qfimf

«3 '
‘

N

‘1‘ 5'

r \
”an
{Uh};
“4 :3

m».

_ v
on}:

a

x"

.m-

V

«4"»
“5.37. .

‘ .dvl

, A
VI
pg;

“1

 

.5 1" (/‘KL/ 5'/

5 W} [id-J9 59‘

 

[)ate

0-7 639

This is to certify that the
thesis entitled

Design of an Implantable Micro-Scale
Pressure Sensor for Managing Glaucoma

presented by

Gregory Alan Goodall

has been accepted towards fulfillment
of the requirements for

M . S . degree in MechLnical Engineering

   

Major professor

July 30, 19%

MS U is an Affirmative Action/Equal Opportunity Institution

 

 

 

 

UBTRARY

Michigan State
University

 

 

 

PLACE IN RETURN Box to remove this checkout from your record.
To AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6’01 cJCIFlC/DatoDuepGS-pJS

 

DESIGN OF AN IMPLANTABLE MICRO-SCALE
PRESSURE SENSOR FOR MANAGING GLAUCOMA

By

Gregory Alan Goodall

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE
DEPARTMENT OF MECHANICAL ENGINEERING

2002

 

‘
k

a

{31121

1‘1

3.6

ABSTRACT

DESIGN OF AN IMPLANTABLE MICRO-SCALE
PRESSURE SENSOR FOR MANAGING GLAUCOMA

By

Gregory Alan Goodall

Presented in this thesis is the design of a MEMS wireless pressure sensor that will
implanted in the eye of Glaucoma patients to monitor intraocular pressure (IOP) on a
continuous basis. It is hoped that the device will enable doctors to treat their patients
better by having a more complete patient history of IOP.

The device, made of silicon and glass, will feature an on-chip inductor and a
parallel plate pressure-variable capacitor. The inductor is formed from a planar coil of
gold, while the capacitor is comprised of a non-movable gold electrode housed inside the
sensor and a thin flexible diaphragm exposed to the pressure exerted by the eye fluid.
The sensor is a simple R-L-C resonant circuit. Pressure exerted on the diaphragm by the
aqueous humor results in a micron-scale deflection of the diaphragm causing a change in
the capacitance of sensor. The change in capacitance will in turn change the resonant
frequency of the sensor. The planar inductor coil allows for wireless telemetry to a data
acquisition and processing (DAP) unit by means of inductive coupling. Measuring the
electrical characteristics of the DAP provides a measure of the resonant frequency of the
sensor and thus a direct measure of the capacitance and the pressure in the eye.

This work of thesis consists of the design of a micro-scale sensor and concept
verification by the testing of macro-scale prototypes. Results from testing the models

models reflected the expected theoretical patterns for the frequency responses.

This thesis is dedicated to my parents and all those
that I care about. Without all of you, I never could have

made it this far or enjoyed it so much.

iii

.4 ,

 

Cha

Cha l

 

TABLE OF CONTENTS

LIST OF TABLES .......................................................................
LIST OF FIGURES ......................................................................
KEY TO SYMBOLS ...................................................................
Chapter 1 Introduction ...............................................................
1.1 Thesis Statement ..................................................
1.2 Background and Significance ...................................
1.3 Implant Options ...................................................
1.4 Operating Range ..................................................
Chapter 2 Theoretical Background and Circuit Analysis ....................
2.1 Conceptual Overview .............................................
2.2 Circuit Analysis ...................................................
Chapter 3 Design Parameters and Conceptual Sensor Layout ..............
3.1 Design Parameters ................................................
3.2 Conceptual Sensor Structure ....................................
Chapter 4 Capacitor Plate and Diaphragm Design ............................
4.1 Design Variables ..................................................
4.2 Analysis to Determine the Capacitance Range ................
4.3 Initial Capacitance Value ........................................
4.4 Analysis of Diaphragm Deflection ..............................

4.5 The Capacitance-Pressure Relationship .........................

iv

vii

ix

xiv

18

19

20

23

24

25

26

28

36

4.6 Effects of Residual Stress on the Diaphragm's Dynamics
And Sensitivity ................................................

4.7 Final Capacitor Design ...........................................
Chapter 5 Inductor Design ..........................................................
5.1 Design Variables ..................................................
5.2 Planar Inductors ...................................................

5.3 Design Considerations on Determining the
Inductance Value ..............................................

5.4 Computational Analysis for Design of a Planar Inductor. . ..

Chapter 6 Consideration of Resistance and Quality Factor in
Inductor Design ......................................................

6.1 Resistance and Quality Factor of the Inductor ................
6.2 Summary of the Inductor Design ...............................
Chapter 7 Summary of Micro-Scale Prototype Design ........................
7.1 Design Dimensions ...............................................
Chapter 8 Sensor Fabrication ......................................................
8.1 Fabrication Overview .............................................
8.2 Fabrication of the Glass Wafer .................................
8.3 Fabrication of the Silicon Wafer ................................
8.4 Electrostatic Boding of Wafers ..................................
Chapter 9 Prototype Testing Results .............................................
9.1 Prototype Overview ..............................................
9.2 Testing Procedure ................................................

9.3 Expected Results ..................................................

43

49

51

52

52

53

57

65

71

72

73

77

78

78

81

86

87

88

9O

91

ra.‘ I‘-

(ha

Chat

App

Bibli

 

 

Chapter 10 Important Considerations ..............................................

9.4 Fabrication of the PC Boards ....................................
9.5 Results From Testing First Generation Prototypes ...........

9.6 Results From Testing Second Generation Prototypes ........

10.1 Introduction ........................................................
10.2 Volume of Air Enclosed in the Capacitive Cavity ............

10.3 Drift .................................................................

Chapter 11 Conclusions ...............................................................

Appendix

Bibliography

11.] Summary ..........................................................

vi

92

92

94

103

104

104

105

107

108

110

121

Chm

 

 

 

Cha;

Char

Chap

Appf‘r

 

LIST OF TABLES

Chapter 3 Design Parameters and Conceptual Sensor Layout

Table 3.1 List of Key Sensor Design Parameters ................................ 20
Chapter 4 Capacitor Plate and Diaphragm Design

Table 4.1 Properties of Thin Film Silicon Used in Analysis ................... 30

Table 4.2 Size of Resonant Frequency Range Over a Range of Deflection

of 0-0.5 microns For Various Initial Capacitance Values ...... 43
Table 4.3 Summary of Capacitor Design ......................................... 49
Table 4.4 Summary of Final Diaphragm Design ................................ 50

Chapter 6 Consideration of Resistance and Quality Factor in Inductor Design
Table 6.1 Summary of Inductor Design .......................................... 71
Chapter 9 Prototype Testing Results

Table 9.1 Approximate Inductance Values for Prototypes for a
Capacitance of 1.52 pF ............................................. 96

Table 9.2 Theoretical Approximate Resonant Frequencies for a
Capacitance of 1.74 pF ............................................. 97

Table 9.3 Summary of Prototype Testing Results ............................... 97

Table 9.4 Comparison of Theoretical Resonant Frequencies
to Measured Values .................................................. 102

Appendix
Table A.1 Frequency Response Data for First Generation Prototype ......... 113

Table A2 Frequency Response Data for Device 11 with Capacitance
C=1.52 pF ............................................................ 114

vii

Table A3 Frequency Response Data for Device 11 with Capacitance
C=1.74 pF ............................................................ 115

Table A.4 Frequency Response Data for Device 6 with Capacitance
C=1.52 pF ............................................................ 116

Table A5 Frequency Response Data for Device 6 with Capacitance
C=1.74 pF ............................................................ 117

Table A6 Frequency Response Data for Device 9 with Capacitance
C=1.52 pF ............................................................ 118

Table A.7 Frequency Response Data for Device 9 with Capacitance
C=1.74 pF ............................................................ 119

viii

Cha

 

Cha

 

Chat

Chat

LIST OF FIGURES

Page

Chapter 1 Introduction

Figure 1.1 Options for Implant Location in the Eye .............................. 6
Chapter 2 Theoretical Background and Circuit Analysis

Figure 2.1 Concept Representation ................................................. 8

Figure 2.2 Equivalent Circuit ........................................................ 9

Figure 2.3 Impedances of Individual Elements .................................... 13

Figure 2.4 Equivalent Circuit Including Impedance from Mutual

Inductance ............................................................. 15

Figure 2.5 Illustration of the Voltage Dip Demonstrated
on a Theoretical Voltage Profile Across the Load Resistor. . .. 16

Chapter 3 Design Parameters and Conceptual Sensor Layout

Figure 3.1 Isometric View of Sensor ................................................ 20
Figure 3.2 Isometric View of Glass Wafer Layout ............................... 21
Figure 3.3 Differential Pressure Sensor Concept ................................. 22

Chapter 4 Capacitor Plate and Diaphragm Design
Figure 4.1 Variables for Design of a Capacitor ................................... 24

Figure 4.2 Resonant Frequency as a Function of Capacitance
for Various Inductance Values .................................... 26

Figure 4.3 Required Capacitor Plate Side Length as a Function
of Initial Gap Height to Achieve C0=2.0 pF ..................... 27

Figure 4.4 Diaphragm Shapes and Variables ...................................... 28

Figure 4.5 Required Side Length and Diameter of Stress Free Diaphragms
For Each Case of Maximum Deflection at 60 mmHg ........... 31

ix

Figure 4.6 Basic Size Comparison for Square and Round Diaphragms ......

Figure 4.7 Deflection as a Function of Pressure for Stress Free Diaphragm
(Square or Round) for Various Maximum Deflections
At 60 mmHg ...........................................................

Figure 4.8 Illustration Showing Support Structure on Square Diaphragm
Figure 4.9 Illustration of Round Diaphragm Formation .........................

Figure 4.10 Capacitance as a Function of Pressure for Various Initial
Gap Heights Using an Initial Capacitance Co = 2pF ............

Figure 4.11 Resonant Frequency as a Function of Capacitance for Various
Initial Gap Heights and Maximum Deflections Using an
Inductance of 800 nH ................................................

Figure 4.12 Resonant Frequency as a Function of Pressure for Various
Initial Gap Heights and Maximum Deflections Using an
Inductance of 800 nH ................................................

Figure 4.13 Capacitor Plate Size versus Initial Gap Height as a Function of
Initial Capacitance ...................................................

Figure 4.14 Effects of Residual Stress on Diaphragm Deflection ................

Figure 4.15 Effects of 40 MPa of Residual Stress on a Diaphragm Designed
to Deflect 0.5 microns at 60 mmHg ................................

Figure 4.16 Effects of Residual Stress on the Deflection of a Diaphragm ......

Figure 4.17 Sensitivity as a Function of Deflection for Various Cases of
Maximum Deflection at 60 mmHg of a Square Diaphragm
with Initial Gap =1.5 andAssumed Residual Stress of 40 MPa

Figure 4.18 Required Side Lengths as a Function of Thickness for
Stressed (40 MPa) and Stress Free Diaphragms ..................

Figure 4.19 Sensitivity as a Function of Deflection for Various Initial Gaps
of a 4 micron thick Square Diaphragm with an Assumed
Residual Stress of 40 MPa ..........................................

32

33

35

35

37

39

41

42

44

45

46

47

48

49

 

Iliaml iii... :A:
. .
-.

Cha

Figure 4.20 Illustration of Final Capacitor Plate Design ........................... 50

Figure 4.21 Illustration of Final Diaphragm Design ............................... 50
Chapter 5 Inductor Design

Figure 5.1 Planar Spiral Inductor Layout with n=3 Turns ...................... 52

Figure 5.2 Resonant Frequency as a Function of Capacitance for Various
Values of Inductance ................................................ 54

Figure 5.3 Basic Trends of Circuit Excitation as a Function of Frequency
Towards Changes in Inductance .................................... 55

Figure 5.4 Inductance as a Function of the Number of Turns for Comparing
the Precision of Equations (5.2-5.4) For Various Line
Spacings Using a Constant Line Width of 6 microns ........... 59

Figure 5.5 Inductance as a Function of the Number of Turns for Various
Turn Spacings ......................................................... 61

Figure 5.6 Outside Diameter of the Inductor Coil as a Function of the
Number of Turns for Various Turn Spacing Using a
Line Width w=6 microns ............................................ 62

Figure 5.7 Inductance as a Function of the Number of Turns for Various
Line Widths for a Line Spacing s=4 .............................. 63

Chapter 6 Consideration of Resistance and Quality Factor in Inductor Design

Figure 6.1 Series Resistance and Skin Depth as a Function of Frequency for
Case Where w = 6 microns, tw = 7 microns, 26 windings..... 66

Figure 6.2 Resistance and Q Factor as a Function of Frequency
Using tw =7 microns, w = 6 microns, and 26 Windings ....... 67

Figure 6.3 Resistance of Inductor as a Function of Frequency for Various
Line Thicknesses Using Line Width w = 6 microns,
and 26 Windings ...................................................... 68

xi

Chap

 

 

 

Chapt

Figure 6.4 Resistance as a Function of Frequency for Various Line

Widths Using Line Thickness tw = 9 microns, Spacing
s = 6 microns, and 26 Windings .................................... 70

Figure 6.5 Q Factor as a Function of Frequency for Various Line

Widths Using Line Thickness tw = 9 microns, Spacing
s = 6 microns, and 26 Windings .................................... 70

Chapter 7 Summary of Micro-Scale Prototype Design

Figure 7.1 External Dimensions of Sensor ........................................ 73

Figure 7.2 Dimensions of Diaphragm Structure Created from

Silicon Wafer .......................................................... 74
Figure 7.3 Dimension of Internal Structures and Glass Wafer .................. 75
Figure 7.4 Capacitor Layout ......................................................... 75
Figure 7.5 Inductor Layout .......................................................... 76

Chapter 8 Sensor Fabrication

Figure 8.1 Glass Substrate with the PR Mask to Define the Coil Recess ...... 79
Figure 8.2 Glass Substrate with Coil Recess ...................................... 79
Figure 8.3 Glass Wafer with PR Mask for Electroplating Gold ............... 80
Figure 8.4 Completed Glass Wafer ................................................. 80
Figure 8.5 Orientation of a (100) Silicon Wafer .................................. 81
Figure 8.6 Silicon Wafer with Si3N4 Mask to Define Capacitive Cavity ...... 82
Figure 8.7 Silicon Wafer After Capacitive Cavity Has Been Defined ......... 83
Figure 8.8 Silicon Wafer After Boron Doping .................................... 84
Figure 8.9 Silicon Wafer with PR Mask to Define the Diaphragm ............ 85
Figure 8.10 Completed Silicon Wafer ............................................... 85

xii

Figure 8.11 Set Up For Electrostatic Bonding Process ............................ 86

Chapter 9 Prototype Testing Results

Figure 9.1 First Generation of Prototypes .......................................... 88
Figure 9.2 Second Generation of Prototypes ...................................... 89
Figure 9.3 Experimental Setup ...................................................... 90
Figure 9.4 Expected Results From Prototypes .................................... 91

Figure 9.5 Sensor Voltage and Voltage Across the Load Resistor for
First Generation Prototypes Model # 9 ........................... 93

Figure 9.6 Sensor Voltage and Voltage Across the Load Resistor as a
Function of Frequency for Second Generation Prototypes. 95

Figure 9.7 Sensor Voltage as a Function of Frequency After Increasing
the Capacitance ....................................................... 98

Figure 9.8 Comparison of Sensor Voltages For Two Cases of Capacitance. 99

Figure 9.9 Comparison of Voltage Across Load Resistor For Two

Cases of Capacitance ................................................ 100

Appendix
Figure A.1 Mask For First Generation Prototypes 110
Figure A.2 First Mask For Second Generation Prototypes 111
Figure A.3 Second Mask For Second Generation Prototypes 112

xiii

 

 

 

 

 

 

L!

L\

M

Co

CFS

K1

K2

I«GMD

LMON

LMW

KEY TO SYNIBOLS

Capacitor Plate Area (umz)
Capacitance (Farads)

Initial Capacitance (Farads)
Capacitance at Full-Scale Deflection (Farads)
Young’s Modulus (N/um)

Resonant Frequency (Hz)

Amplitude of an AC Sinusoidal Current (Amps)
Phasor Current

Geometry Dependent Coefficient for Modified Wheeler’s
Equation equal to 2.34

Geometry Dependent Coefficient for Modified Wheeler’s
Equation equal to 2.75

Inductance (Henries)

Inductance Determined from the Current Sheet Method
(Henries)

Inductance Determined from the Empirical Expression
(Henries)

Inductance Determined from the Modified Wheeler Equation
(Henries)

Mutual Inductance (Henries)
Pressure Difference (N/ttm)
Quality Factor

Resistance (Ohms)

xiv

Rs Series Resistance (Ohms)

S Sensitivity (mZ/N)

V Amplitude of an AC Sinusoidal Voltage (Volts)

V Phasor Voltage

X Reactance (Ohms)

Z Impedance (Ohms)

a Half of the Side Length of a Square Diaphragm (um)

c1 Geometry Dependent Coefficient for Current Sheet Method
equal to 1.27

c; Geometry Dependent Coefficient for Current Sheet Method
equal to 2.07

C3 Geometry Dependent Coefficient for Current Sheet Method
equal to 0.18

c4 Geometry Dependent Coefficient for Current Sheet Method
equal to 0.13

d Gap Height Between Capacitor Plates (pm)

dm Inner Diameter of Planar Inductor (um)

dour Outer Diameter of Planar Inductor (um)

h Thickness of a Diaphragm (um)

1 Total length of the Inductor Coil (m)

m Side Length of a Capacitor Plate (um)

11 Number of Turns in a Planar Inductor

r Radius of a Round Diaphragm (um)

s Spacing Between Inductor Coils (um)

XV

. '1’?

 

a2

0‘3

as

Time (s)
Line Thickness of the Inductor Wire (um)
Side Length of Capacitor Plate (um)
Deflection at the Center of a Diaphragm (um)

Geometry Dependent Coefficient for Empirical Expression
Equation equal to 1.62e-3

Geometry Dependent Coefficient for Empirical Expression
Equation equal to —1.21

Geometry Dependent Coefficient for Empirical Expression
Equation equal to —0. 147

Geometry Dependent Coefficient for Empirical Expression
Equation equal to 2.4

Geometry Dependent Coefficient for Empirical Expression
Equation equal to 1.78

Geometry Dependent Coefficient for Empirical Expression
Equation equal to 0.030

Skin Depth (um)

Dielectric Constant of the Material Between the Electrodes

Dielectric Constant of a Vacuum equal to 8.85 X 106 (pF/ttm)

Phase Angle of the Current (degrees)
Fill Ratio of an Inductor
Permeability equal to 1.26e-6 for Gold
Poison’s Ratio

Phase Angle of the Voltage (degrees)

xvi

"all

 

Permeability of Gold equal to 2.21e-8 (ohm-m)
Conductivity of Gold equal to 4.55e7 (ohm’l m")
Residual Stress in a Diaphragm (N/ttm)
Angular Frequency (rad/s)

Resonant Frequency (rad/s)

xvii

Chapter 1

Introduction

- .......i

1.1

C017]

PUT?
teier.
the i.‘

com:—

11mm

3511.};

.Thfi It

 

 

1.1 Thesis Statement

This thesis describes the design phase for an implantable, biomedical pressure
sensor to be fabricated utilizing Microelectrical Mechanical Systems (MEMS)
technologies. The sensor is one of three components in a pressure measuring system that
will be used to monitor intraocular pressure (IOP) on a continuous basis. The second
component in the system is a data acquisition and processing (DAP) unit, while the third
component is a central database that will be utilized for record keeping purposes.

The pressure sensor will be implanted in the eye and will provide wireless
measurements of IOP. The device is small enough that the patient’s vision and the
function of the eye will not be affected. The data acquisition unit serves multiple
purposes. The device generates a signal that is transmitted to the sensor through wireless
telemetry, as well as acquires, processes, and temporarily stores the data that returns from
the implanted sensor. The information can then be uploaded to the central database so a
complete time record of IOP measurements can be maintained.

The work in this thesis is the first of multiple phases to complete the IOP
monitoring system. The second phase of development will be the fabrication of the
actual device based on the design information obtained from the prototype device
designed in this thesis. Future steps in the process include the design of the DAP unit,
design of the data base unit, component integration, implantation in to cats and primates,
and finally implantation in to humans.

The IOP sensor system design will employ the following general design criteria:
1) Fully implantable, wireless, and passive (without batteries) sensor designed

and built using MEMS technology

2) Precision pressure measurement

3) Continuous or scheduled measurement of IOP

4) Variable data acquisition rate

5) Alarm to alert patient of unsafe pressure levels

6) Remote control of transmitter/receiver unit

7) Portable transmitter/receiver unit with rechargeable batteries

8) Data storage for record keeping

A cure for glaucoma is the ultimate advance, but accurate, remote monitoring of
IOP has the potential to be as important to successful management of glaucoma in
patients as the heart monitor is to heart patients. Saving people’s vision is the ultimate
goal.
1.2 Background and Significance

Glaucoma is one of the most menacing diseases of the eye that exists today.
Patients may suffer significant eye damage, including blindness, without experiencing a
noticeable amount of pain or discomfort. Glaucoma is the second leading cause of
blindness in the United States and is the leading cause of blindness among African
Americans [1]. There are several types of glaucoma; the most common of which is called
primary open-angle glaucoma (POAG). POAG affects more than 3 million people with
an additional 3-6 million Americans considered to be susceptible because they have one
or more of the risk factors associated with the disease [1].

Glaucoma is a progressive disease that is characterized by a specific pattern of
damage to the optic nerve [1]. Development of the disease can be attributed to many risk

factors, including but not limited to high IOP, a family history of glaucoma, myopia,

 

 

 

 

bio

in:

~|

}.

 

 

blood pressure, and diabetes. Age also is a critical factor [2]. The incidence of glaucoma
increases approximately 10-fold between 50 and 70 years of age, ranging from about
0.2% of the population between the ages of 50 and 54 to 2.0% of the population aged 70-
74. Also, primates with experimentally induced elevations of intraocular pressure show
structural [3-6] and functional [7-10] changes that are characteristic of humans with
POAG, so implantation in to primates for testing will precede implantation in to humans.

While it is important to note that elevated IOP is neither synonymous with
glaucoma nor a guaranteed predictor of disease, it remains the most important risk factor
related to the disease [1]. IOP can be associated with much of the development and
progression of glaucoma damage that occurs through time. Patients with unilateral
elevation of intraocular pressure that is secondary to other eye disorders often develop
glaucoma.

In the normal eye, intraocular pressure is maintained at ~16 millimeters of
Mercury (mmHg) by a balance in the production and drainage of aqueous humor from the
anterior chamber of the eye. This clear, blood-derived fluid flows from the ciliary body
through the pupil to the Schlemm’s canal. The aqueous humor is then discharged
through the venous system into the vascular sclera by passing through the trabecular
meshwork, a sponge-like structure located in the anterior angle of the eye [11]. If the
balance of the rate of production of aqueous humor and the rate of discharge is changed,
the IOP is affected.

A patient’s IOP experiences cyclical change on a daily basis. Fluctuations in IOP
around the average value occur due to every day activity and changes in environment.

IOP can show many different patterns of changes throughout a day that include impulses,

.. some.“

-iv r.

t
'.‘ I

 

“bar.
d‘f ~ls \

piss-\h"

IOP Y-

1C]

 

 

In Anti.

 

prolonged periods of high pressure, or periods of sub-normal pressure without the
patient’s knowledge [12].

Measuring and monitoring of IOP is crucial for the diagnosis, treatment,
management, and research of the disease. At the present time, the most common method
for measuring a patient’s IOP is a procedure called tonometry [11]. While this method is
considered to be very accurate for measuring IOP, there are several drawbacks. Only a
single reading for the particular instant in time that the test is performed is possible.
Also, a visit to a physician’s office is generally required, thus individual measurements
may be separated by long periods of time. Permanent damage to many parts of the eye.
including the optic nerve and retina, can result within hours of the onset if the pressures
are high enough [1]. It is critical that IOP levels be monitored on a continuous basis so
that pressure relieving drugs can be administered immediately after the onset of high
pressures to minimize the risk of permanent damage.

This monitoring system would provide benefits in both clinical and research
applications. Clinically, the primary targets for such a device would be patients with
severe cases of glaucoma. From a research standpoint, there are many questions that are
unanswered about the true effects of IOP. Doctors still do not know what the largest
concern is; the peak pressure over 24 hours, the difference between the high and low
pressure measurements for a day, the cumulative IOP over a period of time, or an average
IOP level [1]. It is quite possible that one or all of these factors plays a significant role in
the progression of glaucoma. In this regard, such a device could lead to an extensive gain

in knowledge of glaucoma and better methods of treatment.

 

 

locai

1.1.

dew.

 

 

 

 

1.4 0

[1.
(b

1.3 Implant Options

There are two options for the location of the sensor implant. The device will be
located either in the vitreal chamber or the anterior chamber of the eye, shown in Figure
1.1. The implant will be attached to the wall of the eye or attached to a tether so that the

device can easily be located if there is a need for it to be removed.

Sensor . .
chera Option 1 ° 1)V1treal chamber implant

      

\

‘.
‘x
-
——

\‘
\
~--...

  
 
  

gs
l
1

$2

Optic Nerve \

97/

Fi re 1.1 O tions for Im lant Location in the E e

I Cornea
(Macula '

Vrlreous humor '

0 2) Anterior chamber implant

Sensor
Option 2

 

1.4 Operating Range

Normal levels of IOP are considered to be around 16 mmHg. Pressures over 22
mmHg are considered to be moderately high while pressures greater than 45-50 mmHg
can be extremely dangerous [1]. The pressure sensor has been designed to measure
pressures in the range 0 to 60 mmHg. It should be noted that all parameters were
designed with the intent of manufacturing a device that can accurately produce full-scale
measurements up to 60 mmHg. However, additional safety factors were included so that
the device would remain functional even if the IOP should exceed the 60 mmHg limit of

the design.

Chapter 2
Theoretical Background
and

Circuit Analysis

.1- w'11nrrr I 594‘

2.1

 

I,

 

 

 

2.1 Conceptual Overview

The IOP monitoring system consists of three separate components; 1) a wireless,
remote pressure sensor that is implanted inside the eye of the patient (secondary circuit),
2) a data acquisition and processing (DAP) unit located external to the body (primary
circuit), and 3) a central data storage system that maintains a time record of the patient’s
IOP measurements.

The primary and secondary circuits communicate by means of inductive
coupling (Figure 2.1). The primary circuit generates and transmits a time-wise periodic
signal to the secondary circuit, or sensor. The excitation of the sensor feeds back to the
primary circuit and changes the characteristics of the primary circuit. Measuring the
frequency response to the periodic signal of the primary circuit provides information
about the electronics, specifically the capacitance, of the sensor circuit, which is directly

related to the pressure that is being exerted on the sensor.

   
 
  

   
 
 
   
  

Inductive

Telemetry

Between
Sensor

 
 

\

’3 » ' , _ and
External .
Central Data . Device "
Database Acqursitron
and And Processing
Data Storage (DAP) Unit
Unit (Primary Circuit)

Figure 2.1 Concept Representation

Implanted
Sensor

(Secondary
Circuit)

11%:w34. qu “a“

A.»

CIR.

$5?»

“0..

p.

Ik..
I€\..l

w!

A schematic of the equivalent R-L—C circuit is shown in Figure 2.2. The primary
circuit will have a current (i) and consists of a sinusoidal AC voltage source (V), an
inductor (L), and a resistor (R). This resistor is referred to as the load resistor. The
secondary circuit will be an energy-conserving transducer that utilizes a pressure
sensitive, variable capacitor (C5), and an inductor (L5). Any practical inductor must be
wound with a wire that has some resistance, so it is impossible to have an inductor
without some finite resistance. The resistance in the coil can be considered as a separate

resistor R5 in series with the inductor L3 [13].

Data Acquisition and
Processing Device Sensor

 

 

 

 

External to body Implanted in eye

 

A A
V '

Figure 2.2 Eguivalent Circuit

2.2 Circuit Analysis
Assume that the voltage generated by the source is a forcing function of the form

v(t) = V cos (wt) (2.1)

For the circuit analysis, Euler’s equation will be used. Euler’s equation for

complex numbers can be written as

a“ = cos (out) + j sin (wt) (2.2)

where we define
Re [ei‘m] = cos (wt) (2.3)
Im [em] = sin (wt) (2.4)

From equation (2.3), equation (2.1) can be rewritten as
v(t) = Re [v ei‘m] (2.5)
or more specifically
v(t) = Re [V cos (wt) + j V sin (0)0] (2.6)

Equation (2.6) states that the original assumption for v(t) in equation (2.1) can be
written as the sum of two functions; one real and one imaginary. The real part of the
equation (2.6) is the initial assumed form for v(t) from equation (2.1) with a non—existent
imaginary part. However, the complex notation in (2.5) is convenient for the circuit
analysis, so it will be used noting that the imaginary component is non-existent in the
solution.

If the voltage v(t) in a circuit can be represented as a cosine function, then, in
order to satisfy Kirchov’s Current and Voltage Laws (KCL and KVL respectively), the
current i(t) must also be represented as a cosine function of the same frequency. As a
consequence of linearity of the KVL and KCL equations, the principle of superposition
holds, and the current can be derived from the expression for voltage as

i(t) = I cos (cot + o) = Re [I ei‘m’] (2.7)

10

 

 

PIA
AL
it
mum
\ .hd
C n
. .. 1MP . l
.1 -. it
L .\
Jew
.
H“
II n i
l,
mu

SILT

undo-1J1 .idiyladflirmii. A

Every steady state voltage or current in the circuit will have the same form and
same frequency a) as a result of KVL. Another suitable expression for the voltage is as a
complex number with magnitude and phase information
v(t) = Re [vzo em] = Re [V20° ei‘m] (2.8)
where O is the phase angle of the voltage equal to 0° for a pure cosine wave.
Similarly, an expression can be developed for i(t).
i(t) = Re [12¢ 9“] (2.9)
Noting that the real part of the voltage expression is desired, the notation can be
dropped for simplification. Also, the complex numbers (V40° and 11¢) represent the
voltage in terms of magnitude and phase. This complex representation is referred to as a
phasor and is denoted by bold letters. Rewriting our voltage and current expressions with
phasor notation provides V = VAO° and I = 14¢. After substituting the phasor notation
in the complex number notation of (2.8) and (2.9), the following expressions are left.
v(t) = V cm" (2-10)
i(t) = 1 cm (2.11)
The differential equation for the primary circuit determined from KVL is thus

mm + LES—to- = v(t) (2.12)

Substituting equations (2.10-2.11) in to equation (2.12) gives

Rrej‘”l + Lfileja’I = Vej‘“t (2.13)

Note that e"m is common to every term in equation (2.13), so it can be eliminated
after the differentiation, leaving just the phasors. The following equation is left

R1 + ijI=V (2.14)

11

W111i; 3/

Fr

Lae-

 

t}

es~

 

 

 

Impedance is defined as the ratio of the phasor voltage to the phasor current.

From (2.14), the impedance of the primary circuit in reference to the voltage source is
Z=lI/—=R+ij (2.15)

In rectangular form, the impedance can be written in a general form as a complex
number with real (resistive) and imaginary (reactive) components.

2(a)) = R(u)) + j X((o) (2.16)

For the case of the primary circuit, the impedance from (2.15) must fit the general
from in (2.16), so R(0)) must be equal to R and X(0)) must be (0L. Thus it can easily be
seen that the total impedance of the circuit has a component proportional to the sum of
the impedances of each of the individual elements present in the circuit.

Each individual element has an associated impedance. Resistive impedance is
simply the real resistance in a circuit, while inductive and capacitive impedances are both
dependent on the reactance. Since inductors and capacitors respond to current, these
elements are called reactive, and the opposition to current by these elements is then called
reactance. Inductive reactance (XL) is defined as

XL = 00L (2.17)

Capacitive reactance (Xc) is given by

1
XC 3"; (2.18)

When the primary and secondary circuits are in close proximity to each other, the
flux in the inductor of the primary circuit couples with the inductor in the secondary
circuit, and a flux is thus induced in the secondary circuit [13]. When this happens a

mutual inductance (M) occurs between the circuits.

12

\
.k k.- l-Le'xa 1 ".0 .6512? I

 

 

 

 

This mutual inductance serves as the pseudo driving voltage and a current is
induced in the secondary circuit. From (2.15) we recall that the impedance is the ratio of
the phasor voltage and current, and the total impedance is equal to the sum of the
impedances of the individual elements of the circuit. An expression for the total

impedance of the secondary circuit (ZS) driven by the mutual inductance can be derived.

Zs(w) = Rs(w) + jXLS ((0) + jXCS ((0) (2.19)
After substitution for XL and Xc in to (2.19) we get

. j
Z ((1)) =R ((0)+_]0)L —— (2.20)
S S S at:
S

Notice that the resistance in (2.20) is a function of 0.). As will be seen in Chapter
6, Rs has frequency dependence because of the skin effect. This is not important to the
circuit analysis that follows, but the notation will be maintained for the purpose of
accuracy.

The total impedance of the primary and secondary circuits based on the preceding

circuit analysis is shown in Figure 2.3.

External Sensor

 

 

 

 

 

 

Z(w)=R-+jml. ZSUDfi=R5(m)+-flan-jhocs

 

A A
f 7

Figure 2.3 lmflances of Individual Elements

13

.,\ .. . armed—2.:

 

 

 

 

 

 

 

“he

 

 

Based on equation (2.20), the total impedance of the secondary circuit is a
function of frequency. The capacitive and inductive impedances will cancel out at a
particular frequency so the impedance at that frequency will be purely resistive. This
frequency is called the resonant frequency and corresponds to the maximum excitation of
the secondary circuit.

For the inductive impedance and capacitive impedance to cancel, we must have

. j
aid _ 2021
J S wCS ( )

Algebraically reorganizing leads to

1
of: 1 ::m== Q23

LSCS ’ ,iLSCS

measured in units of radians per second.

 

 

However, it is often more convenient to use the following form
1

: 2n,/LSCS

where Fr is the resonant frequency measured in hertz.

E- (223)

As a result of the inductive and capacitive impedances canceling at the resonant
frequency, the total impedance is due to the resistance only. At resonance, a local
minimum in the secondary circuit’s impedance occurs. This local minimum in the
impedance corresponds to a maximum degree of excitation for the secondary circuit.

The mutual inductance between the circuits results in an additional impedance of
the primary circuit (XM). The result is that the total impedance of the primary circuit is
related to the total impedance of the secondary circuit. The equivalent circuit is shown in

Figure 2.4.

14

 

 

measurement

   

 

Z((o) = R +ij+ij(w)

Figure 2.4 Egulvalent Circuit Including lrngdance from Mutual Inductance

The impedance due to the mutual inductance seen in Figure 2.4 is given by [13]

v
x M (w) = = (2.24)

 

After substituting in the impedance of the secondary circuit, the expression for

reactance due to the mutual inductance becomes

2
XM (60) = (CUM) . (2.25)

Rs(a))+ja)LS 7‘;

 

 

s
XM((o) is inversely proportional to the impedance of the secondary circuit (ZS).
As stated previously, the impedance of the secondary circuit is at a local minimum at the
resonant frequency since the inductive and capacitive reactance cancel. As a result,
XM((0) will have a local maximum which is dependant on Rs((o) only.
Equation (2.15) imposes the constraint that the total voltage drop through the

circuit must be equal to the voltage of the source or

Z=¥=R+ij+jXM (2.26)

15

COT

 

ll.

£113

{of

i -11 I'III" "'.‘<\—

After algebraically reorganizing, (2.26) becomes

[ -
2
Z=¥=R+jw L+ “M (2.27)

1
R (w)+jat -.
S S Jafs

 

 

 

 

d

The magnitude of each cycle of the forcing function is constant. Since the
combined impedance due to the inductor and the mutual inductance (jcoL + jXM) shows a
local maximum at the resonant frequency, the voltage drop due to these elements is also
at a maximum. To satisfy the governing equation (2.27) and the constraint of the voltage
to have a constant magnitude, the magnitude of the voltage drop across the load resistor
will dip (as seen in Figure 2.5) and show a local minimum since the voltage drop across

the other elements is maximized.

 

3095-

    

 

 

 

 

7 Voltage Dip i

 

 

     

 

1CD 1(5 110 115 120 15 13) 1:5 140 145 13)
Regatta/(Mt)

Figure 2.5 Illustration of the Voltage Dip Demonstrated
on a Theoretical Voltage Profile Across the Load Resistor

16

asst—H

Sweeping a periodic signal through a particular frequency range and measuring
the voltage across the load resistor will lead to determining the resonant frequency by
finding the frequency at which the minimum occurs.

While the exact measure of the dip is not significant in identifying the resonant
frequency, a sharply defined dip with a large magnitude is desired so that the local
minimum can be easily identified with a small margin of error. Several factors influence
how sharply the voltage will dip and how large the following voltage rise will be. The
effect of the resistance of the secondary circuit is to increase the frequency range that is
required for the peak to occur after the voltage dip. As the resistance increases, the
voltage dip will occur prior to the resonant frequency, and the rise will occur after the
resonant frequency. With a resistance of 50 Ohms in the secondary circuit, for example,
the frequency range will be about 5 MHz, with the dip occurring about 2 MHz prior to
the resonant frequency and the peak of the rise occurring about 3 MHz after the resonant
frequency. However, there is an inflection point between the voltage dip and the peak of
the rise where the phase is equal to zero. This is the true location of the resonant
frequency. The measurement unit could include the ability to determine phase of the
signal even though phase analysis could not be performed during testing of the prototypes
(Chapter 9) due to lack of equipment availability.

Once the resonant frequency has been determined, equation (2.23) can be used to
determine the capacitance. Since the inductance is a known, fixed value, the only
variable in the equation is capacitance. The capacitance, in turn, is dependant on pressure
only. Once the appropriate relationship between capacitance and pressure has been

determined, the resonant frequency provides a direct measure of pressure.

17

Chapter 3
Design Parameters
and

Conceptual Sensor Layout

18

 

3.]

"amnesia. .i 5-8.1.1. 4
. . l. 4

 

 

“ILL

07.;

(1‘7.

1.11.3

prt ".

C0::

pm ‘1

3.1 Design Parameters

The design of the pressure sensor required optimization of the many linked
parameters. The analysis and decision making process became complex as trade-offs in
one area had to be made to improve another aspect of the design.

First, the pressure sensor will be implanted in the human eye so overall size of the
device is the most critical issue. The ophthalmologists associated with this project have
constrained the largest dimension to not exceed about 3 millimeters. Anything larger
than this could result in interference with normal vision or complicate the implantation
process. Since the overall size of the pressure sensor must be less than 3 mm, this
constraint is the most important parameter and will take precedence over all of the other
factors in the design. Once it has been insured that the size constraint has been satisfied,
maximizing the sensitivity of the device is the primary concern.

It is imperative that the sensor must be made of biocompatible materials. Most
MEMS sensors utilize silicon and glass, which are biocompatible. Silicon is utilized
because so much is known about it, and fabrication processes used to manufacture silicon
devices are much more developed than for other materials [14]. Glass is readily available
and is very compatible with many fabrication processes. For these reasons, silicon and
glass were chosen as the materials for all of the external structures.

The design also involves optimization of the physical dimensions for each of the
components. The list of important parameters that were considered and optimized is

provided in Table 3.1.

19

III ‘njb’...’
11.1. .3... ..

 

el

Table 3.1 List of Key Sensor Desig Parameters

 

apacitance Capacitor Plate Side Length

ductance Capacitor Plate Separation
Frequency Range Capacitance Range
Diaphragm Shape Inductor Shape
Diaphragm Side Length Number of Windings
Diaphragm Deflection Inductor “Wire” Thickness
Diaphragm Thickness Wire Height
Effects of Intrinsic Stress Gap Between Windings

on Diaphragm Dynamics Quality Factor and Resistance

 

 

 

3.2 Conceptual Sensor Structure
The base of the pressure sensor is a rigid structure, and the top surface is a
flexible diaphragm (see Figure 3.1). The sensor substrate and the diaphragm are

electrostatically bonded together.

Thin, Flexible
Diaphragm

    

Diaphragm
Support

Si Wafer

Glass
Substrate

Figure 3.1 Isometric View of Sensor

20

The substrate, or bottom wafer, will be made of glass (Pyrex). This wafer will
house the electrical components of the sensor. These components include a planar spiral
inductor and a conductive electrode that are deposited on to the glass substrate. The basic

layout is illustrated in Figure 3.2.

Gold Glass
Capacitor Substrate
Plate
Gold
Inductor
Coils

 

Figgre 3.2 Isometric View of Glass Wafer Layout

The top wafer will be made of (100) silicon. This wafer will be micro-machined
and heavily doped with Boron to form a thin pM silicon diaphragm. The heavy doping
makes the material conductive so the diaphragm can be used as a variable capacitor along
with the electrode that is housed on the glass wafer. The pressure exerted on the sensor
due to the fluid in the eye will produce micron scale deflections of the diaphragm. The
capacitance is a function of the electrode plate area and the gap height between the plates.
The movement of the diaphragm will result in a change in capacitance due to the change

in the gap height, resulting in a variance of the resonant frequency of the sensor. The

21

device is sealed with atmospheric pressure inside the capacitive chamber (a defined gap

between the two wafers). The sensor system provides measurements relative to the

pressure inside the cavity (Figure 3.3).

 

 
 

,-
,—"
’0
‘-
5'
—
—
a
"

Diaphragm

  

 

 

P++ Silicon
Membrane

 

4! .e N r-v '

\ Fixed Cap Plate /

Inductor Coils
Support Substrate(G]ass)

         

 

      

 

Figt_1re 3.3 Differential Pressure Sensor M

The inductor will be a planar spiral that will be made of gold electroplated on the
glass substrate. A square spiral was chosen because of the ease of the layout and the
symmetry. In general, planar inductors have a relatively low quality factor, or ability to
absorb or emit energy, compared to other common forms of inductors, but the inductance
value is well defined over a wide range and is tolerant to process variations [15]. This is
important because MEMS processes typically have a relatively high degree of variability
due to the micron-scale features that are present [14]. The quality factor is discussed in

detail in Chapter 6.

22

Chapter 4
Capacitor Plate

and Diaphragm Design

23

uni-.312: .
is...

.2

 

 

 

 

 

4.1 Design Variables

The variable capacitor consists of two parallel conductive plates (see Figure 4.1).
One of the plates in the sensor is a glass wafer with a thin layer of gold electroplated on
to it. The second plate is made from the p” silicon diaphragm. A square capacitor plate
was chosen so that the sensor would be symmetrical. Symmetry of the sensor will ensure
that the electric field around the sensor will be symmetric as well. This way, orientation
of the sensor inside the eye will not affect the quality of the inductive coupling between

the circuits.

 

 

 

 

figure 4.1 Va_riables for Desigp of a Capacitor
The capacitance between 2 parallel plates is given by

880A
C = d (4.1)

 

Since the capacitor plate is square, A is equal to (m x m = m2).

24

A sensitivity study will be performed to determine the optimum capacitance range
and corresponding resonant frequency range of the sensor, which will, in turn, dictate the
physical dimensions of the capacitor plate. Again, the goal is to optimize the sensitivity
of the device to pressure.

4.2 Analysis to Determine the Capacitance Range

The full-scale deflection of the diaphragm and the maximum change in
capacitance from the initial value is designed to occur at a pressure of 60 mmHg. The
magnitude of the deflection is the key result that will be used to prescribe all of the other
parameters.

The design of the sensor was an iterative process. The first step in the design
process was to estimate the initial capacitance of the device. It is desired to have as large
a range for the resonant frequency as possible so that a small change in pressure produces
a relatively large change in the resonant frequency. Equation (2.22) shows the
dependence of the resonant frequency on the inductance and capacitance values.

1

21rd LC

Equation (2.23) is used in Figure 4.2 to calculate the resonant frequency as a

 

Fr = (2.23)

function of capacitance for various inductance values. The inductances that were chosen
are on the order of hundreds of nano-Henries due to the constraints imposed by

fabrication.

25

 

 

     

 

 

 

 

:ii 140«

I“.

>. 120 a

2

g 100 ~

E 80 .

IL

‘5 60 4

E

c 40

C

O

a: 20 . .
0 0.005 0.01 0.015 0.02 0.025 0.03

Capacitance (nF)

+ L=600 nH + L=700 nH + L=800 nH -)(— L=1200 nH + L=2000nH

Figure 4.2 Resonant Frequency as a Function
of Capacitance for Various Inductance Values

It can be seen in Figure 4.2 that the change in frequency due to a change in
capacitance greatly increases as the capacitance decreases. This basic trend is true
regardless of the inductor value that is used in the calculation. As shown by the steep
slop of the plots in this region, the sensitivity of the resonant frequency range to
capacitance change is highest when the capacitance is on the order of 1 to 3 pF.

4.3 Initial Capacitance Value

To begin the design process, an initial capacitance of 2.0 pF was chosen for the
first iteration. Six gap heights were considered so sensitivity to gap height could be
revealed, and an optimum gap height could be determined. The gap heights used in the
analysis are 1.5 um, 1.6 um, 1.7 um, 1.8 mm, 1.9 um, and 2.0 urn.

The next step was to determine the side length of the capacitor plate that is
required to achieve the desired capacitance for several different initial gap heights.
Figure 4.3 shows the required side length of a square capacitor plate as a function of the

initial gap height to achieve an initial capacitance Co = 2 pF from equation (4.1). It can

26

q .3 it“! 5... c.1313. I
’-

p

be seen that the side length of the capacitor plate increases from 582 microns to 672 for
an initial gap height increase of only 0.5 microns. The capacitor plate size that is
required to achieve a particular capacitance is very sensitive to small changes in the gap

height.

 

 

Capacitor Plate Side Length (um)

 

 

 

1.5 1.6 1.7 1.8 1.9 2
Initial Gap Height (um)

Fig 4.3 Required Capacitor Plate Side Length as a
Function of Initial Gap Height to Achieve Co=2.0 pF

Figure 4.3 shows two valuable pieces of information. First, by reducing the gap
height one can reduce the required side length of the capacitor plate. Second, the actual
capacitance of the device is highly dependant on the accuracy of the value of the
capacitive gap. For example, if an initial gap height of 1.5 microns is desired for a
capacitance of Co = 2.0 pF (i.e. the electrode has a side length of 582 microns) and the
actual gap height is 1.9 microns, the actual capacitance will be C0 = 1.57 pF. Thus, the
actual initial capacitance Co will be 21% smaller than the expected value. This problem
can easily be accounted for during calibration of the device, but it is still an issue during

manufacture.

27

4.4 Analysis of Diaphragm Deflection

The next step in the process was to determine the relationship between the
capacitance and the pressure. The deflection of the diaphragm due to the application of
an external pressure is dependant on the diaphragm’s shape. There are two shapes of
diaphragrns that are commonly used in MEMS devices; square and round (see Figure
4.4). Of course, it is possible to use rectangular shaped diaphragms. However, for the
rectangular shape non-uniform stress distributions develop due to the lack of symmetry of
the structure, thus decreasing the sensitivity of the sensor so a rectangular shape was

never considered.

Length = 2a Diameter = 2r

Length: 2a

 

Thickness = h

      

i

Support Rim

 

Figpre 4.4 Diaphram Shaw and Variables

28

The relationship between pressure difference, diaphragm dimensions, material
properties and deflection for a stress free square diaphragm is given by [16]

24 h3

4 w w 3
P=——E—P— 4.20—9+1.58—C— (4.2)
l-V a h

and the relationship for a stress free round diaphragm is given by [14]

3

 

 

E E 16wc+(7-v)wC

p:
l—v2 r4 311 3h3

(4.3)

It should be noted that the diaphragm is supported at the edges as seen in Figure
4.4 so the maximum deflection occurs at the center of the diaphragm. The maximum
stress due to bending occurs at the edges.

A major part of the design to address is the selection of the material of the
diaphragm. In MEMS applications, the films are generally on the order of a few microns
thick, and thus they may not have the same material properties as the bulk material [17].
Silicon is not an isotropic material so both the stress and strain are second rank tensors
with a stiffness matrix consisting of 81 coefficients [17]. However, due to symmetry
along several cryptographic planes of the silicon molecule, the stiffness matrix of silicon
only has three independent coefficients. As a result, an isotropic average must be used in
the determination of Young’s modulus. There are many published values for Young’s
modulus, Poison’s ratio, and the density of thin film silicon. For the purposes of this

analysis, the following values were used.

29

 

Table 4.1 Promrties of Thin Film Silicon Used in Analysis |17 |

 

Young's
Modulus 160 GPa

Poison's Ratio 0.05

Density 2300 ngmAS

Typical theoretical models for pressure sensors utilize small-deflection plate

 

 

 

 

theory and neglect built in stress (called intrinsic or residual) in the diaphragm that result
from the fabrication processes [16]. Analysis will begin with a model, which assumes the
diaphragm to be stress free, and then the effects of built in stresses due to fabrication will
be introduced.

There are two reasons for choosing an initial gap height significantly larger than
the maximum deflection of a particular design. First, it is possible for a patient to
experience IOP higher than the upper limit of 60 mmHg that the device is designed for.
For this reason, it is important that the plates do not touch as such a condition could
jeopardize the device’s functionality. The larger gap height accounts for a safety factor
against a short circuit in the sensor.

Second, the fabrication of the device (see Chapter 8) requires an etching step to
define the gap between the capacitor plates. Current silicon fabrication processes can
control silicon etching to within about 1 micron so there is a window of error associated
with the fabrication [14]. To account for this, a larger gap will be used as a safety factor
to account for variations due to the fabrication processes.

For the thin plate model to be accurate, the deflection must be relatively small
compared to the thickness of the diaphragm. The analysis is conducted over a range of

maximum deflection magnitudes from 0.3 microns to 0.5 microns.

30

The next step was to determine the side length (square diaphragm) or diameter
(round diaphragm) of the diaphragms so that a comparison of the relative size for each of
the theoretical designs can be made. Figure 4.5 presents a comparison of the required
side length/diameter as a function of thickness to achieve each of the three deflections at
a pressure of 60 mmHg. Equations (4.2) and (4.3) were used to generate Figures 4.5a and

4.5b respectively

 

700 m. ....._.... 1..
a) Square Diaphragm

 

 

 

 

 

 

 

 

 

geso ~ /

.§ 600 — » ~ ~ ~

‘8' 550

g . V . I ,. _

‘6) /

5 500 //" ‘

_I

o 450 -+

2

‘0 400 . .

E 3 0 0.3 micron deflection

_ 5 H o e

§300 0.4 micron deflectlon

1: . .
0.5 micron deflection

 

 

 

 

 

01 01
O
O

1

 

.b

01

C
1

0.3 micron deflection

 

0.4 micron deflection

 

 

(D h
01 C
O o
‘1 l

 

Required Diameter (microns)

 

 

0.5 micron deflection

 

(.0
O
O
{

 

3 3.5 4 4.5 5 5.5 6 6.5 7
Diaphragm Thickness (microns)

l"
01

Figure 4.5 Required Side Length and Diameter of Stress Free
Diaphram For Each Case of Maximum Deflection at 60 mmHg

31

The side length/diameter of the diaphragm that is required to achieve a specific
magnitude of deflection greatly increases with an increase in thickness. This intuitively
makes sense since the diaphragm’s resistance to bending, or stiffness, increases with
thickness. The stiffness is reduced by increasing the side length so the desired magnitude
of deflection can be achieved. The diameter of a round diaphragm of a particular
thickness is about 6.3% larger than the side length of a square diaphragm of the same
thickness for each of the three designs (Figure 4.6). When taking in to account that the
diagonal of the square diaphragm is about 30% larger than the diameter of a round
diaphragm, the total amount of space occupied by either shape on a wafer is similar.
There is not a clear advantage of choosing one shape over another from a size

perspective.

Diameter = 2r

Length = 2a

 

 

 

2rz l .063 (2a)

Fi re 4.6 Basic Size Com arison for S uare and Round Dia hra ms

 

32

For both the square and round diaphragms, an increase in the maximum deflection
at 60 mmHg increases the required side length/diameter of the diaphragm for a particular
thickness. Again, this intuitively makes sense. If it is desired to achieve a larger
deflection at the maximum pressure of 60 mmHg, the diaphragm’s stiffness must be
reduced by increasing the side length/diameter of the diaphragm.

It should be noted that the first term in (4.2) and (4.3) dominates at small wC/h so
the relationship between pressure difference and deflection becomes almost linear as seen

in Figure 4.7. Since the deflection is very small, equation (4.2) can be written as

 

 

 

 

4 w3 4
P = E 2 3,-1— 4.20&+1.58—39 a E 2 EXP-203$] (4.4)
l— V a h h 1— v a h
and equation (4.3) becomes
4 3 4
16 7 - V w
P=—E——L WC+( )C 5 E h—5.331C— (4.5)
l—V2 r4 311 3h3 l—v2 r4 h
0'5 0.5 micron deflection design
0.45
0.4 0.4 micron deflection design
‘3‘
E 0'35 0.3 micron deflection design
2 0.3
E.
c 0.25
3 0 2
g 01.5
8 e

.0
.—L

0.05

 

0 1 0 20 30 40 50 60
Pressure (mmHg)

Figure 4.7 Deflection as a Function of Pressure for Stress Free Diaphragm
(Sguare or Round) for Various Maximum Deflections at 60 mmHg

33

The plots in Figure 4.7 are for both a square and a round diaphragm. Since the
side length/radius in equations (4.2) and (4.3) respectively are designed for the same
pressure and deflection ranges, the constants in front of the deflection terms are already
included in the aside length/radius calculations. Figure 4.7 shows the maximum that the
diaphragm will deflect as a function of pressure if the side length/diameter have been
designed for each case of deflection at 60 mmHg.

A square diaphragm can easily and accurately be fabricated because of the
anisotropic nature of the silicon crystal structure. The (100) and (111) crystallographic
planes in the silicon lattice intersect at right angles on the surface of a (100) silicon wafer.
Since there are multiple (111) planes in a silicon crystal, the intersection pattern makes it
easy to etch square and rectangular features [14]. This way, the capacitive cavity and
diaphragm can be defined by etching both the top and the bottom of the silicon wafer.
The support structure used to suspend the diaphragm above the glass wafer is a part of the
silicon wafer. An illustration showing the diaphragm can be seen in Figure 4.8. The
details of the square diaphragm fabrication are explained more thoroughly in Chapter 8.

While the crystalline structure is very conducive to etching in straight lines, it
makes precisely etching circular patterns in to silicon impossible. Instead etching away
small areas of a silicon wafer to define the support structure along with the diaphragm
like described previously, the round diaphragm must be defined by other methods. The
area of a round diaphragm must be defined by doping a portion of the silicon making it
conductive, and all of the non-dOped material is dissolved away. Since the support
structure cannot be conductive because it would interfere with the on-chip electronics, it

cannot be fabricated as part of a round diaphragm for this application (Figure 4.9).

34

Bottom View

 

Side View

Diaphragm

    

i

\ Support Structure /

And Bonding Surface

4.8 Illustration Showin Su rt S cture on S uare Dia hra

 

 

 

 

 

 

4
Doped Rgion
,. , .2
a
Diaphragm

Top View

 

 

 

 

 

 

4.9 Illustration of Round Diapm Formation

35

adage . We'd-131E v.7”
.

For most applications, creating a support structure on the substrate does not pose a
problem. However, the inductor is housed on the glass wafer below the diaphragm, and
since the electronics are housed on the substrate, it would be difficult to deposit an
additional fihn on the substrate and pattern it properly so that the support structure could
be constructed without compromising the quality of the electronics. As a result, it was
decided to utilize a square diaphragm instead of a round structure.

4.5 The Capacitance-Pressure Relationship

The capacitance as a function of pressure difference for various initial gaps and
maximum deflections is seen in Figure 4.10. The plots are generated by combining the
results from the deflection-capacitance relationship in (4.1) with the pressure-deflection

relationship in (4.2) while assuming an initial capacitance of 2.0 pF.

36

 

9:... mini... r I

 

 

[‘3
or

 

 

 

 

a) 0.3 micron deflection V
A 2.4 ,xfx/r
IL ,x .
9; ”x )(_..X/././l’.
a 2 s .w
: fer” ‘
g )6)“
g 2.2 - fl; """
O. .2
8
2.1 a
2
2.8

 

L b) 0.4 micron deflection 1

  

 

  
 
  

I"
o:

Capacitance (pF)
N
A

 

 

Capacitance (pF)

0 10 20 30 40 50 60
Pressure (mmHg)

+ initial Gap = 2um + Initial Gap = 1.9 um + initial Gap =1.8 um
mew Initial Gap = 1.7 um —4— Initial Gap = 1.6 um —e— initial Gap = 1.5 um

Figure 4.10 Capacitance as a Function of Pressure for Various Initial
Gap Heights Using an Initial Capacitance Co = 2pF

37

Figure 4.10 reveals several important trends. First, the capacitance is more
sensitive to pressure difference as the initial gap height becomes smaller. This is seen by
the larger capacitance change over the full-scale pressure differential range shown by the
capacitor with a 1.5 micron gap than for the capacitor with a 2.0 micron gap. For the 0.5
micron maximum deflection case, the capacitance value changes 1.0 pF over the 0-60
mmHg scale when the initial gap is 1.5 microns, while the capacitance change when the
gap is 2.0 microns is 33% less at 0.67 pF. The difference in the capacitance range
between a 1.5 micron gap and a 2.0 micron gap for the 0.4 micron maximum deflection is
31% and 28% for the 0.3 micron maximum deflection design. Using a smaller initial gap
and a larger total deflection for 60 mmHg increases the sensitivity of the capacitance to
pressure.

It is important next to understand how resonant frequency changes as a result of
the capacitance change. The relationship between capacitance and the resonant
frequency can be seen in Figures 4.11 assuming a constant inductance of 800 nH, an
initial capacitance of 2.0 pF, and using the capacitance ranges from Figure 4.10 for each

of the three cases of deflection.

38

314.3” Unifiih IA -.

 

 

. a) 0.3 micron deflection

 

 

 

 

 

 

 

 

 

 

' b) 0.4 micron deflection

 

 

 

 

 

—LA—L—t—bA—L—L-L—L—A—L—L—t-A—L—L—A—l—A—L—L—L—L—L-L—L—L
COCO-AAdiiNNNNNOOOO-‘A-‘A-‘NNNNN
Nkmmow#mmON-bmmN-kmmON-meON-kwm

 

 

c) 0.5 micron deflection

 

 

 

 

 

l L l i 1 i l l l l 1
1 i . 1

.J—L-L—L—L—L—L—L—L-L—t—L—L—L
0000 44-5-4410 NNNN
mem om-tsaamo N-kmm

 

 

I . I I

2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3
Capacitance (pF)
+lnitial Gap = 2 um --a-- Initial Gap = 1.9 um --*-—- Initial Gap = 1.8 um
~-2~e- Initial Gap = 1.7 um —-1— Initial Gap = 1.6 um —e—initial Gap = 1.5 um

Resonant Frequency (MHz) Resonant Frequency (MHz) Resonant Frequency (MHz)

Figure 4.11 Resonant Frequency as a Function of Capacitance for Various Initial
Gap Heights and Maximum Deflections Using an Igluctance of 800 n_H

39

 

H. “11.1.90. 1....ij . >/

 

 

Figure 4.11 shows that the resonant frequency range increases as the capacitance
range increases. This agrees with the information shown in Figure 4.2. The capacitance
range increases with the maximum deflection. The trends in the figure indicate that a
larger deflection will result in a larger resonant frequency range.

All of the analysis presented previously in this chapter leads to the decision to use
a maximum deflection of 0.5 microns and a capacitance gap of 1.5 microns. As a check,
the relationship between the resonant frequency and the pressure is plotted for each of the
three deflection cases from Figure 4.11.

Figure 4.12 shows the resonant frequency as a function of pressure difference for
various initial gap heights and maximum deflections using an inductance of 800 nH. It
can be observed that the largest change in resonant frequency for an incremental change
in pressure occurs when the maximum deflection is 0.5 microns and the initial gap is 1.5

microns.

40

 

 

126
124 — —-

120
118i
115 -
114 .

Resonant Frequency (MHz)

 

122 4 A A. ,-

a) 0.3 micron deflection

 

 

 

 

I
777177

 

112

 

125
122
119
116
113
110

Resonant Frequency (MHz)

 

 

 

 

 

 

107

 

 

 

126

—l
d

.5
1

110 4

106 ‘

Resonant Frequency (MHz)

 

\\
\“_
122«~ ~ ~
\N;

 

 

 

 

 

 

102

0 10

+Initial Gap = 2 um
,. |nitia| Gap = 1.7 um

I

20 30
Pressure (mmHg)
+Initial Gap = 1.9 um

——1—initial Gap = 1.6 um

40 50

+Initial Gap = 1.8 um
—e—-lnitial Gap = 1.5 urn

Figure 4.12 Resonant Frequency as a Function of Pressure for Various Initial

Gap Heigpts and Maximum Deflections Using an Inductance of 800 nH

41

The final parameter to be addressed is the initial capacitance value. Figure 4.13
provides the required capacitor plate side length required as a function of initial gap
height for various values of initial capacitance. Decreasing the size of the capacitor plate

allows for the diaphragm size to decrease allowing for a smaller final device, which is

highly desirable.

 

 

O)
\l
O

~c0=2.0p1= ~ A -

 

6501 C0=1.9pF .2 2- I , _,_,-_

630 - (30:13 PF 2 4 ,
C0=l.7 pF ' 5 K
610 - , O

590 ~

 

 

 

 

 

570 a

550 "

Required Capacitor Plate Side Length (um)

 

 

530 ~
1.5 1.6 1.7 1.8 1.9 2

Initial Gap Height (um)

 

Figure 4.13 Capacitor Plate Size versus Initial Gap
Height as a Function of Initial Capacitance

Table 4.2 shows that the total resonant frequency range increases when the initial
capacitance value decreases. The resonant frequency range is 8.5% larger for an initial
capacitance of 1.7 pF than for an initial capacitance of 2.0 pF. Observations from Figure

4.13 and Table 4.2 support using an initial capacitance of 1.7 pF.

42

Table 4.2 Size of Resonant Frequency Range Over a Range of
Deflection of 0-0.5 microns For Various Initial Capacitance Values

 

 

Frequency Range
Capacitance (pF) (MHz)
1 .7 25.04
1 .8 24.34
1 .9 23.69
2 23.09

 

 

Based on the previous analysis, the capacitor will have an initial gap height of 1.5
microns with an initial capacitance of 1.7 pF. From Figure 4.13, a side length of 537
microns is required to achieve this capacitance. The full-scale deflection of the device
will be 0.5 microns at 60 mmHg resulting in a capacitance of 2.55 pF.

4.6 Effects of Residual Stress on the Diaphragm’s Dynamies and Sensitivity

Almost all thin films have a certain amount of residual stress built in [14].
Residual stress significantly influences the load-deflection behavior of diaphragms. The
diaphragm will be made of silicon that is heavily doped with Boron. Introducing the
Boron impurities in to the silicon wafer introduces considerable residual tension in the
diaphragm [18]. It is typical for the residual stress in p++ silicon to be around 40 MPa
[19]. Residual tension results in a resistance to bending in a diaphragm. The additional

pressure needed to deflect the diaphragm is calculated by equation (4.6) [20].

PS : [EC—h] (4.6)

2
a

The principle of superposition allows for this term to be added to the original

expression given in equation (4.2).

 

 

4 w3 4 2
P: E h [4.20%+1.58 C+ 05“ WC] (4.7)

l—v2 a4 h3 E 113

43

0’. 9.101.153 P”. /.

The presence of a residual tensile stress increases the stiffness in a diaphragm so it
will not displace as much for a given pressure load as will a stress free diaphragm. A plot
using dimensionless units of displacement and position across the length of the
diaphragm is shown in Figure 4.14 [14]. As a result of the increased stiffness, a
diaphragm designed for a particular deflection at 60 mmHg will deflect less than

expected if there were no residual stress.

-O.2 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I 7 i i 1
° " " ‘ 1 1 1
"‘ 0'2 ~ ‘ ‘ os=ZSOMPa .
0.41 r ‘ . .' '
£05 "‘ “N 100 " L -
0.8 . 25 10 1—
1 ‘. "“_ 03:0
| l L
0 20 40 60 so 100
Position

Fi re 4.14 Effects of Residual Stress on Dia hra Deflection 14

 

Figure 4.15 contains the deflection pattern of a diaphragm designed to deflect 0.5
microns at 60 mmHg. The plot shows the expected deflection of the stress free
diaphragm as predicted by equation (4.2) and the deflections that will result when 40
MPa of stress is present in the- diaphragm from equation (4.7). The relationship between
the deflection and pressure difference will be the same for a stress free diaphragm of any
thickness as long as the side length is designed accordingly. The line representing the
general stress free state in Figure 4.15 is independent of thickness. However, the

deflection that will result from introducing residual stress into the diaphragm depends

greatly on the thickness. A thick diaphragm is less affected by the presence of residual
stress than a thinner diaphragm. A 7 micron thick diaphragm designed with an
appropriate side length for a stress free state by equation (4.2) will deflect 36% less than
expected if the actual stress is 40 MPa. The stress has a more significant effect on a 2.5
micron thick diaphragm. The deflection is reduced by 50% compared to the stress free

deflection.

 

 

0'5 T General Stress Free State

 

 

 

0'45 I 7 micron diaphragm thickness

0.4 . 4
4 micron diaphragm thickness

 

 

0.35 ~

 

2.5 micron diaphragm thickness 7 , fl .

 

 

.0
CO
1
1

 

.0
N
or

Deflection (microns)
.0
N

p
.2
01

0.1 »- ~ ~ , ~

0.05 -.

 

 

 

0 10 20 30 40 50 60
Pressure (mmI-lg)

Figure 4.15 Effects of 40 MPa of Residual Stress on a
Diaphragm Desiged to Deflect 0.5 microns at 60 Mg

The reduction in deflection that occurs when introducing residual stress compared
to the stress free state will result in a smaller capacitance range than would be expected
since the gap height is related to the deflection. In turn, a smaller resonant frequency
range will be covered over the full-scale pressure range. As a result, the sensor system

will not operate according to theory.

45

Closely associated with the deflection is the overall sensitivity of the device to
pressure variation. The sensitivity S of a variable gap capacitive pressure sensor is given
by [14]

_ 2 4
1 V 337—(m2/N) (4.8)
h d

 

S = 0.0746

The silicon diaphragm will be in tension due to the Boron impurities that were
introduced in to the silicon to form the p++ silicon. Figure 4.16 shows that the sensitivity

of a diaphragm’s deflection to pressure decreases as the tensile stress is introduced.

 

100

cznrta DEFLECTION
to (councssaou)

reassure sensmvnv
(coueacssmn)

 

 

 

"casual: ssnsrrwrrv
. (751151011)

  

 

czurca DEFLECTION J

NORMALIZED PRESSURE SENSITIVITY
AND DIAPi-RAGM CENTER DEFLECTION

 

 

0.1 (reason)
0.0: j v v v v v r u 1 I r T v Y r 1 r I 1 ‘l’ I v 11111
0.1 I 10 100

DIMENSIONLESS STRESS, (1-u’)a,a’/£h’

Figure 4.16 Effects of Residual Stress on the Deflection of a Diaphram |14|

Equation (4.8) shows that the sensitivity is a function of the size of the diaphragm,
the material properties, and the capacitive gap. As a result, the sensitivity of the device
changes as the diaphragm is deflected.

Figure 4.17 shows the sensitivity of the device to pressure as a function of
deflection for various maximum deflections at 60 mmHg. It is apparent that a device

designed for a large deflection (0.5 microns) is 97% more sensitive than the device

46

designed for a small deflection (0.3 microns). This again supports the decision to design

for a 0.5 micron deflection.

 

  
   

 

 

 

 

 

 

 

 

 

 

 

 

6.7000E-03
5.7000E-03 - ' * ' , D
7.: 47000503 ‘ 0.5 micron deflection
in
a: 9999
E , g a.-
E .. Q.:L: : 3 .
E 3.7000E-03 fi 04 . (1 fl ti '
. rmcron e ec on
E \‘
.3 M
r:
«3 270005-03 - ~~
1.7000E-03
0.3 micron deflection
7.0000E-04

 

0 0.1 0.2 0.3 0.4 0.5
Deflection (microns)

Figure 4.17 Sensitivity as a Function of Deflection for Various
Cases of Maximum Deflection at 60 mmHg of a Square Diaphragm

with Initial Gap =1.5 and Assumed Residual Stress of 40 ME;

 

So that the desired full-scale deflection and a high sensitivity can be achieved, the
side length of the diaphragm must be increased to compensate for the residual stress.
Figure 4.18 provides a comparison of the new required side length that accounts for 40

MP3 of residual stress to the former side length from the stress free model.

47

 

850

750*

650 ~

550 —

450 ~

 

Required Side Length 2a (microns)

 

 

 

2.5 3 3.5 4 4.5 5 5.5 6 6.5 7
Thickness (microns)

+0.3 Design w/ Stress +0.4 Design w/ Stress +0.5 Design w/ Stress
—~%-- 0.3 Design w/o Stress -B-— 0.4 Design w/o Stress +0.5 Design w/o Stress

Figure 4.18 Required Side Lengths as a Function of Thickness for
Stressed (40 MPa) and Stress Free Diaphw

The electrode and diaphragm must have roughly the same area. It was decided to
use a side length of 537 microns for the capacitor plate in Section 4.5 with a maximum
deflection of 0.5 microns at 60 mmHg. The diaphragm must have a side length equal to
or slightly greater than 537 microns. From Figure 4.18, the thickness of the diaphragm
must be 4 microns, and the side length will be 551 microns.

The final observation is the effect of the capacitive gap on the sensitivity. Figure
4.19 shows the sensitivity as a function of the deflection for various initial gaps. It can be
observed that the sensitivity can be increased by 50% by decreasing the initial capacitive

gap from 2 microns to 1.5 microns.

48

 

5.7000503
520005034 4
4.7000503. . . _ - _- _ . W,

4.2000E-03 5

 

3.7000E-03 ., " '

Sensitivity (mmHgA-1)

 

3.2000E-03 V I . I - , - -. ,1

 

 

2.7000E-03 i . ~
0 0.1 0.2 0.3 0.4 0.5

Deflection (microns)

+2.0 micron Cap gap +1.9 micron Cap gap +1.8 micron Cap gap
-e<-~ 1.7 micron Cap gap --1—1.6 micron Cap gap —e— 1 .5 micron Cap gap

Figure 4.19 Sensitivity as a Function of Deflection for Various
Initial Gaps of a 4 micron thick Square Diaphragm with an
Assumed Residual Stress of 40 0123
4.7 Final Capacitor Design

Table 4.3 Summagy of Capacitor Desigp

 

Shape Square
Plate Side Length 537 microns
Initial Separation 1.5 microns
initial Capacitance 1.7 pF
Separation at Full Scale Deflection 1.0 microns
Final Capacitance 2.551F

 

 

 

49

c0=1.7 pF
CFS=2.55 pF

 

   
 

/ Diaphragm

1.5 micron
Initial Gap

 
 
    
  
 

1.0 micron
Gap at Full
Deflection

537
microns

 

Fixed C apacitor Plate

Figpre 4.20 Illustration of Final Capacitor Plate Desig

Table 4.4 Summagy of Final Diaphram Desigp

 

Shape Square
Diaphragm Thickness 4 microns
Side Length 551 microns
Full-Scale Deflection 0.5 microns

   

54.7 °

   

551 microns
\

   

| «.x'
a.

4 microns

l

 

 

F igpre 4.21 Illustration of Final Diaphram Design

50

Chapter 5

Inductor Design

51

5.1 Design Variables

The design of the inductor consists of determining the line thickness, number of
turns, turn spacing, width, inside and outside diameter while maximizing the quality
factor (Q) and minimizing parasitic resistance within the overall device design.
5.2 Planar Inductors

Planar inductors of any shape are characterized by the number of turns (11), the
spacing between turns (s), the line width of the conductive material (w), inner and outer
diameters (due and dom- respectively in Figure 5.1), and the fill ratio defined as

Tl = (dour- diN) / (dour+ dm) [15]-

 

 

 

 

 

 

Ifigpre 5.1 Planar Spiral Inductor Layout with n=3 Turns |15|

52

In the specific case of this pressure sensor, the capacitor plate will be in the
center, and the inductor will spiral away from the capacitor plate. The turn spacing and
the size of the capacitor plate determine the inner diameter (Figure 5.1). The inner
diameter will be equal to the size of the capacitor plate plus two times the turn spacing.

The thickness of the wire (tw) imparts only a very small effect on the inductance,
so it can be neglected in the inductance calculations [15]. However, any practical
inductor must be wound with wire that has a finite resistance, so the coil will have
resistance associated with it due to the length of wire. From the RLC circuit point of
view, the resistance can be considered to be a separate resistor in series with the inductor
[13]. The line thickness is very important when determining the resistance of the
inductor. This part of the analysis is contained in the following chapter.

5.3 Design Considerations on Determining the Inductance Value

The design of the inductor was an iterative process similar to the process used to
determine the optimum capacitance in the previous chapter. The first step of the design
was to make an estimate for the inductance. Again, the most important design parameter
that is dependant on the inductance is the desired resonant frequency range. Equation
(2.22) describes the dependence of the resonant frequency on the inductance and
capacitance values.

1

21rd LC

Figure 5.2 shows the resonant frequency range as a function of the capacitance for

Fr:

 

(2.23)

six values of inductance based on the design considerations in Chapter 4.

53

 

 

Resonant Frequency (MHz)

 

 

 

 

0.0017 0.0019 0.0021 0.0023 0.0025
Capapcitance (nF)

-O— L=600 nH + L=700 nH + L=800 nH -X-— L=1200 nH + L=2000nH

Figure 5.2 Resonant Frequency as a Function of

Capacitance for Various Values of Inductance

The total range of the resonant frequency for a particular capacitance change is
important to observe in Figure 5.2. Lowering the inductance value increases the total
range of the resonant frequency for a particular capacitance range. For example, for a
capacitance range of 0.0017 to 0.00255 nF, the range of resonant frequencies with an
inductance of 2000 nanohenries (nH) is about 16 Megahertz (MHz) while the range with
an inductance of 600 nH is about 29 MHz. Thus, a smaller inductance is beneficial in
improving the sensitivity of the resonant frequency to a capacitance change based on the
observation that the size of the frequency range becomes larger as the inductor value
decreases.

However, computational simulations indicate that larger inductors increase the
magnitude of the responses for both the primary and secondary circuits. As the

inductance value becomes larger, the voltage across the sensor’s capacitor at resonance

54

 

[1.1-4

4 ’1’0I 1.4., .0)

increases. Also, the magnitude of the voltage dip across the load resistor increases with
higher inductor values. This observation is important because the frequency at which the
voltage dip occurs is used as the measurement to determine the pressure in the eye. It is
desired to maximize the magnitude of the dip so that the resonant frequency will be easily
identified. The general trends of the frequency responses as measured across the load

resistor and the sensor capacitor is shown in Figure 5.3.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

h
'2 02
a! ' 5 u 5
3 As inductance increases }
a:
1: 0.15;;
8...
3%01
§e
g
0 0.05:
a
’3
> 0
53 2
“’0
g% 1.5
5.8
<0 1 . . , _
O“ i 1‘
mn- } i

to
O
>

01 , , T

 

90919293949596979899100
Frequency(MI-Iz)

Figure 5.3 Basic Trends of Circuit Excitation as a
Function of Fregpency Towards Changes in Inductance

Figure 5.2 shows that a smaller inductance value improves the sensitivity of the
resonant frequency to changes in capacitance. However, a large inductance is needed to

increase the magnitude of the frequency responses. A balance between both sensitivity

55

'I‘.

I- \~v

and accuracy must be made to optimize the sensor’s overall performance. The balance
will be established by considering limitations on fabrication capabilities and a
comparative look at the relative importance of the inductor value on the sensitivity and
the magnitude of the frequency responses.

Information from discussions with several MEMS fabrication facilities indicates
that it is difficult to obtain inductances larger than about 1200 1111 on MEMS devices.
The inductance value that can be obtained is limited by the size constraints imposed
because the device will be implanted in the eye. Planar inductors grow quite quickly in
radius, so the size of the device is significantly affected by attempts to increase the
inductance. Therefore, an inductance of 1200 nH will be considered to be the upper limit
that can be obtained for this particular device.

Based on Figure 5.2, the resonant frequency range for an inductance value of
1200 nH is about 20% smaller than the range for an inductance of 800 nH. Additionally,
the resonant frequency range with an inductance of 800 1111 is still 13% smaller than with
an inductance of 600 nH.

The magnitude of the voltage dip increases by roughly 33% by increasing the
inductor value from 600 nH to 800 nH, and another 33% by increasing the inductance
from 800 ml] to 1200 nH. The magnitude of the voltage dip increases for higher resonant
frequencies. Decreasing the inductance value results in the shifting of the frequency
range to higher frequencies (Figure 5.2). By lowering the inductance value, the resonant
frequency will occur at higher frequencies, and the magnitude of the voltage dip will be

larger.

56

An inductance of 600 nH will result in a small voltage dip across the load resistor
(~ 7 mV). A 7 mV voltage dip will be very difficult to observe. It was decided to use a
larger inductance to increase the magnitude of the voltage dip for the purpose of
improving the accuracy despite the decrease in sensitivity of the resonant frequency to
capacitance. However, the magnitude of the voltage dip increases with resonant
frequency. Thus, the range of resonant frequency becomes larger and occurs at higher
frequencies for a smaller value of inductance. For this reason, it would be undesirable to
chose the maximum inductance of 1200 nH. Also, the size of the device increases with
increases in inductance so an moderate value of 800 nH was chosen to balance between
the sensitivity and the accuracy of the device.
5.4 Computational Analysis for Design of a Planar Inductor

Mohan provides three different design equations for calculating the inductance of
a square spiral [15]. The first method is a simple modification of Wheeler’s formula and

is given as

n2[dou*r +dIN]
2

(5.1)

 

LMW = Klpo 1+ K21]

Mohan’s second equation is based on the current sheet method. This method
considers each of the sides of the spiral as symmetrical current sheets of equivalent

current densities. The expression for inductance is given by

 

2
an d c c
LGMD = 2V0 1 [ln[—;-]+c3p+c4p2] (5.2)

57

 

159V! ... .E. a g... .P. H/

 

 

The final equation used by Mohan to evaluate the inductance is the empirical
expression

LMON = [SdOUTOll aszVGU3na4su5 (5.3)

All of the calculations in this chapter are performed with the intent of designing a
sensor with an inductance of about 800 nH. However, it is desired to have a symmetric
device so that orientation of the device inside the eye does not compromise the quality of
the wireless telemetry. The 800 nH inductance was not held as a strict limit so that a
symmetric device could be designed. The following calculations were performed for
each full turn of wire. Fractions of turns were not allowed. The analysis was performed
using all three equations. Consider first an inductor that has a line width of 6 microns.
The inductance can be found as a function of the number of turns of wire for each of the

three equations for various line widths, as seen in Figure 5.4.

58

 

 

900 ~ , .
a) Spacmg = 10 rmcrons

 

 

 

750 -

O)
O
O

450 .

300

Inductance (nH)

150 -

 

 

 

 

 

 

‘ b) Spacing = 6 microns

 

 

 

\l

0'!

O
1

Inductance (nH)
.p
U!
o

 

 

 

 

 

c) Spacing = 4 microns

 

 

 

Inductance (nH)
. a g e a a g

 

 

 

O 2 4 6 8101214161820222426
Turns(#)
-x— 15015.1 —e—EJ\I5.2 +EN5.3

Figure 5.4 Inductance as a Function of the Number of Turns for
Comparing the Precision of Equations (5.2-5.4) For Various Line

Spacings Using a Constant Line Width of 6 microns

59

 

.34. . _.

pl . In. IE Iv.)

 

 

An inductance 800 nH can be achieved with 25-26 turns of wire based on Figure
5.4. It was decided to use 26 turns initially because it was shown in Section 5.3 that a
higher inductance would result in increased magnitude of the frequency response of the
primary and secondary circuits.

The three equations produce very similar results. The difference between the
largest and smallest values at 26 turns is 3.2% of the smallest value in Figure 5.4a. The
difference at 26 turns in Figure 5.4b is 5.7 % of the smallest value, and the difference in
Figure 5.4c is 2.7%. Inductor tolerance is usually on the order of several percent [15],
and the errors associated with all three methods when compared to field solver
simulations performed by Mohan are on the order of 1-3%. Previously published results
studied by Mohan typically show errors on the order of 20% so the expressions in (5.1)-
(5.3) are the most accurate expressions for inductance that could be identified [15]. All
three expressions for the inductance approximation are equally valid for the purposes of
this model so there is no need to continue the analytical modeling using all three
expressions.

Equation (5.3) will be used in the subsequent calculations because the equation is
the result of a curve fit of over 19,000 known inductors [15] so it is proven to be quite
accurate.

Figure 5.5 shows that the inductance is affected by the turn spacing (about 10%
difference between a spacing of 4 microns and 10 microns). If a spacing of 10 microns
and a line width of 6 microns are used, the number of turns can be reduced to 25.
However, the 25 turns of coil will have an outer diameter of 1337 microns, where the

outer diameter of 26 turns with 4 microns between each is 1057 microns; a 26.4%

60

difference. Even though the number of turns required will be greater for the smaller
spacing, the outer diameter will be less, so the overall size of the sensor will be reduced.

These trends can be observed in Figures 5.6 and 5.7.

1 000

 

900 .
800 ~
700 -
600 *
500 _
400 .

Inductance (nH)

300 4 ~
200 -

 

 

 

 

0 5 1 0 15 20 25
Turns (#)

+s=4 -G—s=6 +s=10

Figure 5.5 Inductance as a Function of the Number of
Turns for Various Turn Spacings

61

 

.3 A ,
o 1400 >
'5 1300—
‘3
g 1200 , ..
:371100 . = '
O E ' 3 2 <
§§1ooo~ .. , ., ‘
gé 900~ , c z z
.2 c =
a 800 s =
'3 700 ' ‘ a
_ . w-
' 5’
g 600 ,4!"

 

 

 

02468101214161820222426
Turns(#)

+sz4 +S=6 +s:10

Figure 5.6 Outside Diameter of the Inductor Coil as a Function of the Number of
Turns for Various Turn Spacings Using a Line Width w=6 microns

To ensure that the overall size of the sensor is minimized, it is desired to keep the
spacing between turns as small as possible. Also, this improves the interwinding
magnetic coupling [15]. However, the line spacing cannot be infinitesimally small
because a finite distance between lines is required so that the gold will form distinct coils
and not just a single connected mass.

It is difficult to create features that are quite tall compared to the width, especially
when the features are very close to each other as with the inductor coils. The reason for
this is that it is difficult to deposit a material deep in to a relatively thin recess [14]. For
this reason, a spacing of 4 microns will be assumed as the limit so that analysis can be
continued.

The last variable related to the inductance and size of the spiral is the line width.

As with the turn spacing, a larger line width will result in a larger outer diameter. The

62

main issue is then to determine what effect the line width has on the total inductance of

the spiral. Equation (5.3) is used to generate a plot of the inductance as a function of the

number of turns for various line widths, and the results can be seen in Figure 5 .7.

 

Inductance (nH)

 

 

 

0 2 4 6 8 10 12 14 16 18 20 22 24 26
Turns(#)

+w=6 —e—w=8 +w=15

Figure 5.7 Inductance as a Function of the Number of
Turns for Various Line Widths for a Line Spacing s=4

Small changes in the line width produce only a very small difference in the total
inductance (4.2% difference between largest and smallest at 26 turns). A larger line
width will result in making the inductor larger for the same number of turns, and the
difference in inductance is minimal so minimizing the line width is desirable.

It has been shown that the inductance of a planar coil is very robust against small
changes in both line width and turn spacing. To minimize the total size of the sensor, the
line width and spacing should be kept at a minimum. However, the analysis of the
inductor design is not complete. The resistance of the coil needs to be considered to

optimize the sensor’s performance. This analysis will be completed in the next chapter.

63

Chapter 6
Consideration of the Resistance
And Quality Factor in the

Inductor Design

6.1 Resistance and Quality Factor of the Inductor

A planar inductor will have a resistance associated with it due to the resistivity of
the coil material [13]. This resistance is in series with the inductor, and thus it will be
referred to as the series resistance.

The resistance in a planar coil is not constant due to a frequency dependence
referred to as the skin effect. The skin effect is the tendency of alternating current to flow
near the surface of a wire at high frequencies thus making the effective area of the wire
smaller than the actual cross-sectional area [21]. The skin effect is caused by the self-
inductance of the conductor, which causes an increase in the inductive reactance at high
frequencies. The skin depth is the depth at which the current density has dropped to l/e

(~37%) and can be calculated by [22]

2
muoc

 

(6.1)

The series resistance of the wire (measured in Ohms) then has frequency

dependence due to the skin depth, dimensions of the wire, and the resistivity [22]

RS = ‘01 (6.2)

wall-W")

where l, w, and tw are measured in meters.

 

 

The series resistance and skin depth for the theoretical frequency range resulting
from using an inductance of 800 nH and capacitance range of 1.7 pF to 2.55 pF (as
calculated in Chapter 4) is shown in Figure 6.1. The actual resonant frequency range of
the device will not be known until the final inductance value is determined at the end of

the chapter. A line thickness of 7 microns was chosen as a starting value.

65

 

 

 

 

 

 

 

63 7.1
'1”,
62.51 , $5,; -_ 7
A 62« ”g." -
II a" “r 6.9 m
E. 61.55 ,c”~ as.
o .c" 3
V 617 5"" ’7 6.8 9
8 1:
g 60.5 -« 6.7 :5:
.2 ,6" 3
O 60 5 1 65’ 5'
£3 g
g 59.5 3
b 5’
8 59— ,3."
58.5 a"
58 . . 6.3
111 116 121 126 131 136

Frequency (M Hz)

Figure 6.1 Series Resistance and Skin Depth as a Function of Frequency
For Case Where w = 6 microns, tw = 7 microns, 26 windings

The major measure of an inductor’s performance is the quality factor, Q. The
quality factor is the ratio of the reactance to the resistance of an inductor and provides a
measure of how well the inductor emits/absorbs energy. It is desired to maximize the Q

factor for optimum effectiveness of the wireless telemetry.
Q = — (6.3)

A plot of the Q factor along with the series resistance of the circuit as a function

of frequency is shown in Figure 6.2.

66

 

 

 

 

 

 

 

 

62
'3 61.5 «
5 ‘ o
9 61 g‘
g 60 5 §
5; ; S.
3 60 g
a; 59.5 «.

59 .

58.5
56 4
111 116 121 126 131 136
Frequency (M Hz)

Figure 6.2 Resistance and Q Factor as a Function of Frequency
Using tw =7 microns, w = 6 microns, and 26 Windings

llt is apparent that the Q factor and the resistance increase directly with the
frequency. This is counterintuitive based on equation (6.3), but it is important to recall
that the resistance grows slowly as a function of frequency. As a result, the frequency
term in equation (6.3) dominates, so Q actually grows despite the increased resistance
due to the skin effect.

Figure 6.3 shows that the resistance due to the inductor is a strong function of the

line thickness. The effective cross-sectional area of the wire from equation (6.2) is thus

A = w5\/(1—e_tW/6) (6.4)

 

67

Resletance (Ohms)

Figure 6.3 Resistance of Inductor as a Function of Frequency for Various Line
T_hicknessw Using Line Width w = 6 microns, and 26 Windiyg

becomes larger, so the series resistance, equation (6.2), will be lower for a particular
frequency. A six micron wide wire with a line thickness of seven microns has 6.5% more
resistance than if the line thickness were nine microns. Also, as the resistance becomes
lower at a particular frequency due to increasing the line thickness, the Q factor will

increase as revealed by equation (6.3).

The actual line thickness will show some variability between manufacturing runs. The

 

64 1

7 micron Line Thickness

 

 

63

8 micron Line Thickness

 

62‘

 

9 micron Line Thickness

 

 

61‘

60 ~

59*

582

57

56*

551

 

 

 

111

As the line thickness becomes larger, the effective cross-sectional area of the wire

The goal for the fabrication process should be to maximize the line thickness.

116 121 126

Frequency (M Hz)

68

131

136

 

resolution in feature size in typical MEMS devices is generally about 1 micron [14].
Exact precision when depositing the gold on to the glass wafer to make the coils is not
possible, so a certain amount of variability will occur on the order of about i: 1 micron
depending on the capabilities of the fabrication facility.

Also, the spacing between windings is desired to be as small as possible to keep
the size of the device at a minimum. Since the spacing is so small between the wire
windings, it is difficult to make structures that are larger than about 10 microns thick
[14].

The following analysis assumes that a 9 micron line thickness is achieved. This
value is chosen because it is near the upper limit and allows for some variability in the
fabrication process before the upper limit is reached.

The effects of changing the line width on the resistance and Q factor can be seen
in Figures 6.4 and 6.5. As the line width becomes larger, the effective cross-sectional
area of the wire becomes larger, which lowers the series resistance. A nine micron tall
wire with a line width of 6 microns has 23.1% more resistance than if the line width were
eight microns. More importantly, the Q increases by 23.0% by increasing the line width
by two microns from six to eight microns. A larger line width should then be utilized to
maximize the Q of the sensor. A sacrifice in size must be made so that the sensor’s
performance can be improved. It is common for planar inductors to be fabricated with a
ratio of w:s of 2:1 [23] so this ratio will be used for this device giving a line width of

eight microns.

69

 

 

    
 

6 micron line width

 

 

 

 

 

 

 

 

 

8 micron line width

Resistance (Ohms)
t 4:. A 01 01 g 01 01 ca
0: 00 o to a: on o

 

 

 

A
N

 

 

A
O
l

111 116 121 126 131 136
Frequency (MHz)

Figure 6.4 Resistance as a Function of Frequency for Various Line Widths
Using Line Thickness tw = 9 microns, Spacing s = 6 microns, and 26 Windipgg

 

15.5

14.5 *-

 

     
   
 
    

135 _, 8 micron line width

 

.
p
A -
---'-
-0 c'
‘-
»--
-

o
-
n o
2 5 - - ’ d v
I —‘ ' - a- ’ v
. -
’ v

-
a'-
--

7 micron line width

 

 

11.5 a

 

0 Factor (dimensionless)

10. 5 - 6 micron hne wrdth

 

 

 

 

 

9.5 1 .
111 116 121 126 131 136

Frequency (MHz)

Figure 6.5 Q Factor as a Function of Frequency for Various Line Widths
Using Line Thickness tw = 9 microns, Spacing s = 6 microns, and 26 Windings

70

6.2 Summary of Inductor Design
Combining the results from the Chapters 5 and 6 with the capacitance range from

Chapter 4, the device will have the following characteristics

Table 6.1 Summary of Inductor Desim

 

Spiral Shape Square
Turns 26
Inductance 800.2 nH
Line Thickness 9 microns
Line Width 8 microns
Turn Spacing 4 microns

Inner Diameter 545 microns

Outer Diameter 1161 microns
Resonant Frequency
At 0 mmHg 136.46 MHz
Resonant Frequency
At 60 mmHL 111.42 MHz

 

 

 

71

Chapter 7
Summary of Micro-Scale

Prototype Design

72

7.1 Design Dimensions

The dimensions of the prototype device are shown in Figures 7.1-7.5.

Thin, Square
Flexible SI
membrane

(551 microns)

  
  
  
  

2000 microns

525-1000

2000 rmcrons microns

*Depends on availability of Ultra-thin Si wafers
Figure 7.1 External Dimensions of Sensor

The device will be a box with width and length of 2000 microns. The height of
the device will depend on the availability of ultra thin silicon wafers. The glass wafers to
be used for the substrate are typically available with a standard thickness of 500 microns.
The ultra thin silicon wafers are only 25-30 microns thick, but are not commonly
available. If they are not available, a standard silicon wafer is 500 microns thick. The
total thickness of the device is anywhere from about 525 to 1000 microns depending on
the materials available.

The diaphragm will have a thickness of 4 microns as determined in Chapter 4 (see
Figure 7.2 for dimension locations). The bottom of the silicon wafer will be etched so
that a 3.5 micron deep recess is created to define the capacitive gap. The 3.5 micron

depth includes 2.0 microns to account for the electrode height above the surface of the

73

 

 

glass wafer and 1.5 microns to account for the initial capacitive gap between the non-
deflected diaphragm and the electrode. The side length of the recess is 1200 microns to
ensure that the inductor coil will not touch the diaphragm. A 400 micron wide support
structure surrounds the recess on the bottom of the wafer to be used as the bonding
surface between the silicon wafer and the glass substrate. The top of the silicon wafer
will be etched to form a 551 micron by 551 micron diaphragm. All of the etches will
result in a side wall at an angle of 54.7° with the horizontal due to the crystalline

structure of silicon [14].

Depends on
W afer Thickness

   
 
 

L l l 8 2—500

 
     

 

1‘ '1‘ l '1 microns*
400 3.5 1200 Depends on
microns microns microns Availability of
Ultra-Thin Si
Wafers

Figpre 7 .2 Dimensions of Diaphragm Structure Created from Silicon Wafer
The capacitor plate will be square with a side length 537 microns (see Figures 7.3
and 7.4). The gold will be etched so that the total thickness is 2.0 microns. This is so
that the gap between the plate and the non-deflected diaphragm will be 1.5 microns. The
initial capacitance will be Co=1.70 pF and the capacitance at full-scale deflection will be

CFS=2.55 pF.

74

 
  
  
 
 
  

2000 microns 2000 microns

500
microns

Inductor Coils
(26 Turns)
5 37

microns

Fi re 7.3 Dimension of Intern Structures and lass Wafer

C0=1.7 pF
Cr-s=2-55 pF

 

  
     
 

/ Diaphragm

1.0 micron
Gap at Full
Deflection .
microns

 

Fixed Capacitor Plate

Fi re 7.4 Ca acitor La out

75

The inductor will consist of 26 turns of gold wire. The wire will be electroplated
on to the glass substrate. The physical dimensions are shown in Figure 7.5. The inside
diameter of the coil (dm) will be 545 microns with a 4 micron gap (3) between each turn.
The wire will have a line width (w) of 8 microns and line height (tw) of 9 microns. As a
result of these dimensions, the outer diameter (dour) is 1161 microns, and the final
inductance of the device is then 800.2 nH.

Due to the inductance value and capacitance range of the device, the size of the
resonant frequency range of the device will be 25.04 MHz with a resonant frequency of
136.46 MHz corresponding to 0 mmHg pressure difference across the diaphragm, and

111.43 MHz corresponding to 60 mmHg.

 

 

 

 

    

(1001:1161

Figpre 7.5 Inductor Layout

76

Chapter 8

Sensor Fabrication

77

 

8.1 Fabrication Overview

A possible fabrication “recipe” for the sensor is presented in the following
sections. The illustrations presented in the text show the cross-section of a single device
so that each step can be clearly understood and visualized. However, in the actual
fabrication of the devices, many individual devices will be made from a single wafer, and
the entire wafer will be fabricated at once. Hundreds of devices will be completed
simultaneously.

8.2 Fabrication of the Glass Wafer

First, the wafers are carefully cleaned so that the surface finish is of high quality.
It is important that imperfections on the substrate are smaller than 500 Angstroms so that
the final bonding procedure can be successful [14]. Next, a layer of photoresist (PR) is
spun and baked on the wafer.

A lithography process is then required to define the coil recess. During the
lithography, a mask is used to define the patterns for the features on the substrate (see
Figure 8.1). The wafer and mask are then exposed to a UV source. The PR is developed
and a pattern is left on the glass wafer that is used as a mask for etching. This entire
process, including spinning the PR, will be referred to as the lithography process for the

remainder of this description.

78

, it’ll lur.ln..filrr.- /
f N I . .

/ Photoresist
V

 

Figpre 8.1 Glass Substrate with the PR Mask Q Defing the Coil Recess

After a recess of about 10 microns is etched into the glass substrate, the PR is

removed and the structure seen in Figure 8.2 remains.

 

Figu_re 8.2 Glass Substrate with C01] Recess

Next, a lithography process is required to define the capacitor plate, the electrical
contacts that will be used to connect the upper and lower wafers, and the inductor coils.
Multiple depositions of PR may be required so a thick layer can be obtained since the

structures to be defined are thin and tall.

79

 

Fi 8.3 Glass Wafer th P Mask for Electro Gold

A thin seed layer (Ti/Au) is deposited on the substrate. This seed layer allows
thicker layers of gold to be deposited that will become the capacitor plate and the
inductor coils. The gold is deposited by electroplating. The electroplating is continued
until the inductor coils are at a thickness of 7 to 9 microns tall. An additional etch step
may be desired to make the capacitor plate thinner.

After the PR has been removed, the glass wafer is complete. The completed glass
wafer with all of the on chip electronics can be seen in Figure 8.4.

Contact to Upper Wafer Cap. Plate Coils

  

Figpre 8.4 Completed Glass Wafer

80

fit. . ..nll.ltld1.l.'...lnAtuI-u’

 

8.3 Fabrication of the Silicon Wafer

The second wafer to be processed is a (100) silicon wafer (see Figure 8.5). The
(100) wafer is a thin, circular disk of silicon that has a (100) crystallographic plane as its
top surface. A “flat” is located on the edge of the disk that corresponds to the (110)
plane. This means that the <100> direction is normal to the top surface and the <110>

direction is normal to the flat.

<100>

 

Figpre 8.5 Orientation of £11100) Silicon Wafer

If possible, ultra-thin silicon wafers will be used so that the device size can be
minimized. The thickness of these ultra-thin wafers is 25 to 30 microns. To complete
the fabrication, both sides of the silicon wafer must be processed. A thin layer of Si3N4 is
deposited on the silicon substrate. The nitride will be used as the mask to etch the
capacitive cavity. The nitride can be deposited in a number of ways, but Low-Pressure
Chemical Vapor Deposition (LPCVD) is quite common. In LPCVD, the substrate is
heated to a temperature typically greater than 300°C in a low-pressure chamber, and a gas
is introduced in the chamber. The reaction used to create silicon nitride is

SIH4+N2+NH3=SI3H4+N2+H2 (8.1)

81

The reaction takes place as gas species hit the substrate. The deposited films from
LPCVD are usually of quite high quality and uniformity, which is a major advantage over
several other deposition processes [14].

A lithography process is then performed to etch the nitride so the capacitive

cavity will be defined. The silicon wafer and mask are shown in Figure 8.6.

 

Fi re 8.6 Silicon Wafer with Si 4 Mask to Define Ca acitive Cavi

This cavity is etched to a depth of 3.5 microns seen in Figure 8.7. This accounts
for the 2 micron thick capacitor plate and the 1.5 microns capacitive gap. The silicon will
etch at an angle of 54.7° because of the crystallographic structure of the silicon atom.
The (100) and (111) planes intersect at an angle of 54.7° within the crystal lattice. KOH
is used as the etchant for this procedure. KOH has a selectivity ratio of 400:1 for (100)
over the (111) planes [14]. This means that 400 microns in the <100> direction will etch
for every 1 micron that is etched in the <111> direction. The nitride mask is then etched

away.

82

 

Figpre 8.7 Silicon Wafer After Camdtive Cavity Has Been Defined
A lithography process is performed to define the diaphragm area and electrical

contacts. The photoresist is used as a mask for a diffusion step. A process called Ion
Implantation is used to introduce Boron to the surface of the membrane. A high-energy
beam of Boron ions is directed at the silicon wafer and Boron is literally forced in to the
surface of the silicon. The substrate is then annealed in an oven at a temperature in the
range of 600-900 °C. This annealing step allows the Boron ions to diffuse further in to
the silicon to a depth of 4 microns to define the diaphragm thickness. The diffusion
depth is a function of the intensity of the energy beam, temperature, and time. This

creates a region of pH silicon seen in Figure 8.8.

83

 

Silicon

Figpre 8.8 Silicon Wafer Aftep Boron Doping

The Boron diffusion serves two purposes. First, a concentration dependant etch-
stop is formed in the silicon wafer. PH silicon will not etch in common etchants such as
KOH and Ethylene Diamine Pyrocatechol (EDP) as long as the concentration is high
enough. Boron must have a concentration greater than 1020 cm'3 or 5 X 1019 cm‘3 to be
an etch stop in KOH or EDP respectively. Concentration dependant etch stops allow for
very accurate etching so the diaphragm thickness can be controlled to within about 0.1
microns [14]. This is particularly important for controlling the dynamic response of the
diaphragm to pressure as explained in Chapter 4. The second purpose of the diffusion
step is that p++ silicon is a conductive material where non-doped silicon in not
conductive. This makes it possible for the diaphragm to be an electrode in the variable
capacitor. A lithography process is then performed on the top of the wafer to define the

diaphragm window, and etching is performed.

84

 

2W ,

 

Etch
Mask

Figpre 8.9 Silimn Wfier with PR Mask to Define thg mapm
Again, the silicon will etch at an angle of 54.7° because of the crystallographic
structure of the silicon atom. The etching will continue until the boundary of the pH
silicon has been reached. The shape of the silicon wafer can be seen in Figure 8.10 after

the completion of the etch step removal of the mask.

 

Silicon

Silicon

Figpg 8.10 Completed Silicon Wafer

85

8.4 Electrostatic Bonding of Wafers

The two wafers are brought together by an electrostatic bond. The set up can be
seen in Figure 8.11. The top of the glass wafer is brought in to contact with the bottom of
the silicon wafer and sandwiched between two electrodes. The positive electrode is in
contact with the silicon while the negative electrode is in contact with the glass. The
sandwich is raised to a temperature of about 400°C and a DC voltage of about 1000 Volts
is applied. The voltage causes mobile sodium ions to pull toward the negative electrode,
which leaves oxygen at the interface between the two wafers. The electrostatic voltage
also pulls the two wafers very close. The oxygen ions in the glass bond to the Si atoms at
the surface and a very strong SiOz bond is created. The bond is stronger than either the
Si-Si bond or the glass. However, this process is very sensitive to contaminants or
surface roughness. This is the reason that the wafers are carefully cleaned before hand.
The bonding is to be performed in a nitrogen ambient so that a pocket of nitrogen is

enclosed inside the sensor.

     

   

  

Vs
Top Electrode
_ = Glass
In WES/x“ f’j’ Silicon

 

 

 

s1+202-= Sio2

Fi re 8.11 Set U For Electrostatic Bondin Process

 

86

Chapter 9
Prototype Testing Results

87

9.1 Prototype Overview

As proof of concept, macro-sized prototypes of the sensor were constructed. The
prototype of the primary circuit consists of an unshielded inductor (600 nH) connected in
series with a 47 Ohm resistor. The inductor and resistor were attached to a BNC
connector so that the device could be used with a function generator. Two sets of
prototypes were developed. The first generation of sensors consisted of an inductor
formed from a printed circuit board (see Figure A.1 of Appendix for mask) attached to a
variable capacitor. As will be seen from the results, these crude models illusu-ated that
the desired effect was taking place, however, the accuracy and clarity of the results were

questionable. A photograph of these prototypes can be seen in Figure 9.1.

. ‘4 Load Resistor .

   

s

 

Figure 9.1 First Genera on of Prototypes
L-R Model Primary Circuit, Inductor Famed From PC Board, Completed
Secondagy Circuit with Inductor, Capacitor and BNC Connector

88

 

 

The second generation prototypes more accurately model the sensor structure.
They consist of an inductor and capacitor plate formed from a single printed circuit board
to resemble the layout of the glass substrate (Figure A2 in the Appendix). Connected in
series to this board is another PC board with a single capacitor plate made to resemble the
diaphragm (Figure A3 in the Appendix). Rubber spacers between the two boards
provided the capacitive gap. These prototypes are of significantly better quality and the
results are much more clear than from the first prototypes. Figure 9.2 shows a

photograph of the second generation prototypes.

' Inductor Coils
‘

Rubber Spacer

 

Figure 9.2 Second Generation of Prototypes
L-top PC Board Representing the Glass Substrate with Capacitor Plate and
Inductor Coil, L-bottom PC Board Representing Diaphragm,
R-Completed Secondag Circuit

89

f1. - 4.... .1... it... a,

9.2 Testing Procedure

To test the prototypes, the primary circuit was connected to a function generator.
The frequency of a sinusoidal signal was swept through a frequency range of 10 to 100
MHz. The primary circuit was placed at rest perpendicular to the sensor circuit so that
the inductive coupling between the circuits could be maximized. The point of contact
was recorded so to eliminate variability between uials. Even though the inductor is in
contact with the sensor, there is a 1.5 mm distance between the inductors due to the 1.5
mm thickness of the PC board. A low capacitance probe (1.3 pF) was connected across
the capacitor of the secondary circuit. The voltage across the capacitor was measured for
various frequencies across the range and plotted. Then the procedure was repeated with
the probe connected across the load resistor of the primary circuit. The voltage profiles

were then compared to observe similarities and trends. The point of contact between the

circuits and the connections to the equipment are shown in Figure 9.3.

 

 
 

To Function
Generator

     
 

 

 

 

  

To Oscilloscope '+._

 

Point of Contact Between
Prim. and Sec. Circuits

Figpre 9.3 Experimental Setup

 

 

 

90

9.3 Expected Results

Recall that the sensor is at a maximum degree of excitation at resonance so the
voltage measured through the secondary circuit should peak at the resonant frequency.
Also, the voltage across the load resistor should dip at resonance. The expected trends
are shown in Figure 9.4. Note that the indicated frequency range in Figure 9.4 is not
characteristic of the models and is used simply for illustrative purposes. Also, ideally,
the phase of the voltage across the load resistor would be measured to find the exact
resonant frequency of the sensor. Recall from Chapter 2 that the voltage dip occurs prior
to the resonant frequency and the peak of the voltage rise occurs after the resonant
frequency. The only accurate way to determine the actual resonant frequency is to
determine where the phase of the signal equals zero. The frequency where there was a

phase of zero would be the resonant frequency, but the equipment was not available

 

 

 

 

   

 

 

 

 

 

perform the phase analysis.

0.2 1.1

.5. 0.18 q, 0 9
'3 0.16 - m
o o
g 0.14 0.7 g
3 :9? 0.12 5
g '3 0.1 §
0 Z, a:
5, 0.08 o
g, 0.06 g
:5 0.04 V

0.02
o . -0.1
90 92 94 96 98 100
Frequency (M Hz)

Figpre 9.4 Expggted Results From Prototyms

91

 

The magnitude of each of the signals depends on several factors including the
relative proximity of the primary and secondary circuits, the coupling coefficient, and
inductor size. The magnitude of the response is not important at this stage of the
analysis. The important information that is desired is to verify that the sensor is
displaying the basic concept, and that the resonant frequency can be measured on an
external device.

9.4 Fabrication of the PC Boards

PC Boards were prepared by using a masked, copper clad PC Board with a
photosensitive coating and exposing it to a UV source. The masks for each board can be
found in the Appendix (Figures A.1-A.3). Once the boards had been exposed to the UV
source for about ten minutes, the image was developed using a standard PC Board
Developing Solution. The boards were then immersed in a Ferric Chloride Solution for
about an hour to etch the copper away of the board and leave the desired pattern from
each mask on the boards. The photosensitive chemical was then removed from the
boards with PC Board Stripping Solution. The boards were then ready to be cut and
assembled.

9.5 Results of Testing First Generation Prototypes

Results from testing the first generation prototypes (see Figure 9.5) showed that
the concept was occurring, but the resonant frequency was not as clearly defined as was
hoped. The voltage in the sensor has a definite peak at 74 MHz and the voltage across
the load resistor shows the expected pattern as seen in the computational simulations.
However, the results obtained from the models were not nearly as well defined as the

simulation results. The voltage dip occurred at about 4 MHz prior to the resonant

92

 

frequency and the peak of the voltage rise occurs about 6 MHz after the resonant
frequency. A major area of concern is the relative location of the resonant frequency
compared to the voltage dip and corresponding voltage rise. The magnitude of the
frequency range for the dip and rise to occur is a function of the circuit resistance. More
circuit resistance translates into a wider frequency range between the dip and the peak. In
a perfect resonant circuit, the resistance would be infinitesimally small so the voltage dip
and rise would occur exactly at the resonant frequency. The voltage dip and the rise
occur over a much broader range than in the simulations as a result of the resistance. The
frequency range between when the voltage dips and the rise peaks is about 0.4 MHz in
the simulation, where it takes 10 MHz in the model. The circuit has a relatively high
resistance so the dip occurs slightly prior to the resonant frequency, and the rise reaches a
peak after the resonant frequency. While the results seen from these prototypes are not

surprising considering the size of the components, the concept was not shown with a high

 

 

 

 

degree of certainty.
350 . 900
330 J «- 850
9 310 « , <
. w 800 O
E 290 « '~ ‘ . 31 if
g: 270 ‘ ' “ 75° 3.3
a 250 . «- 700 6 5
> ,1 o
3 230 « -~ 650 g 8
0 210 ~ I'
C
600 °
(3 190 . a
170 « *“ 55°
150 . 500
50 60 7o 80 90 100

Frequency (MHz)

Figure 9.5 Sensor Voltage and Voltage Across the
Load Resistor for First Generation Prototypes Model # 9

93

 

It appears that the concept works; however, it would be impossible to determine
the resonant frequency accurately enough to produce a pressure measurement. A new set
of models was developed to obtain a more precise simulation.

9.6 Results From Testing Second Generation Prototypes

It is believed that the capacitor created a high resistance in the first prototype
circuit that deteriorated the quality of the results. To reduce the resistance, the second set
of prototypes was made to more closely resemble the sensor structure and uses only
printed circuit boards. The voltage values seen in the following plots are the average
peak-to peak voltages of six periods of the signal. The error bar associated with the
sensor voltage is roughly i 1.5 mV and roughly :t 3.5 mV for the voltage across the load
resistor. Two 2 mm rubber spacers were placed between the capacitor plates to produce

the initial gap.

94

 

 

 

 

5...»? >03: roan 38.32 <0..er >03: reed meet»... <o=euo >032- ..25 33.22

 

 

 

»
4

 

 

a) Device 11

 

 

 

 

H 7

 

 

 

 

 

b) Device 6

 

\

 

 

 

 

 

l
a ll

mm

mwmmeeomm

9'5 ems-x; .oeeem

 

Ki... .11. _
m m m m m

9.5 ouo=o> .oeeom

I4l..l it

m

 

a a a mama a m a m w as.” m m -m m

 

 

 

 

 

c) Device 9

 

 

 

 

5.8 w m .8.

9E. omu=o> 328m

 

0

13)

120

WW“)

1 10
Figure 9.6 Sensor Voltage and Voltage Across the Load

1CD

 

regime); for Second Generation Prototym

 

Resistor as a Function of F

95

The second set of prototypes performed significantly better than the first set. The
sensor voltage displays a clear peak at a particular resonant frequency unique to each
device, and the voltage dip provides a rough indication of the resonant frequency.

The voltage dip corresponds exactly to the peak of the sensor voltage for Devices
11 and 6. However, the voltage dip actually occurs 2 MHz after the peak of the sensor
voltage for Device 9. Even though the performance of Device 9 does not exactly
replicate the performance of the other two models, the concept is clearly demonstrated,
and the sharpness of the peaks is significantly better than with the first prototypes.

Due to equipment limitations, it was impossible to accurately measure the
capacitance and inductance of the models. However, approximations for each quantity
could be made from the dimensions of the capacitor plates and the resonant frequencies
that appear in the Figure 9.6. Each of the capacitor plates is roughly 1.0 cm2. The
spacing between the capacitor plates was 4 mm. An estimate for the capacitance can be
found from equation (4.1). Additionally, there is 1.3 pF of capacitance due to the probe.
The approximate total capacitance is 1.52 pF. Based on this capacitance and the resonant
frequencies for each device in Figure 9.6, the inductance can be approximated by

equation (2.22). The approximate inductances for each device are found in Table 9.1.

Table 9.] Approximate Inductance Values for Prototypes
for a Capacitance of 1.52 pF

 

Device 11 1101.5 nH
Device 6 1138.2 nH
Device 9 1119.6 nH

 

96

 

 

As the number of spacers between the capacitor plates is decreased from two to
one, the capacitance doubles, and the resonant frequency of the circuit decreases. The
capacitance gap is 2 mm resulting in an approximate capacitance (including the 1.3 pF of
probe capacitance) of 1.74 pF. Based on this capacitance and the approximate
inductances in Table 9.1, the theoretical resonant frequency can be determined as seen in

Table 9.2.

Table 9.2 Theoretical Approximate Resonant Frequencies
for a Capacitance of 1.74 2F

 

Device 11 114.96 MHz
Device 6 113.09 MHz i
Device 9 114.03 MHz ‘

 

As the capacitance increases, the resonant frequency shifts to the left of the
frequency scale. The measured frequency responses of the sensor and primary circuit can
be seen in Figure 9.7. A comparison of the results for the two cases of capacitance can be

seen in Figures 9.8 and 9.9.

Table 9.3 Summary of Prototjm Tesg' g Results

 

 

 

 

 

Peak of Sensor Voltage Voltage Dip
Device 11 Case 1 123 MHz 123 MHz
Case 2 109 MHz 109 MHz
Device 6 Case 1 121 MHz 121 MHz
Case2 113 MHz 110 MHz
Device 9 Case 1 122 MHz 124 MHz
Case 2 105 MHz 106 MHz

 

97

 

 

<28? >03.- E 3.2%.! .35

 

<0; >03: roan 38.82 .35

700

 

 

 

5 5 5 5 5 5 5 0

2 2 2 2 2 2 2 0

7 6 5 4 3 2 1 8

Il:-...__IIL .. +7 fi + F fl . “Ii
_

1 n.

1 6
e C
C C

c 1 o l
V W
a b

 

 

 

 

 

 

 

0 0 0 0 0 O
0 0 0 0 0
5 4 3 2 1

9.5 83.3 323m

    

600
500

A
v

 

 

0 o 0

o o o

5 4 3
9.5 035:; concom

- 300

liltlhtlllllni ‘ \.

‘1‘. \ol‘titcllll‘ll

200

 

 

<0..qu >268 roan 38.30135

 

 

 

 

 

 

 

 

 

 

0 O 0 O 0 0 0 0
0 O 0 0 O 0 0 0
2 1 7 6 5 4 3 2
_ F F
. 4 i a _ a

9

e

C

.1

W

\I

C
t

>
.1
a
0 O 0 O 0 0 O 0
0 O 0 O 0 0
1 5 4 3 2 1
9.5 33:5 30:3

150

140

30

120

110

100

90

Frequency (M Hz)

re 9.7 Sensor Volta e as a Function of Fre uen After Increasin Ca acitance

Fi

98

(J... I- 4. 1 n}... (I. .6 Its).-
_ . .

Sensor Voltage (mV)

Sensor Voltage (mV)

Sensor Voltage (mV)

 

 

550 a) Device 11
500

450 -«
400
350 a
300
250
200 4
150

 

 

Increasing Capacitance

 

 

 

{z} 13 ",1. ‘;

 

 

 

 

 

 

800 b) Device 6 ' ‘ "F ‘

 

 

 

 

 

500JI

 

 

c) Device 9 ' 5%

 

 

 

 

 

 

 

 

90 100 110 120 130 140 150
Frequency (MHz)

Figpre 9.8 Comparison of Sensor Voltages For Two Cases of Capacitance

99

 

Voltage Across Load Resistor (mV) Voltage Across Load Resistor (mV)

Voltage Across Load Resistor (mV)

900
800
700
600
500
400
300
200
100

 

i a) Device 11

 

 

 

 

 

 

 

 

Increasing Capacitance

 

 

900
800
700
600
500
400
300
200
100

700
650
600
550
500
450
400
350
300
250
200

 

 

 

 

 

 

b) Device 6

 

 

 

 

 

 

 

 

 

 

c) Device 9

 

 

 

    

 

f ’ " .i y

90 100

 

 

 

110 120 30 140 150
Frequency (Mi-I2)

Figure 9.9 Comparison of Voltage Across Load Resistor
For Two Cases of Capacitance

100

 

 

There are several important trends to notice from Figures 9.7-9.9. First, Device
11 remained consistent in its performance. The voltage dip across the load resistor and
the sensor’s peak voltage occurred at the same frequency for both cases of capacitance.

Device 6 was less consistent. For the first case of capacitance, the voltage dip and
the peak of the sensor voltage occurred at the same frequency. After increasing the
capacitance, the dip occurs 3 MHz prior to the peak of the sensor voltage. However, this
device required repair between trials to fix a loose wire that is a likely cause of the
inconsistency.

Device 9 did not perform according to theory for the first trial. The voltage dip
occurred 2 MHz after the peak of the sensor voltage. However, the device was fairly
consistent because the voltage dip occurred 1 MHz after the resonant frequency for the
second case of capacitance as well. Since measurements were taken at intervals of 1
MHz, it is likely that the 1 MHz difference in the results is due to the resolution of the
measurements.

It should be noted as well that the magnitude of the responses is similar between
the devices, but not identical. Also, the magnitude of the response for a particular device
is not maintained once the capacitance has changed. After multiple trials, it has been
determined that the differences in magnitude between different devices and even the
same device for different capacitances is due to the coupling. The point of contact
between the primary circuit and the secondary circuit for each trial and held consistent for
a particular. However, due to the small size of the devices being tested, there was an
immeasurably small difference in the location of the contact point between trials. This

resulted in slight differences in the magnitude of the responses.

101

 

 

Table 9.4 Comparison of Theoretical Resonant
Frauencies to Measured Values

 

Theoretical Measured
Device 11 114.96 MHz 109 MHz
Device 6 113.09 MHz 113 MHz

 

 

Device 9 114.03 MHz 105 MHz

 

Notice that the resonant frequencies calculated by theory do not correspond
exactly with the measured frequencies. This is not a necessarily a surprise since the
capacitance and inductance are very sensitive to the dimensions of the on-chip
components. The printed circuit boards were fabricated at one time using multiple masks
on the same substrate. Small changes in the masks from sample to sample could easily
result in a difference in capacitance or inductance of the devices. This is most likely the
case since the resonant frequency of each device was not the same for the initial test used
to provide Figure 9.6. Also, there will be an amount of inductance and capacitance in
each sensor due to the connection wires and solder that are used to assemble the models.

The important trend to notice is that the measured resonant frequency is measured
to be equal to or less than the theoretical value. The additional inductance and
capacitance that are present would result in the resonant frequency of the device being
lower than predicted. The results support the hypothesis.

Despite the obvious difference in size, the macro-models clearly demonstrate the
basic concept for the sensor. The quality of the prototypes pales in comparison to the
quality level that can be achieved for MEMS devices. The difference in the results
between the first and second set of prototypes show that the quality of the results that can
be obtained is directly related to the quality of the device. The MEMS pressure sensors

will be a drastic improvement on the macro-sized models.

102

 

Ft"

 

Chapter 10

Important Considerations

103

 

 

 

10.1 Introduction

Once the device has been completed, there are several issues that need to be
considered about the performance of the device over its lifetime. These issues include
quantifying the actual volume of gas enclosed in the capacitive cavity, determining the
temperature dependence of the device, development of an off-set in the readings, and
drift. These issues are all important to consider and understand before the device is
implemented into humans because it is not desirable to remove the sensor after
implantation to verify calibration.

10.2 Volume of Air Enclosed in the Capacitive Cavity

The first issue to be considered is to quantify the actual pressure inside the sensor.
This pressure is used as a reference and the sensor measures only the differential
pressure. Theoretically, since the device will be sealed in ambient conditions, the
pressure in the cavity should be equal to 1 ATM. Initially, air was chosen as the gas to be
present in the device. However, during the electrostatic bond a quantity of the oxygen
would be consumed to form Si02 bonds on the surface of the diaphragm. This will result
in lowering the pressure enclosed in the cavity.

There is a sufficient amount of silicon atoms at the surface of the capacitive cavity
to react with all of the oxygen present so it stands to reason that the pressure enclosed
inside the cavity would actually be reduced by 0.2 ATM [24]. The actual volume
enclosed in the cavity would only be about 0.8 ATM (608 mmHg) as opposed to the
theoretical pressure of 1 ATM (760 mmHg).

Bonding the wafers in a nitrogen ambient instead of air eliminates the reaction.

Another common solution is to seal the device in vacuum so that there is no gas inside

104

 

 

the device. The device then becomes an absolute pressure sensor instead of a differential
sensor. However, the size of the diaphragm becomes too large, and the size constraints
on the device do not allow the luxury of manufacturing an absolute sensor.

Another factor to consider is the temperature dependence of the sensor. Since the
sensor is sealed in air instead of vacuum the sensor becomes dependant on temperature
due to the expansion of the gas trapped inside the cavity [24]. Fortunately, the
temperature in the eye is maintained nearly constant by the body so the temperature will
not fluctuate more than a few degrees. However, the electrostatic bond that seals the
device occurs at a temperature of about 400°C. The gas will compress slightly as the
temperature is reduced and the pressure inside the cavity will be lower than 1 ATM [22].
Testing will provide the actual pressure inside the cavity. It is possible to seal the device
at an elevated pressure, so possibly device could be sealed initially with greater than 1
ATM of pressure so that the final pressure after cooling is 1 ATM.

10.3 Drift

Another parameter important to sensor performance is drift. Drift is the tendency
of a device to show different patterns of operation than expected due to changes in
material properties. The calibration of the device will shift slightly so the output of the
device will not exactly correspond to the input in the predicted manner. Drift is very
difficult to predict as it is often caused by changes in material properties due to repeated
movement of the sensor’s components such as the diaphragm [14]. IOP fluctuations
between 20 and 60 mmHg for one patient will result in a different rate of degradation of

the diaphragm than another patient showing fluctuations between 20 and 25 mmHg.

105

 

 

These issues are not obstacles that will limit the device’s ability to accurately
measure IOP, but they are issues that need to be considered and accounted for during

manufacturing, testing, and further development stages.

106

 

1"" "

 

Chapter 11

Conclusions

107

11.1 Summary

This thesis has outlined the design of an implantable, biomedical pressure sensor
to be fabricated by standard Microelectrical Mechanical Systems (MEMS) technologies.
The objective of this invention is to design and develop a micro-sensor intraocular
pressure measuring system that can be implanted in the patient’s eye for the purpose of
glaucoma treatment/management. Future research will be performed to complete the
remaining components of the measurement system.

The previous chapters presented the steps and decision process required to
achieve a final design of the sensor. The design was an iterative process since there is no
single correct solution to the problem. The goal was to implement many gradual changes
to an initial, tentative design to achieve a very accurate and precise device.

At times, finite limits had to be placed on parameters based on common sense and
judgment, as an equation is not available to specifically predict the capabilities of a
fabrication facility. There is room for many small adjustments in the design to improve
performance such as changing the feature size of a structure by a few microns. The
capabilities of a fabrication facility will dictate the exact feature size and process
precision that is available, but the design in this thesis is a viable solution to the problem.

It is hoped that this device will allow physicians to better care for their patients,
provide new insight in Glaucoma, save patients vision, and ultimately aid in the
development of a cure for glaucoma and many other pressure related problems of the

body.

108

 

"1L 6: ‘

 

Appendix

109

 

 

 

 

   

Figure Ai Mask For-
First Generation Prototpytlfi

 

110

 

@i—QQ

tr

 

   

 

 

 

 

.l l I: 11--.!» 01.4

 

     

     

     

       

Figure A3 Second Mask For Second Generation Prototypes

112

Table A.l Frequency Resmnse Data for First Generation Protom

 

Freq Sensor V mv Freq “Resistor V
1 5 1 35 0.1 35 1 5 2
20 140 0.14 20 1.76
25 1 65 0.1 65 25 1 .5
30 1 85 0.1 85 30 1 .42
35 235 0.235 35 1 .41
40 325 0.325 40 1 .45
43 400 0.4 43 1 .43
45 330 0.33 45 1 .37
50 300 0.3 50 1 .15
55 330 0.33 55 0.94
60 360 0.36 60 0.78
65 360 0.36 62 0.765
66 370 0.37 63 0.76
67 370 0.37 64 0.74
68 380 0.38 65 0.725
69 385 0.385 66 0.695
70 370 0.37 67 0.7
71 370 0.37 68 0.71
72 320 0.32 69 0.72
73 330 0.33 70 0.715
74 330 0.33 71 0.705
75 320 0.32 72 0.705
80 280 0.28 73 0.73
85 220 0.22 74 0.735
90 200 0.2 75 0.74
95 1 80 0.1 8 80 0.77
100 170 0.17 85 0.73

90 0.7
95 0.66
1 00 0.605

 

 

 

 

 

 

 

113

 

 

 

0.0.0 o 0><
0...? 50;
05.0 5V0
or; 50.0
0%... 05.0
00.? 5...0
00.5 00...
00.5 50...
00.0 00.0
00... 00.5
05.0 556
006 00.0
00.0 50.5
00.? 50...
00.0 05.0
00.0 00.0
00.0 00.0
00.0 00.0
00.0 50.0
00.0 05...
00.0 50;
00.0 00.0
00.0 0v...
00.0 00...
00.0 00.0
00.0 55...
00.0 00.0

0 .meou ..Otm .

0v.0
00.0
00.0
50.0
0V0
50.0
00.0
50.0
00.0
00.?
50.0
00.5
00.0
05.5
50.5
00.0
00.0
00.0
05.5
00. P
50.0
00. F
50.5
50.0
9.0
50.0
50:0 +

B. as.
2.84
8.3:.
8.48
54.84
8.854
B. 64
8.80
886
54.84
8.88
$03
538
8.08
a F .m 3
8.84
8.09
3.84
8.84
50.8..
$.80
8.05m
8.8a
9.8%
5 F .855
2.85
6>$>

0. 0e 0.00v 30¢ 00 5
5.00v v.5? 3‘3 03
0.03 5.31.. v.33. 005
0.000 0.00“‘ 0.000‘ 00 F
0.3V 0.00%. 0.00v 00F v0.5 0 0><
0.05v 0.05v 05¢ 00 F
0. EV 00v 0. ..0v 50F 00. P 00.0
5.000 0.000 0.000 00. 0 F0 50. F
F. F 50 0.000 0.050 00F 0.00 00. 5
5.000. 0.00v v.00v «0? 00.0 0.00
p.000 000 0.000 005 0: 00.0
0650 0.050 550 00F 05.0 50. P
0.000 0.30 V00 05 00. F 00.0
0.500 0. 500 000 00F 00.0 00.0
5.53 0.05 F0; 0: 00.0 0:
00¢ 5.00”. 0.00v 0: 00.0 0 F0
30... 00v 5.000V 5: 00.0 50.0
0. EV 0.00v F500 0: 0: 50.0
5.05». 0.50v 00v. 0: 00.0 00.0
0.00v 0.000 0.00v 0: 00.0 0 _..5
0.000 .000 000 00 P 00. F 00.0
0.050 0.050 0.050 00? 00. P 00.0
0.500 0.000 500 00 00.0 50. P
500 5.000 0.000 00 00. F 00.0
0.055 055 0.055 00 00.0 50.0
0.005 5.005 0.005 05 00.0 00.0
0> 0> F> 09. o 32 5:0 -
.025

00...
00.0
05.5
00.0
00.0
00.0
00.5
0V0
50...
50.0
00. ..
00.0
5V0
5v;
50.0
50.0
00. ..
00.0
50.0
5V0
..Otm +

8.53
5m. am
88m
808
2.8.”
$08
8.0%.
8.80
8.84
9.8m
$.80
team
8.8“
2. E
8.52
209
53$
939
6.8
no.8
.o><.>

0.03.
...000
5600
0.000
0.000
0. ..00
@400
0.000
0.00v
0.000
0.000
0.000
0.000
0.05..
0.50..
0.00w
5.00..
0.0:
0.00
0 5.50
0)

5.3
000
0.000
0.30
0.000
0.000
0.000
0.000
5.000
000
0.0.0
000
0.000
.V. 55..
‘50..
060..
#005
v.00..
0.00
00.00
0>

0.53.
5. ..00
0.000
0.000
0. P00
0. P00
000
000
0.50v
0.000
#000
...000
000
0.055
0.00..
F005
0.0:
0. ..05
0 5.00
00.00
P>

00..
3;
005
005
50..
005
00..
v05
00..
00..
50..
00..
0:
0:
00..
00..
00
00
00

05
09.

0005.00

 

 

 

 

 

 

hdlumAno 353.3000 .53 2 80:5 .80 5.5 85003— 350030 «J. 030,—.

114

 

 

 

 

00.0 0196 00.F m m>m
0 F0 00.0 00.0 3.0 F¢ 5. F0¢ 00¢ 0.0 F¢ 00F 00. F 50.0 00.0 5¢.00F F.00 F 0.00F F. F0 F 00F
05.0 50.0 0 F.¢ 50.00¢ 0.00¢ 0. F0¢ 00¢ 00F 00.0 00.0 50.0 00.09 0.00F 0.00F ¢.00F 03
00. F 05.0 00.0 05.00¢ 0. F0¢ 00¢ 0.00¢ 00F 00. F 00.0 00.0 00. FOF 0. FOF 0.00F FOF 00F
00.0 05.0 55.0 05.00¢ 05¢ 5.00¢ 0.00¢ 00F 05.0 50.0 0¢.0 50.000 5.000 F.000 000 50F
00. F 50.0 00.0 50.000 0. F00 000 0.0 F0 0F F 00. F 55.0 0 F. F 50.05 F 0.05F 0.55.. 0.05F 00F
00.0 00.0 50. F 05. F00 F00 0.000 ¢.000 0 F F 0 F. F 50.0 00.0 55.09 0. FOF 0.09 0.03 5F F
05.0 00.0 50.0 00.¢00 0.¢00 0.¢00 0.¢00 0F F 00. F 05.0 00.0 05.000 0.¢00 000 0.000 0F F
00.0 00.0 50.0 0¢.0¢0 0. F¢0 0.0¢0 0.0¢0 F F F 0 F0 50.0 00.0 5F.000 F.000 0.000 0.000 0F F
00. F 00.0 00.0 00. F00 F. F00 0. F00 5.000 0F F 00.0 0¢.0 00.0 00.0¢¢ ¢.0¢¢ 5¢¢ F.0¢¢ F F F
00. F 05.0 50.0 0 F500 000 500 ¢.000 09 00.0 50. F 05.0 50. F00 F000 0.000 0.000 0F F
0 F0 0 F. F 50.0 05.00F 0.02 0.09 5.52 0.03 00.0 00.0 00. F 00.000 0.500 ¢.000 0. F F0 00F
00.0 5 F. F 05. F 50.000 000 F000 5.000 09 0 F.¢ 0¢.0 05. F 00.50¢ 0.00¢ 0.00¢ 0.00¢ 09
00.0 0¢. F 00.0 00. F00 000 F000 ¢.000 53 05.0 50.0 00.0 50.0¢¢ 0.0¢¢ 0.0¢¢ 0.5¢¢ 50 F
0¢.0 5 F0 00. F 50.50¢ 0.00¢ 0.00¢ 0.00¢ 00F 00. F 0¢.0 00.0 0¢. F00 0. F00 F00 000 09
00.0 00.0 00.0 00.000 0.000 ¢.050 0. ..50 00 F 0¢.0 00.0 5 F0 00.000 ¢.000 0.000 000 00 F
00¢ 50.0 0¢.0 50.000 0.0 F0 0.000 F000 00 0¢.0 00.0 00. F 00.09 F.50F ¢.50F 0.09 00
00.0 00. F 05. F 00.¢00 5.000 0.¢00 F000 00 0¢. F 05.0 50.0 00.00F ¢.00F 0.0¢F FOF 00
00.¢ 00.0 00.0 0¢.055 0.055 ¢.555 0. F05 00 00. F 05.0 00.0 00.5F F 0.5F F 0.9 F 0.9 F 00
00.0 50. F 00.0 5 F. F05 0. F05 F005 F005 05 0¢.0 00.0 00.0 00.05 0 F. F5 00.05 05.05 05
o .92 5:0 - 8:0 + .0><.> 0> 0> F> cm... 0 .32 8:0 - 5:0 + A0><v> 0> 0> F > 00:.
:m>:c :omcom

 

 

 

 

 

m ¢5AHU 853.90 00 :33 2 8.50 .80 30m— 8: 8m 95: 8.0 0.4 03$

115

 

 

405.000 0 0><
0F... 0¢.0
0F.0 0 F. F
00.0 00. F
00.¢ 00.0
00.0 00.0
00.0 00. F
00.0 00.0
0¢.0 00...
00.0 0 F0
00.0 0F.0
00.0 00.0
00.0 50.¢
05.0 05. F
00.¢ 50.0
00.0 0¢. F
00. F 50.0
00.0 50...
0¢.¢ 5¢.0
0¢. F 05.0
00.0 00. ..
0F.0 50.0
00¢ 50.0
00. F 00.0
00. F 05.0
2.0 50.0
00.0 0¢.0
0 .05.

 

50.0
50.0
5 ...0
00. F
5 F. F
00.0
0¢.F
50. F
50.0
0 F0
00. F
0¢.0
00. F
00. ..
50. F
00. F
00.0
00. F
05.0
50.F
00.0
00. F
50.0
50.0
00.0
50.0

00.0 ..¢
00.00¢
0 F .00¢
00.¢0¢
00.00¢
0¢.00¢
00.00¢
00.00¢
00.05¢
00.00¢
00.¢00
5...¢50
0 ...000
50.¢ F¢
00.00¢
50.¢0¢
50. F0¢
50.00¢
00.55¢
05.00¢
50.000
55.000
00.000
05.000
50.5 F5
00. F00

5:0 - 5:0 + .0><.>

0F¢
0.00¢
0.00¢
F.00¢
0.00¢
0.00¢
5.00¢
0.50¢
0.05¢
F0¢
0.000
0.050
¢.500
0.0F¢
0.00¢
5.00¢
F. F0¢
0.00¢
0.05¢
0.05¢
00¢
0.000
5.500
0.000
0.55
0. F00
0>

0.0 F¢
F.¢0¢
0. F0¢
0.00¢
00¢
F.00¢
0. F0¢
0.00¢
F.05¢
0.00¢
0.000
F.050
0.000
...0F¢
0.00¢
0.¢0¢
00¢
0.05¢
0.55¢
0.00¢
F000
F000
0.000
0.000
0.5 ..5
0. F00
0>

0. F F¢
0.¢0¢
0. F0¢
5.00¢
0.00¢
0.50¢
¢. F0¢
05¢
F.05¢
0.00¢
5.000
0.050
F.050
5.¢F¢
0.00¢
F.¢0¢
0.00¢
0 00¢
0.55¢
5.00¢
F.00¢
5.¢00
0.000
000
0.5 F5
0.000
F>

00F
0¢F
0¢F
00F
00F
50F
00F
00F
¢0F
00F
00F
FOF
00F
0FF
0FF
5FF
05.
02.
0:.
0FF
00..
00..
00
00
00
05

00:.

:0>tn

¢00000. F m 0><

00.0
0¢.0
00.0
00.0
05.0
00.0
00.0
05.0
0F. F
00.0
00.0
00.0
00.F
00.F
00.F
00.0
05.0
00.0
00.0
00.0
00. F
3.0

0 =05.

5¢.0
5 F0
5 F0
0 F0
00.0
00.0
00.0
50. F
00.0
50.F
50.0
0 F0
0¢.0
00.0
05.0
50.0
0¢.0
50.0
00.0
00.0
50.0
05.0

00.0
00.0
0 F0
0 F0
0¢.0
00.0
50.0
0 F...
00.0
00. F
00.0
5 F .0
55.0
50.0
00.0
00.0
50.0
0¢.0
50. F
00.0
00.0
00. F

5¢.0¢0
50.000
5 F .00¢
00. F00
00.000
00.¢0¢
0 F .0 F0
50. F00
00.005
50. F05
50.005
0 F050
0¢.000
00.00¢
00.000
50.000
0¢.000
50.05F
0¢.0¢F
00.00F
55.00..
05.05

5:0 - 5:0 + 00><v>

0.0¢0
¢.000
00¢
0.000
¢.000
0.¢0¢
0.¢F0
...000
5.005
F.005
0. ..05
0.050
0. F00
0.00¢
0.000
F.¢00
5.000
0.05F
0.0¢F
0.00F
F.00..
0...05
0>

0.0¢0
0.000
0.00¢
F00
0. F00
0.00¢
0.¢F0
F.000
005
0.005
0.005
050
...000
0.00¢
¢.000
0.000
0.000
0. ..5F
0.0¢F
F.00F
0.50..
5 F05
0>

0¢0
0.000
0.00¢
F. F00
5. F00
0.¢0¢
5.0 F0
0.000
F005
5. ..05
5.005
F.050
000
0.00¢
0.000
0.000
000
5.05..
0.53.
0.00F
0.00..
00.05
..>

00F
0¢F
00F
00F
50F
00..
00F
00F
0.FOF

..0F
00F
0FF
5FF
0FF
0FF
0....
00F
00F
00
00
00

05
00:

..Owcmw

 

 

 

 

rad 00.FHU 00:3.0|0000 5.3 0 0030: 5.. 50¢ 0mEflm0¢ 0000:0000 ¢.< 030,—.

116

 

I:

P|i.r JI.

 

 

 

 

 

 

0F.0

0¢.0
0 F0
00. F
00¢
00. F
00.0
00¢
0¢. F
00.0
00.0
00¢
0¢. F
00.0
0F.¢
00.0
00. F
00.0
00.0
00.0
0F.0
0 .050

0 0><

05.F
55.0
50.0
5¢.0
00.0
5 F0
00.0
00.0
00.0
0¢.F
50.F
05.0
0 F0
0F.0
0¢.0
00.F
0¢. F
00.F
50. F
00.0
..Otm u

05.F
00.0
00.0
00.F
00.0
00. F
50. F
00.0
00.0
50. F
0 F0
50.0
5 F. F
00.0
00.0
50.0
00.0
55.0
00. F
0 F0
.0500 +

00.000
50.0 F¢
5 F .0¢¢
55.000
0 F .000
5¢.000
0 F .550
0 F .000
00.000
00.500
55.50F
0¢.000
00.050
0 F 00¢
00.00¢
00. F50
00.0 F0
00.000
50.055
0¢.005
AG><V>

F.¢00
0.0 F¢
0.0¢¢
0.¢00
F000
F050
0.550
0.000
0.000
000
0.00F
5.500
0.050
F.¢0¢
0.00¢
0.000
0.0 F0
¢.500
F.¢55
¢.500
0>

0.000
5.0F¢
F.0¢¢
0.000
500
000
F.050
0.500
F000
5.000
0.00F
0 .000
0.050
0.00¢
¢. F5¢
0. F50
¢.5 F0
F.000
¢.055
0 .005
0>

0.500
0.00¢
0. F¢¢
5.500
0.000
0.000
F050
0.500
000
0.000
0.50F
F.000
0.050
00¢
0.00¢
5. F50
5.0 F0
¢.000
0.055
0.005
F>

00F
0¢F
00F
00F
0FF
0FF
¢FF
0FF
0FF
FFF
0FF
00F
00F
50F
00F
00F
00
00
00
05

00:

525

05.0

00.0
00.0
0¢.0
00.0
00.0
0¢. F
00. F
00.0
00. F
00.0
00.0
00.0
0¢.0
00. F
0¢.0
00.0
00. F
00.0
00.0
00.0
00.0

0 .99

0 0><

5¢.0
50.0
0F.0
50.0
00.0
00.0
50.0
0¢.0
00.0
50.0
0¢.0
00.0
0 F0
00.0
50.0
50.0
50.0
00.0
5¢.0
0 F0
0¢.0

.920 .

0¢.0
00.0
50.0
00.0
00.0
00.0
00.0
5¢.0
50.0
00.0
0¢.0
50.0
50.0
5¢.0
0 F0
00.0
05.0
00.0
00.0
0 F0
00.0

5:0 + .0><V>

50.00F
50.000
00.000
5¢.000
00.00¢
0¢.000
50.050
0F.005
00.005
50.500
00.¢00
0F.000
00.05¢
0¢.00¢
5¢.550
55.¢F0
5 F000
00.00F
50.00F
0¢.0F F
00.05

F.00F
000
F.000
5.000
0.00¢
0. F00
¢.050
0.005
0.005
F.500
0.¢00
0.000
¢.05¢
0. F0¢
0.550
5.¢F0
0.000
F.00F
0.00F
0.0F F
0 F05
0>

0.00F
0.000
F.000
0.000
0.00¢
000
0.050
5. F05
0.005
5.500
0.000
0.000
0.05¢
0.00¢
0.550
F0 F0
0.¢00
0.00F
5.00F
¢.0F F
00.05
0>

00F
0.000
0.000
0.000
F.00¢
0.000
0.050
F.005
0.005
0.500
0.¢00
000
¢.05¢
0.00¢
0.550
0.¢ F0
0.000
00F
F.00F
0.0F F
00.05
F>

00F
0¢F
00F
00F
0FF
0FF
0FF
¢FF
0FF
0FF
FFF
0FF
00F
00F
50F
00F
00F
00
00
00

05
00:

.0050“...

 

 

 

 

“04.05.30 005850000 .53 0 0030a 50 3.5 0m:aw0~— mop—0:300 0.< 030%

117

 

00.0
0F.0
00.0
00.0
00.0
00.0
00.F
00.0
05.0
00.0
05.0
00.0
00.0
00.0
00.0
00.0
00.0
05.0
05.0
0F.¢
05.F
0¢.0
05.0
0F.F
05.F
0F.F
00.F
0 .92

 

50050.0 0 0><

00. F
05.0
00. F
05. F
00.0
0 F. F
50.0
50.0
00. F
50. F
0¢.0
50. F
50. F
00.0
55.0
00.0
00. F
5¢.0
55. F
50. F
00.0
00. F
00. F
00.0
0 F. F
5¢.0
00.0
.Ohhm .

05. F
0¢.0
00.0
5 F. F
0F. F
05. F
05.0
00.0
50.0
05. F
50.0
00.0
00. F
00.0
00.0
5¢.0
50. F
00.0
00.0
0 F0
0F. F
5 F. F
05. F
50.0
00.0
00.0
5F. F
..Otm +

2.3..
8.08
8.94
3.03.
8. $4
8.8..
B. 5..
3.20.
8. :0.
$.02
8.03
5.80
3.80
8.80
5.0:.
8.09.
8.03.
8.8..
2.8..
Bot.
80%
9.08
2.80
8.80
2.90
$.80
8.80
.0><.>

¢.0F¢
0.00¢
0.0¢¢
0. F¢¢
¢.00¢
0.00¢
5.00¢
0.05¢
¢. F0¢
0.05¢
F.0¢0
¢.000
0.000
0.000
0.0 F¢
0.0¢¢
0. F0¢
F.¢0¢
F.¢0¢
0.00¢
¢.00¢
0.00¢
¢.000
0.000
0.5¢0
0.005
¢.000
0>

0.0 F¢
0 00¢
00¢
F.¢¢¢
F. F0¢
00¢
0. F0¢
0.00¢
0.00¢
¢.05¢
5.0¢0
¢.000
0.000
0 .000
¢.0 F¢
0.50¢
0.0¢¢
¢.00¢
¢. F0¢
F.05¢
0.¢0¢
0.00¢
000
0.000
0.0¢0
F.005
0.000
0>

0.¢ F¢
0.00¢
0¢¢
5.¢¢¢
¢.00¢
0 00¢
¢. F0¢
F.05¢
0.00¢
05¢
0.0¢0
0.000
F.¢00
F000
F.0 F¢
0 .50¢
¢.0¢¢
F.¢0¢
¢0¢
¢.05¢
5.¢0¢
0.00¢
5.00¢
5.000
0.5¢0
¢.005
F.000
F>

00F
0¢F
00F
00F 8F 0 0><
FOF
00F 00. F 00.0
00F 05.0 50.0
00F 00.0 00.0
50F 00.0 00.0
00 F 00.0 00.0
00F 05.0 55. F
3.0 F 00.0 50.0
00F 0¢. F 00.0
00F and 00.0
FOF om. F 00.0
00F 00.0 00.0
0F F 00.0 00.0
0F F 00.0 0¢.0
5F F 00.0 0¢.0
0 F F and 0 F .0
3 F 00. F 00. F
09 9. F 5¢.0
09 00.0 0¢.0
mm 00.0 0¢.0
om 0F. F 50.0
cm om. F 00.0
05 0¢.0 00.0
00: 0 .05. 5:0 -
525

05.0
00.0
0¢.0
5¢.0
00.0
00.0
00.0
00.0
00.0
05.0
50.0
00.0
00.0
00.0
5 F0
50.0
00.0
00.0
0¢.0
00.0
00.0
00.0

5:0 + AO><V>

0¢.00F
50.000
05.000
0F.000
0¢.000
50.000
50.00¢
00.000
00.000
00.50¢
0¢.¢0¢
00.0 F¢
00.050
00.500
0F.0¢0
00 .00F
50.00F
0F.0 FF
00.0F F
0F. F0
F0.¢5
00.00

0.00F
5.000
0.000
000
F.000
0.¢00
50¢
F.000
0.000
0.00¢
0.¢0¢
F.0F¢
0.050
F.500
0.0¢0
0.00F
F.00F
0F F
0.0F F
00.00
00.05
F5.00
0>

F.¢0F
0.000
0.000
0.000
¢00
F.000
¢.00¢
¢. F00
F000
5.50¢
0.¢0¢
0.0 F¢
F.050
000
F.0¢0
0.50 F
0.00 F
5.¢F F
0.0F F
00. F0
0¢.05
0 F. F0
0>

0.00F
000
F.500
0.500
F000
5.¢00
0.00¢
000
000
0.00¢
0.¢0¢
0.0 F¢
0.050
¢.500
0¢0
F.00F
0.00F
0.0F F
F.0F F
¢ F. F0
¢0.¢5
00.00
F>

00F
0¢F
00F
50F
00F
00F
¢0F
00F
00F
FOF
00F
0FF
0FF
5FF
0FF
0FF
00F
00F
00
00
00

05
00:

.50me

 

 

 

 

.m um.—HU 0000300 0D 5.3 a 00.59 50 80G 0m: 00% 0:0: 0...0 0.< 0.00F

 

118

 

-' uo.’ iii}. 3'...» I 4
. I

1 . .

 

 

 

505050.¢ 0 0><
00.0 50.0
0¢.F 00.0
0F.F 00.0
00.0 00.F
0F.0 00.F
00.0 05.F
00¢ 00.0
00.0 00.0
00.0 00.0
00.F 00.F
0¢.0 5F.0
0F.F 5¢.0
0F.F 00.0
00.F 50.0
00.0 00.0
00.F 00.F
0¢.0 0F.0
00.0 00.0
00.00 00.¢0
00.¢ 55.F
00.0 0¢.0
00.0 00.F

0 _m~0u .0006 n

 

0¢. F
00.0
50.0
0 F0
00.F
50.0
50. F
55.F
50.0
00.0
00.0
00.0
50.0
00.0
0¢.0
00.0
00. F
00.0
0 F.¢F
00.0
00.0
00. F

50.500
05.50¢
0¢.00¢
00. F0¢
00.0¢¢
00.00¢
00.00¢
00 .00¢
0¢.00¢
00.000
50. F00
50.0 F¢
00.00¢
50.50¢
00.¢00
00. F00
00.000
00.0¢0
00.000
50. F¢0
00.¢05
0¢.5¢0

5:0 + A0><v>

F.000
0.50¢
00¢
0.00¢
0. $4.
0.0¢¢
0.50¢
0.00¢
0.00¢
F.¢00
F00
0 .0 F¢
0.00¢
50¢
F.¢00
5. F00
F.¢00
F.0¢0
5.000
F.¢¢0
F. F05
0¢0
0>

0.000
0.00¢
¢.00¢
00¢
0.0¢¢
F.00¢
0.00¢
0.00¢
¢.00¢
F.¢00
0.000
¢.0 F¢
5.¢0¢
0.50¢
000
0.000
0.¢00
0.0¢0
¢.0¢0
¢. F¢0
505
0.0¢0
0>

0.000
0.00¢
0.50¢
0.00¢
0.0¢¢
5.0¢¢
0.50¢
0 .¢0¢
5. F0¢
0.000
0. F00
5.0 F¢
0.00¢
0.00¢
5.¢00
0.000
0. F00
0.0¢0
5.050
F.0¢0
¢.005
5.0¢0
F>

00F
0¢F
00F
00F
0FF
0FF
00F
00F
50F
00F
00F
¢0F
00F
00F
FOF
00F
00
00
00
00
00
05

00:

525

050000. F 0 0><

00.0
00. F
05. F
05.0
00.0
00.0
00.0
00.0
00.0
0¢. F
0¢.0
00. F
00.0
00.0
0¢.0
00.0
00.0
00. F
05.0
00.0
00.0
5.0

0 .050

0 F0
00.0
55.0
0¢.0
5¢.0
5 F0
50.0
00.0
5¢.0
50.0
5 F0
05.0
5¢.0
0 F .0
00.0
00.0
00.0
00.0
0¢.0
00.0
50. F
¢¢.0

00.0
00.0
00.0
00.0
0¢.0
0 F0
05. F
0¢.0
00.0
05.0
00.0
00. F
00.0
00.0
5 F0
50.0
00.0
5¢.0
00.0
50.0
00. F
5¢.0

00.¢0F
00.00F
50.05F
00.50F
5¢.00F
5¢.000
50.500
0¢.00¢
5¢. F5¢
50.000
55.550
0 F000
50.00¢
05.50¢
00.050
00.000
00.000
00.000
00.0 F0
05.00F
50.0F F
00. F0

5:0 - 5:0 + AO><V>

0.¢0F
0. FOF
0.05F
0.00F
0.00F
0.000
0.000
0.00¢
F5¢
5. F00
0.550
0.050
0.50¢
0.50¢
0.050
0.000
0.000
0.000
F.0F0
5.00F
0.¢F F
00. F0
0>

0.¢0F
00F
0.00F
00F
0.00F
0.000
5.500
0.00¢
0. F5¢
F.000
5.550
0.000
0.00¢
0.50¢
0.050
F000
0 .000
0.050
0.0 F0
00F
0.¢F F
00.00
0)

0.¢0F
5.00F
0.05F
0.50F
00F
0.000
F000
0.00¢
0. F5¢
0.000
050
¢.000
¢.00¢
0.50¢
5.050
5.000
F.¢00
F.000
¢.0F0
0.00F
0.0F F
00. F0
F>

00F
0¢F
00F
00F
0FF
0FF
00F
00F
50F
00F
00F
¢0F
00F
00F
FOF
00F
00
00
00
00
00

05
00:

..Omcww

 

 

 

 

h ¢5AHU 00:00.00 00 5.3 0 00309 ..8 S09 0000 00“ 0:0: 00.0 5.< 0300.

 

119

Bibliography

120

10.

11.

BIBLIOGRAPHY

. New York Glaucoma Research Institute. www.glaucoma.net/nvgri/questions.

W.M Hart, Jr. “The epidemiology of primary open-angle glaucoma and ocular
hypertension”, in R. Ritch, M.B. Shields, T. Krupin (eds): The Glaucomas. St.
Louis, CV. Mosby Co., 1989, pp 789-795.

H.A. Quigley. “Pathophysiology of the optic nerve in glaucoma”. In: J .A.
McAllister, R.P. Wilson, eds. Glaucoma. London: Butterworths; 1986:30-53.

J .C. Morrison, C.G. Moore, L.M.H. Deppmeier, B.G. Gold, C.K. Meshul, E.C.
Johnson. “A rat model of chronic pressure-induced optic nerve damage”. Exp. Eye
Res. 1997; 64:85-96.

E. Garcia-Valenzuela, S. Shareef, J. Walsh, S.C. Shanna. “Programmed cell death
of retinal ganglion cells during experimental glaucoma”. Exp Eye Research. 1995;
61: 33-44.

S.W. John, R.S. Smith, O.V. Saviova, N.L. Hawwes, B. Chang, D. Tumbull, M.
Davisson, T.H. Roderick, J .R. Heckenlively. “Essential iris atrophy, pigment
dispersion, and glaucoma in DBA/2J mice.” Invest Ophthalmol Vis Sci. 1998; 39:
951-62.

M.S. Marx, I. Bodis-Wollner, S.M. Podos, C.S. Teitelbaum. “The pattern ERG
and VEP in glaucomatous optic nerve disease in the monkey and human”, in R.Q.
Cracco, I. Bodis—Wollner (eds): Evoked Potentials. New York, Alan R. Liss, Inc.,
1986, pp 117-126.

M.S. Marx, I. Bodis-Wollner, J .S. Lustgarten, S.M Podos. “Electrophysiological
evidence that early glaucoma affects foveal vision.” Doc Ophthalmol 1988(a);
67:28] -301 .

LJ. Frishman, F.F. Shen, L. Du, J .G. Robson, R.S. Harwerth, E.L. Smith 3“, L.
Carter-Dawson, M.L. Crawford. “The scotopic electroretinogram of macaque

after retinal ganglion cell loss from experimental glaucoma.”lnvest Ophthalmol
Vis Sci. 1996; 37:125-41.

R.S. Harwerth, L. Carter-Dawson, F. Shen, E.L. Smith 3”, ML Crawford.
“Ganglion cell losses underlying visual field defects from experimental
glaucoma.” Invest Ophthalmol Vis Sci. 1999; 40: 2242-2250.

A. S. Kobayashi, “Mechanics and Analysis of Tonometry Procedures by Finite

Eleement Modeling of the Comeoscleral Shell,” Biomechanics of Medical
Devices, Marcel Dekker, Inc., New York, New York, 1981.

121

 

 

 

 

 

F11 O.V.ltl fifh It, .fl

.\

 

 

12

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

R. Puers, G. Vandevoorde and D. De Bryker, “Electrodeposited copper inductors
for intraocular pressure telemetry,” J. Micromech. Microeng., 10, pp. 124-129,
2000.

The Bureau of Naval Personnel. “Basic Electricity.” Dover Publications. New
York, New York. 1969.

K. Najafi. Lecture Notes from EECS 498 at The University of Michigan. Fall
Lecture 10, p.21, Fall 2001.

S. S. Mohan, M. del Mar Hershenson, S. P. Boyd, and T. H. Lee, “Simple
Accurate Expressions for Planar Spiral Inductances,” IEEE J. Solid-State Circuits,
vol. 34, no. 10, pp.1419-1424, Oct. 1999.

H. Chan, and K. D. Wise, “Scaling Limits in Batch-Fabricated Silicon Pressure
Sensors,” IEEE Transactions on Electron Devices, vol. ED-34, no. 4, pp. 850-
858, April 1987.

SD. Sentun’a. “Microsystem Design,” Kluwer Academic Publishers. Boston.
2001.

F. Maseeh and S. Senturia, “Plastic Deformation of highly Doped Silicon,”
Sensors and Actuators, A21-A23, pp. 861-865, 1990.

S. T. Cho, K. Najafi and K. D. Wise, “Internal Stress Compensation and Scaling
in Ultrasensitive Silicon Pressure Sensors,” IEEE Trans. Electron Devices, vol.
39, no. 4, pp. 836-842, April 1992.

J .H. Jerman, “The Fabrication and Use of Micromachined, Corrugated Silicon
Diaphragms,” IC Sensors, Custom Product Papers and Briefs, May 2, 1989.

M. Weik. “Communications Standard Dictionary.” 2nd ed. Van Nostrand
Reinhold Co., New York, NY. 1989.

O. Akar, T. Akin and K. Najafi, “A wireless batch sealed absolute capacitive
pressure sensor,” Sensors and Actuators, A 95, pp. 29-38, 2001.

M. Husak, “One-chip integrated resonance circuit with a capacitive pressure
sensor,” J. Micromech. Microeng., 7, pp. 173-178, 1997.

D. Goustouridis et a1, “Ultraminiature capacitive pressure-sensing elements
obtained by silicon fusion boding,” Sensors and Actuators, A 68, pp. 269-274,
1998.

122

 

 

 

 

 

 

 

   

*I'iifltllilflili1.1111"