A novel self-sensing piezoelectric microcantilever-based ...1627/... · are equipped with external...

A Dissertation Presented

by

Samira Faegh

to

The Department of Mechanical and Industrial Engineering

in partial fulfillment of the requirements

for the degree of

Doctor of Philosophy

in the field of

Mechanical Engineering

Northeastern University

Boston, Massachusetts

June 2013

A NOVEL SELF-SENSING PIEOZELECTRIC

MICROCANTILEVER-BASED SENSOR FOR DETECTION OF

ULTRASMALL MASSES AND BIOLOGICAL SPECIES

i

ABSTRACT

Nanotechnological advancements have made great contributions in developing label-free and

highly sensitive biosensors. Development of biosensing tools has contributed significantly to

high-throughput diagnosis and analytical sensing exploiting high affinity of biomolecules.

Detection of ultrasmall adsorbed masses has been enabled by such sensors which translate

molecular interaction into detectable physical quantities. More specifically microcantilever

(MC)-based biosensors have caught a widespread attention for offering label-free, highly

sensitive, and inexpensive platform for detection. MC-based systems with different applications

are equipped with external devices and instruments for actuation and read-out purposes which

makes the entire platform expensive and bulky. Although there have been a number of

measurement techniques, a compact detection platform with the capability of miniaturization,

low power consumption, cost effective, and yet sensitive methodology is highly desirable.

This dissertation presents a unique self-sensing piezoelectric MC-based sensor for the purpose of

detecting ultrasmall masses and biological species. The entire developmental process is covered

and presented which includes: development of comprehensive mathematical modeling

framework, numerical simulation, designing, building and testing the sensor. In the beginning

chapters of this dissertation, the main focus is on analytical studies investigating modeling and

simulation of piezoactive MC-based systems with diverse applications along with the relative

experimental verification. Sophisticated comprehensive mathematical modeling frameworks

capable of describing static and dynamic behavior of MCs are presented. A unique self-sensing

strategy utilizing direct and inverse piezoelectric properties was developed which eliminates the

need for any bulky and expensive external equipment. The ability of the self-sensing platform to

measure ultrasmall masses was mathematically modeled and simulated, and then experimentally

tested. Similar experimental setup was built using optical-based equipments for comparison and

verification of the self-sensing platform. High level of accuracy was achieved both theoretically

and experimentally implementing the self-sensing platform for detection of adsorbed biological

species over MC surface. High mode vibrational studies were conducted for sensitivity

enhancement of the system. A new model of measurement was developed to overcome the

challenges of mechanical measurements in different environment (e.g. both gaseous and

ii

aqueous). The developed platform was further utilized to detect physiological concentrations of

glucose as low as 500 nM in liquid media. The developed platform can be implemented for

detecting gasses, chemical compounds and biological species with embedded miniaturized

actuator and sensor being capable of functioning both in gaseous and aqueous media with the

simplest and most inexpensive equipments.

iii

ACKNOWLEDGEMENTS

I would like to take this opportunity to thank those who have supported me during this chapter of

my life. First of all, my sincerest appreciation goes to my advisor, Prof. Nader Jalili, for his

guidance and inspiration at every step of this study. His wide knowledge and logical way of

thinking have been of great value to me. His understanding, encouraging and personal guidance

both in academical and non-academical aspects of life were substantial keys to make this journey

possible and rewarding and make me feel grateful and blessed to have worked with him.

I also would like to offer my special appreciation to my co-advisor, Prof. Srinivas Sridhar, for his

continuous support and guidance throughout this study. His great passion for research,

willingness to help and availability at any time has enlightened the path of my research.

I give my sincere gratitude to my committee member, Prof. Sinan Müftü, for all his guidance,

feedback and support during the process of completing my dissertation.

The financial supports of National Science Foundation through the IGERT fellowship program,

NSF-DGE-0965843 is greatly appreciated as well.

In addition, I would like to specially thank Dr. Ali Marzban for providing such useful guidance

and insights on my research and most importantly for making me believe that nothing is

impossible.

Furthermore, I would like to offer my appreciation to my friends, colleagues and lab mates, Dr.

Arman Hajati, Dr. Ozgur yavuzcetin, Dr. Sohrab Eslami and Nima Sarli for assisting me

patiently with my experiments and their honest suggestions and feedbacks.

Last but not least, I would like to dedicate this work to my family and thank them for their

everlasting love and support.

iv

TABLE OF CONTENTS

ABSTRACT ........................................................................................................................................... i

ACKNOWLEDGEMENTS .............................................................................................................. iiii

TABLE OF CONTENTS .................................................................................................................... iv

LIST OF FIGURES ............................................................................................................................vii

LIST OF TABLES............................................................................................................................... xi

CHAPTER 1. MOTIVATION AND PROBLEM STATEMENT .................................................... 1

1.1. Problem Statement ................................................................................................................ 1

1.2. Contributions ........................................................................................................................ 2

1.3. Dissertation Overview .......................................................................................................... 3

CHAPTER 2. INTORDUCTION AND PRELIMINARIES ............................................................. 6

2.1. ImmunoAssay Techniques .................................................................................................... 7

2.1.1. Enzyme-Linked ImmunoSorbent Assay (ELISA) ....................................................... 8

2.1.2. RadioAllergoSorben Test (RAST) ............................................................................. 10

2.1.3. RadioImmunoAssay (RIA) ......................................................................................... 11

2.1.4. Immunofluorescence ................................................................................................... 12

2.1.5. Enzyme-Linked Immunosorbent Spot (ELISPOT) ................................................... 12

2.1.6. Disadvantages of immunoassay diagnosis ................................................................. 12

2.2. Diagnosis Based on Nanomaterial Immunoassay ............................................................. 14

2.2.1. Nanoparicle-based immunosensors ............................................................................ 14

2.2.2. Bio-Barcode technology for protein detection........................................................... 16

2.2.3. Nanowire array for protein detection ......................................................................... 17

2.2.4. Carbon nanotube-based electrochemical immunosensor .......................................... 19

2.3. Electrochemical Immunosensors ........................................................................................ 20

2.3.1. Quartz Crystal Microbalance (QCM) ......................................................................... 22

2.3.2. Diagnosis with MC-based biosensors ........................................................................ 23

2.4. Key Challenges and Unique Opportunities ....................................................................... 25

CHAPTER 3. COMPREHENSIVE MATHEMATICAL MODELING OF PIEZOACTIVE

MICROCANTILEVER-BASED SYSTEMS .................................................................................. 31

3.1. Introduction.......................................................................................................................... 31

3.2. Mathematical Modeling ..................................................................................................... 34

3.3. Piezoresistive Modeling ..................................................................................................... 39

3.4. Piezoelectric Sample Modeling .......................................................................................... 40

v

3.5. Numerical Simulation ......................................................................................................... 41

3.6. Sensitivity Analysis ............................................................................................................. 43

3.7. Chapter Summary ................................................................................................................ 44

CHAPTER 4. COMPREHENSIVE MATHEMATICAL MODELING OF PIEZOELECTRIC

MICROCANTILEVER USED FOR ULTRASMALL MASS SENSING .................................... 46

4.1. Introduction.......................................................................................................................... 46

4.2. Beam Modeling ................................................................................................................... 48

4.2.1. Mathematical modeling ............................................................................................... 48

4.2.2. Numerical simulations and results .............................................................................. 51

4.3. Plate Modeling..................................................................................................................... 53

4.3.1. Mathematical modeling ............................................................................................... 54

4.3.2. Free vibration analysis................................................................................................. 57


4.4. Experimental Verification................................................................................................... 62

4.4.1. Non-functionalized MC: verification with modeling ................................................ 64

4.4.2. Detection of adsorbed mass ........................................................................................ 64

4.5. Chapter Summary ................................................................................................................ 68

CHAPTER 5. SELF-SENSING ULTRASMALL MASS DETECTION USING

PIEZOELECTRIC MICROCANTILEVER-BASED SENSOR ..................................................... 69

5.1. Introduction.......................................................................................................................... 69

5.2. Mathematical Modeling and Preliminaries ........................................................................ 72

5.2.1. Beam modeling ............................................................................................................ 72


5.3. Adaptive Estimation ............................................................................................................ 77

5.3.1. Adaptation law ............................................................................................................. 79

5.3.2. Simulation results for adaptive estimation ................................................................. 81

5.4. Experimental Setup ............................................................................................................. 82

5.4.1. Non-functionalized MC: verification with modeling ................................................ 83

5.4.2. Functionalized MC: detection of adsorbed mass ....................................................... 85

5.5. Chapter Summary ................................................................................................................ 88

CHAPTER 6. IMPLEMENTATION OF SELF-SENSING PIEZOELECTRIC

MICROCANTILEVER SENSOR AT ITS ULTRAHIGH MODE FOR MASS DETECTION . 90

6.1. Introduction.......................................................................................................................... 90

6.2. Mathematical Modeling ...................................................................................................... 92

6.3. Numerical Simulations and Results ................................................................................... 93

vi

6.4. Experiment and Results ...................................................................................................... 97

6.5. Chapter Summary ..............................................................................................................104

CHAPTER 7. DETECTION OF GLUCOSE IN A SAMPLE SOLUTION USING THE

DEVELOPED SELF-SENSING PLATFORM .............................................................................106

7.1. Introduction........................................................................................................................106

7.2. Materials and Methods ......................................................................................................109

7.2.1. Immobilizing GoX over MC surface ........................................................................110

7.2.2. Detection in air...........................................................................................................111

7.2.3. Detection in liquid .....................................................................................................112

7.3. Results and Discussions ....................................................................................................115

7.3.1. Immobilized mass detection in air (Laser vibrometer and Self-sensing circuit) ...115

7.3.2. Immobilized mass detection in liquid (Self-sensing circuit’s resonance) ..............116

7.3.3. Detection of marker protein in liquid (Self-sensing circuit’s resonance) ..............117

7.4. Chapter Summary ..............................................................................................................121

CHAPTER 8. CONCLUSIONS AND FUTURE WORKS ..........................................................123

8.1. Concluding Remarks .........................................................................................................123

8.2. Future Works .....................................................................................................................130

REFERENCES ................................................................................................................................134

vii

LIST OF FIGURES

Figure 2.1. Effect of interference of autoantibody and anti-reagent antibodies in sandwich immunoassay

[Hoofnagle and Wener, 2009], with permission. ............................................................. 13

Figure 2.2. Mechanism of bio-barcode assay A) design of the assay, B) Detection of PSA and

identification of DNA [Chen et al. 2009], with permission. .............................................. 16

Figure 2.3. a) Immunoassay consisting of array of nanowires, b) set of array of three nanowires

functionalized with antibodies specific for PSA, CEA, and mucin-1 over silicon nanowires

1, 2, and 3 respectively, c) plot of conductance versus time as a result of detection of PSA,

CEA, and mucin-1 [Zheng et al. 2005, Chen et al. 2009], with permission. ...................... 18

Figure 2.4. Label free electrochemical immunosensor based on array of microelectrodes modified with

SWCNs which are functionalized through immobilization of antibodies specific for disease

antigens [Okuno et al. 2007], with permission. ................................................................ 19

Figure 2.5. Microelectrode array on a silicon chip for detection of multiple analytes [Chen et al. 2009],

with permission. .............................................................................................................. 21

Figure 2.6. a) Schematic of a quartz crystal as the main part of QCM(R2) , b) a commercially available

QCM(R3) , with permission. .............................................................................................. 22

Figure 2.7. Schematic of disease diagnosis through MC-based biosensor. .......................................... 23

Figure 2.8. Array of MCs with functionalized surfaces through biomolecules for disease biomarkers.

Microchannels are used to bring sample to respective MC. The intermolecular binding

between the disease biomarker and the immobilized biomolecules over cantilever surface

induces differential stress thus deflects MCs. The amount of MC deflection can be

measured through any readout device. ............................................................................. 24

Figure 3.1. Schematic of piezoresistive MC sensor ............................................................................ 33

Figure 3.2. Schematic of the proposed distributed-parameters modeling of the piezoresistive MC

sensor, (sys. 1) ................................................................................................................ 35

Figure 3.3. Schematic of the proposed distributed-parameters modeling of the piezoresistive MC-based

PFM, (sys. 2)................................................................................................................... 35

Figure 3.4. a) tip deflection of the cantilever, w(L,t) in sys.1 b) output voltage, V0(t) in sys.1 and c)

contact force, fc(t) in sys.1 all in non-dimensional form, d) tip deflection of the cantilever,

w(L,t) in sys.2 e) output voltage, V0(t) in sys.2. and f) tip force, Ftip(t) in sys.2, (Faegh and

Jalili, 2011) ................................................................................................................... 42

Figure 3.5. a) Error of area under contact tip force, fc versus length of piezoresistive layer in sys. 1, b)

System’s amplitude versus local spring constant of piezoelectric sample in sys. 2. c)

System’s amplitude versus location of piezoresistive layer in sys. 2. ................................ 43

Figure 4.1. Veeco Active Probe® with the self-sensing layer attached at the probe. ........................... 47

viii

Figure 4.2. Schematic representation of Veeco Active Probe with ZnO stack on top extended from 0 to

L1 (Salehi-Khojin et al. 2009c), with permission. ............................................................. 49

Figure 4.3. Numerical results: (a) tip deflection of microcantilever, w(L,t), (b) shift in the first natural

frequency as a result of functionalization, (c) the effect of added surface mass due to

functionalization on the first natural frequency, (d) the effect of added surface mass on

vibration amplitude as a result of functionalization. ......................................................... 53

Figure 4.4. Veeco active probe with ZnO stack on top extended from 0 to L1..................................... 56

Figure 4.5. Eigenfunction for the first mode of the rectangular cantilever plate, W11. ......................... 60

Figure 4.6. (a) time response of microcantilever, q11(t), (b) Deflection of microcantilever at the tip of

the MC in the middle, w(L,

,t), (c) FFT of the response of the system representing

system’s first natural frequency and the effect of added absorbed mass in the shift of

natural frequency............................................................................................................. 63

Figure 4.7. MC mounted on a holder placed over a 3D stage positioned under laser vibrometer head. 64

Figure 4.8. (a) Decibel versus frequency, FFT of the output signal showing first resonance frequency at

56.1 kHz, (b) Amplitude ratio versus frequency. .............................................................. 65

Figure 4.9. Shift of the first resonance frequency as a result of: (a) GoX functionalization, (b)

immobilization of Amin solution and enzyme solution consequently.. ............................. 66

Figure 4.10. Quantification of frequency shift as a result of adsorbed mass exploiting mathematical

modeling framework.. ..................................................................................................... 67

Figure 5.1. Veeco Active Probe® with ZnO self-sensing layer deposited on the probe....................... 71

Figure 5.2. Micrograph/photograph of a Veeco Active Probe with a ZnO stack on top extended from 0

to L1 (Salehi-Khojin et al. 2009c), with permission. ........................................................ 73

Figure 5.3. (a) Pure capacitive bridge, and (b) Resistive-Capacitive (R-C) bridge (Gurjar and Jalili,

2006)............................................................................................................................... 73

Figure 5.4. Numerical results: (a) tip deflection of microMC, w(L,t), (b) Input voltage, Vc(t), output

voltage, V0(t), and self-induced voltage, Vs(t), (c) FFT response of the system with 1st

natural frequency highlighted, (d) the effect of added surface mass due to functionalization

on the first natural frequency (Faegh et al. 2013a)............................................................ 78

Figure 5.5. Sensitivity of the vibration amplitude of the tip of MC with respect to C1. ....................... 79

Figure 5.6. Schematic of the adaptive self-sensing strategy (Faegh et al. 2010, 2013). ....................... 80

Figure 5.7. (a) Tip deflection of MC, wL(x,t), (b) FFT response of the system with 1st natural frequency

highlighted. ..................................................................................................................... 81

Figure 5.8. The effect of θ on the calculation of self-induced voltage, ........................................ 82

Figure 5.9. Veeco Active Probe mounted on a holder (a) connected to the pure capacitive bridge for

self-sensing implementation, (b) placed under laser vibrometer head. .............................. 83

ix

Figure 5.10. (a) FFT of the response of the system using self-sensing bridge, (b) Input, output and self-

induced voltages, (c) FFT of the response of the system using laser vibrometer. .................... 84

Figure 5.11. Shift in the first resonance frequency measured by (a) self-sensing bridge,

(b) Laser vibrometer. ....................................................................................................... 87

Figure 5.12. Quantification of frequency shift as a result of adsorbed mass exploiting mathematical

modeling framework. ...................................................................................................... 88

Figure 6.1. (a) Veeco Active probe® used in this study for modeling and experiment, (b) schematic of

the beam used for modeling ............................................................................................. 92

Figure 6.2. Normalized Mode Shapes (MS) (a) MS 1-5, and (b) MS 4-7............................................ 94

Figure 6.3. FFT of the response of the system, where n=20, depicting a) first 10 and b)

next 10 resonance frequencies of the system. ............................................................. 95

Figure 6.4. Frequency shift as a result of different amount of mass immobilization on (a) 10th mode,

(b) 11th mode, (c) 12th mode, (d) 15th mode, with n=20. ................................................ 98

Figure 6.5. Shift in resonance frequency calculated for different mode numbers as a result of different

amount of mass immobilization ...................................................................................... 98

Figure 6.6. Veeco Active Probe mounted on a holder (a) connected to the pure capacitive bridge

mounted on a bread board for self-sensing implementation, (b) placed under laser

vibrometer head............................................................................................................. 100

Figure 6.7. Resonance frequencies measured by (a) self-sensing method running the system in its tenth

mode, (b) laser vibrometer running the system in its third mode..................................... 101

Figure 6.8. Shift in the resonance frequencies in the a) first mode, b) second mode, and c) third mode

of vibration measured by self-sensing platform.. ............................................................ 102

Figure 6.9. Shift in the resonance frequencies in the a) first mode, b) second mode, and c) third mode

of vibration measured by laser vibrometer.. ................................................................... 103

Figure 6.10. Increase in frequency shift with the first three modes of vibration measured with self-

sensing platform and laser vibrometer ........................................................................... 103

Figure 7.1. Veeco Active Probe® with ZnO self-sensing layer deposited on the probe..................... 107

Figure 7.2. a) Self-sensing circuit for actuating and sensing the system (b) MC mounted on a holder

placed over a 3D stage positioned under laser vibrometer head. ..................................... 111

Figure 7.3. Circuit model to find equivalent impedance, Zeq. .......................................................... 112

Figure 7.4. Schematic of a model of MC molecular probe interface biosensor including three

capacitors in series (Faegh et al. 2013b).. ....................................................................... 114

Figure 7.5. Effect of values of (a) C1and Cr and (b) L on circuit’s sensitivity in detecting shift in

resonance frequency. ..................................................................................................... 115

Figure 7.6. First resonance frequency of MC and shift in the resonance frequency in air as a result of

GoX functionalization measured with (a) self-sensing circuit, and (b) laser vibrometer. . 115

x

Figure 7.7. Quantification of amount of adsorbed mass with respect to shift of mechanical resonance

frequency of system utilizing comprehensive distributed-parameters mathematical

modeling framework, (Faegh and Jalili, 2013, Faegh et al. 2013a).. ............................... 116

Figure 7.8. Shift in the resonance frequency of the self-sensing circuit consisting of MC as a result of

GoX functionalization over sensor MC surface.. ............................................................ 117

Figure 7.9. Resonance frequency of the circuit consisting of sensor MC and reference MC and the shift

in resonance frequency in liquid as a result of injecting (a) 0 glucose, (b) 500 nM glucose,

(c) 1 μM glucose, (d) 100 μM glucose, (e) 200 μM glucose (Faegh et al. 2013b).. .......... 118

Figure 7.10. Differential Shift in the resonance frequency of the circuit with sensor and reference MC

(Δfref – Δfsensor) as a result of injecting different concentrations of glucose (Faegh et al.

2013b).. ......................................................................................................................... 119

Figure 8.1. The proposed diagnostic kit involving one refrence and more than one sensor probes

equipped with a compact fluidic setup, injection valve, and syringe pump.. ................... 131

xi

LIST OF TABLES

Table 2.1. An illustrative comparison between various immunoassay techniques and cantilever-based

diagnosis. ........................................................................................................................ 26

Table 2.2. MC-based measurement techniques. ............................................................................ 27

Table 3.1. Numerical values used in the simulation ..................................................................... 41

Table 4.1. The system parameters used for modeling................................................................... 52

Table 4.2. Comparing the results obtained from mathematical modeling presented in parts I and II to the experimental results.. ............................................................................... 65

Table 5.1. The system parameters used for modeling................................................................... 76

Table 5.2. Comparing the results obtained from mathematical modeling presented in Sections 2

and 3 with the experimental results.. ............................................................................ 85

Table 6.1. Calculated resonance frequencies using different order model (n).. .......................... 96

Table 6.2. Shift in the resonance frequency as a result of mass immobilization (1 ng-10 μg) for

all modes 1st-20th.......................................................................................................... 99

Table 6.3. Resonance frequencies running the system in its tenth mode calculated theoretically

and measured experimentally. ...................................................................................... 99

Table 7.1. Quantification of adsorbed mass with respect to circuit’s resonance frequency

calibrated by mechanical response of the system ......................................................120

Table 7.2. Comparison of detection limit of measuring glucose concentration.. ......................120

1

CHAPTER 1

MOTIVATION AND PROBLEM STATEMENT

1.1. Problem Statement

Nanotechnological advancements have significantly contributed to the development of Nano-

and Micro- Electromechanical Systems (NEMS and MEMS). Label-free and highly sensitive

methodologies for detection of ultrasmall masses and biological species have been discovered for

detection and diagnostic purposes utilizing micro and nano scale environmental, gas, and

biological sensors. High-throughput diagnosis and analytical sensing require advanced

biosensing tools exploiting high affinity of biomolecules. There are a number of useful

biosensing techniques such as electrophoretic separation and spectrometric assays.

Electrophoretic separation operates based on spatiotemporal separation of analytes whereas

changes in the mass or optical properties of target proteins are utilized in spectrometric assays.

One of the most promising methodologies developed for detection is utilizing high affinity of

molecules. Identification and quantification of target molecules has been made possible based on

molecular recognition which is transferrable to detectable physical quantities (Fritz et al. 2000).

Therefore, two main elements determining the success of sensors include: i) sensitive molecular

probe interacting with target molecules where recognition occurs, and ii) transducer which

transforms the molecular recognition into a detectable physical quantity.

There are a number of instruments developed for mass sensing purposes which are equipped with

these elements including quartz crystal microbalance (QCM), surface plasmon resonance (SPR),

enhanced-Raman spectroscopy, field effect transistors (FET) and MicroCantilever (MC)-based

2

systems. MC-based systems have become very popular due to offering a simple, inexpensive and

highly sensitive sensing platform with possible miniaturization capabilities.

Although MC-based biosensors have received a widespread attention for label-free detection,

there are not enough analytical studies investigating modeling and simulation of piezoactive MC-

based system along with the relative experimental verification. Therefore, there is still a need for

a more comprehensive mathematical modeling framework capable of describing static and

dynamic behavior of MCs. Along this line of reasoning, a very comprehensive mathematical

modeling framework for a variety of piezoactive MC-based systems with diverse application is

presented here. Numerical simulations at high vibrational modes as well as fundamental modes

are performed. Relative experimental setup for each section is built and verified with

mathematical modeling. Finally, a unique self-sensing piezoelectric MC-based platform is

developed, both theoretically and experimentally, and tested for detection of ultrasmall masses

and biological species. The platform is further utilized as a gas sensor for detection of alcohol

vapors with high sensitivity.

1.2. Contributions

The major contributions of this dissertation can be summarized as:

Development of comprehensive mathematical modeling for piezoresistive MC-

based systems specifically implemented for Piezoresponse Force Microscopy

(PFM) and as a biological sensor operating in contact mode.

Development of an extensive modeling framework for piezoelectric MC-based

sensor using both thin plate theory and Euler-Bernoulli beam theory and

conducting free and forced vibration analyses to verify and compare beam and

plate theories.

3

Development of an extensive experimental setup for verification of the theoretical

modeling frameworks in previous steps.

Development of a unique self-sensing piezoelectric MC-based sensor for

detection of ultrasmall masses and biological species. This design and

implementation processes include:

1) Development of analytical modeling framework for the entire platform,

2) Conducting numerical simulations,

3) Adopting an adaptive strategy to compensate for variations of piezoelectric

material embedded in the structure of the sensor,

4) Conducting high-mode vibrational analysis for sensitivity enhancement both

theoretically and experimentally,

5) Designing and building the senor and verifying the capability of the self-

sensing strategy for measurement by comparison to optical-based techniques,

6) Implementing the developed sensor for detection of different concentrations

of glucose in a sample solution and measuring the sensitivity of the system.

1.3. Dissertation Overview

In order to have a precise MC-based system, a very comprehensive modeling needs to be

developed and utilized. In almost all of the studies regarding MC-based systems, simple lumped-

parameters modeling was used which is not capable of describing the dynamics within the

cantilever and the consequent sensing characteristics.

Along with this line, Chapters 3 and 4 are devoted to develop a comprehensive mathematical

model for piezoactive (including both piezoresistive and piezoelectric) MC-based

4

nanotechnological systems. Different systems are investigated and extensively modeled and

simulated which are:

Piezoresistive MC sensor implemented for measuring intermolecular force in contact

mode,

Piezoresistive MC sensor implemented for Piezoresponse Force Microscopy (PFM),

Piezoelectric MC used for mass sensing and detection modeled as Euler-Bernoulli

beam,

Piezoelectric MC used for mass sensing and detection modeled as non-uniform

rectangular plate.

In Chapter 5, a unique self-sensing detection technique for piezoelectric MC-based sensor is

developed. It provides a laser-free, portable and cost-benefit sensing platform for detection of

ultrasmall masses and biological species. Direct piezoelectric property is used to sense the self-

induced voltage generated in the piezoelectric layer as a result of beam deformation. At the same

time, inverse property of piezoelectric material is used to generate deformation and bring the

system into vibration as a result of applying a harmonic voltage to it.

Comprehensive mathematical modeling is developed and simulated. An experimental setup is

built and tested. Theoretical results are compared to experiment and the entire setup is verified

with optical-based measurement techniques.

High mode resonating MC has been investigated and implemented as an effective solution for

sensitivity enhancement. However, there have not been any analytical distributed-parameters

modeling for systems operating in their high modes. As a result, in Chapter 6, a comprehensive

mathematical modeling for a piezoelectric self-sensing MC-based sensor operating at ultrahigh

mode (e.g. 20th

mode) is presented. The effect of adsorbed mass on the frequency shift are

5

investigated. An experimental setup is built implementing the systems at its higher modes and

tested for mass sensing capabilities at different modes. Optical method is tested for verification

as well.

Once the capability of the self-sensing strategy was verified both at high mode as well as

fundamental mode, the developed platform was implemented as a biological sensor. One

important factor determining the success of all biological sensors performing based on analytical

sensing of high affinity of biomolecules is the ability of the sensor to operate in liquid media

with high sensitivity. We have addressed this challenge by operating the proposed self-sensing

biosensor in dynamic mode in liquid media by exciting the system at high frequency. In Chapter

7, glucose detection implementing the self-sending MC-based sensor is presented. Rapid,

continuous, and highly sensitive measurement of molecular recognition was measured. The use

of self-sensing circuit’s resonance frequency instead of MC mechanical resonance frequency is

extensively discussed. Circuit modeling is developed and experimental setup is built to detect

different concentrations of Glucose in liquid sample solution.

The same study was performed using interdigitated electrodes (IDE) as the sensing element.

Self-sensing circuit was applied implementing the IDE as a capacitive-based biosensor. Change

of capacitance of the sensing element as a result of molecular binding was measured and

compared with the MC-based sensing platform.

Finally, concluding remarks and future work are discussed in chapter 8.

6

CHAPTER 2

INTRODUCTION AND PRELIMINARIES

Identifying signatures of disease also known as biomarkers is the main factor in disease

diagnosis. The expression level of these biomarkers is related to a specific disease which forms

the basis of monitoring different diseases. Most of the traditional methods of diagnosis rely on

animal models experiments and relating the results to similar cases in human’s benefits.

However, the inherent differences between animal’s and human’s immune system triggers new

efforts and methodologies for studying human’s immune system directly. In order to achieve this

purpose, short time process of multiple sample and measurement of a great number of

parameters is necessary with the aid of technological advancements.

Speaking generally, different diagnosis techniques include:

ImmunoAssay Techniques

– Enzyme Linked ImmunoSorbent Assay (ELISA)

– RadioAllergoSorbent Test (RAST)

– RadioImmunoAssay (RIA)

– ImmunoFluorescence

– Enzyme Linked Immunosorbent Spot (ELISPOT)

Nanomaterial-based ImmunoAssays

– Nanoparticles

– Bio Barcode technology

7

– Nanowire-array-based detection

– Carbon Nanotubes

Label Free Electrochemical Immunosensors

– Quartz Crystal Microbalance (QCM)

– MC-based biosensors

These techniques are briefly discussed next. The advantages and disadvantages of each technique

are disclosed and conclusive statements are presented. This comparative study and brief review

would help the reader to better realize the motivation behind this dissertation.

2.1. ImmunoAssay Techniques

One of the commonly used methodologies for measurement of concentration of materials such as

analytes in biological samples is ImmunoAssay technique. It is capable of quantitatively

measuring the presence of biomarkers in sample liquids such as serum or urine. Molecular

interaction of antibodies with specific antigens of particular disease forms the basis of

immunoassay detection. The success of this methodology highly relies on the degree of

specificity of the receptor to the corresponding analytes and creating specific interaction which

should dominate the unspecific binding that might occur as a result of presence of other

substances in the sample.

The main requirement of a detection technique is that it should be equipped with sufficient tools

to recognize the specific binding that takes place between specific analytes and corresponding

receptors and transducing the obtained signal into some detectable physical property. Changes in

refractive index and light scattering have been used a lot for this purpose. Some labels that have

been used for this purpose include: enzymes, coenzymes, selenium colloidal particles,

8

fluorescent, phosphorescent, etc. Intermolecular interaction can be recognized as the label-

produced signal changes.

In immunoassay techniques, usually a reference sample is utilized which contains no analyte.

Comparing the response of the sample containing the minimum detectable level of concentration

of analyte with the reference sample provides a good source of quantitative measurement of

biomarker concentration in the sample solution.

In general, there are two main categories of immunoassay techniques:

a) Competitive Immunoassay: In this technique, a few number of antigens in the sample

solution are labeled which produce the binding signals. The obtained signal is inversely

proportional to the concentration of the analyte contained in the sample which competes

with the labeled analytes. Therefore, higher number of analytes in the sample would

create lower signal produced by the labeled analytes.

b) Noncompetitive Immunoassay (Sandwich Assay): In this method, some antibodies are

labeled. The labeled antibodies make a bound with the antigens in the sample which

themselves interact with antibody site. Therefore, the response produced by the labeled

antibodies reflects the amount of antigens in the sample.

There are a number of immunoassay techniques that are used for detection of the concentration

of analytes in a sample. These techniques are discussed next:

2.1.1. Enzyme-Linked ImmunoSorbent Assay (ELISA):

This immunoassay technique is utilized as a method of diagnosis for measuring the concentration

of an antibody or an antigen contained in a sample solution. The experimental procedure of

9

ELISA includes (Engvall and Perlman, 1971, Leng et al. 2008, Lequin, 2005, Wide and Porath,

1966):

a) Immobilizing an amount of antigen (unknown) over a substrate (specifically or non-

specifically),

b) Adding the detection antibody to make specific binding with the immobilized antigen,

c) Linking the detection antibodies to an enzyme or conjugating the detection antibodies

to secondary antibody and then linking the secondary antibody to an enzyme,

d) Adding an enzymatic substrate which physical quality’s changes with the

concentration of the antigen in the sample solution.

An important step that should take place in order to prevent nonspecific binding of antibodies or

other substances is to use detergents to wash plate.

Several materials have been used to produce signals due to presence of antigens in a sample in

this technique which include chromogenic, fluorogenic, and electrochemiluminescent signal

producers which work based on changing the color of substrate. A reference solution is prepared

containing a standard concentration of analyte of a sample disease. Signal produced from test

samples containing an unknown amount of analytes can be compared to the reference solution

and evaluated accordingly which forms the basis of detection in this immunoassay technique.

There are two typical formats of ELISA which are quantitative and qualitative. In qualitative

ELISA, comparison of produced signal from the test sample to the reference sample would

reveal positive or negative evaluation with positive meaning stronger signal thus higher

concentration of analyte and vice versa.

There are three main types of ELISA which include indirect, sandwich, and competitive ELISA.

In indirect ELISA, the solution containing antigens is added to a microplate. A sample with

10

unknown concentration of primary antibodies is brought into contact with the microplate which

results in creation of specific interaction between primary antibodies and immobilized antigens.

Enzyme-linked secondary antibody is added thus binding occurs between primary and secondary

antibodies. This interaction changes the color of the enzyme substrate indicating the reaction

between antigen and antibody thus the concentration of primary antibody. Passivation of

microplate with non-reacting proteins would decrease unspecific binding.

In sandwich ELISA, a known concentration of antibody is immobilized over a substrate. Sample

solution containing unknown amount of antigen is then added which binds to the immobilized

antibodies. Enzyme-linked antibodies are brought into contact with sample which further

interacts with the antigens. Adding enzyme-substrate, concentration of antigen can be evaluated

from the detectable signal observed in the substrate.

In Competitive ELISA, a sample containing antigen bounded to its specific antibody is prepared

and brought to an antigen immobilized well. The unbounded antibodies in the solution would

then bind to the immobilized antigen on the well. Therefore, higher concentration of antigen in

the sample would result in lower binding of antibody with to antigen in well. Enzyme-linked

secondary antibody is added and finally is linked to a substrate which change of its properties

can be a measure of concentration of antigen in the sample solution.

2.1.2. RadioAllergoSorben Test (RAST)

This immunoassay technique is used to determine the specific response of IgE which is the

antibody associated with Type I allergic response. It evaluates the allergy of a person to a known

allergen through the concentration of produced IgE against that specific allergen. In this

technique, the sample solution containing antibody associated with a know allergen is added to

an insoluble material where the allergen are immobilized. As a result, specific binding occurs

11

between IgE antibodies and allergens. Secondary antibodies which are radio-labeled are added

and bind to primary antibodies. The concentration of antibodies in serum can be detected from

the radioactive signal produced form interaction of secondary and primary antibodies. Stronger

radioactive signal means higher concentration of IgE antibodies in the serum bounded to

allergen, thus higher allergy of the person to that particular allergen. This method is suggested

over the simple skin-prick testing especially when there is a widespread allergy, and high

sensitivity of the patient to a specific allergen. However, it is not as sensitive and specific as the

skin-prick test (Ten et al. 1995).

2.1.3. RadioImmunoAssay (RIA)

Radioimmunoassay is a very sensitive method for detection of concentration of antigens in a

sample utilizing radioactive substances with high accuracy. In this technique, a solution is

prepared with a known amount of antibodies. Specific antigens for that antibody are radio-

labeled usually with gamma-radioactive isotopes and are brought into contact with the solution

where specific bindings occur between labeled antigens and antibody (Acebedo et al. 1975,

Yalow and Berson, 1960). The competitive assay takes place when the patient sample solution

containing unknown amount of antigens is added; therefore, unlabeled antigens in the sample

solution and radio-labeled antigens try to bind with the antibodies. The higher concentration of

antigens in sample solution means the higher interaction with antibodies and the higher

concentration of the remained unbounded radio-labeled antigens. Therefore, the radioactivity of

the unbounded labeled antigens would be a good source of concentration of unknown antigens in

the patient’s sample fluid. Colorimetric signals utilized in ELISA are sometimes implemented in

RIA instead of radioactive signal in order to reduce the required precautions of dealing with

radioactive materials.

12

2.1.4. Immunofluorescence

Immunofluorescence is widely utilized for detecting the location of antibodies through use of

fluorophores. This technique is used in light microscopy for visualization of individual cells and

distribution of proteins and small biomolecules to name a few. There are two main types of

immunofluorescence methods which are direct and indirect.

In direct immunofluorescence, one antibody labeled with fluorophore binds to its receptor which

can be visualized through microscope. This technique reduces non-specific binding thus

background signal. However, in the indirect immunofluorescence, one antibody, which is

unlabeled, targets its receptor and a secondary antibody which is labeled with fluororphore binds

to the first antibody and can be visualized.

There is a certain limitation in using this technique in vivo. Challenges with labeling

biomolecules and problems resulting from photobleaching are the main drawbacks of this

technique.

2.1.5. Enzyme-Linked Immunosorbent Spot (ELISPOT)

This immunoassay technique is mainly used for detection of immune responses. It enables

monitoring antigen-specific immune system response. Type of immune antibody and number of

cells producing this response can be monitored implementing ELISPOT.

The technique is very similar to sandwich type of ELISA. A modified version of ELISPOT

which utilizes multiple fluorescent anticytokines for detection is named FluoroSpot (Czerkinsky

et al. 1983).

2.1.6. Disadvantages of immunoassay diagnosis

13

Even though immunoassay techniques have been widely used for detection, there are certain

disadvantages accompanied with them. One of the main drawbacks of this technique is the lack

of consistency between different immunoassay platforms. The main step in diagnosis of a disease

is to detect proteins secreted from damaged tissues at very low concentration, and the main

approach in immunoassay techniques is selecting proper antigen for this approach. However, the

results obtained from one assay may vary to the other. As a result and in order to detect a

particular analyte, different antibody targets different epitope in assays. Examples may include

different detection results obtained from immunoassay techniques for thyroid stimulating

hormone, and tumor biomarkers for pancreatic (Rawlins and Roberts, 2004, La’ulu and Roberts,

2007).

Another important challenge associated with immunoassay techniques is the interference of

autoantibodies. This interference leads to a false results obtained from immunoassay platform

due to the fact that autoantibodies target antigens that are recognized by reagent antibodies and

interacts with them (Spencer et al. 1998, Spencer and Lopresti, 2008).

Non-specific aggregation caused by anti-reagent antibodies is also an important factor that has to

be considered using immunoassay technique. Anti-reagent antibodies are capable of attaching to

Figure 2.1 Effect of interference of autoantibody and anti-reagent antibodies in sandwich

immunoassay [Hoofnagle and Wener, 2009], with permission.

14

capture antibodies and then can be targeted by reagent antibodies thus leading to false evaluation

(Dale et al. 1994, Kricka, 1999, Levinson and Miller, 2002, Sapin et al. 2007). The interference

of anti-reagent antibodies has been reported to affect biomarkers of particular diseases (Morgan

and Tarter, 2001, Preissner et al. 2003, Rotmensch and Cole ,2000, Willman et al. 1999).

The aforementioned interferences are demonstrated in Figure 2.1 where a sandwich bound takes

place on a magnetic bead coated with streptavidin. Biotin binds to streptavidin as a result of high

affinity between these two molecules and it further captures antibody which binds to the

analytes. Reagent antibodies which are enzyme-labeled target the analyte and can be detected by

various methods. However, as shown in Figures 2.1 B and C, the presence of autoantibodies and

non-specific binding of anti-reagent antibodies distorts the sandwich immunoassay.

There is another phenomenon in immunoassay techniques known as high dose hook effect. It

happens in sandwich immunoassays where false evaluation is obtained as the concentration of

analyte in the sample solution increases higher than a certain amount. Analytically, increase in

the concentration of analyte increases the response of the immunoassay platform. However,

theoretically, when concentration of analyte reaches a specific value, the response shows a

reverse effect and decreases which is not accurate. Some studies have demonstrated the high

dose hook effect in patient samples containing high concentration of analytes (Fleseriu et al.

2006, Furuya et al. 2001, McCudden et al. 2009).

2.2. Diagnosis Based on Nanomaterial Immunoassay:

Nanomaterial Immunoassay techniques have a potential alternative to conventional

immunoassay detection techniques. Different nanomaterial research and developments are

discussed as follows.

2.2.1. Nanoparicle-based immunosensors

15

Nanoparticles have received a widespread attention in disease diagnosis during past few years

for their unique potential in offering a suitable bioanalysis platform. Their unique characteristics

such as high surface-to-volume ratio and capability of biomolecule immobilization make them a

proper alternative for conventional clinical immunoassay techniques. Quantum dots, gold and

magnetic nanoparticles have been utilized for developing immunoassays for detecting tumor

markers.

A label-free nanoparticle based immunoassay has been developed consisting of five electrodes

including a reference electrode integrated on a glass substrate. Each electrode contains

NiFe2O4/SiO2 nanoparticles with a different antibody immobilized on its surface. The interaction

between antibody and antigen in the sample solution changes the electrode potential which

consequently produces a detectable signal. Four tumor markers including AFP, CEA, CA 125,

and CA 15-3 have been detected simultaneously implementing this nanoparticle-based

immunosensor (Tang et al. 2007a). Gold Nanoparticles have also been used for detection of CEA

tumor marker. Gold nanoparticles modified with a glutathione monolayer were employed for

immobilization of CEA antibodies and the whole bioconjugate was integrated on Au electrode.

Formation of CEA antibody-antigen complexes could be detected by changes in the resistance of

the electrode (Tang et al. 2007b). The immunosensor enables detection in the range of 0.5-20

ng/mL with the resolution of 0.1 ng/mL.

Gold nanoparticles being characterized with electrocatalytic property has been used for signal

amplification in electrochemical detections. Gold-nanocatalyst labels were demonstrated to

enhance produced signal in detection of Prostate Specific Antigen (PSA) (Das et al. 2006).

16

2.2.2. Bio-Barcode technology for protein detection

Figure 2.2 Mechanism of bio-barcode assay A) design of the assay, B) Detection of PSA

and identification of DNA [Chen et al. 2009], with permission.

17

The bio-barcode technology has been proposed for detection of PSA biomarkers utilizing

combination of gold and magnetic nanoparticles (Nam et al. 2003).

The system consists of magnetic microparticle with iron oxide core coated with polyamine with

the diameter of 1 μm. The magnetic microparticle is functionalized with antibodies specific for a

target protein such as PSA. On the other hand, gold nanoparticles are functionalized with DNA

unique for that target protein plus antibodies capable of creating a sandwich with the target

protein captured by the magnetic microparticle. After formation of sandwich, a magnetic field is

applied which results in separation of magnetic mircoparticle and consequently dehybridization

of bar-code DNA. Identifying the DNA sequence allows the determination of the presence of the

target protein. The mechanism of bio-barcode assay is demonstrated in Figure 2.2. This

technique provides a highly sensitive method for detection of protein markers due to the fact that

a great number of bar-code DNA can be loaded on nanoparticle surface for detection of each

protein marker. It is also capable of detecting multiple protein markers simultaneously (Nam et

al. 2007, Stoeva et al. 2006).

One of the main limitations of this technique is the challenge associated with design and

preparation of microparticle probe and nanoparticle. Silica nanoparticles have also been used for

development of electrochemical immunosensors due to their unique properties such as being

biocompatible, stable, and functionalized with bioreagents. Detection of PSA was reported

through silica nanoparticle-based immunosensor (Qu et al. 2008).

2.2.3. Nanowire array for protein detection

Immunoassay nanodevices based on nanowires are also promised to be a suitable tool for protein

detection due to unique properties of nanowires such as high surface-to-volume ratio and

electron transportation properties. It consists of arrays of 1D semiconductor or conducting

18

polymer nanowire array. The nanowire arrays

can be functionalized with a great number of

capturing biomolecules such as antibodies.

Having a high surface-to-volume ratio,

nanowires create assays of multiple disease

markers by immobilizing antibodies specific

to disease antigen thus offering a highly

selective and simultaneous detection

nanostructure. Molecular interaction between

immobilized antibodies over nanowire surface

and disease antigens imposes surface

perturbations on nanowire array thus changes

its electronic conductance due to novel

electron transportation properties of

nanowires. Zheng et al. (2005) performed a

study implementing real-time, label free,

multiplexed immunoassay based on arrays of

nanowires for detection of four cancer markers as shown in Figure 2.3. The immunoassay device

consists of plenty of silicon nitride metal electrodes connected to nanowires. Figure 2.3b

demonstrates array of three silicon-nanowires functionalized with antibodies specific for PSA,

CEA, and mucin-1 on nanowires 1, 2, and 3 respectively. Intermolecular binding induces

conductance change which is depicted in Figure 2.3c as a function of time.

Figure 2.3 a) Immunoassay consisting of array

of nanowires, b) set of array of three nanowires

functionalized with antibodies specific for PSA,

CEA, and mucin-1 over silicon nanowires 1, 2,

and 3 respectively, c) plot of conductance versus

time as a result of detection of PSA, CEA, and

mucin-1 [Zheng et al. 2005, Chen et al. 2009],

with permission.

19

Electrochemical alkaline phosphatase nanowire-based assay was implemented to detect lung

cancer biomarkers (interleukin-10 and osteopontin) (Ramgir et al. 2007) and metal oxide

nanowire-based immunoassay was implemented for detection of tumor marker proteins (Li et al.

2005).

2.2.4. Carbon nanotube-based electrochemical immunosensor

Carbon nanotubes and their utilization in electrochemical immunosensors have caught

widespread attention due to their unique electrical and mechanical properties. Single Walled

Carbon Nanotubes (SWNT) having a high aspect ratio and electron transfer property promises a

suitable tool for electrochemical measurement (Okuno et

al. 2007). Biosensors consisting of arrays of

microelectrodes modified with carbon nanotubes have

been utilized for detecting marker proteins (Okuno et al.

2007, Yu et al. 2006, Briman et al. 2007).

A label-free electrochemical immunosensor based on

carbon nanotubes was developed for detection of cancer

biomarker T-PSA (Okuno et al. 2007) as shown in Figure

2.4. It consists of arrays of microelectrodes modifies with

SWNTs. Having a high aspect ratio, SWNTs offer

immobilization of a great number of anti-T-PSA over their

surface. Interaction occurs between PSA and anti-PSA

immobilized over SWNT surface. Peak current as a result

Figure 2.4 Label free

electrochemical immunosensor

based on array of microelectrodes

modified with SWCNs which are

functionalized through

immobilization of antibodies

specific for disease antigens

[Okuno et al. 2007], with

permission.

20

of antigen-antibody binding produces the signal which can be a source of measurement of

concentration of PSA. Sensitivity of 0.25 ng/mL was reported using this device (Okuno et al.

2007).

2.3. Electrochemical Immunosensors

Due to the fact that most cancers have more than one marker proteins, simultaneous detection of

multiple analyets plays a crucial requirement in developing a label free and cost effective

immunoassay devices. Performance of immunoassays is highly dependent on selection of

antibodies considering crucial properties such as sensitivity, specificity, cross-reactivity and

costs. Therefore, it asks for the development of new immunoassay techniques with higher

sensitivity and specificity.

Immunosensors with the capability of dynamic analysis of immunoreactions have been

implemented for detection of tumor markers. There are a number of immunosensor devices

which include electrochemical (potentiometric, capacitive, amperometric, and impedimetric),

optical (fluorescence, luminescence, refractive index), microgravimetric, thermometric, and

immunosensors supplementing other techniques such as flow injection analysis (Chou et al.

2004, Fu et al. 2006, Nakamura et al. 2001, Zhang et al. 2007a). Protein chips-based

electrochemical immunosensors with the capability of transducing molecular recognition into

detectable electrical signals has caught a widespread attention for offering advantages such as

low detection limit, small analyte volume, and integration in protein chips (Shi et al. 2006).

There are two main types of electrochemical immunosensor including 1) labeling detection

techniques such as in fluorescence and electrochemical methods, and 2) label-free detection

techniques such as Quartz Crystal Microbalance (QCM), and cantilever-based detections. In

electrochemical imuunosensors, biomolecules such as proteins, peptides, oligonucleotides, and

21

others are immobilized in arrays on the substrate with the capability of retaining activity and

remaining stable. These immobilized biomolecules over substrate also known as probes are then

brought into contact with serums or cellular extracts where molecular recognition occurs.

Elechtrochemical sensors enable miniaturization and developing a lab-on-a-chip device. Short

assay time and high sensitivity is possible and enhance the detection of immunological reactions

(Wang et al. 2001, Yakovleva et al. 2002, Zheng et al. 2005). One important factor that should

be considered utilizing electrochemical immunosensors is that the immobilized biomolecules on

the substrate should have a very high specificity with the biomarkers. Otherwise, unspecific

interactions and cross-over to non-specific biomolecules immobilized at other spots may produce

false signals and distorts the results obtained from the biosensor.

In many cancer diagnoses, detection of only one marker associated with the cancer is not

enough since most cancers have more than one biomarker. Therefore, developing an

immunosensor with the capability of detecting multiple analytes simultaneously is necessary.

One approach to this strategy is developing multiple arrays of immobilized immunological

biomolecules. Miniaturized arrays of microelectrodes on a silicon chip for multichannel

Figure 2.5 Microelectrode array on a silicon chip for detection of multiple analytes [Chen et al. 2009], with

permission.

22

electrochemical measurement has been developed and used for detection of multiple anayltes

simultaneously as shown in Figure 2.5 (Chen et al. 2009).

There are other methods that can be incorporated into protein chips such as mass sensitive

methods including QCM and MC-based biosensors which offer suitable tools for label-free

biodetection. These techniques are briefly discussed next.

2.3.1. Quartz Crystal Microbalance (QCM)

The microgravimetric QCM has been utilize for biosensing applications and its capability in

detection of DNA hybridization has been demonstrated (Zhou et al. 2000). It is capable of

measuring sub-nanogram levels of mass changes. QCM is made of a thin quartz disc sandwiched

between a pair of electrodes as shown in Figure 2.6. By applying an AC voltage across its

electrodes, the crystal oscillates as a result of piezoelectric properties of crystal.

The mass absorbed to the crystal surface changes the resonance frequency of the crystal surface

which forms the basis of QCM operation. It can be used in both vacuum and liquid

environments. Surfaces functionalized with recognition sites can be used for determining the

molecular interaction in QCM.

Miccrocantilever resonance-based detection is somehow similar to QCM in the vibration-

working mode with some fundamental differences. These differences include:

1) MC based sensors are much smaller than QCM with the capability of miniaturization of

the entire platform. As a result, lower amount of target molecules is required to produce a

detectable signal.

2) High throughput analysis for detection of multiple analytes is possible using arrays of

MCs and functionalizing each MC with a different receptor, therefore allowing for making

simultaneous measurement with high efficiency, which is not the case with QCM.

23

3) Integration of QCM is difficult as a result of complicated structures and electronics,

however, MCs can be integrated and therefore creating a simpler platform for detection.

2.3.2. Diagnosis with MC-based biosensors

Cantilever-based biosensors at micro- and nano-scale have caught a widespread attention during

the past couple of decades for offering label free biodetection. They have greatly been used as

force sensor in Atomic Force Microscopy (AFM), (Binnig et al. 1987, Sepaniak et al. 2002,

Bradley et al. 2010, Bashash et al. 2010, Pishkenari et al. 2006, Jalili and Laxminarayana, 2004,

Eslami et al. 2009), for discovering protein expression patterns, bacterial cells, antibodies (Ilic et

al. 2004, Zhang and Feng, 2004, Savran et al.

2003), detecting vapors (Baller et al. 2000),

pathogens, and separating proteins from cellular

extracts. A mechanism was suggested for DNA

hybridization by Cantilever-based Sensor

(Hansen et al. 2001). Chemical, industrial,

physical and medical applications of MCs have

Figure 2.6 a) Schematic of a quartz crystal as the main part of QCM(R2)

, b) a commercially

available QCM(R3)

, with permission.

a b

Figure 2.7 Schematic of disease diagnosis through

MC-based biosensor.

Antigen

Antibody

Specific

Recognition

MC

24

been extensively demonstrated (Yang et al. 2003, Dareing and Thundat, 2005, Bumbu et al.

2004, Zhang and Ji, 2004, Tzeng et al. 2009, 2011, Delnavaz et al. 2009, 2010, Mahmoodi et al.

2008 a,b, 2009, 2010, Mahmoodi and Jalili, 2007, 2008, 2009, Salehi-Khojin et al. 2008, 2009a,

Bradley et al. 2009, Bashash et al. 2009, Saeidpourazar and Jalili, 2008 a,b, 2009, Afshari and

Jalili, 2007, Eslami and Jalili, 2011). MC array biosensor (McKendry et al. 2000) offers a

suitable microdiagnostic kit for detection of multiple protein markers of a particular disease

simultaneously. Specific interaction between immobiliezed biomoelecules over cantilever

surface and disease biomarkers induces differential surface stress thus cantilever deflection.

Figures 2.7 and 2.8 depict the schematic of cantilever based detection. This mechanism offers a

variety of advantages over other common immunoassay detection techniques such as enzyme

linked immunosorbent assay, immunodiffusion, and radioimmunoassay.

Detection of PSA which is the marker of early detection of prostate cancer has been enabled

implementing piezoresistive self sensing MC-based biosensors (Wu et al. 2001, Wee et al. 2005).

Polyclonal anti-PSA antibody was immobilized over MC surface as a ligand. Specific interaction

between this ligand and unbounded PSA in the sample target solution deforms MC which

Figure 2.8 Array of MCs with functionalized surfaces through biomolecules for disease

biomarkers. Microchannels are used to bring sample to respective MC. The intermolecular

binding between the disease biomarker and the immobilized biomolecules over cantilever surface

induces differential stress thus deflects MCs. The amount of MC deflection can be measured

through any readout device.

Inlet for sample

Ligand

Receptor

Microchannels

Antigen

Antibody

Target

DNA

Probe

DNA

25

consequently changes surface stress. The induced surface stress can be read out through different

devices thus enabling measurement of diagnostic PSA concentration range.

Level of Glucose in blood has been detected utilizing MC biosensors coated with enzyme

(Subramanian et al. 2002). MC surface was coated with gold and functionalized with enzyme

glucose oxidase. Interaction between glucose and glucose oxidase induces surface stress and

causes the MC to deflect which can be measured by read-out devices.

Funtionalizing MC with anti-creatin kinase and anti-myoglobin antibodies, cardiac biomarker

proteins such as creatine kinase and myoglobin were detected utilizing this technique (Arntz et

al. 2003). Detection of human leukocyte antigen sequences which contains single nucleotide

polymorphisms utilizing piezoresistive MC arrays has been suggested for evaluation of

susceptibility to autoimmune diseases (Adami et al. 2010). Detection of DNA and protein on the

same array was also reported using MC-based platforms (Huber and Aktaa, 2003).

2.4. Key Challenges and Unique Opportunities

Although there have been a number of well-established detection techniques and other detection

methodologies under development, MC-based systems have emerged as an outstanding tool for

offering a label-free, simple, inexpensive, and yet highly sensitive detection platform (Tzeng et

al. 2009,2011, Delnavaz et al. 2009, Bradley et al. 2009, Mahmoodi et al. 2008, Afshari and

Jalili, 2007). It has a number of advantages over other detection techniques. Table 2.1 shows an

illustrative comparison between various commonly used immunoassay techniques and MC-based

detection.

26

MC-based biosensors operate in two main modes; i) static mode and ii) dynamic mode. In static

mode, deflection of MC from a stable baseline is indeed a measure of detection (Gupta et al.

2004, Yang et al. 2003); however in dynamic mode, the system is brought into excitation at or

near its resonance frequency. The shift in resonance frequency as a result of mass absorption can

be quantitatively related to the amount of adsorbed mass and species (Blake et al. 2012, Chen et

al. 1995; Daering and Thundat, 2005, Gurjar and Jalili, 2007, Faegh et al. 2013a).

All MC-based techniques are equipped with read-out methodologies including optical,

capacitive, and piezoactive (piezoelectric and piezoresistive). Table 2.2 provides a list of the

measurement techniques that MC-based techniques are equipped with.

Table 2.1 An illustrative comparison between various immunoassay techniques and cantilever-based

diagnosis.

Parameters Immuno- Enzyme-linked Radio Fluoroscent Cantilever-

diffusion Immunosorbent ImmunoAssay ImmunoAssay based

Assay (ELISA) (RIA) (FIA) Diagnosis

Sensitivity(ml) 3-20 mg 0.1-1.0 ng 0.1-1.0 ng 1.0 ng In the order

of picogram

Cost Costly Costly Highly costly Highly costly Economical

Safety Safe Safe Hazardous Safe Safe

Small diagnostic

platform

Possible Possible Not possible Not Possible Possible

No. of steps More More More More Less

Assay duration 4-5 days 2 hours <1 hour 2 hours < 30 min

Sample required In ml In ml In ml In ml In μl

Personnel

required

Highly

skilled

Highly

skilled

Highly skilled Highly skilled Average

Multianalyte

sensing in a

single step

Not Possible Not Possible Not Possible Not Possible Possible

27

The most common measurement technique is optical-based which is extensively used in AFM. It

operates based on shining a laser beam over the surface and measuring the shift in the angle of

the laser beam reflected from the surface. Although being very sensitive, this method has a

number of disadvantages such as being bulky, expensive and having surface preparation

requirement. Moreover, laser alignment and adjustment, high power consumption and the

restriction of conducting the experiment in a transparent chamber have always been certain

downsides to this technique. Refraction of the laser beam as a result of traversing liquid makes it

a limitation of usage in aqueous media. Miniaturizing the detection platform is one of the key

elements in developing a micro and nano sensor. The need for having an external lighting setup

for sample illumination and photodetector for capturing the reflected laser beam off the surface

makes it impossible to miniaturize the whole optical-based sensing platform.

Implementing optical based sensing in dynamic mode, there is always a need for actuating the

system. Using external actuation is the most common methodology. However external actuators

are bulky and expensive. Using piezoelectric excitation by applying voltage to a piezoelectric

Table 2.2 MC-based measurement techniques.

Measurement Technique Downsides

Optical Shift in laser beam reflected on the

photodetector surface

High cost, surface preparation, optical

alignment and adjustment requirement

Capacitive Change of the capacitance of a

plane capacitor

Not suitable for large displacement,

complicated electronic circuits and fabrication

processes, does not work in electrolyte

solutions

Piezoelectric Change of voltage of piezoelectric

layer over cantilever surface

Complicated electronic circuit

Piezoresistive Change of resistivity of

piezoresistive layer over cantilever

surface

Difficulty in fabrication of the sensor with

embedded resistor

28

layer embedded in the structure of the system is an alternative method which addresses the

mentioned disadvantages. Using optical-based measurement in dynamic mode with piezoelectric

actuator was introduced measuring the changes in the frequency of MC by reading the laser

beam reflected from the surface (“Microbar Sensor”, Wachter et al., U.S. Patent No. 5445008

issued Aug. 29 1995). Using such a system for chemical sensing through functionalized MC with

specific receptor was invented by Thundat et al. (“Microcantilever Sensor”, Thundat et al., U.S.

Patent No. 5719324 issued Feb. 17, 1998). MC-based gas sensor for detection of explosive gases

was invented using AFM systems with optical based measurement (“Microcantilever Detector

for Explosives”, Thundat, U.S. Patent No. 5918263 issued Jun. 29, 1999).

Alternative methods are capacitive-based measurement where change of the capacitance of a

plane capacitor is the base of measurement. However, it is not suitable for large displacements

and measurement in electrolyte solutions. Piezoresistive read out methods have extensively been

used which address some of the limitations of optical-based systems. It measures the change of

resistivity of the piezoresistive layer embedded in the structure of the MC as a result of MC

deflection. As a result, this allows for miniaturizing the system and saving the overall cost of the

platform. However, it comes with complicated electronic circuit and the power consumption is

still high. Moreover, it results in self-heating and drifting. Since the piezoresistive layer is

employed for only reading out system’s response, there is still a need for actuating the system in

dynamic mode. It is either provided by using an external actuator which is bulky and expensive

or through depositing an extra piezoelectric layer and applying voltage to it.

The concept of piezoelectric actuator for the purpose of eliminating external actuator is disclosed

in “Active probe for an atomic force microscope and method of use thereof”, Adderton et al.,

Patent No. 6189374, issued Feb. 20, 2001.

29

Piezoresistive MC-based sensors with piezoelectric-based actuator have been built and used for

imaging and sensing purposes. Piezoelectrically-driven MC with piezoresistive read-out was

used in scanning probe microscopy operating in constant force mode. Piezoelectric patch on the

MC provides excitation and also controls the distance between tip and sample. This concept is

disclosed in “Cantilever for Scanning Probe Microscope including Piezoelectric Element and

Method of Using the Same”, Minne et al. U.S. Patent No. 5742377 issued Apr. 21, 1998. and

“Atomice Force Microscope for High Speed Imaging Including Integral Actuator and Sensor”,

Minne et al., U.S. Patent No. 5883705 issued Mar. 16, 1999.

Another measurement technique is piezoelectric-based systems where a piezoelectric material is

used in order to create voltage as a result of induced surface stress due to mechanical

deformation of the beam. This technique provides a simple sensitive read-out mechanism.

Utilizing a single piezoelectric layer for both sensing and actuating purposes was introduced in

MC sensing technology for the purpose of mass detection which was disclosed in “Apparatus

and Method for Measuring Micro Mass Using Oscillation Circuit”, Lee et al. U.S. Patent No.

7,331,231 issued Feb. 19, 2008. and also for detection purposes as disclosed in “Self-Sensing

Array of MicroCantilevers for Chemical Detection”, Adams, U.S. Patent No. 2006/0257286

issued Nov. 16, 2006. Even though, sensitive measurement can be perfomed using MC in air,

detection of analytes in liquid media utilizing the shift of the fundamental resonance frequency

of MC does not provide a suitable detection tool due to heavy hydrodynamic damping effects.

Moreover, ther is still need for bulky monitoring devices such as network analyzer.

Although there have been a number of measurement techniques, a compact detection platform

with the capability of miniaturization, low power consumption, cost effective, and yet sensitive

methodology is highly desirable. MCs with the purpose of detecting gasses, chemical compounds

30

and biological species with embedded miniaturized actuator and sensor being capable of

addressing all deficiencies of the measurement techniques that was discussed is therefore

desired. The measurement capability of the platform both in air and aqueous media with the

simplest and most inexpensive actuation and sensing equipment is still required.

This dissertation is focused on developing a MC-based sensor for the purpose of detecting

ultrasmall masses (e.g., chemical compounds, biological species, gasses, etc). Two main studies

are carried out in order to achieve this purpose which are: a) developing extensive mathematical

modeling and simulation for MC-based systems and specifically MC-based sensing platform,

,and b) conducting relative experiments to verify the developed theory and to design, build, and

test the sensing platform.

31

CHAPTER 3*

COMPREHENSIVE MATHEMATICAL MODELING OF PIEZOACTIVE

MICROCANTILEVER-BASED SYSTEMS

3.1. Introduction

MCs with their implementation in force sensing applications have caught a widespread attention

in the past decade because of their sensitivity and capability in detecting small forces,

mechanical stresses, and added adsorbed mass molecules (Rieth and Schommers, 2004, Yang

and Saif, 2007, Haque and Saif, 2002, Jang et al. 2006, Enikov et al. 2005). This technology has

found its application in different disciplines such as biology, materials science, chemistry, and

rheology (Tao and Yung, 2003, Yang et al. 2003, Chen et al. 1995, Daering et al. 2005, Tzeng et

al. 2009, 2011, Delnavaz et al. 2009, 2010, Mahmoodi et al. 2008 a,b, 2009, 2010, Mahmoodi

and Jalili, 2007, 2008, 2009, Salehi-Khojin et al. 2008, 2009a, Bradley et al. 2009, Bashash et al.

2009, Saeidpourazar and Jalili, 2008 a,b, 2009, Afshari and Jalili, 2007, Eslami and Jalili, 2011).

They have been implemented for discovering protein expression patterns, bacterial cells,

antibodies (Zhang and Feng, 2004, Savran et al. 2003), detecting vapors (Thundat et al. 1995,

Baller et al. 2000), pathogens, and separating proteins from cellular extracts. Disease diagnosis

has been enabled utilizing MC-based biosensors by detecting the marker proteins relative to the

specific disease. PSA and C-protein concentration in a sample target solution has been detected

implementing piezoresistive self-sensing MC-based biosensors (Wee et al. 2005). Chemical,

industrial and physical applications of MCs have been extensively demonstrated (Hansen et al.

* The contents of this chapter may have come directly from our previous publication (Faegh and Jalili, 2011).

32

2001, Dareing and Thundat, 2005, Bumbu et al. 2004, Zhang and Ji, 2004, Corbeil et al. 2002,

Berger et al. 1996, Tian et al. 2004, Nagakawa et al. 1998). Two main applications of MC-based

nanotechnology can be listed as:

a) Piezoresponse Force Microscopy (PFM) which is a powerful device for nanoscale

imaging, spectroscopy, and characterization of local properties of piezoelectric and ferroelectric

materials (Su et al. 2003, Felten et al. 2004, Guthner and Dransfeld, 1992, Gruverman et al.

1997, Salehi-Khojin et al. 2009a,b). High resolution imaging in nanometer level as a result of

piezoelectric coupling in biomaterials has been enabled using PFM. PFM functions based on

detecting bias-induced surface deflection and is complementary to Atomic Force Microscopy

(AFM)-based imaging. An oscillatory electrical field applies between a MC conducting tip and

the electrode attached to the piezoelectric sample. The applied voltage results in deformation of

the piezoelectric sample which consequently oscillates MC. The amplitude of MC oscillation

gives a good insight into the surface characteristics (Hidaka et al. 1996, Kalinin and Bonnel,

2002, Kalinin et al. 2004, Bashash et al. 2009).

b) Biological Sensors also known as biosensors for monitoring diseases by detecting the

marker proteins relative to that specific disease. Measuring molecular binding force and

detecting concentration of an antigen in a sample fluid has been enabled using arrays of MCs.

There are a number of available read-out techniques in MC-based systems including

piezoelectric, piezoresistive, capacitive, and optical laser-based systems. Piezoelectric-based MC

sensors operate based on change of voltage in piezoelectric patch due to beam deflection. Two

patches of piezoelectric material deposited over the surface of the MC makes it difficult to

miniaturize the structure of the sensor. Moreover, complicated electronic circuit is required to

process the signal. Capacitive-based MC sensors monitor capacitance change as a result of beam

33

deflection. There are some limitations

accompanied with this type of sensor which

include low resolution, complicated electronic

circuits and fabrication processes. Optical force

measurement which is a very powerful device in

measuring small deflections is widely utilized in

AFM. The inherent disadvantages of this technology are high cost, surface preparation, and

optical alignment and adjustment requirement.

Piezoresistive force sensors work based on change of resistance in the piezoresistive layer when

MC bends as a result of external tip force. The change of resistance can be measured utilizing the

output voltage of the system. Piezoresistive MCs offer a great advantage over other types of MC

sensors, especially the optical measurements where sample preparation and laser alignment and

adjustment are serious limitations. The schematic of a piezoresistive sensor is shown in Figure

3.1. They have found their application in atomic data storage systems, AFM cantilevers, portable

cantilever-based sensors, pressure sensors, and accelerometers (Hong et al. 2001). MC deflection

and surface stress measurement has been enabled utilizing piezoresistive layer over MC surface

(Harley and Kenny, 1999, Boisen et al. 2000).

In order to have a precise MC-based system, a very comprehensive modeling needs to be

developed. In most of the studies regarding piezoresistive MC-based system, simple lumped-

parameters modeling was used which is not capable of precisely describing the dynamics within

the MC (Harley and Kenny, 1999, Boisen et al. 2000, Thaysen et al. 2001). This study is aimed

at developing a comprehensive mathematical model for MC-based nanotechnological systems

Figure 3.1 Schematic of piezoresistive MC

sensor.

34

with specific implementations as described in a) and b) above. Therefore, two main sections are

included in this study investigating:

I) An extensive distributed-parameters modeling of MCs operating in contact

mode (System 1): Utilizing such a precise model, the output voltage of the

piezoresistive layer can be obtained as a function of the slope of the beginning and

end points of the piezoresistive patch over the MC surface. Moreover, the interaction

forces between the MC tip and sample can be measured having the deflection of the

MC. Therefore, it provides an inexpensive and portable read-out system.

II) A distributed-parameters mathematical modeling of MC-based PFM

implementing on piezoelectric sample which performs tip-excitation (System 2):

A mathematical model is proposed relating the response of the piezoelectric sample to

the response of the MC and consequently the output voltage of the system which is

the main source of the read-out equipment.

Having such precise mathematical modeling of piezoresistive MC-based sensors and force

microscopy, any phenomenon occurring both at the MC tip and within the MC can be described

which gives a thorough insight into the behavior of the system. Implementation of piezoresistive

read-out technique provides information of the system eliminating the need for bulky expensive

laser-based feedback and read-out equipment.

3.2. Mathematical Modeling

An analytical model is reported which describes the behavior of the piezoresistive MC. The

piezoresistive MC is assumed to be an Euler-Bernoulli beam which is modeled as a distributed-

parameters system. Figures 3.2 and 3.3 show the schematic of piezoresistive MC sensor (sys. 1)

35

and PFM (sys. 2), respectively. The MC beam is attached to a base with mass mb at one end

which moves vertically. S(t) represents the base motion. An unknown tip mass me is attached at

the other end of the MC. The beam is considered to have length L, thickness tb, and volumetric

density ρb. The piezoresistive layer over the top surface of the MC has a length of L2 – L1,

thickness tp, and volumetric density ρp. Both MC and piezoresistive layer are considered to have

width b. w(x,t) denotes the midplane deflection of MC with the equivalent tip deflection w(L,t).

MC deflection is assumed to be small and the system properties are taken linear in developing

the equations of motion.

Kinetic and potential energies of sys. 1 can be written as:

𝐾𝐸 =1

2𝑚𝑏��

2(𝑡) +1

2 𝑚𝑒(��(𝑡) + ��(𝐿, 𝑡))2 +

1

2∫ 𝜌(𝑥)(��(𝑡) + ��(𝑥, 𝑡))2𝐿

0𝑑𝑥 (3.1)

𝑃𝐸 =1

2∫ 𝐸𝐼(𝑥)𝐿

0[𝑤 ′′(𝑥, 𝑡)]2𝑑𝑥 (3.2)

whereas for sys. 2 are:

𝐾𝐸 =1

2𝑚𝑏��

2(𝑡) +1

2 𝑚𝑒(��(𝑡) + ��(𝐿, 𝑡))2 +

1

2∫ 𝜌(𝑥)(��(𝑡) + ��(𝐿, 𝑡))2𝐿

0𝑑𝑥 (3.3)

Piezoresistive Layer

fb(t)

w(x,t)

fc(t)

L

L1 L2

mb

S(t)

Piezoelectric

sample

fb(t)

w(x,t)

L

L1 L2

m

b

S(t)

Kz Cz fc

V(t)

Electrode

Piezoresistive Layer

Figure 3.2 Schematic of the proposed

distributed-parameters modeling of the

piezoresistive MC sensor, (sys. 1).

Figure 3.3 Schematic of the proposed distributed-

parameters modeling of the piezoresistive MC-

based PFM, (sys. 2).

36

𝑃𝐸 =1

2∫ 𝐸𝐼(𝑥)𝐿

0[𝑤 ′′(𝑥, 𝑡)]2𝑑𝑥 +

1

2𝐾𝑧𝑤

2(𝐿, 𝑡) (3.4)

where ρ(x) and EI(x) are defined as

𝜌(𝑥) = 𝜌𝐴 = 𝜌𝑏𝑏𝑡𝑏 + 𝜌𝑝𝑏𝑡𝑝𝐺(𝑥) (3.5)

𝐸𝐼(𝑥) =1

12𝐸𝑏𝑡𝑏

3𝑏 + 𝐸𝑝𝑡𝑝𝑏 (𝑡𝑝2

3+

𝑡𝑏𝑡𝑝

2+

𝑡𝑏2

4)𝐺(𝑥) (3.6)

with G(x) = H(x-L1) –H(x-L2), and H(x) being the Heaviside function. Eb and Ep represent the

Young’s modulus of elasticity of beam and piezoresistive layer, respectively.

Virtual work for sys. 1 is given by

𝛿𝑊 = ∫ (−𝐵��(𝑥, 𝑡) − 𝐶��′(𝑥, 𝑡))𝛿𝑤(𝑥, 𝑡)𝑑𝑥 + 𝑓𝑏(𝑡)𝛿𝑆(𝑡) + 𝑓𝑐(𝑡)𝛿𝑤(𝐿, 𝑡) 𝐿

0 (3.7)

and for sys.2 is:

𝛿𝑊 = ∫ (−𝐵��(𝑥, 𝑡) − 𝐶��′(𝑥, 𝑡))𝛿𝑤(𝑥, 𝑡)𝑑𝑥 + 𝑓𝑏(𝑡)𝛿𝑆(𝑡) + 𝑓𝑐(𝑡)𝛿𝑤(𝐿, 𝑡)𝐿

0

−𝐶𝑧��′(𝐿, 𝑡)𝛿𝑤(𝐿, 𝑡) (3.8)

which is a result of damping, base force, and contact tip force. B and C represent the coefficients

of viscous and structural damping respectively (Duc et al. 2007, Dadfarnia et al. 2004). Kz and Cz

denote spring constant and damping coefficient of the piezoelectric material, respectively.

Utilizing Extended Hamiltonian principle, equations of motion of the system are obtained as

𝜌(𝑥) (��(𝑥, 𝑡) + ��(𝑡)) + 𝐸𝐼(𝑥)𝑤 ′′′′(𝑥, 𝑡) + 𝐵��(𝑥, 𝑡) + 𝐶�� ′(𝑥, 𝑡) = 0 (3.9a)

(𝑚𝑏 +𝑚𝑒 + 𝜌(𝑥)𝐿)��(𝑡) + ∫ 𝜌��(𝑥, 𝑡)𝑑𝑥𝐿

0+𝑚𝑒��(𝐿, 𝑡) = 𝑓𝑏(𝑡) + 𝑓𝑐(𝑡) (3.9b)

with the following boundary conditions

w(0, t) = w′(0, t) = w′′(L, t) = 0 (3.10a)

𝑚𝑒 (��(𝐿, 𝑡) + ��(𝑡)) − 𝐸𝑏𝐼𝑏𝑤′′′(𝐿, 𝑡) = 𝑓𝑐(𝑡) (3.10b)

37

𝑚𝑒 (��(𝐿, 𝑡) + ��(𝑡)) − 𝐸𝑏𝐼𝑏𝑤′′′(𝐿, 𝑡) + 𝐾𝑧𝑤(𝐿, 𝑡) + 𝐶𝑧��(𝐿, 𝑡) = 𝑓𝑐(𝑡) (3.10c)

Equations (3.10a) and (3.10b) apply to sys. 1 and Eqs. (3.10a) and (3.10c) to sys.2. In order to

solve the equations of motion of the system, the partial differential equations (PDEs) given by

(3.9a,b) should be converted into ordinary differential equations (ODE).

For this reason, the obtained boundary conditions need to be homogenized utilizing the following

change of variables so that the term 𝑓𝑐(𝑡) is omitted in the boundary condition using standard

discretization techniques (Jalili, 2010):

𝑤(𝑥, 𝑡) = 𝑧(𝑥, 𝑡) + 𝑓𝑐(𝑡)𝑔(𝑥) (3.11)

with g(x) defined as (Dadfarnia et al. 2004)

𝑔(𝑥) =−1

9𝐸𝐼(𝑥)𝐿𝑥4 +

5

18𝐸𝐼𝑥3 −

𝐿

6𝐸𝐼𝑥2 (3.12)

Implementing the suggested change of variables, equations of motions can now be rewritten as

𝜌(𝑥) (��(𝑥, 𝑡) + ��(𝑡)) + 𝐸𝐼(𝑥)𝑧 ′′′′(𝑥, 𝑡) + 𝐵��(𝑥, 𝑡) + 𝐶�� ′(𝑥, 𝑡) = −(𝜌𝑔(𝑥)𝑓��(𝑡) +

𝐵𝑔(𝑥)𝑓��(𝑡) + 𝐶𝑔′(𝑥)𝑓��(𝑡) + 𝐸𝐼(𝑥)𝑔′′′′(𝑥)𝑓𝑐(𝑡)) (3.13a)

(𝑚𝑏 +𝑚𝑒 + 𝜌𝐿)��(𝑡) + ∫ 𝜌��(𝑥, 𝑡)𝑑𝑥𝐿

0+𝑚𝑒��(𝐿, 𝑡) = 𝑓𝑏(𝑡) + 𝑓𝑐(𝑡) − 𝑓��(𝑡) ∫ 𝜌𝑔(𝑥)𝑑𝑥

𝐿

0

(3.13b)

with the homogenized boundary conditions

𝑧(0, 𝑡) = 𝑧 ′(0, 𝑡) = 𝑧 ′′(𝐿, 𝑡) = 0 (3.14a)

𝑚𝑒 (��(𝐿, 𝑡) + ��(𝑡)) − 𝐸𝑏𝐼𝑏𝑧′′′(𝐿, 𝑡) = 0 (3.14b)

𝑚𝑒 (��(𝐿, 𝑡) + ��(𝑡)) − 𝐸𝑏𝐼𝑏𝑧′′′(𝐿, 𝑡) + 𝐾𝑧𝑧(𝐿, 𝑡) + 𝐶𝑧��(𝐿, 𝑡) = 0 (3.14c)

The new set of governing equations for MC can be solved numerically using Galerkin’s method

by discretizing z(x,t) as follows:

𝑧(𝑥, 𝑡) = ∑ 𝜙𝑗(𝑥)𝑛𝑗=1 𝑞𝑗(𝑡), 𝑗 = 1,2, … . . , 𝑛 (3.15)

38

where φj(x) and qj(t) represent the clamped-free beam eigenfunction and generalized coordinates

respectively. fc(t), which appears in the equations of motion, represents the contact force between

the tip of MC and the sample where in sys.1, it can be found from the following equation (Jalili

et al. 2004)

𝑓𝑐(𝑡) =4𝐸∗√𝑅

3(𝑆(𝑡) + 𝑤(𝐿, 𝑡))3 2⁄ (3.16)

where R denotes the radius of MC tip, and 𝐸∗ denotes the reduced elastic modulus obtained from

1

𝐸∗=

(1−𝜈𝑠2)

𝐸𝑠+

(1−𝜈𝑇2)

𝐸𝑇 (3.17)

with 𝐸𝑠 and 𝐸𝑇 being the elastic modules of the sample and MC tip respectively, and 𝜈𝑠 and 𝜈𝑇,

the poisson’s ratio of the sample and MC tip respectively. Implementing the change of variable

suggested in equation (3.11), 𝑓𝑐(𝑡) can be written as

𝑓𝑐(𝑡) = 𝜆(𝑆(𝑡) + 𝑧(𝐿, 𝑡))3 2⁄ , 𝜆 =4𝐸∗√𝑅

3 (3.18)

with ��(𝑡) and 𝑓(𝑡) being the first and second derivative of 𝑓(𝑡) as follows

𝑓��(𝑡) =3

2𝜆(��(𝑡) + ��(𝐿, 𝑡))(𝑆(𝑡) + 𝑧(𝐿, 𝑡))1 2⁄ (3.19)

𝑓��(𝑡) =3

2𝜆 [(��(𝑡) + ��(𝐿, 𝑡)) (𝑆(𝑡) + 𝑧(𝐿, 𝑡))

1 2⁄+

1

2(��(𝑡) + ��(𝐿, 𝑡))

2

(𝑆(𝑡) + 𝑧(𝐿, 𝑡))−1 2⁄

]

(3.20)

Substituting equations (3.18), (3.19), and (3.20) into the governing equations (3.13a,b), the

nonlinear differential equations of the MC for sys.1 can be obtained as follows

𝜌(𝑥) (��(𝑡) + ∑ 𝜙𝑖(𝑥)𝑛𝑖=1 ��𝑖(𝑡)) +

3

2𝜆𝜌𝑔(𝑥) [(��(𝑡) + ∑ 𝜙𝑖(𝐿)

𝑛𝑖=1 ��𝑖(𝑡)) (𝑆(𝑡) + ∑ 𝜙𝑖(𝐿)

𝑛𝑖=1 𝑞𝑖(𝑡))

12⁄

+

1

2(��(𝑡) + ∑ 𝜙𝑖(𝐿)

𝑛𝑖=1 ��𝑖(𝑡))

2

(𝑆(𝑡) + ∑ 𝜙𝑖(𝐿)𝑛𝑖=1 𝑞𝑖(𝑡))

−12⁄ ] + 𝐵∑ 𝜙𝑖(𝐿)

𝑛𝑖=1 ��𝑖(𝑡) +

39

𝐶 ∑ 𝜙′𝑖(𝐿)𝑛

𝑖=1 ��𝑖(𝑡) +

(𝐵𝑔(𝑥) + 𝐶𝑔′(𝑥)) [3

2𝜆 (��(𝑡) + ∑ 𝜙𝑖(𝐿)

𝑛𝑖=1 ��𝑖(𝑡)) (𝑆(𝑡) + ∑ 𝜙𝑖(𝐿)


12⁄ ] +

𝐸𝐼(𝑥)∑ 𝜙𝑖′′′′(𝑥)𝑛

𝑖=1 𝑞𝑖(𝑡) + 𝐸𝐼(𝑥)𝑔′′′′(𝑥)𝜆(𝑆(𝑡) + ∑ 𝜙𝑖(𝐿)𝑛𝑖=1 𝑞𝑖(𝑡))

32⁄ = 0

(3.21a)

(𝑚𝑏 +𝑚𝑒 + 𝜌𝐿)��(𝑡) + ∫ 𝜌(𝑥)∑ 𝜙𝑖(𝑥)𝑛𝑖=1 𝑑𝑥 ��𝑖(𝑡)

𝐿

0+𝑚𝑒 ∑ 𝜙𝑖(𝐿)

𝑛𝑖=1 ��𝑖(𝑡) − 𝜆(𝑆(𝑡) +

∑ 𝜙𝑖(𝐿)𝑛𝑖=1 𝑞𝑖(𝑡))

32⁄ +

3

2𝜆 ∫ 𝜌𝑔(𝑥)𝑑𝑥 [(��(𝑡) + ∑ 𝜙𝑖(𝐿)

𝑛𝑖=1 ��𝑖(𝑡)) (𝑆(𝑡) + ∑ 𝜙𝑖(𝐿)


12⁄

+1

2(��(𝑡) +

𝐿

0

∑ 𝜙𝑖(𝐿)𝑛𝑖=1 ��𝑖(𝑡))

2

(𝑆(𝑡) + ∑ 𝜙𝑖(𝐿)𝑛𝑖=1 𝑞𝑖(𝑡))

−12⁄ ] = 𝑓𝑏(𝑡) (3.21b)

The obtained equations were solved in MATLAB. As a result, deflection of MC, w(x,t) and base

motion S(t) were obtained in both sys.1 and 2, from which the tip deflection can be calculated.

In order to observe the deflection w(x,t) in the piezoresistive MC system, the output voltage

should be represented in terms of w(x,t). Therefore, a piezoresistive modeling framework is

presented in the following section.

3.3. Piezoresistive Modeling

When MC tip is brought into contact with the sample, MC deflects as a result of contact force.

MC deflection consequently results in the change of resistance of piezoresistive layer deposited

over MC surface. Change of resistance of piezoresistive layer can be obtained from the following

equation (Saeidpourazar and Jalili, 2009)

∆𝑅 = (𝜕𝑤(𝐿2,𝑡)

𝜕𝑥−

𝜕𝑤(𝐿1,𝑡)

𝜕𝑥) × 𝐶𝑝𝑧

𝐶𝑝𝑧 = (−𝑧𝜕𝑅

𝜕𝑙𝑝−

𝑧𝜈𝑤𝑝

𝐿2−𝐿1

𝜕𝑅

𝜕𝑏 −

𝜌𝐸𝑧(𝜋𝑥−𝜈𝜋𝑦)

(1−𝜈2)(𝐿2−𝐿1)

𝜕𝑅

𝜕𝑟𝑝) (3.22)

40

where z is the distance between the geometrical surface of the piezoresistive layer and the neutral

axis of the MC. Lp (= L2 – L1 ) and b denote the length and width of piezoresistive layer

respectively. rp represents the resistivity of piezoresistive layer with πx and πy being the

longitudinal and transverse piezoresistance coefficients. Cpz was evaluated experimentally to be

equal to 4.99571×104

(Saeidpourazar and Jalili, 2009).

Implementing the change of variables proposed in Eq. (3.11) results in

(𝜕𝑤(𝐿2,𝑡)

𝜕𝑥−

𝜕𝑤(𝐿1,𝑡)

𝜕𝑥) = (

𝜕𝑧(𝐿2,𝑡)

𝜕𝑥−

𝜕𝑧(𝐿1,𝑡)

𝜕𝑥) + 𝑓(𝑡) (

𝜕𝑔(𝐿2)

𝜕𝑥−

𝜕𝑔(𝐿1)

𝜕𝑥) (3.23)

Having the change of resistivity in the piezoresistive layer and R, which is the resistance of the

piezoresistive layer in a Wheatstone bridge, the output voltage of the system can be obtained by

(Harley and Kenny, 1999)

𝑉0 =1

4𝑉𝑏

∆𝑅

𝑅 (3.24)

where V0 and Vb are the output voltage and supply voltage of the Wheatstone bridge,

respectively. The deflection of the MC at any time can be obtained through the developed

equations. As a result, the output voltage can be calculated.

The proposed approach in modeling the piezoresistive MC as a distributed-parameters system

offers many advantages over lumped-parameters modeling such as describing the dynamics of

the system at any location of the MC. The slope of the MC at the beginning and end point of the

piezoresistive patch which is crucial in obtaining the output voltage of the piezoresistive layer

can be found through distributed-parameters modeling. Whereas, the lumped-parameter

modeling is capable of describing only the MC tip movements. Numerical simulations are

performed to solve the equations of motion of the system and to demonstrate the capability of the

proposed approach.

3.4. Piezoelectric Sample Modeling

41

The piezoelectric sample is characterized with piezoelectric and viscoelastic behavior in all

directions. An electrode is attached to the rear side of the sample. An external electric field is

applied between the sample and MC tip which causes the sample to undergo both piezoelectric

and piezoviscoelastic deformations. The piezoelectric response of the sample can be modeled as

an electromechanical force applied at the MC tip which is proportional to the applied voltage and

material’s piezoelectric coefficient, i.e., fc(t) = γV(t).

The value of sample’s piezoelectric coefficient, γ is considered to be 2.54 nN/V in this study. The

viscoelastic response of the sample can be modeled as a parallel spring and damper (Kelvin-

Voigt viscoelastic model), (Dadfarnia et al. 2004, Salehi-Khojin et al. 2009a) as shown in Figure

3.3. Therefore, the total forces applied at the MC tip would be the combination of spring,

damping, and electromechanical forces obtained as follows

𝐹𝑡𝑖𝑝 = −𝐾𝑧𝑤(𝐿, 𝑡)−𝐶𝑧��(𝐿, 𝑡) + 𝑓𝑐(𝑡) (3.25)

3.5. Numerical Simulations

In order to demonstrate the effectiveness and accuracy of

the proposed model, a set of numerical simulations is

implemented. The equations of motion obtained were

solved numerically in MATLAB. In sys.1, a sinusoidal

base force of amplitude of 1 × 10−3 N and frequency of

1.25 × 103 Hz was applied at the base of the MC.

However, in sys.2 a sinusoidal bias voltage of the

amplitude of 10 V and frequency of 200 Hz was applied

between the conductive MC tip and the surface. This

Table 3.1 Numerical values used in the

simulation.

Parameters Value Unit

L 500×10-6

m

Lp 375×10-6 m

𝜌𝑏 2330 kg m-3

𝜌𝑝 7660 kg m-3

tb 4×10-6 m

tp 4×10-6 m

Eb 150×109 Pa

Ep 160×109 Pa

mb 5×10-6 kg

me 0.5×10-6 kg

Vb 2.5 V

R 675 Ω

Es 1000 Pa

ET 150×109 Pa

νs 0.2

νT 0.3

42

introduces a new method of excitation (tip excitation), different from base excitation or

excitation through piezoelectric layers deposited over MC surface. It can find its application in

the mass sensing devices which eliminates the need for other commonly used methods of

excitation.

The value of 𝐶𝑝𝑧 was found to be 4.99571 × 104 from the experience (Johnson et al. 1985).

Solving the equations of motion numerically, deflection of MC at any point in different times,

w(x,t) and the movement of the base, S(t), are obtained from the contact force between the MC

tip and sample. Consequently, the output voltage of the piezoresistive layer, V0(t), can be

calculated through Eq. (3.24) developed in piezoresistive modeling section 3.2. Numerical values

of the system’s parameters utilized in simulation are listed in Table 3.1.

Figure 3.4 a) tip deflection of the cantilever, w(L,t) in sys.1 b) output voltage, V0(t) in sys.1 and c) contact force, fc(t)

in sys.1 all in non-dimensional form, d) tip deflection of the cantilever, w(L,t) in sys.2 e) output voltage, V0(t) in sys.2.

and f) tip force, Ftip(t) in sys.2, (Faegh and Jalili, 2011).

0 5 10 15 20 25-0.1

-0.05

0

0.05

0.1

Time

Tip

Deflection,

wL

0 10 20 30 40 50-0.2

0

0.2

0.4

0.6

Time

Ou

tpu

t V

olta

ge,

V0

0 10 20 30 40 50-5

0

5

10

15x 10

-8

Time

Conta

ct

Forc

e,

f c

0 0.02 0.04 0.06 0.08 0.1-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Time (s)

Tip

Deflection,

wL (

nm

)

0 0.02 0.04 0.06 0.08 0.1-4

-3

-2

-1

0

1

2

3

4x 10

4

Time (s)

Outp

ut

Voltage,

V0 (

nV

)

0 0.02 0.04 0.06 0.08 0.1-3000

-2000

-1000

0

1000

2000

Time (s)

Tip

Forc

e,

Ftip

(nN

)

a b c

d e f

43

Simulation was performed using two modes. Temporal non-dimensionalization was implemented

in sys.1 in order to save computational time and effort. Figure 3.4 a,b, and c show the tip

deflection of the MC, w(L,t), contact force, fc(t), and output voltage, V0(t), in non-dimensional

form respectively in sys.1. Figure 3.4 d, e, and f, on the other hand, show the tip deflection of the

MC, w(L,t), tip force, Ftip(t), and output voltage, V0(t), respectively.

It is observed from the results that utilizing piezoresistive MC, the output voltage of the system

reveals the information of the MC deflection which can further be utilized in obtaining the

contact force between the MC tip and the sample. Using larger number of modes in the

distributed-parameters modeling would result in more precise results.

3.6. Sensitivity Analysis

In order to study the sensitivity of these systems, two cases were investigated. In sys. 1, the error

of area under contact tip force was calculated versus the length of the piezoresistive layer, Lp,

over MC. A very nice trend was observed in the error of contact tip force versus Lp. As depicted

in Figure 3.5a, the error decreases with increasing Lp. On the other hand, changes in system’s

amplitude were monitored in sys. 2 while changing the location of the piezoresistive layer over

MC surface.

Figure 3.5 a) Error of area under contact tip force, fc versus length of piezoresistive layer in sys. 1, b)

System’s amplitude versus local spring constant of piezoelectric sample in sys. 2. c) System’s amplitude

versus location of piezoresistive layer in sys. 2.

0 0.2 0.4 0.6 0.81.8

2

2.2

2.4

2.6x 10

-7

Lp/L

Err

or

of

Are

a,

Aerr

or

0 2 4 60.011

0.012

0.013

0.014

Kz/EbIb (1/m3)*10-15

Am

plit

ud

e (

nm

)

0 0.5 10

0.2

0.4

0.6

0.8

L1/L

Am

plit

ude (

nm

) a b c

44

The length of the piezoresistive layer was kept constant at 0.3 times the total piezoresistive

length, Lp. Figure 3.5b demonstrates the effect of local spring constant of piezoelectric sample on

the vibration amplitude. The value of Kz was selected based on the proposed system

identification method for evaluating the proper range of system parameters (Salehi-Khojin et al.

2009a). It shows that the amplitude of vibration increases almost linearly with spring constant of

piezoelectric material. Figure 3.5c shows the change in amplitude versus the location of

piezoresistive patch denoted by the ratio of the length of the beginning point of it, L1, to the total

MC length, L. It is observed that the location of piezoresistive patch affects system’s amplitude

significantly while it does not have a noticeable influence on the shift in the resonance frequency

of the system.

3.7. Chapter Summary

In this chapter, a distributed-parameters modeling framework was developed for MC-based

biosensor (sys.1) and MC-based PFM (sys.2) equipped with piezoresistive read-out system.

Hamiltonian Principle was used to obtain the equations of motion of the system. Sys.1 operates

in contact mode where the contact force was modeled as a function of MC deflection and

introduced into the equations of motion. Whereas in sys.2, MC tip was brought into contact with

the piezoelectric sample and an external periodic electric field was applied between the

conducting tip and the sample. The piezoelectric and piezoviscoelastic deformations of the

sample served as the source of excitation of the system.

The obtained equations were simulated in MATLAB from which MC deflection as a function of

time and space, w(x,t), was obtained. The contact tip force, change of resistivity of the

piezoresistive patch, and consequently output voltage of the system was calculated utilizing

MC’s deflection. Simulation results have been presented and verified the capability of the

45

proposed distributed-parameters model. Sensitivity of the systems with respect to length and

location of piezoresistive layer over MC and the value of local spring constant of piezoelectric

sample were studied in sys.1 and sys. 2, respectively.

Compared to lumped-parameters modeling, the proposed model addressed the uncertainties and

unmodeled dynamics which are required for a precise MC-based force sensor. The reported

modeling framework can be utilized for predicting system’s behavior in many different aspects.

46

CHAPTER 4†

COMPREHENSIVE MATHEMATICAL MODELING OF PIEZOELECTRIC

MICROCANTILEVER USED FOR ULTRASMALL MASS SENSING

4.1. Introduction

MC-based biosensors have become a good alternative in place of conventional mass sensing

techniques such as surface plasmon resonance detectors (Nelson et al. 2002) and QCM (Bizet et

al. 1998). Although MC-based biosensors have received a widespread attention for label-free

bio-detection, there are not enough analytical studies investigating modeling and simulation of

piezoactive MC-based biosensors. Most of the related studies are based on simple lumped-

parameters system modeling the biosensor using Euler-Bernoulli beam theory (Yena et al. 2009,

Boisen et al. 2000, Thaysen et al. 2001, Duc et al. 2007).

Finite Element Method (FEM) has been extensively implemented for numerically modeling MC

based systems (Meroni and Mazza, 2004, Edler et al. 2004, Huber and Aktaa, 2003, Liu et al.

2003, Han and Kwak, 2001, McFarland et al. 2005, Chen et al. 2006, Fernando and Chaffey,

2005, Nardicci et al. 2006, Reed et al. 2006). It has emerged as a promising tool for estimating

geometry and bending stiffness of MCs (McFarland et al. 2005), identifying material and

geometrical parameters of microstructures (Chen et al. 2006), verification of analytical models

(Fernando and Chaffey, 2005) and fabrication (Nardicci et al. 2006) of MCs.

3D dynamic behavior of an eight-MC array structure was analyzed numerically by AFM

showing good agreement in lower mode but not in higher modes (Reed et al. 2006). However,

such systems (lumped-parameters modeling) and such numerical analysis are not capable of

† The contents of this chapter may have come directly from our previous publication (Faegh and Jalili, 2013).

47

describing all dynamics and phenomena occurring within the MC with any type of designs and

geometries and in all vibrational modes. Therefore, there is still a need for a more comprehensive

mathematical framework capable of describing static and dynamic behavior of MCs with any

shape and design in both low and high modes. Having such a model is crucial for having a

precise biosensing tool.

In this chapter, a comprehensive distributed-parameters modeling is proposed for piezoelectric

MC. Veeco Active probe® is taken to be the MC which has the capability of self excitation

through ZnO stack mounted at the base of the probe as shown in Figure 4.1. Other than being

implemented on the Dimension AFM (Itoh and Suga,1994, Itoh et al. 1996, Li et al. 1996,

Jamitzky et al. 2006), high speed imaging (Salehi-Khojin et al. 2008, Senesac et al. 2003, Oden

et al. 1996, Zhang et al. 2007b, Saeidpourazar et al. 2008b, Lee and Chung, 2004, Grbovic et al.

2006) and active control (Saeidpourazar and Jalili, 2008a,b, 2009, English et al. 2006, Lee,

2007), these probes can be used as biosensors. Therefore, the proposed comprehensive modeling

helps to understand performance of these probes acting as actuator as well as biosensor.

This chapter is organized in three parts; the first two parts presents mathematical modeling of the

piezoelectric MC-based biosensor, while the third part deals with experimental results carried out

Figure 4.1 Veeco Active Probe® with the self-sensing layer attached at the probe.

ZnO stack (consisting of 0.25µm

Ti/Au, 3.5µm ZnO, 0.25µm Ti/Au)

1 - 10 Ocm Phosphorus (n) doped Si

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48

to verify the theoretical results presented in the first two parts. In the first part, the Euler-

Bernoulli beam theory is used to derive the equation of motion along with the response of the

system and natural frequencies. In second part, the same system is modeled as a nonuniform

cross-section rectangular plate with a uniform piezoelectric layer on its surface.

The equations of motions of the rectangular plate actuated by piezoelectric layer are derived.

Free and forced vibration analyses are performed using estimated function and Galerkin’s

method respectively in order to solve the equation of motion. Finally, in last part of this chapter,

an experimental setup is developed and extensive testing is performed on Veeco Active probe®

equipped with piezoelectric layer. The piezoelectric property of the active probe is used as an

actuator in this study while a laser vibrometer is used to measure the response of the system. The

results obtained from the experiment are compared and verified with the theoretical results

obtained in the preceding two parts.

4.2. Beam Modeling

In this section comprehensive mathematical modeling framework followed by numerical

simulation is presented.

4.2.1. Mathematical modeling

An analytical model is adopted assuming the Active Probe to obey the Euler-Bernoulli beam

theory assumption. Distributed-parameters modeling is used to describe the behavior of active

probes acting as biosensor. Figure 4.2 depicts the schematic of Veeco Active Probe with ZnO

stack mounted on the base of the probe and extended close to the tip. The beam is considered to

have length L, thickness tb, and volumetric density ρb. The piezoelectric layer over the top

surface of the MC has length L1, thickness tp, and volumetric density ρp. Both MC and

piezoresistive layer are considered to have width b. w(x,t) denotes the midplane deflection of MC

49

with the tip deflection as w(L,t). Small deflection and linear system properties assumptions are

taken into account. The Extended Hamilton’s principle is used in developing the equations of

motion. The system is excited by applying a sinusoidal voltage to the piezoelectric layer with the

frequency close to system’s first natural frequency and the amplitude of 5 Volts.

What it follows next, is a distributed-parameters modeling framework for the transverse

deflection of the beam, w(x,t). For this, the kinetic energy of the system is written as

𝐾𝐸 =1

2∫ 𝜌(𝑥) [

𝜕𝑤(𝑥,𝑡)

𝜕𝑡]2𝐿

0𝑑𝑥 (4.1)

where

𝜌(𝑥) = 𝜌𝐴(𝑥) = 𝜌𝑏𝑏𝑡𝑏 + 𝜌𝑝𝑏𝑡𝑝𝐺(𝑥) (4.2)

with G(x) = 1 –H(x-L1), and H(x) being the Heaviside function. Considering that beam only

extends in the x-direction, potential energy of the system can be written as

𝛿𝑃𝐸 = ∫ 𝑥𝐿

0𝛿 𝑥𝑑𝑥 (4.3)

where the stress-strain relationship for beam and piezoelectric layer can be obtained from

𝑥𝑏 = 𝐸𝑏εx (4.4)

Figure 4.2 Schematic representation of Veeco Active Probe with ZnO stack on top extended from 0

to L1 (Salehi-Khojin et al. 2009c), with permission.

l1 l2

L

50

𝑥𝑝 = 𝐸𝑝εx + 𝐸𝑝d31

V(t)

tp (4.5)

with Eb and Ep being beam and piezoelectric elastic moduli, respectively. V(t) is the applied

voltage which is the input to the system, and d31 is the piezoelectric constant (Jalili, 2010, Mehta,

2009).

Strain in the x-direction is related to the transverse deflection of the beam by εx = −𝑦∂2w(x,t)

∂x2

which should be modified as εx = −(𝑦 − yn)∂2w(x,t)

∂x2 when used for piezoelectric section as a

result of shift in the neutral axis. yn is defined as

𝑦𝑛 =𝐸𝑝𝑡𝑝(𝑡𝑝+𝑡𝑏)

2(𝐸𝑝𝑡𝑝+𝐸𝑏𝑡𝑏) (4.6)

Therefore, the virtual potential energy can be written as

𝛿𝑃𝐸 = ∫∂2

∂x2[𝐸𝐼(𝑥)

𝐿

0

∂2w(x,t)

∂x2]𝑑𝑥 + 𝑀𝑝0𝑉(𝑡) ∫

∂2G(x)

∂x2

𝐿1

0𝑑𝑥 (4.7)

where Mp0 is defined as follows

𝑀𝑝0 = 𝑏𝐸𝑝𝑑31 [1

2(𝑡𝑏 + 𝑡𝑝) − 𝑦𝑛] (4.8)

The varying stiffness of the system 𝐸𝐼(𝑥) is

𝐸𝐼(𝑥) = 𝐸𝑏𝐼𝑏(𝑥) + 𝐸𝑝𝐼𝑝(𝑥)

𝐼𝑏(𝑥) =1

12𝑏𝑡𝑏

3 + 𝐺(𝑥)𝑏𝑡𝑏𝑦𝑛2

𝐼𝑝(𝑥) = [1

12𝑏𝑡𝑝

3 + 𝑏𝑡𝑝𝑦𝑛2 (

1

2(𝑡𝑏 + 𝑡𝑝) − 𝑦𝑛)

2

] 𝑏𝐺(𝑥) (4.9)

The virtual work due to ever-present viscous and structural damping terms is given by

𝛿𝑊 = ∫ (−𝐵��(𝑥, 𝑡) − 𝐶��′(𝑥, 𝑡))𝛿𝑤(𝑥, 𝑡)𝑑𝑥𝐿

0 (4.10)

where B and C represent the coefficients of viscous and structural damping, respectively

(Dadfarnia et al. 2004). ( )′ denotes the partial derivative with respect to spatial coordinate x,

51

while ( ) represents temporal derivative. Utilizing Extended Hamilton’s principle, the equations

of motion of the system can be obtained as

𝜌(𝑥)∂2𝑤(𝑥,𝑡)

∂𝑡2+

∂2

∂𝑥2[𝐸𝐼(𝑥)

∂2𝑤(𝑥,𝑡)

∂𝑥2] + 𝐵

∂𝑤(𝑥,𝑡)

∂𝑡+ 𝐶

∂2𝑤(𝑥,𝑡)

∂𝑥 ∂𝑡= −𝑀𝑝0𝑉(𝑡)𝐺

′′(𝑥) (4.11)

with the boundary conditions

𝑤(0, 𝑡) = 𝑤 ′(0, 𝑡) = 0 (4.12a)

𝑤 ′′(𝐿, 𝑡) = 𝑤 ′′′(𝐿, 𝑡) = 0 (4.12b)

4.2.2. Numerical simulations and results

The obtained governing equations of motion of the system are solved numerically using

Galerkin’s method. The PDE (4.11) can be converted into ODE using the following

discretization proposition

𝑤(𝑥, 𝑡) = ∑ 𝜙𝑗(𝑥)𝑛𝑗=1 𝑞𝑗(𝑡), 𝑗 = 1,2, … . . , 𝑛 (4.13)

with φj(x) and qj(t) being the clamped-free beam eigenfunction and generalized coordinates,

respectively. Therefore, the equation of motion can be represented as a function of time in a

matrix form. The ODE for the system can now be represented as

��(𝑡) + ��(𝑡) + 𝑞(𝑡) = 𝑉(𝑡) (4.14)

where

𝑞 = {𝑞1, 𝑞2, … . 𝑞𝑖} , �� = {��1, ��2, … . ��𝑖}

= {𝑀𝑖𝑗},

𝑀𝑖𝑗 = ∫ 𝜌𝐴(𝑥)𝐿

0

𝜙𝑗(𝑥)𝜙𝑖(𝑥)𝑑𝑥, , 𝑗 = 1,2, … . . , 𝑛

= { 𝑖𝑗},

𝑖𝑗 = 𝐵∫ 𝜙𝑗(𝑥)𝜙𝑖(𝑥)𝐿

0

𝑑𝑥 + 𝐶∫ 𝜙𝑗′ (𝑥)𝜙𝑖(𝑥)

𝐿

0

𝑑𝑥

52

= {𝐾𝑖𝑗},

𝐾𝑖𝑗 = ∫ 𝐸𝐼(𝑥)𝜙𝑗′′(𝑥)𝜙𝑖

′′(𝑥)𝐿

0𝑑𝑥

= {𝐾 𝑗},

𝐾 𝑗 = −𝑀𝑝0 ∫ 𝜙𝑗′(𝑥)𝛿(𝑥 − 𝐿1)

𝐿

0𝑑𝑥 = −𝑀𝑝0𝜙𝑗

′(𝐿1) (4.15)

The ODEs represented by Eqs. (4.14) and (4.15) are solved in MATLAB using the numerical

values given in Table 4.1. Forced vibration problem is solved with the input, the applied voltage

to ZnO stack, being a sinusoidal function with the amplitude of 5 Volts and the frequency close

to systems first natural frequency.

Selecting appropriate admissible functions‡,

𝜙𝑗(𝑥) and using Eq. (4.13), the deflection of the

MC at any location of the beam at any time can

be obtained. The tip deflection of the MC, w(L,t),

is then plotted in Figure 4.3(a). Taking the Fast

Fourier Transform (FFT) of the response, the

system’s first natural frequency is obtained to be

52.99 kHz as shown in Figure 4.3(b). The effect

of adsorbed ultrasmall mass as low as 200 ng was

calculated numerically. The added mass was

modeled as surface mass over the active area of

functionalization on MC surface (0-L1). As a

result of the adsorbed mass, resonance frequency

‡ Simple functions that provide approximate solution to the structures with complicated geometries satisfying

boundary conditions.

Table 4.1 The system parameters used for

modeling.

Parameters Value Units

L 486 μm

L1 325 μm

L2 360 μm

Wb1 230 μm

Wb2 40 μm

Wp 180 μm

b 50 μm

tb 4 μm

tp 4 μm

ρb 2330 kg.m-3

ρp 6390 kg.m-3

Eb 105 GPa

Ep 104 GPa

νb 0.33

d31 11 pC/N

𝑠12𝑆 -4.05×10

-12 m2/N

mb 5 μg

Cs 10 Ns/m

Ks 200 kN/m

53

of the system varies which is depicted in Figure 4.3(b).

Reduction in the first natural frequency about 1 kHz occurs as a result. Figure 4.3(c) and (d)

illustrate the effect of functionalization over MC surface on its first natural frequency and

vibration amplitude, respectively.

4.3. Plate Modeling

This section presents a precise modeling framework for the same system modeled as a

nonuniform rectangular thin plate. Free and forced vibration problems were solved. Numerical

simulation results are presented.

0 0.002 0.004 0.006 0.008 0.01-3

-2

-1

0

1

2

3

Time (s)

Tip

Deflection w

L (m

)

48 50 52 54 560

10

20

30

40

50

Frequency (kHz)

Am

plit

ude o

f V

ibra

tion (

nm

)

200 ng51.28 kHz

52.99 kHz

0 100 200 300 40049.5

50

50.5

51

51.5

52

52.5

53

Adsorbed Mass (ng)

Fre

qu

en

cy (

kH

z)

0 100 200 300 40025

30

35

40

45

Adsorbed Mass (ng)

Am

plit

ud

e o

f V

ibra

tio

n (

nm

)

Figure 4.3 Numerical results: (a) tip deflection of microcantilever, w(L,t), (b) shift in the first

natural frequency as a result of functionalization, (c) the effect of added surface mass due to

functionalization on the first natural frequency, (d) the effect of added surface mass on

vibration amplitude as a result of functionalization (Faegh and Jalili, 2013).

a b

c d

54

4.3.1. Mathematical modeling

In this section, an analytical model is proposed assuming the Active Probe to be a rectangular

plate with a piezoelectric layer on top. Distributed-parameters modeling is used to describe the

behavior of active probes acting as biosensor and the equations of motion are derived using

Hamilton’s principle. Figure 4.4 shows the schematic of Veeco Active Probe presented as a

nonuniform plate with ZnO stack mounted on its base and extended close to the tip. The

dimensions of the system are kept similar to beam section with Wb, and Wp being the width of the

beam and piezoelectric layers, respectively.

Neglecting the electrical kinetic energy, the kinetic energy of the system can be written as

follows (Jalili, 2010)

𝑇 =1

2∫ ∫ 𝜌(𝑥, 𝑦) [

𝜕𝑤(𝑥,𝑦,𝑡)

𝜕𝑡]2𝐿

0

𝑊

0𝑑𝑥 𝑑𝑦

=1

2∫ ∫ 𝜌𝑏𝑡𝑏 [


𝜕𝑡]2𝐿1

0

𝑊𝑏1

0𝑑𝑥 𝑑𝑦 +

1

2∫ ∫ 𝜌𝑝𝑡𝑝 [


𝜕𝑡]2𝐿1

0

𝑒1+𝑊𝑝

𝑒1𝑑𝑥 𝑑𝑦

+1

2∫ ∫ 𝜌𝑏𝑡𝑏 [


𝜕𝑡]2𝐿2

𝐿1

𝑊𝑏1

0𝑑𝑥 𝑑𝑦 +

1

2∫ ∫ 𝜌𝑏𝑡𝑏 [


𝜕𝑡]2𝐿

𝐿2

𝑒2+𝑊𝑏2

𝑒2𝑑𝑥 𝑑𝑦 (4.16)

where

𝜌(𝑥, 𝑦) = 𝜌𝑏𝑡𝑏 + 𝜌𝑝𝑡𝑝𝐺(𝑥, 𝑦) (4.17)

with G(x,y) = [1 –H(x-L1)][H(y-e1) – H(y-(Wp+e1)], and H(x) being the Heaviside function.

The volumetric strain energy of the system including the strain energy of the plate and

piezoelectric actuator can be written as

𝑈 =∭(𝜋𝑏 + 𝜋𝑝)𝑑𝑣 (4.18)

where 𝜋𝑏 and 𝜋𝑏 represent strain energy of plate and strain energy of piezoelectric layer,

respectively defined as follows

55

𝜋𝑏 =1

2[( 𝑥𝑥 𝑥𝑥)𝑏 + ( 𝑦𝑦 𝑦𝑦)𝑏 + ( 𝑥𝑦 𝑥𝑦)𝑏]

𝜋𝑝 =1

2[( 𝑥𝑥 𝑥𝑥)𝑝 + ( 𝑦𝑦 𝑦𝑦)𝑝 + ( 𝑥𝑦 𝑥𝑦)𝑝] (4.19)

where the stress-strain relationship for the piezoelectric material can be obtained from the

fundamental equation

휀𝑝 = 𝑠𝑝𝑞𝐸 𝑞 + 𝑑𝑖𝑝𝐸𝑖 (4.20)

with 휀𝑝 being mechanical strain, 𝑠𝑝𝑞𝐸 being the elastic compliance matrix, 𝑞 being the

mechanical stress, 𝑑𝑖𝑝 being the piezoelectric charge constant, and 𝐸𝑖 being the electric field

vector. Eq. (4.5) can also be written in the following form

𝑞 = 𝑐𝑝𝑞𝐸 휀𝑝 − 𝑒𝑞𝑗𝐸𝑗 (4.21)

where 𝑐𝑝𝑞𝐸 represents elastic stiffness under constant electric field and 𝑒𝑞𝑗 = 𝑐𝑝𝑞

𝐸 𝑑𝑞𝑗.

Having the above fundamental equations accompanied with the plate equations, the stress-strain

relationship for the plate with a piezoelectric layer can be obtained as (Mehta, 2009)

[

𝑥𝑥 𝑦𝑦 𝑥𝑦

] =

[

𝐸𝑝

1−𝜗𝑝2

𝜗𝑝𝐸𝑝

1−𝜗𝑝2 0

𝜗𝑝𝐸𝑝

1−𝜗𝑝2

𝐸𝑝

1−𝜗𝑝2 0

0 0𝐸𝑝

2(1−𝜗𝑝)]

[

휀𝑥𝑥휀𝑦𝑦휀𝑥𝑦

] −

[

𝐸𝑝

1−𝜗𝑝2

𝜗𝑝𝐸𝑝

1−𝜗𝑝2 0

𝜗𝑝𝐸𝑝

1−𝜗𝑝2

𝐸𝑝

1−𝜗𝑝2 0

0 0𝐸𝑝

2(1−𝜗𝑝)]

[𝑑31𝑑320

]𝑉(𝑡)

𝑡𝑝 (4.22)

with 𝜗𝑏 being beam’s Poisson’s ratio and 𝜗𝑝 the piezoelectric’s Poisson’s ratio which can be

calculated as (Jalili, 2010)

𝑠11𝑆 =

1

𝐸𝑝, 𝑠12

𝑆 =−𝜗𝑝

𝐸𝑝 (4.23)

in which 𝑠𝑝𝑞𝑆 represents piezoelectric’s compliance coefficient.

Based on Eqs (4.21-4.23), the total strain energy (Eq. 4.18) can be written as

56

𝑈 = ∫ ∫ 1𝐿2

0

𝑊𝑏1

0[𝜕2

𝜕𝑥2(𝜕2𝑤

𝜕𝑥2+ 𝜗𝑏

𝜕2𝑤

𝜕𝑦2) +

𝜕2

𝜕𝑦2(𝜕2𝑤

𝜕𝑥2+ 𝜗𝑏

𝜕2𝑤

𝜕𝑦2) + 2(1 − 𝜗𝑏)

𝜕2

𝜕𝑥𝜕𝑦(𝜕2𝑤

𝜕𝑥𝜕𝑦)] 𝑑𝑥𝑑𝑦 +

∫ ∫ 2𝐿1

0

𝑒1+𝑊𝑝

𝑒1[𝜕2

𝜕𝑥2(𝜕2𝑤

𝜕𝑥2+ 𝜗𝑝

𝜕2𝑤

𝜕𝑦2) +

𝜕2

𝜕𝑦2(𝜕2𝑤

𝜕𝑥2+ 𝜗𝑝

𝜕2𝑤

𝜕𝑦2) + 2(1 − 𝜗𝑝)

𝜕2

𝜕𝑥𝜕𝑦(𝜕2𝑤

𝜕𝑥𝜕𝑦)] 𝑑𝑥𝑑𝑦 +

∫ ∫𝜕2

𝜕𝑥2

𝐿1

0

𝑒1+𝑊𝑝

𝑒1[

𝐸𝑝

2(1−𝜗𝑝2)𝑉𝑎(𝑡)(𝑡𝑝 + 𝑡𝑏 − 𝑧𝑛)(𝑑31 + 𝜗𝑝𝑑32)] +

𝜕2

𝜕𝑦2[

𝐸𝑝

2(1−𝜗𝑝2)𝑉𝑎(𝑡)(𝑡𝑝 + 𝑡𝑏 −

𝑧𝑛)(𝑑32 + 𝜗𝑝𝑑31)] 𝑑𝑥𝑑𝑦 + ∫ ∫ 1𝐿

𝐿2

𝑒2+𝑊𝑏2

𝑒2[𝜕2

𝜕𝑥2(𝜕2𝑤

𝜕𝑥2+ 𝜗𝑏

𝜕2𝑤

𝜕𝑦2) +

𝜕2

𝜕𝑦2(𝜕2𝑤

𝜕𝑥2+ 𝜗𝑏

𝜕2𝑤

𝜕𝑦2) + 2(1 −

𝜗𝑏)𝜕2

𝜕𝑥𝜕𝑦(𝜕2𝑤

𝜕𝑥𝜕𝑦)] 𝑑𝑥𝑑𝑦 (4.24)

where D1 and D2 are defined as

1 =1

12

𝐸𝑏𝑡𝑏3

1−𝜗𝑏2,

2 =1

12

𝐸𝑝𝑡𝑝3

1−𝜗𝑝2 +

𝐸𝑝𝑡𝑝

1−𝜗𝑝2 (

𝑡𝑝

2+

𝑡𝑏

2− 𝑧𝑛)

2 +𝐸𝑝

1−𝜗𝑝2 (𝑊𝑏1𝑡𝑏𝑧𝑛

2) (4.25)

Since the combined thickness of the plate and piezoelectric in not constant as a result of

piezoelectric layer on the surface, the neutral axis is shifted from the mid-section. This upward

shift in the neutral axis due to non-uniformity in plate thickness can be given as (Mehta, 2009)

𝑧𝑛 =𝐸𝑝𝑡𝑝𝑊𝑝(𝑡𝑝+𝑡𝑏)

2(𝐸𝑝𝑡𝑝𝑊𝑝+𝐸𝑏𝑡𝑏𝑊𝑏1) (4.26)

The virtual work due to damping forces can be written as

𝛿𝑊 = ∫ ∫ [−𝐵𝜕𝑤

𝜕𝑡𝛿𝑤(𝑥, 𝑦, 𝑡)] 𝑑𝑥

𝐿

0𝑑𝑦 + ∫ ∫ [−𝐶

𝜕3𝑤

𝜕𝑥𝜕𝑦𝜕𝑡𝛿𝑤(𝑥, 𝑦, 𝑡)] 𝑑𝑥

𝐿

0𝑑𝑦

𝑊𝑏

0

𝑊𝑏

0 (4.27)

L1

L2

L

Wp Wb1 Wb2

x

y e1

L1

L2

L

Figure 4.4 Veeco active probe with ZnO stack on top extended from 0 to L1.

57

where B and C represent the coefficients of viscous and structural damping, respectively.

By evaluating the variations of kinetic and potential energies along with the virtual work and

substituting them into the extended Hamilton’s principle

∫ 𝛿(𝑇 − 𝑈 +𝑊)𝑑𝑡 = 0𝑡2

𝑡1, (4.28)

the following equation of motion can be obtained

𝜌𝑡(𝑥)∂2𝑤(𝑥,y,𝑡)

∂𝑡2+

∂2

∂𝑥2[ 1 (

𝜕2𝑤

𝜕𝑥2+ 𝜗𝑏

𝜕2𝑤

𝜕𝑦2) + 2 (

𝜕2𝑤

𝜕𝑥2+ 𝜗𝑝

𝜕2𝑤

𝜕𝑦2)] +

∂2

∂𝑦2[ 1 (

𝜕2𝑤

𝜕𝑦2+ 𝜗𝑏

𝜕2𝑤

𝜕𝑥2) +

2 (𝜕2𝑤

𝜕𝑦2+ 𝜗𝑝

𝜕2𝑤

𝜕𝑥2)] + 2

𝜕2

𝜕𝑥𝜕𝑦[(1 − 𝜗𝑏) 1 (

𝜕2𝑤

𝜕𝑥𝜕𝑦) + (1 − 𝜗𝑝) 2 (

𝜕2𝑤

𝜕𝑥𝜕𝑦)] + 𝐵

∂𝑤(𝑥,y,𝑡)

∂𝑡+

𝐶∂3𝑤(𝑥,𝑦,𝑡)

∂𝑥 ∂𝑦 ∂𝑡= −𝑀𝑝1𝑉𝑎(𝑡)

𝜕2𝐺(𝑥,𝑦)

𝜕𝑥2−𝑀𝑝2𝑉𝑎(𝑡)

𝜕2𝐺(𝑥,𝑦)

𝜕𝑦2 (4.29)

where 𝑀𝑝1 and 𝑀𝑝2 are given as

𝑀𝑝1 =𝐸𝑝

2(1−𝜗𝑝2)(𝑡𝑝 + 𝑡𝑏 − 𝑧𝑛)(𝑑31 + 𝜗𝑝𝑑32)

𝑀𝑝2 =𝐸𝑝

2(1−𝜗𝑝2)(𝑡𝑝 + 𝑡𝑏 − 𝑧𝑛)(𝑑32 + 𝜗𝑝𝑑31) (4.30)

By inspecting Eq. (4.29), it can be seen that the system’s input is the voltage applied to the

piezoelectric layer which creates responses in both x- and y-directions.

4.3.2. Free vibration analysis

In order to solve the free vibration problem, eigenfunctions and eigenvalues need to be obtained.

Eigenfunctions are the exact solution of the free vibration problem satisfying all the boundary

conditions including both geometrical and natural boundary conditions. However, in complex

and nonuniform problems, finding the exact eigenfunction solution is very tedious. In these

cases, an approximate solution or what is referred to as admissible function is typically utilized.

Since the plate under study here is nonuniform in thickness and cross-section, an approximate

solution is desired with acceptable accuracy. Increasing number of modes in solving the forced-

58

vibration problem can also compensate for the approximation considered in solving the free-

vibration problem.

A number of studies have investigated the exact free-vibration solution of MC plate exploiting

different methods such as Rayleigh Ritz, superposition, and separation of variables (Gorman,

1976, 1982, 1984, 1995, Rao, 2007, Yu, 2009). In order to obtain an admissible function,

symmetric and antisymmetric free vibration modes of MC plate was calculated using Gorman’s

method of superposition (Gorman, 1982). Three building blocks were considered developing

Levy-type solution for each building block and forcing the solutions to satisfy boundary

conditions. Alternative to this method is to find the exact analytical solution to the free-vibration

problem using separation of variables (Gorman, 1982). Both of these methods have been used;

however, the exact analytical solution (Gorman, 1982) provided more accurate eigenfunctions

and eigenvalues, and so this method is followed in this study.

In order to find the solution of the free, undamped vibration problem of a rectangular plate with

total length of L and width Wb1 as depicted in Figure 4.4(a), the following equation needs to be

solved [Rao, 2007]

𝜌𝑡(𝑥)𝜕2𝑤(𝑥,𝑦,𝑡)

𝜕𝑡2+ 𝛻2( (𝑥, 𝑦)𝛻2𝑤(𝑥, 𝑦, 𝑡)) = 0 (4.31)

The solution is assumed to take the following form utilizing the concept of separation of

variables with respect to location and time

𝑤(𝑥, 𝑦, 𝑡) = 𝑊(𝑥, 𝑦)𝑇(𝑡) (4.32)

By substituting Eq. (4.32) into Eq. (4.31), the following two equations are obtained which are

separated in time and position (x,y) assuming constant plate stiffness, D(x,y) = D and plate

thickness t(x) = t,

1

𝑇(𝑡)=

𝑑2𝑇(𝑡)

𝑑𝑡2= −𝜔2 (4.33a)

1

(4.33b)

with ω being the natural frequencies and β1 defined as

. The general solution of Eq.

(4.33a) can be expressed in terms of harmonic functions as follows

(4.34)

while Eq. (4.33b) can be written as

(4.35)

with

. The general solution of Eq.(4.33b), W(x,y), can be obtained by superposing

W1(x,y) and W2(x,y) each of which satisfies the following equations

(4.36a)

(4.36b)

Each of W1(x,y) and W2(x,y) can be obtained in terms of harmonic functions as follows

(4.37a)

(4.37b)

where . Therefore, the general solution of W(x,y) is

(4.38)

In order to find a unique solution for W(x,y), the eight coefficients C1-C8 need to be found which

can be evaluated using the boundary conditions. The applied boundary conditions for the

rectangular MC plate are clamped at one edge where x=0, and free at the other three edges (Fig.

4). Therefore, the eight boundary conditions can be written a

60

@𝑥 = 𝐿: 𝜕2𝑊(𝑥,𝑦)

𝜕𝑥2+ 𝜗

𝜕2𝑊(𝑥,𝑦)

𝜕𝑦2= 0 ,

𝜕3𝑊(𝑥,𝑦)

𝜕𝑥3+ 𝜗

𝜕3𝑊(𝑥,𝑦)

𝜕𝑦3= 0

@𝑦 = 0: 𝜕2𝑊(𝑥,𝑦)

𝜕𝑦2+ 𝜗

𝜕2𝑊(𝑥,𝑦)

𝜕𝑥2= 0 ,

𝜕3𝑊(𝑥,𝑦)

𝜕𝑦3+ 𝜗

𝜕3𝑊(𝑥,𝑦)

𝜕𝑥3= 0

@𝑦 = 𝑊𝑏1 : 𝜕2𝑊(𝑥,𝑦)

𝜕𝑦2+ 𝜗

𝜕2𝑊(𝑥,𝑦)

𝜕𝑥2= 0 ,

𝜕3𝑊(𝑥,𝑦)

𝜕𝑦3+ 𝜗

𝜕3𝑊(𝑥,𝑦)

𝜕𝑥3= 0 (4.39a-d)

Introducing the eight boundary conditions into Eq. (4.38), the eigenvalues and eigenfunctions

can be obtained. The eignefunctions are calculated and plotted for the first mode as depicted in

Figure 4.5.


The obtained equation of motion represented by (4.29) was solved numerically using MATLAB.

For this, the partial differential equation (PDE) was converted to ODE discretizing system

response, w(x,y,t), with respect to both spatial and temporal components exploiting Galerkin’s

method as

𝑤(𝑥, 𝑦, 𝑡) = ∑ ∑ 𝑊𝑚𝑛(𝑥, 𝑦)𝑁𝑚=1 𝑞𝑚𝑛(𝑡)

𝑁𝑛=1 (4.40)

Figure 4.5 Eigenfunction for the first mode of the rectangular cantilever plate, W11.

61

For a clamped-free-free-free rectangular plate with continuous geometry, the equations of motion

can be expressed in terms of function of time in the matrix form as follows

𝑀{��(𝑡)} + {��(𝑡)} + 𝐾{𝑞(𝑡)} = 𝐾 1𝑉(𝑡) + 𝐾 2𝑉(𝑡) (4.41)

where

𝑀 = {𝑀𝑟𝑠𝑚𝑛},

𝑀𝑟𝑠𝑚𝑛 = ∫ ∫ 𝜌(𝑥, 𝑦)𝑡(𝑥)𝑊𝑟𝑠(𝑥, 𝑦)𝑊𝑚𝑛(𝑥, 𝑦)𝑑𝑥𝑑𝑦𝐿

0

𝑊𝑏1

0

, 𝑠,𝑚, 𝑛 = 1,2, . . ,

= { 𝑟𝑠𝑚𝑛},

𝑟𝑠𝑚𝑛 = 𝐵∫ ∫ 𝑊𝑟𝑠(𝑥, 𝑦)𝑊𝑚𝑛(𝑥, 𝑦)𝐿

0

𝑊𝑏1

0

𝑑𝑥𝑑𝑦 + 𝐶∫ ∫ 𝑊𝑟𝑠(𝑥, 𝑦) 2𝑊𝑟𝑠

𝑥 𝑦

𝐿

0

𝑊𝑏1

0

𝑑𝑥𝑑𝑦

𝐾 = {𝐾𝑟𝑠𝑚𝑛},

𝐾𝑟𝑠𝑚𝑛 = ∫ ∫ (𝑥, 𝑦)∇2𝑊𝑟𝑠∇2𝑊𝑚𝑛𝑑𝑥𝑑𝑦

𝐿

0

𝑊𝑏1

0

𝐾 1 = {𝐾 1𝑟𝑠},

𝐾 1𝑟𝑠 = −𝑀𝑝1 ∫ ∫𝜕𝑊 𝑠

𝜕𝑥

𝐿1

0

𝑊𝑝+𝑒1

𝑒1

𝜕𝐺(𝑥,𝑦)

𝜕𝑥𝑑𝑥𝑑𝑦 = −𝑀𝑝1 ∫

𝜕𝑊 𝑠

𝜕𝑥(𝐿1, 𝑦)𝑑𝑦

𝑊𝑝+𝑒1

𝑒1

𝐾 2 = {𝐾 2𝑟𝑠},

𝐾 2𝑟𝑠 = −𝑀𝑝2∫ ∫ 𝑊𝑟𝑠

𝑦

𝐿1

0

𝑊𝑝+𝑒1

𝑒1

𝐺(𝑥, 𝑦)

𝑦𝑑𝑥𝑑𝑦 =

−𝑀𝑝2 ∫𝜕𝑊 𝑠

𝜕𝑦(𝑥, 𝑒1) −

𝜕𝑊 𝑠

𝜕𝑦(𝑥, (𝑊𝑝 + 𝑒1))𝑑𝑥

𝐿1

0 (4.42)

The ODE represented by Eqs. (4.41) and (4.42) were solved in MATLAB using the numerical

values given in Table 4.1. The piezoelectric material was assumed to be transversely isotropic.

This assumption results in the piezoelectric constant d32 to be equal to d31 (Jalili, 2010). Forced

vibration problem was solved with the input being the applied voltage to ZnO stack which was

taken to be a sinusoidal function with the amplitude of 5 Volts and the frequency close to systems

62

first natural frequency of about 56 kHz. The time response of the MC, q11(t) is obtained for 10

ms of operation of MC. Deflection of any point of MC, w(x,y,t), can be calculated having

admissible function, Wmn(x,y), obtained from section 4.3. Multiplying Wmn(x,y) by the respective

generalized coordinates, qmn(t), the response of the system can be found at any particular location

and at any time.

Figure 4.6 depicts the results obtained from solving the equation of motion based on the

mathematical modeling framework presented. Time response of the MC for the first mode, q11(t),

is plotted in Figure 4.6(a).

Deflection of MC at an arbitrary point which is selected to be at the free end of the MC in the

middle corresponding to x = L and y = 𝑊𝑏1

2 is calculated and plotted in Figure 4.6(b). Taking the

FFT of the time response, the system’s first resonance frequency is observed to be 56.34 kHz as

clearly seen in Figure 4.6(c).

The ultimate goal of this study is to quantitatively detect the ultrasmall absorbed mass on the

surface of the MC with the intention of implementing the presented system as a highly sensitive

biological sensor. Operating the presented MC in the dynamic mode, the shift in natural

frequency was calculated giving a good insight into the amount of absorbed mass to the surface

of MC. Figure 4.6(c) depicts the shift in the first natural frequency of the system as a result of

absorbed mass as low as about 200 ng.

4.4. Experimental Verification

The experimental section of this study includes the measurement of ultrasmall added surface

mass using MC and verifying the results with the mathematical modeling presented in the

preceding sections. Veeco Active Probe® is used with the capability of excitation through the

ZnO stack mounted at the base of each probe (see Figure 4.1).

63

The Active probe® was mounted on a holder which was fixed on a 3D stage and placed under

the laser vibrometer as shown in Figure 4.7.

A sinusoidal input voltage with the amplitude of 1 Volt and excitation frequency of 50 kHz was

generated through oscilloscope (Agilent InfiniiVision 2000 X-Series-sw Oscilloscope). The input

voltage applied to the ZnO stack produces excitation to the system. The produced signal is read

out as velocity by laser vibrometer (Polytec CLV-2534).

0 0.002 0.004 0.006 0.008 0.01-5

0

5x 10

-3

Time (s)

q1 (

nm

)

0 0.002 0.004 0.006 0.008 0.01-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

Time (s)

Tip

De

fle

ctio

n,

w(L

,wb1/2

) (n

m)

52 54 56 58 60

0.05

0.1

0.15

0.2

0.25

0.3

Frequency (kHz)

Am

plit

ude (

nm

) 54.01 kHz

204 ng

56.34 kHz

Figure 4.6 (a) time response of microcantilever, q11(t), (b) Deflection of microcantilever at the tip

of the MC in the middle, w(L,𝑊𝑏1

2,t), (c) FFT of the response of the system representing system’s

first natural frequency and the effect of added absorbed mass in the shift of natural frequency

(Faegh and Jalili, 2013).

a b

c

64

4.4.1. Non-functionalized MC: verification with modeling

The first step of the experiment is performed on a non-functionalized MC. The excitation

frequency is swept from 0 kHz to 100 kHz and the first natural frequency of the system is

captured to be around 56 kHz which exactly matches the theoretical result of modeling the

system as a rectangular non-continuous plate presented in Section 4.3. Figure 4.8(a,b) shows the

FFT of the system’s response captured by optical measurement.

Comparing the results obtained from mathematical modeling with the experimental results, it is

shown that mathematical modeling presented in both Part I and II, i.e., modeling the system as

Euler Bernoulli and rectangular plate, respectively, predict the real situation with a great level of

accuracy. Although the Euler Bernoulli modeling provided explanation of dynamics and

behavior of the proposed platform in this case, it will not be sufficient for modeling other

geometries of the similar platform. Since geometry of MC in biosensors dramatically influences

the sensitivity of the system, there is always a need to optimize geometrical properties such as

using shorter and wider MCs. Therefore, having a

comprehensive modeling framework describing all geometries

and designs of MC provides a powerful theoretical layout for

such systems and explains the necessity of modeling

complexity and effort. Table 4.2 compares the theoretical

results with the experiment.

4.4.2. Detection of adsorbed mass

In the second step of the experiment, the Active Probe is used

for detection of ultrasmall adsorbed mass. The MC operates in

dynamic mode where it is brought to excitation close to its

Figure 4.7 MC mounted on a

holder placed over a 3D stage

positioned under laser

vibrometer head.

65

first resonant frequency by applying a sinusoidal voltage to the piezoelectric layer with the

amplitude of 1 Volt.

In this study, the detection of i) Amino groups, and ii) Glucose Oxidase (GoX) enzyme layer

formed on top of MC surface is investigated. The absorbed mass is sensed as a result of shifted

laser beam reflected from tip of the MC captured by laser vibrometer and monitored by the

scope. Taking the FFT of the response of the system illustrates the change of system’s resonant

frequency. In order to functionalize enzyme layer, the active part of the MC surface is used

0 200 400 600 800 1000 1200-80

-60

-40

-20

0

20

Frequency (kHz)

Decib

le r

ele

tive t

o 1

Volt (

dB

V)

56.1 kHz

0 100 200 300 400 500 6000

1

2

3

4

5

Frequency (kHz)

Am

plit

ude R

atio

56.1 kHz

First Resonance

Frequency,

wn1 (kHz)

Theory 1: Beam

Modeling

52.99

Theory 2: Plate

Modeling

56.34

Experiment 56.1

Figure 4.8 (a) Decibel versus frequency, FFT of the output signal showing first resonance frequency at

56.1 kHz, (b) Amplitude ratio versus frequency.

a b

Table 4.2 Comparing the results obtained from mathematical

modeling presented in parts I and II to the experimental

results.

66

which is the extended electrode coated with gold. Gold is employed for immobilizing Gox

enzyme which is itself a receptor for biomolecules such as Glucose.

Materials: Glucose Oxidase, Gox, 8.0% glutaraldehyde, 2-aminoethanethiol were purchased

from Sigma. A 0.1M phosphate buffer solution was prepared. Its pH was adjusted to 7 using

dilute HCl and NaOH. Deionized water was used for preparing solutions.

Procedure: Before starting functionalization, the Active Probe was washed in acetone and

ethanol for 10 minutes. A Teflon chamber was designed in order to dip in the MC into a droplet

of liquid such that it only wets the MC and does not proceed to the electronic circuits. A 3D

stage with resolution of submicron was used in order to navigate the MC in x-, y-, and z-direction

and place it into the droplet.

A 0.1M of aminoethanethiol solution was prepared by dissolving 2-aminoethanethiol powder

into deionized water. A single layer of aminoethanethiol was formed on the gold surface by

attachment of thiol groups to gold. The change in the first resonant frequency is measured and

recorded.

50 100 150 200 250 300 350

-80

-60

-40

-20

0

20

40

Frequency (kHz)

Am

plit

ude (

V)

Unfunctionalized MC

MC functionalized with GoX42.9

48.88

50 100 150 200 250

-80

-60

-40

-20

0

20

Frequency (kHz)

Am

plit

ude (

V)

Unfunctionalized MC

MC functionalized with Amin groups

MC functionalized with GoX

49

44.53

41.50

Figure 4.9 Shift of the first resonance frequency as a result of: (a) GoX functionalization, (b)

immobilization of Amin solution and enzyme solution consequently.

a b

67

Enzyme solution is then prepared by dissolving 0.2% glutaraldehyde and 0.1 unit/ml Gox into a

pH 7.0 buffer solution. Dipping MC into the enzyme solution aldehyde groups of glutaraldehyde

react with the Amino groups at one end and with GoX at other ends letting layer of enzyme to

grow over the surface.

Once the enzyme functionalization is complete, new measurement is taken by exciting the MC

and sweeping the frequency. Taking the FFT of the response of the system, the shift in resonance

frequency as a result of formation of enzyme can be illustrated.

Figure 4.9 shows the shift in the first resonance frequency of the system as a result of

immobilization amin groups and enzymes over the gold surface of MC. Measurement was

performed eight times with the average of 49 kHz and standard deviation of 0.2098. Figure 4.9

(a) depicts a shift of 5.98 kHz as a result of GoX functionalization. Figure 4.9 (b) shows 4.47

kHz shift in resonance frequency as a result of Amin immobilization which is followed by 7.50

kHz as a result of higher concentration of GoX immobilization.

Exploiting the mathematical modeling presented in this study the amount of adsorbed masses can

be quantified having the shifts in resonance

frequency. Figure 4.10 shows the shift in the

first resonance frequency as a result of

adsorbed mass utilizing the mathematical

modeling framework providing the

relationship between the added mass and

frequency change. Based on this method of

quantification, the adsorbed mass as a result of

Amino and GoX functionalization depicted in

0 100 200 300 4000

0.5

1

1.5

2

2.5

3

3.5

Adsorbed mass (ng)

Fre

qu

en

cy s

hift

(kH

z)

y = 0.0081*x + 0.043

y = - 1.5e-006*x2 + 0.0087*x + 0.011

Figure 4.10 Quantification of frequency shift as a

result of adsorbed mass exploiting mathematical

modeling framework.

68

Figure 4.9 (b) would be about 545 ng and 368 ng respectively.


Comprehensive distributed-parameters modeling framework was presented for piezoelectric MC-

based biosensor with the purpose of detecting ultrasmall biological species. Two models of the

system were exploited as either Euler-Bernoulli beam or a rectangular clamped-free-free-free

plate. Performing extensive numerical simulations for both cases in dynamic mode, the effect of

absorbed mass was modeled and illustrated. An experiment was also set up and performed on

Veeco Active Probes being self-excited with piezoelectric layer. Laser vibrometer was used to

measure system’s response which was further verified with the mathematical models presented

in this study. Active probe was then implemented for detection of ultrasmall adsorbed mass.

The immobilized biomolecules were detected operating the system in dynamic mode and

quantified exploiting the proposed mathematical framework. Experimental results were further

verified with the presented theory. It was shown that both Euler-Bernoulli beam theory and

rectangular plate theory provide powerful modeling frameworks for predicting the dynamics of

the proposed system. A high level of accuracy was achieved utilizing both modeling

frameworks. Although the Euler-Bernoulli modeling also satisfied the explanation of dynamics

and behavior of the proposed platform in this case, it will not be sufficient for modeling other

geometries of the similar platform. Since geometry of MC in biosensors dramatically influences

the sensitivity of the system, there is always a need to optimize geometrical properties such as

using shorter and wider MCs. Therefore, having a comprehensive modeling framework

describing all geometries and designs of MC provides a powerful theoretical layout for such

systems and explains the necessity of modeling complexity and effort.

69

CHAPTER 5§

SELF-SENSING ULTRASMALL MASS DETECTION USING PIEZOELECTRIC

MICROCANTILEVER-BASED SENSOR

5.1. Introduction

MC sensors have generated widespread interest as a result of their sensitivity and capability in

detecting small forces, mechanical stresses, and added adsorbed mass molecules (Tao and Yung,

2003). One of the most inspiring applications of MC sensors has been their implementation as an

inexpensive, sensitive, label-free platform for real-time detection of biomolecules (Arntz et

al. 2003, Pei et al. 2003,2004, Shin et al. 2008, Shin and Lee, 2006, Sree et al. 2010a,b, Wu et

al. 2001, Yang and Chang, 2010). Multiplexed detection of concentrations of antigens in a

sample fluid has also been enabled utilizing arrays of MCs.

Most of the studies regarding identification of molecular affinities have been performed in the

static mode where the induced surface stress as a result of deflection of MC from a stable

baseline was used to measure molecular binding (Pei et al. 2003,2004, Wu et al. 2001, Huber et

al. 2007, Shu et al. 2008, Jeetender et al. 2006, Álvarez and Tamayo, 2005, Thaysen et al. 2001,

Grogan et al. 2002, Yena et al. 2009, Zhou et al. 2009, Cherian et al. 2005, Backmann et al.

2005, Zhang et al. 2006). Arrays of MCs have been used for high-throughput measurements

(Arntz et al. 2003, Sree et al. 2010a, Yang and Chang, 2010, Huber et al. 2007, Cherian et al.

2005, Backmann et al. 2005, Zhang et al. 2006). On the other hand, in dynamic mode, the system

is brought into excitation at or near its resonance frequency. The shift in the resonance frequency

§ The contents of this chapter may have come directly from our previous publication (Faegh et al. 2013a).

70

as a result of molecular recognition yields a good insight into the amount of adsorbed mass

(Johnson and Mutharasan, 2012, Von Muhlen et al. 2010).

There are two main features determining the success of all biological sensors: first, the molecular

binding between the receptor and the biomolecule of interest; second, the read-out system capable

of transducing the molecular binding into detectable physical property. There are a number of read-

out methodologies including optical-based, capacitive-based, piezoresistive-based and piezoelectric-

based measurement techniques. The concept of these methods and the challenges associated with

them was extensively discussed in Chapter 2.

In order to overcome the aforementioned challenges, a unique self-sensing piezoelectric-based

MC sensor is reported in this chapter. In self-sensing MC sensors both direct and inverse

properties of a piezoelectric material is utilized to play the role of both sensor and actuator.

Direct piezoelectric property is used to sense the self-induced voltage generated in the

piezoelectric layer as a result of beam deformation. At the same time, inverse property of

piezoelectric material is used to generate deformation and bring the system into vibration as a

result of applying a harmonic voltage to it. Therefore, a single piezoelectric layer embedded in

the MC sensor is utilized to both actuate and sense the system exploiting a capacitance bridge

network (Faegh et al. 2013a). This provides a simple and inexpensive platform for mass sensing

and detection purposes with the opportunity of miniaturizing the platform. A Veeco Active

Probe® is used here where a ZnO stack is used to implement the MC in self-sensing mode as

shown in Figure 5.1.

As described in previous chapters, most of the available mathematical modeling targeting

piezoactive MC-based systems includes lumped-parameters modelings which are not capable of

71

Figure 5.1 Veeco Active Probe® with ZnO self-sensing layer deposited on the probe.

describing all dynamics and phenomena occurring within the MC with any type of designs and

geometries and in all vibrational modes. This drives the need for a more comprehensive

mathematical framework capable of describing static and dynamic behavior of MCs. Therefore,

in the first part of this chapter mathematical modeling is developed for self-sensing piezoelectric-

based MC followed by simulation results.

In the final part of the chapter, an experimental setup is developed and extensive testing is

performed on Veeco Active Probe® equipped with piezoelectric layer functioning in dynamic

mode. A capacitance bridge network is utilized to implement the active probe in self-sensing

mode. Detection of adsorbed biological species, which is the covalent binding of thiol gourps of

Aminoethanethiol, was made possible through the proposed self-sensing piezoelectric-based MC

sensor. Similar mass detection setup was built and performed utilizing optical-based method and

the results were compared to the self-sensing methodology to verify the applicability of the

proposed platform. Quantification of adsorbed masses was carried out and the sensitivity of the

system was measured.

Piezoelectric properties at the nanoscale are sensitive to temperature and other ambient

variations. In order to have a precise model of the actuation/sensing, an adaptation strategy needs

500 µm

ZnO stack (consisting of 0.25 µm

Ti/Au, 3.5 µm ZnO, 0.25 µm Ti/Au)

1–10 Ocm Phosphorus

(n) doped Si

72

to be implemented in order to compensate for the variation of piezoelectric property (here ZnO

stack). For this, a mathematical adaptation law is presented in Section 5.3 followed by simulation

results and comparison with those of Section 5.2. The experimental results were verified with the

theories presented in Sections 5.2 and 5.3. Based on the results, the accuracy of the proposed

modeling frameworks is demonstrated.

5.2. Mathematical Modeling and Preliminaries

Precise modeling framework for the defined system is reported here followed by numerical

analysis and results.

5.2.1. Beam modeling

A comprehensive mathematical modeling is proposed in this section using a distributed-

parameters model. The system includes a Veeco Active probe® as a self-sensing MC in dynamic

mode. The MC beam is assumed to obey the Euler-Bernoulli beam theory. The use of Euler-

Bernoulli beam theory was proven to model the current system with a high level of accuracy

compared to plate theory in Chapter 4 and (Faegh and Jalili, 2013). The self-sensing mode can be

implemented through the ZnO stack mounted on the base of the probe extending close to the tip

as shown in Figure 5.2. The MC beam is narrowed in the tip which adds to the sensitivity of the

system. The MC is modeled as a nonuniform cross-section beam with the total length of L and an

active length (piezoelectric layer) of L1 which is used for functionalization. Other system

properties are the same as those described in Chapter 4, Section 4.2.1.

73

Figure 5.2 Micrograph/photograph of a Veeco Active Probe with a ZnO stack on top

extended from 0 to L1 (Salehi-Khojin et al. 2009c), with permission.

The following distributed-parameters modeling is proposed for the response of the system to the

applied input. For this, the kinetic energy, potential energy and virtual work of the system were

developed as presented in Chapter 4, Section 4.2.1.

Two main impedance bridges have been used to supply voltage and sense the induced voltage in

the piezoelectric patch (Gurjar and Jalili, 2006,2007). They are mainly pure capacitive and

resistive-capacitive bridges as shown in Figure 5.3.

(a) (b)

Figure 5.3 (a) Pure capacitive bridge, and (b) Resistive-Capacitive (R-C) bridge

(Gurjar and Jalili, 2006).

(a) (b)

(a) (a)

74

The piezoelectric actuator is modeled as a capacitor and a voltage source in series as shown in

the dashed box in Figure 5.3. Cp represents the effective capacitance of the piezoelectric element

and Vs is the induced voltage in the piezoelectric patch. For the purpose of self-sensing, the

piezoelectric actuator is connected in a bridge with other elements (i.e., the capacitors C1, Cr

and/or resistors R, R1). In this study, pure capacitive bridge network in employed as shown in

Figure 5.3(a). Vc(t) is the voltage applied across the capacitor bridge. Therefore, the voltage

applied across the piezoelectric actuator can be written as:

𝑉(𝑡) =𝐶1

𝐶1 + 𝐶𝑝𝑉𝑐(𝑡) −

𝐶𝑝

𝐶1 + 𝐶𝑝𝑉𝑠(𝑡) (5.1)

The self-induced voltage generated in the piezoelectric layer as a result of induced surface stress

due to beam vibration can be written as (Gurjar and Jalili, 2006,2007):

𝑉𝑠(𝑡) =1

𝐶𝑝𝑏𝐸𝑝𝑑31 (

1

2(𝑡𝑏 + 𝑡𝑝) − 𝑦𝑛) [𝑤

′(𝐿1, 𝑡) − 𝑤′(0, 𝑡)] (5.2)

Implementing Extended Hamilton’s principle, the equation of motion of the system can be

derived as:

𝜌(𝑥)𝜕2𝑤(𝑥,𝑡)

𝜕𝑡2+

𝜕2

𝜕𝑥2[𝐸𝐼(𝑥)

𝜕2𝑤(𝑥,𝑡)

𝜕𝑥2] + 𝐵

𝜕𝑤(𝑥,𝑡)

𝜕𝑡+ 𝐶

𝜕2𝑤(𝑥,𝑡)

𝜕𝑥𝜕𝑡−

𝑝

𝑝+ 1𝑏𝐸𝑝𝑑31

(1

2(𝑡𝑏 + 𝑡𝑝) − 𝑦𝑛) [𝑤

′(𝐿1, 𝑡) − 𝑤′(0, 𝑡)]𝐺′′(𝑥) = −𝑀𝑝0𝑉𝑐(𝑡)𝐺′′(𝑥)

(5.3)

with the boundary conditions:

𝑤(0, 𝑡) = 𝑤′(0, 𝑡) = 0 (5.4)

𝑤′′(𝐿, 𝑡) = 𝑤′′′(𝐿, 𝑡) = 0 (5.5)

The self-sensing nature appears in the equation of motion such that 𝑉𝑐(𝑡) appearing in the right

hand side of the equation is employed for actuation, and at the same time, the sensing effect is

75

observed in the left hand side (with the extra term being a function of slope of the beginning and

end points of piezoelectric layer).

That is, from Eq. (5.3), it is observed that the voltage generated in the piezoelectric layer, 𝑉𝑠(𝑡),

is a function of the slope of the beginning and end point location of the piezoelectric layer which

contain the information of the response of the system. In order to acquire this signal, its

introduction into the output voltage of the capacitive bridge should be analyzed. For this, the

bridge output voltage is expressed as (Gurjar and Jalili, 2007):

𝑉0(𝑡) = [𝐶𝑝

𝐶1 + 𝐶𝑝−

𝐶𝑟𝐶1 + 𝐶𝑟

] 𝑉𝑐(𝑡) +𝐶𝑝

𝐶1 + 𝐶𝑝𝑉𝑠(𝑡) (5.6)

In order to extract the induced voltage from the bridge output signal, the bridge should be

balanced by selecting the appropriate bridge elements such as C1 and Cr. Frequency analysis of

the obtained self-induced signal would reveal information about the resonance frequencies of the

system. Being able to have an insight into the resonance frequencies of the system, the effect of

adsorbed mass on the MC surface can be analyzed running the system in dynamic mode.


In order to solve the obtained governing equations of motion, Eq. (5.3), it is discretized using

Galerkin’s method (Gurjar and Jalili, 2007, Faegh et al. 2010). For this, the PDE (5.3) is

converted into ODE using the following discretization:

𝑤(𝑥, 𝑡) = ∑𝜙𝑗(𝑥)

𝑛

𝑗=1

𝑞𝑗(𝑡), 𝑗 = 1,2, … . . , 𝑛 (5.7)

with φj(x) and qj(t) being the clamped-free beam eigenfunction and generalized coordinates,

respectively. Therefore, the equation of motion can be expressed as a function of time in a matrix

form. The ODE for the system can be then represented as:

76

𝑀��(𝑡) + ��(𝑡) + 𝐾𝑞(𝑡) = 𝐾 𝑉(𝑡) (5.8)

where

𝑞 = {𝑞1, 𝑞2, … . 𝑞𝑖} , �� = {��1, ��2, … . ��𝑖}

𝑀 = {𝑀𝑖𝑗}, 𝑀𝑖𝑗 = ∫ 𝜌𝐴(𝑥)𝐿

0

𝜙𝑗(𝑥)𝜙𝑖(𝑥)𝑑𝑥, , 𝑗 = 1,2, … . . , 𝑛

= { 𝑖𝑗}, 𝑖𝑗 = 𝐵∫ 𝜙𝑗(𝑥)𝜙𝑖(𝑥)𝐿

0

𝑑𝑥 + 𝐶∫ 𝜙𝑗′(𝑥)𝜙𝑖(𝑥)

𝐿

0

𝑑𝑥

𝐾 = {𝐾𝑖𝑗}, 𝐾𝑖𝑗 = ∫ 𝐸𝐼(𝑥)𝜙𝑗′′(𝑥)𝜙𝑖

′′(𝑥)𝐿

0

𝑑𝑥

−𝑀 0

𝐶1 + 𝐶𝑝𝐾𝑠[𝜙𝑗

′(𝐿1) − 𝜙𝑗′(0)][𝜙𝑖

′(𝐿1) − 𝜙𝑖′(0)]

𝐾 = {𝐾 𝑗}, 𝐾 𝑗 = −𝑀𝑝0∫ 𝜙𝑗′ (𝑥)𝛿(𝑥 − 𝐿1)

𝐿

0

𝑑𝑥 = −𝑀𝑝0𝜙𝑗′ (𝐿1)

(5.9)

Table 5.1 The system parameters used for modeling.

Parameters Value Units

L 486 μm

L1 325 μm

L2 360 μm

b 50 μm

tb 4 μm

tp 4 μm

ρb 2,330 kgm−3

ρp 6,390 kgm−3

Eb 105 GPa

Ep 104 GPa

d31 11 pC/N

77

The system parameters used for simulation are listed in Table 5.1. The forced vibration problem

represented by ODE (5.8) was solved in Matlab with the input being the applied voltage to the

ZnO stack mounted on active probes.

A harmonic voltage with the amplitude of 2.5 Volts and frequency close to system’s first natural

frequency was applied and the system’s generalized coordinates for at least two modes, 𝑞1(𝑡)

and 𝑞2(𝑡) were obtained. 𝜙𝑖(𝑥) was selected to be the admissible function of a clamped-free

beam with the modified mass and stiffness properties of a beam with piezoelectric layer. The

values of C1 and Cr were selected to be 30 pF. The deflection of MC with respect to location and

time, w(x,t), was calculated using Eq. (5.7).

Consequently, deflection of the tip of the MC, w(L,t), output voltage, 𝑉0(𝑡), and self-induced

voltage, 𝑉𝑠(𝑡), were obtained and plotted in Figure 5.4(a,b). Taking the FFT of the system’s

response, the first natural frequency of the system was obtained to be 52.99 kHz as illustrated in

Figure 5.4(c). The effect of ultrasmall adsorbed mass was modeled as added surface mass over

the gold-coated MC surface, length of 0-L1. The amount of adsorbed mass was assumed to be as

low as 200 ng which resulted in the reduction of the 1st natural frequency to the amount of 1.8

kHz. The shift in natural frequency is depicted in Figure 5.4(d).

Sensitivity of vibration amplitude of the MC tip with respect to the selected C1 was also studied

and it was shown that the amplitude of tip vibration increased by increasing the value of C1 as

shown in Figure 5.5.

5.3. Adaptive Estimation

This section adopts an adaptation law to compensate for variation of piezoelectric material.

Numerical simulations using this law is performed and presented as follows.

78

(a) (b)

(c) (d)

Figure 5.4 Numerical results: (a) tip deflection of microMC, w(L,t), (b) Input voltage, Vc(t),

output voltage, V0(t), and self-induced voltage, Vs(t), (c) FFT response of the system with 1st

natural frequency highlighted, (d) the effect of added surface mass due to functionalization

on the first natural frequency (Faegh et al. 2013a).

0 0.002 0.004 0.006 0.008 0.01-400

-300

-200

-100

0

100

200

300

400

Time (s)

Tip

Deflection w

L (

nm

)

0 0.01 0.02 0.03 0.04 0.05

-2

-1

0

1

2

Time (ms)

Voltage (

V)

Vc

V0

Vs

50 51 52 53 54 55 560

2

4

6

8

Frequency (kHz)

Tip

Am

p.

of

Vib

ratio

n (

nm

)

X: 52.99 kHz

Y: 9.573 nm

50 51 52 53 54 55 560

2

4

6

8

Frequency (kHz)

Tip

Am

p.

of

Vib

ratio

n (

nm

) X: 51.19 kHz

Y: 7.611 nm

X: 52.99 kHz

Y: 9.573 nm

200 ng

79

Figure 5.5 Sensitivity of the vibration amplitude of the tip of MC with respect to C1.

5.3.1. Adaptation law

Considering the fact that the properties of the piezoelectric materials vary with ambient

temperature and time, compensating for these variations would dynamically improve the

proposed self-sensing implementation. An adaptive compensatory self-sensing strategy (Law et

al. 2003) is utilized in order to estimate the variations of the capacitance of piezoelectric

material, Cp, with respect to time.

In order to compensate for time variation of Cp, a parameter called θ is defined which is the ratio

of impedances in the bridge as follows:

=𝐶𝑝

𝐶1 + 𝐶𝑝 (5.10)

The estimation of the measured parameter θ is defined to be which needs to be obtained. In

order to find the estimated parameter, , a parametric error is defined as = − which should

be driven to zero. Figure 5.6 shows the schematic of the adaptive self-sensing strategy. Ψ(t) is a

low power persistent excitation signal which is applied to measure . It should be low enough

such that it does not introduce vibration in the MC and contribute to the self-induced voltage.

0 200 400 600 800 1000 12000.01

0.015

0.02

0.025

0.03

0.035

0.04

C1 (pF)

Tip

Am

p.

of

Vib

ration (m

)

80

Referring to Figure 5.6, the voltage of the upper branch of the bridge can be written as:

𝑉1 = (𝑡) (5.11)

with 𝑉1 being the estimation of 𝑉1 as:

𝑉1 = (𝑡) (5.12)

Therefore, the bridge output voltage can be expressed as:

Figure 5.6 Schematic of the adaptive self-sensing strategy (Faegh et al. 2010, 2013).

𝑉0(𝑡) = 𝑉1(𝑡) − 𝑉1(𝑡) = ( − ) (𝑡) = (𝑡) = 𝑒(𝑡) (5.13)

The proposed adaptation law for estimation of parameter θ is as follows (Law et al. 2003):

(𝑡) = − 1𝑒1 − 𝑃1(𝑡)

𝑒12 (5.14)

which can be further simplified as

(𝑡) = − 1 − 𝑃(𝑡) 2 (5.15)

where k1 and P(t) represent a constant gain and time-dependent adaptation gain, respectively.

The time-varying adaptation gain can be replaced by a constant gain in order to simplify the

calculation. Therefore, the update law can be simplified to

81

(𝑡) = − 1𝑒1 − 𝑃0

𝑒12 (5.16)

and consequently

(𝑡) = − 1 − 𝑃0 2 (5.17)

where P0 represents the constant adaptation gain (P0 > 0). Available references (Gurjar and Jalili,

2007) and (Law et al. 2003) provide more information regarding the implementation of this

adaptation law.

5.3.2. Simulation results for adaptive estimation

In this section, the equations of motion presented in Section 5.2.1. are simulated considering

the estimated time-varying piezoelectric capacitance, Cp obtained through implementing adaptive

estimation strategy. All other conditions are kept the same as those in Section 5.2.1. The

system’s response along the beam at any time, w(x,t), is obtained. Consequently tip deflection

and frequency response of the system are calculated and plotted as depicted in Figure 5.7.

(a) (b)

Figure 5.7 (a) Tip deflection of MC, wL(x,t), (b) FFT response of the system with 1st

resonance frequency highlighted.

45 50 55 60 650

0.2

0.4

0.6

0.8 X: 51.6Y: 0.872

Frequency (kHz)

Am

plit

ud

e (

nm

)

0 0.2 0.4 0.6 0.8-500

0

500

Time (ms)

Tip

De

fle

ctio

n,

wL (

nm

)

82

It is shown that the first natural frequency of the system is obtained to be 51.6 kHz, which is

about 1.3 kHz less than that obtained in Section 5.2.2. The contribution of the self-induced

voltage in the bridge output signal is dependent on the unknown gain defined as θ. A study was

conducted to investigate the effect of the defined θ on the reasonable and maximum contribution

of the 𝑉𝑠(𝑡). The result is depicted in Figure 5.8 demonstrating that by increasing θ, the

calculated self-induced voltage gets closer to the output voltage.

Figure 5.8 The effect of θ on the calculation of self-induced voltage, 𝑉𝑠(𝑡).

5.4. Experimental Setup

In this section, the capability of the self-sensing strategy is validated experimentally and the

results are compared with those obtained from the mathematical modeling presented in Sections

5.2 and 5.3. The same experiment was performed using a laser vibrometer as the read-out

method to verify the self-sensing measurement technique.

A Veeco Active Probe® was utilized with the self-sensing capability. A pure capacitive bridge

(Figure 5.3(a)) was used to send a harmonic voltage to the ZnO stack mounted at the base of

each probe and at the same time receive the output voltage as a result of MC vibration. The

Active Probe was mounted on a holder which was fixed on a 3D stage with submicron moving

-3 -2 -1 0 1 2 3

x 10-5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Time (s)

Vo

lta

ge

, (V

)

V0

Vs

= 0.7

= 0.8

= 1

= 2

= 0.55

= 0.6

= Cp/(C

p+C

1)

83

capabilities in x-, y-, and z-directions. Figure 5.9(a) shows the experimental setup for

implementing self-sensing strategy. The value of θ = 0.5 was used experimentally. The same

platform is placed under the laser vibrometer (Polytec CLV-2534) in order to measure MC

vibrations through optical method as shown in Figure 5.9(b).

(a) (b)

Figure 5.9 Veeco Active Probe mounted on a holder (a) connected to the pure capacitive

bridge for self-sensing implementation, (b) placed under laser vibrometer head.

5.4.1. Non-functionalized MC: verification with modeling

Measurement of the first resonance frequency of a non-functionalized MC was made in this

section implementing both self-sensing strategy and optical read-out systems. In order to obtain

the frequency at which the system resonates, the excitation frequency of system’s input was

swept from 0 kHz to 100 kHz with resolution of 10 Hz. The amplitude was kept at 2.5 V. Taking

the FFT of the output voltage obtained from the bridge, it was observed that the first resonance

frequency of the non-functionalized MC was captured at 51.50 kHz which is in a great level of

accuracy with the theoretical result obtained through implementing adaptive strategy. Having the

input voltage, Vc(t), and measuring the output voltage, V0(t), through the self-sensing bridge and

(a)

a

84

(a)

(b)

(c)

Figure 5.10 (a) FFT of the response of the system using self-sensing bridge, (b) Input, output

and self-induced voltages, (c) FFT of the response of the system using laser vibrometer.

0 50 100 150

-100

-80

-60

-40

-20

0

Frequency (kHz) A

mplit

ude (

V)

Self-sensing Circuit51.50kHz

-0.03 -0.02 -0.01 0 0.01 0.02 0.03

-2

-1

0

1

2

Time (ms)

Vo

lta

ge

(V

)

Vc

V0

Vs

0 50 100 150

-60

-40

-20

0

20

Frequency (kHz)

Am

plit

ude (

V)

Laser Vibrometer51.69 kHz

85

consequently calculating self-induced voltage, Vs(t), relatively similar results were obtained

compared to the theoretical part. Figure 5.10(a) shows the FFT of the response of the system

while Figure 5.10(b) shows input, output and self-induced voltages. Performing the same

experiment through a laser vibrometer, the resonance frequency of the system was captured to be

51.69 kHz which proves the capability of the self-sensing strategy with the precision of 99.63%.

The obtained frequency response is depicted in Figure 5.10(c). Table 5.2 shows a comparison

between the experimental results to theoretical ones obtained from Sections 5.2 and 5.3.

Table 5.2 Comparing the results obtained from mathematical modeling presented in Sections

2 and 3 with the experimental results.

First Resonance

Frequency,

wn1 (kHz)

Precision

(%)

Theory Section 5.2: Self-sensing 52.9 97.48

Theory Section 5.3: Self-sensing, Adaptive estimation 51.6 99.82

Experiment: Self-sensing 51.50 99.63

Experiment: Laser vibrometer 51.69 —

5.4.2. Functionalized MC: detection of adsorbed mass

In this section, the main application of the developed platform is tested. Same active probe

equipped with a self-sensing read-out mechanism was implemented to detect the adsorbed mass

over the gold surface. The system was operated in dynamic mode where the MC was brought

into excitation by applying a harmonic voltage to the self-sensing bridge with a frequency close

to system’s first resonance frequency.

Thiol groups which attach to many biomolecules were immobilized over the MC surface by

making a covalent binding to gold creating a self-assembled monolayer. The gold-coated surface

86

was washed in acetone, ethanol and DI water for 10 minutes. The main challenge in

functionalizing the self-sensing active probe is the integrated electronics on the base of the

probe. Therefore, washing and submerging it into any solution comes with the risk of damaging

or destroying the whole platform. In order to address this issue, a Teflon chamber was designed

such that creating any droplet of liquids over the chamber’s surface was made possible. The

Active Probe was then mounted on a holder and placed over a 3D stage with resolution of

submicron which was used to place MC tip into the droplet such that it does not wet any

electronics in the vicinity of the probe.

A 0.1M of aminoethanethiol solution was prepared by dissolving 2-aminoethanethanethiol

powder in deionized water. The tip of the MC was dipped into a droplet of the prepared solution.

As a result, self-assembled monolayer of aminoethanethiol was formed over the gold surface by

attachment of thiol groups to gold.

In order to find the frequency at which the system resonates after functionalization, the excitation

frequency was swept between 0-100 kHz. The response of the system was measured by both self-

sensing bridge and the laser vibrometer as shown in Figure 5.11. The amount of shift in the first

resonance frequency of the system was observed to be equal to 3.98 kHz and 3.69 kHz as

obtained from self-sensing bridge and laser vibrometer, respectively. Measurements were

performed multiple times and a frequency sweep was carried out each time. The standard

deviation was calculated to be 0.2098. The results obtained by the laser vibrometer reinforce

those obtained by the self-sensing bridge. However, there are certain limitations with

implementing laser vibrometer measurements in liquid media which can be addressed by

adopting the self-sensing platform.

87

(a) (b)

Figure 5.11 Shift in the first resonance frequency measured by (a) self-sensing bridge,

(b) Laser vibrometer.

The amount of absorbed mass can be quantitatively calculated implementing the mathematical

modeling framework presented in Sections 5.2 and 5.3. Comparison of the experimental results

to those obtained from Sections 5.2 and 5.3 verifies the accuracy of the mathematical models.

Adopting the mathematical modeling presented in this study the amount of adsorbed masses can

be quantified having the shifts in resonance frequency. Figure 5.12 shows the shift in the first

resonance frequency as a result of adsorbed mass utilizing the mathematical modeling

framework providing the relationship between the added mass and frequency change.

The amount of adsorbed mass measured with self-sensing circuit and laser vibrometer was

calculated to be 486.04 ng and 450.24 ng, respectively, utilizing this method of quantification.

The sensitivity of the reported platform was measured to be about 122 pg/Hz.

20 30 40 50 60 70 80

-60

-40

-20

0

20

Frequency (kHz)

Am

plit

ude (

V)

Unfunc.MC

Func. MC

48 kHz 51.69kHz

20 30 40 50 60 70 80

-100

-80

-60

-40

-20

0

Frequency (kHz)

Am

plit

ude (

V)

Unfunc. MC

Func. MC

47.52kHz 51.50kHz

88

Figure 5.12 Quantification of frequency shift as a result of adsorbed mass exploiting

mathematical modeling framework.


A unique laser-less MC-based sensor which utilizes a Veeco Active Probe as a piezoelectric MC

with self-sensing capabilities was proposed in this study. A pure capacitive bridge was designed

to implement the detection platform in the self-sensing mode where the system was excited by

applying a harmonic voltage to the piezoelectric layer which simultaneously produces output

voltage as a result of the system’s response. Utilizing the proposed platform, one self-sensing

bridge can be exploited for both exciting the system and measuring the response of the system,

thus eliminating the need for bulky and expensive optical based detection techniques.

Three main sections were presented for proving the concept of self-sensing methodology and

testing its capability to be used as a mass sensing platform. A comprehensive distributed-

parameters modeling framework was proposed for the self-sensing MC biosensor performing in

dynamic mode. Since piezoelectric properties of material vary at the nanoscale, an adaptation

law was exploited in order to compensate for the changes of piezoelectric properties of the ZnO

0 100 200 300 400 5000

1

2

3

4

5

Adsorbed mass (ng)

Fre

quency s

hift

(kH

z)

dw

r = 0.0081*dm + 0.043

Calculated

Linear curve fit

89

stack embedded in the active probe. Numerical simulations were carried out in Matlab and

presented. It was shown that the level of accuracy for measuring the fundamental resonance

frequency of MC increases from 97.48% to 99.82% using adaptation strategy. In order to utilize

the platform for mass sensing purposes, the capability of measurement system was compared and

verified with optical-based read-out and a 99.63% accuracy was illustrated.

Implementing the proposed platform as a biological sensor, an extensive experimental setup was

built to detect thiol groups immobilized over the MC surface. The shift in the first resonance

frequency as a result of mass adsorption was obtained through both optical and self-sensing

methods indicating the immobilization of mass over the MC surface.

The present study paves the way towards implementing such a system for detection of the

concentration of any type of biomolecules and further developing a laser-less, cost-effective and

portable diagnostic kit for any biomarker protein or biomolecule. It is planned to improve the

proposed platform with higher sensitivity and selectivity for detection of smaller proteins such as

PSA and myocardial infarction marker proteins, and also hybridization of DNA with the

implementation of sensor and reference MC in the diagnostic platform.

90

CHAPTER 6**

IMPLEMENTATION OF SELF-SENSING PIEZOELECTRIC MICROCANTILEVER

SENSOR AT ITS ULTRAHIGH MODE FOR MASS DETECTION

6.1. Introduction

The demand for detection of ultrasmall masses and biological species drives the need for

developing ultrasensitive MC-based sensors. Sensitivity has been recognized as one of the main

elements in the success of sensors. As far as sensitivity is concerned, several investigations have

been carried out to enhance the functionality of MCs. Two common operational modes of MC-

based techniques are static mode where changes in the surface stress is measured (Arntz et al.

2003, Pei et al. 2003,2004, Wu et al. 2001, Huber et al. 2007, Shua et al. 2008, Stiharu et al.

2005, A´ lvarez and Tamayo, 2005, Thaysen et al. 2001, Grogan et al. 2002, Yena et al. 2009,

Zhou et al. 2009, Cherian et al. 2005, Backmann et al. 2005, Zhang et al. 2006) and dynamic

mode where differences in resonance frequency of MC are detected (Campbell et al. 2007, Ilic et

al. 2001,2004, Lee et al. 2004, Thundat et al. 1995, Gupta et al. 2004, Ono et al. 2003, Ekinci et

al. 2004). It has been shown that operating MC in its dynamic mode provides higher sensitivity

compared to measurement of surface stress change in static mode. Introducing stress

concentration regions over MC surface has been proven to enhance sensitivity using finite

element modeling (Amarasinghe et al. 2009). Employing nanoparticle-enhanced MCs (Chaa et

al. 2009, Lee et al. 2009), assembling carbon nanotubes (He et al. 2006) and nanowires (Lee et

al. 2007) over MC surface have been reported to dramatically improve sensing capabilities and

**

The contents of this chapter may have come directly from our previous publication (Faegh et al. 2013c).

91

MC sensitivity. Geometrical modification of MCs has been proven both numerically (Finite

element methods) and experimentally to substantially affect MC sensitivity (Fletcher et al. 2008,

Lim et al. 2010, Loui et al. 2008, Morshed et al. 2009, Shin et al. 2008).

One of the most promising methods adopted for sensitivity enhancement was operating MC in

modes other than its fundamental resonance flexural mode. Higher quality factor thus higher

sensitivity was achieved resonating MC in its in-plane mode comparing to out-of plane

resonance mode as a result of decreasing liquid drag force (Tao et al. 2011). Using torsional and

lateral resonance of MCs was also reported to result in an order of magnitude higher mass

sensitivity compared to conventional fundamental flexural mode (Sharos et al. 2004, Xie et al.

2007). Resonating MC in high modes generally has been proven both numerically and

experimentally to increase quality factor thus sensitivity. Higher sensitivity was reported

operating MC in its second (Jin et al. 2006) and fourth (Dohn et al. 2005) resonance bending

mode for mass sensing applications. Operating MC in its seventh flexural mode resulted in two

orders of magnitude increase in sensitivity compared to its fundamental flexural mode as

reported by Zurich research laboratory group (Ghatkesar et al. 2007).

Although high mode resonating MC has been investigated and implemented as an effective

solution for sensitivity enhancement, there has not been any analytical distributed-parameters

modeling which addresses all dynamics and phenomenon of the system in its higher modes.

Conventional lumped-parameter model has been used correlating mass change to frequency shift

which is not capable of describing the behavior of system in its high modes. As a result, for the

first time in this study, we are presenting a comprehensive mathematical modeling for a

piezoelectric self-sensing MC biological sensor operating at its ultrahigh mode (20th

mode).

Effect of adsorbed mass on the frequency shift was investigated and reported analytically for

92

100 μm

a

high modes as well as fundamental and lower modes. Mode convergence theory was adopted in

order to get the best estimation of resonance frequencies at different modes.

An extensive experimental setup was developed operating the MC sensor at different resonance

modes. Veeco Active Probe® equipped with piezoelectric layer was used operating in dynamic

mode. A capacitance bridge network is utilized to implement the active probe in self-sensing

mode. Detection of ultrasmall adsorbed biological species, which is Amino groups of

aminoethanethiol solution, was made possible through the proposed self-sensing piezoelectric-

based MC sensor. Operating MC in high resonance mode and detecting the shift in high mode

resonance frequency, the quality factor was estimated and reported. Similar mass detection setup

was built and performed utilizing optical-based method comparing and verifying the capability

of the self-sensing platform for mass detection.

6.2. Mathematical Modeling

Distributed-parameter mathematical modeling is presented in this section using Extended

Hamilton’s principle for describing spatiotemporal behavior of self-sensing MC sensor. The MC

utilized is Veeco Active Probe® with extended piezoelectric layer embedded in its structure

which is adopted to implement the system in self-sensing mode. Figure 6.1 shows the MC used

L1

L2

L

b

Figure 6.1 (a) Veeco Active probe® used in this study for modeling and experiment, (b) schematic of

the beam used for modeling.

93

being hold on a base with piezoelectric (ZnO) layer which is gold coated on the surface. As seen

in the figure, MC is non-uniform in its cross section and depth which is all accounted for in the

comprehensive modeling presented. Euler Bernoulli beam theory is adopted in developing the

model. Using Euler Bernoulli beam theory was proven to model the current system with high

level of accuracy comparing to plate theory (Faegh and Jalili, 2013). Small deflection and linear

system properties are assumed. Other system properties and geometry are the same as those

presented in Chapters 4 and 5. Equation of motion of the system is derived using Extended

Hamilton’s principle. Using distributed-parameter modeling and assuming that beam only

extends in x-direction, kinetic and potential energies and virtual work of the system were derived

as shown in Eqs. (4.1- 4.10).

Using the pure capacitive bridge (Figure 5.3a) and exploiting the piezoelectric self-induced

voltage and ultimately output voltage of the system (Eqs. 5.1 and 5.2), the following equations of

motion for the self-sensing piezoelectric MC was derived

𝜌(𝑥)∂2𝑤(𝑥,𝑡)

∂𝑡2+

∂2

∂𝑥2[𝐸𝐼(𝑥)

∂2𝑤(𝑥,𝑡)

∂𝑥2] + 𝐵

∂𝑤(𝑥,𝑡)

∂𝑡+ 𝐶

∂2𝑤(𝑥,𝑡)

∂𝑥 ∂𝑡−

𝑝

𝑝+ 1𝑏𝐸𝑝𝑑31

(1

2(𝑡𝑏 + 𝑡𝑝) − 𝑦𝑛) [𝑤

′(𝐿1, 𝑡) − 𝑤′(0, 𝑡)]𝐺′′(𝑥) = −𝑀𝑝0𝑉𝑐(𝑡)𝐺′′(𝑥) (6.1)

with the boundary conditions

𝑤(0, 𝑡) = 𝑤′(0, 𝑡) = 0 (6.2a)

𝑤′′(𝐿, 𝑡) = 𝑤′′′(𝐿, 𝑡) = 0 (6.2b)

This equation is numerically solved and simulated at high modes in the following section.

6.3. Numerical Simulations and Results

Galerkin’s method (Gurjar and Jalili, 2007) is used to solve the obtained governing equations of

motion (Eq. 6.1). ODE is obtained using the following descretization

94

𝑤(𝑥, 𝑡) = ∑ 𝜙𝑗(𝑥)𝑛𝑗=1 𝑞𝑗(𝑡), 𝑗 = 1,2, … . . , 𝑛 (6.3)

where φj(x) and qj(t) are the clamped-free beam eigenfunction and generalized coordinates,

respectively. Using the above descretization in time and space, ODE for the system can be

expressed as

��(𝑡) + ��(𝑡) + 𝑞(𝑡) = 𝑉(𝑡) (6.4)

where , , , and were defined in Eq. (5.9).

System parameters used for simulation are provided in Chapter 5. Forced vibration problem

represented by ODE (6.3) was solved in Matlab with the input being a harmonic voltage applied

to the ZnO stack mounted on active probes. 𝜙𝑖(𝑥) was selected to be the admissible function of a

clamped-free beam with modified mass and stiffness properties of a beam with piezoelectric

layer. Values of C1 and Cr were selected to be 30 pF considering the effect of stray capacitances

in experiment.

The equation was simulated for different modes as high as 20th

mode and system’s response,

deflection of MC with respect to location and time, w(x,t) was calculated using Eq. (6.14).

Figure 6.2 Normalized Mode Shapes (MS) (a) MS 1-5, and (b) MS 4-7.

0 100 200 300 400 500-1

-0.5

0

0.5

1

MC Length (m)

Mo

de

Sh

ap

es

MS1

MS2

MS3

MS4

MS5

0 100 200 300 400 500-1

-0.5

0

0.5

1

MC Length (m)

Mode S

hapes

MS 4

MS 5

MS 6

MS 7

a b

95

In order to analyze the sensing characteristics of the system being implemented in dynamic

mode, resonance frequencies of the system should be obtained. Taking Fast Fourier Transform

(FFT) of system’s response, w(x,t), the resonance frequencies were obtained. Normalized mode

shapes were calculated and are partially (1st -7

th modes) depicted in Figure 6.2. FFT plot

illustrating first twenty resonance frequencies of the system is shown in Figure 6.3. Mode

convergence study was conducted calculating responses of the system in different modes and

monitoring the convergence of the resonance frequencies as number of modes, n, increases.

Table 6.1 shows the calculated resonance frequencies using n=12-28 order model illustrating the

convergence of resonance frequencies as increasing the model order. Based on convergence

theory, the type and number of trial functions influence the convergence of the approximate

solution to the actual one. If the trial function is appropriately selected (not a simple polynomial),

then it can be expected that the first 𝑛

2 solutions are accurate if running the system for n

th order

model. Therefore, in this study, the simulation runs for 20th

order model providing converged

and accurate solution for the first ten eignevalues.

Figure 6.3 FFT of the response of the system, 𝑤(𝑥, 𝑡) where n=20, depicting a) first 10 and b) next 10

resonance frequencies of the system.

0 2000 4000 6000 80000

0.005

0.01

0.015

0.02

0.025

Frequency (kHz)

Am

plitu

de (

nm

)

53

229

391

927

1472

7489

6116

4970

3886

29512024

10 15 20 25 300

1

2

3

4

5

x 10-3

Frequency (MHz)

Am

plitu

de

(n

m)

9.224

10.69

29.19

25.8122.4819.52

17.05

14.69

12.38

7.489

Excitation Freq.a b

96

Simulation was performed for different amount of masses immobilized over MC surface on its

active area which is gold coated (length 0-L1). Masses in the range of 10 pg-10 μg were assumed

to be immobilized and simulation was carried out for 20th

mode which have been proven to

produce converged results. The shift in the resonance frequency as a result of each amount of

mass immobilization was calculated for each mode running the system for n=20. Figure 6.4

shows the frequency shift plots versus different immobilized mass for some modes.

Table 6.2 shows the frequency shift as a result of mass immobilization for all modes 1st -20

th. It is

clearly shown that sensitivity of mass detection increases with the number of modes. In order to

Table 6.1. Calculated resonance frequencies using different order model (n).

Resonance Frequencies (kHz)

Mode n=12 n=14 n=15 n= 16 n= 17 n=18 n= 20 n= 22 n= 24 n= 26 n= 28

1 53 53 53 53 53 53 53 53 53 53 53

2 231 231 230 230 230 230 229 230 227 227 227

3 394 394 393 393 393 393 391 393 391 390 390

4 929 929 928 928 928 927 927 927 927 927 927

5 1482 1474 1474 1474 1474 1474 1472 1471 1464 1463 1456

6 2041 2031 2028 2028 2028 2026 2024 2023 2020 2019 2016

7 3002 2990 2971 2969 2964 2956 2951 2946 2946 2945 2945

8 3975 3930 3909 3895 3895 3890 3886 3881 3875 3873 3866

9 5145 4994 4990 4987 4978 4971 4970 4967 4962 4960 4956

10 6714 6357 6231 6216 6200 6143 6116 6081 6077 6074 6073

11 8481 7901 7634 7548 7548 7519 7489 7470 7469 7467 7463

12 10240 9755 9488 9328 9251 9238 9224 9212 9212 9210 9207

13 11930 11680 11390 11050 10770 10690 10570 10550 10530 10530

14 14150 13960 13540 12990 12570 12380 12330 12310 12300 12300

15 16160 15850 15420 15080 14690 14630 14580 14580 14570

16 18420 18210 17900 17050 16430 16380 16290 16290

17 21020 20790 19520 18620 18510 18440 18420

18 23510 22480 21640 21160 21120 21030

19 25810 24910 23710 23410 23320

20 29190 28270 26720 26010 25940

97

better visualize the increase of sensitivity with mode number, shift in the resonance frequency

versus mode number is plotted in Figure 6.5 for different amount of mass immobilization.

6.4. Experimental Setup and Results

In this section, an experimental setup was built in order to i) verify the functionality of self-

sensing method to measure high mode responses of the system, and ii) implement the self-

sensing platform to detect ultrasmall adsorbed mass over MC surface. Veeco Active Probe®

equipped with piezoelectric layer (ZnO stack) was utilized to operate the system in self-sensing

mode (self-excitation/self-sensing) through using a capacitance bridge network. The active probe

was mounted on a holder which was fixed on a 3D stage. Figure 6.6(a) shows the experimental

setup for implementing self-sensing strategy. The same platform is placed under laser vibrometer

(Polytec CLV-2534) in order to measure MC vibrations through optical method as shown in

Figure 6.6(b).

The excitation frequency was swept between 1 kHz to 10 MHz and the resonance frequencies

were captured using both self-sensing and optical methods. Resonance frequencies up to tenth

mode were measured using self-sensing method. On the other hand, resonance frequencies were

measured using optical method running the system up to its third mode. Higher resonance modes

could not be captured due to the limitations of the available version of laser vibrometer.

98

5950 6000 6050 61000

2

4

6

8

10

x 10-3

Frequency (kHz)

Am

plit

ud

e (

nm

)

dM=0 g

dM=1 ng

dM=5 ng

dM=10 ng

dM=20 ng

dM=50 ng

dM=100 ng

dM=10 g

6115

61166112

6108

6100

6038

6077

5930

7380 7400 7420 7440 7460 74800

2

4

6

8

10

12

x 10-4

Frequency (kHz)

Am

plit

ude (

nm

)

dM=0 g

dM=1 ng

dM=5 ng

dM=10 ng

dM=20 ng

dM=50 ng

dM=100 ng 7429

7370

7489

7488

7483

7477

7465

9100 9150 92000

1

2

3

4

5

x 10-3

Frequency (kHz)

Am

plit

ud

e (

nm

)

dM=0 g

dM=1 ng

dM=5 ng

dM=10 ng

dM=20 ng

dM=50 ng

dM=100 ng

9196

9154

90869217

922292249210

14.45 14.5 14.55 14.6 14.65 14.70

2

4

6

8

x 10-3

Frequency (MHz)

Am

plit

ud

e (

nm

)

dM=0 g

dM=1 ng

dM=2 ng

dM=5 ng

dM=10 ng

dM=20 ng

dM=50 ng

dM=100 ng

14.68714.685

14.682

14.662

14.638

14.56514.446

14.675

Figure 6.4 Frequency shift as a result of different amount of mass immobilization on (a) 10th mode, (b)

11th mode, (c) 12

th mode, (d) 15

th mode, with n=20.

5 10 15 20

0

200

400

600

800

1000

1200

1400

1600

Mode Number

Resonance F

req.

Shift

(kH

z)

6 8 10 12 14 160

20

40

60

80

100

120

140

Mode Number

Resonance F

req.

Shift

(kH

z)

Figure 6.5 Shift in resonance frequency calculated for different mode numbers as a result of different

amount of mass immobilization.

dM=1ng

dM=2ng

dM=5ng

dM=10ng

dM=20ng

dM=50ng

dM=100ng

dM=10μg

a b

a b

c d

99

Shift in Resonance Frequency (kHz)

Mode# 1 ng 2 ng 5 ng 10 ng 20 ng 50 ng 100 ng 10 μg

1 0 0 0 0 0 1 1 28

2 0 0 0 0 0 1 1 79

3 0 0 0 1 1 3 6 133

4 0 0 1 2 3 7 15 71

5 0 0 1 1 3 7 14 177

6 0 1 2 3 6 15 29 430

7 0 1 2 4 8 21 43 92

8 0 1 3 5 11 27 52 432

9 1 2 4 7 14 34 68 764

10 1 2 4 8 16 39 78 186

11 1 3 6 12 24 60 119 688

12 2 4 7 14 28 70 138 1148

13 1 2 6 12 24 60 118 301

14 2 4 10 21 40 99 195 851

15 2 5 12 25 49 122 242 974

16 3 6 14 28 55 135 266 1628

17 4 7 17 35 69 170 334

18 4 8 21 43 86 215 423

19 5 11 26 52 104 256 504

20 6 12 30 60 120 297 583

Table 6.2. Shift in the resonance frequency as a result of mass immobilization (1 ng-10 μg)

for all modes 1st-20

th.

Table 6.3 Resonance frequencies running the system

in its tenth mode calculated theoretically and

measured experimentally.

Resonance Frequencies (kHz)

Theory Experiment

Self-Sensing

Experiment

Optical

Quality

Factor

wr1 53 48.16 48.31 126.94

wr2 229

wr3 391 320.6 321.1 144.5

wr4 927 908.6 910.9 180.55

wr5 1472 1123

wr6 2024 1935

wr7 2951 2840

wr8 3886 3611

wr9 4970 4803

wr10 6116 5667

wr11 7489 6908

100

Figure 6.7(a) shows the resonance frequencies running the system in its tenth mode while

measuring system’s response through self-sensing bridge. Similar study was conducted using

laser vibrometer measuring resonance frequencies up to third mode, as shown in Figure 6.7(b)

which verifies the results obtained by self-sensing method. Table 6.3 shows a comparison

between the calculated resonance frequencies using distributed-parameters modeling and

measured resonance frequencies experimentally (self-sensing/optical). It was observed that the

proposed mathematical model was able to approximately predict the resonance frequencies

measured experimentally with a reasonable level of accuracy. Quality factor was calculated for

the first three modes measured optically as listed in Table 6.3. Higher quality factor was

observed with increasing the number of modes therefore higher sensitivity is expected at higher

modes.

(a)

Figure 6.6 Veeco Active Probe mounted on a holder (a) connected to the pure capacitive bridge

mounted on a bread board for self-sensing implementation, (b) placed under laser vibrometer head.

a

b

101

Once the capability of the self-sensing platform to measure system’s response was verified both

with optical method and theoretical result, the platform was implemented as a mass sensor to

detect added ultrasmall adsorbed mass. For this purpose, Amino groups of aminoethanethiol was

immobilized over MC on the gold surface. 2-aminoethanethiol was purchased from Sigma.

Active Probe was first washed in acetone and ethanol for 10 minutes. A Teflon chamber was

designed in order to dip the MC into a droplet of liquid such that it only wets the MC and does

not proceed to the electronic circuits. A 3D stage with resolution of submicron was used in order

to navigate MC in x-, y-, and z-direction and place it into the liquid.

A 0.1M of aminoethanethiol solution was prepared by dissolving 2-aminoethanethiol powder

into deionized water. A single layer of aminoethanethiol was formed on the gold surface by

attachment of thiol groups to gold. The change in resonance frequencies is measured both by

self-sensing and optical methods and recorded. Figures 6.8 and 6.9 illustrate the change in

resonance frequencies as a result of mass immobilization over MC surface measured by self-

0 1000 2000 3000 4000 5000 6000 7000

-100

-80

-60

-40

-20

0

Frequency(kHz)

Am

plit

ude (

dB

V)

6908

5667

3611

1935

1130

2840 4803

48.16

320.6910

0 500 1000 1500-80

-60

-40

-20

0

20

Frequency (kHz)

Am

plit

ude (

dB

V)

48.31 321.1

910.9

Figure 6.7 Resonance frequencies measured by (a) self-sensing method running the system in its tenth

mode, (b) laser vibrometer running the system in its third mode.

a b

102

sensing circuit and laser vibrometer respectively. A high level of accuracy was observed

comparing the resonance frequency shifts measured by self-sensing and optical methods.

It was observed that the shift in resonance frequency as a result of a definite amount of mass

immobilization increases with increasing number of modes. Figure 6.10 illustrates the amount of

increase in frequency shift for the first three modes of vibration indicating the accuracy of the

reported self-sensing platform to detect absorbed mass over MC surface. It is clearly shown that

the sensitivity of measurement in detection of frequency shift increases with the number of

modes. Correlating the amount of frequency shift obtained experimentally to the theoretical

results, the amount of immobilized mass can be estimated to be about 1-2 µg.

20 30 40 50 60 70-100

-80

-60

-40

-20

0

20

Frequency(kHz)

Am

plit

ude (

dB

V)

Unfunc. MC

Func. MC45.20 47.80

150 200 250 300 350 400 450 500-100

-80

-60

-40

-20

0

20

Frequency(kHz)

Am

plit

ude (

dB

V)

Unfunc. MC

Func. MC317.5 333.0

400 600 800 1000 1200 1400

-80

-60

-40

-20

0

20

Frequency(kHz)

Am

plit

ude (

dB

V)

Unfunc. MC

Func. MC910.0874.2

Figure 6.8 Shift in the resonance frequencies in the a) first mode, b) second mode, and c) third mode of

vibration measured by self-sensing platform.

a b

c

103

0.02 0.03 0.04 0.05 0.06 0.07 0.08

-60

-40

-20

0

20

40

Frequency (kHz)

Am

plit

ude (

dB

V)

Unfunc. MC

Func. MC47.82

45.42

250 300 350 400 450

-80

-60

-40

-20

0

20

Frequency (kHz)

Am

plit

ude (

dB

V)

Unfunc. MC

Func. MC319.1 332.0

700 800 900 1000 1100 1200

-100

-80

-60

-40

-20

Frequency (kHz)

Am

plit

ude (

dB

V)

Unfunc. MC

Func. MC877.1910.8

Figure 6.10 Increase in frequency shift with the

first three modes of vibration measured with self-

sensing platform and laser vibrometer.

Figure 6.9 Shift in the resonance frequencies in the a) first mode, b) second mode, and c) third mode of

vibration measured by laser vibrometer.

a b

c

02.4

12.9

15.5

32.9

35.8

Fre

qu

en

cy S

hift

(kH

z)

Self-Sensing measurement

Optical measurement

wr2

wr3

wr1

104


Sensitivity enhancement of MC-based systems being one of the key elements in success of any

sensor has been investigated extensively. Different studies were conducted to enhance the

sensitivity of any type of MC systems including geometry modification, exploiting nanoparticles

and carbon nanotubes in the structure of the system, and resonating MCs in vibration modes

other than flexural mode such as lateral and torsional modes. Resonating MCs in high modes has

been one of the most promising approaches in sensitivity enhancement through increasing

quality factor.

A comprehensive mathematical model was presented in this study which extensively describes

the dynamics and behavior of MC operating at its ultrahigh mode. Distributed-parameters

modeling using Extended Hamilton’s principle was developed for MC-based sensor being

implemented in self-sensing mode. Mode convergence theory was used to accurately estimate

the resonance frequencies of the system at high modes. Extensive numerical simulations using

Matlab were carried out for the proposed model and also to investigate the effect of mass

immobilization over MC surface.

A complete experimental setup was built in order to verify the theoretical modeling framework.

Laser vibrometer was utilized in order to optically measure the response of MC up to its third

mode. The results were compared to self-sensing methodology thus verifying the capability of

self-sensing method to characterize system’s behavior at high modes. The system was then

implemented as a biosensor for detection of ultrasmall mass which was Amino groups of

aminoethanethiol solution being immobilized over MC surface. The shift in the resonance

frequencies were measured and plotted and the amount of mass adsorption was then estimated

105

utilizing the mathematical modeling framework. It was proved that resonating MC at modes

higher than its fundamental mode would clearly increase the sensitivity of the system to detect

the adsorbed mass as a result of increase in quality factor of the system.

106

CHAPTER 7††

DETECTION OF GLUCOSE IN A SAMPLE SOLUTION USING THE DEVELOPED

SELF-SENSING PLATFORM

7.1. Introduction

Reducing the dimensions of electromechanical systems to micro- and nano-scale has enabled the

identification of biological molecules utilizing mechanical biosensors. High-throughput

diagnosis and analytical sensing require advanced biosensing tools exploiting high affinity of

biomolecules. There are a number of useful biosensing techniques such as electrophoretic

separation where spatiotemporal separation of analytes is possible. Another important technique

is identifying the changes in the mass or optical properties of target proteins using spectrometric

assays. Identification and quantification of target biomolecules due to high affinity which is

based on molecular recognition has been known as one of the most reliable biosensing

mechanisms.

There are two main elements in a biosensor which are i) sensitive biological receptor probe

which interacts with target proteins and ii) transducer which transforms the molecular

recognition into detectable physical quantity. There are a number of instruments equipped with

these elements developed for biodetection such as quartz crystal microbalance (QCM), surface

plasmon resonance (SPR), enhanced-Raman spectroscopy, field effect transistors (FET) and MC-

based biosensors. Among these techniques, MC-based biosensors have emerged as an

outstanding sensing tool for being highly sensitive, label-free, and cost effective (Arntz et al.

††

The contents of this chapter may have come directly from our previous publication (Faegh et al. 2013b).

107

2003, Pei et al. 2003,2004, Shin and Lee, 2006, Shin et al. 2008, Sree et al. 2010a,b, Wu et al.

2001, Yang and Chang, 2010). Detection of proteins and pathogens, physical parameters,

(Corbeil et al. 2002, Lee, C., and Lee, G., 2003), and biochemical agents, (Pinnaduwage et al.

2004, Tang et al. 2004, Ji et al. 2000, 2001, Ilic et al. 2001, Zhang and Feng, 2004, Gupta et al.

2004), has been enabled utilizing this type of sensors. All MC-based sensors are equipped with a

read-out device which is capable of measuring the mechanical response of the system. There are

a number of conventional read-out systems among which optical based measurement is the most

commonly used. They have been widely used in AFM and measure the mechanical changes of

the system by calculating the difference of the angle of laser beam reflected from the surface of

the MC. Even though being sensitive, there are certain limitations with this technique which are

mainly high cost, being bulky and surface preparation requirement. Moreover, laser alignment

and adjustment and the requirement of the sample solution and liquid chamber to be transparent

imposes serious challenges for adopting such a method as a read-out device in molecular sensing

tools.

In order to address all the aforementioned challenges, we are proposing a unique self-sensing

technique where a single piezoelectric layer deposited over MC surface performs as both an

Figure 7.1 Veeco Active Probe® with ZnO self-sensing layer deposited on the probe.

ZnO stack (consisting of 0.25µm

Ti/Au, 3.5µm ZnO, 0.25µm Ti/Au)

1 - 10 Ocm

Phosphorus (n)

doped Si

500 µm

108

actuator and sensor. Direct piezoelectric property is used to sense the self-induced voltage

generated in the piezoelectric layer as a result of beam deformation. At the same time, inverse

property of piezoelectric material is used to generate deformation and bring the system into

vibration as a result of applying a harmonic voltage to it. Therefore, a single piezoelectric layer

embedded in the MC sensor is utilized to both actuate and sense the system through

implementing a resonating circuit. This provides a simple and inexpensive platform for mass

sensing and detection purposes with opportunity of miniaturizing the platform. The piezoelectric

MC used is Veeco Active Probe with a ZnO stack embedded in MC providing the self-sensing

capability as shown in Figure 7.1.

There are two main operational modes of MC-based sensors which are i) static and ii) dynamic

modes. Most of the studies regarding identification of molecular affinities have been performed

in the static mode where the induced surface stress as a result of deflection of MC from a stable

baseline is used to measure molecular binding, (Pei et al. 2003, 2004, Wu et al. 2008, Shua et al.

2008, Stiharu et al. 2005, Thaysen et al. 2001, Grogan et al. 2002, Yena et al. 2009, Zhou et al.

2009). Arrays of MCs have been used for high-throughput measurements, (Arntz et al. 2003,

Huber et al. 2007, A´ lvarez and Tamayo, 2005, Thaysen et al. 2001, Cherian et al. 2005,

Backmann et al. 2005, Zhang et al. 2006). On the other hand, in dynamic mode, the system is

brought into excitation at or near its resonance frequency, (Ruzziconi et al. 2012). The shift in

the resonance frequency as a result of molecular recognition yields a good insight into the

amount of adsorbed mass. Different studies have been conducted enhancing the sensitivity of

MEMS, (Faegh et al. 2013c, Jin et al. 2006). In a study by Zhang and Turner, (2005a,b),

parametric resonance-based mass sensing was reported measuring dc offset instead of frequency

shift resulting in 1-2 orders of magnitude sensitivity enhancement.

109

One important factor determining the success of all biological sensors performing based on

analytical sensing of high affinity of biomolecules is the ability of the sensor to operate in liquid

media with high sensitivity. However, high dampening and viscous effect of solutions indeed

imposes a burden on the performance of biological sensor in liquid environment. Some

approaches have been developed to overcome this challenge by i) operating the system in humid

gas-phase media, (Lee et al. 2009), and ii) dipping the sensing probe in the solution, and then

removing and desiccating it and finally doing the measurement, (Oliviero et al. 2008). However

these methods deviate from the reality, increase the interference of unspecific biomolecules, and

prohibit real-time and continuous monitoring.

This challenge is addressed in this study by operating the reported self-sensing biosensor in

dynamic mode in the liquid media by exciting the system in high frequency.

A self-sensing circuit is used to apply the voltage to MC. Circuit’s resonance frequency and the

shift of the resonance frequency as a result of the change in the capacitance due to molecular

binding is measured while operating the system in liquid, therefore allowing for rapid,

continuous, and highly sensitive measurement of molecular recognition.

In this study, the reported diagnostic kit is implemented for detection of concentration of glucose

in sample solution. An extensive experimental setup is built including a reference MC and a

sensor MC. Active surface of the sensor MC is functionalized with the receptor biomolecule

which is glucose oxidase (GoX) in this study. MCs are then exposed to different level of glucose

concentration and the limit of sensitivity is determined.

7.2. Materials and Methods

The reported diagnostic kit includes a reference MC to compensate for all background noises and

undesired interferences by allowing for measurement of differential response. One or more

110

sensor MC involve depending on the number of analytes to be measured. The MCs are mounted

in series and dipped in the Teflon chamber that is designed such that only MCs be exposed to the

solution without wetting the probe base with electronics attached.

In order to functionalize MC by enzyme layer, the active part of the MC surface is used which is

the extended electrode coated with gold. Gold is employed for immobilizing GoX enzyme which

is itself a receptor for biomolecules such as Glucose.

Materials: Glucose Oxidase (GoX), 8.0% glutaraldehyde, 2-aminoethanethiol were purchased

from Sigma. Deionized water was used for preparing solutions.

7.2.1. Immobilizing GoX over MC surface

Sensor MC was washed in acetone, ethanol and DI water consequently. A Teflon chamber was

designed in order to dip in the MC into a droplet of liquid such that it only covers the MC and

does not proceed to the electronics attached to the probe base. A 3D stage with resolution of

submicron was used in order to navigate the MC in x-, y-, and z-direction and place it into the

droplet.

A 0.1M of aminoethanethiol solution was prepared by dissolving 2-aminoethanethanethiol

powder into deionized water. MC was dipped into a droplet of the prepared solution for self-

assembled monolayer of aminoethanethiol to form on the gold surface by attachment of thiol

groups to gold.

An enzyme solution was then prepared by dissolving a definite amount of GoX into DI water

which was 5 mg/mL. 0.2% glutaraldehyde was used as a cross linking reagent being capable of

binding to both the enzyme and Amino groups of aminoethanethiol monolayer already formed

on the gold surface. Dipping MC in enzyme solution, the aldehyde groups of glutaraldehyde

111

react with the Amino groups at one end and with GoX at other ends letting layer of enzyme grow

over the surface.

Binding Detection: Veeco Active Probe is used as the self-sensing MC with the capability of

self-excitation through the ZnO stack mounted on the base of each probe (Figure 7.1).

7.2.2. Detection in air

Fundamental resonance frequency of the MC is measured employing two different measurement

systems which are i) laser vibrometer (Polytec CLV-2534, Figure 7.2(b)), and ii) self-sensing

circuit (Figure 7.2(a)). A harmonic voltage was generated through oscilloscope (Agilent Infinii

Vision 2000 X-Series-sw Oscilloscopes). The shift in the resonance frequency as a result of

molecular binding is then measured with both measurement systems and compared.

This process of detection serves two purposes which are: i) prove the capability of the self-

sensing circuit to detect the change of frequency as a result of adsorbed mass, and ii) calibrate

the mass detection in liquid by correlating the amount of adsorbed mass calculated from

Vin(t)

Vo(t)

Cp

Cr

V1

V2

C1

C1

Vs(t)

MicroCantilever

L

a

Figure 7.2 (a) Self-sensing circuit for actuating and sensing the system (b) MC mounted on a holder

placed over a 3D stage positioned under laser vibrometer head.

b

112

mechanical resonance frequency shift to the

circuits frequency shift as a result of variation

of capacitance of the molecular interface.

7.2.3. Detection in liquid

Even though the ultrasmall masses

functionalized over MC surface could be

detected through self-sensing circuit with ultrahigh sensitivity, measuring the shift in mechanical

resonance frequency of MC does not provide an effective tool for detection of marker proteins in

liquid environment due to high dampening effect. Instead, another sensitive method using the

capacitance of the gold electrodes was used. The circuit consisting of capacitor and inductor with

the MC element modeled as a capacitor and a voltage source resonates at a certain frequency.

The theoretical modeling for finding the resonance frequency of such a system can be developed

by calculating the equivalent impedance of the system.

In order to find the equivalent impedance of the circuit from the output port, the circuit shown in

Figure 7.2a is turned into the circuit illustrated in Figure 7.3 with Vx being an imaginary source

of voltage, Zc the impedance as a result of induced stray capacitance (Cc) and resistance (Rc)

from the connecting cable, Zp and Zr, the impedance resulting from other elements of the circuit

including capacitors (C1 and Cr) and inductor (L). Each of these impedances can be calculated as

follows

𝑝 =1

1𝑤𝑗+ 𝑝𝑤𝑗 (7.1)

𝑟 =1

1𝑤𝑗+1

1

(7.2)

𝑐 =1

1

+ 𝑤𝑗

(7.3)

Vx Zc

Zp

Zr

Ix

Vx Zeq

Ix

Figure 7.3 Circuit model to find equivalent

impedance, Zeq.

113

𝑒𝑞 =1

1

+

1

𝑝

(7.4)

with w being the frequency of the circuit. Based on the above equations, Zeq can be calculated

which is a complex function. Setting the imaginary part of Zeq to zero, the following equation is

obtained

[𝐴𝐹 + 𝐸𝐵] × [𝐶𝐺 − ] − [𝐴𝐸 − 𝐹𝐵] × [𝐶 + 𝐺] = 0 (7.5)

where A-H is given as follows:

𝐴 = −𝐶1𝑅𝑐𝑤 − 𝑅𝑐(𝐶1 + 𝐶𝑝)𝑤 + [1 − 𝐶1𝐿𝑤2]𝑤𝐶𝑐𝑅𝑐

2 − (𝐶1 + 𝐶𝑝)𝐿𝐶𝑐𝑅𝑐2𝑤3

𝐵 = 𝑅𝑐(1 − 𝐶1𝐿𝑤2) − 𝑅𝑐(𝐶1 + 𝐶𝑝)𝐿𝑤

2 + 𝐶1𝐶𝑐𝑅𝑐2𝑤2 + 𝐶𝑐𝑅𝑐

2𝑤2(𝐶1 + 𝐶𝑝)

𝐶 = −(𝐶1 + 𝐶𝑝)(1 − 𝐶1𝐿𝑤2)(𝑤 + 𝑤3𝐶𝑐

2𝑅𝑐2)

= −𝐶1(𝐶1 + 𝐶𝑝)(𝑤2 +𝑤4𝐶𝑐

2𝑅𝑐2)

𝐸 = 𝐶

𝐹 =

𝐺 = −(𝐶1 + 𝐶𝑝)(1 − 𝐶1𝐿𝑤2)𝑅𝑐𝑤 + 𝐶1(𝐶1 + 𝐶𝑝)𝑤

3𝐶𝑐𝑅𝑐2 − 𝐶1𝑤 − (𝐶1 + 𝐶𝑝)𝑤 − 𝐶1𝐶𝑐

2𝑅𝑐2𝑤3

− (𝐶1 + 𝐶𝑝)𝑤3𝐶𝑐𝑅𝑐

2

= −𝑅𝑐𝐶1(𝐶1 + 𝐶𝑝)𝑤2 + (𝐶1 + 𝐶𝑝)(1 − 𝐶1𝐿𝑤

2)𝑤2𝐶𝑐𝑅𝑐2 + (1 − 𝐶1𝐿𝑤

2) − (𝐶1 + 𝐶𝑝)𝐿𝑤2 +

(1 − 𝐶1𝐿𝑤2)𝑤2𝐶𝑐

2𝑅𝑐2 − (𝐶1 + 𝐶𝑝)𝑤

4𝐿𝐶𝑐2𝑅𝑐

2 (7.6)

Solving Eq (7.5) for w, the resonance frequency can be obtained which is a function of the

varying capacitance Cp.

Molecular affinity that occurs over the surface of MC resulting in the binding between receptor

and target biomolecule changes the capacitance of the MC element thus affects the value of Cp in

the circuit. The model presenting the effect of binding on the change in the total capacitance of

this element was shown by Tsouti et al. (2011). The total capacitance of the MC element shown

in the circuit can be modeled as three main capacitors in series including the capacitance of the

114

insulating layer, Cins, functionalization layer, Cbind, and diffuse layer, Cdif, as shown in Figure 7.4.

Therefore, total capacitance, Cp can be written as

1

𝑝=

1

𝑠+

1

𝑏 +

1

(7.7)

When binding occurs, the capacitance of the functionalization layer (Cbind) varies thus the total

capacitance Cp changes. The change in the capacitance of MC produces a detectable shift in the

resonance frequency of the circuit which can be calculated adopting the circuit modeling

presented in this study therefore providing qualitative and quantitative insight into the amount of

binding and consequently the concentration of target biomolecule in the solution.

The effect of different values of circuit’s elements which are capacitors and inductors (C1, Cr,

and L) on the sensitivity of the circuit to measure the change in resonance frequency was also

investigated. It was observed that decreasing the values of C1, Cr and L obviously increases

circuit’s sensitivity. Figure 7.5 (a) and (b) illustrates the effect of C1, Cr and L on circuits

sensitivity to measure shift in resonance frequency respectively. In order to optimize circuit’s

Cins

Cbind

Cdif

Cins

Cbind

Cdif

target

biomolecule

receptor

biomolecule

microcantilever

insulating layer

functionalization layer

Sample solution containing

target biomolecules

Figure 7.4 Schematic of a model of MC molecular probe interface biosensor including three

capacitors in series (Faegh et al. 2013b).

115

response, the values of circuit’s elements were chosen such that they fall in the sensitive region

based on the results illustrated in Figure 7.5.

7.3. Results and Discussions

One sensor and one reference MC were used in this study. The sensor MC was functionalized

with receptor biomolecule which was GoX while the reference MC was left unfunctionalized in

order to compensate for all non-specific binding, background noises and unwanted interferences.

7.3.1. Immobilized mass detection in air (Laser vibrometer and Self-sensing circuit)

The capability of the self-sensing circuit was first verified with the laser vibrometer measuring

0 50 100 150

-120

-100

-80

-60

-40

-20

0

Frequency (kHz)

Am

plit

ud

e (

V)

1st

Res., Unfinc. MC

1st

Res., GoX-Func. MC

44.3

31.8

50 100 150

-80

-60

-40

-20

0

20

40

Frequency (kHz)

Am

plit

ud

e (

V)

1st

Res., Unfunc. MC

1st

Res., GoX-func. MC

44.5

32

Figure 7.6 Fundamental resonance frequency of MC and shift in the resonance frequency in air as

a result of GoX functionalization measured with (a) self-sensing circuit, and (b) laser vibrometer.

Figure 7.5 Effect of values of (a) C1and Cr and (b) L on circuit’s sensitivity in detecting shift in resonance

frequency.

0 50 100 150

10-2

10-1

100

C1=Cr (pF)

Log(R

es.

Fre

q.

Shift)

(M

Hz)

L=16 HC

p1=20 pF, C

p2=30 pF

0.05 0.1 0.15

10-1

100

L (mH)

Lo

g(R

es.

Fre

q.

Sh

ift)

(M

Hz)

C1=C

r=18 pF

Cp1

=20 pF, Cp2

=30pF

a b

a b

116

the shift in the fundamental resonance frequency of MC as a result of GoX-functionalization.

The first resonance frequency of MC was measured with both self-sensing circuit and laser

vibrometer by applying a sinusoidal voltage with a sweeping frequency of 0-100 kHz. It was

measured to be 44.50 and 44.30 kHz by laser vibrometer and self-sensing circuit respectively.

The shift of 12.5 kHz was measured with both laser vibrometer and self-sensing circuit as a

result of GoX- functionalization. Figure 7.6 shows the FFT of the response of MC at its

fundamental resonance.

Utilizing a comprehensive distributed-parameters mathematical modeling framework that was

presented in Faegh and Jalili, (2013), Faegh et al. (2013a). the amount of mass immobilization

can be quantified having the shift in the resonance frequency. Adopting the mathematical

modeling and simulation illustrated in Figure 7.7 the frequency shift of 12.5 kHz correlates to the

mass immobilized over the surface of the amount of 1531 ng. This amount of mass detection was

further correlated to the shift of circuit’s

resonance frequency which was measured

in liquid media. Implementing such a

comprehensive modeling framework was

advantageous in calibrating the mass

detection in liquid when electrical response

of the system is utilized.

7.3.2. Immobilized mass detection in liquid

(Self-sensing circuit’s resonance)

Even though the reported self-sensing method

is capable of measuring small adsorbed masses

Figure 7.7 Quantification of amount of adsorbed

mass with respect to shift of mechanical

resonance frequency of system utilizing

comprehensive distributed-parameters

mathematical modeling framework, (Faegh and

Jalili, 2013, Faegh et al. 2013a).

0 100 200 300 400 5000

1

2

3

4

5

Adsorbed mass (ng)

Fre

quency s

hift

(kH

z)

dw

r = 0.0081*dm + 0.043

Calculated

Linear curve fit

117

with ultrahigh sensitivity, it does not produce

an effective method to detect target proteins in

liquid media due to high viscoelastic damping

and losses in the surrounding liquid. As a

result, the resonance frequency of the circuit

consisting of MC was monitored instead of

the mechanical resonance of MC. The

reported circuit consisting of capacitors and

inductor resonates at a certain frequency which

was modeled calculating the equivalent

impedance of the whole system. This resonance frequency was measured and recorded while

putting both sensor and reference MCs in DI water. The shift in the resonance frequency as a

result of GoX functionalization over the sensor MC was measured to be 2.612 MHz using the

resonance frequency of the circuit as shown in Figure 7.8.

7.3.3. Detection of marker protein in liquid (Self-sensing circuit’s resonance)

Different concentrations of glucose ranging from 500 nM to 200 μM was injected in DI water

and the resonance frequency of the circuit with both sensor and reference MCs was measured

after each injection while exciting MCs inside the sample solution. It was shown that increasing

the amount of glucose concentration in the liquid results in higher amount of shift in the

resonance frequency of the circuit with sensor MC. On the other hand the resonance frequency of

the circuit with reference MC does not change significantly. Figure 7.9 (a-e) depicts the

resonance frequency of the circuit for both sensor and reference MC as a result of glucose

injection.

Figure 7.8 Shift in the resonance frequency of

the self-sensing circuit consisting of MC as a

result of GoX functionalization over sensor MC

surface.

5 10 15 20

-80

-60

-40

-20

0

Frequency (MHz)

Am

plit

ude

Unfunc. MC

MC Func. with GoX

9.056.438

118

It is shown that the resonance frequency of the circuit with reference MC stays within 9.102-

9.106 MHz when implementing the system in solutions with different concentrations of glucose.

0 5 10 15 20

-80

-60

-40

-20

0

20

Frequency (MHz)

Am

plit

ude

0 M Glucose

Ref. MC

Sensor MC

6.438

9.104

2 4 6 8 10 12 14

-80

-60

-40

-20

0

Frequency (MHz)

Am

plit

ude

500 nM Glucose

Ref. MC

Sensor MC

6.407

9.102

5 10 15

-80

-60

-40

-20

0

20

Frequency (MHz)

Am

plit

ude

1 M Glucose

Ref. MC

Sensor MC

9.1066.401

5 10 15 20

-80

-70

-60

-50

-40

-30

-20

Frequency (MHz)

Am

plit

ude

100 M Glucose

Ref. MC

Sensor MC6.400

9.105

5 10 15

-80

-60

-40

-20

0

20

Frequency (MHz)

Am

plit

ude

200 M Glucose

Ref. MC

Sensor MC

6.400 9.103

a

c b

d e

Figure 7.9 Resonance frequency of the circuit consisting of sensor MC and reference MC and the

shift in resonance frequency in liquid as a result of injecting (a) 0 glucose, (b) 500 nM glucose, (c) 1

μM glucose, (d) 100 μM glucose, (e) 200 μM glucose (Faegh et al. 2013b).

119

On the other hand, detectable changes

were observed in the circuit with GoX-

functionalized MC. Figure 7.10 shows

the differential shift of circuit’s

resonance frequency between sensor and

reference MC with respect to glucose

concentration. No significant change of

resonance frequency was observed

injecting concentration of glucose higher

than 200 μM indicating the saturation of

functionalized surface of sensor MC.

The main and most dominant nature of the nonlinearity between glucose concentration and

frequency shift arises from the saturation of the sensing element. The response is the highest for

the first and second injection and then it saturates as more injections take place. Adopting the

theoretical circuit model presented in the previous section, the corresponding change of

capacitance as a result of molecular binding over the surface was calculated having the amount

of shift in circuit’s resonance frequency as is depicted in Figure 7.10.

Calibrating the system with the mechanical response obtained in the above section the mount of

mass adsorption was quantified and presented in table 7.1. Considering the fact that

physiological level of glucose in blood is about 4-20 mM, the present platform is capable of

detecting even lower amount of glucose with very high sensitivity.

Comparing to glucose studies where the amount of glucose concentration was measured

mechanically using MC in static mode, (Pei et al. 2003, 2004) and electrically using modified

Figure 7.10 Differential Shift in the resonance

frequency of the circuit with sensor and reference MC

(Δfref – Δfsensor) as a result of injecting different

concentrations of glucose (Faegh et al. 2013b).

0.5 1 100 200

29

35

3737

Glucose Concentration (M)

Diffe

rential F

req.

Shift(

kH

z) dC

p (pF)

1.69

1.66

1.47

(g/ml) 0.09 0.18 18 36

120

Circuit’s resonance

freq. Shift (kHz)

Amount of mass

adsorption (ng)

29 17.08

35 20.62

37 21.79

Table 7.1 Quantification of adsorbed mass with respect to circuit’s resonance frequency

calibrated by mechanical response of the system.

Detection of Glucose

Methodology Sensitivity Reference

MC-static mode, using

optical based read-out

0.2 mM Pei et al. Oak

ridge national lab.

(2003, 2004)

polytyramine-modified

gold electrode

1 μM Labib et al. (2010)

AuNanoparticle modified

electrode

180 μM Shan et al. (2010)

Glucose Oxidase–

graphene–chitosan

modified electrode

0.02 mM Kang et al. (2009)

MC, present self-sensing

method

0.5 μM Current study.

Table 7.2 comparison of detection limit of measuring glucose

concentration.

121

gold electrodes, (Labib et al. 2010), utilizing the self-sensing circuit provides a very simple,

laser-free, and cost effective MC-based platform with the capability of detection of glucose level

lower than its physiological limit with high sensitivity. Table 7.2 shows a comparison of the

amount of sensitivity utilizing the reported self-sensing technique to the other studies detecting

glucose.

There are certain limitations with the reported detection platform including the low dynamic

range which results from saturation of receptor biomolecules over the surface of MC. To address

this limitation two approaches are considered for the future work which are i) increasing the

surface area of the molecular interface resulting in higher number of immobilized receptor which

can be accomplished by utilizing a different molecular probe such as interdigitated electrodes or

depositing nanoparticles over MC surface, and ii) using a chemical solvent which only rebounds

GoX-glucose, and not the functionalized receptor molecules over the surface, therefore, making

MC reusable for a higher number of steps.


A unique piezoelectric MC-based biological sensor for detection of molecular binding was

reported in this study. Implementing a self-sensing circuit, the system was performed in

dynamic, self-sensing mode by exciting the piezoelectric MC and sensing its response

simultaneously. Utilizing the reported circuit, the need for bulky and expensive optical based

system was eliminated. Two MCs, one sensor and one reference MCs were implemented. The

sensor MC was functionalized by receptor enzyme, GoX, while the reference MC was left

unfunctionalized to compensate for all undesired interactions. In the first step of this study the

capability of self-sensing circuit to detect the functionalized mass (Amino groups and GoX) was

verified by comparing it to optical based measurement (laser vibrometer).

122

A high level of accuracy and sensitivity was observed monitoring the shift in the fundamental

mechanical resonance frequency of sensor MC. In order to detect the target molecules (glucose)

the system had to be operated in aqueous media. Therefore, the resonance frequency of the

circuit consisting sensor and reference MC was measured and monitored separately. Dipping

both MCs in solutions containing a certain level of glucose, binding occurs over the surface of

functionalized MC changing its capacitance thus shifts the measured resonance frequency

obtained from the circuit. On the other hand, the resonance frequency of the circuit consisting of

unfunctionalized reference MC does not change significantly.

A detectable shift in the resonance frequency of the circuit with sensor MC was measured and

reported when injecting different amount of glucose (500 nM-200 μM) in DI water. At the same

time, negligible changes in resonance frequency of the circuit with reference MC was reported

indicating the capability of the sensor to detect the molecular binding.

As a result, the reported biological sensor provides a very simple, cost-effective, and highly

sensitive platform aiming at being implemented as a diagnostic tool. Increasing the level of

sensitivity, testing selectivity, and operating the sensor in greater dynamic range with the

reported platform are under study.

123

CHAPTER 8

CONCLUSIONS AND FUTURE WORKS

8.1. Concluding Remarks

This dissertation presented the entire developmental process of a unique piezoelectric MC-based

sensor. Although MC-based biosensors have received a widespread attention for label-free

detection, there are not enough analytical studies investigating modeling and simulation of

piezoactive MC-based systems along with the relative experimental verifications. Most of the

studies implementing MC-based systems in specific applications exploited simple lumped

parameters modeling frameworks. On the other hand, the available sophisticated analytical

studies are not complementary with the relative experimental verifications. Therefore, in this

dissertation, an extensive investigation has been conducted on the piezoactive MC-based sensors

both on theoretical and experimental aspects. The whole developmental process of the sensor

that was presented in this dissertation includes the following important steps and developments.

1) Extensive mathematical modeling of piezoactive MC-based systems with different

applications,

2) Comparison of Euler-Bernoulli beam modeling and plate modeling of piezoelectric MC-

based sensors with experimental verification,

3) Reporting a unique self-sensing piezoelectric MC-based sensor for detection of ultrasmall

masses and biological species and comparison with optical based methods,

4) Exploiting adaptation strategy to compensate for variations of piezoelectric material,

124

5) Implementing the system at high modes for sensitivity enhancement including the

simulation and experimental results

6) Implementing the self-sensing platform for detection of different concentrations of

glucose,

7) Implementing the self-sensing platform as a gas sensor for detection of ethanol and water

vapors.

In Chapter 3, two piezoactive-based systems were investigated. Sys. 1 was defined to be

piezoresistive MC-based sensor operating in contact mode; whereas, Sys. 2 was a MC-based

PFM functioning on piezoelectric sample with tip excitation. An external periodic electric field

was applied between the conducting tip and the sample. The piezoelectric and piezoviscoelastic

deformation of the sample served as the source of excitation of the system.

These two systems were investigated extensively. Comprehensive mathematical modeling

framework were developed and simulated for the aforementioned systems. Extended

Hamiltonian’s principle was used and system’s response, deflection of MC, was obtained from

which contact tip force, change of resistivity of the piezoresistive patch, and consequently output

voltage of the system was calculated utilizing the developed model. Moreover, the effect of

length and location of piezoelectric layer over MC on the sensitivity of Sys. 1 was simulated. On

the other hand, the sensitivity of Sys.2 with respect to local spring constant of piezoelectric

sample was studies and presented. It was shown that the amplitude of vibration increased almost

linearly with spring constant of piezoelectric material. Moreover, it was observed that the

location of piezoresistive patch affects system’s amplitude significantly while it does not have a

noticeable influence on the shift of the resonance frequency of the system. The presented

125

modeling frameworks addressed the uncertainties and unmodeled dynamics which are required

for precise MC-based systems compared to lumped-parameters modeling.

One of the main areas of application of MC-based systems is their implementation as sensors.

Detection of ultrasmall masses and marker proteins has been made possible using MCs due to

their tremendous advantages including low cost, simplicity and sensitivity. The main focus of

this dissertation has been on development of a unique self-sensing piezoelectric MC-based

sensor for the purpose of detecting ultrasmall masses and biological species. The entire

developmental process is presented in this dissertation. A comprehensive mathematical modeling

framework was developed for the sensing platform. In the first step along that line, different

modeling methods were adopted and compared.

In Chapter 4, the piezoelectric MC-based system was modeled as a non-uniform rectangular thin

plate and also as an Euler-Bernoulli beam. Distributed-parameters modeling using Extended

Hamilton’s principle was adopted developing the equations of motions of the system. Free and

forced vibration problems were solved and simulated. The system was performed in dynamic

mode by self-excitation through applying voltage to piezoelectric layer. Fundamental resonance

frequency of the system was measured. The capability of the proposed system in detection of

ultrasmall masses was tested by measuring the shift in the resonance frequency as a result of

absorbed mass over MC surface. The amount of 2.33 kHz shift in resonance frequency was

observed as a result of adsorption of ~ 200 ng surface adsorbed mass illustrating a satisfying

level of mechanical sensitivity. Relative experimental setup was built to verify the theoretical

modeling frameworks. Veeco Active probe® was used to measure absorption of thiol groups

over MC surface. It was observed that both Euler-Bernoulli beam theory and plate theory were

adequate to predict the current system’s behavior with high level of accuracy.

126

Although the Euler-Bernoulli model also satisfied the explanation of dynamics and behavior of

the proposed platform in this case, it will not be sufficient for modeling other geometries of the

similar platform. Since geometry of MC in biosensors dramatically influences the sensitivity of

the system, there is always a need to optimize geometrical properties such as using shorter and

wider MCs. Therefore, having a comprehensive modeling framework describing all geometries

and designs of MC provides a powerful theoretical layout for such systems and explains the

necessity of modeling complexity and effort.

The main concept of developing a laser-free self-sensing MC-based sensor was discussed in

Chapter 5. A MC with a single piezoelectric layer embedded in its structure along with a pure

capacitive bridge was used to implement the system in self-sensing mode. Inverse piezoelectric

property was used to actuate the system by applying voltage to it. Simultaneously, system’s

response was sensed through direct piezoelectric property by measuring output voltage of the

bridge. As a result, the need for bulky and expensive external actuator and read-out systems was

eliminated resulting in an inexpensive, simple platform with miniaturization capability.

In order to have a thorough insight into the dynamics of the self-sensing mechanism, two

approaches were taken. First, a comprehensive distributed-parameters mathematical modeling

framework was developed for the aforementioned mechanism. The system was simulated and

solved in Matlab. Second, an adaption law was exploited to compensate for the variations of

piezoelectric property of the material used in MC with respect to temperature or other

environmental interferences. The system was again simulated using the adaptation strategy.

Finally, an extensive experimental setup was built to test and prove the capability of the self-

sensing mechanism. A pure capacitive bridge was built and attached to the piezoelectric MC

(Veeco active probe®). The system was performed in dynamic mode. A harmonic voltage was

127

applied to the bridge and at the same time, the output voltage of the bridge was measured and

monitored. Fundamental frequency of the system was measured taking FFT of system’s response

captured by self-sensing mechanism. The same procedure was repeated measuring system’s

response optically through laser vibrometer. A 97.50% precision of accuracy was observed

comparing the experimental results with those obtained from mathematical modeling. It was

shown that exploiting adaptation law, the precision of accuracy was improved to 99.98%. The

capability of the proposed self-sensing method was therefore proved with the theoretical results

and moreover, it was compared to optical based measurement. Comparing the measurements

from optical method to those from self-sensing technique, a 99.74 % precision of accuracy was

illustrated.

Sensitivity enhancement of the developed platform was extensively studied in this dissertation.

Sensitivity, being one of the most important elements determining the success of each sensor has

been investigated using different methods. Both numerical and experimental studies were

conducted for increasing sensitivity in MC-based systems. Techniques such as geometry

modification, exploiting nanoparticles and carbon nanotubes in the structure of the system, and

exciting MCs in vibration modes other than flexural mode (e.g. lateral and torsional modes) were

investigated. Resonating MCs in high modes has emerged as one of the most promising

approaches in sensitivity enhancement through increasing quality factor. Although being

investigated, there have not been enough analytical high fidelity models describing all dynamics

and behavior of MCs operating in high modes along with experimental verifications.

In Chapter 6 of this dissertation, a comprehensive mathematical modeling framework for

piezoelectric self-sensing MC operating at its ultrahigh mode (20th

mode) is presented. Changes

in resonance frequencies as a result of added mass is calculated for high modes as well as

128

fundamental and lower modes. Accurate level of estimation for resonance frequencies was made

adopting mode convergence theory. Extensive experiment was carried out operating MC at its

high mode using both self-sensing and optical measurement methodologies. The obtained results

are compared and verified with theoretical results. The same platform is used to detect

immobilized ultrasmall mass. Amino groups of aminothenethaiol solution are immobilized over

MC surface by covalent binding to gold. Shift in resonance frequencies in higher modes are

measured and the quality factor is calculated for each mode proving the fact that sensitivity of

MC to detect adsorbed masses was enhanced as the number of modes increased.

The ultimate goal of developing the self-sensing piezoelectric MC-based sensing platform was to

implement it as a biological sensor for detecting ultrasmall biological species in a sample

solution. Accomplishing the extensive analytical and numerical studies and proving the

capability of the self-sensing platform to perform accurately for measurement in Chapters 3-6,

the final step of the development which was the real implantation of the platform for detection

was precisely discussed in Chapter 7. The sensing platform involved two MCs. One MC was

implemented as the reference which was left unfunctionalized in order to compensate for all

unspecific interactions and background noises.

On the other hand, the sensor MC was functionalized with the receptor molecule specific to

target molecules to be detected. Detection of glucose was tested as the target molecule using

glucose oxidase as the receptor enzyme which was proved to have high affinity with glucose.

First, detection of functionalized receptors which were Amino groups and glucose oxidase was

reported using self-sensing platform and compared to the results measured optically by laser

vibrometer. Performing the system in dynamic mode, the shift in the fundamental mechanical

resonance frequency of sensor MC was measured with high level of accuracy comparing to

129

optical-based method. The system ought to operate in aquesous media for the second step of

measurement which was measuring different concentrations of glucose in a sample solution. Due

to high dampening effect and viscoelastic behavior of the surrounding media, the mechanical

responses of MCs did not provide a sufficient tool for this step of measurement. To overcome

this challenge, the resonance frequency of the circuit consisting of sensor and reference MCs

were monitored. Variation of circuit’s resonance frequency as a result of change of capacitance

due to molecular binding was studied following the model introduced by Tsouti et al. 2001.

Dipping both MCs in solutions containing a certain level of glucose, binding occurs over the

surface of functionalized MC changing its capacitance thus shifted the measured resonance

frequency obtained from the circuit. On the other hand, the resonance frequency of the circuit

consisting of unfunctionalized reference MC did not change significantly.

A detectable shift in the resonance frequency of the circuit with sensor MC was measured and

reported when injecting different amount of glucose (500 nM-200 μM) in DI water. At the same

time, negligible changes in resonance frequency of the circuit with reference MC was reported

indicating the capability of the sensor to detect the molecular binding. Extensive circuit modeling

was presented correlating the amount of frequency shift to the change of capacitance and

consequently to the added adsorbed mass.

As a result, a compact detection platform with the capability of miniaturization, low power

consumption, cost effective, and yet sensitive methodology is developed and reported in this

dissertation. The measurement capability of the platform both in air and aqueous media with the

simplest and most inexpensive actuation and sensing equipments was presented both

theoretically and experimentally.

130

8.2. Future Works

There are certain improvements on the developed sensing platform for future investigations

which are discussed as follows.

I- Sensitivity enhancement using geometrical modifications of MC such as

decreasing the size of MC provides a certain improvement in the functionality of

the sensing platform. Testing selectivity and operating the sensor in greater

dynamic range are other important improvements to be considered for future

investigations.

II- The entire research on the self-sensing piezoelectric MC that was presented in this

dissertation was performed on Veeco Active Probe® with the piezoelectric layer

that was embedded in the structure of the MC. These probes were designed for

AFM applications and were not optimized for sensing purposes. However, the

developed sensing platform was optimized using Veeco active probes in order to

remove the fabrication process and save time, effort and financial resources for

other aspects of developments which included: analytical study, numerical

simulation, designing and testing the platform. As a result, one important direction

for future improvements would be fabrication of MCs with designs and

geometries modified and optimized for the self-sensing platform and sensing

applications.

III- Moreover, High throughput analysis can be performed using arrays of MCs each

of which functionalized with a different receptor that is specific to different

marker proteins. Therefore, fabrication of an array of MC with any piezoelectric

layer with an output port that is attached to the circuit is necessary.

131

Sample inlent

Microsyringe Pump

Veeco Active Probes

V01

Functionalized

active probe tip

V02

V03

Figure 8.1 The proposed diagnostic kit involving one refrence and more than one

sensor probes equipped with a compact fluidic setup, injection valve, and syringe pump.

132

IV- Developing a portable and compact microfluidic setup equipped with an inlet

valve for injection of sample solutions and a syringe pump to withdraw the

solution at a certain rate is highly desirable. The Figure 8.1 provides the schematic

of the proposed fluidic setup including one reference probe and an optional

number of sensor probes depending on the number of analytes that needs to be

measured.

V- Another important feature determining the success of the reported sensing

platform is developing a high quality factor resonating circuit. The higher the

quality factor of the self-sensing circuit accompanied with the molecular probe,

the simpler and more sensitive the detection of frequency shift. Using high quality

factor crystals and microresonators is strongly suggested.

VI- Testing the improved sensing platform on different analytes would be a major

direction for future investigations. Analyzing gene expression at the genomic and

proteomic level is the main source to understand cell responses to changes in their

environment. A number of methodologies have been developed for analyzing

gene expression which includes Enzyme-Linked ImmunoSorbent Assays

(ELISA), Surface Plasmon Resonance (SPR), 2D electrophoresis, and DNA

microarrays. Microcantilever-based biosensor technology allows for label-free

fast detection of transcription factors, does not require cloning, scaling up the

number of microcantilevers on an array in not a limit, provides analysis of

multiple transcription factors in a single step, and provides higher sensitivity

compared to all other techniques. Therefore, utilizing the proposed improved self-

133

sensing platform for detection of DNA hybridization with specific selection of

DNA sequences would be very promising.

VII- Implementing the sensing platforms on applications other than biosensor

is another major direction. Exploiting this platform, different areas of application

can be targeted which includes:

a) Environment as an environmental sensor: enables detection of toxic

chemicals and biological agents. Screening potential environmental

contaminants such as endocrine disrupting chemicals or detection of

microbial pathogens in water and other environmental samples would

have a great impact in monitoring and saving environmental resources.

b) Shipping industry, customs and border patrol and homeland security as a

gas sensor: enables screening high explosive gases and toxic chemicals.

Detecting tiny masses in air and differentiating particles based on a

signature would be revolutionary since current real time instrumentation

cannot differentiate between engineered and incidental nanoparticles.

134

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