1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331.1 Motivation and Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . 331.2 Introduction to MEMS . . . . . . . . . . . . . . . . . . . . . . . . . . 351.3 Introduction to Piezoelectric Materials and Devices . . . . . . . . . 361.3.1 Typical Piezoelectric Materials . . . . . . . . . . . . . . . . . . . . . . . . 371.4 The Proposed Device: Piezoelectric Micro-Cantilever . . . . . . . . . 411.4.1 The PiezoMUMPs Process . . . . . . . . . . . . . . . . . . . . . . . . . . 411.4.2 Micro-Cantilever Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 421.5 Wireless Sensor Nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . 451.6 Low Power Electronics for Wireless Sensor Nodes . . . . . . . . . . . 471.6.1 Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471.6.2 Wireless Transceivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481.6.3 Microcontrollers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491.6.4 Power Consumption of the System . . . . . . . . . . . . . . . . . . . . . . 51

2 MATERIALS AND METHODS . . . . . . . . . . . . . . . . . . . . 532.1 Overview of the Technological Advances in Piezoelectric Micro-

Cantilevers for Energy Harvesting . . . . . . . . . . . . . . . . . . . . 532.2 Study of Ambient Vibration Sources . . . . . . . . . . . . . . . . . . . 572.3 Overview of Auxiliary Circuits for Energy Harvesting . . . . . . . . . 582.3.1 Rectifier Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592.3.2 Voltage Multiplier Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 622.3.3 DC-to-DC Converters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642.3.4 Voltage Regulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 662.3.5 Impedance Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672.4 Analytical Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 682.4.1 Resonance Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 692.4.2 Electromechanical Coupling Coefficient . . . . . . . . . . . . . . . . . . . 712.4.3 Mechanical Damping Coefficient . . . . . . . . . . . . . . . . . . . . . . . 722.4.4 Leakage Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 742.4.5 One-Dimensional Power Estimation Model . . . . . . . . . . . . . . . . . . 752.4.6 Equivalent Electric Circuit Model . . . . . . . . . . . . . . . . . . . . . . . 772.5 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 822.5.1 Preparation of the Device Under Test . . . . . . . . . . . . . . . . . . . . 822.5.2 Preliminary Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

2.5.3 Test-bench Development . . . . . . . . . . . . . . . . . . . . . . . . . . . 852.5.4 Frequency Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 872.5.5 Optimal Load Measurement . . . . . . . . . . . . . . . . . . . . . . . . . 872.5.6 Vibration Sensitivity Curve . . . . . . . . . . . . . . . . . . . . . . . . . . 882.5.7 Measurement of the Mechanical Damping Coefficient . . . . . . . . . . . . 89

3 RESULTS AND ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . 913.1 Considerations About the Analytical Results . . . . . . . . . . . . . . 913.1.1 Reference Values for the Material Properties and Calculated Parameters . . 913.2 One-Dimension Power Estimation Model Results . . . . . . . . . . . 933.3 Equivalent Circuit Model Results . . . . . . . . . . . . . . . . . . . . 963.4 Analytical Results Analysis . . . . . . . . . . . . . . . . . . . . . . . . 1003.5 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1013.5.1 Optimal Resistive Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1023.5.2 Frequency Response Curve . . . . . . . . . . . . . . . . . . . . . . . . . . 1033.5.3 Mechanical Damping Coefficient Measurement . . . . . . . . . . . . . . . 1043.5.4 Vibration Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1053.6 Semi-Empirical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 1073.7 Applicability Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 1103.7.1 Energy Harvester . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1103.7.2 High Sensitivity Vibration Sensor . . . . . . . . . . . . . . . . . . . . . . . 112

4 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1134.1 Summary of the Presented Work . . . . . . . . . . . . . . . . . . . . 1134.2 Suggested Topics for Future Works . . . . . . . . . . . . . . . . . . . 1144.3 Final Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

33

1 Introduction

1.1 Motivation and Goals

With the continuous growth of the electronic industry, the demand for high perfor-mance low power compact devices has increased. That demand is met by the developmentand improvement of sophisticated micro-fabrication techniques in semiconductors, usingspecial equipment and facilities that supports the large scale production of integratedcircuits (ICs) with increasingly higher density of components embedded within. The highintegration density enables the design of complex devices, with advanced functionalities,in tiny chips that operates with very low power consumption.

The micro-fabrication techniques of the electronics industry were extended for theminiaturization of several types of sensors, like accelerometers, pressure and temperaturesensors, which have been increasingly integrated into mobile devices and consumer elec-tronics. The same pattern has been observed in wireless communication systems, wherehigher operation frequencies has led to smaller antennas, of a few millimeters of lengthfor the GHz spectrum, enabling integration with micro-fabrication processes.

These technological advances indicate a trend for the development of wireless sen-sors and autonomous systems, pushing the demand for miniaturized low-consumptionsensors and effective solutions for powering these devices. With that in mind, researchin the field of micro-power generation1 is necessary, since an effective, cheap, compact,practical strategy for powering these devices is still a challenge. Due to the technologicaladvances in the last couple of decades, viable solutions for this issue might be found usingenergy harvesting strategies.

Among the power generation strategies for these systems, the use of photovoltaicenergy, which relies on the incidence of light of reasonably intensity, stands out. Exten-sive research has been done in that field and the use of photodiodes and photovoltaic cellsfor micro-power generation is widely known. Another strategy lies on the use of ambientmechanical vibration energy, using electrostatic, magnetic or piezoelectric generators toconvert vibrations to electricity. Out of these three kinds, the magnetic is the one with thehighest energy density, followed by the piezoelectric. The problem is that the magneticvibration generator is not compatible with micro-fabrication techniques, therefore its ap-plication is limited due to the physical space required by them. The electrostatic energyharvester can be micro-fabricated, however, they provide lower energy density compared1 In this work, the term micro-power generation is related to the micro-metric dimensions of these

devices, and with the power generation in the order of micro-Watts (µW). The term energy harvestingwill be used with the same intent.

34 Chapter 1. Introduction

to the piezoelectric equivalent and also requires biasing to generate power, which wouldmake it unfeasible in a completely autonomous system, without a battery. Lastly, thereare piezoelectric vibrational energy harvesters, that can meet the desired demands for amicro-fabricated autonomous wireless sensor system and also work as a vibration sensor.

Therefore, this work will focus on the research of a micro-fabricated piezoelectricdevice and its application for energy harvesting and vibration sensing. The following topicswill be addressed:

∙ Review of the energy consumption requirements of low-power devices that can beused for wireless sensor applications.

∙ Review of the state of the art in piezoelectric energy harvesters, evaluating theapplication potential.

∙ Study of ambient vibration sources, with focus on the average acceleration intensityand the fundamental frequency of these vibrations.

∙ Design of an effective piezoelectric micro-cantilever for energy harvesting and vi-bration sensing, compatible with a commercial micro-fabrication process currentlyavailable.

∙ Investigation of models to predict the behavior of similar piezoelectric devices, esti-mating the power generation based on the parameters of the designed device.

∙ Preparation of a test sample, the device under test, deriving an alternative packagingsolution for the micro-cantilever chip.

∙ Development of an experimental setup to test the device. Discussion of the resultsand analysis of the experiments.

∙ Comparison between analytical and experimental results. Proposition of a semi-empirical model.

∙ Application analysis and re-design recommendations.

In summary, this work aims to provide a comprehensive understanding of theprocess of design, fabrication, modeling, testing and application of a micro-fabricatedpiezoelectric device, focusing in the application as an energy harvester and vibrationsensor for wireless sensors and autonomous electronic devices.

1.2. Introduction to MEMS 35

1.2 Introduction to MEMS

MEMS is an acronym for micro-electromechanical systems and encompasses a classof micro-fabricated structures with electrical, mechanical and, or, structural functional-ities. Despite the suggestive acronym, a MEMS device does not necessarily has to havean electrical or mechanical functionality, they could be designed and used, for instance,in microfluidics to realize micro-canals, therefore having a structural role. However, allMEMS devices have in common the use of techniques and processes of microelectronicsfor its fabrication.

A great variety of MEMS devices can be fabricated by the combination of severaldistinct processes, but they are usually made using micrometer technology nodes2, whichby today standards in the electronic industry is considered a very large node. Therefore,MEMS technologies usually have higher tolerances compared to modern nano-electronictechnologies, being relatively easier to fabricate.

Among the several different application for MEMS devices their use as transducersstands out, being used as sensors for measuring and detecting several types of physicalquantities, such as pressure, acceleration and gas concentration, or as micro and nanoactuators, in applications for RF (radio frequency) switching, microfluidic pump, movingmicro-mirror and lenses in micro-optical systems (GARDNER; VARADAN; AWADELKA-RIM, 2001a; SENTURIA, 2002; SOLGAARD; GODIL; HOWE, 2014).

The market for MEMS devices has been growing in the last decade and its appli-cation can be seen in several day-to-day consumables. Smartphones and tablets featureMEMS accelerometers, microphones and micro-speakers; automobiles use MEMS crashsensor for their air-bag control; ink-jet printers have MEMS printer-heads with piezo-electric MEMS actuator to control the ink dispersion flow. The trend for innovative IoT(internet of things) devices, with the development of compact, smart and interconnectedsystems for applications in smart cities, electrical smart grids, autonomous vehicles, alsopushes the MEMS technology development, which will continue to grow according torecent forecasts (BOGUE, 2013).

The substitution of traditional sensors for MEMS devices with equivalent func-tionality brings obvious advantages, such as lower fabrication cost, smaller size and re-duced power consumption. Those advantages are keen for the development of autonomouswireless sensors, using low-power wireless transducers, micro controllers and an effectivestrategy of micro-power generation. Through the use of MEMS technology it is possibleto fabricate the sensor and the energy harvester in the same chip, using piezoelectricmaterials compatible with micro-fabrication processes.

Piezoelectric materials have been widely used in MEMS sensors, for application as2 Refers to the dimension of the smaller features that can be fabricated.


microphones; pressure sensors; accelerometers; gyroscopes; precision micro-balance; highfrequency filters; biochemical sensors in resonators and acoustic wave devices3 (KOVACS,1998; LI; ZHOU, 2013). The application for MEMS actuators is limited due to the fact thatrelatively high voltages must be applied to the piezoelectric materials in order for themto produce an expressive displacement. However, the force produced and the responsespeed (frequency) are very high, being applicable for the usage as ultrasound generators,micro-pump for microfluidcs and deformable mirrors for adaptive micro-optical systems(NGUYEN; HUANG; CHUAN, 2002; KANNO et al., 2007).

Although piezoelectric materials can be used for several applications in MEMSdevices, in many situations there are other kinds of devices that can provide a betterperformance for the same application4. In general, piezoelectric MEMS devices are advan-tageous due to the small size; high frequency response; low or absent power consumption;and high sensitivity. The biggest disadvantage is the fact that they can not provide asustained response5, in a way that they cannot operate in very low frequencies, providingonly transient responses. That shortcoming does not affect the use as vibrational energyharvester and vibration sensor, which are the aimed applications in this work, discussedin detail in specific sections ahead.

1.3 Introduction to Piezoelectric Materials and Devices

The piezoelectric effect is a phenomenon associated to a class of materials in whichthe deformation of the atomic crystalline lattice leads to the onset of an electrical po-larization. Therefore, the effect generates an electrical field directly proportional to themechanical stress onto the material. The contrary effect, called inverse piezoelectric ef-fect, can also happen, meaning that applying an electrical field across the material willcause a proportional mechanical deformation, which is reversible, ceasing to exist whenthe electrical field is no longer applied.

In most piezoelectric materials, small deformations of the material cause highvoltages to appear, but with small currents. The contrary is also valid, meaning that it isnecessary to apply high voltages to induce an expressive displacement. For that reason,generally, piezoelectric materials present high sensitivity to mechanical disturbances, buthave a limited operation as actuators due to the need of high voltages to induce smalldisplacements.

The piezoelectricity is highly dependent on the crystalline orientation of the ma-terial, being stronger or weaker in different directions. Among the piezoelectric material3 SAW, surface acoustic wave; APM, acoustic plate mode; FPW, flexure plate wave; FBAR, film bulk

acoustic resonator4 E.g. capacitive membranes for microphones; electrostatic actuator for deformable micro-mirrors.5 E.g. Piezoelectric accelerometers can not measure stationary acceleration, like the earth’s gravity.

1.3. Introduction to Piezoelectric Materials and Devices 37

properties that are dependent of orientation it is important to mention the piezoelectriccoefficient, 𝑑𝑖𝑗, modeled by a tensor that associates the charge generated in a specificdirection, 𝑖, by the force applied in another direction, 𝑗. Therefore, that parameter is themeasure of the material sensitivity, represented by units of electrical charge by force, usu-ally as pico-coulomb per newton, pC/N, representing the charge generated in one axis bythe force in another (or in the same axis, such as in the 𝑑33 coefficient). A formal reviewof the piezoelectric theory and its equations is not in the scope of this work, but it canbe found in (JAFFE; COOK; JAFFE, 1971).

There are two main operation modes for the piezoelectric devices, the longitudinaland transversal mode, associated, respectively, with the 𝑑33 and 𝑑31 coefficients. Usinga Cartesian coordinate system as a reference, these coefficients represent the generatedelectrical field on the Z axis due to application of force along the Z axis, for the 𝑑33, andalong the X axis, for the 𝑑31, as shown in figure 1. Regarding piezoelectric MEMS devices,generally, the operation in the longitudinal mode is achieved by the use of inter-digitatedelectrodes on top of the piezoelectric material, requiring only one metal-conductive layer.The transversal mode uses electrodes placed on top and bottom of the piezoelectric ma-terial, requiring the use of two conductive layers. Figure 2 shows a illustration and amicroscope image of a real device that makes use of inter-digitated electrodes, operat-ing in the longitudinal mode, and a cross section diagram explaining how this electrodesconfiguration enables the operation in the longitudinal mode. The transversal mode op-eration will be discussed in detail in specific sections ahead, since it is the mode used forthe device designed and tested in this work.

1.3.1 Typical Piezoelectric Materials

The piezoelectricity is a phenomenon observed naturally in a variety of materials.It can be seen in crystals such as quartz and tourmaline and also in organic materialssuch as bone, silk and hair. Among these the quartz6 stands out, having a widespreaduse for commercial devices, such as in sonars for military applications, high frequencyfilters for wireless communications and high frequency clock generators used in severalelectronic devices. However, the use of piezoelectric materials has spread to a wider rangeof applications due to the fabrication of specific ceramic materials with much strongerpiezoelectric characteristics, having piezoelectric coefficients dozens to hundreds timesgreater than the ones found in natural materials. These ceramic materials are in the classof ferroelectric materials, in which it is possible to align the resulting electric dipole vectorto a specific desired crystalline orientation, by the means of applying a strong externalelectrical field (GHODSSI; LIN, 2011).

6 A pure, controlled, chemically grown variety of quartz, called 𝛼-quartz is used, not the natural crystalextracted from nature.


Figure 1 – Representation of the two modes of operation in piezoelectric materials. (a)Longitudinal mode, associated with the 𝑑33 coefficient; (b) Transversal mode,related to the 𝑑31 coefficient. Figure taken from (HEHN; MANOLI, 2015).

The ceramic materials having a Perovskite crystalline lattice structure may presentstrong piezoelectric characteristics and, in many cases, it is possible to adjust its properties(piezoelectric, mechanical and dielectric), within a certain range, by modifying its chemicalcomposition. These materials can be produced by the combination of specific proportionsof metallic oxides, being heated and bound by an appropriate organic material, and thenshaped in a desired form (usually in a form of disks or bars). Next, the material is heated ina high temperature furnace and goes through a poling process, consisting in the applicationof a strong electrical field while the material is kept in a high temperature. The polingprocess is responsible for creating the piezoelectric characteristics of the material andit can be reversed if the material is submitted to a temperature above its Curie point,which is a specific temperature for each material. That happens due to the fact the theelectrical dipoles, in a molecular level, are oriented by the external electrical field and thehigh temperature enables the molecules to move. If there is no external electrical fields,at sufficient high temperature, the dipoles are reoriented into random positions and thepiezoelectric properties are lost.

Typical materials in the Perovskite class are the barium titanate (BaTiO3), lead

1.3. Introduction to Piezoelectric Materials and Devices 39

Figure 2 – a) Diagram of a piezoelectric micro-cantilever with inter-digitated electrodes;b) Microscope photograph of the device represented in the diagram; c) Crosssection diagram explaining the longitudinal mode with inter-digitated elec-trodes. Figures in a) and b) were taken from (DUTOIT; WARDLE; KIM,2005).

titanate (PbTiO3), lithium niobate (LiNbO3), lead-zirconium titanate (PbZr𝑥Ti𝑥−1O3,where 0 < 𝑥 < 1), better know as PZT (of several types such as PZT-5A, PZT-5H,etc.), and many others. Among these materials the PZT stands out due to its very highpiezoelectric coefficient (𝑑33 > 150pC/N).

The PZT is mostly used in discrete (non integrated) piezoelectric elements, inthe form of disks and small bars, for applications such as pressure, vibration, impactsensors, and as actuators for buzzers, small audio speakers, controlled vibration generatorsand in situations that requires fast, strong (elevated forces) actuation, but with smalldisplacements. Although widely used in discrete applications, the PZT has limitations forits use in MEMS due to the high complexity of integration in micro-fabrication processes.That arises from the fact that it is difficult to deposit a thin uniform film of this material,although it is possible with highly controlled and sophisticated processes. Another aspectlimiting its application is the fact that PZT is a brittle material, having limited robustnesswhen applied to malleable structures such as thin membranes and cantilevers, and beinga ferroelectric material its piezoelectric properties are irreversibly lost when submitted tohigher temperatures. Despite its limitation, it is still a widely used material in MEMS,specially for micro-generation applications, but the scenario is changing due to the useof other suitable materials such as the aluminum nitrade (AlN), which is much easier tointegrate into micro-fabrication processes.


The aluminum nitride is also a ceramic material, but it has a different type ofcrystalline structure, belonging to the class of Wurtzite materials. These materials arenot ferroelectric, so it is not possible to reorient the electric polarization vector in thecrystalline structure thorough the application of an external electrical field, meaning thatthe poling process is not applicable. On one hand this is advantageous, because thesematerials present piezoelectricity naturally, even when submitted to high temperatures,but the downside is that it is not possible to choose and control the direction of thepiezoelectric effect, being a consequence of the crystalline arrangement of the materialand difficult to predict and control during the deposition of these materials in micro-fabrication processes. The piezoelectric coefficient of the aluminum nitride is about 20 to50 times smaller than that of the PZT, however the AlN has many desirable characteristicsthat sustain its usage over the PZT. Among these desirable characteristics the followingstand out:

∙ High acoustic propagation velocity, resulting in low mechanical losses in the struc-ture.

∙ Excellent dielectric properties, having a very high energy gap and resulting in verylow leakage currents.

∙ High compatibility with micro-fabrication techniques, being relatively easy to de-posit a high quality (high uniformity, low roughness) thin film, using a reactivesputtering process.

∙ Great thermal conductivity (for a dielectric material).

∙ Does not use heavy metals, like lead, in its composition, being acceptable for usageon devices that follows the regulatory trend of restricting hazardous substances(RoHS, restriction of certain hazardous substances).

∙ Unlike ferroelectric materials, the AlN maintain its piezoelectric properties evenafter submitted to high temperatures, also having a high melting point of 2200 ∘C.

Specifically due to the low acoustic propagation losses and the well known processfor depositing thin films of the material, AlN has been used in high-frequency resonatorsand filters (PIAZZA; STEPHANOU; (AL)PISANO, 2006), enabling devices with highquality factor, being promising for RF applications and gaining potential in the MEMSscenario. Its use in vibrational energy harvesters has been explored and several researcheshave reported excellent results with this material (ELFRINK et al., 2010; MARZENCKI;AMMAR; BASROUR, 2008). In (RENAUD et al., 2008) an analytical comparison be-tween a micro-power generator device using PZT and AlN was made, using an experi-mentally validated model, and the AlN device has shown better results, generating 19 µWagainst 6 µW generated from the PZT device.

1.4. The Proposed Device: Piezoelectric Micro-Cantilever 41

Therefore, it is safe to conclude that the aluminum nitride is a suitable piezoelectricmaterial to use in a micro-fabricated vibrational energy harvester. Considering that avibration sensor might benefit from the same characteristics that makes a good micro-power generator, it makes this material a good choice for the purpose of this work. Aswill be seen in the next section, a commercial MEMS process using the AlN is availableand this work will focus on a device that was designed for and fabricated by that process.

1.4 The Proposed Device: Piezoelectric Micro-Cantilever

The proposed device is one of the several structures designed in a MEMS chipfabricated by the PiezoMUMPs process provided by the MEMSCAP foundry, a pure-playcompany specialized in MEMS technology for multi-project-wafer (MPW) runs. In orderto understand the studied device, a quick introduction to its fabrication process will begiven in the section ahead.

1.4.1 The PiezoMUMPs Process

The PiezoMUMPs process in one of the five MUMPs (Multi-user MEMS project)processes offered by the MEMSCAP company, enabling access to cheap prototypingthrough sharing process wafers with several users, a common strategy used by the mi-croelectronics industry to reduce development expenses, known as MPW (multi-project-wafer). The base substrate, the wafer, can have up to dozens of thousands o chips and in aMPW process its area is shared to fabricate the designs of several users, in a way that eachuser only receives a few chips, thus reducing fabrication costs for the end user. Typically,the dies (chips) for the MUMPs processes have dimensions of 11 × 11mm2 in 150 mmwafer7, fitting about 500 dies per wafer, which is a much smaller throughput comparedto microelectronic technologies that produces dozens of thousands dies per wafer.

The PiezoMUMPs process uses SOI (silicon on insulator) wafers as a substrateand has five photolithography steps, thus realizing the pattering of geometric shapes infive different layers. Those layers are the following, ordered from the bottom to the topof the wafer:

∙ Base substrate, with coarse patterns in the form of trenches and holes that maypierce throughout the chip, from bottom to top.

∙ Top silicon, where the patterns of the structures, that can have free moving partsoscillating above the trench region, are made. It also functions as bottom elec-trodes/conductive layer, due to high superficial doping executed on this material.

7 Diameter dimension, also known as 6-inch wafer.


Figure 3 – Cross-section diagram of the layers in the PiezoMUMPs process, out of scale.Figure adapted from an image provided in (COWEN et al., 2014).

∙ Thermal silicon oxide, dielectric material that functions as an electric insulator.

∙ Thin film of aluminum nitride, the piezoelectric material.

∙ Metal layer, made of one thin film of chromium followed by a thicker layer of alu-minum. Serves as a conductive layer, used as top electrodes, conductive tracks andpads for the contact with gold wires connected to the package and/or external con-nections.

A detailed explanation about the process is given in (COWEN et al., 2014). Fig-ure 3 presents a cross section diagram of the process layers, with dimensions out of scale,showing a possible pattern configuration in the layers that were described. The interme-diate buried oxide is part of the wafer and makes the electrical insulation between thetop silicon and the base substrate, and it is not accessible to independent patterning,reproducing the features drawn in the base substrate trench.

There are several design rules that must be followed in order to submit a validdesign for fabrication. These rules, described in full in (COWEN et al., 2014), gives theguidelines for minimal dimensions, spacing and overlapping for the patterns in the differentlayers. An example of a design rule is the minimal feature that can be fabricated. Theminimal feature is different across layers, being the smallest in the top silicon layer, 2 µm,and the largest in the base substrate, 200 µm. Therefore, the design of structures mustbe made in accordance with these rules and other guidelines provided by MEMSCAP.

1.4.2 Micro-Cantilever Design

The main goal for the structure design was for it to work as a vibrational energyharvester, being a vibration sensor the secondary goal derived from the effectiveness ofharnessing vibration energy from the environment. The project was made according to

1.4. The Proposed Device: Piezoelectric Micro-Cantilever 43

the limitations imposed by the design rules for the technology, that translates as lim-itations and tolerances of the fabrication process. A preliminary study was conducted,observing the design of successful devices for the proposed application, submitted byother researchers ((ELFRINK et al., 2010), (JEON et al., 2005; CHOI et al., 2006),(MARZENCKI; AMMAR; BASROUR, 2008), (SHEN et al., 2008), (RENAUD et al.,2008)). From this study, it was possible to conclude that a simple cantilever structure,with a mass attached to the tip, was an effective design for a vibrational energy harvester.The structure is highly sensitive to the mechanical disturbances with harmonic frequenciesclose to its resonance frequency.

It is straightforward to understand the physical working principal of the device.The ambient vibrations causes the mass on the tip to oscillate, generating a mechanicalstress on the anchored base, which has a thin film of piezoelectric material deposited.The piezoelectric material, submitted to strain, is thus deformed, generating an electri-cal charge that becomes an electrical potential difference (voltage) at the electrodes ontop and bottom of the piezoelectric film. The accumulated charge in the electrodes flowsto whichever electrical load is connected to the device, thus generating electrical energy.When the cantilever bends the resulting stress is mostly aligned with the length of thebeam, having only a small parcel associated with compression, which is aligned verti-cally with the thickness of the beam. For that reason, the device operates mostly on thetransversal piezoelectric mode, with the 𝑑31 coefficient accounting for the majority of theeffect. It is important to note that there is also a small contribution from the 𝑑33 coeffi-cient, due to the compression of the beam, which can be more significant in smaller lengthcantilevers.

In order to have a device sensitive to ambient vibrations, its resonance frequencywould have to be low, since the most energetic harmonics in ambient vibrations are usuallybelow 200 Hz. To better understand the influence of the structure shape and dimensions atthe resonant frequency, finite-element analysis simulations were made, using the COMSOLMultiphysics software. The simulation also showed a color-map of the stress intensity onthe cantilever, indicating that the best region to position the piezoelectric material isindeed close to the anchored base, as shown in figure 4. The stress simulation was madeusing the model of a previous design of the cantilever, with a similar shape and slightlydifferent dimensions 8.

Due to the micrometer dimensions, the structure tends to have a high resonantfrequency. However, the use of a relatively heavy mass on the tip and a long (high length)cantilever contributes to lower the frequency. The width of the cantilever does not affectthe resonance frequency, but having a high length-to-width ratio increases the mechanicalstress on the piezoelectric film, generating higher voltages, but with lower current due to

8 The free trial licence of the COMSOL software was expired when the current design was made.


Figure 4 – Simulation of the stress generated by the displacement of the tip mass of thecantilever, using the COMSOL Multiphysics software.

the reduced electrode area and, also, lower mechanical robustness due to the narrowerbeam. With those considerations in mind the device design was made.

Figure 5 shows a three-dimensional model of the designed device, with indicationsof some dimensions in µm. Note that the piezoelectric layer is hidden right underneaththe metal layer, displayed in grey, close to the anchored base in the bar region subdued tothe highest mechanical stress. The curved geometry on the top silicon layer, connectingthe cantilever to the bar anchorage and to the tip mass, is a design recommendationfor the PiezoMUMPs process, to guarantee a higher mechanical robustness during thefabrication steps. The effect of that curvature will not be taken into consideration duringthe analytical modeling, due to increased modeling complexity. The device dimensionsare provided in table 1

All the layer thicknesses were defined by the fabrication process, not being subjectto alteration. In order to have the lowest possible resonant frequency the bar length andthe tip mass size were maximized. The tip mass size had the maximum dimensions allowedby the design rules and the total length was limited only by the other structures of the chip.The width was chosen in order to have a good trade-off between mechanical robustnessand high stress under the piezoelectric material, abiding by the PiezoMUMPs length-to-width ratio recommendation. The electrodes were positioned in the highest stress region,as shown by the simulation in figure 4, but having the shortest length as possible in ordernot to provide a considerable increase in the cantilever stiffness, which would undesirablyincrease the resonant frequency.

1.5. Wireless Sensor Nodes 45

Figure 5 – Three-dimensional model of the piezoelectric micro-cantilever proposed, withcorresponding dimensions in µm.

Table 1 – Proposed device dimensions

Dimension Symbol Value [µm]

Total length 𝐿𝑡𝑜𝑡 3200

Bar length 𝐿𝑏 2100

Bar width 𝑊𝑏 400

Length and width of the tip mass 𝐿𝑝𝑚 1000

Top electrode length 𝐿𝑒 800

Top electrode width 𝑊𝑒 375

Base substrate thickness 𝑡𝑝𝑚 400*

Top silicon layer thickness 𝑡𝑠 10*

Thermal silicon oxide layer thickness 𝑡𝑜𝑥 1*

Piezoelectric layer thickness 𝑡𝑝 0.5*

Metal layer thickness 𝑡𝑚 1.015*

Total volume 𝑉𝑡𝑜𝑡 0.4084 mm3

* - Thicknesses defined by the PiezoMUMPs process.

1.5 Wireless Sensor Nodes

In order to have a better understanding of a potential application for the micro-cantilever, an introduction to wireless sensor nodes (WSN) will be given. Those electronicdevices can either be used as standalone units or compose a larger wireless sensor networkof several nodes. The development of cheap integrated circuits, with low power consump-


tion, high processing speed and wireless data transmission, among with microfabricatedsensors capable of measuring several physical quantities, has enable the use of WSN for awide range of applications. Some interesting possibilities, described in detail in (DARGIE,2012), are:

∙ Monitoring the structural integrity of large infrastructures, such as buildings, bridgesand dams.

∙ Environmental monitoring, measuring wind speed, temperature, pressure, humidity,etc.

∙ Monitoring animal behavior, attaching a sensor node to a wild animal or cattle.

∙ Study of volcanic activity.

∙ Precision agriculture, measuring soil properties such as the pH, humidity, nutrientconcentration, etc.

∙ Monitoring the health of patients and detecting fall of elderly people.

The specific constituent elements of a wireless sensor node might depend uponthe application, but all these systems have in common the use of four basic components:a microcontroller unit (MCU); a wireless transceiver; at least one type of sensor; and apower unit containing a power source, typically a battery. Most applications requires thenodes to function for an extended period of time, sometimes working for years before abattery change is required. For that reason, the components used for such systems musthave the lowest possible power consumption. The other strategy used for saving energyis to work with a reduced duty cycle, being in a low consumption sleep or standby modefor most of the time, while switching to the active state very briefly, when measurementsand data transmission and reception occur. Since most applications do not require acontinuous measurement and data transmission, the operation in a low duty cycle is anexcellent strategy to save power.

The proposed micro-cantilever could be used in a wireless sensor node as a low-power vibration sensor and also as a power source, working as a vibrational energy har-vester, provided that the ambient vibrations are abundant and of sufficient intensity inorder for it to generate enough power. Evaluating if the micro-cantilever can be usedfor powering these systems is one of the goals of this work. For that reason, the powerconsumption of elements that can be used to assemble a wireless sensor node will be dis-cussed, providing a better understanding of the minimal power that the micro-cantilevershould generate.

1.6. Low Power Electronics for Wireless Sensor Nodes 47

1.6 Low Power Electronics for Wireless Sensor NodesAs seen before, the three main elements in a wireless sensor node that consumes

power are: the sensors, the wireless transceiver and the MCU. Nowadays, a wide varietyof commercial devices is cheaply available for these classes of devices, however, only theones designed for low power consumption should be used for a wireless sensor node. Thegoal of this section is to give a brief introduction to each of these types of componentsand to establish a benchmark for the lowest possible consumption in a theoretical wirelesssensor node that could be assembled with commercial components.

1.6.1 Sensors

A great variety of different sensors exists to measure virtually all kinds of phys-ical quantities. Sensors are typically used to measure temperature, acceleration, strain,pressure and luminosity. The advances in MEMS technology has increased the realm ofpossibilities for microfabricated sensors, which are getting smaller, cheaper and consum-ing less power. It is recommended reading (GARDNER; VARADAN; AWADELKARIM,2001b) for detailed information about MEMS sensors. Some types of microfabricated sen-sors are not built using MEMS technology. Light detectors and temperature sensors canbe made using a standard CMOS (complementary metal-oxide-semiconductor) microelec-tronic technology, and some MCUs come with a built-in temperature sensor. Microfab-ricated accelerometers and pressure sensors are typically made with MEMS technology,relying on the capacitance change of an mobile or flexible inner structure due to the me-chanical perturbations to be measured. These same physical quantities can also be mea-sured using the piezoresistive effect, not to be confounded with the piezoelectric effect,which is the change in a material electrical resistance due to the mechanical deformation.Piezoresistive based sensors can also be used for strain measurement, which is probablythe main application for such devices.

It is important to note the mentioned types of sensors require power to work. Thepower consumption of these elements is highly variable, depending upon several factorssuch as the type of sensor and the physical quantity being measured, the sensitivity,measuring range and accuracy. Nevertheless, for most wireless-sensor-node applications,the sensor consumption is lower than the power consumption from the other elements. Toachieve the goal of investigating the power consumption of a WSN, an application usingonly one type of sensor will be discussed. The low power sensor chosen is a 3-axis MEMSaccelerometer, the LIS3DH from STMicroelectronics. The sensor can work with a powersupply ranging from 1.7 V to 3.6 V and has an operational current of 6 µA to 11 µA,consuming about 22 µW of power in the active mode (STMICROELECTRONICS, 2016).The device also has a low-power mode of operation that consumes about 5 µW. Themeasured data output uses the SPI (serial peripheral interface) or I2C (inter integrated


circuit) digital communication protocols, so an MCU capable of communicating in at leastone of these protocols is required. The LIS3DH consumption will be used as a baseline todetermine the WSN consumption.

1.6.2 Wireless Transceivers

The wireless transceiver module is responsible for sending and receiving data usingradio frequency waves, typically in a range from 100 MHz to 5 GHz. The transceiver mustbe able to send data, measured from the sensor and other types of signals indicating thesystem status, to a central data processing station or to a nearby WSN, transmitting theinformation sequentially through nodes, thus enabling a wider range of data transmission.In that way, for a wireless-sensor-network application, where multiple nodes that cancommunicate with each other, the wireless transceiver module must also be able to receiveinformation. Most commercially available wireless transceiver circuits have both modesof operation, being able to transmit and receive data.

There are many types of wireless communication circuits suitable for a variety ofapplications. They can be characterized by the RF frequency; the transmission range anddata rate; the receiving sensitivity; the power consumption; the wireless protocol used;the presence of a dedicated MCU and the peripherals available; among several other char-acteristics. The transceivers that are suitable for a WSN application should have thelowest possible power consumption, but they should also be able to receive and transmitdata reliably. A compromise must be made between the energy requirement the trans-mission range and data rate. A low-power consumption is only achievable for relativelyshort ranges and low data transmission rates. The RF communication frequency is alsorelated to the power consumption, in a way that higher frequencies requires more power,but have the advantages of higher data transmission rate and feature a smaller antenna,enabling smaller devices. The communication protocol used can also influence the powerconsumption, as they can be designed to have an efficient pattern for sending and receivinginformation, ensuring the reliability and integrity of the information while minimizing thedata package size and the required processing power. The Wi-fi and Bluetooth protocolsare well known due to consumer-electronics applications in internet and mobile commu-nications, but there are better protocols for WSN, such as ZigBee and BLE (BluetoothLow Energy), particularly suited for low power applications and smaller data transmissionrates.

During the data transmission and receiving operation, the device can have a sig-nificant power consumption. For that reason, it is expected that the wireless transceiverwill account for most of the WSN consumption. Although the technological advancesin microelectronics has enabling a drastic reduction in MCUs power consumption, whilemaintaining or even increasing their functions and processing power, these advances have


not significantly improved the power consumption of wireless transceivers. The fact thatthe energy of propagating electromagnetic waves decays with the distance, and the impos-sibility of greatly increasing the receiver sensitivity, imposes a power cap for the energyrequirements of wireless transceivers. The strategy used for saving energy is, as mentionedearlier, operation in a low duty cycle, transmitting and receiving information for brief pe-riods of time relative to the standby low-power mode. Most applications for WSN do notrequire continuous communication, sending one measurement, every one or ten minutes,or at longer intervals, would probably be sufficient.

To obtain a benchmark for the consumption of wireless transceivers, that couldbe used in a WSN, a suitable commercially available device will be discussed briefly.The nRF24L01+, provided by the Nordic Semiconductor, operates in the 2.4 GHz usingthe ESB (enhanced ShockBurst) protocol, and has a very low power transceiver capableof transmitting data at a rate up to 2 Mbps in a short range, up to 50 m in openareas (NORDIC SEMICONDUCTOR, 2008). The device can be powered with a supplyvoltage ranging from 1.9 V to 3.6 V, having an internal voltage regulator, and has fourtransmission power modes of operation, in 0 dBm, -6 dBm, -12 dBm and -18 dBm. Inthe lowest power mode, -18 dBm, the current consumption is 7 mA and in the maximumpower, 0 dBm, which yields a better transmission range, the current is 11.3 mA. Thereceiving mode has three modes of operation, associated with three transmission rates,2 Mbps, 1 Mbps and 250 kbps, having the highest sensitivity, of -94 dBm, and consumingthe lowest current, 12.6 mA, in the 250 kbps mode. The nRf24L01+ has a low-consumptionstandby mode and an even lower consumption power-down mode, that consumes only900 nA and waits for an MCU signal to start the active operation mode of transmissionor receiving data. Considering the lowest supply voltage, the lowest power consumptionfor the transmission mode is 13.3 mW, for the receiving mode it is 24 mW and in thepower-down mode it would be 0.0017 mW. It is important to note that this device requiresan MCU, with the SPI communication protocol, to control its operation.

1.6.3 Microcontrollers

The microcontroller units, MCUs, are single-chip computers that perform severalimportant functions for a variety of different applications. For the WSN context, the MCUdevice can be responsible for sending signals to the sensor, to begin and stop measure-ments, processing and temporarily storing the measurement data, and coordinating thecommunication with the wireless transceiver. For the operation in a low duty cycle, whereonly sporadic measurements are made and the systems stay in a low-power standby statefor most of the time, the MCU can be responsible for "waking up" modules, with an inter-nal periodic interruption signal from a RTC (real time clock), or triggered by an externalstimuli, such as a perturbation in a monitored input.


There are several types of commercially available MCUs with a plethora withdifferent functions, suitable for a wide range of applications. Some important features toevaluate the choice of an MCU are presented in the following list.

∙ Number of bits of the processor architecture, can be 4, 8, 16, 32 or 64 bits. Usuallya higher number of bits translates into a higher processing power, for the samefrequency, and enables more memory, but has a higher complexity and requiresmore power.

∙ Clock frequency, associated with the speed in which the processor operations aremade. A higher frequency demands more power. It is not unusual for a an MCU tohave several different operation frequencies for the user to choose from.

∙ Memory, that can be categorized in two types: the program memory, which containsthe specific programmed instructions for a desired application; and the data mem-ory, which can be used for general purpose, to store information during the MCUexecution. The most common type of program memory is the EPROM (erasable pro-gramable read only memory), and MCUs that have more EPROM can have morecomplex instructions. The typical data memory is of two kinds, RAM (random ac-cess memory) and flash memory (non volatile), and this is the memory that wouldbe used for storing the sensor measurements before sending it to the transceiver, ina WSP application.

∙ Number of digital I/Os (input/output), that can be programmed to control, moni-tor and interact with other devices according the desired function demanded for aspecific application.

∙ Digital communication protocols, to program the MCU and interact with othercomponents. The presence of SPI and I2C communication is typical, but othertypes of protocol exist.

∙ Types of peripherals available, such as ADCs (analog to digital converter), PWM(pulse width modulation) output, RTC, comparators, and several other possibilities.

The microcontroller unit consumption is highly dependent on its functions andon the processing frequency, in a way that complex devices, which perform more oper-ations and deal with a higher number of peripherals in less time, would have a largerconsumption. The advances in the microelectronics technologies have greatly reduced theconsumption of MCUs, while increasing or retaining the same functionality and processingpower, enabling applications that requires ultra low power consumption, such as wirelesssensor nodes. There are several commercially available MCUs that fit the requirementsfor a WSN. The Texas Instruments (TI) company leads the development of ultra low


power MCUs, having a whole family of products dedicated to cope with energy restrictiveapplications. The MSP430 MCU products are advertised by the company as "ultra lowpower sensing and measurement MCUs", and that claim is supported by the technicalspecification of these products (TEXAS INSTRUMENTS, 2018).

To fulfill the goal of obtaining a baseline for a low-power WSN, a class of de-vices in the MSP430 family, with particularly low-power consumption was chosen. TheMSP430FR2xxx9 devices can operate in a voltage range from 1.8 V to 3.6 V and havean active current consumption as low as 100 µA/MHz, for active non-volatile memorywriting operations. Note that the power consumption is closely related to the processingfrequency. Choosing the lowest operation frequency of 1 MHz, and the lowest supply volt-age, yields a power consumption of 720 µW. The low-power standby mode has a muchlower power consumption and can operate with a RTC to wake up the MCU to the activestate in regular predetermined time intervals. The standby consumption can be as low as0.35 µA, requiring only 0.63 µW of power when the supply voltage is in the lower range.

1.6.4 Power Consumption of the System

A theoretical WSN could be assembled using the components discussed in theprevious sections. The power consumption of the resulting device would be dependentupon the chosen operation mode, as the active power drawn when the device is measuring,sending and receiving data is orders of magnitude higher than the power required for thestandby, idle mode. To determine the power consumption, a fixed duty cycle, consistingof the proportionate time that the WSN is either active or idle, would have to be chosen.The power consumption of the three main components in the WSN is summarized in table2.

Table 2 – Consumption of Low Power Components for WSN

Component Type Manufacturer Device ActivePower

StandbyPower

Acceleration Sensor STMicroelectronics LIS3DH 22 µW 5 µW

Wireless Transceiver -Transmission Mode

Nordic Semiconductor nRF24L01+ 7000* µW 1.7 µW

Wireless Transceiver -Receiver Mode

Nordic Semiconductor nRF24L01+ 24000* µW 1.7 µW

Microcontroller Unit Texas Instruments MSP430FR2xxx 720 µW 0.63 µW

* - The lowest consumption for the transmission and receiver mode.

In the active mode, the system consumes 24742 µW for receiving data and 7742 µWfor transmitting data, most due to the transceiver consumption. In the standby mode the9 There are several devices in this class with different options regarding peripherals, number of I/Os

and memory, but they share similar power consumption characteristics.


device would require only 7.33 µW. The power consumed in each operation mode is definedby summing the power consumed by the three components for that mode. The averagepower is calculated as a weighted average using the time spend on each mode as thefactors, as shown by the following equation:

𝑃𝑎𝑣𝑔 = 𝜏𝑠𝑡𝑎𝑛𝑑𝑏𝑦𝑃𝑠𝑡𝑎𝑛𝑑𝑏𝑦 + 𝜏𝑎𝑐𝑡𝑖𝑣𝑒𝑃𝑎𝑐𝑡𝑖𝑣𝑒

𝜏𝑠𝑡𝑎𝑛𝑑𝑏𝑦 + 𝜏𝑎𝑐𝑡𝑖𝑣𝑒

(1.1)

Where 𝑃𝑎𝑣𝑔 is the average power consumed by the system, 𝜏𝑠𝑡𝑎𝑛𝑑𝑏𝑦 and 𝑃𝑠𝑡𝑎𝑛𝑑𝑏𝑦 arethe time spend and the total power consumed in the standby mode, and 𝜏𝑎𝑐𝑡𝑖𝑣𝑒 and 𝑃𝑎𝑐𝑡𝑖𝑣𝑒

are the same variables for the active mode.

Considering an application where the device would make one measurement ev-ery 20 minutes, and assuming that it would take 1 second to wake up the components,perform the measurement and send the data, the average consumption would be about13.7 µW. The average consumption for receiving data would be about two times higher. Ifwe consider that the device will spend much more time in the standby mode, the averageconsumption would tend to the consumption value of that mode, which is 7.33 µW. As-suming that it is possible to completely shut down the power to the sensor and transceiverduring the MCU standby mode, the power would be much lower, tending to the idle con-sumption of the MCU, which is 0.63 µW.

It is important to note that there are other factors that influence the power con-sumption in a real WSN. There losses associated with other required components, suchas leakage current in the capacitors, and resistive losses in the connections. If a batteryand a power conditioning circuit are used, there are also losses associated with thosecomponents. The goal was to establish some power consumption baseline to evaluate theapplication of the micro-cantilever as an energy harvester for powering such systems.Since there is a large variety of suitable components for assembling a WSN, and that thechoice of components is highly biased toward the specific application, several WSN pos-sibilities may present a lower power requirement. When discussing the micro-cantileverapplicability, at the end of the results chapter, these considerations will be taken intoaccount.

53

2 Materials and Methods

2.1 Overview of the Technological Advances in Piezoelectric Micro-Cantilevers for Energy HarvestingSeveral works of different authors have been published in the area of vibrational

energy harvesting and a special interest was given to piezoelectric devices, confirming theiradvantageous use for this kind of application. These works provide important insights tounderstand power capabilities, limitations and the verification of the modeling and testingmethodologies used for these devices. Therefore, the goal of this section is to provideinsightful data gathered from piezoelectric vibrational micro-power generators, fabricatedand tested by prominent researchers in the field. The review will provide the followinginformation:

∙ The type of piezoelectric material and the operation mode (transversal, 𝑑31, orlongitudinal, 𝑑33) used;

∙ The device dimensions and resonance frequency;

∙ The acceleration intensity of the vibration source;

∙ The type and magnitude of the electrical load connected to the device and the powergenerated in these conditions.

A summary of the collected data is given in table 3.

Table 3 – Data from similar devices published by other authors

Author Material Mode Volume Frequency Power Acceleration Load

Elfrink AlN 𝑑31 *20 mm3 325 Hz 85 µW 17.2 m/s2 -

Jeon PZT 𝑑33 0.027 mm3 13.9 kHz 1 µW 103.7 m/s2 5.2 MΩ

Marzencki AlN 𝑑31 0.51 mm3 1496 Hz 0.8 µW 19.6 m/s2 450 kΩ

Shen PZT 𝑑31 0.652 mm3 461 Hz 2.15 µW 19.6 m/s2 6 kΩ

* Estimated value based on the data provided in the paper; - Unknown value.

It has been reported by (ELFRINK et al., 2010) a vibrational micro-power genera-tor, in the shape of a MEMS piezoelectric cantilever, powering a complete wireless sensormodule that sends temperature measurements every 15 seconds to a receiver positioned15 meters away. The module, shown in figure 6, consumes less than 10 µW of average

54 Chapter 2. Materials and Methods

Figure 6 – Autonomous wireless sensor module, with a piezoelectric vibrational energyharvester in a vacuum package as the only energy source. Figure taken from(ELFRINK et al., 2010).

power, with a peak current of 13 mA that occurs for 0.5 ms during the data transmission.The researchers developed and tested ten versions of micro-cantilever, each with slightlydifferent dimensions, evaluating the effect that a vacuum/low-pressure sealed package hasin the reduction of the mechanical damping and in the consequent increase in the qualityfactor and the maximum power generated. The design that showed the best results wasthe one with the largest mass on the tip, generating 85 µW when submitted to vibrationsof 17.2 m/s2 of intensity in the resonant frequency of the device, 325 Hz, outside thepackage. The device was fabricated in a SOI wafer, following a micro-fabrication processsimilar to the PiezoMUMPs, also using a thin film of aluminum nitride as the piezoelectricmaterial. The study made with low-pressure1 sealed packaging indicated an increase inthe power generated of three to four times, compared to the same devices operating inambient pressure. However, the package imposed space limitations for the displacementof the tip mass to freely oscillate when submitted to higher vibration intensities, thuslimiting the maximum intensity of ambient vibrations at which the device can operate.In that situation, using a vacuum sealed package, the same device provided 17 µW to anoptimal load, when submitted to vibrations of 6.3 m/s2 of intensity.

The use of inter-digitated electrodes, exploring the longitudinal operation mode,𝑑33, was reported in (JEON et al., 2005; CHOI et al., 2006). The fabricated device de-

1 Pressures lower than 0.01 mbar.

2.1. Overview of the Technological Advances in Piezoelectric Micro-Cantilevers for Energy Harvesting55

scribed in these two papers, showed as an example in the figure 2 in chapter 1, consists ofa cantilever made of a thin silicon oxide and silicon nitride structure with a photoresit tipmass, having a PZT material deposited on top of the bar acting as the piezoelectric mate-rial. The micro-cantilever, with length and width of 190 × 240 µm2, was able to generate1 µW of power to an optimal load of 5.2 MΩ, when submitted to vibrations of 103.7 m/s2

of acceleration in the resonant frequency of 13.9 kHz. A analytical model was developed,in (DUTOIT; WARDLE; KIM, 2005), to predict the behavior of piezoelectric vibrationenergy harvesters and the experimental results of this device were used to validate theconstituent equations of the model.

A vibrational micro-power generator fabricated in a SOI wafer, using AlN as thepiezoelectric material, was successfully used to power a wireless sensor node, as reportedin (MARZENCKI; AMMAR; BASROUR, 2008). The fabrication process used to makethe device is very similar to the PiezoMUMPs process. The energy harvester consists ofa thin silicon cantilever, of 5 µm thickness, with a tip mass of 1200 × 800 × 0.525 µm3 oflength, width and thickness, respectively. The figure 7 shows a SEM (scanning electron mi-croscopy) photography of the device and the cross section diagram of its constituent layers,where it is possible to note how similar the fabrication technology is to the PiezoMUMPsprocess. The device was able to provide 0.8 µW of power to an optimal resistive load,of 450 kΩ, when excited with vibrations of 19.6 m/s2 of acceleration in its resonancefrequency, 1496 Hz. The wireless sensor node system powered by the micro-cantilever de-vice consists of a 4-bit RISC (reduced instruction set computer) microprocessor, EM6607,a wireless transceiver, nRF24L01 and a temperature and acceleration sensor, AD7814and LIS3LV02DQ. The system operates in a low duty cycle, performing only one ac-tion every 10 minutes, having an average consumption of approximately 0.15 µW. Themicro-cantilever was used in conjunction with a rectifier and multiplier circuit to powerthe system. It was possible to power the wireless sensor node even in lower magnitude,3.9 m/s2, ambient vibrations, using an array of five micro-cantilevers that occupies a totalvolume of about 5 mm3.

A micro-cantilever with similar shape and dimensions to the one proposed in thiswork was reported in (SHEN et al., 2008). The figure 8 shows a microscope photographyof the structure, which consists of a cantilever with dimensions of 4800 × 400 × 36 µm3

with a tip mass of 1360 × 940 × 456 µm3. The device was able to provide 2.15 µW ofpower to an optimal load of 6 kΩ, when submitted to vibrations of 19.6 m/s2 of intensityin the resonant frequency of 461 Hz. In the reference paper the author also provides abrief review of similar works published by other researchers, comparing his results withother devices.

A direct comparison of the power generation performance of the mentioned de-vices can not be done, since all devices have different dimensions and were tested under


Figure 7 – SEM photography of the micro-cantilever, in the left; cross section diagramof the device layers, in the right. Figure taken from (MARZENCKI; AMMAR;BASROUR, 2008).

Figure 8 – SEM photography of the device as seen from top, in the left, and from bottom,in the right. Figure taken from (SHEN et al., 2008).

different circumstances, using different vibration intensities. A performance criterion typ-ically used for normalizing the power, taking into account the different device size, is thepower density, provided in µW/cm3. That parameter consists of the power divided by theeffective device volume. However, the power output is related to the vibration intensity,in a way that higher intensities will, up to a breakdown limit, give a higher power outputfor the same device. Analytical modeling of the power generated by a piezoelectric micro-cantilever suggests that the power is directly proportional to the squared acceleration ofthe vibration. Therefore, it is reasonable to have that into account for normalizing theperformance results. Indeed, it was verified in (MILLER et al., 2011) the use of this nor-malization criteria, in which the comparison parameter consists of the power divided bythe squared intensity of the vibration. But the typical power density was not used, so inthis work it is proposed that the normalization is extended to take into account these twofactors: the device volume and the intensity of the vibrations. In that way, the comparisonunit would consist of the power density divided by the squared vibration intensity, havinga unit of µW/cm3/m2/s4 that will be called PU (per unit) for simplification purposes.

2.2. Study of Ambient Vibration Sources 57

This parameter will be called performance factor and the equation to calculate it will bepresented in section 3.1. Using this normalization it is possible to compare the differentdevices presented in this section. It is possible to verify that the device reported by El-frink is indeed the one with the best performance, with a performance factor of 14.4 PU,followed by the device proposed by Shen, with 8.6 PU, and then the one by Marzencki,4.1 PU, and Jeon’s in the last place, with 3.4 PU.

2.2 Study of Ambient Vibration Sources

In order that the piezoelectric micro-cantilever generates power, it is necessary thatthe device is excited by ambient vibrations of adequate intensity and frequency. Therefore,it is important to study commonly found ambient vibration sources and determine whichones are appropriate for power generation.

Ambient vibrations are present virtually anywhere on the planet. Whether dueto acoustic wave propagation, wind or movement of nearby structures, the environmentis full of sources of mechanical vibrations. However, most vibration sources do not haveenough intensity in the right harmonic frequencies to be effectively harnessed for micro-power generation. It is important to evaluate the maximum power harmonic frequency,that being the frequency in the harmonic spectrum of the vibration source that hasthe highest intensity. Typically, ambient vibrations are of low frequency, with the mostenergetic harmonics in its spectrum being under 200 Hz.

It will be seen, in the analytical modeling section, that the power generated bythe piezoelectric micro-cantilever is highly dependent upon the relationship between itsresonance frequency and the vibration source frequency, delivering the highest power whenboth frequencies match. Because of that it is important to design the cantilever with alow resonance frequency, matching the maximum intensity harmonics in typical vibrationsources.

It is possible to measure the intensity of a vibration source using a high sensitiv-ity accelerometer, along with a data acquisition system. The frequency spectrum can bedetermined applying the FFT (Fast Fourier Transform) to the accelerometer measureddata. Since different vibration sources present a different frequency spectrum, ideally, avibrational energy harvester would be designed having a resonant frequency for the spe-cific vibration source in which the device will work, and the auxiliary circuitry would bedesigned having in mind the voltage levels generated, according to the intensity of the vi-brations provided by the source. However, in most situations that is very impractical andexpensive. A better approach would be to evaluate typical vibration sources, establishinga benchmark for the micro-power generator operation. Therefore, a search for studies ofvibration sources was made, taking note of the intensity and frequency spectrum of com-


monly found sources. The data presented in table 4 was taken from (ROUNDY; WRIGHT;RABAEY, 2003; DUTOIT; WARDLE; KIM, 2005), representing the maximum intensityharmonic, in the "Frequency" column, and the average acceleration in these harmonics, inthe "Intensity" column.

Table 4 – Intensity and frequency of common ambient vibration sources

Source Intensity [m/s2] Frequency [Hz]

Car engine compartment 12 200

Industrial machine base 10 70

Blender 6.4 121

Person nervously beating his/her foot 3 1

Car dashboard 3 13

Door frame right after the door closing 3 125

Small microwave oven 2.5 121

Air conditioning venting tube in an office 0.2 - 1.5 60

Window nearby a busy road 0.7 100

Office desk 0.09 120

Small tree 0.003 30

Table based on the study presented in (ROUNDY; WRIGHT; RABAEY, 2003; DUTOIT; WAR-DLE; KIM, 2005).

Analyzing the data shown in the table it is possible to conclude that, in general,the average intensity of ambient vibrations is very low, being higher than 9.8 m/s2 onlyat industrial environments in close proximity to medium size motors. Therefore, it isreasonable to use an intermediate intensity source as a baseline for the analytical powergeneration calculations, considering ambient vibrations generated by a small microwaveoven, of 2.5 m/s2, with a frequency spectrum ranging from 120 to 200 Hz. Note that thefrequency presented in the table is the maximum intensity harmonic, the actual frequencyspectrum might have a much broader range.

2.3 Overview of Auxiliary Circuits for Energy HarvestingIt is expected that the signal generated by the micro-cantilever would be sinusoidal

with a frequency dependent upon the ambient vibration excitation frequency. Therefore,the device output is not appropriate for directly powering typical electronic circuits or forcharging a capacitor or battery, which require a constant voltage. The usage of auxiliarycircuitry is required for conditioning the micro-cantilever signal for the energy harvestingapplication. These auxiliary circuits can have, among others, the following roles:

∙ Rectification, converting the alternated current (AC) signal into direct current (DC).

2.3. Overview of Auxiliary Circuits for Energy Harvesting 59

∙ Boost/Multiplication of the voltage, in case the generated signal voltage is lowerthan the voltage required for the powered circuits.

∙ Regulation of the voltage, converting the micro-cantilever variable voltage amplitudesignal (which depends on the intensity of the ambient vibrations) into a stabilizedvoltage in an appropriate range for the load to be powered.

∙ Impedance matching, to improve the power transfer from the micro-cantilever, typ-ically having a high output impedance, to the powered load, which can have a muchlower input impedance. For that reason, without an impedance matching circuit thepower transfer could be very inefficient.

Possible implementations for circuits that performs these roles will be given in thefollowing sections. It is important to note that there are several circuit topologies thatperform these functions. This present work only contains an overview of a few popular sig-nal conditioning strategies. A review of several different circuits used in energy harvestingis given in (HEHN; MANOLI, 2015).

2.3.1 Rectifier Circuit

The typical rectifier circuit is composed of a diode bridge and a capacitor in paral-lel with the output. The figure 9 shows the schematic of a diode-based full-wave rectifiercircuit. The micro-cantilever is represented in the schematic as an ideal voltage source,supplying a sinusoidal voltage of constant amplitude and frequency, and the load is rep-resented by a resistance.

The plot in figure 10 shows the waveform of the input voltage, generated by themicro-cantilever, and the rectified voltage with and without the capacitor. Note thatincreasing the capacitance value the output voltage ripple (oscillation) is reduced. It isimportant to note that there is a voltage drop due to the diode forward polarizationvoltage, 𝑉𝑑. In the full-wave configuration that voltage drop is equal to twice the 𝑉𝑑,since the generated current passes through two diodes in each oscillation. If the voltageamplitude generated by the micro-cantilever is lower than two times the 𝑉𝑑 of the chosendiodes, the output voltage would be zero, therefore the device would not generate anypower. For that reason it is very important to choose diodes with the lowest possible 𝑉𝑑.Typical 𝑉𝑑 values are in the 0.7 V to 1 V range, but there are some diodes that have the𝑉𝑑 as low as 0.2 V.

Since the micro-cantilever generated voltage is expected to be quite low, it is veryimportant to minimize the voltage drop in the rectification circuit. Another rectificationstrategy, that uses MOSFET (metal-oxide-semiconductor field effect transistor) transis-tors, instead of diodes, may be used to increase the circuit efficiency. The MOSFET can


Figure 9 – Schematic of a diode based full-wave rectifier circuit.

Figure 10 – Waveform plot of the voltages in the diode based full-wave rectifier circuit.


Figure 11 – Schematic of a MOSFET based full-wave rectifier circuit.

be seen as a voltage controlled switch that is activated, enabling the current conductionbetween the drain and source terminals, when the voltage between the gate and sourceterminals, 𝑉𝑔𝑠, is larger than the threshold voltage, 𝑉𝑡. Although the MOSFET basedfull-wave rectifier circuit also has a minimum voltage requirement, the 𝑉𝑡, it may not posean expressive voltage drop in the output, like the diode based rectifier. The schematicfor the circuit is shown in figure 11. The circuit uses two branches of MOSFETs, onecontaining pMOS transistors and the other with nMOS transistors2. The output voltagedrop is equal to the product of the conduction resistance of the transistors by the currentgenerated by the micro-cantilever. That drop is represented by the sum of the 𝑉𝑑𝑠 voltagesin the nMOS and the pMOS transistors, in one branch of the circuit.

As seen in section 2.1, the power generated by the micro-cantilever structuresis very low, being in the µW range for high impedance loads. Therefore, the generatedcurrents are very small, so the voltage drop, associated to the 𝑉𝑑𝑠 voltage, is expected tobe very low. However, it is very important to choose transistors that have a 𝑉𝑡 lower thanthe voltage generated by the micro-cantilever, otherwise the transistors will not enterconduction mode and the output voltage will be zero. Having a transistor with lowerthreshold voltage means that the conduction will occur sooner (relative to the generatedvoltage cycle) and a larger portion of the input signal will be rectified. The plot in figure

2 The difference between these types of transistors is the kind of majority charge carrier in the channelregion of the semiconductor material that the device is made of. The practical difference is that thepMOS has a negative threshold voltage, entering conduction mode when the voltage between the gatesource is negative and larger, in magnitude, than 𝑉𝑡. The nMOS is the opposite, meaning that itconducts when a positive voltage larger than 𝑉𝑡 is applied between its gate and source terminals.


Figure 12 – Waveform plot of the voltages in the MOSFET based full-wave rectifiercircuit, without the capacitor in parallel with the load. Comparison madewith transistors of different threshold voltages.

12 shows the waveform of the rectified voltages for different values of 𝑉𝑡, for the same inputvoltage and without accounting for the 𝑉𝑑𝑠 voltage drop. From the plot, it is possible tosee how the 𝑉𝑡 affects the output signal, showing the advantage of choosing transistorswith lower 𝑉𝑡. Although, a transistor with a very low 𝑉𝑡 might be too sensitive to externalnoise, conducting even when the input signal is zero, so a compromise must be made whenchoosing the MOSFETs for the circuit.

There are other types of rectification circuits, such as the synchronous rectifiersthat present even higher conversion efficiencies. However, these are active circuits, requir-ing some power consumption for operation, and hence, having a limited application forrestrictive consumption circuits. In (LE et al., 2006) the authors were able to obtain goodresults using these circuits for rectifying the voltage generated by piezoelectric energyharvesters, but, due to the consumption limitations, the two passive rectifier topologieswill be preferred in the present work.

2.3.2 Voltage Multiplier Circuit

The use of inductive transformer elements is a simple and common strategy foraltering the voltage from an AC source. However, transformers are usually costly, heavy,voluminous components, and the may introduce significant losses due to wiring resistanceand the electromagnetic coupling, hence, being mostly unsuitable for the application with


the micro-cantilever. The successful use of a cascade voltage multiplier, for interfacingthe piezoelectric energy harvester with the wireless circuit powered by it, was reported in(MARZENCKI; AMMAR; BASROUR, 2008). The proposed circuit was able to doublethe input voltage for each multiplication stage, composed of simple diodes and capacitors,with the drawback of requiring several voltage cycles to completely charge the capacitorsinto the maximum voltage. The circuit uses the known Villard cascade voltage multipliertopology, shown in the schematic in figure 13.

Figure 13 – Schematic of a Villard cascade voltage multiplier with two stages.

Note that the presented circuit has two multiplication stages, therefore the outputvoltage would be equal to four times the peak value of the input voltage minus thevoltage drop in the diodes. Any number of multiplication stages can be used to complywith the desired voltage in the powered load, however the addition of stages correspondsto the requirement of more time to charge the capacitors. It is important to consider theleakage current of the capacitors, which imposes an inevitable loss of power, and the factthat adding more stages will increase those losses. Another important consideration isthe fact that the ambient vibrations intensity might vary, altering the amplitude of thevoltage generated by the micro-cantilever, and hence, changing the output voltage by amultiplicative factor. If unexpected voltage peaks occurs, as a result of higher mechanicalperturbations, the output voltage might be too high for the powered load. In this case,an overvoltage protection strategy should be applied.

A plot showing the output voltage for the presented multiplier circuit can be seenin figure 14. When using the voltage multiplication circuit there is no need for a rectifiercircuit, as the output voltage delivered is continuous, with a ripple (oscillation) that isproportional to the electrical load connected. The ripple can be minimized by addingan additional capacitor in parallel with the load, but there is a compromise of increasedcharge time and higher losses due to the additional capacitor leakage current. Note thatit takes some time for the capacitors to fully charge, and hence, for the output voltageto reach its steady state maximum value. The maximum voltage is dependent upon theload connected to the circuit output. The plot shows a comparison of the voltage in


Figure 14 – Waveform plot of the output voltage of the multiplier circuit, without load(open circuit) and with a 500 kΩ resistive load.

the open circuit configuration and with a resistive load of 500 kΩ connected. Note thatthe steady state voltage reaches the highest value in the open circuit configuration. It ispossible to verify that the steady state voltage decreases when the connected load has alower resistance value, being zero for the short-circuit configuration where the resistanceis zero.

2.3.3 DC-to-DC Converters

The voltage regulation and impedance matching functionalities can be imple-mented by electronic DC-to-DC converters. These circuits operates with a controlledswitching of transistors, in a relatively high frequency (5 kHz to 1 MHz), and thereforerequires power to work. If the converter power demand is higher or close to the gener-ated by the micro-cantilever, its usage may not be viable. However, the voltage regulationand impedance matching might be required depending on the powered system of interest.Therefore, it is worthwhile to investigate the means to implement these functions withthe least possible power consumption.

The aforementioned functions can be implemented using typical topologies of DC-to-DC converters, being those the Buck, Boost and Buck-Boost converters, that can beseen, respectively, as circuits that can lower, raise and lower and/or raise the voltage. Sincethe expected voltage generated by the micro-cantilever is very low, the Buck converterwould be hardly used. Therefore, the Boost and Buck-Boost converters are the ones mostused, and both can be used to implement voltage regulation and impedance matching.

Figure 15 shows the schematic for these latter circuits. Note that the control circuit,


Figure 15 – Schematic of the Boost and Buck-Boost converters.

that generates the switching pulses for the transistors, was omitted for simplificationpurposes and due to the fact that different strategies may be used to implement it. Theaverage value of the output voltage in these circuits is dependent on the pulse width of thecontrol signal in the transistors. The parameter that measures this pulse width is calledduty cycle, 𝑑𝑐, and it is defined by the following equation:

𝑑𝑐 = 𝜏𝑜𝑛

𝑇𝑠𝑤

(2.1)

Where 𝑇𝑠𝑤 is the switching period of the pulses and 𝑡𝑜𝑛 is the amount of time inwhich the pulse stays in the high voltage, having a logical value of one. Therefore the dutycycle is simply the ratio in which the pulse signal is raised, being a dimensionless numberbetween 0 and 1. The average value of the output voltage in the Boost and Buck-Boostconverters is given, respectively, by the following equations:

𝑉𝐵𝑜𝑢𝑡 = 𝑉𝑑𝑐

1 − 𝑑𝑐

(2.2)

𝑉𝐵𝐵𝑜𝑢𝑡 = −𝑉𝑑𝑐𝑑𝑐

1 − 𝑑𝑐

(2.3)


Note that in the Boost converter, for any duty cycle value the average outputvoltage is greater or equal to the input voltage, 𝑉𝑑𝑐. In the Buck-Booster converter theoutput voltage will be larger than the input voltage if 𝑑𝑐 > 0.5, and lower if 𝑑𝑐 < 0.5. Acomplete analysis of these circuits operation is beyond the scope of the present work, andthe intent of this section is to present these circuits and point out how they can be used forimplementing a voltage regulator and an impedance matching circuit. More informationabout these converters can be found in (UNDELAND; ROBBINS, 2002). The followingsections will address the application of these circuits for the desired mentioned functions.

2.3.4 Voltage Regulator

The voltage regulation circuit is capable of maintaining its output voltage constantat a desired value, despite of variations in the connected load and in the input voltagesource. The input voltage value is dependent upon the intensity of the ambient vibrationsthat would make the micro-cantilever oscillate, being thus prone to variation. As seenpreviously in section 1.6.4, the wireless circuits that would be powered by the micro-cantilever have two very distinct modes of operation. An active mode that draws a peakcurrent, during the receiving and transmission of data, and a standby mode, that consumesa much smaller current. Therefore, the load of interest, as seen by the micro-cantilever,has two distinct values. If the output voltage variation, due to the load and to the micro-cantilever generated voltage variation, exceeds the voltage range in which the poweredload circuit can operate, a voltage regulation strategy should be implemented.

As seen in the previous sections, in equations 2.2 and 2.3, the average voltage in theoutput of the presented DC to DC converters is not dependent on the connected load value.However, the rectified input voltage, 𝑉𝑑𝑐, supplied by the micro-cantilever can alter theoutput voltage. For that reason, in order for the converter to work as a voltage regulator,a feedback control strategy must be used, changing the control pulses in accordance tothe perturbations observed in the input voltage, which would be known by monitoring theoutput voltage. Most conventional MCU components possess the function to implementthis control strategy. There are only two basic requirements, an ADC (analog to digitalconverter), to convert the output voltage signal into a digital form that can be interpretedby the MCU; and a PWM (pulse width modulation) output, to generate the control pulsesfor the converter. The required feedback control can be implemented by measuring theoutput voltage, using the MCU ADC, comparing it to a reference voltage of a desiredvalue, which is simply a digital value that can be set in the MCU memory, and changingthe control pulse width in order to minimize the voltage error. In that way, the outputvoltage would be actively maintained at the desired value.


2.3.5 Impedance Matching

The impedance matching can significantly increase the power transfer from themicro-cantilever to the load. It is known from the circuits theory that the maximumpower transfer between any power source and load occurs when the load value is equal tothe complex conjugate value of the source impedance. Since the source, the piezoelectricmicro-cantilever, has a capacitive impedance, the optimal load would be inductive withthe same magnitude. To emulate and inductive load of a specific value would requirethe use of discrete elements of significant size and cost, defying the purpose of a compactautonomous wireless system. It would be much easier to emulate a resistive load of optimalvalue, which would not draw as much power as the optimal inductive load but it wouldensure a very good power transfer. It is important to note that implementing such strategycomes with a power consumption cost, as the circuits that emulate an optimal resistiveload are active.

As it will be seen in the analytical modeling section, there is an optimal value ofresistive load that maximizes the power transferred by the device. If the desired circuitto be powered has an impedance value which is much different from the optimal loadvalue, the power transfer would be much lower and most likely insufficient for any use. Inthat case, a circuit that implements an impedance matching strategy should be used. Itis possible to implement such strategy using the DC-to-DC converter circuits previouslydiscussed. The apparent load resistance can be adjusted by changing the pulse widthsignal that controls the transistor, as described by Kong in (KONG et al., 2010).

The specific circuit topology used by Kong is shown in figure 16, which consists ofa diode base full-wave rectifier, without the output capacitor, followed by a Buck-Boostconverter. Note that the pulse control circuit is explicitly shown in the schematic, beingcomposed of a low power oscillator, a comparator circuit and a few other components.The switching frequency and the duty cycle of the pulses can be adjusted for the de-sired/required values by changing the values of the resistances 𝑅𝐶1 and 𝑅𝐶2 and of thecapacitor 𝐶𝐶 . If the 𝑅𝐶2 resistance is chosen as to have a much higher value in compari-son to the 𝑅𝐶1, the duty cycle, 𝑑𝑐, and the switching period (which is the inverse of theswitching frequency), 𝑇𝑠𝑤, can be approximated by the following equations:

𝑑𝑐 ≈ 𝑅𝐶1

𝑅𝐶2(2.4)

𝑇𝑠𝑤 ≈ (𝑅𝐶1 + 𝑅𝐶2)𝐶𝐶 ln(2) (2.5)

The equivalent load resistance, 𝑅𝑙𝑖𝑛, as seen by the source, is related to the controlpulses period, to the duty cycle, and to the Buck-Boost circuit inductance, 𝐿𝐵𝐵𝑖𝑛𝑑, in the


Figure 16 – Schematic of the circuit used by Kong for impedance matching. Figure takenfrom (KONG et al., 2010).

following way:

𝑅𝑙𝑖𝑛 = 2𝐿𝐵𝐵𝑖𝑛𝑑

𝑑2𝑐𝑇𝑠𝑤

(2.6)

In this way it is possible to adjust the values of the components in the circuit toobtain the desired value of apparent load. However, it is important to note that in orderfor the equation 2.4 to give a valid approximation, the duty cycle value must be low, andconsequently the converter will operate in the voltage lowering configuration. Therefore,when using this approach, a compromise must be made between having the desired outputvoltage and performing the impedance matching. A way around the voltage reductionwould be using a voltage multiplier circuit, as seen previously, before the converter input.

2.4 Analytical Modeling

The analytical models for predicting the behavior of piezoelectric micro-cantileversin energy harvesting and vibration sensing applications are not entirely well established,since different authors use different models and there is no consensus about the definiteapproach. In most cases, the researchers rely on experimental measurements for deter-mining some of the parameters, like the resonance frequency, mechanical damping and

2.4. Analytical Modeling 69

electromechanical coupling coefficients, to apply to a semi-empirical model.

Despite the variety of approaches for modeling these kind of devices, some findingswere ubiquitous among different modeling strategies. It is possible to verify, based onexperimental results, that the power generated by the micro-cantilever is related to thefollowing parameters: the effective mass of the device; the acceleration intensity of thevibrations; and the resonance frequency of the structure. The generated power is relatedto the device design, but not in a straightforward manner, having a complex relationshipwith the geometric features of the micro-cantilever, as will be seen in the following sections.Also, several works in the field have shown that:

∙ The quality factor of cantilever structures with a tip mass is very high, which im-plicates a narrow bandwidth around the resonance frequency, functioning as anambient vibration high-Q band-pass filter centered in its resonance frequency. Be-cause of that, it is very important that the vibration frequency spectrum has a highenergy harmonic matching the device resonant frequency.

∙ When the piezoelectric material generates electrical charge, it produces an electricaldamping contrary to the mechanical inertial movement, which is related to theelectrical load connected to the piezoelectric material. There is an optimal load thatmaximizes the power transfer.

Due to the impossibility of reviewing all models found in the literature, this workwill discuss and use two different analytical modeling strategies: the one-dimensional sim-plified model presented by DuToit, (DUTOIT; WARDLE; KIM, 2005), for estimatingthe power generation; and the model based on equivalent electrical circuit parameters,presented by Roundy, (ROUNDY; WRIGHT, 2004). Since some of the parameters aredetermined experimentally, means to estimate these parameters without the need for ex-perimentation were investigated, relying in reported properties of materials and geometricaspects of the designed micro-cantilever structure. Later on, parametric corrections basedon experimental results will be made in order to render a more accurate semi-empiricalmodel for the studied device.

2.4.1 Resonance Frequency

The fundamental resonance frequency (first harmonic) of any structure is defined,by classical mechanics equations, as being:

𝑓𝑁 = 12𝜋

√︃𝐾

𝑀(2.7)


Where 𝑀 is the mass and 𝐾 is the spring constant of the structure, which isdefined by geometric aspects and by the effective stiffness of the structure constituentmaterials. For a cantilever-like structure with a tip mass the spring constant is defined bythe following equation, as presented in (BEEBY; WHITE, 2010):

𝐾 = 𝐸𝑊𝑡3

4𝐿3 (2.8)

Where 𝐸 is the effective Young modulus of the structure material, representingits stiffness, 𝑊 , 𝑡 e 𝐿 are the width, thickness and length of the bar, respectively. Themass can be calculated easily from the material density and the structure dimensions.Specifically, for the designed micro-cantilever in silicon, the mass is given by the equation2.9 below, noting that the length and the width of the tip mass have the same value.

𝑀 = 𝜌𝑠𝑖(𝑊𝑏𝐿𝑏𝑡𝑠 + 𝐿2𝑝𝑚𝑡𝑝𝑚) (2.9)

Where 𝜌𝑠𝑖 is the density of silicon and the other parameters were described in table1 in the first chapter.

The proposed micro-cantilever device has several layers, being composed of dif-ferent materials. However, it is reasonable to assume that the biggest contribution forthe structure stiffness is given by the silicon top layer, which is made of monocrystallinesilicon. Therefore, the silicon Young modulus will be used for the calculations, ignoringthe stiffness of the other layers, which are much thinner and do not have a significantcontribution for this parameter.

Equation 2.8 assumes that the mass is concentrated in the tip of the structure. Acorrection in the spring constant should be made to account for the fact that the devicecenter of mass is, approximately, in the center of the tip mass. Therefore, as showedin (SHEN et al., 2008), an effective spring constant, 𝐾 ′, should be used, which can becalculated by the following equation:

𝐾 ′ = 𝐾( 𝐿𝑡𝑜𝑡

𝐿𝑡𝑜𝑡 − 𝐿𝑝𝑚/2)3 (2.10)

Where 𝐿𝑡𝑜𝑡 is the total length of the structure and 𝐿𝑝𝑚 is the length of the tipmass, as indicated in figure 17.

Note that the angular frequency and the frequency in Hertz unit is related to eachother by a factor of 2𝜋, therefore the frequency in Hertz is given by:

𝑓𝑁 = 𝜔𝑁

2𝜋(2.11)


Figure 17 – Diagram of the dimensions of a cantilever with tip mass.

Therefore, the angular resonance frequency of the proposed device, 𝜔𝑁 , (in rad/s),is given by the following equation:

𝜔𝑁 =

⎯⎸⎸⎷(︃𝐸𝑠𝑖𝑊𝑏𝑡3𝑠

4𝐿3𝑏𝑀

)︃(︃𝐿𝑡𝑜𝑡

𝐿𝑡𝑜𝑡 − 𝐿𝑝𝑚/2

)︃3

(2.12)

Where 𝐸𝑠𝑖 is the Young modulus of silicon, 𝑊𝑏 is the cantilever width and 𝑡𝑠 isthe thickness of the top silicon layer.

2.4.2 Electromechanical Coupling Coefficient

The electromechanical coupling coefficient is a parameter related to the ratio ofthe mechanical energy, associated to the piezoelectric material deformation due to stress,to the total energy that is converted into electrical charge. Since the piezoelectricity ofa material is orientation dependent, the electromechanical coupling coefficient also is,and the same subscript notation standard adopted by the piezoelectric coefficient is usedfor this parameter. Therefore, it is possible to define the coefficient for operation in thetransversal mode, 𝑘2

31, and for operation in the longitudinal mode, 𝑘233. Since the proposed

micro-cantilever operates in the transversal mode only the 𝑘231 coefficient will be of interest.

The electromechanical coupling coefficient is related to other properties of thepiezoelectric material, being defined, according to the IEEE (Institute of Electrical andElectronics Engineers) standard on piezoelectricity, (MEITZLER et al., 1988), with the


following equation:

𝑘231 = 𝑑2

31𝑠𝐸

11𝜀𝑇33

(2.13)

Where 𝑑31 is the transversal piezoelectric coefficient, 𝑠𝐸11 is the first element of the

compliance matrix of the material, which can be seen as the coefficient that relates themechanical stress applied, related to the force, to the material strain, which causes thedeformation of the crystalline structure. The 𝜀𝑇

33 parameter is the dielectric permittivityof the material. The presence of the superscripts 𝐸 and 𝑇 indicate, respectively, thepresence of a constant or null electric field and mechanical stress. The subscript numbersindicates the matrix position for the parameters, which are related to reference axes inthe Cartesian system. For practical purposes the typical values of these coefficients will beused, reported for the aluminum nitride, and for simplification purposes the superscriptnotation will be removed.

Another important parameter, derived from the electromechanical coupling, isthe effective electromechanical coupling coefficient, defined by the following equation,presented in (DUTOIT; WARDLE; KIM, 2005):

𝑘2𝑒 =

𝑘2𝑖𝑗

1 − 𝑘2𝑖𝑗

(2.14)

Where the subscripts 𝑖 and 𝑗 are related to electric field and stress orientation,according to the same notation standard adopted by the piezoelectric coefficient. Theeffective electromechanical coupling coefficient is used in the power estimation modelpresented by DuToit, therefore it is important to calculate it. More information about theelectromechanical coupling coefficient, and its influence on piezoelectric vibration energyharvesters, can be found in (DENG; ZHAO, 2018).

2.4.3 Mechanical Damping Coefficient

The mechanical damping coefficient is the parameter that accounts for mechan-ical losses in a vibrating structure, which counteract the inertial oscillatory movement.Note that it is very difficult to accurately calculate this parameter analytically, beingtypically measured experimentally. However, it is possible to account the contribution offour dominant phenomena associated with the mechanical losses:

∙ Air drag force.

∙ Squeeze film damping, associated with the air compression underneath and in close-by structures.


∙ Anchorage and support losses.

∙ Internal structural damping in the structure.

For structures in the micro-meter scale, the air drag force dominates the losseswhen the device is operating in free space at atmospheric pressure. For devices wherethe gap between the vibrating structure and the nearest motionless structures is small,the squeeze film damping is dominant. In situations where the structure has free spaceto oscillate, with a big gap between surrounding structures, and operates at a vacuum orlow-pressure environment, the structural damping accounts for the bigger parcel of themechanical losses. Therefore, a way to reduce the damping, consequently increasing thepower output, is to enclose the micro-cantilever in a vacuum package, designing the devicein a way to accommodate a big gap between the oscillatory mass and the surroundingstructures.

Although modeling the mechanical damping is a difficult task, a model based onthe Navier-Stokes equations was developed by (HOSAKA; ITAO; KURODA, 1994) tocalculate these four parcels of the coefficient, for a micro-cantilever structure. Therefore,it is possible to estimate the mechanical damping coefficient through the use of materialparameters and geometric aspects of the structure, and the properties of the fluid in whichthe device operates (dry air), using the following equations:

𝜁𝑚 = 𝜁𝑚,𝑑𝑟𝑎𝑔 + 𝜁𝑚,𝑠𝑞𝑢𝑒𝑒𝑧𝑒 + 𝜁𝑚,𝑎𝑛𝑐ℎ𝑜𝑟 + 𝜁𝑚,𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑎𝑙 (2.15)

𝜁𝑚,𝑑𝑟𝑎𝑔 = 3𝜇𝑎𝑖𝑟𝜋𝑊𝑏 + 0.75𝜋𝑊 2𝑏

√2𝜌𝑎𝑖𝑟𝜇𝑎𝑖𝑟𝜔

2𝜌𝑠𝑖𝑊𝑏𝐿𝑏𝑡𝑠𝜔𝑁

(2.16)

𝜁𝑚,𝑠𝑞𝑢𝑒𝑒𝑧𝑒 = 𝜇𝑎𝑖𝑟𝑊2𝑏

2𝜌𝑠𝑖𝑔30𝑡𝑠𝜔𝑁

(2.17)

𝜁𝑚,𝑎𝑛𝑐ℎ𝑜𝑟 = 0.23𝑡3𝑠

𝐿3𝑏

(2.18)

𝜁𝑚,𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑎𝑙 = 𝜂𝑏𝑒𝑎𝑚

2 (2.19)

Where 𝜁𝑚 is the full mechanical damping coefficient and the terms 𝜁𝑚,𝑑𝑟𝑎𝑔, 𝜁𝑚,𝑠𝑞𝑢𝑒𝑒𝑧𝑒,𝜁𝑚,𝑎𝑛𝑐ℎ𝑜𝑟 and 𝜁𝑚,𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑎𝑙 are the four parcels related to the mentioned phenomena. Theparameters that model the fluid properties of the air are the dynamic viscosity, 𝜇𝑎𝑖𝑟, inunits of N s/m2, and the air density, 𝜌𝑎𝑖𝑟, in g/m3. The damping coefficient is inverselyproportional to the structure density, 𝜌𝑠𝑖, which is made of silicon. The geometric param-eters of the micro-cantilever, 𝑊𝑏, 𝐿𝑏 e 𝑡𝑠, were already described and can be seen in thediagram presented in figure 17.


Note that the damping depends upon the angular frequency of the oscillations, 𝜔,and the resonance frequency of the cantilever, 𝜔𝑁 . The parameter 𝑔0, in m, representsthe minimum free space gap between the oscillatory structure and the nearest neighborstructure, related to the squeeze film damping parcel. Lastly, the structural dampingfactor of the cantilever beam material, 𝜂𝑏𝑒𝑎𝑚, accounts for the internal friction losses inthe structure and can be determined experimentally3, but since it is a very low valuecompared to the other damping factors, it can be neglected.

It is important to note that the presented model does not account for the tip massin the cantilever, requiring some adaptations to obtain a valid damping model for theproposed device. As proposed by (CHOI et al., 2006), a reasonable approach would be tosum separate contributions for the air drag parcel, 𝜁𝑚,𝑑𝑟𝑎𝑔, one related to the cantileverbeam and another for the tip mass. For the other damping parcels the effect of the tipmass will be neglected, which is a reasonable estimation since the first term, the air dragparcel, is the dominant one for the proposed operation (oscillating in free space underatmospheric pressure).

2.4.4 Leakage Resistance

The characterization of a thin film of AlN, deposited by a reactive sputtering pro-cess (which is also used for the same purpose in the PiezoMUMPs process), was made by(ASSOUAR et al., 2002) to study surface acoustic wave devices made from that piezo-electric material. The paper provides sheet resistance values measured as a function ofthe nitrogen concentration the process chamber, which is varied in order to understandthe influence in the desired material properties. The obtained values are in the order of1012Ω/� to 1014Ω/� for an aluminum nitride film of 2 µm of thickness. The electricalresistivity of the material is the product of the sheet resistance by the thickness, being,therefore, a value in the order of 106Ω m to 108Ω m for the AlN.

The leakage resistance, 𝑅𝑝, is related to the AlN resistivity, 𝜌𝐴𝑙𝑁 , and the geometricconfiguration of the electrodes. For the case where the electrodes are of a rectangularshape, the parameter can be calculated with the following equation:

𝑅𝑝 = 𝜌𝐴𝑙𝑁 𝑡𝑝

𝑊𝑒𝐿𝑒

(2.20)

Where the 𝑊𝑒 by 𝐿𝑒 product provides the piezoelectric contact area with theelectrodes. The leakage resistance is an important parameter to model the electrical lossesthrough current leakage in the dielectric material, which is the aluminum nitride for theproposed micro-cantilever device.3 The results found in (DUTOIT; WARDLE; KIM, 2005) suggests a value in the order of 10−6 for their

fabricated device.


2.4.5 One-Dimensional Power Estimation Model

A simple model for estimating the power generated by a piezoelectric cantileverwas presented by (DUTOIT; WARDLE; KIM, 2005) and the author claims that it cancharacterize piezoelectric micro-cantilever vibrational energy harvesters adequately. Themodel was developed based on a generic piezoelectric accelerometer in one-dimension. Amore accurate modeling was also presented by the same author, using distributed param-eters in a two-dimensional model. However, the calculations are much more sophisticatedand through experimental verification the researchers were able to conclude that the pre-dictions made with the simplified model were reasonably accurate. Therefore, for thepurpose of giving a rough estimate of the power generation capabilities, the use of thesimplified model will suffice. The model was originally derived for a cantilever operatingin the longitudinal piezoelectric mode but through a simple adaptation it can be used forthe presented structure that operates in the transversal mode. The adaptation consists insubstituting the longitudinal piezoelectric coefficient, 𝑑33, by the transversal coefficient,𝑑31, in all equations.

Multiplying correction factors for this model were proposed in (ERTURK; INMAN,2008). These correction factors are necessary for devices in which the tip mass and thecantilever beam have similar weights. When the tip mass accounts for most of the deviceweight, these correction factors tend to unity, therefore having no multiplicative effect inthe original equations. For the proposed device the tip mass corresponds to more than98% of the total weight of the structure, so these corrections can be neglected. But fora different design, it is important to know that they can be used to further improve themodel accuracy.

In the simplified model discussed in this section, the power output is related tothe following variables:

∙ Acceleration and frequency of the ambient vibrations, 𝑥𝐵 and 𝜔.

∙ Angular resonance frequency of the cantilever, 𝜔𝑁 .

∙ Effective mass of the cantilever, 𝑀 .

∙ Mechanical damping coefficient, 𝜁𝑚.

∙ Effective electromechanical coupling coefficient, 𝑘2𝑒 .

∙ External load resistance connected to the micro-cantilever electrodes, 𝑅𝑙.

∙ Leakage resistance of the piezoelectric material, 𝑅𝑝.

∙ Micro-cantilever electrical capacitance, 𝐶𝑝.


The model is derived from a simple differential equation, 2.21, that describes thebehavior of the piezoelectric cantilever. As a notation convention, the overhead dot indi-cates the time derivative. 𝑥𝐵 is the base acceleration (intensity of the ambient vibrations);𝑥 the displacement of the tip mass; 𝜔𝑁 is the natural oscillating frequency of the can-tilever; 𝜁𝑚 is the mechanical damping coefficient of the structure; 𝑑31 is the transversalpiezoelectric coefficient of the AlN; and 𝑉 is the voltage across the electrodes.

�̈� + 2𝜁𝑚𝜔𝑁 �̇� + 𝜔2𝑁𝑥 − 𝜔2

𝑁𝑑31𝑉 = ¨−𝑥𝐵 (2.21)

The initial state of the system is described by the equation 2.22, where 𝑅𝑒𝑞 is theparallel equivalent resistance between the electrical load, 𝑅𝑙, and the piezoelectric leakageresistance, 𝑅𝑝, as defined in equation 2.23; 𝑀 is the effective mass of the structure, thatcan be approximated by the tip mass; and 𝐶𝑝 is the parallel plate capacitance of the top-bottom electrode piezoelectric stack, calculated by equation 2.24, where 𝜀0 is the dielectricpermittivity of vacuum, a know constant of approximate value of 8.85 × 10−12F/m, and𝜀𝑝 is the relative permittivity of the dielectric material, in the case of the proposed devicethe piezoelectric material is AlN. Note that 𝜀𝑝 = 𝜀33/𝜀0.

𝑅𝑒𝑞𝐶𝑝�̇� + 𝑉 + 𝑀𝑅𝑒𝑞𝑑31𝜔2𝑁 �̇� = 0 (2.22)

𝑅𝑒𝑞 = 𝑅𝑝𝑅𝑙

𝑅𝑝 + 𝑅𝑙

(2.23)

𝐶𝑝 = 𝜀𝑝𝜀0𝑊𝑒𝐿𝑒

𝑡𝑝

(2.24)

Solving the equations 2.21 and 2.22 the power generated is given by the equation2.25. Steps of the solution are found in (DUTOIT; WARDLE; KIM, 2005). For notationconvenience the following definitions were made: 𝑟 = 𝜔𝑁𝑅𝑒𝑞𝐶𝑝; Ω = 𝜔/𝜔𝑁 and 𝐾𝑖𝑛𝑣 =1 − 𝑘2

𝑒 . The ambient vibration frequency (assuming a monotonic vibration) is representedby 𝜔 and 𝑘2

𝑒 is the effective electromechanical coupling coefficient of the piezoelectricmaterial.

𝑃

𝑥𝐵2 = 𝑀𝑟𝑘2

𝑒𝑅𝑒𝑞Ω2(𝑅𝑙𝜔𝑁)−1

[1 − (1 + 2𝜁𝑚𝑟)Ω2]2 + [𝐾𝑖𝑛𝑣𝑟Ω + 2𝜁𝑚Ω − 𝑟Ω3]2 (2.25)

From equation 2.25 it is possible to see that the generated power has a complexrelation with many parameters, but it is directly proportional to the squared magnitudeof the ambient vibrations; to the tip mass weight; to the match between the device reso-nant frequency and the ambient vibrations frequency; and to the inverse of the dampingcoefficient. For the presented cantilever design, the damping term related to the drag force


of the air is dominant, followed by the squeeze-force term, that can be greatly minimizedby allowing sufficient space between the oscillating structure and the physical barriers inthe surroundings such as the trench walls.

By the equation 2.25 it is possible to verify that there is an optimal load resistancevalue that maximizes the generated power. Considering that 𝑅𝑝 is much larger than𝑅𝑙, the equivalent resistance is approximately equal to the load resistance. With thissimplification, the optimal load can be calculated by the following equation:

𝑅𝑙𝑜𝑝𝑡 = 1𝜔𝑁𝐶𝑝

Ω4 + (4𝜁2𝑚 − 2)Ω2 + 1

Ω6 + [4𝜁2𝑚 − 2(1 + 𝑘2

𝑒)Ω4 + (1 + 𝑘2𝑒)2Ω2] (2.26)

It is important to note that the optimal load is dependent upon the frequency ofthe ambient vibrations.

2.4.6 Equivalent Electric Circuit Model

The modeling of a bimorph4 piezoelectric cantilever with tip mass was done by(ROUNDY; WRIGHT, 2004), using an equivalent electric circuit. The studied devicein the current work is a unimorph cantilever, having only one piezoelectric layer, andthe circuit model presented by Roundy will be adapted for the unimorph configuration.The proposed analysis models the mechanical and electrical systems, and their coupling,using an equivalent circuit as shown in figure 18. Obtaining lumped circuit parameters isadvantageous because it allows the device to be simulated along with complex auxiliaryelectronic circuits, using SPICE (Simulation Program with Integrated Circuit Emphasis)circuit software. As seen before, the micro-cantilever needs to be connected to adequateauxiliary circuitry, either for energy harvesting or vibration sensing applications. Modelingthe interaction between the device and such circuits would be too complex to be done inany other way. Having the micro-cantilever described by circuit parameters makes thatanalysis much easier, using the appropriate computational tools. These circuit parametersare related to the actual system in the following way:

∙ The voltage source 𝜎𝑖𝑛 represents the mechanical stress in the piezoelectric film, dueto ambient vibrations.

∙ The inductance 𝐿𝑚 is related to the inertial mass of the cantilever.

∙ The resistance 𝑅𝑏 is associated with the mechanical losses, related to the mechanicaldamping coefficient.

4 Structure with two piezoelectric layers, which can have or not a central shim passive layer betweenthem.


Figure 18 – Equivalent electrical circuit model for a piezoelectric cantilever with tip mass.Image taken from (ROUNDY; WRIGHT, 2004).

∙ The capacitance 𝐶𝑘 is related to the stiffness, being associated with the Youngmodulus of the structure.

∙ The transformer, characterized by the turn ratio 𝑁 , represents the piezoelectric elec-tromechanical coupling, bridging the mechanical and electrical sides of the circuit.

∙ The capacitance 𝐶𝑝 is the device capacitance, as defined by the equation 2.24 in theprevious section.

Note that in the mechanical side of the circuit (left side of the transformer element)the analogous to the electrical voltage is the mechanical stress, 𝜎𝑖𝑛, and the flux variable,analogous to the current, is the strain rate, �̇�, that models the piezoelectric materialdeformation rate. Note that the upper dot in the variable represents the time derivative.Using the Kirchhoff law of voltages, applied to the mechanical loop, and the Kirchhofflaw of currents, applied to the electrical-side output node (indicated in the figure by thenumber 1 above the node), the following differential equations are obtained:

𝜎𝑖𝑛 = 𝐿𝑚𝑆 + 𝑅𝑏�̇� + 𝑆

𝐶𝑘

+ 𝑁𝑉 (2.27)

𝑖 = 𝐶𝑝�̇� (2.28)

Although in the reference paper the model has been developed for a bimorph can-tilever structure, it is possible to make use of the same equations for a unimorph cantileverwith minor adaptations and the substitution of some parameters. In the paper the au-thor has used the same variable to represent the stiffness coefficient of the piezoelectricmaterial, which is the inverse of the 𝑠11 variable, and the complete structure, using theeffective Young modulus of the piezoelectric material. That was done due to the fact thatthe bimorph structure presented is constituted of two layers of piezoelectric material,


with a very thin layer of metal between them, having the cantilever beam structure beingmade by the piezoelectric material. Therefore, the piezoelectric material dominates thestiffness of the structure and there is no significant difference between these two variables(stiffness of the piezoelectric layer and of the cantilever). However, the device proposed inthis work consists of a silicon beam with a very thin piezoelectric layer deposited on topof it. Therefore, it is necessary to have a distinction between these two variables, as thecantilever stiffness is dominated by the silicon material, having a negligible contributionfrom the piezoelectric film. Therefore, the inverse of the compliance coefficient 𝑠11 wasused in the piezoelectric equations and their derivations, while the silicon Young moduluswas used for the structural mechanics equations and their derivations. Thus, the modelwas consistent with the presented unimorph cantilever.

Another correction was done to obtain the electrical field across the piezoelectricfilm, necessary for calculating the turn ratio, 𝑁 . The voltage across parallel plates, 𝑉 , isrelated to the electrical field, ℰ , and the distance between the plates, 𝑑, by the knownrelationship 𝑉 = ℰ𝑑. For the bimorph structure described in the paper, the distanceis equivalent to two times the piezoelectric material thickness, but for the cantileverpresented in this work that distance would be equivalent to only the thickness of the singlepiezoelectric layer present. Therefore, the two times multiplicative factor was removedfrom the original equation for the turn ratio. In this way the model was consistent withthe studied device.

The equations that relate the physical parameters with the those of the equivalentcircuit model were based on the basic piezoelectricity equations and structural mechanics,as given below:

𝜎𝑖𝑛 = 𝑘1𝑀𝑥𝐵 (2.29)

𝐿𝑚 = 𝑘1𝑘2𝑀 (2.30)

𝑅𝑏 = 2𝑘1𝑘2𝑀𝜔𝑛𝜁𝑚 (2.31)

𝐶𝑘 = 1𝐸𝑠𝑖

(2.32)

𝑁 = −𝑑31

𝑠11𝑡𝑝

(2.33)


The capacitance in the mechanical side of the circuit can be approximated by theinverse of the silicon Young modulus, which is a good estimation for the effective cantileverstiffness. The constants 𝑘1 and 𝑘2 are defined by the following equations:

𝑘1 = 𝑡𝑒𝑞(2𝐿𝑏 + 𝐿𝑝𝑚 − 𝐿𝑒)2𝐼

(2.34)

𝑘2 = 𝐿2𝑏(2𝐿𝑏 + 1.5𝐿𝑝𝑚)

3𝑡𝑒𝑞(2𝐿𝑏 + 𝐿𝑝𝑚 − 𝐿𝑒)(2.35)

𝐼 = 𝑊𝑏𝑡3𝑠

12 (2.36)

Where 𝑡𝑒𝑞 is the effective thickness of the cantilever beam, defined by 𝑡𝑒𝑞 = 𝑡𝑠 + 𝑡𝑝;and 𝐼 is the second inertia moment5 for a cantilever structure. 𝑘1 is a geometric constantthat relates the average mechanical stress, in the piezoelectric film, with the externalforce exerted by the oscillation of the tip mass, due to ambient vibrations. The constant𝑘2 relates the vertical displacement of the tip of the cantilever, 𝑥, with the average strainin the piezoelectric film, 𝑆. The other used parameters were all described previously.

The electrical current, 𝑖, in the left side of the transformer, depends on the strainrate, �̇�, in the following way:

𝑖 = 𝑊𝑒𝐿𝑒𝑑31𝑠−111 �̇� (2.37)

The average strain in the piezoelectric film is calculated according to the forcecreated by the accelerated mass, using the following equation:

𝑆 = 2𝑀𝑥𝐵𝑡𝑒𝑞𝑠11

2𝐼(2𝐿𝑏 + 𝐿𝑝𝑚 − 𝐿𝑒) (2.38)

Based on the electrical current equations, 2.28 and 2.37, an equation for the open-circuit voltage as a function of the average strain is derived:

𝑉𝑜𝑐 = 𝑊𝑒𝑙𝑒𝑑31𝑆

𝑠11𝐶𝑝

(2.39)

Defining 𝑆 based on the intensity of the ambient vibrations it is possible to estimatethe open circuit voltage, 𝑉𝑜𝑐, across the device electrodes. However, in order for the micro-cantilever to generate power, it is necessary to connect an electrical load to its terminals.The analysis using a resistive load, although not very realistic in practical terms, provides5 Also know as second area moment. This physical quantity is typically used in structural engineering.

It should not be confused with the rotational inertia moment, which is the angular mass associatedwith torque.


a baseline for the maximum power that the device can deliver. Therefore, connecting aload resistance, 𝑅𝑙, in parallel to the output of the equivalent circuit model, it is possibleto derive the following equation for the current:

𝑖 = 𝐶𝑝�̇� + 𝑉

𝑅𝑙

(2.40)

But the same current is also defined by the equation 2.37, as a function of theaverage strain. Equating both expressions, isolating the voltage derivative and applyingthe Laplace transform, it is possible to derive the following equation, in the frequencydomain, for the average strain:

ℒ{𝑆} = 𝑉 𝑠11

𝑊𝑒𝑙𝑒𝑑31𝑡𝑝𝑠

(︂𝑠𝐶𝑝 + 1

𝑅𝑙

)︂(2.41)

Where 𝑠 is the Laplace variable. The final expression for the output voltage inthe frequency domain is obtained taking the Laplace transform of the equation 2.27 andsubstituting ℒ{𝑆} obtained in equation 2.41 on it. The equivalent circuit variables wereexpanded in terms of the material properties and geometric parameters of the cantileverand the Laplace variable was replaced by 𝑗𝜔, since 𝑠 = 𝜎 + 𝑗𝜔 and the real part, 𝜎, iszero. The device delivers the maximum power when excited by vibrations that match thestructure resonance frequency, therefore the analysis in the resonance frequency is themost important. The resulting expression is further simplified by the assumption thatthe vibration frequency, 𝜔, matches the resonance frequency. Lastly, applying the basiccircuit-theory equation that relates the power delivered to a resistive load as a functionof the voltage, 𝑃 = 𝑉 2

𝑅, yields the final expression for the generated power:

𝑃𝑐𝑒 = 𝑥𝐵2

𝜔2𝑁

𝑅𝑙𝐶2𝑝

(︁2𝐸𝑠𝑖𝑑31𝑡𝑝

𝑘2𝜀𝑝

)︁2

(4𝜁2𝑚 + 𝑘2

31)(𝑅𝑙𝐶𝑝𝜔𝑁)2 + 2𝜁𝑚𝑘231(𝑅𝑙𝐶𝑝𝜔𝑁) + 4𝜁2

𝑚

(2.42)

The expression considers that the ambient vibrations are sinusoidal, with constantamplitude and frequency matching the resonance frequency. Note that having the equiv-alent circuit parameters it is possible to simulate the device using SPICE software andthe limitations imposed by the analytical derivation of this expression would be over-come. The expression can be used in conjunction to the SPICE simulation to check theconsistency.

The power expression in equation 2.42 can be compared to the equation 2.25,obtained through the one-dimensional model derived in the previous section. The powerproportionality with the micro-cantilever mass is not directly evident in equation 2.42,but considering that the resonant frequency carries an inverse proportionality with themass, the results are consistent. It is possible to verify that both power equations areconsistent with each other in terms of parameter influence and proportionality.


There is a resistance load value that maximizes the power transfer. We can ob-tain an expression for that optimal load value by taking the time derivative of equation2.42, equaling the expression to zero and isolating the 𝑅𝑙 variable, yielding the followingexpression:

𝑅𝑙𝑜𝑝𝑡 = 1𝜔𝑁𝐶𝑝

2𝜁𝑚√︁4𝜁2

𝑚 + 𝑘431

(2.43)

Note that this equation is valid only to find the optimal load in the resonancefrequency, unlike the expression obtained in the one-dimensional model section, 2.43,which is valid for finding the optimal load for any frequency.

2.5 Experimental Design

2.5.1 Preparation of the Device Under Test

The micro-cantilever studied in this work is one of the many structures designed ina MEMS chip that was fabricated with the PiezoMUMPs process. Fifteen dies were made,each containing four sub-dies, with different structures in each of them. A photograph ofthe sub-die containing the micro-cantilever can be seen in figure 19. The sub-die wasdelivered glued to a protective base, and without encapsulation, which facilitates theaccess to its contact pads. In order to make the chip appropriate for testing, protectedagainst mechanical damage and with its electrodes easily accessible for connection withexternal devices and instruments, several steps were taken to prepare a test sample, thedevice under test (DUT). These steps are briefly described in the following list:

Figure 19 – Photograph of the sub-die containing the micro-cantilever structure.

2.5. Experimental Design 83

∙ Thermal process, using a hot plate, to release the sub-die through the evaporationof the glue holding the sub-die in the protective support.

∙ A double sided gold plated universal PCB (printed circuit board) was prepared toreceive the chip. The board was cut to an appropriate size and a hole was drilled inits center to avoid obstructing the oscillation of the micro-cantilever tip mass.

∙ The die was carefully glued to the PCB with a low strain optical adhesive. A micro-metric precision optical manipulator was used in order to place the adhesive onlyat the chip edges, leaving the structures in the middle free to oscillate. The glueddie is shown in figure 20.

Figure 20 – Sub-die glued to the gold plated universal PCB.

∙ A wire-bonding process was done, soldering 25 µm thick gold wires connecting thechip pads to the PCB. The equipment used was the TPT HB10. This step was chal-lenging due to the difficulty in adhering the gold solder bump to the chip aluminumpads. Several attempts were made before coming up with a successful recipe for themachine parameters.

∙ The same optical adhesive used to fix the die to the PCB was used to protect thefrail gold wire connections. The precision optical manipulator was used to pour theadhesive on top of the connections. After curing with UV (ultra violet) light theglue becomes solid, protecting the gold wires, as shown in figure 21.


Figure 21 – Sub-die after the wire-bonding process and with the adhesive coating pro-tecting the frail gold wire connections.

∙ External wires were soldered to the other side of the PCB, in the terminals connectedto the die, and two rows of connection headers were soldered on each side of theboard, in order to connect a second PCB on top to protect the exposed micro-structures in the die. A photograph and a front view cross section diagram of thecomplete DUT can be seen in figure 22.

Figure 22 – a) Photograph of the device sample, DUT, ready for testing; b) Front viewcross section diagram of the DUT.

After these steps, the electrical terminals of the micro-cantilever were accessibleand it was possible to easily handle the device.


2.5.2 Preliminary Tests

Before performing the lengthy preparations for the more elaborate experiments, itwas important to conduct simple tests to check if the micro-cantilever device was working.

To ensure that there was no short circuit between the gold wire connections and theconductive die surface, and that the dielectric properties of the piezoelectric material wereintact, a simple resistance measurement can be done, using an inexpensive ohmmeter. Theaccurate measurement of the resistance between the two terminals of the micro-cantileverwould indicate the value of the leakage resistance, 𝑅𝑝, but since its value is in the order ofgiga-ohms it would require a special instrument. The inexpensive ohmmeter can be usedto indicate the order of magnitude of the resistance, which should be equivalent to theopen-circuit measurement. If there were short circuits in the gold wire connections or ifthe piezoelectric film was compromised, the measurement would indicate a much lowervalue of resistance, in the ohm or kilo-ohm range.

A very simple functional test for the micro-cantilever is to connect its terminalsto an oscilloscope, with high impedance input, and check the voltage signal while cre-ating mechanical disturbances, by knocking on the surface where the device is placed,for instance. The oscilloscope should register a damped sinusoidal signal in the resonantfrequency of the cantilever. Knocking on the nearby surface would create a mechanicalimpulse on the device, therefore having a step-like frequency spectrum and resonatingthe micro-cantilever in its natural oscillating frequency. The device should be sensitiveenough to respond to low intensity indirect impacts, meaning that if there is no responsethe device is not working.

2.5.3 Test-bench Development

In order to evaluate the device performance in the desired application, as a vi-brational energy harvester and vibration sensor, it is necessary to generate controlledmonotonic mechanical vibrations, with adjustable intensity and frequency. A shaker isthe appropriate equipment for that, but since it is a costly instrument that was notavailable in the laboratory an alternative approach was sought.

An audio acoustic speaker, with the cone removed and with a PCB glued to itsvibration axis, was used to produce the required controlled vibrations. By connecting asignal generator directly to the speaker terminals, it was possible to produce arbitraryvibrations, within a certain intensity and frequency range. The device would be attachedto the PCB in the speaker axis, being submitted to the controlled perturbations definedin the signal generator. For the vibration intensity range of choice (up to 20 m/s2) nosignal amplification was needed, as the signal generator was able to provide enough powerto drive the speaker.


The mechanical perturbations thus generated were monitored by measuring themusing a commercial accelerometer connected to an oscilloscope. The measurements resultshave shown that the vibrations induced by a sinusoidal signal, generated by the signalgenerator, were almost sinusoidal, with very small harmonic contributions from otherfrequencies. The vibration intensity, measured in m/s2, was modulated by the electricalsignal voltage, and an intensity up to 20 m/s2 could be reached with the maximum voltagesupplied by the signal generator, which was about 2 V for the 8 Ω impedance of the audiospeaker. Therefore, the alternative shaker had the necessary desired characteristics toconduct the experiments with the micro-cantilever device. The specific equipment andmaterials used for the test-bench are described below. A photograph of the experimentalsetup is shown in 23.

Figure 23 – Audio speaker adapted for generating controlled vibrations, with the deviceunder test and an accelerometer placed in its vibration axis.

∙ Signal generator - Agilent 33522A.


∙ Oscilloscope - Keysight MSOX2024A.

∙ Audio speaker of 8 inches with impedance of 8 Ω.

∙ Commercial MEMS accelerometer module - MMA7361.

∙ Voltage source of 3.3 V, to power the accelerometer.

∙ Protoboard, cables, connectors and 3.3 nF capacitor to connect in the accelerometeroutput (as a filter recommended by the manufacturer).

2.5.4 Frequency Response

As seen in the analytical modeling section, the micro-cantilever response to theambient vibrations is highly dependent on the vibration frequency. When the vibrationfrequency coincides with the resonant frequency of the cantilever, the generated signalis maximized. But since the ambient vibrations might not have the higher intensity har-monics in the resonant frequency, it is important to evaluate the device behavior whensubmitted to other frequencies. Therefore, it is advisable to obtain the frequency responsecurve, which gives the relationship between the cantilever response and a wider range ofvibration frequencies.

Using the test-bench setup described in the section 2.5.3, it is possible to measurethe cantilever response to vibrations of different frequencies while maintaining the sameintensity. The accelerometer must be used to monitor if the vibration intensity remainsconstant, while changing the frequency. The experimental procedure consists in moni-toring the cantilever voltage and the accelerometer output using the oscilloscope, thusregistering the voltage peak value for different vibration frequencies, which are controlledby the signal generator output. It is expected that the device response would change moreabruptly when the frequency is closer to the resonant frequency. Therefore, it is advis-able to choose a smaller frequency step within the resonance frequency range, obtaininga higher resolution in the peak area of the frequency response curve. The control signalvoltage should be adjusted in order to maintain the vibration intensity constant, thusmaintaining the same peak voltage from the accelerometer output.

2.5.5 Optimal Load Measurement

The cantilever voltage output is dependent on the electrical load connected to itsterminals and there is an optimal load value that maximizes the power transfer. For theapplication as an energy harvester it is very important to determine the optimal loadvalue and to understand the relationship between the powered load resistance and thegenerated voltage. A simple way to obtain that relationship is to measure the cantileveroutput voltage when connected to different resistive loads, while submitted to ambient


vibrations of constant intensity and frequency. It is important to note that the inputimpedance of the instrument used to measure the cantilever voltage can affect the result,as it would introduce an additional parallel resistance, modifying the resulting load valueseen by the cantilever. To avoid that issue a buffer, consisting of a op-amp in the voltagefollower configuration, could be used between the resistive load and the measurementinstrument. The experimental procedure to obtain the cantilever voltage vs the load isdescribed as follows:

∙ In order to submit the cantilever to controlled vibrations, the test-bench setup de-scribed in the section 2.5.3 is used. A fixed vibration frequency and intensity ischosen for the entire experiment. To maximize the cantilever response, the signalgenerator output is set to the device resonant frequency. The vibration intensitymust be held constant, being monitored by means of the signal from the accelerom-eter.

∙ The cantilever output is connected to a protoboard containing several values ofelectrical resistances, in an arrangement that facilitates changing the resistive loadseen by the cantilever. A variable resistance such as a trimpot or a potentiometercould be used, but the resistance value should be measured at each step. Usingdiscrete values of resistance and manually changing the load seen by the cantileverwas the chosen approach.

∙ An operational amplifier in the voltage follower configuration is used between theconnected resistance and voltmeter used to measure the cantilever peak voltage.

∙ The cantilever output voltage is measured for each resistance value and the powerdelivered to the load is calculated after each measurement, in order to obtain theoptimal load value. Smaller increments in the resistance value are used around theoptimal load value, ensuring higher accuracy in determining its value.

2.5.6 Vibration Sensitivity Curve

The experiments previously described characterize the micro-cantilever behaviorwhen changing the vibration intensity and load resistance, deriving the frequency responseand the voltage vs load curve. However, the analysis would not be complete withoutexamining the device response when changing the vibration intensity, thus deriving thevibration sensitivity curve.

The analytical modeling reviewed in previous sections states that the power gen-erated by the cantilever is proportional to the squared value of the vibration intensity,so it is expected that the power delivered to a constant resistive load would quadruplewhen the vibration intensity doubles. A simple experiment to obtain that relationship


can be conducted using the same test-bench setup used for the other experiments. In-stead of changing the frequency or the load resistance, the vibration intensity is changed,by altering the output voltage delivered by the signal generator. The corresponding vi-bration intensity is measured by the accelerometer output, which is monitored using theoscilloscope.

2.5.7 Measurement of the Mechanical Damping Coefficient

In order to validate the analytical models and derive a more accurate semi-empiricalmodel for the cantilever it is necessary to measure the device mechanical damping coeffi-cient. Since the quality factor for cantilever structures tends to be very high, the expectedresponse to an impulse would be a damped sinusoidal signal in the resonance frequency,where the exponential decay fitting curve coefficient is directly related to the dampingcoefficient. Figure 24 shows a plot of a generic damped oscillatory signal, with the corre-sponding exponential decay fitting curve defined as a function of the damping coefficient.

Figure 24 – Generic damped oscillation signal, with the associated exponential decaycurve related to the damping coefficient.

Therefore, it is possible to measure the damping coefficient by determining theexponential curve parameters associated with the signal decay. A simple experiment toobtain that curve is described as follows.

Using the test-bench setup described in the section 2.5.3, the cantilever response tothe sinusoidal vibrations induced by the adapted speaker is monitored in the oscilloscope.To be able to observe the damping, after submitting the device to controlled vibrations,with the oscilloscope registering the cantilever response, the mechanical stimuli should be


abruptly ceased. In that way, the oscilloscope displays the decay curve needed to obtainthe damping coefficient. The coefficient is not related to the signal intensity, meaningthat different vibration intensities could be used having no interference in the parametervalue. To ensure the robustness of the results, several measurements should be made,using different vibration intensities.

After extracting the measurement data, typically in a CSV (comma separatedvalue) format, the damping coefficient can be calculated from the exponential curve fittingparameters, using computational methods. There should not be a significant deviation inthe parameter value obtained from the different measurements, therefore the final dampingcoefficient could be the average value obtained from the different measurements.

91

3 Results and Analysis

3.1 Considerations About the Analytical Results

The main goal of the analytical modeling is to obtain an estimation of the powergenerated by the micro-cantilever, for different load values and frequencies, in order tobetter understand the device behavior in a real application as an energy harvester. Inaddition, observing these results would also give some perspective on the micro-cantileverperformance as an vibration sensor. As indicated by the reviewed models, the powerbears a direct proportionality with the squared value of the ambient vibration intensity,therefore the power curves presented could be easily adapted to any vibration intensity,applying an appropriate scaling of the presented values. A moderate vibration intensityvalue of 4 m/s2 was used as a standard for the analytical results.

As suggested in the end of section 2.1, the performance of different energy har-vesting devices can be compared using a performance factor. To calculate that factorthe information about the maximum generated power, for the resonant frequency, theintensity of the vibrations, given in m/s2 units, and the total volume of the device wouldbe used. To cope with the standard units of power density used in the reports of similardevices in the field, the power should be given in µW and the device volume in cm3. There-fore, the performance factor of a micro-cantilever based piezoelectric energy harvester isdefined by the following equation:

𝐹𝑝 = 𝑃

𝑉𝑡𝑜𝑡𝑥𝐵2 (3.1)

To obtain a high performance factor is much more important than obtaining a highgenerated power value, which might be a result of unrealistic high vibration intensities.For that reason the vibration intensity chosen for the analytical results calculations was ofa moderate low value, of 4 m/s2. As a reminder, the highest value of performance factorfound in the literature was of 14 PU, reported by Elfrink in (ELFRINK et al., 2010).Therefore, that value would be used as a benchmark for the performance of the deviceproposed in this work.

3.1.1 Reference Values for the Material Properties and Calculated Parameters

The reference values for the material properties and other important physicalquantities, that were used for the calculation of parameters of interest for the analyticalmodels, are given in this section. The table 5 contains the values of the properties for

92 Chapter 3. Results and Analysis

the different materials used, followed by the reference in the literature where those valueswere found.

Table 5 – Material Properties

Material Parameter Symbol Value Reference

Monocrystalline Silicon Density 𝜌𝑠𝑖 2320 kg/m3 (HAK, 2006)

Young Modulus 𝐸𝑠𝑖 160 GPa (HAK, 2006)

PiezoelectricCoefficient 𝑑31 −2.8 pC/N (GUY; MUENSIT;

GOLDYS, 1999)

Aluminum Nitride

Compliance 𝑠11 3.5 pm2/N (DEFAÿ, 2011)

Relative DielectricPermittivity 𝜀𝑝 10

(BRIAND;YEATMAN;

ROUNDY, 2015)

Electrical Resistivity 𝜌𝐴𝑙𝑁 252 MΩ m (ASSOUAR et al.,2002)

Dry Air Dynamic Viscosity 𝜇𝑎𝑖𝑟 17.6 µN s/m2 (YAHYA, 2006)

Density 𝜌𝑎𝑖𝑟 1.13 kg/m3 (YAHYA, 2006)

The values of air density and viscosity were taken considering the standard ambienttemperature of 20 ∘C and with an atmospheric pressure at an altitude of 800 m above sealevel, which is the average altitude of the city of Belo Horizonte (Minas Gerais, Brazil),where the measurements have been taken.

Based on the material properties and the device dimensions, the parameters de-scribed in the analytical modeling section were calculated. Table 6 provides the obtainedvalues, along with the reference equations that were used for the calculation. Note thatthe structural dimensions of the micro-cantilever were already given in table 1, in theintroductory chapter.

Table 6 – Calculated ParametersParameter Symbol Valor Equation

Device Mass 𝑀 0.947 µ kg 2.9

Angular Resonance Frequency 𝜔𝑁 926.24 rad/s 2.12

Resonance Frequency 𝑓𝑁 147.41 Hz 2.11

Effective Spring Constant 𝐾 ′ 0.813 N/m 2.10

Mechanical Damping Coefficient 𝜁𝑚 0.0053 2.15

Device Capacitance 𝐶𝑝 53.25 pF 2.24

Leakage Resistance 𝑅𝑝 420 MΩ 2.20

Second Inertia Moment 𝐼 3.33 × 10−20 m4 2.36

3.2. One-Dimension Power Estimation Model Results 93

In the calculation of the mechanical damping coefficient, the parameter 𝑔0, thatgives the distance between the oscillating micro-cantilever beam structure to the otherneighboring fixed structures, is equal to 400 µm and the 𝜁𝑚,𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑎𝑙 component, whichis expected to be much smaller than the other components, was neglected. The otherimportant calculated parameters will be discussed in the modeling results sections.

3.2 One-Dimension Power Estimation Model Results

Equation 2.25, derived in section 2.4.5, which estimates the power generated bythe micro-cantilever to a resistive load, was implemented in Python. In order to betterunderstand the behavior of the device, plots varying the frequency and load were drawn,using the MatplotLib Python package. As mentioned before, all the calculations made inthe analytical model results sections used a vibration intensity of 4 m2/s.

As seen in the previous section, the calculated resonance frequency for the de-vice was 147.41 Hz. Maintaining a constant frequency, equal to the indicated value, theconnected load value was varied from 500 kΩ to 40 MΩ and the power and associatedvoltage were calculated using equation 2.25. The voltage is related to the power and theload value according to the known relationship from the electrical circuits theory, where𝑉 =

√𝑅𝑃 . Figure 25 shows the generated curve, with the power on the left axis and the

voltage on right axis.

The curve shows that a maximum power of 363.84 nW occurs when the load

Figure 25 – Power and voltage versus load resistance plot, according to the one-dimensionpower estimation model.


resistance value is 7.66 MΩ, with an effective voltage of 1.67 V. As expected, the generatedpower tends to zero when the resistance value is too low or too high, and the maximumvoltage occurs in the open-circuit configuration, when the load resistance tends to infinity.The open circuit voltage is around 2.8 V. It is important to note that these results wereobtained using a simplified model and can give only an estimate of the real values. As it willbe seen in the experimental results section, this power estimation is overly optimistic, butit is in the right order of magnitude. According to these results the obtained performancefactor is of 55.7 PU, which is significantly higher than the best device reviewed, whichscored 14 PU.

It is important to note that the optimal load value is dependent upon the excitationfrequency. For that reason, a plot was made calculating the optimal load value for thedesired range of frequencies. The associated voltage for each load value was also obtained,generating the plot in figure 26. It is possible to note that at the two flexion points forthe load value curve a resonance frequency occurs. The first point is at the calculatedresonance frequency, and corresponds to the optimal load value and associated voltageshown in the power versus load plot. The second point is called anti-resonance frequency1

and it is the point of local maximum voltage. The frequency value difference betweenthese points is closely related to the electromechanical coupling coefficient of the device,in way that a bigger value for the coupling coefficient results in a bigger difference betweenthese frequencies (DUTOIT; WARDLE; KIM, 2005).

The plot from figure 27 was generated combining the optimal resistive load valuesfor each frequency with the power generated at those frequencies for those loads. Thecurve in blue represents the power versus the excitation frequency for the optimal loadcalculated for the resonance frequency (as obtained in the power versus load curve infigure 25), and the curve in green accounts for the specific optimal load value for eachfrequency. Considering a wider frequency range of operation, it is possible to note thathaving the optimal load value for each frequency improves the average power generated.Considering a 30 Hz range centered in the resonance frequency, the average power in-creases about 36%, from 51.2 nW to 69.6 nW, when using the optimal load value for eachfrequency. The anti-resonance frequency mentioned earlier is also evident in the greencurve shown in the plot in figure 27, corresponding to the point at a frequency slightlyabove the power peak. The operation in the anti-resonance frequency, which is about5 Hz above the resonance frequency, might be advantageous due to the higher voltagegenerated, with only a slightly decrease in the power output. It is important to note,from the frequency response curve, that the micro-cantilever generated power is highly

1 In the scope of piezoelectric energy harvesters, the anti-resonance frequency is a point of local maxi-mum power, with a frequency shift from the resonance frequency governed by the electromechanicalcoupling coefficient, (DUTOIT; WARDLE; KIM, 2005). This phenomenon should no be confoundedwith anti-resonance in general oscillatory systems, produced by destructive interference, which is apoint of minimal signal amplitude.

3.2. One-Dimension Power Estimation Model Results 95

Figure 26 – Optimal load resistance and voltage versus the excitation frequency.

Figure 27 – Frequency response curve, showing the generated power as function of the ex-citation frequency. The curve in blue represents the power for a fixed value ofresistive load, calculated for the resonance frequency. The curve in green wasgenerated using different values of resistive load, optimized for each frequencyvalue.


dependent upon the match between the excitation frequency and the device resonance oranti-resonance frequency. The generated power for frequencies that deviates more than10% from these frequencies is practically zero.

3.3 Equivalent Circuit Model ResultsThe equivalent circuit model main advantage is the possibility of simulating the

micro-cantilever behavior in conjunction with auxiliary circuits, using a SPICE softwarefor circuit simulation. The equations to calculate the device equivalent circuit elements,presented in section 2.4.6, were implemented in Python and the obtained values were usedin the SPICE software LTspice. The first simulation conducted was the frequency response,obtained through an AC analysis. However, the resulting curve showed a discrepancy inthe resonance frequency value. After some deliberation, the discrepancy was deemed tothe fact that the spring constant correction factor, discussed in section 2.4.1 and definedin equation 2.10, was not accounted for in the reference paper in which the equivalentcircuit model is presented. That correction factor is used to shift the geometric locationof the center of gravity of the micro-cantilever from the tip of the beam, to the center ofthe tip mass, giving a much better estimation for actual structure center of mass.

In the equivalent circuit model there is a relationship between the spring constant,𝐾, and the constants 𝑘1 and 𝑘2, given by the following equation:

𝐾 = 𝐸𝑠𝑖

𝑘1𝑘2(3.2)

Using the calculated values of these constants, without applying the correctionfactor, yields the resonance frequency found in the SPICE simulation. The frequencyfound is the same as the calculated using the spring constant equation defined in section2.4.1, without the correction factor. This finding suggests that the discrepancy foundin the equivalent circuit is due to the fact that such corrections were not made in theoriginal equations. Applying the correction factor to the 𝑘1 constant solves this issueand the resulting resonance frequency, obtained from the SPICE simulation, is consistentwith the one calculated using the equations presented in section 2.4.1. Therefore, a correctconstant, 𝑘′

1, was used, calculated by the following equation:

𝑘′1 = 𝑘1

(︃𝑙𝑡𝑜𝑡

𝑙𝑡𝑜𝑡 − 𝑙𝑝𝑚/2

)︃3

(3.3)

In this way, the calculated equivalent circuit parameters are given in table 7.

Note that the value of the circuit elements in the mechanical side is very high. Thathappens because those elements are related to the mechanical stress in the micro-cantilever

3.3. Equivalent Circuit Model Results 97

Table 7 – Equivalent Circuit Parameters

Parâmetro Símbolo Valor Equação

Mechanical Stress 𝜎𝑖𝑛 4370 × 103 2.29

Inductance in the Mechanical Side 𝐿𝑚 198 × 103 2.30

Resistance in the Mechanical Side 𝑅𝑏 1945 × 103 2.31

Capacitance in the Mechanical Side 𝐶𝑘 6.25 × 10−12 2.32

Turn Ratio 𝑁 1.6 × 106 2.33

Optimal Load* 𝑅𝑙 8.03 MΩ 2.43

* - Optimal load in the frequency of 143 Hz.

structure, not corresponding to real electrical quantities. The only value that resemblestypical electrical component values is the capacitance, 𝐶𝑘, which is defined by the inverseof the micro-cantilever stiffness. Since the monocrystalline silicon material has a very highYoung modulus (stiffness), it is expected that the mechanical capacitance would have avery low value. According to the electrical circuit theory, the resonance frequency for theproposed equivalent circuit is given by 1/

√𝐿𝑚𝐶𝑘, in rad/s. Using the obtained circuit

parameters for that calculation yields a frequency of 143 Hz, which deviates only slightly(about 3% smaller) from the value obtained from the equations in section 2.4.1.

The equivalent circuit, shown in figure 28, was implemented in the LTspice soft-ware. The software does not provide a direct implementation of the transformer elementcharacterized by the turn ratio, 𝑁 . The way to implement that element is to use mutuallycoupled inductances. The relationship between the turn ratio and the value of the coupleinductances is as follows:

𝑁 =√︃

𝐿𝑝

𝐿𝑠

(3.4)

Where 𝐿𝑝 and 𝐿𝑠 are the values of inductance corresponding, respectively, to theprimary and secondary side of the transformer, which are represented by the 𝐿3 and 𝐿4inductors in the presented schematic. Therefore, to obtain a turn ratio of 1.6 × 106, theprimary inductance should be 2.56 × 1012 times higher than the secondary inductance.Since the inductive elements introduce an unaccounted interference to the circuit behavior,the added inductors should have the lowest possible value. In the mechanical side ofthe circuit, the added inductance can be compensated from the 𝐿𝑚 value, subtractingfrom the calculated value of 𝐿𝑚 in order to maintain the desired equivalent inductancevalue. However, in the electrical side, there is no modeled inductance, so the secondaryinductance should have a negligible value. The values of the transformer inductance werechosen observing these considerations. Note that in the presented schematic, the value of𝐿𝑚 has the inductance in the primary side subtracted from it, in a way the sum has the


Figure 28 – Electrical circuit schematic used for the simulation in the LTspice software.

198 × 103 value reported in table 7. A resistive load of optimal value, for the resonancefrequency, was added in parallel to the circuit output. The resistance value was calculatedusing equation 2.43, presented in the equivalent circuit model section.

An AC analysis was made in order to obtain the frequency response of the circuitand confirm the expected resonance frequency value. The plot in figure 29 shows thefrequency response curve, where the left axis corresponds to the output voltage magnitudein dB units as referenced by the voltage source, which represents the mechanical stress,and the right axis represents the phase shift. To keep the consistency in the plot style andalso to facilitate any further analysis with the data, the results were exported in a CSV fileand the plot was made using Python. Converting the voltage magnitude decibel values,which are relative to the voltage source amplitude, to volt units yields a maximum outputvoltage of 2.79 V at the frequency of 143 Hz. It is important to note that the voltage valueobtained is the amplitude of the signal in the output, to calculate the power it is necessaryto use the effective voltage, which for sinusoidal voltages is simply the amplitude valuedivided by

√2. In this way, the power dissipated in the output load, according to the

frequency response simulation, is 484 nW.

Figure 29 – Frequency response curve.

3.3. Equivalent Circuit Model Results 99

Figure 30 – Output voltage obtained from the transient simulation.

A transient analysis simulation was made, setting the voltage source to output asine voltage with the amplitude value of the stress parameter, 𝜎𝑖𝑛, and frequency equalto the obtained resonance frequency. To evaluate the decay of the output voltage whenthe stress signal ceases, which would correspond to the situation where the excitationvibration stops abruptly, the voltage source was set to provide 100 cycles of voltage andthe simulation time was set as 2 seconds. For these settings, the output voltage as afunction of time is given in figure 30. The amplitude value of signal was highlighted in thegreen curve, obtained using a simple peak detector algorithm. Note that the output has aninitial transient stage before reaching the maximum amplitude value. This transient stagecan be related to inertia of the micro-cantilever mass, that requires some time to oscillateat the maximum amplitude. The decay after the excitation signal stops is associated withthe mechanical damping coefficient, as discussed in section 2.5.7.

The maximum power, dissipated in the resistive load, was calculated based onthe effective voltage associated to the maximum voltage amplitude value found in thetransient simulation. The value obtained, 445 nW, was different from the one found in thefrequency response simulation, 484 nW. A possible explanation for this discrepancy lies inthe fact that the transient simulation uses a different model than that of the AC analysis.Nevertheless, the goal of the analytical models was to provide only an rough estimationfor the micro-cantilever power capabilities, and to better understand its behavior and howconstructive parameters influence the results. Since the obtained power difference was notvery significant, no further effort was made to systematically identify the cause of thedeviation.


It is important to mention that this model has some limitations. The transientanalysis results are consistent only when the frequency set in the voltage source matchesthe resonance frequency, or it is very close to it2. Another limitation is the fact that it isnot possible to simulate the device behavior when the connected resistive load changes,as its value has no impact on the output voltage. Because of that, it is also not possibleto simulate the operation in the anti-resonance mode, as it requires the use of a differentfrequency and the calculation of the optimal load for that frequency. Additionally, theequation used to calculate the optimal load, in the equivalent circuit model (equation2.43), is only valid for the resonance frequency. Therefore, it can not be used to derivethe optimal load versus vibration frequency relationship, in order to obtain the anti-resonance frequency from that plot, following the same procedure that was presented inthe one-dimension model results.

3.4 Analytical Results AnalysisA summary of the results, obtained using the two different models, is given in

table 8. A comparison between the values of the maximum generated power, 𝑃𝑚𝑎𝑥, theoptimal resistive load, 𝑅𝑙𝑜𝑝𝑡, and the associated effective voltage, 𝑉𝑃 𝑚𝑎𝑥, current, 𝑖𝑃 𝑚𝑎𝑥,and performance factor, 𝐹𝑝, was done using the percentage difference between the values.The percentage difference is simply the absolute difference divided by the average betweenthe two values.

Table 8 – Summary of the Analytical Results

Model 𝑃𝑚𝑎𝑥 𝑅𝑙𝑜𝑝𝑡 𝑉𝑃 𝑚𝑎𝑥 𝑖𝑃 𝑚𝑎𝑥 𝐹𝑝

1D Model 364 nW 7.66 MΩ 1.67 V 218 nA 55.7 PU

Circuit Model* 445 nW 8.03 MΩ 1.89 V 235 nA 68.1 PU

Percentage Difference 20.02 % 4.72 % 12.36 % 7.51 % 20.02 %

* - According to the results of the transient analysis, which yielded the lowest power.

The largest discrepancy in the values obtained from both models was in the gen-erated power, having a difference of 20%. Although this difference may seem significant,considering the difficulty in modeling the studied device and that two very distinct mod-eling strategies were used, the fact that the power is in the same order of magnitudeshows a good consistency in the results. The one-dimension model greatly simplifies themicro-cantilever structure, and was meant only for giving an estimation for the devicebehavior. The equivalent circuit model was originally developed for a much larger can-tilever (not micro-fabricated), and no special considerations were made to account for themicro-meter dimensions of the device that was presented in this work. It is also important2 Less than 2 % of deviation.

3.5. Experimental Results 101

to note that several parameters, that have a great impact on the calculated results, suchas the electromechanical coupling coefficient, the mechanical damping coefficient and theresonance frequency, were not accurately determined.

The electromechanical coupling coefficient was based on a value of a piezoelec-tric coefficient, 𝑑31, reported for the Aluminum Nitride material for another device, andvariations in such parameter can occur due to the fabrication process. The mechanicaldamping coefficient was calculated using a simplified model for the micro-cantilever ge-ometry, and the structural damping element of that coefficient was neglected, consideringthat it would be too small compared to the other elements. Some simplifications were alsomade in the calculation of the resonance frequency, that does not account for the stiff-ness of the layers of the cantilever that are not the silicon layer, such as the piezoelectricfilm and the top metal electrode. Some geometric simplifications were also made, as theoriginal micro-cantilever design, as shown in figure 5, has a curved, arc like, geometryin the anchorage base of the beam, done to increase the structure robustness during thefabrication.

Therefore, it is not expected that these presented results would reflect accuratelythe actual device performance. If the micro-cantilever can generate power in the sameorder of magnitude calculated, the analytical modeling would have served its purpose.The obtained value for the performance factor stands out, for it is about four to fivetimes higher than the highest performance factor found in the reviewed works. That caneither be, an indicative of a very good micro-cantilever design for energy harvesting, orthat both models are overestimating the power output of the device. Nevertheless, theanalytical results were important to better understand the device behavior and to interpretthe experimental results that will be presented in the next section. A much more accuratesemi-empirical model will be derived from the one-dimension model in conjunction withthe experimental results.

3.5 Experimental Results

Before conducting the experiments, a few preliminary tests were done to confirmthat the micro-cantilever was functioning properly. The resistance measurement betweenthe device terminals showed that there was no short circuit and that the piezoelectric filmin the micro-cantilever was apparently intact, as a very large value of resistance was found,reaching the ohmmeter top measurement range of dozens of mega ohms. Connecting theDUT terminals directly to the oscilloscope it was possible to assess the device responseto uncontrolled mechanical stimuli. A simple test of pounding/beating the hands in thetable were the DUT was supported showed that the micro-cantilever was working, asthe oscilloscope clearly indicated the device response to such stimuli, which delivered a


sinusoidal voltage of a few hundreds of milli-volts of amplitude.

After confirming that the device was working, the measurements using the experi-mental setup described earlier, in the 2.5.3, were conducted. The first step was to find thedevice resonance frequency. A preliminary measurement was done, varying the frequencyof the signal generator, while maintaining the vibration intensity constant, until the max-imum amplitude value for the micro-cantilever response was found. The correspondingfrequency found was of 162 Hz, which was close enough to the expected calculated valueof 147 Hz.

3.5.1 Optimal Resistive Load

Since the voltage generated by the cantilever depends on the connected load value,it is important to analyze the device response when submitted to several different values ofresistive load, determining the optimal load value that maximizes the power transfer. Toaccomplish that analysis, a procedure to obtain the power and voltage versus load curvewas done, as discussed in section 2.5.5. The resistive load was varied in a range from 10 kΩto 48.86 MΩ, with 43 values in between. Smaller increments in the resistance value weredone when approaching the optimal load value, in order to have a better precision in themeasurement of its value. The signal generator was set to deliver a sinusoidal voltage, withthe measured resonance frequency and with an amplitude that corresponds to vibrationsof approximately 10 m/s2, as measured by the accelerometer. Figure 31 shows the plotobtained from these measurements, with the power dissipated in the load being calculatedfrom the effective voltage value measured for each resistance value.

Figure 31 – Measured power and voltage generated by the micro-cantilever for severaldifferent values of resistive load connected.


The optimal load value found was 8.2 MΩ, for which the device delivered aneffective voltage of 1.84 V with a power of 415 nW. Note that these experimental resultsshows a power versus load curve that is very similar (in shape) to the one calculated fromthe 1D analytical model, in section 3.2.

3.5.2 Frequency Response Curve

Using the experimental setup described in section 2.5.3 and following the proce-dure presented in section 2.5.4, the frequency response curve was measured. In order tohave the highest generated power for a given vibration intensity, the measured optimalresistive load value was connected to the micro-cantilever output. To avoid the interfer-ence of the oscilloscope input impedance, an operational amplifier in the voltage followerconfiguration (buffer) was used to interface the signal voltage to the oscilloscope input,similar to the procedure used for obtaining the power versus load curve. The vibrationfrequency was varied from the 100 Hz to 200 Hz range, by changing the frequency ofthe signal generator. The vibration intensity was monitored by reading the signal fromthe accelerometer and the signal generator amplitude was adjusted in order to maintainthe same vibration intensity, of about 10 m/s2, throughout the entire frequency range.The voltage amplitude reading from the oscilloscope was converted to an effective voltagevalue and the power generated was calculated, resulting in the plot given in figure 32.

Figure 32 – Measured frequency response curve, with the power dissipated in a 8.2 MΩresistive load, on the left axis, and the associated effective voltage, on theright axis.


The maximum power of 492 nW occurs in the frequency of 162.2 Hz, with aneffective voltage of 2.01 V, for vibrations of about 10 m/s2 of intensity. That result corre-sponds to a performance factor of 12 PU, which is very close to the highest performanceachieved by a similar device3, reviewed in section 2.1.

The power measured in this experiment was almost 20% higher than the onemeasured in the experiment to determine the optimal load value. That might be becauseof the uncertainty in the vibration intensity value, due to accuracy limitations of theaccelerometer used and the absence of a procedure to calibrate the instrument. Thatdifference is of little significance, given that the goal was to obtain the frequency responsecurve and the optimal load value. The relationship between the micro-cantilever responseas a function of the intensity of the vibrations will be discussed in section 3.5.4, and theappropriate procedure to calibrate the accelerometer will be undertaken.

3.5.3 Mechanical Damping Coefficient Measurement

The mechanical damping coefficient was measured from the voltage decay signal ofthe cantilever, obtained following the procedure described in section 2.5.7. Four measure-ments were made, using different vibration amplitudes4, and the obtained results wereconsistent in all measurements, deviating only in the fifth decimal digit of the parameter.Figure 33 shows the curve derived from one of these measurements. The original micro-cantilever signal, extracted from the oscilloscope, is shown in blue, while the envelopecontaining the signal amplitude is represented by the orange curve and the correspondingexponential fitting is presented in green.

As seen in section 2.5.7, the exponential fit is described by a curve in the 𝐴𝑒(𝐵𝑡)

form, and the mechanical damping coefficient is calculated from the 𝐵 parameter, inconjunction with the frequency of the oscillatory signal. The frequency that was set inthe signal generator was equal to the device resonance frequency, 162 Hz. In this way,the measured mechanical damping coefficient, 𝜁𝑚, was 0.0015, corresponding to a qualityfactor, 𝑄 of 340, using the known 𝜁𝑚 = 1/(2𝑄) equation. The calculated coefficient,using the analytical model previously discussed, was 0.0053, which is more than threetimes higher. The discrepancy can be explained by the measurement error and the modellimitations.

It is important to note that the inertia of the audio speaker vibration axis, usedto generate the mechanical stimuli, introduces an error to the measurement, as the axishas its own decay curve and does not stop vibrating immediately after the stimuli is3 The micro-cantilever presented by Elfrink achieved 14.4 PU. The second best result was the device

published by Shen, with 8.6 PU.4 Ranging from 1 m/s2 to 10 m/s2, approximately. The vibration intensity was not measured for this

experiment, but it can be inferred using the relationship between the micro-cantilever peak voltageand the vibration intensity obtained in the following section.


Figure 33 – Measured voltage decay curve, with the associated voltage amplitude andexponential fit curve highlighted. A vibration intensity of approximately2.5 m/s2 was used for the measurement.

ceased. That error could be mitigated if the speaker axis were physically locked or heldat the moment that the stimuli stops, but that procedure was not conducted. Anotherpossible explanation for the discrepancy between the calculated and measured values is thefact that the model used to calculate the damping coefficient assumes some geometricalsimplifications in the device. Therefore, a considerable error in the analytical calculationcould be expected. The fact that the calculated value was in the same order of magnitudeof the measured parameter indicates some consistency between the values.

3.5.4 Vibration Sensitivity

To obtain the vibration sensitivity curve, the intensity of the mechanical pertur-bations driving the micro-cantilever should be measured accurately. While performing theprevious experiments, the accuracy limitation of the accelerometer used was evident, asthe same intensity was set for the optimal load and frequency response measurements, andyet the power outcome was different. Afterwards, it was discovered that the sensor supplyvoltage and the temperature influence the measurements and that a simple calibrationprocedure can be done to greatly increase its accuracy.

The two accelerometer parameters that suffer influence from external factors arethe zero acceleration voltage, 𝑉0, which is the output voltage when the acceleration sum inaxis of interest is zero, and the sensor sensitivity, 𝜎, that provides the relationship betweenthe acceleration intensity and the output voltage, 𝑉𝑜𝑢𝑡. The measured acceleration value,


𝑥𝐵, depends on these two parameters according to the following equation:

𝑥𝐵 = 𝑉𝑜𝑢𝑡 − 𝑉0

𝜎(3.5)

The calibration procedure ensures an accurate determination of these parameters.The procedure is done using the known gravity acceleration value as reference. The sensoris placed on a flat surface and the output voltage, related to the axis orthogonal tothe surface, is measured. The procedure is repeated with the sensor flipped at 180 ∘ inrelation to the surface. In this way, the first measurement, 𝑉+𝑔 , corresponds to the gravityacceleration, 9.81 m/s2, and the second measurement, 𝑉−𝑔, is equal to minus the gravityacceleration, -9.81 m/s2. Based on these two measurements, the zero acceleration voltage,𝑉0, and the sensor sensitivity, 𝜎, are calculated as follows:

𝑉0 = 𝑉+𝑔 − 𝑉−𝑔

2 + 𝑉−𝑔 (3.6)

𝜎 = 𝑉+𝑔 − 𝑉0

9.81 (3.7)

In this way, after performing the accelerometer calibration, the experiment toobtain the micro-cantilever sensitivity to the vibrations intensity was done, according tothe procedure described in section 2.5.6. The signal generator was configured to delivera sinusoidal voltage at the device resonance frequency, and the voltage delivered to theadapted speaker, which generates the controlled vibrations, was incremented in steps of0.05 V. The resulting micro-cantilever voltage versus acceleration plot is given in figure34. Note that the signal generator voltage was plotted in red with the values on the righty-axis, to show that the control voltage was increased linearly.

The obtained results were different than the analytical models suggested, as themicro-cantilever voltage does not have a linear relationship with the vibration intensity.In order for the device generated power to be proportional to the squared value of theacceleration, the associated voltage would have to vary linearly with the vibration inten-sity. The plot in figure 34 suggests that the expected linear relationship does not occur.A possible explanation for this behavior could be derived by the fact that the model useddoes not account for several factors, such as changes in the structure stiffness, due to thevibration intensity, different resonance modes and anharmonic components.

The fact that the relationship found is different than the expected is very interest-ing, and these results will be used to derive a better semi-empirical model that accountsfor a non linear behavior between the micro-cantilever generated voltage and the vibrationintensity. The semi-empirical model will be presented in the following section.

3.6. Semi-Empirical Model 107

Figure 34 – Micro-cantilever voltage, in blue, and corresponding signal generator controlvoltage, in red, versus the vibration intensity measured by the accelerometer.

3.6 Semi-Empirical Model

Comparing the results obtained from the analytical calculations with the mea-sured results, it is possible to see that there was a large discrepancy between the valuesfound. It is important to note that the vibration intensity chosen to derive the analyticalcalculations was about half the value of the one used in the experiments (4 m/s2 against9.8 m/s2). Considering the expected quadratic relationship between the power and theintensity of the vibrations, it was expected that the measured power would be about fourtimes higher than the calculated value. In reality, the power measured for vibrations of9.8 m/s2 would correspond to the same value calculated for vibrations of 4.64 m/s25,according to the one-dimension model.

Although a large discrepancy could be expected, due to the fact that a simplifiedmodel was used, the reasons for such a difference can be explained by the findings in theexperimental results. The model outcome is greatly influenced by the resonance frequencyvalue, the mechanical damping coefficient and the squared value of the vibration intensity.The first two parameters were measured and the obtained values differ significantly fromthe calculated estimations. The vibration sensitivity experiment showed that the powergenerated by the cantilever does not have a direct quadratic relationship with the intensityof the ambient vibrations. The rate at which the power increases is reduced progressivelywith the increase in the vibration intensity, as can be seen from the plot in figure 34.Therefore, some corrections to the original one-dimension model can be applied, using

5 Applying a quadratic proportionality to the power value calculated for vibrations of 4 m/s2.


the experimental results.

Using the data from the vibration sensitivity experiment, a second order polyno-mial fit was performed to substitute the original model quadratic relationship betweenpower and acceleration. In this way, it is proposed that a new acceleration fit variable,𝐴𝑓𝑖𝑡, given in equation 3.8, would substitute the original 𝑥𝐵 in the power equation, 2.25,resulting in the semi-empirical model described by equation 3.9.

𝐴𝑓𝑖𝑡(𝑥𝐵) = 𝑎2𝑥𝐵2 + 𝑎1𝑥𝐵 + 𝑎0 (3.8)

To obtain the polynomial fit parameters, a baseline power coefficient was calculatedusing the one-dimension model, with the measured values for the resonance frequencyand the mechanical damping coefficient. The voltage measurements from the vibrationsensitivity plot were converted to power, using the known 𝑃 = 𝑉 2/𝑅 relationship. Themeasured power was divided by the baseline power coefficient, 𝑃𝑐𝑜𝑒𝑓𝑓 , and the secondorder polynomial fit was calculated using the measured acceleration values. If the fittingwas done using only the data from the experiment, the resulting fitting coefficients wouldrelate the acceleration to the generated voltage (or power if the data was converted).For that reason, calculating a baseline power coefficient was necessary for obtaining thedesired 𝐴𝑓𝑖𝑡 parameter, in a way that the semi-empirical model would be defined by thefollowing equation:

𝑃 (𝑥𝐵) = 𝐴𝑓𝑖𝑡(𝑥𝐵)𝑃𝑐𝑜𝑒𝑓𝑓 (3.9)

Where the 𝑃𝑐𝑜𝑒𝑓𝑓 is calculated by equation 2.25, from the one-dimension model,without the acceleration term, as shown in the following equation:

𝑃𝑐𝑜𝑒𝑓𝑓 = 𝑀𝑟𝑘2𝑒𝑅𝑒𝑞Ω2(𝑅𝑙𝜔𝑁)−1

[1 − (1 + 2𝜁𝑟)Ω2]2 + [𝐾𝑖𝑛𝑣𝑟Ω + 2𝜁Ω − 𝑟Ω3]2 (3.10)

Following this procedure, the calculated fit parameters were as follows: 𝑎2 =−0.0408; 𝑎1 = 1.2203; 𝑎0 = −0.1427. Plotting the new model curve, obtained from equa-tion 3.9 converted to voltage, along with the results obtained from the vibration sensitivityexperiment yields the plot in figure 35. It is possible to note that the new model is ade-quate to fit the experimental data.

A comparison between the frequency response curves was done, using the measuredresults, the pure analytical calculations and the new semi-empirical model. The resultingplot is shown in figure 36. In order to display the different results, a plot with semi-logarithmic scale was used. It is possible to conclude that the first model predicts verypoorly the actual power output of the cantilever, but the corrected semi-empirical modelgives a acceptable estimate. For the lower power values, in the lower and upper frequencies

3.6. Semi-Empirical Model 109

Figure 35 – Measured and simulated vibration sensitivity, using the polynomial fittingparameters.

the discrepancy, although very large, is insignificant due to the power being very close tozero. The measured power was derived from the voltage measurements, which could beinfluenced by noise that would dominate the measured voltage when the micro-cantileveroutput is very low. That fact could explain that discrepancy at the lower and higherfrequency range. The power peak value obtained was 2.33 µW, 0.46 µW and 0.49 µWfor the analytical, semi-empirical and measured results, respectively. The error in thecalculation of the resonant frequency was expected, due to the geometrical simplificationsthat were made, which disregards the effect of the thin films in the equivalent beamstiffness, considering only the contribution of the silicon beam. Accounting for these thinfilms in the calculation, the beam stiffness would be slightly higher, explaining the higherresonance frequency, of 161 Hz, measured.

It is important to note that due to the fact that a second order polynomial fitwas used, the semi-empirical model accuracy has a limited range of vibration intensities.Since the quadratic coefficient, 𝑎2, is negative, at higher acceleration intensities the fittingparameter, 𝐴𝑓𝑖𝑡, will be negative, resulting in an unrealistic negative power output. Sincethe micro-cantilever has a limited robustness, and it will break when submitted to veryhigh vibration intensities, that limitation is not much of an issue. Nevertheless, it isimportant to point out the model limitations. Further experiments would be required todetermine that accuracy range. A better model could be obtained if more measurementpoints were made for the vibration sensitivity curve, yielding a wider range of acceleration


Figure 36 – Comparison between the frequency response curve, obtained from the pureanalytical calculations, the semi-empirical model and the measured results.

values to perform the fitting. Also, a different kind of fit could also be used, such as alinear or a logarithmic fit. Those semi-empirical model enhancements could be topics forfuture research.

3.7 Applicability DiscussionConsidering the experimental results obtained, the feasibility of using the micro-

cantilever in wireless sensor nodes, as an energy source and vibration sensor, will bediscussed in this section.

3.7.1 Energy Harvester

The power generation capability simulated previously by the analytical model in-dicated that the application for energy harvesting was feasible. That was mainly becauseof the squared relationship of the generated power to the ambient vibrations intensity,in which for moderate intensity accelerations, easily found in industrial environments,the power generated could suffice to feed a low-power wireless sensor node. However, theexperiments conducted showed that the actual relationship of the generated power tothe vibration intensity was not as expected, and the actual power generated was aboutfour times lower than the predictions made by the analytical model. The values obtained,although considerably lower, still shows some potential for this application, but the pow-

3.7. Applicability Discussion 111

ered devices should have an extremely low consumption, and the rectification and energystorage strategy used would have to be very efficient.

A MEMS chip containing a single micro-cantilever would hardly be enough topower a WSN, but a chip containing an array of six6 micro-cantilevers could provideenough power. Using the WSN power consumption values discussed in section 1.6.4, thedevice would have to generate at least 0.63 µW to power the chosen MCU in standbymode, and 7.3 µW to power the entire WSN in idle mode. Assuming that it is possibleto operate the WSN powering only the microcontroller, with the other components beingcompletely shut down until a wake-up signal from the MCU turns all systems to the activemode, the absolute minimal requirement would be 0.63 µW. As discussed in section 1.6.4,when the WSN operation spends much more time in the standby mode, the averageconsumption tends to the consumption of that mode. With these considerations a singlemicro-cantilever could provide enough power for the suggested WSN when excited withvibrations of higher intensity than the ones used in the conducted experiments. A betterscenario would occur using a chip containing several micro-cantilevers and a WSN thatrequires less power. Such an application was demonstrated by (MARZENCKI; AMMAR;BASROUR, 2008), which reported a low power wireless sensor node, consuming an averagepower of only 150 nW and being fed by an array of piezoelectric micro-cantilevers. Otherenergy harvesting strategies, such as photovoltaic and electromagnetic induction, and arechargeable battery could be used alongside the proposed device to provide a more robustsolution to power a WSN.

It is important to note that the energy harvesting application requires auxiliarycircuitry with, at the very least, a rectification circuit. An unsuccessful attempt to rectifythe micro-cantilever signal and charge a capacitor was made. The problem was that thecurrent generated was lower than the minimum reverse polarization current required forthe used diodes, so the rectification did not occur. The use of special diodes, with very lowreverse polarization current, could solve this issue. Another consideration is the leakagecurrent of the capacitor, that should be much lower than the generated current, otherwiseit would not charge. It is very hard to find a suitable capacitor, since most commercialcomponents have a leakage current in the order of micro-amperes, and the generatedcurrent is in the order of nano-amperes.

Considering that the main limitations for the use of the micro-cantilever wererelated to the low current generated, it is proposed a re-design, increasing the beamwidth to obtain a higher current. A compromise between generated voltage and currenthas being made during the design, and the voltage was prioritize by designing a beamwith relatively low width, which yields a higher stress in the piezoelectric material when

6 Due to the die size limitations of the PiezoMUMPs process, a maximum of six micro-cantilevers, withthe proposed design, could be made into a single MEMS chip.


the tip mass oscillates. Increasing the width would lower the stress but would increase thepiezoelectric material area in the high stress region of the beam (closer to the anchoredbase), which would provide a higher current. Since the experimental results have showedthat the generated voltage is relatively high, redesigning the device choosing a wider beamcould be the solution to improve the feasibility of using the micro-cantilever as an energyharvester.

3.7.2 High Sensitivity Vibration Sensor

There are several different applications for vibrations sensors and depending onthe application certain characteristics will be required. Some situations may require a highsensitivity sensor, capable of detecting very low intensity vibrations, others may requirea very robust sensor that can withstand high intensity vibrations and mechanical shocks.The accuracy in the vibration intensity measurements and the frequency range, of themechanical vibration harmonics, that can be measured are other important considerationswhen determining if a sensor is appropriate for a specific application. The feasibilityof using the studied micro-cantilever as a vibration sensor will be discussed with thesecharacteristics in mind.

Looking at the plot in figure 34 it is possible to note that the voltage does nothave a linear relation to the vibration intensity, being better modeled by a quadraticcurve. For the acceleration range used, the proportionality is well defined, meaning thatthe measurement of the cantilever voltage can be accurately used to predict the intensityof the vibration harmonics in the resonant frequency of the cantilever. However, the high-Q, calculated from the damping coefficient, shows how frequency selective the device is,meaning that any vibration harmonic outside a narrow bandwidth close to the resonantfrequency would not produce a significant response. For that reason, the device is onlysensitive to vibration harmonics that are very close to its resonance frequency, having avery limited frequency range. An array of cantilevers with slightly different dimensionscould be designed for sensing different frequencies, having a high sensitivity vibrationsensor tailored for the application vibration harmonics of interest. That kind of devicehas a potential use to monitor industrial machinery vibration and looking for harmonicsthat indicate excessive wear-out, preventing failure and indicating the need for preventivemaintenance.

It is important to mention that an experiment to determine the micro-cantileverrobustness was not done, so the maximum acceleration that the device can safely operate isunknown. During the DUT preparation a couple of samples were damaged, suggesting thatthe device cannot withstand mechanical shocks or higher vibration intensities. Therefore,a further study would have to be conducted to assess the vibration intensity range withinwhich the device can operate.

113

4 Conclusion

4.1 Summary of the Presented Work

A brief introduction to the MEMS technology and the piezoelectric materials usedin micro-fabrication was given, pointing out the advantages of the aluminum nitride, whichwas the material of choice in the PiezoMUMPs process, used to fabricate the studiedMEMS device. The device of interest, a piezoelectric micro-cantilever, was presented,with discussions on its fabrication, design and principle of operation both as a vibrationalsensor and as a micro energy harvester. An introduction to wireless sensor nodes wasgiven, providing a context for the micro-cantilever application. The power consumptionof the main components of a WSN was evaluated, proposing a theoretical low powersystem with commercially available components, in order to obtain a baseline of powerconsumption to, later on, assess the feasibility of using the micro-cantilever to power theconsidered system.

Similar works in the area were reviewed, highlighting the power generating per-formance of the micro-cantilevers studied in those publications. A discussion of ambientvibration sources, pointing out the frequency and intensity of commonly found vibra-tion sources, was given in order to better understand the expected operation conditionsfor the studied device. A study of auxiliary-circuit topologies, to enable the usage of themicro-cantilever as an energy harvester, was presented, discussing rectifier circuits, voltagemultiplier and DC-to-DC converters that could be used for the intended application.

The mathematical background to obtain important parameters to predict the de-vice behavior was given, explaining the calculations for the resonance frequency, the me-chanical damping coefficient and the electromechanical coupling coefficient. Two analyti-cal models to estimate the power generated by the micro-cantilever, as a function of theambient vibrations intensity and frequency and the connected resistive load value, werediscussed.

A strategy to package the fabricated device chip was derived and the procedurewas undertaken, obtaining a viable test sample, DUT, of the micro-cantilever. An experi-mental setup, able to generate controlled vibrations for the DUT testing, was developed.The experimental procedures to obtain the frequency response, the optimal load value,to measure the damping coefficient and to obtain the vibration sensitivity curve weredescribed.

The parameters used in the analytical models were calculated and the obtainedvalues were summarized in table 6. The two analytical models provided insights regarding

114 Chapter 4. Conclusion

the device operation and gave an estimate for the power generation capability of the micro-cantilever. The results obtained were displayed as plots of frequency response, power andvoltage versus load resistance, and optimal load versus frequency. The obtained values ofimportant parameters were given in table 8.

Experiments were conducted to assess the actual performance of the device andevaluate the validity of the analytical models. The results showed a good consistency re-garding the values of the resonance frequency and optimal load, but discrepancies werefound in the mechanical damping coefficient value and the power generated. Using theexperimental results, a semi-empirical model was derived, obtaining a much better pre-diction1 than the original models.

An assessment of the feasibility of using the micro-cantilever for the two intendedapplications was made. The conclusion is that it would be very hard to use the currentmicro-cantilever device to generate enough power for feeding a WSN. The use of themicro-cantilever could be feasible under the right circumstances, namely, that the ambi-ent vibrations have a high intensity (above 10 m/s2) frequency harmonic that matchesthe device resonance frequency; that an appropriate rectification circuit, that can rec-tify currents in the order of hundreds of nano-amperes, is used; and that the WSN hasan extremely low average power consumption, under 500 nW. A redesign of the struc-ture, increasing the beam width, is proposed as a way to tackle that. For the applicationas a vibration sensor, the device seems promising for some specific applications due toits very high vibration sensitivity in a narrow frequency spectrum. An array of similarmicro-cantilevers with different beam lengths could be designed to cover a specific fre-quency spectrum, enabling the measurement of specific vibration harmonics which couldbe potentially useful to monitor industrial motors and machines, identifying prematurefailure.

4.2 Suggested Topics for Future WorksThis work has presented a comprehensive study of a piezoelectric micro-cantilever,

evaluating models to predict its behavior, conducting experiments to characterize a fab-ricated device and assessing the possibilities for its application. However, the conductedwork has by no means exhausted the research possibilities in the area, in fact, it hasshowed many opportunities for further development. A brief list of some interesting top-ics for future works is given below.

∙ Design and build a suitable rectification circuit, using diodes with a low reverse1 The semi-empirical model is only accurate for a limited range of vibration intensities due to the nature

of the polynomial fit used, and the low number of measurements taken for the vibration sensitivityplot.

4.3. Final Considerations 115

polarization current and a very low-leakage capacitor. Perform experiments to assessthe micro-cantilever behavior with the rectification circuit and using it to power anelectronic circuit.

∙ Obtain a vibration sensitivity curve with a wider range of acceleration measure-ments, confirming the relationship between the generated power and the vibrationintensity. The results could be used to derive a more accurate semi-empirical model,valid for a wider range of accelerations.

∙ Perform an experiment to determine the mechanical failure point of the micro-cantilever, increasing the vibration intensity until the beam breaks.

∙ Redesign the device to obtain a higher current, using the semi-empirical model tooptimize the micro-cantilever dimensions.

∙ Build a WSN and use the micro-cantilever as a vibration sensor and/or as powersource.

∙ Design a better procedure to package the micro-cantilever chip. An appropriatepackage for MEMS devices can be a challenge due to the presence of moving parts.

4.3 Final ConsiderationsIn summary, the goals for this work have been met and some interesting results

were found, despite the fact the studied device did not meet all expected performanceindices. A discrepancy between the analytical calculations and the experimental resultscould be explained considering the simplification that were made for the modeling de-velopment. Nevertheless, the results have not ruled out the deployment of the device forthe intended applications, showing feasibility provided that some specific conditions aremet. As the technological advancements continue to lower the power requirements forelectronic circuits, the application of the proposed device proposed will be favorable.

117

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