Design of Spring-Supported Diaphragm Capacitive MEMS Microphone · 2017-03-01 · on my initial research work and gives some valuable advices to further enhance my microphone design

Design of Spring-Supported Diaphragm

Capacitive MEMS Microphone

Norizan Mohamad

Submitted in total fulfilment of the requirementsof the degree of

Doctor of Philosophy

November 2016

Faculty of Science, Engineering and TechnologySwinburne University of Technology

Victoria, Australia

Abstract

In this research project, the design and performance optimization techniques of a micro-

electromechanical (MEMS) condenser microphone will be studied and described using

several established plate theories and numerical analysis. MEMS microphone is shown

to have been increasingly popular to be used in various consumer electronic products

especially in the mobile phone industry and hearing aid devices. Thus, it is important

for the microphone designers to be able to design and improve a microphone’s perfor-

mance given sets of design constraints in the shortest time possible while reducing the

overall overhead cost associated with the mass production exercise.

The proposed new spring-supported diaphragm MEMS microphone has a higher

open-circuit sensitivity, sufficiently high pull-in voltage, adequate frequency response

in the audio range bandwidth, and uses fewer fabrication masks to reduce the overall

production cost and possibly reduce the production rejection rate. The mathematical

modelling of the proposed spring diaphragm has been described in detail to relate its

performances with several of its structural dimensions such as spring width and length,

diaphragm area, air gap distance, and diameter of backplate holes. Coventor FEM soft-

ware has been used to simulate the mechanical performances of the final structure and

to verify the mathematical modelling derived for the proposed spring microphone.

Numerical results from Matlab and Coventor FEM software show that the pro-

posed spring diaphragm has about 100 times higher sensitivity compared with the edge-

clamped diaphragm microphone of the same diaphragm area. Various numerical perfor-

mance analysis graphs have been presented and used to obtain the optimized microphone

parameters by taking the points where the open-circuit sensitivity will be the highest, op-

erating bandwidth of at least 20kHz, and the pull-in voltage threshold is at least 3 times

its bias voltage.

ii

Acknowledgement

I would like to give my greatest gratitude towards my first supervisor, Assoc. Professor

Dr. Pio Iovenitti, for his continuous support, invaluable advices and comments on this

research work and publications, as well as his patience on me as his postgraduate stu-

dent. I would also like to give my sincere thankful to my second supervisor, Dr Thurai

Vinay of RMIT, for his support and willingness to help me out on the use of RMIT

MEMS laboratory and comments on my research publications.

I will not forget the various support from Swinburne Research and FSET (previously

known as FEIS) staffs who help me out with the research documentations and some of

the financial supports to attend two conferences and one jurnal publication. I must also

give my sincere credits to Dr Erol Harvey of Minifab for his willingness to comment

on my initial research work and gives some valuable advices to further enhance my

microphone design. I will also like to thanks Assoc. Professor Dr. Sharath Sriram and

Assoc. Professor Dr. Madhu Bhaskaran for their time and willingness to help me on the

initial fabrication work of my proposed spring MEMS microphone.

My greatest thankful should also be given to my employer and financial aid providers,

the Universiti Teknikal Malaysia Melaka and the Malaysia Higher Education Ministry,

for their full 4 years financial supports on my education fees and monthly allowances.

Last but not least, I should also thanks my beloved wife, Norashikin Ahmad, and our

two cheerful children, Arfa Hadhirah Norizan and Aarif Qayyum Norizan, my late fa-

ther, Mohamad Joko, and mother, Jamilah Suhud, for their continuous supports and

patience throughout the years needed to complete this research and thesis work.

iii

Declaration

This thesis contains no material which has been accepted for the award of any other

degree or diploma, except where due reference is made in the text of the thesis. To the

best of my knowledge, this thesis contains no material previously published or written

by another person except where due reference is made in the text of the thesis.

................................

Norizan Mohamad

29 November, 2016

iv

Table of Contents

Abstract ii

Acknowledgement iii

Declaration iv

Table of Contents v

List of Figures viii

List of Tables xi

List of Acronyms xii

Glossary of Symbols xiii

Glossary of Symbols xiv

Glossary of Symbols xv

Chap 1: Introduction 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Research Objectives and Scope . . . . . . . . . . . . . . . . . . . . . . 21.3 Capacitive MEMS Microphone Development . . . . . . . . . . . . . . 41.4 Research Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 111.5 Research Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . 121.6 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Chap 2: Performances Review of Capacitive MEMS Microphone 152.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2 Acoustical Measurements Review . . . . . . . . . . . . . . . . . . . . 16

2.2.1 Properties of Sound . . . . . . . . . . . . . . . . . . . . . . . . 162.2.2 Capacitor to Measure Sound Pressure . . . . . . . . . . . . . . 17

2.3 Microphone Performances Review . . . . . . . . . . . . . . . . . . . . 182.3.1 Open-circuit Sensitivity . . . . . . . . . . . . . . . . . . . . . 192.3.2 Pull-in Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . 20

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TABLE OF CONTENTS

2.3.3 Mechanical Thermal Noise . . . . . . . . . . . . . . . . . . . . 212.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Chap 3: Mathematical Modelling of Capacitive MEMS Microphone 243.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2 Equivalent Circuit Diagram Theory . . . . . . . . . . . . . . . . . . . . 253.3 Spring-supported Diaphragm Microphone Modelling . . . . . . . . . . 29

3.3.1 Open-circuit Sensitivity . . . . . . . . . . . . . . . . . . . . . 333.3.2 Frequency Response . . . . . . . . . . . . . . . . . . . . . . . 353.3.3 Pull-in Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . 383.3.4 Mechanical Thermal Noise . . . . . . . . . . . . . . . . . . . . 40

3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Chap 4: Numerical Analysis and Optimization of a Spring- Supported Di-aphragm Microphone 43

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.2 Finite-element Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 444.3 Spring-Supported Diaphragm Microphone Performances . . . . . . . . 454.4 Effects of Microphone Parameters on Performances . . . . . . . . . . . 51

4.4.1 Viscous Damping Structure Dimensions . . . . . . . . . . . . . 524.4.2 Diaphragm Structure Dimensions . . . . . . . . . . . . . . . . 56

4.5 Effective Diaphragm Area . . . . . . . . . . . . . . . . . . . . . . . . 594.6 Microphone Performance Optimization . . . . . . . . . . . . . . . . . 674.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Chap 5: Capacitive MEMS Microphone Fabrication 725.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725.2 MEMS Microphone Fabrication . . . . . . . . . . . . . . . . . . . . . 735.3 MEMSCAP Multi-Projects Wafer (MPW) . . . . . . . . . . . . . . . . 745.4 Spring-supported Diaphragm Microphone Fabrication . . . . . . . . . . 775.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Chap 6: Conclusions and Recommendations for Future Work 886.1 Conclusions Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 886.2 Research Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 90

vi

TABLE OF CONTENTS

6.3 Recommendations for Future Work . . . . . . . . . . . . . . . . . . . . 92

References 93

List of Publications 103

vii

List of Figures

Figure 2.1 Parallel plate capacitor showing plate charges Q1 and Q2, equipo-tential surface, and flux lines [1] . . . . . . . . . . . . . . . . . 17

Figure 3.1 Equivalent circuit diagram in analogy to mechanical system . . . 26Figure 3.2 Microphone diaphragm with spring structure. . . . . . . . . . . 30Figure 3.3 Microphone backplate structure with perforated holes. . . . . . . 31Figure 3.4 Microphone cross-sectional view. . . . . . . . . . . . . . . . . . 31Figure 3.5 Corner supported diaphragm. . . . . . . . . . . . . . . . . . . . 32Figure 3.6 Doubly-clamped beam center deflection. . . . . . . . . . . . . . 32Figure 3.7 L-shaped spring dimensions. . . . . . . . . . . . . . . . . . . . 33Figure 3.8 A numerical linear curve fitting for factor C1 vs. diaphragm

thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Figure 3.9 Equivalent circuit diagram of a MEMS microphone. . . . . . . . 36Figure 3.10 Simulated frequency response of a spring-supported diaphragm

microphone with Matlab and Coventor FEM using parameters inTable 3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Figure 4.1 The diaphragm mask for the spring-supported microphone. . . . 45Figure 4.2 The cross-section schematic of the spring-supported microphone. 45Figure 4.3 The cross-sectional view of a spring-supported diaphragm mi-

crophone with perforated backplate. . . . . . . . . . . . . . . . 46Figure 4.4 The cross-sectional view of an edge-clamped diaphragm micro-

phone with perforated backplate. . . . . . . . . . . . . . . . . . 46Figure 4.5 Maximum centre deflection versus sound pressure of an edge-

clamped and spring-supported diaphragms. . . . . . . . . . . . . 48Figure 4.6 Three-dimensional view of a spring-supported diaphragm deflec-

tion using Coventor FEM software. . . . . . . . . . . . . . . . . 49Figure 4.7 Maximum centre deflection versus frequency of an edge-clamped

diaphragm under a sound pressure of 60 dB SPL. . . . . . . . . 49Figure 4.8 Maximum centre deflection versus frequency of a spring-supported

diaphragm under a sound pressure of 60 dB SPL. . . . . . . . . 50Figure 4.9 Maximum centre deflection versus residual stress of an edge-

clamped and spring-supported diaphragm. . . . . . . . . . . . . 51

viii

LIST OF FIGURES

Figure 4.10 Microphone bandwidth versus air-gap distance, number of back-plate holes (holes count), and backplate hole radius change. . . . 53

Figure 4.11 Microphone sensitivity (bias voltage = 3V) versus air-gap dis-tance, number of backplate holes (holes count), and backplatehole radius change. . . . . . . . . . . . . . . . . . . . . . . . . 54

Figure 4.12 Microphone pull-in voltage with air-gap distance, number of back-plate holes (holes count), and backplate hole radius change. . . . 55

Figure 4.13 Microphone thermal noise with air-gap distance, number of back-plate holes (holes count), and backplate hole radius change. . . . 56

Figure 4.14 Microphone bandwidth with diaphragm thickness, diaphragm andbackplate width, spring width, and spring length change. . . . . 57

Figure 4.15 Microphone sensitivity with diaphragm thickness, diaphragm andbackplate width, spring width, and spring length change. . . . . 58

Figure 4.16 Microphone pull-in voltage with diaphragm thickness, diaphragmand backplate width, spring width, and spring length change. . . 58

Figure 4.17 Microphone thermal noise with diaphragm thickness, diaphragmand backplate width, spring width, and spring length change. . . 59

Figure 4.18 Different types of condenser MEMS microphone diaphragms. . . 62Figure 4.19 FEM simulation result on different types of microphone diaphragm. 64Figure 4.20 Capacitance value versus maximum diaphragm centre deflection

of different types of microphone. . . . . . . . . . . . . . . . . . 65Figure 4.21 Diaphragm effective area ratio versus maximum diaphragm cen-

tre deflection of different types of microphone. . . . . . . . . . . 65Figure 4.22 Diaphragm effective area ratio versus capacitance value of dif-

ferent types of microphone. . . . . . . . . . . . . . . . . . . . . 66Figure 4.23 The spring length and spring width dimensions on the fabricated

spring microphone . . . . . . . . . . . . . . . . . . . . . . . . . 68Figure 4.24 The operating bandwidth of each microphone samples (without

the diaphragm holes) as calculated by Matlab. . . . . . . . . . . 69Figure 4.25 The open circuit sensitivity of each microphone samples (without

the diaphragm holes) using 1 V bias voltage as calculated byMatlab. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Figure 5.1 Microphone cross-sectional view with back chamber . . . . . . 74

ix

LIST OF FIGURES

Figure 5.2 Microphone cross-sectional view fabricated on top of a siliconwafer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Figure 5.3 Cross-sectional view of the MEMS fabricated layers using Poly-MUMPs process . . . . . . . . . . . . . . . . . . . . . . . . . . 76

Figure 5.4 The MEMSCAP footprint layout for the 9 spring microphonesof different dimensions and one flat-clamped microphone (M10)as a reference . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

Figure 5.5 The PolyMUMPs process flow to fabricate a spring-supporteddiaphragm microphone . . . . . . . . . . . . . . . . . . . . . . 79

Figure 5.6 The Coventor’s 3-dimensional layout for the spring microphone . 81Figure 5.7 The enlarged masks view of the first spring microphone sample

(M1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82Figure 5.8 The Coventor’s 3-dimensional layout for the 9th. microphone

sample (M9) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82Figure 5.9 The edge-clamped fabricated microphone (M10) which serves as

a reference microphone . . . . . . . . . . . . . . . . . . . . . . 84Figure 5.10 The enlarged section of top-left spring edge of the spring-supported

microphone in Fig. 5.11 . . . . . . . . . . . . . . . . . . . . . . 84Figure 5.11 The top view of the fabricated spring-supported diaphragm mi-

crophone (M9). . . . . . . . . . . . . . . . . . . . . . . . . . . 84Figure 5.12 The SEM picture of a spring-supported diaphragm microphone. . 85Figure 5.13 The SEM picture of a spring-supported diaphragm microphone

taken at x3000 magnification. . . . . . . . . . . . . . . . . . . . 85Figure 5.14 A 3-dimensional view of the spring microphone in Fig. 5.12

simulated using Coventor FEM software. . . . . . . . . . . . . . 86

x

List of Tables

Table 1.1 Development history of various capacitive MEMS microphones. 6

Table 3.1 Optimised microphone parameters used for the numerical simu-lations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Table 4.1 Material Properties and Dimensions of an Edge-Clamped andSpring-Supported Diaphragm Condenser MEMS Microphone. . 47

Table 4.2 Microphone parameters’ changes used for the performance anal-ysis simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Table 4.3 Material properties and dimensions of condenser MEMS micro-phone types. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Table 4.4 The spring length and spring width sizes for each of the fabri-cated spring microphones . . . . . . . . . . . . . . . . . . . . . 68

Table 5.1 PolyMUMPs’ layer names, thicknesses and lithography levels . . 76Table 5.2 PolyMUMPs’ process layers showing the light and dark field levels. 77

xi

List of Acronyms

Abbreviation Description

FEM Finite Element Modeling

FEA Finite Element Analysis

MEMS Microelectromechanical system

MOS Metal Oxide Semiconductor

MPW Multi Projects Wafer

PECVD Plasma-Enhanced Chemical Vapor Deposition

PSG Phosphosilicate Glass

SEM Scanning Electron Microscope

SPL Sound Pressure Level

xii

Glossary of Symbols

Symbol Description

a acceleration

A effective plate area

b damping coefficient

c sound velocity

C0 initial capacitance

Ca air gap compliance

Cg time varying capacitance

Cm mechanical compliance

Co microphone initial capacitance

Cs microphone stray capacitance

d distance

E modulus of elasticity

ε0 electric permittivity of vacuum

εr capacitor dielectric constant

f sound pressure frequency in Hertz

F Force

Fnet net force

Fs sound pressure force

h diaphragm thickness

hg air-gap thickness

xiii

Glossary of Symbols

Symbol Description

I electrical current

k spring constant

kB Boltzmann constant

L inductance

Lb beam length

Lp acoustic pressure level

Ls spring length

m mass

Mm lumped effective mass

n number of backplate holes

∆P sound pressure force

ρ polysilicon density

ρo density of air

q capacitor charge

rh hole radius

R resistance

Rg air gap viscosity loss

Rh backplate holes viscosity loss

S open-circuit sensitivity

Se electrical sensitivity

xiv

Glossary of Symbols

Symbol Description

Sm mechanical sensitivity

SN A-weighted mechanical thermal noise

T absolute temperature (in Kelvin)

µo viscosity of air

v Poisson’s ratio

Vb bias voltage

Vm diaphragm velocity

Vo output voltage

w1 diaphragm’s center deflection

wb beam width

wd diaphragm length and width

ws spring width

∆w deflection of a microphone diaphragm

x displacement

x mass velocity

Zt total impedance

ZC complex impedance of a capacitor

ZL complex impedance of an inductor

ZR complex impedance of a resistor

xv

1Introduction

1.1 Introduction

A microphone is a device used to convert an acoustic energy into an electrical energy.

The resulted electrical energy will then be amplified by means of an electronic circuitry

and normally feeds back into another energy conversion device such as a speaker to

transform the energy back into its original form. Microphones have been widely used

to record several acoustical signals such as human speech, music, and environmental

noise for various applications including telecommunication, media storage, and medi-

cal. A high performance and small size microphone to reproduce a high-quality sound

signal is increasingly demanded in telecommunication and medical applications such as

mobile phones and hearing aid devices [2]. Due to the increasing demand for smaller

technological devices, the internal components of these devices must use as small com-

ponent size as possible to make the devices more compact, lighter, and possibly cheaper.

The smaller component size demands have led to the use of microelectromechanical

system (MEMS) technology using silicon micromachining to build various millimeter

and micrometer size components and devices such as a microphone, accelerometer, and

pressure sensor.

1

CHAPTER 1. INTRODUCTION

Many commercial portable devices today needs to consume as low electrical power

as possible to prolong its power supply life. A high-performance capacitive microphone

normally needs a high voltage and power to boost its sensitivity. In order to use a

lower operating voltage while maintaining the high sensitivity, the mechanical sensitiv-

ity of the microphone has to be exploited and improved. The microphone’s performance

parameters and their corresponding equations are thoroughly discussed in Chapter 2.

There have been several research works carried out to increase the mechanical sensitiv-

ity starting from the use of a corrugated diaphragm, the use of a low-stress polysilicon

diaphragm, and the use of a spring type diaphragm. However, very little significant work

has been done to explain the detailed modelling of various spring type diaphragm struc-

ture and its relationship with the electrical properties of the capacitive microphone. The

scientific work in this thesis is therefore trying to explain the behaviour of a new vari-

ation of spring-supported diaphragm microphone by investigating its mechanical and

electrical characteristics via mathematical modelling development and numerical analy-

sis using finite element analysis software. The microphone model with several different

structure dimensions will then be fabricated on top of a silicon wafer using PolyMUMPs

processes which utilize three layers of doped polysilicon material with several microm-

eters space between each of them. Only the first two polysilicon layers will be used to

form a capacitive spring microphone in this project.

1.2 Research Objectives and Scope

The need for a smaller, lower cost, lower power consumption, but high-performance mi-

crophone using MEMS technology is increasing as previously described. Since smaller

size condenser microphones will result in smaller operating capacitance, thus having a

lower open circuit sensitivity. The commonly used methods to increase its sensitivity

2


is either increasing its bias voltage or reducing its diaphragm stiffness to increase its

mechanical deflection. However, the needs for a low voltage and a lower power con-

sumption device means that the option to use a higher bias voltage is not favourable.

This means that the only option to increase the microphone’s sensitivity is to reduce its

diaphragm stiffness. There have been several works done on reducing the diaphragm

stiffness including the use of corrugated diaphragms and different types of spring di-

aphragms. However, there is a limit to how much softer the diaphragm or the spring

needs to be designed since the attractive force caused by the electrostatic charge between

the capacitor plates will pull the diaphragm completely towards its backplate when the

bias voltage has exceeded its pull-in voltage threshold. So, a microphone which uses a

higher bias voltage needs a stiffer diaphragm compared to the microphone with a much

lower bias voltage.

The work described in this thesis is based on a newly designed spring-supported di-

aphragm condenser MEMS microphone. In order to fully understand and optimize the

performance of the newly designed microphone, it is important to describe its behaviour

by means of any form of mathematical modelling, and be able to simulate and analyze

its theoretical characteristics to fine tune the model. The mathematical modeling for

a spring diaphragm microphone in this thesis is derived based on several lumped me-

chanical and acoustic parameters in analogy to the electronic components which forms

a closed circuit diagram. A variable output voltage expression of the resulted circuit di-

agram will then be used to describe and analyze the behaviour of the spring diaphragm

microphone. The main objectives and scope of this thesis are therefore to describe

the behaviour of the spring-supported diaphragm microphone mathematically and nu-

merically, identify its advantages and limitations, and to use the knowledge to design

a miniature capacitive microphone with higher sensitivity, better performance, lower

power consumption, and possibly lower cost.

3


1.3 Capacitive MEMS Microphone Development

This section reviews the development of capacitive MEMS microphone and their per-

formances so far. The need for a better performance spring-supported diaphragm mi-

crophone will be highlighted.

Capacitive MEMS microphone consists of two charged plates which produce a vari-

able voltage across its plates when one of its plates (diaphragm) vibrates with sound

pressure. The sensitivity of the microphone is characterized by its electrical and me-

chanical sensitivities. The microphone’s electrical sensitivity is directly dependent on

its bias voltage and plate area, but inversely dependent on the plates’ gap (air gap) dis-

tance. Therefore, the higher the bias voltage used between the diaphragm and backplate,

the higher the sensitivity would be, and the larger the plate area, the higher the sensitiv-

ity. However, the main objective of the current application for mobile consumer devices

such as mobile phones and hearing aids requires the microphone to be as small as pos-

sible. This would also mean that the microphone will use the least material possible

to reduce its total cost and possibly make the earth greener by having less waste. Even

though a higher bias voltage could increase the microphone’s sensitivity, however, this is

not favourable since most current consumer devices need to use the least battery power

as possible, thus limits the bias voltage that could be used. The most common voltage

used in consumer electronics and digital electronics is between 3 Volt and 5 Volt.

Consequently, the microphone’s mechanical sensitivity is directly dependent on the

stiffness of the diaphragm (softer diaphragm will have more deflection). Even though

the diaphragm could be made much softer to get a higher mechanical sensitivity, too

soft diaphragm suffers from a higher chance of breaking, and limits the bias voltage that

could be used due to the electrostatic force pulling the diaphragm towards the backplate.

Therefore, it is always a challenge to design a high sensitivity microphone given all the

4


constraints to find the balance between high sensitivity, small size and low power device.

A high sensitivity capacitive microphone can be designed by adjusting several pa-

rameters:

• A higher bias voltage is applied between the plates to increase the electrical sen-

sitivity. However, the pull-in voltage threshold will limit the highest bias voltage

that could be applied. The electrostatic force resulted from the bias voltage will

attract the diaphragm to touch the backplate if the voltage has exceeded the pull-in

voltage threshold.

• A smaller air gap is used to increase the capacitance. A larger capacitance value

will result in a larger open circuit voltage of the microphone for the same di-

aphragm deflection. However, a small air gap (several micrometers) introduces a

squeeze-film damping to the microphone’s diaphragm which will reduce its me-

chanical sensitivity and affect its frequency response.

• A larger plate area is used to increase the capacitance. However, many consumer

applications today needs a small size microphone, thus its plate area must be de-

signed to be as small as possible.

• A softer diaphragm plate is used to increase the mechanical sensitivity. A softer

diaphragm along with a low residual stress diaphragm will allow it to have a large

deflection with sound pressure. However, a softer diaphragm will result in a lower

resonance frequency (lower operating bandwidth) and higher thermal noise. Thus,

the diaphragm stiffness needs to be designed according to the operating bandwidth

and minimum noise requirements.

In 1983, Royer et al. [3] was the first to fabricate a piezoelectric MEMS micro-

phone using zinc oxide and silicon micromachining technique along with MOS buffer

5


amplifier. The technique was then used to fabricate a capacitive MEMS microphone as

demonstrated by many researches [4–30]. Table 1.1 shows the development of various

types capacitive MEMS microphones for the past 24 years.

Table 1.1: Development history of various capacitive MEMS microphones.

Year Author Diaphragm Size (Type) Air-gap(µm)

Sensiti-vity(mV/Pa)

BiasVoltage(V)

Band-width

1992 Scheeperet al. [6]

1.5mm x 1.5mm (silicon ni-tride flat diaphragm)

1.1 2.0 16.0 100 Hz -14 kHz

1993 Bergqvist,J. [31]

2.0mm x 2.0mm (monocrys-talline silicon flat di-aphragm)

2.3 2.4 10 20 kHz

1996 Zou etal. [8]

1.0mm x 1.0mm (multilayercorrugated diaphragm)

1.0 14.2 25 100 Hz -16 kHz

1998 Hsu etal. [9]

2.0mm x 2.0mm (polysiliconflat diaphragm)

4.0 20 13 25 kHz

1998 Pedersenet al. [10]

2.2mm x 2.2mm (polyimideflat diaphragm)

3.6 10 14 100 Hz -15 kHz

2000 Torkkeliet al. [11]

1.0mm x 1.0mm (low stresspolysilicon flat diaphragm)

1.3 4.0 2.0 10 Hz -12 kHz

2000 Li etal. [13]

1.0mm x 1.0mm (sin-gle deeply corrugateddiaphragm)

2.6 9.6 5.0 100 Hz -19 kHz

2002 Rombachet al. [15]

2.0mm x 2.0mm (polysiliconflat diaphragm, dual back-plate)

0.9 13 1.5 20 kHz

2003 Tajima etal. [17]

2.0mm x 2.0mm (crystallinesilicon flat diaphragm)

24 4.5 48 75 Hz -24 kHz

2003 Scheeperet al. [16]

1.95mm radius (silicon ni-tride flat diaphragm)

20 22 200 47 Hz -51 kHz

2005 Liu etal. [21]

0.23mm radius (flat di-aphragm, dual backplate)

2.0 0.28 18(AC)

180 kHz

2006 Kim etal. [22]

0.5mm radius (flexure hingediaphragm)

2.5 0.2µm/Pa

16 20 kHz

Continued on next page

6


Table 1.1 – Continued from previous page

Year Author Diaphragm Size (Type) Air-gap(µm)

Sensiti-vity(mV/Pa)

BiasVoltage(V)

Band-width

2007 Goto etal. [24]

2.0mm x 2.0mm (crystallinesilicon flat diaphragm)

10 6.7 48 30 Hz -20 kHz

2009 Ganji etal. [29]

0.5mm x 0.5mm (perforatedaluminum flat diaphragm)

1.0 0.2 105 20 kHz

2011 Esteves etal. [32]

0.5mm x 0.5mm (perforatedaluminum flat diaphragm)

2.0 17.8 1.0 8 kHz

2011 Chan etal. [33]

0.5mm radius (polysiliconrigid diapgrahm with springbackplate)

2.0 12.63 – 20 Hz -20 kHz

2012 Hur etal. [34]

1.0mm radius (polysiliconflat diaphragm)

3.0 8.3 12 20 Hz -27.4kHz

2012 Lee etal. [35]

0.3mm radius (aluminumflat diaphragm)

2.8 4.12 10.4 80 kHz

2013 Ahmad-nejad etal. [36]

0.5mm x 0.5mm (perforatedpolysilicon flat diaphragm)

1.0 7.1 2.3 70 kHz

2014 Grixti etal. [37]

0.675mm x 0.675mm (per-forated polysilicon flat di-aphragm)

2.0 8.4 6.0 28 kHz

2015 Lo etal. [38]

0.3mm radius (polysilicondiaphragm with planar inter-digitated sensing electrodes)

– 0.99 – 1 kHz -20 kHz

2015 Kim etal. [39]

0.3mm radius (polysiliconspring diaphragm)

4.0 12.0 10 37 kHz

2016 Zawawi etal. [40]

0.68mm x 0.68mm (siliconcarbide flat diaphragm)

3.0 4.3 µm/20 µPa

– 70 kHz

In 1992, Scheeper et al. [6] had proposed and demonstrated a new condenser micro-

phone design which consists of a plasma-enhanced chemical vapor deposition (PECVD)

silicon nitride film and can be fabricated using the sacrificial layer technique. The sacri-

ficial layer will form the required air-gap for the microphone. The technique in etching

sacrificial layer to form the air-gap will reduce the needs for critical wafer alignment

7


and high temperature treatment during bonding of the diaphragm and backplate wafer

plate [4]. Even though the new microphone was fabricated on a single wafer without

using any bonding technique, the microphone has a relatively low sensitivity (about 2

mV/Pa) using a bias voltage of 16 V. An adequate sensitivity of about 10 mV/Pa should

be achieved for audio applications such as hearing aid devices [6].

In order to increase the sensitivity without using a high bias voltage, a mechanical

sensitivity could be increased. This can be achieved by reducing the diaphragm stiffness

and stress by reducing its thickness or using a softer material such as polysilicon [9, 11,

15, 27, 28], polyimide [10], and aluminium [29]. Other than using a softer diaphragm

to increase its deflection, a corrugated diaphragm [7, 8, 14, 41, 42] and a spring type

diaphragm [22, 23, 26] has been used to reduce the diaphragm’s initial stress.

The use of a corrugated diaphragm in a capacitive microphone has been demon-

strated by Scheeper et al. [7] in 1994 and followed by several other researchers [8, 14,

41, 42]. Scheeper et al. [7] has fabricated a silicon nitride diaphragm of 2 mm x 2 mm

with a diaphragm thickness of 1 µm and having 8 circular corrugations. Corrugations on

the diaphragm are used to reduce the initial stress of a clamped diaphragm depending

on the diaphragm fabrication process. Scheeper et al. [7] showed that a measured me-

chanical sensitivity of a diaphragm with 4 µm corrugation depth is 25 times larger than

the mechanical sensitivity of a flat diaphragm with equal size and thickness. Moreover,

the corrugated diaphragm has been shown experimentally to have a larger linear range

than a flat diaphragm and a reduced influence of thermal stress.

Hsu et al. [9] demonstrated a capacitive microphone using a square low-stress polysil-

icon diaphragm without having any corrugations. The 2 mm2 square diaphragm micro-

phone was fabricated and tested to have a sensitivity of 20 mV/Pa using a 13V bias

voltage. The use of a low-stress polysilicon diaphragm in capacitive microphone was

8


further demonstrated by Torkkeli et al. [11] in 2000. The fabricated 1 mm2 square mi-

crophone had only about 2 Mpa residual stress, and achieved a sensitivity of 4 mV/Pa

using a bias voltage of only 2 V.

The use of polyimide (plastic type diaphragm) in capacitive microphone fabrica-

tion has been introduced by Pedersen et al. [10] in 1998. Polyimide diaphragm can be

fabricated using a low-temperature fabrication process directly on substrates containing

integrated circuits without causing any damage to the circuits itself. The fabricated 2.2

mm by 2mm square polyimide diaphragm microphone had a sensitivity of 10 mV/Pa

using an equivalent bias voltage of 14 V. The actual device was using only 1.9 V power

supply, but the input voltage was amplified by the built-in DC-DC voltage converter to

supply a bias voltage of 14 V to the microphone plates.

In 2006, Kim et al. [22] had designed and fabricated a spring type diaphragm ca-

pacitive microphone. The circular aluminum diaphragm consists of three circular slits

and bridges near its edge to form a spring-like structure. The fabricated 0.5 mm radius

circular diaphragm resulted in a center diaphragm deflection about 250 times higher

than the equal size edge clamped flat diaphragm. Another spring type diaphragm micro-

phone was designed and fabricated by Weigold et al. [23] at Analog Devices in 2006.

The measurement using a low noise amplifier circuit yields a sensitivity of about 4.47

mV/Pa.

The other possible method to increase the microphone sensitivity is to reduce the

air gap between the capacitor plates. The air gap for a typical MEMS condenser mi-

crophone is within several micrometers thick. This very small air gap introduces a

squeeze-film damping to the microphone’s diaphragm which will reduce its mechanical

sensitivity during high frequency operation [43]. Since the smaller air gap will increase

an air-streaming resistance at high frequency operation [43–49], perforated holes on the

backplate are often used to enable the air to pass through the holes thus increase the

9


microphone’s sensitivity [4–6, 9–13, 17–19, 21, 24–28, 31, 50–53].

In 2011, Chan et al. [33] has introduced a new concept in condenser MEMS micro-

phone operation. Instead of using a conventional diaphragm and backplate structure,

they introduced the use of a rigid diaphragm that is connected with a spring backplate in

order to reduce the effect of diaphragm deformation due to the thin film residual stress.

The fabricated microphone of 0.5mm diaphragm radius had achieved an open-circuit

sensitivity of 12.63 mV/Pa within a frequency range between 20 Hz to 20 kHz.

In order to further reduce the effect of thin film damping between microphone di-

aphragm and backplate (acoustic impedance) during operation, Lo et al. [38] in 2015

has introduced a new microphone design which consists of a polysilicon flat diaphragm

with planar interdigitated sensing electrodes. This new microphone structure does not

any backplate, thus does not have any pull-in voltage problem and possibly reduces the

problem of process stiction between diaphragm and backplate. The fabricated micro-

phone with 0.3mm radius diaphragm and 42 pairs sensing electrodes gives an open-

circuit sensitivity of 0.99 mV/Pa within a frequency range between 1 kHz and 20 kHz.

Recently in 2016, Zawawi et al. [40] has investigated the use of a silicon carbide

(SiC) diaphragm for a MEMS microphone for sonic detection in a harsh environment.

The MEMS microphone could detect the specific acoustic wave that is emitted by the

dangerous gas leakage. SiC has superior properties in terms of chemical inertness and

corrosion resistance compared to silicon. The fabricated 0.68 mm x 0.68 mm SiC di-

aphragm with the thickness of 1.0 µm gives 4.3 µm diaphragm deflection using 20 µPa

sound pressure with a frequency range up to 70 kHz.

10


1.4 Research Contributions

The contributions of this thesis to the capacitive MEMS microphone field of study are

listed below:

• A comprehensive review of the capacitive microphone development for the past 24

years was done to identify the problems and improvements needed to the existing

microphone design. The current trend in consumer electronic devices demanded

a high-quality microphone, but small size, low cost, and using low power.

• A new spring-supported diaphragm structure which has very low residual stress,

higher effective diaphragm area, and high mechanical sensitivity is proposed. It

has a simple and balance spring design which can easily be adjusted to suit the

application requirements. A numerical analysis shows that the new structure has

a linear and stable diaphragm deflection up to the first resonance frequency.

• A mathematical modelling for the new diaphragm structure is developed using an

established plate theory and clamped beam equation. Numerical analysis carried

out using finite element modeling shows that the model can accurately define the

new microphone’s performances.

• A mathematical modelling for the new spring-supported diaphragm microphone is

defined based on the equivalent circuit diagram using linear lumped parameters.

Numerical analysis using Matlab software was used to verify that the model is

within the acceptable accuracy.

• A new microphone design which can be fabricated without etching any part of the

silicon disc and using the least fabrication masks was proposed. Theoretical and

11


numerical analysis were carried out thoroughly to find the optimum microphone

performances based on the design requirements and constraints.

1.5 Research Methodology

This section explains the methodology used to undertake the research project. A brief

background is given which shows the trends and major issues being pursued by re-

searchers, followed the major stages of the research to achieve the outcomes.

The literature review has revealed that a lower residual stress diaphragm includ-

ing a corrugated and free moving diaphragm has been used to increase the capacitive

MEMS microphone as demonstrated by various research works. The current trend to-

wards using a smaller diaphragm area to reduce the overall device size along with a

lower residual stress diaphragm has demanded the use of a lower bias voltage (typically

several Volts). The use of a low bias voltage will result in a lower microphone sensitiv-

ity, which is usually overcome by reducing the air-gap thickness. However, a thin-film

air damping caused by the air compression becomes more significant as the air-gap is

reduced. Therefore, it is always a challenge to achieve a balance in designing a small

size microphone, but having a high sensitivity and stability, low bias voltage, low air-gap

damping and low thermal noise. Thus, the work in this thesis is outlined in three main

stages which highlight the design of a spring-supported diaphragm microphone and the

analysis required to find the optimum balance between its key performances.

The first stage of the work was to design a microphone diaphragm which has the

highest mechanical sensitivity as possible. A new spring diaphragm was proposed which

consists of a square diaphragm with all its four edges suspended on four L-shaped spring

structure. The total area occupied by the diaphragm and all four springs was designed

not to exceed 3x3 mm2. The mathematical modelling for the new spring-supported

12


diaphragm was developed using an established plate and clamped beam theory. The

lumped mechanical and acoustic parameters in analogy to the electrical circuit compo-

nents were used to develop the microphone’s theoretical modelling using an equivalent

circuit diagram. The theoretical model would be used to predict the behaviour of the

microphone and to find its optimum operating parameters.

The second stage of the work was to analyze and find the optimum parameters for

the new spring-supported diaphragm microphone theoretically and numerically. Various

numerical analyses were done to verify the theoretical modeling of the microphone.

Further theoretical analyses were carried out to determine the effects of microphone’s

parameters variations on its performances. The theoretical analysis results were then

used to determine the microphone’s parameters which will give an optimum operating

performance based on the design requirements and constraints.

The final stage of the work was to compare and verify the new microphone’s theoret-

ical performances against the fabricated microphone’s measured performances. A Poly-

MUMPs fabrication process was used to fabricate the spring diaphragm microphone at

the MEMSCAP facilities which uses minimal fabrication masks and is not etching any

part of the silicon wafer. However, the experimental results could not be obtained due

to various measurement equipment availability and suitability problems.

1.6 Thesis Outline

In order to achieve the objectives and scope of this thesis, a review of acoustical mea-

surements methods and terminologies, as well as the discussions on several key micro-

phone’s performances, are presented in Chapter 2.

Chapter 3 reviews the mechanical and acoustical parameters conversion technique to

its equivalent electronic components and presents a current approach to model several

13


types of condenser MEMS microphones. A mathematical modelling of a mechanical

system is usually useful to analyze and predict the behaviour of the system and possi-

bly optimize its parameters for a desired application. An equivalent circuit diagram in

analogy to the mechanical system is employed in this thesis to model a condenser mi-

crophone. A similar approach is then used to model a newly designed spring-supported

diaphragm condenser microphone. The modelling for several key performances of the

microphones is also presented in this chapter.

In Chapter 4, theoretical and numerical analyses of the spring-supported diaphragm

microphone’s model presented in Chapter 3 were carried out. Its performance behaviour

was analysed by varying some of its structural parameters in order to find a possible

optimised structure based on the design requirements and constraints.

In Chapter 5, current silicon processing techniques are used to fabricate MEMS mi-

crophones are reviewed and discussed. A new fabrication technique is proposed which

uses less fabrication masks and is possibly lower in cost.

Lastly in Chapter 6, general conclusions of the work are drawn. Several suggestions

for future research to further enhance and optimize the spring diaphragm microphone

are also presented at the end of this chapter.

14

2Performances Review of Capacitive MEMS

Microphone

2.1 Introduction

The first part of this chapter reviews the properties of audio sound and the use of capac-

itance method to detect the sound pressure and convert it into its equivalent electrical

signal. The surrounding audible sound is measured by sensing its pressure and com-

pared with the lowest pressure that could be detected by human ears and the ratio is

called a sound pressure level (SPL). A high-quality microphone will be able to detect

and measure the lowest sound pressure level as possible with a good linearity.

The second part of this chapter reviews several main performances of a MEMS con-

denser microphone. Since the performance of a microphone is related to its mechani-

cal properties, an optimization of the microphone’s performance is often necessary by

adjusting its mechanical properties based on the design requirements. Mathematical

equations are often needed to help characterize the mechanical behaviour of a structure

and could be used to optimize several of its dimensional properties. This chapter reviews

some of the established equations related to the key MEMS microphone’s performances.

15

CHAPTER 2. PERFORMANCES REVIEW OF CAPACITIVE MEMS MICROPHONE

2.2 Acoustical Measurements Review

The acoustical sound is caused by the vibration of particles of a medium (eg. air) [54].

In the absence of any particle such as vacuum, the sound could not be propagated since

there are no vibrating particles to propagate the sound from one point to the other [55].

The vibrating particles could be measured by a suitable mechanical system such as a hu-

man eardrum, and a thin diaphragm membrane in a pressure sensor. In order to convert

sound pressure into its equivalent electrical signal, a capacitor with variable capacitance

could be used and will be reviewed in this section.

2.2.1 Properties of Sound

The sound is propagating through an elastic medium at a certain frequency. The fre-

quency is the number of cycles per second (in Hertz or Hz) and is related to its wave-

length by [55]:

Wavelength (m) =Speed of sound (m/s)

Frequency (Hz)(2.1)

Equation (2.1) is valid for only a single sine wave sound. Speech and music contain

an irregular shape of sound which could be separated into several multiple frequency

sine waves called harmonics [55]. A speech by human consists of several harmonics

with the first or fundamental harmonic is having the lowest frequency, but the highest

peak value, the second harmonic has twice the fundamental frequency, but at a lower

peak value, the third harmonic with three times the fundamental frequency, and so on.

The acoustic intensity or power per unit area is highest at its source and fades away

as it travels through a medium. The acoustic power is proportional to the square of

the acoustic pressure, thus the acoustic pressure level could be measured by dividing

16


the acoustic pressure, p1 at a certain point by a reference sound pressure, p2 (normally

20 µPa - the lowest sound pressure that can be detected by a human ear called Sound

Pressure Level or SPL). The acoustic pressure level, Lp in decibels (dB) is given by [55]:

LP = 20logp1

p2(2.2)

2.2.2 Capacitor to Measure Sound Pressure

The capacitive sensor could also be used in various measurement applications such as

proximity, pressure, liquid level, thickness measurement and be used as switches [1].

Capacitive sensor can easily be fabricated on a silicon substrate using micromachining

and be more stable against temperature, humidity, or mechanical misalignment [1].

Figure 2.1: Parallel plate capacitor showing plate charges Q1 and Q2, equipotentialsurface, and flux lines [1]

When two capacitor plates have an opposite charge Q1 and Q2, separated by a dis-

tance d as in Figure 2.1, the force exerted on the plates is given by [1]:

F =Q1Q2

4πε0εrd2 (2.3)

17


where ε0 is the electric permittivity of vacuum (ε0 = 8.854x10−12 F/m), εr is the ca-

pacitor dielectric constant, and d is the distance between the upper and lower capacitor

plates. It can be seen that the electrostatic force, F will become higher as the charge Q1

and Q2 are increased, and as the plate separation, d was decreased.

If a voltage, V (in Volt) is applied between upper and bottom plate of a capacitor with

an overlapping area, A (in meter2), the energy stored in the capacitor is given by [1]:

E =12

CV 2 =ε0εrAV 2

2d(2.4)

It can be seen from equation (2.4) that the capacitance, C is given by:

C =ε0εrA

d(2.5)

A condenser microphone with an initial capacitance, C0 will have a time varying ca-

pacitance, Cg when one of its plates is deflected by a sound pressure. Since the electrical

charge between the capacitor plate is constant under high frequency plate vibration, the

output voltage of the microphone with a bias voltage, Vb is given by [56]:

eoc =Vb

(C0

Cg−1)

(2.6)

2.3 Microphone Performances Review

A capacitive microphone is mainly characterized by its open-circuit sensitivity (in V/Pa),

frequency response and bandwidth (in Hz), and mechanical thermal noise. Since a

MEMS capacitive microphone is designed to have a very small air-gap thickness, the

thin-film damping effects towards sensitivity and bandwidth often need to be consid-

ered in the microphone design.

18


In this section, the main characteristics on a capacitive microphone which affect its

overall performances are reviewed. Due to a complex relationship between the micro-

phone performance factors, the last part of this section reviews several possible ways to

optimise the performance according to the design requirements and limitations.

2.3.1 Open-circuit Sensitivity

A thin silicon membrane in a parallel-plate capacitive MEMS microphone is sensitive to

the sound pressure force. Since the other plate in the structure is made to be more rigid,

the vibration of the thin membrane with sound pressure creates a variable capacitance

value. The sensitivity of a capacitive microphone consists of a mechanical and electrical

sensitivity components [43]. The mechanical sensitivity, Sm is given by the deflection of

a microphone diaphragm, ∆w with the increase of a sound pressure force, ∆P:

Sm =∆w∆P

(2.7)

The electrical sensitivity of a capacitive microphone is defined by the change of the

voltage across the capacitor plate, ∆V with the change of the air-gap thickness, ∆hg:

Se =∆V∆hg

(2.8)

An open-circuit sensitivity of the capacitive microphone is simply given by the prod-

uct of mechanical and electrical sensitivity:

Soc = Sm ×Se (2.9)

When a constant bias voltage is applied between the top and bottom plate of the

variable capacitor in Figure 2.1, an open-circuit sensitivity (in Volt per Pascal) of the

19


capacitive microphone is given by [31]:

S =Vb

∆P.∆hg

hg.

1(1+Cs/Co)

(2.10)

where Vb is the bias voltage (in Volt), ∆P is the sound pressure (in Pascal), hg is the initial

air gap distance (in meter) between microphone diaphragm and its backplate, Co and Cs

are the microphone initial capacitance and stray capacitance (in Farad) respectively.

Equation (2.10) contains a stray capacitance, Cs which attenuates the microphone

sensitivity. The initial or working capacitance, Co of the microphone is given in Equation

(2.5).

2.3.2 Pull-in Voltage

A condenser MEMS microphone pull-in voltage is caused by the attractive force be-

tween the diaphragm and backplate when a constant bias voltage is applied during

its operation. Its value is mainly determined by the spring restoring force of the di-

aphragm [57]. Assuming a linear spring restoring force, the net force, Fnet acting on the

diaphragm is given by [58]:

Fnet = k(hg −hd)−εoAV 2

b

2h2d

(2.11)

where spring constant, k can be calculated from the inverse of the diaphragm compliance

(k = 1/Cm) in which Cm is the microphone diaphragm’s mechanical compliance, hg and

hd are the air-gap distance with zero and the constant bias voltage respectively. A is the

effective parallel plate area (the backplate area minus the area occupied by the holes).

The first part of the expression in Eq. (2.11) is the spring force upward by the diaphragm,

and the second part of the expression is the downward electrostatic force caused by the

20


constant bias voltage. At equilibrium, the net force is equal to zero:

Fnet(PI) = 0 (2.12)

The pull-in occurs at the air-gap distance [58]:

hnet(PI) =23

hg (2.13)

Equating Eqs. (2.11) and (2.12), and substituting Eq. (2.13) for the pull-in air-gap

yields:

k =εoAV 2

PI

h3PI

(2.14)

where VPI is the pull-in voltage at pull-in air-gap distance,hPI. Substituting Eq. (2.13)

into Eq. (2.14) yields the pull-in voltage, VPI expression:

VPI =

√8kh3

g

27εo(w2d −nπr2

h)(2.15)

where wd is the diaphragm width, rh is the backplate hole radius, Rg is the air gap

viscosity loss, and Rh is the backplate holes viscosity loss.

2.3.3 Mechanical Thermal Noise

A good condenser microphone is designed to pick up the lowest possible sound pres-

sure, which is limited by the mechanical thermal noise and the preamplifier noise of

the microphone [47]. The A-weighted mechanical thermal noise, SN (in Pascal) can be

calculated by [47]:

21


SN =

√∫ f2

f14kBT (Rg +Rh)A2( f )d f (2.16)

where f1 and f2 are 20 Hz and 20 kHz respectively, kB is the Boltzmann constant, and

T is the absolute temperature (in Kelvin). The A-weighted filter function, A( f ) is given

by:

A( f ) =122002. f 4

( f 2 +20.62)( f 2 +122002)

× 1√( f 2 +107.72)( f 2 +737.92)

(2.17)

where f is the sound pressure frequency in Hertz.

It can be seen in Eq. (2.16) that a mechanical thermal noise can be reduced by re-

ducing the backplate holes viscous damping. However, the viscous damping reduction

will increase the resonant peak of the microphone diaphragm. Thus, optimum param-

eters need to be calculated to get the lowest mechanical thermal noise according to the

frequency response requirements.

2.4 Conclusions

This chapter had presented an important review on the key performances of a MEMS

microphone. A sound pressure level (SPL) which is the measure of the acoustical ratio

between the measured sound pressure and the lowest pressure that could be detected by

human ears has been discussed. The design of a high quality MEMS microphone should

be able to detect the sound pressure level at the lowest point possible with a relatively

high linearity response.

The concept of parallel plate capacitor operation to detect the sound pressure is also

22


discussed. Some established equations related to the variable capacitance value have

been presented and explained. Using a constant bias voltage between the capacitor

plates, a high frequency plate vibration will cause a constant electrical charge between

the plates, which results in the variation of an output voltage proportional to the sound

pressure when one of the plates vibrates in response to the sound pressure exerted on its

surface.

Lastly, several key performances of a MEMS microphone have been reviewed and

discussed. Several established equations related to the microphone’s open-circuit sensi-

tivity, pull-in voltage, and mechanical thermal noise were presented. The next chapter

will present the use of an equivalent circuit diagram to describe the dynamic behaviour

of a MEMS microphone. The mathematical modelling of a newly proposed spring-

supported diaphragm MEMS microphone will also be thoroughly presented and dis-

cussed.

23

3Mathematical Modelling of Capacitive MEMS

Microphone

3.1 Introduction

A capacitive or condenser microphone is a device that converts an acoustical energy into

its corresponding electrical energy. Since the microphone itself is a mechanical device,

there exists a complex relationship to describe the energy conversion phenomena. First,

the quasi-static properties of the microphone which describes the relationship between

the mechanical structure and the electrical signal has to be known and solved. Second,

the dynamic behaviour of the microphone which relates the whole microphone oper-

ation caused by the acoustical signal flow inside and around the microphone needs to

be derived. An equivalent circuit diagram is commonly used to describe the dynamic

behaviour of the microphone with the use of analogies between acoustical, mechanical

and electrical domain [31,43]. The acoustic and mechanical properties will be converted

into its corresponding lumped parameter components of resistor, capacitor, and inductor

inside a closed loop of a circuit diagram [31]. The model will then be used to simulate,

predict and optimize the behaviour of the real microphone.

24

CHAPTER 3. MATHEMATICAL MODELLING OF CAPACITIVE MEMSMICROPHONE

In this chapter, the expressions to describe the diaphragm mechanical behaviour of

the proposed spring diaphragm microphone will be derived. The diaphragm equation

will then be used to solve the quasi-static behaviour of the diaphragm under the influ-

ence of a direct current (DC) bias voltage between the diaphragm and backplate. The

open-circuit sensitivity equation for the spring-supported diaphragm will be derived us-

ing the plate theory and doubly-clamped beam equation which will be modified to take

into account the L-shaped form of the microphone beam. An equivalent circuit dia-

gram approach will be used to derive the frequency response equation for the spring-

supported diaphragm microphone. Lastly, the mechanical thermal noise of both types

of microphones which determines the lowest possible sound that could be detected by a

condenser microphone will be described and investigated.

3.2 Equivalent Circuit Diagram Theory

A mechanical-acoustic transducer such as condenser microphone can be modelled us-

ing an equivalent circuit diagram obeying the Kirchoff’s Laws in an analogous electrical

circuit [31,43]. A condenser microphone’s structure can be represented by a lumped pa-

rameter system consists of mechanical, acoustical, and electrical components [31]. A

voltage in the circuit is analogous to the sound pressure while a current is analogous

to the fluid (eg. air) velocity flow caused by the sound pressure [9, 31, 43]. The me-

chanical properties of the microphone such as mass and compliance are analogous to

the inductance and capacitance, respectively. Acoustical properties such as air gap and

back chamber which introduce a mechanical damping to the system will be represented

by resistors. The microphone electrode itself will form a small capacitor in parallel to

the circuit output.

In order to understand how the equivalent circuit diagram can be used to describe the

25


microphone’s behaviour with an analogy to the mechanical system, mathematical mod-

elling for a simple spring-mass-dashpot system as shown in Fig. 3.1 will be presented

in this section. The connection for lumped circuit elements in a closed circuit diagram

should follow these two basic concepts [58]:

1. Mechanical elements that share a common flow and displacement are connected

in series.

2. Mechanical elements that share a common effort or force are connected in parallel.

Figure 3.1: Equivalent circuit diagram in analogy to the mechanical system [58]. Thisfigure shows (a) a simple spring-mass-dashpot system, and (b) a conversion of spring,dashpot, and mass into its equivalent electrical components.

In Fig. 3.1, the mass m is resting on a frictionless platform and subjected to a force

F that will pull the mass to the right with a displacement x in a case of a static force, or

oscillate between the equilibrium position x = 0 in a case of an oscillating force. The

mass m is connected to the static wall by two mechanical components: a spring with a

spring constant k and a dashpot with a damping coefficient b.

Consider a spring with a mass system without a dashpot in Fig. 3.1(a). When the

mass is pulled to the right, the spring will exert a force to pull the mass backward to

26


the left. This spring pulling force is known as a spring restoring force and is denoted

by a spring constant, k. The relation between the force, F and the spring with spring

constant, k is given by the Hooke’s Law [59]:

Fk(x) =−kx (3.1)

The force, F in (3.1) has a negative value since it is actually directed towards the left of

the mass. The momentum of the mass while it is moving to the right can be described

using Newton’s second law, F = ma. In the case of a spring-mass system, (3.1) will

become:

Fm(x) =−kx = ma (3.2)

A differential equation for the spring-mass system can be derived by substituting accel-

eration, a = x = d2x/dt2 into (3.2) to get [59]:

md2xdt2 + kx = 0 (3.3)

In the present of a mechanical damper such as compressible air in a spring-mass-dashpot

system in figure 3.1(a), a dashpot will introduce a damping effect which reduces the

velocity of the mass. The dashpot has a damping coefficient, b (in N.s/m), and its

damping force is given by:

Fb(x) =−bx =−bdxdt

(3.4)

Total force acting on the mass, m is given by Fm+Fb+Fk =F which can be rewritten

in a differential equation form:

27


md2xdt2 +b

dxdt

+ kx = F (3.5)

The solution for a capacitor charge, q can be found using Kirchoff’s voltage law for a

closed loop circuit in figure 3.1(b). The voltage law stated that the total voltage drop

across all components inside a closed loop is equal to zero [60]:

−VF + eC + em + eR = 0 (3.6)

Considering a time-dependant voltage, VF(t), time-dependant current, i(t) and substi-

tuting the voltages for the capacitor, resistor, and inductor into their corresponding dif-

ferential equation expression, equation (3.6) will become:

−VF(t)+1C

∫ t

−∝

i(τ)dτ+Ldidt

+Ri(t) = 0 (3.7)

Substituting i(t) = dq/dt into (3.7) and rearranging:

Ld2qdt2 +R

dqdt

+1C

q(t) =VF(t) (3.8)

Comparing the differential equation given by (3.5) and (3.8), it can be noted that the

mass, m (kg) is analogous to the inductor, L (H); the damping coefficient, b (N.s/m) is

analogous to the resistor, R (Ω); and the spring constant, k (N/m) is analogous to the

capacitor compliance, 1/C (1/F). The force acting on the mass, F (N) is analogous to

the voltage source, VF (V); and the mass velocity, x (m/s) is analogous to the electrical

current, I (A), or dqdt .

Complex impedance representation

For ideal and linear components in figure 3.1(b), the differential equation in (3.8)

28


can be rewritten in terms of complex impedance of each components. The complex

impedance of a resistor is represented by ZR =R, an inductor by ZL = jωL, and capacitor

by ZC = 1/( jωC) [58]. Thus, total complex impedance of the closed loop circuit in

figure 3.1(b) is given by:

ZT = ZL +ZR +ZC = jωL+R+1

jωC(3.9)

Using complex voltage, VF , complex current, I, and Ohm’s law, the voltage in figure

3.1(b) is given by:

VF = IZT = I jωL+ IR+I

jωC(3.10)

3.3 Spring-supported Diaphragm Microphone Modelling

A spring-supported diaphragm presented here has a structure as shown in Fig. 3.2. The

square diaphragm is suspended on a four L-shape spring structure at all its four corners.

Its matched size backplate with several perforated holes is shown in Fig. 3.3. The cross-

sectional view of the microphone structure is shown in Fig. 3.4. A mathematical model

to describe the diaphragm movement under an oscillating sound pressure was developed

by dividing the diaphragm into two main parts: a) a diaphragm with four corners simply

supported by a fixed point, and b) four doubly clamped L-shaped springs.

Assuming a linear displacement, the corner-supported diaphragm’s center deflection,

w1 in Fig. 3.5 is given by [61]:

w1 =0.12P(wd)

4(1− v2)

Eh3 (3.11)

where P is the sound pressure perpendicular to the top of the diaphragm in Pascal, h is

29


Figure 3.2: Microphone diaphragm with spring structure.

the diaphragm thickness, wd is the diaphragm length and width. E and v are the modulus

of elasticity, and Poisson’s ratio of the diaphragm material respectively.

The deflection of an L-shaped spring is derived from a doubly-clamped beam center

deflection [58]. Assuming small and linear diaphragm deflection, a center beam deflec-

tion, wbc in Fig. 3.6 is given by:

wbc =Pb(wb)

2(Lb)3

CbEwbh3 (3.12)

where wb is the beam width, h and Lb are the beam thickness and beam length respec-

tively. A constant factor Cb was determined numerically by varying the beam thickness,

width, and length to give Cb ≈ 17.4. Modifying Eq. (3.12) by introducing a factor C1 to

compensate the differences between the doubly-clamped beam and the L-shaped spring

deflection in Fig. 3.7 gives:

w2 =Ps(ws)

2(2Ls −ws)3

17.4C1Ewsh3 (3.13)

30


Figure 3.3: Microphone backplate structure with perforated holes.

Figure 3.4: Microphone cross-sectional view.

where w2 is the L-shaped spring center deflection, h, ws, and Ls are the spring thickness,

spring width, and spring length respectively.

Since the microphone diaphragm’s corner is attached to the center of the L-shaped

spring, Eq. (3.13) was modified to include the effect of diaphragm’s corner deflection to

give:

w2 =P(wd)

2(2Ls −ws)3

17.4C1Ewsh3 (3.14)

31


Figure 3.5: Corner supported diaphragm.

Figure 3.6: Doubly-clamped beam center deflection.

The centre deflection of the square spring-supported diaphragm, wc for small di-

aphragm deflection (wc < h) is given by the sum of the diaphragm deflection in Eq.

(3.11) and L-shaped spring deflection in Eq. (3.14):

wc =0.12P(wd)

4(1− v2)

Eh3 +P(wd)

2(2Ls −ws)3

17.4C1Ewsh3 (3.15)

Fig. 3.8 shows the numerical relationship of a factor, C1 with the diaphragm thickness.

A linear curve fitting on the graph gives:

C1 = 5.802−0.056h (3.16)

32


Figure 3.7: L-shaped spring dimensions.

3.3.1 Open-circuit Sensitivity

A condenser microphone operates using the principle of a variable capacitor which pro-

duces a variable output voltage when one of its charged capacitor plates is moving par-

allel to the other plate, thus varying its plate gap. The open-circuit sensitivity (in Volt

per Pascal) of a condenser microphone is given by [31]:

S =Vb

∆P.∆hg

hg.

1(1+Cs/Co)

(3.17)

where Vb is the bias voltage (in volt), ∆P is the sound pressure, hg is the initial air gap

distance (in meter) between microphone diaphragm and its backplate, Co and Cs are the

microphone initial capacitance and stray capacitance (in Farad) respectively. The initial

or working capacitance can be calculated using the parallel-plate capacitor equation.

The narrow air gap in this microphone leads to an increase in the viscous damping. A

number of backplate holes were used to reduce the viscous damping effect [4, 47] (see

Fig. 3.3). Subtracting the backplate holes from the backplate area and assuming a flat

33


Figure 3.8: A numerical linear curve fitting for factor C1 vs. diaphragm thickness.

diaphragm deflection, the initial capacitance, Co is given by:

Co =εrεo

(w2

d −nπr2h)

hg(3.18)

where εr is the dielectric constant of the air gap (εr ≈ 1 for air), εo is the absolute

permittivity of a vacuum, n and rh are the number of backplate holes and hole radius

respectively.

Substituting Eq. (3.15) for the ∆hg into Eq. (3.17) yields a frequency dependent

open-circuit sensitivity of a spring diaphragm condenser microphone:

SOC =

[0.12(wd)

4(1− v2)

Eh3 +(wd)

2(2Ls −ws)3

17.4C1Ewsh3

]× Vb

hg (1+Cs/Co)(3.19)

34


3.3.2 Frequency Response

A condenser microphone is often designed to operate in a desired operating frequency

range. The frequency response of the microphone must be flat within the desired range

to reproduce a good quality sound. In this thesis, the microphone will be designed to

operate in an audio operating bandwidth of up to 20 kHz. Table 3.1 shows the optimised

parameters for the MEMS microphone design discussed in Section 4.4 and 4.6.

Table 3.1: Optimised microphone parameters used for the numerical simulations.

Parameter Symbol Value

Poisson’s Ratio v 0.3Young’s Modulus E 1.7 x 105 MPaPolysilicon density ρ 2230 kg.m−3

Air density (20oC) ρo 1.2 kg.m−3

Air viscosity(20oC) µo 1.84 x 10−5 kg/m-sSound velocity (20oC) c 343 ms−1Boltzmann constant kB 1.38 x 10−23 JK−1

Diaphragm thickness h 4 µmDiaphragm width wd 1 mmBackplate hole radius rh 25 µmBackplate thickness hb 8 µmBackplate width wb 1 mmBackplate holes count n 25Initial air gap distance hg 4 µmSpring length Ls 0.4 mmSpring width ws 0.1 mmBias voltage Vb 3 V

The frequency response of a condenser microphone can be analysed using linear

lumped elements in a network modelling. Fig. 3.9 shows an equivalent circuit diagram

to represent various lumped elements of a condenser MEMS microphone where Fs is

the sound pressure force in Volt, Vm is the diaphragm velocity in Ampere, and Vo is

the output voltage in Volt. The mechanical compliance, Cm of the diaphragm is given

by [31]:

35


Figure 3.9: Equivalent circuit diagram of a MEMS microphone.

Cm =∆h

∆P.w2d

(3.20)

Substituting Eq. (3.15) for ∆h into Eq. (3.20) gives a spring-supported diaphragm com-

pliance (in meter/Newton):

Cm =0.12(wd)

2(1− v2)

Eh3 +(2Ls −ws)

3

17.4C1Ewsh3 (3.21)

The lumped effective mass, Mm (in kg) of the microphone can be approximated by the

total diaphragm and L-shaped spring mass:

Mm = ρhw2d +4ρhws(2Ls −ws) (3.22)

where ρ is the polysilicon density for both diaphragm and L-shaped spring. The air gap

viscosity loss, Rg (in N.s/m) and its compliance, Ca (in m/N) can be expressed as [9]:

Rg =12µow2

dπnh3

g.

[α

2− α2

8− lnα

4− 3

8

](3.23)

36


Ca =hg

ρoc2α2w2d

(3.24)

where µo and ρo are the viscosity and density of air respectively, n is the number of

backplate holes, hg is the air-gap distance with zero bias voltage, α is the surface fraction

occupied by the backplate holes, and c is the sound velocity at room temperature. The

backplate holes viscosity loss, Rh (in N.s/m) is given by [31]:

Rh =8µohbw2

d

nπr4h

(3.25)

The total impedance, Zt of the circuit in Fig. 3.9 can be expressed as:

Zt = jωMm +1

jωCm+

Rg +Rh

1+ jω(Rg +Rh)Ca(3.26)

Thus, the frequency dependent sensitivity and frequency response of the microphone (in

Volt/Pascal) can be calculated as:

S(w) =Vo(w)

P=

Vbw2d

jwhgZt(3.27)

A theoretical frequency response of a spring-supported diaphragm microphone was

calculated using Matlab based on the modelling Eq. (3.27). The microphone’s initial

parameters in Table 3.1 were used for the calculation. The Matlab calculation result was

shown by the orange line in Fig. 3.10. The blue dash-dotted line in the figure shows

the simulated frequency response using the same microphone parameters in Table 3.1

but using a Coventor software to simulate the diaphragm centre deflection with vary-

ing frequency (FEM calculation), and the microphone open circuit sensitivity was then

calculated using Eq. (3.17) by neglecting the stray capacitance.

37


Figure 3.10: Simulated frequency response of a spring-supported diaphragm micro-phone with Matlab and Coventor FEM using parameters in Table 3.1.

It can be seen in Fig. 3.10 that the two calculations show a similar frequency re-

sponse with a Coventor FEM has a bit higher sensitivity values but nearly identical

resonance frequency at around 18kHz.

3.3.3 Pull-in Voltage

The sensitivity of a condenser MEMS microphone depends on various structures and

electrical parameters as discussed in the previous section. A bias voltage is required to

create a charge on microphone plates which will result in an oscillating voltage propor-

tional to the oscillating sound pressure on its diaphragm. A higher bias voltage is often

needed to increase the sensitivity of a condenser microphone as given in Eq. (3.27).

A condenser MEMS microphone pull-in voltage is caused by the attractive force

between the diaphragm and backplate when a constant bias voltage is applied during its

38


operation. Its value is mainly determined by the spring restoring force of the diaphragm

[57] and the L-shaped spring in this project. Assuming a linear spring restoring force,

the net force, Fnet acting on upper plate (diaphragm and L-shaped spring) is given by

[58]:

Fnet = k(hg −hd)−εoAV 2

b

2h2d

(3.28)

where spring constant, k can be calculated from the inverse of the spring-supported

diaphragm compliance (k = 1/Cm), hg and hd are the air-gap distance with zero and

constant bias voltage respectively. A is the effective parallel plate area (the backplate

area minus the area occupied by the holes). The first part of the expression in Eq. (2.11)

is the spring force upward by the diaphragm and L-shaped spring, and the second part of

the expression is the downward electrostatic force caused by the constant bias voltage.

At equilibrium, the net force is equal to zero:

Fnet(PI) = 0 (3.29)

The pull-in occurs at the air-gap distance [58]:

hnet(PI) =23

hg (3.30)

Equating Eqs. (3.28) and (3.29), and substituting Eq. (2.13) for the pull-in air-gap

yields:

k =εoAV 2

PI

h3PI

(3.31)

where VPI is the pull-in voltage at pull-in air-gap distance,hPI. Substituting Eq. (2.13)

into Eq. (3.31) yields the pull-in voltage, VPI expression:

39


VPI =

√8kh3

g

27εo(w2d −nπr2

h)(3.32)

A theoretical calculation of a pull-in voltage given in Equ. 3.32 using Matlab and

the microphone parameters in Table 3.1 yields a value of 13V. This equation will also

be used to calculate the pull-in voltage values shown in Fig. 4.12 and Fig. 4.16.

3.3.4 Mechanical Thermal Noise

A good condenser microphone is designed to pick up the lowest possible sound pres-

sure which is limited by the mechanical thermal noise and the preamplifier noise of

the microphone [47]. The A-weighted mechanical thermal noise, SN (in Pascal) can be

calculated by [47]:

SN =

√∫ f2

f14kBT (Rg +Rh)A2( f )d f (3.33)

where f1 and f2 are 20 Hz and 20 kHz respectively, kB is the Boltzmann constant, and

T is the absolute temperature (in Kelvin). The A-weighted filter function, A( f ) is given

by:

A( f ) =122002. f 4

( f 2 +20.62)( f 2 +122002)

× 1√( f 2 +107.72)( f 2 +737.92)

(3.34)

where f is the sound pressure frequency in Hertz.

It can be seen in Eq. (3.33) that a mechanical thermal noise can be reduced by re-

ducing the backplate holes viscous damping. However, the viscous damping reduction

40


will increase the resonant peak of the microphone diaphragm. Thus, optimum param-

eters need to be calculated to get the lowest mechanical thermal noise according to the

frequency response requirements.

3.4 Conclusions

In the first part of this chapter, the use of a lumped parameter system to model a con-

denser microphone’s structure has been discussed. Several mechanical and acoustical

parameters of a condenser MEMS microphone were translated into its equivalent elec-

trical components to form a closed circuit diagram in order to get the final equation that

relates its output voltage with all the relevant mechanical and acoustical parameters.

The modelling of a newly proposed spring-supported diaphragm microphone has

been thoroughly derived and discussed using several established plate theories and doubly-

clamped beam equations. The open-circuit sensitivity equation was derived using the

resulting spring diaphragm deflection equation with a constant bias voltage.

The frequency response equation of the spring-supported diaphragm microphone

was formulated using the spring diaphragm equation in an equivalent circuit diagram.

The comparison between a Matlab calculated frequency response with a Coventor FEM

software simulation using the same microphone parameters shows that they have a sim-

ilar response with a small sensitivity difference.

The pull-in voltage and mechanical thermal noise equations have also been discussed

in the last part of this chapter. The pull-in voltage equation shows a complex relation

between the microphone pull-in voltage threshold and its structure dimensions. The next

chapter will present and discuss a numerical analysis of various types of condenser mi-

crophone and the optimization of the spring-supported diaphragm microphone using the

microphone equations presented in this chapter as well as the Coventor FEM simulated

41


results.

42

4Numerical Analysis and Optimization of a Spring-

Supported Diaphragm Microphone

4.1 Introduction

In this chapter, the performance of the proposed spring-supported diaphragm micro-

phone will be investigated and analysed numerically using Coventor FEM software and

Matlab. Several microphone’s structural dimensions such as spring width, spring length,

air gap distance, diaphragm width and length will have various effects on the micro-

phone’s performance such as open circuit sensitivity, resonance frequency, and pull-in

voltage threshold. The final objective of the microphone design is always to maximise

the open circuit sensitivity while having the highest resonance frequency as possible. A

higher pull-in voltage threshold is required depending on the applied bias voltage during

the microphone’s operation.

The effective diaphragm area ratio of a non-flat deflection diaphragm of a micro-

phone will also be investigated and analysed in this chapter. Comparisons will be made

between the proposed spring-supported diaphragm and some other microphones’ design

43

CHAPTER 4. NUMERICAL ANALYSIS AND OPTIMIZATION OF A SPRING-SUPPORTED DIAPHRAGM MICROPHONE

in order to understand the effects of various structural designs to the microphone’s effec-

tive area ratio. Lastly, the microphone performances optimization will be analysed and

discussed using numerical analysis results by varying several microphone’s structural

dimensions in relation to its key performance factors.

4.2 Finite-element Analysis

Finite element analysis (FEA) is a method to solve a complex engineering structure nu-

merically. FEA had been used widely in the applications of structure and stress analysis,

heat transfer, electromagnetic analysis, acoustics, as well as fluid flow. FEA starts by

dividing a plate or a structure into some smaller fixed unit called finite elements. All

the finite elements are connected together at a nodal point and boundary lines of each

element. Then all the nodal points will be calculated to determine the structure’s dis-

placement and other quantities such as stresses and strains [62].

The finite elements could be divided into one, two, or three-dimensional elements.

One-dimensional line elements are used for a simple analysis of a beam. The two-

dimensional elements such as triangle and rectangular could be used for an analysis of

plates. Lastly, the three-dimensional elements such as tetrahedron, rectangular prism,

and hexahedron could be used for an analysis of a more complex 3D structure. The

number of finite elements is related to the accuracy of the results, however, a larger num-

ber of elements will increase the calculation time and consumes much larger computer

memory area [62]. Most of the numerical analyses in this project were using tetrahe-

dron elements of 25 µm in size in order to get acceptable estimates of the microphone’s

performances with a moderate simulation time.

In this project, Coventor FEM software was used to realize the 3-D microphone

44


structure and carry out the analysis to determine its various characteristics such as reso-

nance frequency, capacitance value, and pull-in voltage between the diaphragm and the

backplate of the microphone.

4.3 Spring-Supported Diaphragm Microphone Performances

Since FEA could be used to substitute the analytical solutions for a complex structure,

the performance of several types of spring microphones will be simulated and compared.

First, the centre deflection of an edge clamped microphone’s diaphragm will be sim-

ulated and compared with the spring supported microphone’s diaphragm. The spring

diaphragm microphone has a free moving diaphragm which is supported by a spring

mechanism around its corner. Fig. 4.1 shows the microphones diaphragm layout mask

drawn using Coventor FEM software. The cross-sectional views of the microphone are

shown in Fig. 4.2 and Fig. 4.3.

Figure 4.1: The diaphragm maskfor the spring-supported micro-phone.

Figure 4.2: The cross-section schematic of thespring-supported microphone.

.

Fig. 4.1 shows the top mask layout which is the spring-supported diaphragm of the

microphone. It clearly shows the square diaphragm at the centre and being supported by

45


Figure 4.3: The cross-sectional view of a spring-supported diaphragm microphone withperforated backplate.

Figure 4.4: The cross-sectional view of an edge-clamped diaphragm microphone withperforated backplate.

the spring structure at its four corners which has the spring width w1, spring separation

width w2, and spring length Ls. The 3D view of the diaphragm is shown as a green

diaphragm in Fig. 4.3.

This spring microphone is designed to be easily fabricated using existing silicon fab-

rication technology. The new diaphragm can be fabricated using just one material depo-

sition and one mask etching to produce the spring mechanism. The polysilicon material

was proposed to be used as the diaphragm material due to its low stiffness property and

46


to prevent the extra deposition of conductive material on the diaphragm. A rigid back-

plate with perforated holes is used to reduce the viscous damping effect by allowing air

to flow through the holes [4]. The perforated backplate structure could be seen clearly

in Fig. 4.3 which has a gold colour right under the green coloured diaphragm. Fig. 4.4

shows a cross-sectional view of an edge-clamped diaphragm microphone.

In order to make a fair comparison between two different types of microphones, their

material properties and device dimension have been set to be mostly equal. Table 4.1

summarizes the material properties and dimensions of both types of microphones.

Table 4.1: Material Properties and Dimensions of an Edge-Clamped and Spring-Supported Diaphragm Condenser MEMS Microphone.

Microphone Properties Edge-Clamped Spring-Supported

Poisson Ratio 0.3 0.3Youngs Modulus, E (MPa) 1.7x105 1.7x105

Initial Diaphragm Stress (MPa) 90 90Diaphragm Material Polysilicon PolysiliconDiaphragm Thickness (µm) 1.5 1.5Diaphragm Area (mm x mm) 0.8 x 0.8 0.73 x 0.73Backplate Area (mm x mm) 0.8 x 0.8 0.8 x 0.8Air Gap (µm) 4.0 4.0Spring Width, w1 (µm) – 35Spring Length, LS (µm) – 350Spring Hinge Width, w2 (µm) – 100

Fig. 4.5 shows the maximum centre deflection of an edge-clamped and spring-

supported diaphragm for a sound pressure between 0 dB SPL and 140 dB SPL (dB

SPL decibel in reference to the sound pressure level, 0 dB SPL = 2x10-5 Pa). It clearly

shows that the spring-supported diaphragm deflection is linearly related to the sound

pressure decibel and almost in parallel with the edge-clamped diaphragm response, but

with about 100 times higher sensitivity. This also indicates that the spring-supported

diaphragm can be a good candidate to replace or enhance the existing edge-clamped

47


diaphragm condenser MEMS microphone. The spring-supported diaphragm deflection

under a sound pressure view is shown in Fig. 4.6 . This view is generated by Coventor

FEM software and the thickness has been exaggerated to show the deflected diaphragm

and springs more clearly.

Figure 4.5: Maximum centre deflection versus sound pressure of an edge-clamped andspring-supported diaphragms.

An audio microphone is usually designed to have a flat frequency response of up

to 20 kHz. Fig. 4.7 and Fig. 4.8 shows a frequency response of an edge-clamped

and spring-supported diaphragm in terms of their maximum centre deflection versus

frequency under a sound pressure of 60 dB SPL. The edge-clamped diaphragm response

has a higher resonance frequency (about 109 kHz) due to the greater diaphragm stiffness

compared to about 9.75 kHz resonance frequency of a spring-supported diaphragm. In

this case, the bandwidth of a spring-supported diaphragm microphone can be increased

by adjusting the spring constant. A careful design of the spring mechanism should be

able to produce a higher sensitivity condenser MEMS microphone in the audio range.

48


Figure 4.6: Three-dimensional view of a spring-supported diaphragm deflection usingCoventor FEM software.

Figure 4.7: Maximum centre deflection versus frequency of an edge-clamped diaphragmunder a sound pressure of 60 dB SPL.

49


Residual stress of a microphone diaphragm is one of the main concerns when fab-

ricating the edge-clamped diaphragm MEMS microphone on a silicon wafer. Since

the edge-clamped diaphragm must have the lowest possible residual stress to have the

highest mechanical sensitivity, the fabrication process must be carried out carefully to

ensure correct diaphragm dimensions and compositions [6, 11, 16]. On the other hand,

the spring-supported diaphragm is able to eliminate the process by having a free moving

diaphragm.

Figure 4.8: Maximum centre deflection versus frequency of a spring-supported di-aphragm under a sound pressure of 60 dB SPL.

Fig. 4.9 shows the effect of residual stress on the edge-clamped flat and spring-

supported diaphragm. It can be seen that the edge-clamped diaphragm maximum centre

deflection reduces gradually by 97% when the residual stress is increased from no stress

condition (0 MPa) to 100 MPa and reduces by 49% when the stress is increased from 100

to 200 MPa. In contrast, the spring-supported diaphragm maximum centre deflection

reduces by only 32% and 17% respectively. This is an important indicator to show

50


Figure 4.9: Maximum centre deflection versus residual stress of an edge-clamped andspring-supported diaphragm.

that the spring-supported diaphragm is more stable when produced using silicon wafer

technology than the edge-clamped diaphragm.

4.4 Effects of Microphone Parameters on Performances

A capacitive MEMS microphone performance factors such as sensitivity, operating

bandwidth, pull-in voltage, and thermal noise can be analysed by varying some of its

structure parameters. Table 4.2 shows the microphone parameters’ change from a low

to a higher value which was shown as a percentage parameter change in the analysis

graphs throughout this section. Since only one parameter is changed at a time, all other

parameters used in the performance analysis simulations are fixed at a reference value

as given in Table 3.1.

51


Table 4.2: Microphone parameters’ changes used for the performance analysis simula-tions.

Parameter Symbol Value (low - high)

Diaphragm thickness h 1 µm - 5 µmDiaphragm width wd 0.8 mm - 1.8 mmBackplate hole radius rh 10 µm - 35 µmBackplate width wb 0.8 mm - 1.8 mmBackplate holes count n 10 - 50Initial air gap distance hg 2 µm - 7 µmSpring length Ls 0.1 mm - 0.5 mmSpring width ws 50 µm - 175 µm

4.4.1 Viscous Damping Structure Dimensions

Viscous damping of a MEMS microphone is largely affected by the air gap and back-

plate viscosity loss as in Eqs. (3.23) to (3.25). In this section, the spring-supported

microphone’s air gap distance, backplate hole count and hole radius were varied as in

Table 4.2 to observe its performance effects. The objective of a microphone design

is mainly to achieve the highest sensitivity, adequate operating bandwidth (20 kHz for

audio applications), and at least 3 times higher pull-in voltage than its bias voltage to

prevent the diaphragm from collapsing to the backplate during microphone normal op-

eration.

Fig. 4.10 shows that the operating bandwidth of the microphone can be increased

gradually by increasing the backplate hole radius and hole count. The increase in the

number of holes (holes count) from 10 to 50 (400% increase) will increase the micro-

phone operating bandwidth from 11.5 kHz to 25 kHz (117% increase). Similarly, the

increase of the hole radius from 10 µm to 35 µm (250% increase) will increase the mi-

crophone operating bandwidth from 10.5 kHz to 24 kHz (130% increase). Although a

higher operating bandwidth is shown to be easily achieved by having more backplate

52


holes and larger hole radius, they however, have an effect of decreasing the microphone

sensitivity as shown in Fig. 4.11. These two parameter changes, however, have no or

little effect on the pull-in voltage value (see Fig. 4.12). It could also be seen that the

increase of the microphone air gap distance from 2 µm to 7 µm (250% increase) will

decrease the microphone operating bandwidth from 19 kHz down to 13.5 kHz (29%

decrease). Thus, the air gap distance increase has a negative effect on the microphone

operating bandwidth even though it does increase the pull-in voltage gradually from 5V

to 30V (500% increase) as shown in Fig. 4.12.

Figure 4.10: Microphone bandwidth versus air-gap distance, number of backplate holes(holes count), and backplate hole radius change.

Fig. 4.11 shows the effects of viscous damping structure dimensions on the micro-

phone’s sensitivity using a bias voltage of 3V. It is shown in the figure that the increase of

the air gap distance from 2 µm to 7 µm (250% increase) will decrease the microphone’s

sensitivity from 6 mV/Pa down to 3.5 mV/Pa (42% decrease). Similarly, the increase

of the number of holes (holes count) from 10 to 50 (400% increase) will decrease the

microphone’s sensitivity from 8 mV/Pa down to 2 mV/Pa (75% decrease). Lastly, the

53


Figure 4.11: Microphone sensitivity (bias voltage = 3V) versus air-gap distance, numberof backplate holes (holes count), and backplate hole radius change.

increase of the hole radius from 10 µm to 35 µm (250% increase) will decrease the mi-

crophone’s sensitivity from 9.5 mV/Pa down to 2 mV/Pa (79% decrease). Therefore,

it is clear that the increase of the air gap distance, holes count, and hole radius will

decrease the microphone’s sensitivity.

A similar microphone designed by Torkkeli et al. [11] using a low-stress polysilicon

flat diaphragm with an air gap distance of 1.3 µm gives a bandwidth of 12 kHz and a

sensitivity of 4 mV/Pa when using a 2V bias voltage. It could be approximated from Fig.

4.10 and calculated using Eq. 3.27 that the spring-supported diaphragm microphone

gives a higher operating bandwidth of about 22 kHz when using a 1.3 µm air gap distance

and a sensitivity of about 4.6 mV/Pa when using a 2V bias voltage.

Another similar microphone design by Li et al. [13] is using a single deeply corru-

gated diaphragm with an air gap distance of 2.6 µm which gives an operating bandwidth

of 19 kHz and a sensitivity of 9.6 mV/Pa when using a 5V bias voltage. It could be

approximated from Fig. 4.10 that the spring-supported diaphragm microphone could

54


have an operating bandwidth of about 19 kHz using a 2.6 µm air-gap distance and a

sensitivity of about 10 mV/Pa by using a 5V bias voltage. .

A good microphone design must have at least 3 times higher pull-in voltage than its

bias voltage, so the effects of the variations of viscous damping structure dimensions

to the pull-in voltage must be investigated and considered. Fig. 4.12 shows that the

increase of the air gap distance from 2 µm to 7 µm (250% increase) will gradually

increase the pull-in voltage from 5V to 30V (500% increase). However, there are no

significant effects by the increase of holes count and hole radius to the pull-in voltage

threshold.

Figure 4.12: Microphone pull-in voltage with air-gap distance, number of backplateholes (holes count), and backplate hole radius change.

Thermal noise causes an audible noise to be heard on the microphone amplifier

circuitry, thus it must be reduced as much as possible to increase the sound quality

of the microphone. The A-weighted mechanical thermal noise of the spring-supported

microphone is shown to be decreasing with the increasing dimension of air gap distance,

holes count, and hole radius (see Fig. 4.13).

55


Figure 4.13: Microphone thermal noise with air-gap distance, number of backplate holes(holes count), and backplate hole radius change.

4.4.2 Diaphragm Structure Dimensions

Other than the viscous damping structure dimensions as discussed in the previous sec-

tion, a microphone’s open-circuit sensitivity and its frequency response are very much

dependent on its diaphragm structure dimensions as shown in Eqs. (3.19) and (3.27).

Fig. 4.14 shows that the spring width increase from 50 µm to 175 µm (250%) does not

have much effect on the microphone operating bandwidth, but slowly reduces its sensi-

tivity in Fig. 4.15. The spring width increase, however, does raise the pull-in voltage

slightly from about 11 V to 15 V (see Fig. 4.16). This shows that the spring width

increase will increase the spring stiffness, thus the pull-in voltage. In contrast, the use of

a longer spring (from 0.1 mm to 0.5 mm - 400% increase) in a spring-supported MEMS

microphone reduces the microphone operating bandwidth from 18 kHz to 14 kHz (22%

decrease) and pull-in voltage slightly (see Figs. 4.14 and 4.16) even though it causes

some increase in microphone sensitivity from 4 mV/Pa to 6 mV/Pa (Fig. 4.15).

56


Significant microphone performance effects can be seen by varying the diaphragm

and backplate width, as well as the diaphragm thickness. Increasing the diaphragm and

the backplate width from 0.8 mm to 1.8 mm (125% increase) will obviously increase

the capacitor effective area and thus increase its capacitance. This is reflected by the

large increase in microphone sensitivity from 2 mV/Pa to 17 mV/Pa (750% increase) as

shown in Fig. 4.15. However, the diaphragm width increase will also reduce its spring

constant, thus gradually reducing the microphone operating bandwidth from 23 kHz to

5 kHz (78% decrease - see Fig. 4.14), as well as reducing the pull-in voltage from 20 V

to 4 V (80% reduction - see Fig. 4.16).

Figure 4.14: Microphone bandwidth with diaphragm thickness, diaphragm and back-plate width, spring width, and spring length change.

The changes in a diaphragm thickness from 1 µm to 5 µm (400% increase) will

increase its spring constant. The diaphragm thickness increase, however, does reduce its

operating bandwidth up to about 200% thickness change before the bandwidth increases

slightly afterwards (see Fig. 4.14). A thicker microphone diaphragm gives a higher pull-

in voltage that increases from 2V to 20V (900% increase - see Fig. 4.16), but has a large

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negative effect on microphone sensitivity from 8.5 mV/Pa to 3 mV/Pa (65% decrease)

due to a higher spring constant (Fig. 4.15).

Figure 4.15: Microphone sensitivity with diaphragm thickness, diaphragm and back-plate width, spring width, and spring length change.

Figure 4.16: Microphone pull-in voltage with diaphragm thickness, diaphragm andbackplate width, spring width, and spring length change.

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Figure 4.17: Microphone thermal noise with diaphragm thickness, diaphragm and back-plate width, spring width, and spring length change.

The A-weighted mechanical thermal noise is shown not to be affected by the vari-

ations of diaphragm thickness, spring width and spring length, however, the noise be-

comes larger with the increase of the diaphragm and backplate width due the increase in

the capacitor area which will increase the microphone’s air gap and the backplate holes

viscosity loss (see Fig. 4.13). Similar to the viscous damping case, the noise value here

is shown to be more than 10 dB below the lowest hearing threshold (0 dBA SPL).

4.5 Effective Diaphragm Area

Several designs of high sensitivity capacitive microphones have been demonstrated in-

cluding corrugated, low-stress polysilicon, and spring-supported based diaphragm [4,5,

22, 23, 63, 64]. However, the current analytical analysis is based on assumption that the

small diaphragm movement is flat and piston-like to ease the microphone modelling and

calculation involved [43, 56].

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This section highlights the non-flat deflection of a microphone diaphragm and demon-

strates its effects on several types of microphone designs. Numerical analysis was car-

ried out to determine their effective area and capacitance value changes over the di-

aphragm deflection by a uniform sound pressure. Comparison graphs were drawn to

further understand the non-flat deflection effects on the microphone performance. This

understanding is desired to help microphone designers to design a better capacitive mi-

crophone in the future.

The capacitive MEMS microphone was based on a principle of a parallel plate capac-

itor. It normally has a very thin diaphragm which will vibrate with any sound incident

and a rigid backplate to form the bottom plate of a capacitor. The capacitance value is

directly proportional to the plate area and inversely proportional to the plate gap distance

and is given by [65]:

C =Aεrε0

d(4.1)

where A is the effective plate area in m2, εr is the dielectric constant of the air gap,

ε0 is the absolute permittivity of a vacuum (ε0 = 8.85 x 10−12 F/m), and d is the air gap

distance in meter (m). The dielectric constant for an air is equal to 1.

In a capacitive MEMS microphone operation, the vibration of its electrically charged

diaphragm and a rigid backplate will cause a voltage variation across the air gap of the

microphone. Assuming a piston diaphragm movement, this voltage variation is called

the electrical sensitivity of the microphone and is given by [43]:

Se =Vb

d(4.2)

where Vb is the bias voltage across the diaphragm and backplate.

Early condenser MEMS microphones were designed with a thin edge-clamped flat

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diaphragm and a thick perforated backplate to form an upper and bottom part of a vari-

able capacitor [4, 5, 7, 8, 11, 14]. The open circuit sensitivity of a condenser MEMS

microphone is proportional to its electrical and mechanical sensitivity. Different types

of edge-clamped diaphragm designs such as corrugated and low-stress polysilicon di-

aphragm have been investigated to reduce the diaphragm stress and stiffness to increase

its mechanical sensitivity [8, 11, 13, 14]. Several high sensitivity microphones with a

free moving diaphragm have been presented by Kim et al., Weigold et al., and Mo-

hamad et al. [22,23,64]. These microphones have their diaphragm suspended on several

spring mechanisms around its edges to further reduce the diaphragm stress which will

gradually increase its mechanical sensitivity.

This section will investigate the diaphragm effective area effects of four types of mi-

crophone as shown in Fig. 4.18. Type A is a square edge-clamped flat condenser micro-

phone while Type C is a similar type but with a circular diaphragm design. Type B is a

modified square spring-supported condenser microphone as demonstrated by Mohamad

et al. [64]. Type D is a circular spring-supported condenser microphone as demonstrated

by Kim et al. [22]. The grey area near the edge of the diaphragm shows the support struc-

ture area of the square or circular diaphragm. This support area will not vibrate on any

sound incident since it is attached to the microphones backplate.

All microphones were designed to have a 1.1mm x 1.1mm square dimension, 2 µm

diaphragm thickness, 4 µm air-gap, and 15 µm thick backplate perforated with 52 holes

of 40 µm in diameter. The microphones diaphragm was supported on top of its backplate

by the support structure. Therefore, the square diaphragm microphone will have only 1

mm square movable diaphragm and the circular diaphragm microphone will have only 1

mm in movable diaphragm diameter. The four types of condenser MEMS microphones

will be analysed and compared numerically. All microphone types were designed to fit

in 1.1 mm x 1.1 mm square silicon substrate in order to get a fair comparison between

61


Figure 4.18: Different types of condenser MEMS microphone diaphragms.

them. Table 4.3 summarizes the material properties and dimensions for all types of

microphone in this analysis. Note that the diaphragm area of all microphones is about

the same since the diaphragm is made from a polysilicon material which acts as the top

conductive capacitor plate.

Fig. 4.19 shows a static diaphragm deflection of all types of microphone in this anal-

ysis using CoventorWare 2006 finite element analysis (FEA) software. The deflection is

shown at about 2 µm from the initial position using different sound pressure values on

top of the diaphragm due to different diaphragm designs. However, the deflections look

larger since they have been exaggerated to clearly show the deflected shape. Clamped

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Table 4.3: Material properties and dimensions of condenser MEMS microphone types.

Microphone PropertiesType ASquare-

Clamped

Type BSquare-Spring

Type CCircular-Clamped

Type DCircular-Spring

Poisson Ratio 0.3 0.3 0.3 0.3Youngs Modulus, E (MPa) 1.7 x 105 1.7 x 105 1.7 x 105 1.7 x 105

Initial Diaphragm Stress (MPa) 90 90 90 90Diaphragm Material Polysilicon Polysilicon Polysilicon PolysiliconDiaphragm Thickness (µm) 2 2 2 2Diaphragm Area (mm x mm) 1.21 1.20 1.21 1.19Backplate Area (mm x mm) 1.06 1.06 1.06 1.06Air Gap (µm) 4.0 4.0 4.0 4.0Spring Width, w1 (µm) – 48 – 28Spring Hinge Width, w2 (µm) – 200 – 80

Type A and Type C microphones need a higher top sound pressure to get the same di-

aphragm deflection compared to spring Type B and Type C microphones.

It can be seen from Fig. 4.19 that all microphones except spring Type D have about

a parabolic diaphragm deflection. However, clamped Type A diaphragm deflection area

is found to be higher than clamped Type C. This was verified by a slightly higher ca-

pacitance value for the clamped Type A microphone compared to the spring Type B

microphone as shown in Fig. 4.20. Spring Type B and Type D microphones have much

higher capacitance value due to a larger diaphragm deflection area when suspended on

several spring mechanisms. The capacitance change between spring Type B and Type

D is about constant and linear when their spring-supported diaphragm were deflected

downward from zero until about 2 µm before exponentially increases towards the sur-

face of the microphone backplate.

The capacitance value of a parallel plate capacitor is directly proportional to the

effective area of the upper and lower plate of the capacitor. In this case, only the mi-

crophone diaphragm will vibrate with sound pressure while the microphone backplate

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Figure 4.19: FEM simulation result on different types of microphone diaphragm.

is designed and assumed to be rigid and has a negligible vibration. Therefore, only the

diaphragm effective area will be analysed and presented in this thesis. The effective area

ratio is the ratio of the deflected diaphragm effective area over the diaphragm effective

area at the initial position (not deflected).

Figure Fig. 4.21 shows that the effective area ratio of all four types of the micro-

phones diaphragm has almost a linear change when deflected downward from the initial

position until about 3 µm. It can also be seen that the rate of change of the effective area

ratio of spring Types B and D microphone is about 20% less than the rate of change of

the effective area ratio of clamped Types A and C microphone. A lesser change means

64


a higher effective area ratio over a larger diaphragm deflection movement which results

in a larger capacitance value and thus the microphone open circuit sensitivity.

Figure 4.20: Capacitance value versus maximum diaphragm centre deflection of differ-ent types of microphone.

Figure 4.21: Diaphragm effective area ratio versus maximum diaphragm centre deflec-tion of different types of microphone.

The relation between the diaphragm effective area ratio and the microphone capac-

itance can be seen clearly from Fig. 4.22. The capacitance of spring Types B and D

65


Figure 4.22: Diaphragm effective area ratio versus capacitance value of different typesof microphone.

microphone (spring-supported diaphragm) increases gradually when their diaphragms

are deflected downward. This is due to the higher diaphragm effective area and larger

spring-supported diaphragm movement compared to the clamped Type A and C micro-

phones.

It must be noted that the diaphragm stiffness is inversely related to the bandwidth of

the microphone. A softer diaphragm will have a shorter bandwidth. In this project, both

edge-clamped square and circular diaphragms have a higher bandwidth of 195.8 kHz

and 202.5 kHz respectively. The softer spring-supported square and circular diaphragms

have a lower bandwidth of 25.16 kHz and 3.85 kHz respectively. This shows that a

microphone diaphragm can be designed and adjusted to fulfill the required microphone

bandwidth and performance.

All the diaphragms are shown to have a linear effective area for a deflection un-

til up to 3 µm. The spring-supported diaphragms are found to have a 20% less rate

of change of effective diaphragm area ratio compared to the edge-clamped flat micro-

phone of the same size. This shows that the spring-supported diaphragms have about

66


20% higher effective diaphragm area compared to the equal size edge-clamped flat di-

aphragms. The numerical analysis also shows that the capacitance change of spring-

supported diaphragms is about 150% higher than the edge-clamped flat diaphragms. In

addition, the effective area of the spring-supported diaphragm can be increased further

by a more careful design of the spring mechanisms so that the diaphragm can have a flat

deflection over a wider maximum deflection range.

4.6 Microphone Performance Optimization

A microphone’s parameters need to be adjusted and optimised to achieve the best mi-

crophone performance given various design and application constraints such as smaller

device size, wider operating bandwidth, and minimum electrical power usage. In this

project, a spring-supported diaphragm microphone needs at least 20 kHz operating

bandwidth with highest sensitivity and pull-in voltage, as well as lowest thermal noise as

possible. The spring-microphone performance analysis based on structure dimensions

has been discussed in Section 4.4. The analysis graphs show that the increase in band-

width always has a trade-off with the microphone sensitivity, thermal noise, and pull-in

voltage threshold. Therefore, the microphone parameters in Table 3.1 have been chosen

where the bandwidth, sensitivity, and the pull-in voltage threshold are the highest with

a lower thermal noise value. The microphone parameters’ value in the table gives an

approximate operating bandwidth of 15 kHz (resonance frequency at 20 kHz), a sen-

sitivity of 4.67 mV/Pa (-46.5 dB ref. 1 V/Pa at 1 kHz using a bias voltage of 3 V), a

pull-in voltage of 13 V, and a thermal noise of -22 dBA SPL. The theoretical frequency

response of the microphone calculated using Eq. (3.27) and optimised parameters in

Table 3.1 is shown in Fig. 3.10.

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Table 4.4: The spring length and spring width sizes for each of the fabricated springmicrophones.

Label Spring Length, µm Spring Width, µm

M1 275 50M2 300 75M3 325 100M4 300 50M5 325 75M6 350 100M7 325 50M8 350 75M9 375 100

Figure 4.23: The spring length and spring width dimensions on the fabricated springmicrophone.

Parameters optimization can also be done by varying two or more variables at a time.

Since the PolyMUMPs fabrication process selected in Chapter 5 has a fixed polysilicon

thickness and air gap distance, the optimization can only be done on other variables

such as hole number, hole size, spring width, or spring length. The next optimization

attempt was done to study the effect of varying the spring length and spring width to the

microphone’s performances. The chosen lengths and widths of the spring structure are

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shown in Table 4.4 which refers to the spring dimensions in Fig. 4.23.

Figure 4.24: The operating bandwidth of each microphone samples (without the di-aphragm holes) as calculated by Matlab.

Figure 4.24 shows the bandwidth of each fabricated spring microphone samples as

calculated by Matlab using Eq. (3.27). It can be seen in the figure that the first micro-

phone sample (M1) with the shortest spring length and smallest spring width has the

highest bandwidth of about 25.5 kHz. However, a higher bandwidth caused by a stiffer

diaphragm results in the lowest sensitivity as shown in Fig. 4.25 . A structure simula-

tion for the first microphone sample (M1) using Coventor software (Fig. 5.14) shows a

resonance frequency of 15 kHz which gives an effective operating bandwidth of about

12 kHz. The bandwidth is about 50% lower than the bandwidth calculated using Eq.

(3.27). This is mainly due to the effect of having holes on the diaphragm which reduces

the diaphragm stiffness. However, a thorough modification of Eq. (3.27) due to the

diaphragm holes will be left for future investigation.

69


Figure 4.25: The open circuit sensitivity of each microphone samples (without the di-aphragm holes) using 1 V bias voltage as calculated by Matlab.

4.7 Conclusions

The first part of this chapter compares the performance of an edge-clamped diaphragm

microphone with the proposed spring-supported diaphragm microphone. The numerical

simulation results show that the spring diaphragm deflection is linearly related to the

sound pressure, similar and in parallel to the edge-clamped diaphragm deflection, but

having about 100 times higher sensitivity. This clearly shows that the use of a spring

diaphragm design can easily outperform the sensitivity of an edge-clamped diaphragm

of the same size due to a much lower diaphragm stiffness.

A lower diaphragm stiffness, however, causes a lower resonant frequency of the

diaphragm which is necessary to have enough bandwidth in the intended application

(10Hz-15kHz bandwidth for a typical audio range application). The second part of this

chapter shows various numerical simulated results on several spring microphone’s per-

formances such as sensitivity, operating bandwidth, pull-in voltage, and thermal noise

70


with microphone’s structural parameters such as diaphragm thickness, diaphragm width,

spring length, and spring width. All of these interrelated results could be utilised to find

specific parameter’s value for performance optimization given a set of application re-

quirements.

The next part of the chapter discusses about the importance of effective diaphragm

area ratio in order to design a higher sensitivity microphone. Effective diaphragm area

is directly related to the capacitance value of the microphone, the higher the effective

diaphragm area, the higher the value of effective capacitance value. The numerical

simulation results show that the spring diaphragms have about 20% higher effective

diaphragm area compared to the edge-clamped diaphragms of the same size.

Lastly, the microphone performance optimisation techniques were presented at the

end of the chapter. By setting some simple application requirements, the spring micro-

phone’s structural parameters were optimised to get an operating bandwidth of 10.2kHz,

a sensitivity of 4.67 mV/Pa, a pull-in voltage of 13V, and a thermal noise of -22 dBa SPL.

Since the final microphone design will use a diaphragm with a number of holes, the di-

aphragm will become softer, thus, reducing its resonance frequency. The optimization

method using two structural variables shows that the spring-supported diaphragm micro-

phone (without the diaphragm holes) could be designed to get about 25 kHz operating

bandwidth with an acceptable sensitivity of 2.3 mV/Pa at 1 V bias voltage. However,

the effect of adding the diaphragm holes had reduced the bandwidth to about 12 kHz as

simulated by Coventor FEM software.

The next chapter will present and discuss the method used in this project to fabricate

the proposed spring-supported diaphragm microphone on top of a silicon wafer.

71

5Capacitive MEMS Microphone Fabrication

5.1 Introduction

In the early years, the fabrication of a MEMS microphone was carried out using bulk mi-

cromachining techniques [11,12,15–17,21–25,28,42,50]. This is due to the microphone

design itself which has a back-chamber below the microphone’s backplate through the

silicon wafer. However, recently, many researchers have demonstrated the fabrication

of MEMS microphones on the surface of a silicon wafer using just a few metal depo-

sition layers and etching of a sacrificial layer [29, 66]. This technique was used since

the microphone was designed without having to etch the silicon wafer itself. Attempts

were also done to reduce the number of fabrication layers which will directly reduce the

number of fabrication masks needed [29, 66].

In this chapter, several existing MEMS fabrication techniques will be reviewed and

discussed. The fabrication of a spring-supported diaphragm microphone will be done

using a multi-projects wafer (MPW) process by MEMSCAP, USA. The PolyMUMPs

surface micromachining process and design rules will be discussed. Coventor FEM

software will be used to create all the masks needed to fabricate the spring-supported

diaphragm microphone using the selected process.

72

CHAPTER 5. CAPACITIVE MEMS MICROPHONE FABRICATION

5.2 MEMS Microphone Fabrication

MEMS devices can be fabricated either by etching the silicon wafer itself, by mate-

rial deposition on the surface of the silicon wafer, or a combination of both methods.

The selection of the fabrication methods largely depends on the structure geometry and

complexity, the time taken to produce each device, and possibly the total fabrication cost

including the masks and etchant cost.

Bulk micromachining is the most popular technology used for sensor fabrication.

It uses a deep wet or dry etching inside the silicon wafer. On the other hand, surface

micromachining is a technique of depositing materials on top of the silicon wafer and

etching out all the sacrificial layer and unwanted area to form a structure.

Silicon was largely used as the substrate of MEMS device fabrication due to its

cheaper cost, well-established processing techniques, and the possibilities to embed the

integrated circuit along with the mechanical structure [67]. A silicon wafer can be ob-

tained in either 100, 110, or 111 orientation depending on the crystal planes and direc-

tions as designated by Miller indices. However, most of the silicon wafer produced was

either 100 or 111 orientation.

Other than silicon, quartz and glass are also used to fabricate MEMS devices. Quartz

is mostly useful due to its piezoelectrical property and has been used to fabricate sensors

such as gyroscopes and accelerometers. Pyrex was chosen as a favourable glass to

fabricate MEMS devices since it has low thermal expansion similar to silicon.

The capacitive microphone consists of at least a vibrating diaphragm and a static

backplate. In the earlier designs, a back chamber is often needed to reduce the air

damping effects on the vibrating diaphragm as an example shown in Fig. 5.1. However,

a recent microphone design is able to omit the back chamber requirement by having

holes on the diaphragm itself in order to simplify the microphone fabrication process as

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an example shown in Fig. 5.2.

Figure 5.1: Microphone cross sectional-view with back chamber [11]

Figure 5.2: Microphone cross-sectional view fabricated on top of a silicon wafer [29]

5.3 MEMSCAP Multi-Projects Wafer (MPW)

MEMSCAP Inc. has introduced the Multi-User MEMS Processes (MUMPs) to pro-

vide a cost effective, proof-of-concept MEMS fabrication to industry, universities, and

government worldwide. There are three MUMPs standard processes offered by MEM-

SCAP: (1) PolyMUMPs - a three-layer polysilicon surface micromachining process,

74


(2) MetalMUMPs - an electroplated nickel process, and (3) SOIMUMPs - a silicon-on-

insulator micromachining process.

PolyMUMPs process by MEMSCAP was used to fabricate the spring-supported di-

aphragm microphone in this project. PolyMUMPs is a three-layer polysilicon surface

micromachining process, with 2 sacrificial layers and one metal layer. The processes

were initially derived from the work done at the Berkeley Sensors and Actuators Center

(BSAC) at the University of California in the late 80’s and early 90’s. Several mod-

ifications and enhancements to the processes had been done since then to support the

multi-user environment.

Fig. 5.3 shows the cross-sectional view of the seven layers PolyMUMPs process.

There are three polysilicon layers namely Poly0, Poly1, and Poly2. Each has a different

thickness and a lithography level’s name (masking level name) as shown in Table 5.1.

Polysilicon layer is used as the main structural material. The first and second oxide

layers are the deposited phosphosilicate glass (PSG) sacrificial layers which will be

removed or retained later depending on the structure design. The most bottom silicon

nitride layer is used to create the electrical insulation between the polysilicon and the

substrate. Lastly, the metal layer provides a solderable electrical contact between the

polysilicon and the external electronic circuit.

PolyMUMPs Design Rules

MEMSCAP has listed several mandatory design rules and some other advisory rules

based on their fabrication processes to help its customers build their MEMS devices suc-

cessfully. The mandatory design rules need to be followed by all MEMS structure de-

sign while the advisory rules could be violated depending on the structure requirements.

The design rules and precautions for the mask layout have been explained thoroughly in

Section 2.2 of the MEMSCAP PolyMUMPs Design Handbook [68].

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Figure 5.3: Cross-sectional view of the MEMS fabricated layers using PolyMUMPsprocess [68].

Table 5.1: PolyMUMPs’ layer names, thicknesses and lithography levels [68].

Material Layer Thickness(µm) Lithography Level Name

Nitride 0.6 –Poly 0 0.5 POLY0 (HOLE0)First Oxide 2.0 DIMPLE

ANCHOR1Poly 1 2.0 POLY1 (HOLE1)Second Oxide 0.75 POLY1 POLY2 VIA

ANCHOR2Poly 2 1.5 POLY2 (HOLE2)Metal 0.5 METAL (HOLEM)

The dark and light field convention for each process levels is listed in Table 5.2.

MEMSCAP process is using a light field convention to indicate the drawing feature that

should remain in the structure, while the dark field convention to indicate the drawing

feature that would be etched away from the structure. Table 5.2 shows that all the

polysilicon levels are the light field and all oxide levels are the dark field.

The fabrication of spring-supported diaphragm microphone in this project will uti-

lize only the bottom polysilicon layer (POLY0) and the second polysilicon layer (POLY1).

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Table 5.2: PolyMUMPs’ process layers showing the light and dark field levels.

Mnemonic Level Name Field Type Purpose

POLY0 light pattern ground planeANCHOR1 dark open holes for Poly 1 to Nitride or Poly 0 connectionDIMPLE dark create dimples/bushings for Poly 1POLY1 light pattern Poly 1POLY1 POLY2 VIA dark open holes for Poly 1 to Poly 2 connectionANCHOR2 dark open holes for Poly 2 to Nitride or Poly 0 connectionPOLY2 light pattern Poly 2METAL light pattern MetalHOLE0 dark provide holes for POLY0HOLE1 dark provide release holes for POLY1HOLE2 dark provide release holes for POLY2HOLEM dark provide release holes in METAL

The third polysilicon layer (POLY2) will be etched away completely. There will be a 2

µm gap between the first and second polysilicon layer to serve as the capacitor gap for

the microphone.

5.4 Spring-supported Diaphragm Microphone Fabrication

In order to fabricate the microphone on top of the silicon wafer without having any back

chamber, the spring microphone structure described in Section 3.3 has been fabricated

using the Multi-User MEMS Processes (MUMPs) at MEMSCAP, USA. MUMPs is ac-

tually a shared wafer or multi-projects wafer in which several users will share their own

MEMS design to be fabricated on a single silicon wafer using a standard process cre-

ated by MEMSCAP. This helps to reduce the MEMS prototyping cost by the researchers

around the world.

The spring diaphragm microphone in this project was fabricated by designing and

drawing the required masks based on the standard MEMSCAP processes for Poly-

MUMPs using Coventor software. Fig. 5.4 shows the completed masks that have been

77


sent to MEMSCAP for the fabrication process. The figure only shows the top mask of

several layers of masks required to fabricate the microphone structure. The masks used

are to form the microphone polysilicon backplate, polysilicon diaphragm, the air gap

between backplate and diaphragm, and the metal contact pads.

Figure 5.4: The MEMSCAP footprint layout for the 9 spring microphones of differentdimensions and one edge-clamped microphone (M10) as a reference.

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Figure 5.5: The PolyMUMPs process flow to fabricate a spring-supported diahragmmicrophone.

79


There are 10 microphones to be fabricated on top of a 1cm x 1cm square silicon

chip as shown in Fig. 5.4. Each of the microphones has a size of 1mm by 1mm square.

The spring microphones are labelled as M1 through M9, and M10 is an edge-clamped

square diaphragm microphone. Each of the nine spring microphones has different spring

length and width sizes (see Fig. 4.23) as stated in Table 4.4. These spring size variations

were chosen to be fabricated in order to investigate the effect of having two structural

variables changes on the microphone’s performance. All of the microphone samples are

using a 600 µm x 600 µm square backplate size.

Fig. 5.5 shows the simplified steps using the PolyMUMPs process to fabricate the

spring-supported diaphragm microphone structure in this project. The process starts

with n-type silicon wafer which is heavily doped with phosphorus film using a PSG

film as the dopant source (Fig. 5.5a). After the PSG film is removed, a 600 nm layer

of low-stress silicon nitride is deposited on top of the silicon wafer (Nitride - coloured

black) followed by a layer of 500 nm polysilicon (Poly 0 - coloured red). The wafer is

then coated with UV-sensitive photoresist (coloured yellow).

The photoresist is lithographically patterned by exposing it to UV light through the

first level mask (Poly 0) and then developing it. The photoresist in exposed areas is

removed leaving behind a patterned photoresist mask for etching. Plasma etching is

used to remove the unwanted polysilicon. After the etch, the photoresist is chemically

stripped in a solvent bath. This will create the backplate structure of the microphone

(Poly 0 - coloured red in Fig. 5.5b).

The first sacrificial layer, a 2.0 µm layer of PSG is deposited on the wafer by low-

pressure chemical vapor deposition (LPCVD - coloured orange in Fig. 5.5c). The third

level (ANCHOR 1) is lithographically patterned. The unwanted oxide is removed in an

RIE process and the photoresist is stripped. A 2.0 µm layer of polysilicon is deposited by

LPCVD (Poly 1 - coloured blue) followed by the deposition of 200 nm PSG (coloured

80


green in Fig. 5.5d) and a 1050C/1 hour anneal. The anneal serves to both dope the

polysilicon and reduce its residual stress.

The wafer is then coated with photoresist and the second polysilicon (Poly 1) is

lithographically patterned (Fig. 5.5e). The PSG is first etched to create a hard mask and

then Poly 1 is etched by plasma processing. After the etch is completed, the photoresist

and PSG hard mask are removed. The third polysilicon layer (Poly 2) will not be used

in the microphone fabrication.

Figure 5.6: The Coventor’s 3-dimensional layout for the spring microphone in Figure5.4.

The metal layer is used to form the contact pad of the microphone. The wafer is

coated with photoresist and the metal layer (METAL) is lithographically patterned. The

metal (gold with a thin adhesion layer) is deposited by lift-off patterning which does not

require etching. The side wall of the photoresist is sloped at a reentrant angle, which

allows the metal to be deposited on the surfaces of the wafer and the photoresist, but

81


provides breaks in the continuity of the metal over the photoresist step. The photoresist

and unwanted metal (atop the photoresist) are then removed in a solvent bath. The

completed structure is lastly released by immersing the chip in a 49% HF solution which

forms a movable spring-supported diaphragm (Fig. 5.5e).

Figure 5.7: The enlarged masks view of the first spring microphone sample (M1).

Figure 5.8: The Coventor’s 3-dimensional layout for the 9th. microphone sample (M9)in Fig. 5.4

.

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Coventor software has also been used to model and simulate the final structure using

the MEMSCAP standard processes and masks as shown in Fig. 5.6. There are two

wider contact pads on the top left and right of the square silicon which serve as the

ground contact pads for all of the microphones. The other small, square pads are the

contact pad which is connected directly to the diaphragm of each microphone.

Fig. 5.7 shows enlarged masks for the first microphone sample labelled as M1. It

clearly shows the square contact pad on the left and the ground contact pad on the top left

of the microphone. The fixed bottom plate of the microphone is connected to the ground

connector on its right, while the spring-supported top diaphragm of the microphone is

connected to contact pad on its left. Fig. 5.8 shows the 3-dimensional structure of the

9th. sample microphone which clearly shows the diaphragm with perforated holes, and

the spring structure of the microphone. The yellow structure in the figure shows the

bottom plate which is connected to the ground connection, while the large red structure

shows the spring-supported diaphragm.

Nine sets of spring-supported diaphragm microphones which have different spring

length and width as shown in Table 4.4 were fabricated using the PolyMUMPs pro-

cess by MEMSCAP. Figure 5.7 shows the masks drawing to produce the 3-dimensional

microphone model as shown in Fig. 5.8.

A high magnification microscope was used to see and capture the close-up view of

the fabricated microphone. Fig. 5.9 shows an edge-clamped square microphone to be

used as a performance reference for the spring microphone. The image clearly shows

the perforated holes on the microphone’s diaphragm which serves 2 main purposes: 1)

to reduce the effect of thin film air damping, and 2) to help the process of releasing the

diaphragm during the sacrificial layer etching process.

Fig. 5.10 shows the additional perforated holes on the spring structure of the mi-

crophone. The holes were required to help the process of releasing the spring structure

83


from the sacrificial layer. Since the holes are comparatively small in size and small in

number, their effect on the spring constant and behaviour is minimal.

Figure 5.9: The edge-clamped fabricatedmicrophone (M10) which serves as a ref-erence microphone.

Figure 5.10: The enlarged section of top-left spring edge of the spring-supportedmicrophone in Fig. 5.11

.

Figure 5.11: The top view of the fabricated spring-supported diaphragm microphone(M9).

84


Figure 5.12: The SEM picture of a spring-supported diaphragm microphone.

Figure 5.13: The SEM picture of a spring-supported diaphragm microphone taken atx3000 magnification.

85


Figure 5.14: A 3-dimensional view of the spring microphone in Fig. 5.12 simulatedusing Coventor FEM software.

Fig. 5.11 shows a close-up view of one of the fabricated spring microphones. Note

the perforated holes on the diaphragm and the spring structure. The SEM image of one

of the spring microphones is shown in Fig. 5.12. A closer look at the SEM picture in Fig.

5.13 clearly shows one of the square holes, the air-gap distance between the microphone

diaphragm and its backplate, and one of the spring structures. The 3-dimensional view

of the simulated spring-supported diaphragm microphone using Coventor FEM software

is shown in Fig. 5.14.

5.5 Conclusions

The fabrication of a MEMS microphone could be done using a bulk micromachining

process or using a recent method of surface micromachining process in which sev-

eral layers of conductive materials will be deposited and some sacrificial layers will

86


be etched away on top of a silicon wafer. The surface micromachining process has an

advantage of having a shorter fabrication time due to a shorter time required for metal

deposition and sacrificial layer etching.

The use of MEMSCAP PolyMUMPs fabrication technology helps students and re-

searchers around the world to fabricate many complex MEMS prototypes at a lower cost

and reduced fabrication problems. Several spring-supported diaphragm microphones of

different dimensions have been fabricated using the PolyMUMPs process. However,

no experimental results have been successfully carried out due to the unavailability of

suitable microphone interfacing circuit and electrical measurement equipment.

87

6Conclusions and Recommendations for Future

Work

6.1 Conclusions Overview

The research work in this project was done to find and propose a suitable solution for the

needs of a smaller, lower cost, and lower power consumption, but with high sensitivity

condenser microphone using MEMS technology. A high-sensitivity microphone could

easily be achieved by increasing the bias voltage between its diaphragm and backplate,

however, a thinner and smaller size diaphragm could suffer from a pull-in voltage at a

bias voltage of only several volts. The other method is to reduce the diaphragm stiff-

ness by means of using a thinner diaphragm or using a spring-supported diaphragm.

However, this could lead to the problems of having a lower operating bandwidth, lower

pull-in voltage threshold, and higher thermal noise.

This thesis described thoroughly the design of a new type of a spring-supported

diaphragm condenser MEMS microphone which will have a higher open-circuit sensi-

tivity and then optimised to achieve the required audio range bandwidth with a minimum

bias voltage and thermal noise. In order to understand and study the behaviour of the

88

CHAPTER 6. CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK

new spring microphone, a mathematical modelling for the spring diaphragm and its

sensitivity was derived using the existing plate theories and several lumped mechanical

and acoustic parameters in analogy to the electronic components which form a closed

circuit diagram (Chapter 3). The modelled sensitivity equation has been simulated us-

ing Matlab to obtain a theoretical diaphragm deflection, capacitance, and open-circuit

sensitivity, and compared with the structural numerical simulation using Coventor FEM

software to confirm and verify the performance results.

Some numerical simulations (Chapter 4) were done to compare the performance

of an existing edge-clamped MEMS microphone with the proposed spring diaphragm

microphone. It has been shown that the proposed spring diaphragm has a similar di-

aphragm deflection behaviour but with about 100 times more sensitivity compared to

the edge-clamped diaphragm microphone. Since the spring microphone has complex

relations between its mechanical dimensions such as spring length, spring width, di-

aphragm thickness, diaphragm size, and hole size, and with its performance such as

open circuit sensitivity, pull-in voltage, and thermal noise, thus, several numerical simu-

lations were carried out using Coventor FEM software to obtain a graphical relationship

between the device dimensions and its performance.

The design optimization must take into account the requirements for a specific ap-

plication. Generally, a condenser microphone for a consumer electronics applications

needs to be the smallest size as possible, with the highest sensitivity as possible to pick

up any low decibel sound pressure, consuming the lowest battery power, and having the

lowest thermal noise. The graphical analysis for the microphone’s performance analysis

shown in Chapter 4 suggests that the design optimisation could be achieved by taking

the points where the open-circuit sensitivity will be the highest, operating bandwidth of

at least 20kHz, and the pull-in voltage threshold is at least 3 times its bias voltage, and

a lower thermal noise, depending on the required diaphragm size, spring size, air-gap

89


distance, and some other material constraints.

The proposed spring diaphragm in this thesis was then fabricated using the multi-

projects wafer at MEMSCAP, USA using their standard silicon wafer processes. The

resultant MEMS microphone was fabricated on top of a silicon wafer without etching

any part of the silicon base (Chapter 5). Furthermore, only a few mask layers were used

to fabricate all the backplate, air-gap, diaphragm, and contact pads. This design has a

potential of a reduced manufacturing time and possibly lower cost.

6.2 Research Contributions

There is an increasing demand for a smaller, lower cost, lower power consumption, but

also high-performance MEMS microphone. Therefore, the research work on the design

of a high-performance MEMS microphone in this thesis has resulted in several research

contributions as outlined below:

• Research work in Chapter 1 contributes to the review of the development of vari-

ous types of MEMS microphone for the past 24 years. It is shown that researchers

are continuously working on increasing the sensitivity of the condenser MEMS

microphone while trying to design a device which is using a lower bias voltage

to reduce power consumption without sacrificing many microphone’s key perfor-

mances.

• A comprehensive microphone’s key performance was discussed in Chapter 2.

Several established microphone’s performance equations were presented in the

chapter. The mathematical equations for microphone’s open-circuit sensitivity,

pull-in voltage, and mechanical thermal noise could be used to simulate the initial

design of a MEMS microphone, and later used to optimise its structural parame-

ters for the given device requirements and constraints.

90


• The open-circuit sensitivity equation of a newly proposed spring-supported di-

aphragm microphone has been derived using an established plate theories and

doubly clamped beam equations in Chapter 3. The proposed spring microphone

has very low diaphragm residual stress, high effective diaphragm area, and high

mechanical sensitivity as shown and discussed in Chapter 4.

• A mathematical model for the frequency response of the proposed spring di-

aphragm was derived using the diaphragm deflection equation and linear lumped

elements in an equivalent circuit diagram as presented in Chapter 3. The com-

parison of the frequency response calculated using Matlab and simulated using

Coventor FEM software shows a similar resonant frequency with small sensitivity

difference.

• Comprehensive numerical simulations were carried out in Chapter 4 to find the re-

lation between spring MEMS microphone’s performances with its various struc-

tural dimensions. The resulting relationship graphs could then be used to find

a point where the microphone’s performance is the maximum for the intended

application and constraints.

• A new spring microphone design which can be fabricated without etching any part

of the silicon disc and using few fabrication masks was presented and discussed in

Chapter 5. The work in the chapter also outlined a cost effective and faster way to

fabricate any MEMS prototype by using the multi-wafer project (MPW) scheme

offered by MEMSCAP, USA.

91


6.3 Recommendations for Future Work

In this project, comprehensive modelling and numerical analysis of a spring-supported

diaphragm microphone has been presented and discussed. A method to find some opti-

mised mechanical parameters of the microphone has also been used and simulated using

FEM software. However, the optimisation method using design of experiment (DOE)

technique could be employed in future to better find and select the best optimisation

points for the microphone structural dimensions.

Even though the last chapter of this project has presented the fabrication of the spring

microphone using MEMSCAP MPW fabrication scheme, the real mechanical and elec-

trical measurement has not successfully being done to measure the microphone’s per-

formance and mechanical characteristics. This could also be done in future to better

understand the behaviours of the spring MEMS microphone.

Lastly, since the spring microphone is using spring structure on all four of its square

edges, it is very important to do future research work on the spring’s structure strength

and reliability so that the high-performance spring MEMS microphone could be opera-

tional for an indeterminate length of time.

92

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102

List of Publications

Refereed Journal Paper:

• N. Mohamad, P. Iovenitti, and T. Vinay, “Modelling and Optimisation of a Spring-

Supported Diaphragm Capacitive MEMS Microphone,” Engineering, vol. 2, no.

10, pp. 762–770, 2010

Refereed Conference Papers:

• N. Mohamad, P. Iovenitti, and T. Vinay, “High sensitivity capacitive MEMS mi-

crophone with spring supported diaphragm,” Proceedings of SPIE - The Interna-

tional Society for Optical Engineering, vol. 6800, 2008

• N. Mohamad, P. Iovenitti, and T. Vinay, “Effective diaphragm area of spring-

supported capacitive MEMS microphone designs,” Proceedings of SPIE - The

International Society for Optical Engineering, vol. 7268, 2008

Other Conference Papers:

• N. Mohamad, P. Iovenitti, and T. Vinay, “Design of High-Sensitivity Capacitive

MEMS Microphone”, Paper presented at Faculty of Engineering and Industrial

Science (FEIS), Swinburne PG conference, Nov 2008, Swinburne University of

Technology (SUT), Melbourne, Australia.

• N. Mohamad, P. Iovenitti, and T. Vinay, “Spring-Supported Diaphragm Capaci-

tive MEMS Microphone Modelling and Analysis”, Paper presented at Faculty of

Engineering and Industrial Science (FEIS), Swinburne PG conference, Nov 2009,

Swinburne University of Technology (SUT), Melbourne, Australia.

103

Documents

Design of Spring-Supported Diaphragm Capacitive MEMS Microphone · 2017-03-01 · on my initial research work and gives some valuable advices to further enhance my microphone design