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This is to certify that the

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Techniques and Applications of SEM Moire and AFM Moire
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6/01 cJCIRCIDaieDuepss-p. 1 5

TECHNIQUES AND APPLICATIONS OF
SEM MOIRE AND AFM MOIRE

By

Hua-Tang Chen

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Material Science and Mechanics

2001

ABSTRACT
TECHNIQUES AND APPLICATIONS OF SEM MOIRE AND AFM MOIRE
By

Hua-Tang Chen

The SEM moire’ method can obtain deformation measurement and microscopic
observation simultaneously. Some drawbacks exist: (1) the requirement of a vacuum
environment (2) the reinforcement effect of grating material, and (3) the multiple steps of
grating fabrication. To reduce these drawbacks several new techniques were developed.
The AFM moire method allows deformation measurement in a normal laboratory
environment. A new grating technique, direct electron beam deposition, was developed.
This technique deposits a carbonaceous grating on a specimen surface. The thickness of
this carbonaceous grating is reduced to 8 nm instead of 100 nm of PMMA grating,
minimizing the reinforcement effect. A total of six SEM moiré methods were produced
by combining three viewing techniques with two grating fabrication techniques. The
sensitivity of the SEM moire’ method is improved from 0.2% to 0.02% or even higher if a
higher frequency of grating is used. The SEM moiré method was applied to the
deformation measurement of carbon ﬁber reinforced composites. Another application is
the local strain measurement of a two-phase polymer under the stress relaxation
experiment. The interface shifting is observed and the local strain is measured by the

SEM moiré method simultaneously. Accordingly, an analytical solution of dynamic

mechanical properties based on the rule of mixtures was derived. The dynamic
mechanical analysis (DMA) was conducted on two-phase polymer specimens with
different volume fractions in parallel and serial loading conﬁgurations. It seems that the
analytical solution does not predict the experimental data of a two-phase polymer in
serial loading conﬁguration. On the other hand, the dynamic mechanical properties of

specimens in parallel loading conﬁguration match very well with the analytical solution.

Copyright by
Hua-Tang Chen
2001

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ACKNOWLEDGMENTS

I wish to express my deepest appreciation to Dr. André Y.-J. Lee for his constant
guidance, encouragement, and patience during the course of my graduate study at
Michigan State University. Heart felt gratitude goes to Dr. Dahsin Liu for his unlimited
stimuli to my professional growth in my ﬁeld through the many academic challenges he
posed to me. Without his recognition of some critical issues in my research, this work
could not have been completed. I would like to express my greatest respect toward Dr.
K. N. Subramanian for his valuable suggestions in many aspects of my research work.
Deeply appreciation to Dr. Stanley Flegler for showing me the beauty of the scanning
electron microscope and the valuable discussion on the topics related to the scanning
electron microscope. Special thanks go to my friends at Michigan State University for
their helpful discussion and inspiration. Appreciation is expressed to Dr. R. D. Bradshaw
and Dr. L.C. Brinson at Northwest University for the use of their curve-ﬁtting computer
program.

Thanks to Michigan Research Excellence Fund, National Institute of Standards
and Technology, Manufacturing Research Consortium, and Semiconductor Research
Center for their ﬁnancial support during my graduate study at Michigan State University.
Deeply grateful goes to the Graduate School for awarding me the Dissertation
Completion Fellowship.

Last but certain not least, I wish to thank my family for their continuous support
and encouragement of pursuing my dream and for having faith in me of completing my

dissertation.

vi

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................. xi
LIST OF FIGURES ........................................................................................................... xii
CHAPTER 1
INTRODUCTION ............................................................................................................... l
1.1 METHODS FOR MICROSCOPIC DEFORMATION MEASUREMENT ............. 1
1.1.1 Grid Method ....................................................................................................... 1
1.1.2 X-ray Methods .................................................................................................... 2
1.1.3 Digital Image Correlation (DIC) Method ........................................................... 3
1.1.4 Microscopic Moire Interferometry ..................................................................... 4
1.1.5 Speckle Interferometry with Electron Microscopy (SIEM) ............................... 5
1.2 STATEMENT OF PROBLEM ................................................................................. 6
1.3 ORGANIZATION OF DISSERTATION ................................................................. 7
CHAPTER 2
MOIRE IN SCANNING ELECTRON MICROSCOPE ..................................................... 8
2.1 INTRODUCTION ..................................................................................................... 8
2.2 GRATING TECHNIQUE ......................................................................................... 9
2.3 MOIRE FRINGES IN SEM .................................................................................... 16
2.4 VERIFICATION ..................................................................................................... 20
2.5 DISCUSSION ......................................................................................................... 22
camera 3
MOIRE IN ATOMIC FORCE MICROSCOPE ............................................................... 41
3.1 INTRODUCTION ................................................................................................... 41
3.2 GRATING TECHNIQUE ....................................................................................... 42
3.3 MOIRE FRINGES IN AFM ................................................................................... 42

vii

3.4 VERIFICATION ..................................................................................................... 43

3.5 DISCUSSION ......................................................................................................... 45

CHAPTER 4 , ,

NEW GRATING TECHNIQUE FOR AFM MOIRE AND SEM MOIRE ...................... 49
4.1 INTRODUCTION ................................................................................................... 49
4.2 GRATING TECHNIQUES ..................................................................................... 50
4.3 CARBONACEOUS GRATING ............................................................................. 54
4.4 MOIRE FRINGES .................................................................................................. 56
4.5 CONCLUSION ....................................................................................................... 56

CHAPTER 5 ,

NEW VIEWING TECHNIQUES FOR SEM MOIRE ..................................................... 61
5.1 INTRODUCTION ................................................................................................... 61
5.2 ELECTION BEAM LIT HOGRAPHY ................................................................... 62
5.3 FORMATION OF MOIRE FRINGES ................................................................... 66
5.4 NEW TECHNIQUES .............................................................................................. 70

5.4.1 Carbonaceous Grating ...................................................................................... 70
5.4.2 Total Imaging ................................................................................................... 71
5.5 SIX SEM MOIRE METHODS ............................................................................... 73
5.5.1 Lithographic Grating and Monitor Viewing (LM) ........................................... 75
5.5.2 Lithographic Grating and Photograph Viewing (LP) ....................................... 75
5.5.3 Lithographic Grating and Total Imaging (LT) ................................................. 75
5.5.4 Carbonaceous Grating and Monitor Viewing (CM) ........................................ 76
5.5.5 Carbonaceous Grating and Photograph Viewing (CP) .................................... 76
5.5.6 Carbonaceous Grating and Total Imaging (CT) ............................................... 77
5.6 COMPARISON OF THE SIX SEM MOIRE METHODS ..................................... 77
5.7 DEMONSTRATIONS ............................................................................................ 78

viii

5.8 CONCLUSIONS ..................................................................................................... 79

CHAPTER 6 ,

APPLICATIONS OF SEM MOIRE ................................................................................. 87
6.1 INTRODUCTION ................................................................................................... 87
6.2 CARBON FIBER REINFORCED COMPOSITES ................................................ 88

6.2.1 Experimental Procedures .................................................................................. 88
6.2.2 Analytical Calculation ...................................................................................... 89
6.2.3 Discussion ........................................................................................................ 89
6.3 INTERFACE SHIFI‘ING OF TWO-PHASE POLYMERS ................................... 93
6.3.1 Experimental Procedures .................................................................................. 93
6.3.2 Analytical Calculation ...................................................................................... 98
6.3.3 Discussion ........................................................................................................ 99
6.4 MISMATCH OF VISCOELASTIC RESPONSE OF TWO-PHASE POLYMERS
....................................................................................................................................... 99
6.4.1 Experimental Procedures .................................................................................. 99
6.4.2 Analytical Calculation .................................................................................... 107
6.4.3 Discussion ...................................................................................................... 108
6.5 CONCLUSIONS ................................................................................................... 127

CHAPTER 7

CONCLUSIONS ............................................................................................................. 129

APPENDIX A

SEM SETTING PARAMETERS FOR ELECTRON BEAM LIT HOGRAPHY ........... 133

APPENDIX B

COMPARISONS OF VARIOUS SEM MOIRE METHODS BASED ON SPECIMEN

GRATING OF 5000 LINES/MM ................................................................................... 134

APPENDIX C

LOCAL STRAIN CALCULATION OF MATERIAL E AND F IN TWO-PHASE

POLYMER SPECIMEN ................................................................................................. 135

ix

APPENDIX D
ANALYTICAL SOLUTIONS OF TWO-PHASE POLYMERS BASED ON RULE OF

MIXTURE ....................................................................................................................... 136

LIST OF TABLES

Table 2.1 Comparison of grating production and fringe formation. ................................. 14
Table 2.2 Trench width and exposure conditions on different substrates ......................... 17

Table 2.3 Results Of rotation angle calculated from the coordinate method and the SEM
moire method ................................................................................................... 24

xi

LIST OF FIGURES

Figure 2.1 Specimen grating preparation procedures ........................................................ 12
Figure 2.2 Two successful lithographic gratings were deposited on (a) Glass/Epoxy
composite (b) Glass beads/Polyimide composite. ........................................... 15
Figure 2.3 Relationship between electron dosage and line width of grating at different
spot size modes ................................................................................................ 18
Figure 2.4 The principle of the formation of moiré fringes under SEM ........................... 19
Figure 2.5 Geometry of moiré fringes ............................................................................... 21
Figure 2.6 SEM moiré fringe patterns with different rotation angles. .............................. 23

Figure 2.7 Comparison between analytical calculations and experimental measurements.
......................................................................................................................... 25

Figure 2.8 The gratings were partially deposited on specimen surface because of the non-
uniform PMMA coating. ................................................................................. 27

Figure 2.9 Contaminated specimen surfaces resulted in low quality of PMMA gratings
and moiré fringe patterns. Carbonaceous gratings were deposited on
specimen surfaces as well. .............................................................................. 28

Figure 2.10(a) and (b) show no grating at the center of either rubber particle or glass ﬁber
because the specimen surfaces were uneven after polishing ........................... 29

Figure 2.11 The effect of thickness on the image quality of substrate. (a) one layer (b)
two layers (c) three layers of PMMA coatings. .............................................. 30

Figure 2.12 The proximity effect with different thicknesses of PMMA coating. (a) 75 nm,
(b) 113 nm, and (c) 150 nm. ............................................................................ 32

Figure 2.13 The width of trenches at various electron dosages. The line dosage is (a)
0.156 nC/cm (b) 0.312 nC/cm (c) 0.468 nC/cm (d) 0.624 nC/cm (e) 0.780
nC/cm (f) 2.338 nC/cm .................................................................................... 33

Figure 2.14 The over exposed edge of a specimen grating. .............................................. 34

Figure 2.15 Two specimen gratings intersected at (a) 15° and (b) 90°. The middle area in
(b) was overdosed ............................................................................................ 35

Figure 2.l6(a) A PMMA grating on Glass/Epoxy substrate with Al coating. (b) A
PMMA grating on Glass/Epoxy substrate with Au coating. ........................... 37

xii

Figure 2.17(a) The specimen grating was distorted due to the thermal damage caused by
the electron beam. (b) A burst-bubble—like specimen grating was observed
due to the localized poor adhesion between the substrate and the grating after
thermal damaged by the electron beam. .......................................................... 38

Figure 3.1Moiré fringe patterns at various specimen rotation angles. .............................. 44

Figure 3.2 Comparisons between experimental and analytical results of moire fringe
angle with respect to specimen rotation angle. ............................................... 46

Figure 3.3 Coexistence of a specimen grating and moiré fringes. .................................... 48

Figure 4.1 Moire fringe pattern in an alumina specimen with grating based on voltage

contrast. ........................................................................................................... 5 1
Figure 4.2 The formation of carbonaceous grating. .......................................................... 53
Figure 4.3 Carbonaceous grating in an epoxy specimen coated with gold. ...................... 53
Figure 4.4 AFM image of carbonaceous grating ............................................................... 55
Figure 4.5 Outline of a cross-section of carbonaceous grating. ........................................ 55
Figure 4.6 SEM moiré fringes. .......................................................................................... 57
Figure 4.7 Comparisons between theoretical calculations and experimental measurements

for SEM moiré fringes ..................................................................................... 58
Figure 4.8 AFM moiré fringes. ......................................................................................... 59

Figure 4.9 Comparisons between theoretical calculations and experimental measurements
for AFM moiré fringes. ................................................................................... 60

Figure 5.1(a) SEM image of lithographic grating (b) Schematic diagram of cross-section
of grating (c) Moiré fringes. ............................................................................ 64

Figure 5.2(a) Moire grating due to overdosage of electrons and corresponding schematic
diagram. (b) - Moiré grating due to underdosage of electrons and
corresponding schematic diagram. .................................................................. 67

Figure 5.3(a) Total imaging of lithographic grating. (b) Total imaging of carbonaceous
grating .............................................................................................................. 74

Figure 5.4(a) Moiré fringe pattern based on LM method. (b) Comparisons between
analytical calculations and experimental measurements ................................. 80

Figure 5.5(a) Moiré fringe pattern based on LP method. (b) Comparisons between
analytical calculations and experimental measurements ................................. 81

xiii

Figure 5.6(a) Moire fringe pattern based on LT method. (b) Comparisons between
analytical calculations and experimental measurements. ................................ 82

Figure 5.7(a) Moire fringe pattern based on CM method. (b) Comparisons between
analytical calculations and experimental measurements ................................. 83

Figure 5.8(a) Moire fringe pattern based on CP method. (b) Comparisons between
analytical calculations and experimental measurements. ................................ 84

Figure 5.9(a) Moiré fringe pattern based on LT method. (b) Comparisons between
analytical calculations and experimental measurements ................................. 85

Figure 6.1 Moiré fringe patterns at various rotation angles on carbon ﬁber reinforced
composite based on CM method. The frequency of reference grating is 2778
lines/mm. ......................................................................................................... 90

Figure 6.2 Moiré fringe patterns at various rotation angles on carbon ﬁber reinforced
composite based on CM method. The frequency of reference grating is 2667
lines/mm. ......................................................................................................... 91

Figure 6.3 Moiré fringe patterns at various rotation angles on carbon ﬁber reinforced
composite based on CT method. The frequency of reference grating is 2774
lines/mm. ......................................................................................................... 92

Figure 6.4 Comparisons between analytical calculations and experimental measurements
based on CM method. Specimen is carbon ﬁber reinforced composite. ........ 94

Figure 6.5 Comparisons between analytical calculations and experimental measurements
based on CT method. Specimen is carbon ﬁber reinforced composite. ......... 95

Figure 6.6 Molecular structure of (a) diglycidyl ether of bisphenol A (DGEBA) and (b)
polyoxypropylenediamine (JEFFAMINE D-230 where n=2.6, IEFFAMINE
D-400 where n=5.6). ....................................................................................... 96

Figure 6.7 Comparisons of strain obtained from the SEM moire’ method, from interface
position, and from analytical calculation. ..................................................... 100

Figure 6.8 Master curves of storage modulus from experimental data. Specimens are in
parallel loading conﬁguration with various volume fractions. ..................... 102

Figure 6.9 Master curves of storage modulus from experimental data. Specimens are in
serial loading configuration with various volume fractions. ......................... 103

Figure 6.10 Master curves Of tanO from experimental data. Specimens are in parallel
loading conﬁguration with various volume fractions. .................................. 104

Figure 6.11 Master curves of tan5 from experimental data. Specimens are in serial
loading conﬁguration with various volume fractions. .................................. 105

xiv

Figure 6.12 Shift factor at the reference temperature of 25°C. ....................................... 106

Figure 6.13 Master curves of storage modulus from analytical calculation based on
parallel loading conﬁguration and various volume fractions. ....................... 109

Figure 6.14 Master curves of storage modulus from analytical calculation based on serial
loading conﬁguration and various volume fractions. .................................... 110

Figure 6.15 Master curves of tan5 from analytical calculation based on parallel loading
conﬁguration and various volume fractions. ................................................. 111

Figure 6.16 Master curves of tan5 from analytical calculation based on serial loading
conﬁguration and various volume fractions. ................................................. 112

Figure 6.17 Comparison of experimental data and analytical calculation in master curve
of storage modulus. Specimen is in parallel loading with volume fraction
(E/F)= 67.4/32.6. ........................................................................................... 113

Figure 6.18 Comparison of experimental data and analytical calculation in master curve

of tanO. Specimen is in parallel loading with volume fraction (E/F)=
67.4/32.6. ....................................................................................................... 114

Figure 6.19 Comparison of experimental data and analytical calculation in master curve
of storage modulus. Specimen is in parallel loading with volume fraction
(FJF)=50/50. .................................................................................................. l 15

Figure 6.20 Comparison of experimental data and analytical calculation in master curve

of tan8. Specimen is in parallel loading with volume fraction (FJF)=50/50.
....................................................................................................................... 1 16

Figure 6.21 Comparison of experimental data and analytical calculation in master curve
of storage modulus. Specimen is in parallel loading with volume fraction
(E/F)=35.6/64.4. ............................................................................................ 117

Figure 6.22 Comparison of experimental data and analytical calculation in master curve

of tanO. Specimen is in parallel loading with volume fraction
(HF)=35.6/64.4. ............................................................................................ 118

Figure 6.23 Comparison of experimental data and analytical calculation in master curve
of storage modulus. Specimen is in series loading with volume fraction
(E/F)=75/25. .................................................................................................. 1 19

Figure 6.24 Comparison of experimental data and analytical calculation in master curve
of tan8. Specimen is in series loading with volume fraction (E/F)=75/25... 120

Figure 6.25 Comparison of experimental data and analytical calculation in master curve
of storage modulus. Specimen is in series loading with volume fraction
(E/F)=67/33. .................................................................................................. 121

XV

Figure 6.26 Comparison of experimental data and analytical calculation in master curve
of tan5. Specimen is in series loading with volume fraction (FJF)=67/33... 122

Figure 6.27 Comparison of experimental data and analytical calculation in master curve
of storage modulus. Specimen is in series loading with volume fraction
(FJF)=50/50. .................................................................................................. 123

Figure 6.28 Comparison of experimental data and analytical calculation in master curve
of tanﬁ. Specimen is in series loading with volume fraction (E/F)=50/50... 124

Figure 6.29 Comparison of experimental data and analytical calculation in master curve
of storage modulus. Specimen is in series loading with volume fraction
(E/F)=33/67. .................................................................................................. 125

Figure 6.30 Comparison of experimental data and analytical calculation in master curve
of tanﬁ. Specimen is in series loading with volume fraction (E/F)=33/67... 126

xvi

Chapter 1
INTRODUCTION

1.1 METHODS FOR MICROSCOPIC DEFORMATION MEASUREMENT

Defamation measurements of a small specimen or a small area of large
specimens are required in the study of microelectronics and composites. Therefore, the
methods for whole ﬁeld microscopic deformation measurement have been under
intensive development (grid methods, x-ray diffraction methods, digital image correlation
method, microscopic moiré interferometry, Speckle interferometry with electron
microscopy). These methods are brieﬂy introduced. Their applications and sensitivity
are discussed as well.
1.1.1 Grid Method

The grid method relies on the measurement of the distance between small dots on
the specimen surface under different loads to determine the deformation of the specimen.
An array of small dots is deposited on the specimen before deformation. Then, a series of
images is taken before and after loading. These images are analyzed by an image
processing system. The horizontal and vertical displacement ﬁeld of the specimen can be
calculated Simultaneously by measuring the spacing between dots in each image and
correlating the spacing measurement from those images.

Sirkis and Lim[1] developed the automated grid method consisting of a charged
coupled device (CCD) video camera and a personal-computer-based image-processing
system to measure the displacement and strain of a perforated uniaxial tension aluminum

specimen. The sensitivity of their measurement to in-plane and out-Of-plane motion is

1.0 and 3.33 microstrain respectively and their accuracy is i 120 nricrostrain. The results
from this method have a reasonable agreement with the geometric moire method.

Tian and coworkers[2] used the electron beam of the scanning electron
microscope to produce a square array of small dots on the rubber-modiﬁed epoxy. The
deformation ahead of the crack tip can be measured using an image processing system to
correlate the spacing between dots in the pictures and the strain magnitude of the
specimen. The strain resolution in their study was 1%. They predicted achieving 0.2%
with standard image analysis techniques. Further improvements for spatial resolution are
able to achieve 0.5 pm with further spatial reﬁnement of small dots.

The grid method does not require special training to interpret the results.
However, it requires a fast image processing system to achieve a real time measurement.
1.1.2 X-ray Methods

X-ray diffraction imaging is used to map deformation in crystals. In deformed
crystals, the combined effect of dilation and tilt allows only a small region of the crystal
to diffract a given wavelength for a particular sample orientation. From the diffraction
images before and after loading, the deformation ﬁeld can be obtained. There are many
x-ray diffraction methods for mapping deformation ﬁelds, such as section topographic
strain mapping and peak shift/broadening measurement[3].

X-ray diffraction imaging has been used to examine GaAs wafer perfection[4], to
investigate the distribution of dilational and tilt components of the plastic deformation
around the large B-NbH precipitates in Nb crystals [5] and to characterize cleavage of Mo
and Nb [6]. Stock and coworkers are using this technique to map the elastic strain fields

around a notch in a silicon crystal that has been deformed by bending[7].

The other x-ray method is x-ray tomographic microscopy (XTM) that can image
the damage area in crystals. It is based on the different absorbability of x-ray in the
materials. The x-ray absorption of materials depends on their elemental composition,
their density, the length of absorbing materials traversed by the beam, and the x-ray
wavelength(s). Therefore, the differences either in density or in phases can be
determined by mapping differences in x-ray transmission[3].

A unidirectional, continuous ﬁber SiC/Al composite and SiC/Si3N4 composites
[7] and bone and dental enamel[8-10] have been studied using XTM.

Both x-ray methods are suitable for mapping with spatial resolution approaching
1 um and a ﬁeld-of-view-millimeters in extent. Sensitivity and resolution of both
methods depend on how parallel the x-ray beams are, and the highest precision is
obtained if synchrotron radiation is used. In single crystal samples, strains as low as 1
microstrain can be measured by these x-ray diffraction methods. Strain in the 0.01% to
1% ranges of polycrystalline samples can be measured using microbeam diffraction.

X-ray diffraction methods for deformation mapping and x-ray tomographic
microscopy for damage mapping are powerful methods for measuring the deformation
ﬁeld and detecting damages inside the materials. However, the collection of data in these
methods is time consuming and the instruments required are expensive. In addition the
x-ray diffraction method will not be able to measure the deformation of amorphous
materials that did not form x-ray diffraction patterns.

1.1.3 Digital Image Correlation (DIC) Method
The measurement of micro-displacement can be made by the digital image

correlation method called DISMAP[11]. This method measures the difference of two

captured digital images of the same ﬁeld under different loading by using an imaging
processing system. DIC has been used to study the crack growth of various materials in
different loading conditions by measuring the crack opening displacement (COD)[12].

This method holds the advantages of the ﬂexibility in designation of the region
and the density of measurement. The spatial resolution of this technique depends on the
magniﬁcation of the photographs and the choice of grid sizes used for measurement.
Measurements cannot be made closer than each 1 mm. Thus, for example, from a 4000x
photograph it might be possible to measure displacement each 0.25 pm. However, for
higher magniﬁcation the alignment of two photographs, such as pre-loading and post
loading, becomes difﬁcult causing errors.
1.1.4 Microscopic Moiré Interferometry

Based on the concept of moire interferometry the immersion interferometer was
developed to Observe the specimen features and to increase the sensitivity of moiré
interferometry simultaneously by Han and Post[13]. The light is introduced into a
refractive material to decrease its wavelength, which increases the frequency of the
virtual reference grating. This reference grating interferes with the specimen grating and
forms moire fringe patterns which contain displacement information of the specimen.
With the aid of microscope, the small features on specimen surface also can be identified
at the same time with the moire fringe patterns.

The microscopic moire interferometry is used to verify the validity of numerical
models for microelectronics packaging design[14]. The thermal deformation for ﬂip-chip

packages is characterized by this method as well[15].

The sensitivity of moiré interferometry is limited by the frequency of virtual
reference grating formed by two coherent laser beams. One way of increasing the
frequency of virtual reference grating is to reduce the wavelength of the laser by
introducing the laser through a refractive medium. For example, the virtual reference
grating is increased from 3890 lines per millimeter to 5910 lines per millimeter by
passing a green argon laser (its wavelength is 514 nm) through an optical glass (BK7
with refractive index 1.52) to reduce its wavelength to 338 nm.

1.1.5 Speckle Interferometry with Electron Microscopy (SIEM)

To increase the sensitivity of speckle interferometry, Chiang[17] first introduced
the concept of SIEM in 1982. The submicron particles can be created onto a specimen
surface by either a vacuum or physical/chemical vapor deposition processes or other
surface techniques. The several images of speckle patterns are taken under SEM before
and afternoon deformation. Then, an optical ﬁlter is used to these SEM images to yield
fringes of low contrast and high random noise. According to these fringes, the
deformation ﬁeld can be extracted by trained personal using digital image processing
technique.

Chiang and co-workers[18] have developed SIEM combining speckle
photography, electron microscopy and digital image processing to measure the localized
deformation. They have applied the SIEM to determine the interphase mechanical
properties of composites[19], to monitor the mechanical behavior of a single ﬁber[20], to
study the near ﬁeld phenomenon at the bimaterial interfacial crack tip[21,22], to
investigate the effect of adhesive thickness on adhesion[23], and to characterize the

deformation at kink band tip in ﬁbrous composite[24].

1.2 STATEMENT OF PROBLEM

A Scanning Electron Microscope (SEM) moiré method for microscopic
measurements based on electron beam lithography and a scanning electron microscope
has been well developed. Although it has been a reliable method, some drawbacks exist:
(1) requirement of a vacuum environment for testing; (2) reinforcement effects induced
by lithographic grating, (3) multiple procedures of lithographic grating and (4) low
sensitivity of deformation measurement.

SEM moire method requires a vacuum environment to measure microscopic
displacement. A test in a normal laboratory environment will be able to simulate the
mechanical response of a material in real application. A friendly testing environment for
high sensitivity measurement needs to be developed. For example, the Scanning Probe
Microscope (SPM) is currently used for high resolution imaging under normal laboratory
environment.

New grating techniques need to be introduced to reduce reinforcement effects
induced by lithographic grating. New techniques should be able to reduce reinforcement
effects signiﬁcantly by changing to low modulus materials or reducing the thickness of
grating layer without compromising the quality of moire fringes.

Simplifying the grating fabrication procedures will be helpful while using SEM
moire. The most common technique to cast a specimen grating is electron beam
lithography which is well documented in the literature. It takes many steps to cast a
grating on specimen.

Currently, the SEM moiré method is based on the Specimen grating cast by

electron beam lithography and the reference grating generated by viewing scanner of an

SEM. The viewing scanner has a lower scanning rate of 500 lines/mm, which yields the
minimum strain of 0.2% for the SEM moiré method. This strain is quite high for many
engineering materials. Therefore, new techniques need to be introduced to increase the

sensitivity of SEM moiré method.

1.3 ORGANIZATION OF DISSERTATION

In this study, several micro-displacement measurement methods have reviewed in
Chapter 1. The SEM moiré method is investigated in Chapter 2. To measure
microdisplacement in normal laboratory environment the atomic force microscope
(AFM) moire method is developed in chapter 3. A new grating technique has been
introduced in chapter 4 to simplify the grating fabrication procedures and reduce the
reinforcement effects. There are several new methods to increase the sensitivity of SEM
moire, which are stated in Chapter 5. Applications of the SEM moire’ method to carbon
ﬁber reinforced composites and on the local displacement measurement of two-phase
polymers are demonstrated in Chapter 6. Chapter 7 concludes the development and

applications of these new grating techniques and SEM moire methods.

Chapter 2
MOIRE IN SCANNING ELECTRON MICROSCOPE

2.1 INTRODUCTION

After its introduction by Well and Shepard in 1948[25], the moire’ method for
displacement and strain analysis had been improved by introducing new technologies in
both grating production and measurement setup. The geometric moiré method had been
studied intensively from 19405 to the 19705. In the 1980s, the most signiﬁcant
development of moiré method was in moiré interferometry where diffraction gratings
were produced by interference of two plane beams from a coherent light source, such as a
laser[26,27]. The major advance for moiré interferometry was the improvement of the
sensitivity due to the increase of the grating frequency from about 50 lines/mm for
geometric moiré to 4,800 lines/mm.

However, further increases in the sensitivity of moiré interferometry were limited
by the wavelength of light. Kishimoto et. al.[28] ﬁrst introduced the SEM moiré method,
which was able to achieve higher sensitivity, to demonstrate its application on the study
of microdeformation in 1991. In their studies, the moiré fringe patterns were produced
by the interference between the grating on a specimen and the scanning lines of a
conventional scanning electron microscope (SEM). Hence, the SEM moire method
shared the same fundamentals of fringe formation with the geometric moiré. The
principle of the moiré fringe formation was similar to the fringes of video-scanning moire
introduced by Morimoto et. al.[29] in 1984.

In 1993, Dally and Read[30] achieved a high frequency of 10,000 lines/mm by

using high-resolution e-beam lithography. They demonstrated the method for making

high frequency gratings[30] and the application of electron-beam moiré method in
micromechanics[3l,32]. Moreover, they presented a mathematical model to explain the
formation of moiré fringe patterns observed at different magniﬁcations[33]. The
formulae for analyzing moiré fringe patterns are also available in their study.

T 0 make the SEM moiré method more accessible, an alternative technique to
fabricate specimen gratings was developed by using a conventional SEM without having
an electron beam lithography facility. Therefore, the SEM parameters (beam current,
exposure time, and beam size etc.) were optimized to fabricate specimen gratings. These
specimen gratings were able to form moire fringes in conventional SEM to achieve a real
time deformation measurement and a microscopic observation on a specimen surface
simultaneously. The discussion included the quality of specimen grating, which affects
the quality of the moiré fringe pattern, as well as several restrictions of the SEM moiré

method.

2.2 GRATING TECHNIQUE

There are several ways to deposit a high frequency Of gratings on specimen
surfaces, for example, photolithography, e-beam lithography, and x-ray lithography etc.
Usually, a thin ﬁlm of polymethylmethacrylate (PMMA) was deposited on the specimen
by spin coating. This PMMA thin ﬁlm reduced its molecular weight due to the scission
of its main chain by the absorption of energy from photons, electrons, or x-rays. The
exposed PMMA thin film, which contained a lower molecular weight of PMMA, was
dissolved in a suitable solvent while the unexposed one remained intact and a grating was

deposited on the specimen.

In this study, the e-beam lithography was used to deposit a high frequency of
grating on the target specimen because both photolithography and x-ray lithography
required a grating mask, which was fabricated by e-beam lithography. In e-beam
lithography, the electron energy absorbed by the PMMA thin ﬁlm was from incident
electrons, secondary electrons and backseattered electrons, which were generated by the
ﬁlament, substrate, and conductive layer such as aluminum or gold. The etching rate was
controlled by electron energy and etching boundaries were determined by contours of
electron energy deposition, which resulted in the different grade of degradation.

Everheart et. al.[34] had demonstrated the electron interaction volume in PMMA
for acceleration voltage of 20 keV. The etched structures allow direct visualization of
electron penetration and the interaction volume in a low atomic number matrix. The
increase of electron energy or etching time increased the width of etched lines, especially
for the undercut, which was detrimental to achieving a high frequency of gratings.
Hence, to control the desired depth and width of etched lines, these parameters needed to
be optimized for each particular substrate: electron energy, electron dosage, the
developing time in the solvent, and concentration of the solvent.

To optimize these parameters for grating fabrication, a brass disk, aluminum alloy
A5083 strips, rubber-toughened epoxy, and glass/epoxy composites were used as
substrates and a PMMA solution (0.4999g of PMMA and 25 ml of toluene) was prepared
for spin coating. The PMMA photoresist has a relative molecular weight of 950,000.
The rubber-toughened epoxy was a liquid diglycidyl ether of bisphenol A (DGEBA)-
based epoxy resin (DER332, Dow Chemical, USA) cured with a diamine-terminated

poly(propylene oxide), JEFFANﬂNE D230 (Huntsman, USA). The rubber particles used

10

for toughening were carboxyl-terminated random copolymer of butadiene and
acrylonitrile, Hycar CTBN 1300x8 and 1300x13 (Shell Chemical). The composite
material was [0°/90°]s laminated glass/epoxy composite. Figure 2.1 shows the steps of
fabricating gratings schematically. The surfaces of specimens were ground smooth and
flat using a series of water-lubricated abrasive-coated paper and the ﬁnal polish was
ended with 0.05 pm alumina particles. After specimens were polished, the surfaces of
specimens were cleaned with distilled water in an ultrasonic cleaner for 30 minutes and
then were blown dry with clean air.

The specimens were then kept in the desiccator before the PMMA thin film was
spun on the specimens at a Speed of 3000 rpm for 30 seconds. The electrically non-
conductive specimens were coated with a thin layer of Al or Au prior to spin coating.
Then the metal and polymer specimens were placed in the vacuum oven for 60 minutes at
160°C and 100°C respectively to remove residual solvent. This application was not
performed in a class-100 clean room, which was usually used by the others [30].

Right after the PMMA thin ﬁlm was coated on the specimen, a single photo scan
rate (1250 lines/frame) in CamScan 44FE SEM was used to fabricate gratings on the
specimens. SEM was set up with an acceleration voltage of 20 keV, an aperture of
50 run, a spot size of either 9 or 11, and a working distance of 20 mm. The grating
fabrication was performed at different magniﬁcations in order to have a desired
frequency of gratings on the specimen. The following equation was used to calculate the
needed magniﬁcation to fabricate the desired frequency of gratings.

number of scannin lines r frame
fg = . g. I” M. (2.1)
hrght of scanning area

 

11

Steps in Producing the Specimen Grating

 

Specimen _" i J 1.Polish

 

 

Goldlayer _. -- ~ -.

 

 

2. Gold coating

 

PMhiiIiIn —"' >:>.\.::::::>.\>.\\:>\.:\:;\> 3_ Spin on PMMA

thin ﬁlm
Electron @

beam ——>
8 mm... 4. Expose to electrons

Suitable G

solvent —” . ., 5.Develop gratings

@

Goldlayer ——+

 

 

 

 

 

 

 

 

6. Gold coating

 

 

 

 

Figure 2.1 Specimen grating preparation procedures.

12

where M was magniﬁcation factor and ﬁg was desired frequency of specimen grating. The
single photo scanning mode in CamScan was 1250 lines per frame with a scanning area
Of 120 mm x 90 mm at 1:1. Table 2.1 listed the grating areas with their frequency and
magniﬁcation factor of scanning. The condenser lenses, astigmatism, centering of the
aperture and focus were carefully adjusted and tuned in order to obtain the size of the
electron beam as small as possible at the position nearby the desired grating area. Then
the desired exposure area was positioned under the electron beam, which was blocking by
a beam stopper. Four different exposure times were applied to PMMA thin film: 21,42,
85, 171 seconds.

After the exposure, the specimens were developed in a solution consisting of three
parts (by volume) of isopropyl alcohol and one part of methyl isobutyl ketone for
40 seconds. The specimen was immediately rinsed in isopropyl alcohol for 20 seconds
followed by a second rinse in distilled water for 30 seconds. Next, the specimen was
blown dry with clean air. A thin gold layer was coated on top and side of the specimens
later to prevent charging problems as well as damaging of the gratings while viewing the
specimens in SEM.

Figure 2.2 shows some SEM images of successful gratings that were deposited on
the specimens. The linewidth of grating was controlled mainly by beam current and
exposure time, assuming the same acceleration voltage and the smallest probe size. The
following equation was usually used to calculate the necessary electron dosage to

fabricate the desired grating linewidth.

' *
D. = ’8 7w (2.2)

where DL was electron line dosage (nC/cm), is was beam current (nA), t was total

13

Table 2.1 Comparison of grating production and fringe formation.

 

 

 

 

 

 

 

 

 

Grating Production Moire Fringe Formation
(photograph scanner) (monitor viewin )
Frequency Scanning Magniﬁ- Grating Magniﬁ- Viewing Imaging
(lines/mm) Rate cation Area cation Rate Area
(lines/frame) Factor. (Irmz) Factor. (lines/frame) (Jlmz)
2500 1250 180x 666x500 450x 500 268x200
3750 1250 270x 444x333 675x 500 178x133
5000 1250 360x 333x250 900x 500 133x 100
6250 1250 630x 191x143 1575x 500 76x57
10,000 1250 720x 168x125 1800x 500 68x50
20,000 1250 1440x 83x63 3600x 500 33x25

 

 

 

 

 

 

 

14

 

 

(b)

Figure 2.2 Two successful lithographic gratings were deposited on (a) Glass/Epoxy
composite (b) Glass beads/Polyimide composite.

exposure time (seconds) and 'cc' was total distance of scanning line. Table 2.2 lists the
etched width of grating lines associated with their exposure conditions on different
substrates. The plot relating electron dosage and etched width of grating line is given in

Figure 2.3.

2.3 MOIRE FRINGES IN SEM

Figure 2.4 Shows the principle of the formation of moire fringe in an SEM. Three
types of moiré fringes (natural, multiplied, and divided moiré fringes) were observed in
an SEM. Read and Dally[33] used Fourier series to describe the SEM raster scan lines,
the specimen gratings, and the moiré fringes. Their results explained the observation of
these three types of moiré fringes in SEM.

The specimen containing gratings was examined in an SEM. The gratings were
easily identiﬁed at high magniﬁcation, and their pitches were measured from the width of
the trenches and ridges. The moiré fringes were observed in an SEM when there was a
frequency mismatch and/or rotation between the scan raster and the specimen grating.
Using the following equation, the magniﬁcation factor, M, for observing natural moire’
fringes was calculated and the results are listed in Table 2.1.

f * hight of scanning area at l : 1
= g (2.3)

 

scanning lines per frame
where the TV scanning rate for imaging mode is 500 lines per frame in CamScan and the
height of scanning area at 1:1 is 90 mm. There are always carrier fringes in SEM moire’
because the discrete magniﬁcation of an SEM dose not exactly match the frequency of

specimen grating with that of the scan raster.

l6

 

Table 2.2 Trench width and exposure conditions on different substrates

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Acceleration Conductive Mag. Exposure Beam Line Trench
Substrate Voltage (keV) Coating Factor Time Current Dosage Width
(seconds) (nA) (nC/cm) (nm)

180 42 90
Brass 25 None 180 21 NA NA 60
180 85 203
180 21 150
90 21 85
Aluminum 25 None 90 42 NA NA 161
180 21 150
180 85 54
360 21 1.4 0.706 70
Epoxy 20 A1 180 85 1.4 1.428 126
200 85 1.4 1.587 139
360 21 1.3 0.655 54

Single carbon
ﬁber lEpoxy 20 A1 180 85 1.0 1.020 51
Single glass 360 21 1.0 0.504 39
ﬁber/Epoxy 180 85 0.8 0.816 53
20 A1 180 85 1.0 1.020 96
540 21 1.0 0.756 47
Au 450 21 1.0 0.630 45
Glass beads 180 85 0.8 0.816 113
/Polyamide 20 A1 360 21 0.8 0.403 70
200 85 0.8 0.907 89
Rubber 720 2 0.6 0.144 29
Particles 720 4 0.6 0.288 53
lEpoxy 720 6 0.6 0.432 70
720 8 0.6 0.576 100
20 A1 720 6 0.6 0.432 89
720 10 0.6 0.720 146
720 12 0.6 0.864 125
720 14 0.6 1.008 130
720 16 0.6 1.152 111
720 18 0.6 1.296 150
Glass/Epoxy 210 85 1.7 1.964 166
360 21 1.7 0.832 71
20 A1 250 85 1.7 2.338 176
270 85 1.7 2.525 123
180 85 1.7 1.683 150

 

 

 

 

 

 

 

 

 

17

 

 

2.5-
'0
2‘ e
E
4 O O
a ,5“ -. ., .
ﬂ ' I .
Ea . 0 one . o o
o
8 ‘ ° 0
O
I: II . .. . ﬂ... :0
E I Q” ‘. e e . .
A J .. . . o .0 .
0.5- O
‘ 0" ' OS IS 9
4 . . po rze
« . OSpotSizell
0 ﬂiI I I I I I I I I I I I I I I I I I I I I I I I
0 50 100 150 200 250

Line Width (nm)

Figure 2.3 Relationship between electron dosage and line width of grating at different
spot size modes.

18

Aligned PMMA gratings with ﬁxed scanning electron beam

rE7

specimen e-beam

 

 

 

. intensity Of secondary
PMMA grating electrons

Uniformly deformed specimen with ﬁxed scanning electron beam

—->
<— —>
<— —>
—>
——>
4— —>
—>
specimen e-beam T
intensity of secondary

PMMA grating electrons

l

H

 

1

Figure 2.4 The principle of the formation of moiré fringes under SEM

l9

2.4 VERIFICATION

The analysis of the moire’ fringe patterns from geometric moiré had been well
established. These techniques were also applicable to the moire fringe patterns observed
from SEM moire. According to the geometry of moire fringes shown in Figure 2.5, the
rotation angle and model grating pitch of a specimen were calculated by the following
equations[35]:

sin ¢

tan 6 = , and (2-4)

—+cos¢

p'= 6 , (2.5)

‘/l + {if + 2{§]cos¢
P P
where p is the master pitch or raster pitch in the SEM and p' is the specimen grating
pitch, or model pitch. The angle 9 is deﬁned as the acute angle at any point and in any
given state of deformation measured from the ﬁxed master grating lines to the model
grating lines. The fringe angle from the ﬁxed master grating lines to a fringe at a point
measured in the same direction as 0 is designated as d) and may be either acute or obtuse.
6 is the normal fringe spacing.
The strain at any point is represented by[35]
u=N*p,and (2.6)

,. Azmzpﬂ

9 2.
‘ 8x 8x Bx ( 7)

where u is the displacement in x direction, N is the fringe number, p is the raster pitch in
the SEM, and Ex is the strain in x direction. Cloud[36] shows a conceptual procedure of

moire strain analysis.

20

A . n 3
° Moder 0““ ‘°

 

S ' ccimc“ 9
6 9

IP

Reference (Master) Grating

 

 

Figure 2.5 Geometry of moire fringes

21

To demonstrate the feasibility of SEM moire to measure deformation, an
aluminum strip with a grating of 2558 lines/mm was rotated by small angles with respect
to the scanning direction. The moiré fringe patterns associated with different rotation
angles of the specimen were recorded and are shown in Figure 2.6. The coordinates of
the center of the imaging area after each rotation were recorded as well.

The frequency of moire fringes and their angles with respect to the scan direction
were measured from moire’ fringe patterns. By Equation 2.4 the angles between the scan
direction and the specimen grating were obtained. On the other hand, based on the
coordinates of the center of the image area, the rotation angles were obtained by the
following formula.

51’ o I;

ill—Ibi- (2.8)

where a and b were two vectors from the origin to two different coordinates. Table 2.3

c086:

listed the calculated results from the coordinate method and the SEM moire method. The
comparisons of these two methods are shown in Figure 2.7. Rotation angles from the

coordinate method and the SEM moire method Show 0. 14° difference in average.

2.5 DISCUSSION
A. Grating Materials

In this study, a nonconductive photoresist, PMMA, was used for grating
fabrication. However, some conductive metal could be another choice as grating
material. Attwood and Hazzledine[37] deposited a gold grid pattern consisting of gold

lines 0.3 um wide spaced at 10 um intervals. The advantage of using metal as a grating

22

\

\x\

. N

,. 288‘
‘-1\~‘\

. I .
g .s‘
N

a 8‘6: .4
'\ ,5 ‘._"
HERA}

 

Figure 2.6 SEM moiré fringe patterns with different rotation angles.

23

Table 2.3 Results of rotation angle calculated from the coordinate method and the SEM
moire method.

 

Rotation Coordinate R x y Master Fringe Fringe SEM
Angle Method (mm) (mm) (mm) Pitch Angle Pitch Moire

(stage) (Degree) (nm) (Degree) (nm) (Degree)

 

11.0 6.95 9.1706 6.1866 6.7695 183.67 119.5 1428.57 6.81

 

10.0 6.15 9.1713 6.2815 6.6825 183.67 122.0 1578.96 6.00

 

 

 

 

 

 

7.5 3.96 9.1739 6.5332 6.4403 183.67 134.0 2142.84 3.75
5.0 1.48 9.1651 6.7996 6.1453 183.67 161.5 3055.58 1.16
5.0 1.78 9.1666 6.7680 6.1823 183.67 155.0 3157.86 1.49
3.0 0.50 9.1654 6.9042 6.0280 183.67 173.5 3618.99 0.35
2.5 0.00 9.1651 6956159676 183.67 179.5 3666.63 0.03
1.0 1.13 9.1672 7.0736 5.8311 183.67 161.5 3365.08 1.05

 

0.0 3.04 9.1675 7.26495.5915 183.67 137.5 2555.58 2.94

 

-2.5 4.87 9.1738 7.4450 5.3601 183.67 125.0 1904.76 4.78

 

 

 

 

 

 

 

 

 

 

 

-5.0 6.99 9.1820 7.6450 5.0856 183.67 117.0 1418.44 6.99

 

24

 

A
90 I 2?
80 + 3
" .2
70 i’ an
0 -.
60 -— cc 0-
'0 ‘L a 0'
0 50 .. E O.
40 ‘7 a.“
e
30 ‘—
~ 0-
120 4* o. .
10 ~~ 0 experimental
;0 ' analytical

 

-8 -6 -4 -2 0 2 4 6 8
0, specimen rotation angle

Figure 2.7 Comparison between analytical calculations and experimental measurements.

25

material is that the testing temperature will not be limited by the melting temperature of
PMMA, especially for therrnomechanical test.
B. Quality of Specimen Grating

The quality of fabricated specimen grating depends on (1) the roughness and
cleanness of specimen surface, (2) the thickness of PMMA thin film and the width of its
molecular weight distribution, (3) the exposure and energy of electrons, and (4) the
conductive coatings such as Au or Al. These variations affect grating deposition, the
width of the trench, and the aspect ratio of specimen grating.
a. Contaminated surface

Surfaces of the Specimens were prepared by polishing with 0.05 um of alumina
paste. They were then cleaned with the use of ultrasonic cleaner with a distilled water
bath. The cleaned specimens were stored in a desiccator before use. If these steps were
not exercised carefully, there might be scratches, dusts, or grease on the specimen
surface, which affected the quality of specimen gratings as shown in Figure 2.8 and
Figure 2.9. In addition, while containing different hardness of components, the specimen
usually had an uneven surface after being polished. Thisiuneven surface could cause a
non-uniform coating of PMMA thin ﬁlm, resulting in an useless specimen grating for
future application as shown in Figures 210(8) and (b).
b. PMMA thin ﬁlm

The thickness of PMMA layer could affect the aspect ratio of gratings, then the
quality of moire fringes: the higher the aspect ratio of gratings, the higher contrast of
moire fringes, but the lower image quality of substrate. Figures 2.11(a)-(c) Show the

effect of thickness on the image quality of substrate. However, as thickness increased,

26

 

Figure 2.8 The gratings were partially deposited on specimen surface because of the
non-uniform PMMA coating.

27

 

__u.
Figure 2.9 Contaminated specimen surfaces resulted in low quality of PMMA gratings
and moiré fringe patterns. Carbonaceous gratings were deposited on
specimen surfaces as well.

28

 

(b)

Figure 2.10 (a) and (b) show no grating at the center of either rubber particle or glass
ﬁber because the specimen surfaces were uneven after polishing.

29

‘_ Slum

 

Figure 2.11 The effect of thickness on the image quality of substrate. (a) one layer (b)
two layers (c) three layers of PMMA coatings.

30

the proximity effect became more prominent, as shown in Figure 2.12. Therefore, an
optimal thickness needed to be determined.
c. Beam current and exposure time

Beam current and exposure time were key parameters in grating fabrication.
Especially, these parameters affected the width of the trench, which eventually affected
the frequency of the specimen grating. Equation 2.2 was used to calculate the electron
dosage that was absorbed by the specimen. Some gratings were overdosed and
underdosed as shown in Figure 2.13(a) and (b), respectively. During the electron beam
scanning procedure, the scan raster in CamScan usually stayed at the edge of scanning
area longer, which caused over exposure as shown in Figure 2.14.

To fabricate a crossed specimen grating, two perpendicular directions were
scanned at the same area by rotating the scan raster 90°. The stigrnatism and focusing
then were readjusted after rotating the scan raster to assure that the electron beam was as
small as possible. Figures 2.15(a) and (b) exhibit two gratings at 15° and 90°,
respectively. The latter does not have any grating in the cross-section area because the
PMMA layer was overdosed.

d. Conductive coating

Prior to PMMA coating, a conductive layer consisting of Au or Al was coated
onto the specimen. A] coating was better than Au coating because the Al coating yielded
fewer backscattered and secondary electrons due to its lower atomic number. The lower
the interaction volume resulting from these electrons, the fewer proximity effects on
fabricating the grating. Two Glass/Epoxy composite specimens were coated with Al and

Au respectively prior to PMMA coating. Both specimens were then subjected to the

31

. 300nm V

300 nm;

 

-; 300 nm ,
(C)

Figure 2.12 The proximity effect with different thicknesses of PMMA coating. (a) 75 nm,
(b) 113 nm, and (c) 150 nm.

32

- 1MM’MYW'W'~~1-., .. . . ., .. -

-. I§"‘"‘1~J,"~v—~ .

.xxy....-.-q.u.»,~..‘.-.

AMT Nave“ r_.,

 

Figure 2.13 The width of trenches at various electron dosages. The line dosage is (a)
0.156 nC/cm (b) 0.312 nC/cm (c) 0.468 nC/cm (d) 0.624 nC/cm (c) 0.780
nC/cm (f) 2.338 nC/cm.

33

 

lum

Figure 2.14 The over exposed edge of a specimen grating.

34

 

(b)

Figure 2.15 Two specimen gratings intersected at (a) 15° and (b) 90°. The middle area in
(b) was overdosed.

35

same exposure conditions. The Al coated specimen had a more distinguished grating
than the Au coated specimen did as shown in Figures 2.16(a) and (b).
a. Thermal damage

Due to the nonconductive nature of PMMA thin film, the specimen grating
experienced thermal damage during SEM observation because the incident electrons were
accumulated at the PMMA layer, even with a conductive layer of gold on its surface.
Figures 2.17(a) and (b) showed severe thermal damage to gratings such as distortion and
burst bubble respectively.
A. Sensitivity

The sensitivity of displacement measurement of the moire’ method is determined
by the number of moiré fringes per unit displacement. To Obtain one additional moire
fringe from the SEM moire method, the deformed strain needs to be at least 0.2%
(1/500). For example,

in a null field, fs = f, = 590%;

M

one additional moire fringe observed on TV monitor,

i1 . ' i1
FZ'éjzfr—fvfs :fr—E—Ei

M M

strain needed,

 

 

L
O i ' .9_().
8:_p_L:_&_:&—1:-L‘SZ-—l:fs—'fsz M+ : 1_ 20.2%,
ps P. f, f3 302_—_1 500+1
a .92
M M

36

 

(b)

Figure 2.16 (a) A PMMA grating on Glass/Epoxy substrate with Al coating. (b) A
PMMA grating on Glass/Epoxy substrate with Au coating.

37

Sum

 

l()irm

(b)

Figure 2.17(a) The specimen grating was distorted due to the thermal damage caused by
the electron beam. (b) A burst-bubble-like specimen grating was observed
due to the localized poor adhesion between the substrate and the grating after
thermal damaged by the electron beam.

38

where 1%: frequency of initial specimen grating
1“,: frequency of deformed specimen grating
f,: frequency of reference grating
F: frequency of moire’ fringe
M: magnification factor
8: strain

p3: pitch of initial specimen grating

p's: pitch of deformed specimen grating.
D. Image Quality

A higher aspect ratio of grating as well as a sharp corner of edge will result in a
higher contrast of fringe patterns because the intensity of secondary electrons between the
trench and edge will higher. Furthermore, the backscattered electrons are also another
way of imaging fringe patterns as long as the grating exhibits a periodic difference in
atomic number such as diblock copolymer.

E. Restrictions

a. Specimen has to be in the vacuum environment.

b. The PMMA thin ﬁlm coating is reinforcing the testing specimen to some extent since
the Specimens that need be studied are getting smaller.

c. It is important to have stable electronics in SEM, such as for stable magniﬁcation and
scanning raster, since they control the frequency of reference grating.

d. The grating area produced from regular SEM such as CamScan is limited by the
manufacturer's pre-set parameters; for instance, scanning area (120 mm by 90 mm at
1x), scanning lines per frame (1250 lines/frame), and exposure time (21, 42, 85, 171
seconds). Due to these pre-set parameters, it is difﬁcult to control the precise electron
dosage to fabricate high frequency of specimen gratings.

e. To form moiré fringes, the reference grating, which is produced by raster scanning,

has to match the frequency of specimen gratings. The magniﬁcation for moiré fringe

39

formation can be calculated using Equation 2.3. The TV scanning rate for imaging
mode is 500 lines/frame in CamScan and the height of scanning area at 1:1 is 90 mm.
Therefore, the applied strain to observe one extra fringe is 0.2%. Increasing scanning
lines/frame in the TV scanning mode will result in a larger imaging area and higher

sensitivity but will reduce the details of imaging area.

40

Chapter 3
MOIRE IN ATOMIC FORCE MICROSCOPE

3.1 INTRODUCTION

Purely based on interference, geometric moiré was once commonly used in
engineering measurements. With the use of lasers, optical diffraction was integrated with
optical interference to form a more refined moire’ technique, namely moiré
interferometry. The technique of moire interferometry has been well documented by
Post, Han and Ifju [16] and widely demonstrated by them and many other researchers. It
is well recognized that moire’ interferometry is a very powerful and accurate technique for
strain measurements in engineering applications.

By integrating a moiré interferometer with an optical microscope, Han [38]
extended moire’ interferometry to microscopic strain measurements. With the
introduction of a transparent moiré grating, Liu and Shakour [39] further demonstrated
the feasibility of simultaneous viewing and measuring rrricroscopic deformation of
composite materials by a microscopic moiré interferometry. The capability of combining
observation and measurement together accelerated the study of micromechanics. In fact,
this capability had also been demonstrated in electron beam moire by Dally and Read
[30].

The electron beam moire’ [40] is a geometric moiré technique in the microscopic
sense. It utilizes both electron beam lithography to generate moire’ grating on specimen
surface, i.e. specimen grating, and the scan raster of SEM (Scanning Electron
MicrOSCOpe) as reference grating. As a result of interference between the specimen

grating and reference grating, moiré fringes are formed. Hence, both microscopic

41

observations based on SEM and microscopic measurements based on electron beam
moire’ could be obtained simultaneously. The electron beam moiré has proved useful for
many applications which require microscopic measurements.

As an advanced step for microscopic and even nanoscopic observations, scanning
probe microscopes are commonly used for atomic-level investigations. The current study
uses an atomic force microscope (AFM) for microscopic measurements, besides the
conventional use for microscopic observations. The primary goal is to demonstrate the
feasibility of forming moiré fringes in AFM. Further developments similar to that in

electron beam moire are anticipated.

3.2 GRATING TECHNIQUE

A epoxy specimen material was coated with a 14 nm thick of Al and spin-coated
with a layer of polymethylmethacrylate, PMMA, about 110 nm thick. E-beam
lithography was used for fabricating specimen grating. A thin ﬁlm of PMMA was
scanned by an SEM for generating a moiré grating [41] of 3,103 lines per millimeter,
which is a specimen grating. Then the specimen with the PMMA thin ﬁlm was developed
in an organic solvent and coated with gold to protect the PMMA grating even though

such as coating is not required for studies in AFM.

3.3 MOIRE FRINGES IN AFM
The atomic Force Microscope is essentially used for measuring surface
topography with sensitivity in nanometer or even sub-nanometer levels. It is essentially

based on atomic force, i.e. the Coulombic force between the electron shells of two

42

approaching atoms. As a common practice, constant force is used in an AFM system. A
probe with a nano—scale tip attached to a cantilevered beam is then used to detect a target.
If the target is too far or too close from a designated distance, the probe will be bent
convex or concave to keep the right distance and maintain the constant atomic force. A
laser beam is usually used to detect the deﬂection of the cantilevered beam. The
information is then fed to a piezoelectric actuator located beneath the specimen to move it
up and down to level the probe.

In order to collect the topography Of a domain, the probe is kept stationary;
whereas the specimen is moved from one side to the other followed by a constant
advancement. As a consequence, the scanning lines can be used as reference grating.
Once they are superposed on the moiré grating on the specimen surface, a moiré fringe
pattern will be formed and called AFM moire’.

An area of 38.4 um by 38.4um was chosen for investigation. In order to match
the frequency of the specimen grating, a scanning frequency of 128 lines was selected
with a scanning rate of 1 Hz. Hence, the reference grating has a frequency of 3,333 lines

per millimeter. Moire fringes were clearly recorded, accordingly.

3.4 VERIFICATION

In order to verify that the obtained fringes were really due to the interference
between the specimen grating and the reference grating (for instance from the geometric
moiré), the specimen was rotated with small angles with respect to the scanning lines.
Figure 3.1 shows the fringe pattern changes with the rotation angle. As the angle

increases, the frequency of the moiré fringe increases. The result from a careful

43

 

Figure 3.1 Moiré fringe patterns at various specimen rotation angles.

measurement is presented in Figure 3.2 along with the prediction from the analytical
equation [35] given below:

sin 0
Br.
Pr

tan 9 = (2.4)

cos¢ +

where 9 and (I) are specimen rotation angle and moiré fringe angle with respect to the
scanning lines, respectively, and pf , p,, and p, are pitches of moiré fringe, reference
grating, and specimen grating, respectively. The agreement between the experiment and
analysis suggests that the fringes shown in AFM do follow the predictions based on

geometric moiré.

3.5 DISCUSSION

3. The specimen grating in this study was produced by electron beam lithography. It is
also possible to use AFM to a generate specimen grating though the technique needs
to be developed.

b. Only the rotation between the two grating systems was performed to demonstrate the
feasibility of forming AFM moire’. Presumably a testing ﬁxture could also be built to
perform moiré studies based on mechanical loading.

c. The moiré fringe pattern at the initial stage (undeformed condition) is not necessary
to be of a null ﬁeld, due not only to the mismatch of frequency between the reference
grating and the Specimen grating but also to the misalignment between them. The
initial fringe pattern can always be subtracted from that of deformed one in

deformation analysis.

45

 
   

— analytical

 

’53
Q) .
"e O expenmental
V
0
—
i” \
/ 150 -— cu
ea
.. __ .5
h
140 —~ “'1,
q_ 9
F 1 I l I 1 I L IL I l l J l I I I I l l 1 l l I J

 

0, specimen rotation angle (deg)

Figure 3.2 Comparisons between experimental and analytical results of moire fringe
angle with respect to specimen rotation angle.

46

d. AFM moiré is more convenient and economical than the electron beam moire since
the latter requires a vacuum environment for investigation and a conductive layer not
only for preventing thermal damage to non-conductive specimens but also for
avoiding possible contamination to the electron gun.

e. Electron beam moiré is able to provide both microscopic measurements and
observations simultaneously. As a surface topography technique, the AFM moiré
cannot provide microscopic measurements simultaneously with microscopic
observations since the target specimen is coated with moiré grating, as shown in

Figure 3.3.

47

< I an” A‘nnn'wu'u Irina-lawn”. . . a...
. .wrmrm- M‘”u~~c
. . -c... “.3
WW... .
— r 1...-»‘5

. .. . . ,, .. '
'mamm». . ¢v n. “‘1”: In“... t...

‘..‘..~...~.u-‘~cws . , ~ . .
r. ukmwwu‘vwmn-vu 3
. .. .Ax...
4....
. u. an. I.-..4—1-m~..wuu am I...“ «ova... . .. .
r . .. . A ~‘1‘-54ulmgu>u
I)
'61! =V~ >u.r.M~w¢tmu—u~ w.

a . .. A .
. ‘raVv-‘a "Ayn-m...-r.....-.~»_»u.mv.r.. ..
my. .. ~. ' -
x. . . .... 4...

Mg... ,. .
.m Huang.“ -n- .
,‘V ~ ..

4 ~»~f’v~u‘bw~c~i-.§lﬂu “w...“

 

Figure 3.3 Coexistence of a specimen grating and moiré fringes.

48

Chapter 4

NEW GRATING TECHNIQUE 11;? AFM MOIRE AND SEM
MOI

4.1 INTRODUCTION

A moire technique based on an atomic force microscope (AFM), namely AFM
moire’, has been introduced in a previous study [42]. The technique utilizes electron
beam lithography to cast a moiré grating on a specimen surface, i.e. specimen grating,
and utilizes the viewing scanner of the AFM to provide a reference grating. As a result of
interference between these two gratings, moire fringes are formed and can be viewed
instantaneously on the monitor. A demonstration has been presented in the previous
study along with a careful veriﬁcation showing a good agreement between experimental
investigation and theoretical calculation. It has been concluded that AFM moire is
feasible for measurements of microscopic or even nanoscopic deformations. Since an
AFM does not require a vacuum environment, as needed in an SEM (scanning electron
microscope), AFM moire is more convenient than SEM moire [30] in microscopic
measurements.

The electron beam lithography used in preparing specimen grating for AFM
moire and SEM moire requires multiple procedures of coating and developing. Usually,
a specimen is coated with a conductive layer before being coated with a photoresist
material such as PMMA. The photoresist layer is then subjected to preset electron beam
scanning for lithography. It then needs to be developed, ﬁxed and rinsed before being
used as moiré grating. These procedures are time-consuming and labor-intensive. Since

the specimen or the area of interest for microscopic measurements is usually very small,

49

the reinforcement effect of the grating on the specimen should not be neglected. In other
words, the grating layer could reinforce the specimen, at least locally, to some extent and
cause measurement error. Hence, a grating technique capable of reducing the
reinforcement effect to a minimum, such as using a low-modulus material and a thin

coating, should be developed. This chapter presents such a new grating technique.

4.2 GRATING TECHNIQUES

The moire’ phenomenon observed in SEM has long been recognized by SEM
users. The undesired moire fringes in SEM are attributed to specimen topography and
SEM related sources. To reduce, if not to eliminate, the moire phenomenon has been an
important issue in research related to SEM. Besides the specimen topography, there are
two main sources responsible for SEM moire phenomenon, namely the voltage contrast
[43] and the contamination [44]. The former usually occurs in specimens with poor
electrical conductivity. Under direct electron beam scanning, the incident electrons tend
to accumulate along the scanning lines, resulting in non-uniform voltage potential in the
scanned zone. When the electron-rich specimen is further scanned under a different
magnification factor or angle, a moiré fringe pattern can be formed. In that pattern, those
lines consisting of high-density electrons form the specimen grating while‘the scanning
lines of viewing provide the reference grating. Although the moire fringe pattern can be
viewed instantaneously on the monitor, it is really a dynamic phenomenon. When the
lines of accumulated electrons change, the moire’ fringe pattern changes. When the
accumulated electrons fade away, so do the moire fringes. Thus, the moire grating based

on the voltage contrast may be considered as temporary grating. Figure 4.1 shows the

50

 

Figure 4.1 Moiré fringe pattern in an alumina specimen with grating based on voltage
contrast.

51

moiré fringes in an alumina specimen. The specimen grating, not shown in the diagram,
was created by exposing the specimen to a stable beam current of 2 nA, an acceleration
voltage of 4keV and a scanning time of 30 seconds with a working distance of 12 mm.

The other SEM-related moire grating is relatively permanent. It is the deposition
of carbonaceous products derived from the polymerization of contaminated organic
molecules under electron irradiation inside SEM vacuum chambers. The following
sources of contamination are commonly encountered in SEM practices: the vacuum
pump oil, the organic molecules adsorbed on the specimen surface and the specimen
itself. Although cautions have been exercised in SEM practices [44-48], there is no
warranty that SEM chambers can be kept completely contamination free. The
backstreaming of vacuum pump oil into SEM chambers and the organic molecules on
specimens cannot be completely avoided. Because a vacuum is required for SEM
operations, residual vacuum pump oil and organic molecules could be easily vaporized,
polymerized by electron irradiation, and then deposited on the specimen surface. A
schematic diagram shows this process is presented in Figure 4.2. Once the carbonaceous
products are deposited on the specimen surface, carbonaceous lines following the
scanning pattern are built up. If the carbonaceous lines are well arranged, they can be
used as moiré grating lines, i.e. carbonaceous grating.

An application of the carbonaceous grating for microscopic measurements has
been mentioned [49]. Compared to the grating based on voltage contrast, the
carbonaceous grating is more durable, if not permanent. Figure 4.3 shows the
carbonaceous grating in an epoxy specimen coated with gold. The grating was cast by

exposing the specimen to an electron beam with a current of 2 nA, an acceleration

52

e- C C e 6-
1 pump oil vapors
A . _ g, ........ i G absorbed organic
“‘ ‘ ‘ molecules
gold coating
specimen

 

Figure 4.2 The formation of carbonaceous grating.

 

Figure 4.3 Carbonaceous grating in an epoxy specimen coated with gold.

53

voltage of 20keV, a scanning time of 30 seconds and a working distance of 20 mm.

4.3 CARBONACEOUS GRATING

The thickness of PMIVIA coating used in the electron beam lithography is usually
around 100 nm. However, the carbonaceous grating based on contamination in SEM
chamber and testing specimen can be as thin as 4 nm. Accordingly, the carbonaceous
grating is superior to the lithographic grating for AFM moire and SEM moire because the
former produces less signiﬁcant effect of reinforcement on specimens than the latter. The
thickness of carbonaceous grating is dependent on beam current, acceleration voltage and
scanning time. If all of them are well adjusted, it is possible to have grating lines with a
sufﬁcient thickness [50,51]. The thickness can strongly affect the quality of moire fringe
pattern; i.e. the higher the thickness the better the image quality. Experiments have
shown SEM moire’ requires a thickness greater than AFM moire. Figure 4.4 shows an
AFM image of carbonaceous grating. The ridges and trenches can be clearly identiﬁed.
However, it should be noted that it is a very delicate process to obtain grating lines with
sufﬁcient thickness. If the resultant electron dose based on beam current, acceleration
voltage and scanning time is not sufﬁcient, the thickness may be too low. However, if
the carbonaceous deposition is overdone, the ridges may overlap one another and result in
an unrecognizable moiré grating. Figure 4.5 shows an outline of a cross-section of
carbonaceous grating. The outline is of mountainous shape with an average height of 8

nm and pitch of 250 nm.

54

 

Figure 4.4 AFM image of carbonaceous grating.

 

101.0%

pitch i
/\,\ /i\ I;

heigh_t__

 

0

-10.0

 

’WV

V\/V

 

li/\
\i/‘

 

 

0 o.'25 0.50

”M

o.'75

1.00

Figure 4.5 Outline of a cross-section of carbonaceous grating.

55

4.4 MOIRE FRINGES

The carbonaceous grating can be used for both AFM moiré and SEM moire.
Shown in Figure 4.6 are the moiré fringe patterns from SEM. The specimen was
identical to the one used in Figure 4.3. The scan coil of the SEM was rotated by various
angles with respect to the specimen for moire analysis. Equation 2.4 can be used for
analytical calculation. Both results from the experimental measurements and the
theoretical calculations are shown in Figure 4.7 and seem to agree very well.

A similar study was performed in AFM for the epoxy specimen. Figure 4.8
shows the moiré fringes formed by rotating the specimen with respect to the scanning
lines for several angles. Figure 4.9 again suggests a good agreement between the

experimental results and corresponding theoretical calculations.

4.5 CONCLUSION

A careful study of carbonaceous grating based on contamination in SEM chamber
and testing specimen is presented. The new technique is more convenient than that based
on electron beam lithography. Good agreements between experimental results and
theoretical calculations have veriﬁed the feasibility of using the carbonaceous grating for

the AFM moiré and the SEM moiré.

56

v «a; «VERDE - ,
as? W? “ricer ‘

V _ sin-«snare ms:

 

 

 

.1.

Ar ’Y‘w' '—

-.

. :1)

0:10. I 8%:

 

Figure 4.6 SEM moire fringes.

 

 

 

90 7*
“i'
80 1"
“ AA
70 —— an
AA -_ d)
'1:
60 ‘-
AA -~ E A
—~ ea
50 _. g A
40 ~—
“5 .- “6’8
30 7” .
-_ .E
20 ‘” e" A experimental
.. ‘ ,
10 A anaJYIlCal
-6 -4 -2 0 2 4 6

9, Specimen rotation angle

Figure 4.7 Comparisons between theoretical calculations and experimental measurements
for SEM moire’ fringes.

58

  
 

_ O
¢_175.21 ¢=16I.S3°

.\—

 

¢=156.71°

 

Figure 4.8 AFM moire fringes.

59

180 4
170 l
160 : 0
150 i:
140 L
130 I
120 : 0 experimental
110 j: 0 analytical

¢, fringe angle (deg)

100 ..

 

90 I l i I I I I I I 1
0 2 4 6 8 10
0, specimen rotation angle (deg)

 

Figure 4.9 Comparisons between theoretical calculations and experimental measurements
for AFM moire fringes.

60

Chapter 5
NEW VIEWING TECHNIQUES FOR SEM MOIRE

5.1 INTRODUCTION

Based on interference of two sets of grating (lines with periodic spacing), the
geometric moiré method [52] has been an useful tool for displacement measurements. As
technologies advance, new experimental methods and grating producing techniques have
been introduced. These technologies have been integrated into the moire method to
fundamentally change it. One signiﬁcant development in the moire method has been the
use of laser light, and this eventually has led to a completely new method called the
moiré interferometry method. Post, Han and Ifju [16] have summarized the method
comprehensively.

The moiré interferometry method utilizes the interference of two laser beams to
form a moire grating [26,27,53,54]. Being attached to the surface of a specimen, a moire
grating is subjected to loading or deformation identical to that exerted on the specimen.
When the moiré grating is illuminated by two laser beams with special incident angles,
diffracted beams will interfere with each other and form a moire fringe pattern. The
major advancement of the moire interferometry method over the geometrical moiré
method is the increase of frequency from about 50 lines/mm to 2400 lines/mm.
Accordingly, the moire interferometry method is useful for measurements requiring high
accuracy. Its applications have also been proved feasible for microscopic measurement
[13].

By using a medium of high index of refraction, Han [13] has pushed the

frequency of moiré grating up to 4800 lines/mm. However, further increase in grating

61

frequency is hindered by the wavelength of laser light. In order to increase the
frequency, hence the sensitivity of the moire method, a technique independent of light
source is preferred. Based on electron beam lithography, Smith, Chinn and DeGraff [40]
have demonstrated the feasibility of casting grating on specimens and viewing moire
fringes by a scanning electron microscope (SEM). Kishimoto, Egashira, Shinya and
Carolan [55] have named the technique electron beam moiré method by combining
electron beam lithography and scanning electron microscope and used it for microscopic
measurements.

Besides the moire interferometry method, the electron beam moire (or SEM
moiré) method is another signiﬁcant development in moire methods. It is especially
useful for measurements of microscopic deformation and has been proved to be a reliable
technique. Dally and Read [30] have further investigated the details of the technique and
established the fundamental theory of SEM moire method [33]. They have demonstrated
that a frequency of 10,000 lines/mm or higher is feasible [30]. They and other
researchers have used the SEM moire method to measure microscopic deformation of
fiber-reinforced composite materials [31,32,56]. The extension of its applications to

electronic packaging has also been reported [57-60].

5.2 ELECTION BEAM LITHOGRAPHY

Electron beam lithography is a commonly used technique. Similar to the Smith
group, the Kishimoto group and the Dally-Read group have used electron beam
lithography to cast a moire grating, namely lithographic grating. The technique, in fact,

has been primarily used in semiconductor processes and MEMS (microelectromechanical

62

systems) fabrication. It is a technique based on spin-coating a thin PMMA
(polymethylmethacrylate) layer on the surface of a well-polished and gold-coated
(especially for non-conductive materials) specimen. Once the polymer coating layer is
cured, the specimen is then subjected to electron beam scanning for lithography.

After being scanned by an electron beam, the molecular chains of PMMA are
scissored. The specimen is then submerged in a chemical for etching. In that process,
degraded PMMA molecules are dissolved away and removed; whereas the non-degraded
(unscanned) ones remain intact. A solvent (isopropanol mixed with methyl isobutyl
ketone (MIBK) in a 3:1 volume ratio) is usually used for chemical etching. The
specimen is usually etched for 40 seconds. It is then rinsed in a 100% isopropanol ﬁxer
for 20 seconds and followed by a second rinse in distilled water for 30 seconds.

The scanning trajectory of the electron beam in an SEM is controllable. It is
possible to achieve any kind of two-dimensional scanning pattern by adjusting the
magnetic ﬁeld of the scan coil, scanner, to deﬂect the electron beam. A periodic
scanning pattern consisting of straight lines with constant spacing can be achieved by
advancing a constant movement after each line scan. Hence, a moiré grating with a
desired frequency can be obtained. Figure 5.1(a) shows trenches and ridges of a moire
grating based on electron beam lithography. Figure 5.1(b) is a schematic diagram of the
cross section of Figure 5.1(a). The grating has a frequency of 5539 lines/mm or a pitch
of 181 nm.

Both the quality and the frequency of a moire grating are important in
applications of the SEM moire method. The quality can affect the resolution of the moire

fringe pattern while the frequency of a grating is responsible for the sensitivity of the

63

 

ridge trerlch

gold coating 1 itch WEE thickness
\TT—W— _0_ 575719— PMMA
specimen
0?)

 

 

 

 

 

    

’ '

Figure 5.1(a) SEM image of lithographic grating (b) Schematic diagram of cross-section
of grating (c) Moiré fringes.

SEM moiré method. The quality of moiré grating involves many features. The aspect
ratio of thickness-to-width of ridge seems to be the most important element. According
to Figure 5.1(b), the moiré grating shown in Figure 5.1(a) has an aspect ratio
(thickness/width) of 1.14 and is able to give a high-quality moire fringe pattern, such as
the one shown in Figure 5.1(c).

In order to achieve a desired aspect ratio of the moire grating, both electron
dosage and etching rate are important parameters. The electron dosage is a resultant
strength of incident electron beam bombarded on the specimen and includes many
parameters, depending on the SEM used. For the SEM used in this study, the electron
dosage combines effects due to acceleration voltage, beam current, scanning time and
working distance of the electron beam. The etching rate, however, depends upon the
concentration of the solvent and the developing time. Apparently, it requires signiﬁcant
efforts to facilitate a set of parameters for operating the SEM to achieve a desired aspect
ratio. The SEM and its parameters used in casting the moire grating are given in
Appendix A.

The frequency of a moire grating, f8, is dependent on the scanning rate and
scanning area per scanning frame. It is given by

__ number of scanning lines
g _

M (5.1)

 

height of scanning area

where M is a magniﬁcation factor. For example, for a scanner with a scanning rate of
1250 lines/frame and a scanning area of 120 mm-by-90 mm (length x height), the SEM

requires a magniﬁcation factor of 360 to achieve a 5000 lines/mm of moire grating. The
corresponding scanning area is then reduced to only 333 um x 250 um. Accordingly, as

the magniﬁcation factor increases, the frequency of moiré grating increases; whereas the

65

scanning area decreases. However, the magniﬁcation factor displayed on the SEM
console changes in discrete numbers while the control of magniﬁcation factor changes
continuously for the SEM used in this study. Therefore, the frequency of specimen
grating varies even at the same magniﬁcation factor displayed on the SEM console.
Although a frequency of 10,000 lines/mm or higher is possible, according to Equation
5.1, a careful control of scanning and etching processes is required. If the electron
dosage is too high, the roots of grating lines could be very narrow, resulting in a
phenomenon called proximity effect. Figure 5.2(a) shows a grating due to overdosage of
electrons and the corresponding schematic diagram. The overlapping of neighboring
scans destroys the surface integrity of the PMMA layer, leaving a very thin, ambiguous
grating. Conversely, if the dosage is insufﬁcient, the aspect ratio may be too small and
the quality of moiré fringe pattern may become too poor to recognize. Figure 5.2(b)
shows a grating due to underdosage of electrons and the corresponding schematic
diagram of the cross section. A useful grating is shown in Figure 5.1(b) for comparison.
Experiments have shown that a moiré grating with a frequency around 5000 lines/mm

can be repeated consistently based on the facilities used in this study.

5.3 FORMATION OF MOIRE FRINGES

Moiré methods are aimed at forming moire fringe patterns for deformation
measurements. Forming a moire fringe pattern requires two gratings: the specimen
grating and the reference grating. The grating mentioned earlier is made of PMMA and
deposited on the specimen surface; it is the specimen grating. The second grating is

formed by the scanning lines during fringe-viewing stage, and is the reference grating.

66

gold coating

Specimen

 

(a)

gold coating

 

 

 

 

 

 

(b)

Figure 5.2(a) Moiré grating due to overdosage of electrons and corresponding schematic
diagram. (b) Moiré grating due to underdosage of electrons and
corresponding schematic diagram.

67

The interference of these two gratings results in a moiré fringe pattern. Since the
resolution of the moiré gratings is much poor than the moiré fringe pattern under the
fringe-viewing stage, only the moire fringe pattern and the microstructure of the
specimen surface can appear in the SEM image. The moiré grating are usually not
visible.

The frequency of reference grating is dependent on the features of the viewing
scanner (see Appendix A) and is also governed by Equation 5.1. For example, if a
viewing scanner has a viewing rate of 500 lines/frame for a viewing area of 120 mm x 90
mm, the frequency of reference grating will be dependent on the magniﬁcation factor M
only. In other words, the frequency of the reference grating can be changed by adjusting
the viewing area. Matching the frequency of the reference grating with that of 5539
lines/mm of specimen grating requires an adjustment of the magniﬁcation factor to 997.
However, this odd factor may not be achievable due to the difﬁculty in ﬁne tuning the
magniﬁcation. In fact, a perfect match of frequency between the specimen grating and
the reference grating is not necessary. For example, instead of 997, a magniﬁcation
factor of 1000 may be selected. This selection gives a reference grating with a frequency
of 5556 lines/mm and a reduction of the viewing area to 120 um x 90 um. In addition, it
should be noted that there is a difference of 17 lines/mm between these two gratings. The
difference will appear in the SEM image as 17 moire fringes per millimeter and is usually
taken as initial fringes in deformation analysis.

In SEM moiré method practices, both the scanning rate for lithography (e.g. 1250
lines/frame) and the viewing rate for imaging (e.g. 500 lines/frame) are features of the

SEM used in this study. They are usually ﬁxed values. As the magniﬁcation factor

68

increases, the frequencies of the specimen grating and the reference grating increase;
however, the scanning area and the viewing area decrease while the sensitivity of the
SEM moiré method remains the same. The sensitivity is tied only to the ﬁxed value of
the scanning rate or the viewing rate. Since the viewing rate is smaller than the scanning
rate, the former determines the sensitivity of the SEM moiré method. Accordingly, no
matter how small or how large the magniﬁcation factor is, there are only 500 viewing
lines per frame. Since at least one moire fringe should be generated in a scanning frame
for the image to be qualiﬁed as a moiré fringe pattern, a strain of 1/500 (0.2%) is the
minimum requirement. This value is quite high for many engineering materials.

The current SEM moiré method is based on electron beam lithography and
scanning electron microscope. Both of them have been well developed and many details
of the techniques are available in literature. However, as mentioned earlier, the electron
beam lithography relies on a layer of PMMA coating. Although the thickness of the
PMMA layer in the trenches can be dissolved away as shown in Figure 5.1(a), it still
poses a concern of reinforcing the specimen by the thickness of ridges. The
reinforcement effect of grating, the complicated processing of lithographic grating and
the low sensitivity - the minimum strain (0.2%) required for generating a moire fringe -
are drawbacks of the existing SEM moire method. In order to reduce the effects of these
drawbacks, the following developments are required:

(1) a convenient technique for casting moiré grating,
(2) a specimen grating with insigniﬁcant reinforcement effect,

(3) a viewing technique with a higher sensitivity.

69

5.4 NEW TECHNIQUES

Based on the requirements listed above, a new grating-casting technique and a
new fringe-viewing technique are developed.
5.4.1 Carbonaceous Grating

This grating producing technique is based on the well-known contamination in
SEM chambers. It turns the negative defect of SEM to a positive application. This
technique relies on the deposition of carbonaceous products derived from the
polymerization of contaminated organic molecules under electron irradiation inside
evacuated SEM chambers.

The following sources of contamination are commonly encountered in SEM
practices: the vacuum pump oil, the organic molecules adsorbed on the specimen surface
and the specimen itself. Although cautions have been exercised in SEM practices, there
is no warranty that SEM chambers can be kept completely contamination free [44—48].
The backstrearrring of vacuum pump oil into SEM chambers and the organic molecules
on specimens cannot be completely avoided. Because a vacuum is required in SEM
operations, residual vacuum pump oil and organic molecules can be easily vaporized,
polymerized by electron irradiation, and then deposited on the specimen surface. Once
the carbonaceous products are deposited on the specimen surface, carbonaceous lines are
built up following the scanning pattern. If the carbonaceous lines are well arranged, they
can be used as moire grating lines, i.e. carbonaceous grating. Nshaninan, Dove, and
Rajan [49] were the ﬁrst to explore the use of the carbonaceous grating for a microscopic
investigation. Figure 4.3 shows the carbonaceous grating in an epoxy specimen coated

with gold. The grating was cast by exposing the specimen to an electron beam with a

70

current of 2 nA, an acceleration voltage of 20 keV, a scanning time of 30 seconds and a
working distance of 20 mm.

The thickness of PMMA coating used in the electron beam lithography is usually
around 100 nm. However, the carbonaceous grating based on contamination in the SEM
chamber and testing specimen can be as thin as 4 nm. Accordingly, the carbonaceous
grating should give a less reinforcing effect on a specimen than the lithographic grating
does. The thickness of carbonaceous grating is dependent on electron dosage. If it is
well adjusted, grating lines with a sufﬁcient thickness can be achieved [50,51].

The grating thickness can strongly affect the quality of moire fringe pattern, i.e.
the greater the thickness the better the image quality. Figure 4.4 shows an AFM image of
carbonaceous grating. The ridges and trenches can be clearly identiﬁed. Figure 4.5
shows the outline of a cross-section of the carbonaceous grating. The outline has
mountainous shape with an average thickness of 7.5 nm and a pitch of 246 nm.
However, one need to note that a careful control of scanning is required to produce
sufﬁciently thick grating lines. AS in the casting of lithographic grating, if the resultant
electron dosage is not sufﬁcient, the thickness may be too small. On the other hand, if
the carbonaceous deposition is overdone, the ridges may overlap one on another and
result in an unrecognizable moiré grating.

5.4.2 Total Imaging

In order to prepare a specimen grating, a high magnification factor is preferred as
long as the scanning area for grating-casting is larger than that of interest. In the fringe-
viewing stage, however, the magniﬁcation factor needs to be adjusted so that the

reference grating matches the specimen grating as closely as possible. For the SEM used

71

in this study, there are two types of scanning/viewing scanner: the monitor scanner and
the photograph scanner. The fundamental techniques of the two scanners are similar.
Both of them can be used as scanners for lithographic grating and as viewers for
reference grating. However, the monitor scanner presents an instantaneous image on the
SEM monitor while the photograph scanner presents a hardcopy image after a
photographic process.

Besides the difference of image presentations, another difference between the two
scanners is the scanning/viewing rate. For example, for the SEM used in this study, the
monitor scanner has a frequency of 500 lines/frame while the photograph scanner has a
frequency of 1250 lines/frame. Thus, the photograph scanner has a sensitivity higher
than twice of the monitor scanner.

Through the use of the photograph scanner for fringe-viewing, the sensitivity of
the SEM moire method is more than doubled as compared to that using the monitor
scanner since the minimum strain required to form one moire fringe is reduced to a level
well below half, i.e. from 0.2% (1/500) to 0.08% (1/1250). Because the sensitivity is
dependent on the viewing rate, which is a ﬁxed value depending on the SEM used, the
sensitivity cannot be increased according to needs. For example, when the specimen or
the area of interest becomes smaller, it makes more sense to use a smaller strain.
However, with the ﬁxed value of viewing rate, it is impossible to reduce the required
minimum strain to form a single moire’ fringe. In order to improve the sensitivity, a
possible approach is to record the total image of gratings and moire fringe pattern, instead

of only the moire fringe pattern.

72

When a specimen is under deformation and is scanned by an SEM, a grating for
the deformed specimen can be created. This grating, called the deformed specimen
grating, is similar to the specimen grating initially cast on the specimen, i.e. the initial
specimen grating. A moire fringe pattern based on the interference between the deformed
specimen grating and the initial specimen grating can be identiﬁed by viewing these two
specimen gratings by an SEM. The technique used to view both moire grating and moire’
fringe patterns is called total imaging.

A moire fringe pattern obtained from total imaging is of a real image; whereas
that obtained from either monitor viewing or photograph viewing is of a virtual image.
However, it should be noted that the real image is not as distinct as the virtual image
since the former is embedded in the gratings and is an implicit pattern while the latter
stands out of the gratings and is an explicit pattern. Figure 5.3(a) shows a moire fringe
pattern and the corresponding initial specimen grating and deformed specimen grating of
lithographic type. Figure 5.3(b) shows a moiré fringe pattern and the corresponding
initial specimen grating of carbonaceous type. The deformed specimen grating is not

visible though sometimes it is traceable around the boundary of an SEM image.

5.5 SIX SEM MOIRE METHODS

Based on the new techniques mentioned above, there are two grating producing
techniques, i.e. lithographic grating and carbonaceous grating, and three viewing
techniques, i.e. monitor viewing, photograph viewing, and total imaging. A total of six

SEM moire methods can be available by combining one technique from each of the two

groups.

73

moire fringe

‘ initial
‘4— specimen
grating

deformed

\ specimen

grating

 

moire fringe

 

Figure 5.3(a) Total imaging of lithographic grating. (b) Total imaging of carbonaceous
grating.

74

5.5.1 Lithographic Grating and Monitor Viewing (LM)

This is the SEM moiré method currently used by many researchers. It utilizes a
photograph scanner, instead of the monitor scanner, to cast lithographic gating on the
specimen surface because the photogaph scanner has a frequency of 1250 lines/frame,
which is higher than the monitor scanner that has a frequency of 500 lines/frame. The
moire fringe pattern is formed when the specimen is subjected to loading or deformation
and viewed by the monitor scanner. The image of fringe pattern on the monitor is
synchronized with the monitor scanner. Hence, instantaneous or even dynamic
measurements are possible.

5.5.2 Lithographic Grating and Photograph Viewing (LP)

This method is very similar to LM. While very similar to LM, this technique
utilizes the photogaph scanner for both electron beam lithogaphy and moire fringe
formation. Although it has a higher sensitivity than LM, LP is not an instantaneous
technique because it takes a photographic process to obtain the moire fringe image. In
addition, because the magniﬁcation factor used in the LP during the fringe-viewing stage
is lower than that used in the LM, the microstructure of specimen surface from the LP is
not as clear as that from the LM.

5.5.3 Lithographic Grating and Total Imaging (LT)

In this method, a specimen is scanned twice, one under no loading and the other
under loading or deformation, by the photogaph scanner. The specimen then is
subjected to etching. Both the initial specimen gating and the deformed specimen
gating are created on the specimen surface. The total imaging, which is focused on the

two specimen gatings - hence the moiré fringes generated by them - is used in the

75

viewing stage. There is no limit on the magniﬁcation factor for the total imaging. The
moiré fringes are, in fact, organized by the trenches (because of double scanning) located
on the intersecting points of the trenches of these two gatings, as Shown in Figure 5.3(a).
The two possible moire fringe patterns due to interference between these two gatings
and the scanning for total imaging are not visible because the frequencies of these two
gatings and the scanning rate for the total imaging are very different.

5.5.4 Carbonaceous Grating and Monitor Viewing (CM)

In this technique, a specimen is ﬁrst scanned by the monitor scanner to produce
carbonaceous gatings. In order to have a specimen gating with a high aspect ratio, the
electron dosage should be carefully controlled. Based on the carbonaceous gating, the
moire fringe pattern can be formed when the specimen is subjected to loading or
deformation and viewed by the monitor scanner. Again, an instantaneous or even
dynamic image can be seen on the SEM monitor.

5.5.5 Carbonaceous Grating and Photograph Viewing (CP)

This method is based on forming a carbonaceous gating on the specimen by the
monitor scanner of the SEM. Both the microstructure of the specimen surface and a
moire fringe pattern due to interference between the moire gating and the photographic
scanning can be obtained on a photogaph. This method offers a higher sensitivity than
the CM. However, it is not an instantaneous technique as the CM. Besides, the CP gives
a poorer resolution of the microstructure of the Specimen surface than the CM due to the
smaller magniﬁcation factor used in photogaph viewing. As in the LM, the LP and the
CM, only a virtual moire fringe pattern appears on the ﬁnal image (on either an SEM

monitor or a photogaph). The moire gating is not visible.

76

5.5.6 Carbonaceous Grating and Total Imaging (CT)

Two carbonaceous gatings are deposited on the specimen by scanning the
specimen twice with the monitor scanner: one is the initial specimen gating and the other
is the deformed specimen gating. The specimen is then subjected to SEM scanning for
total imaging. Again, there is no magniﬁcation limit during the viewing stage. The
image can be enlarged as much as possible. Besides, as in the LT, the real moiré fringe
pattern is implicit. It is organized by the intersecting points of the two specimen gatings
and requires a careful tracing for identiﬁcation, as shown in Figure 5.3(b). However, one
needs to note that the deformed specimen gating is not visible; neither are the fringes

based on the interference between the two specimen gatings and the SEM viewing.

5.6 COMPARISON OF THE SD( SEM MOIRE METHODS

Based on gating producing techniques, the six SEM moire methods can be
divided into two goups: the lithogaphic gating goup and the carbonaceous gating
goup. The former is based on the well-developed electron beam lithogaphy. However,
the lithogaphic technique is time-consuming and labor-intensive and can cause local
reinforcement of testing specimens. The carbonaceous technique is newly developed and
requires further research to become a well-controlled technique. However, it is more
convenient than the lithogaphic technique.

Based on scanning/viewing techniques, the six SEM moiré methods can be
divided into two goups, the monitor viewing and the photogaph viewing. The total
imaging is based on either monitor viewing or photogaph viewing. Although there are

some differences between the two viewing techniques, such as frequency, the primary

77

difference is that the monitor viewing is of an instantaneous technique while the
photogaph viewing is a photogaphic technique. Since the photogaph viewing has a
higher scanning rate than the monitor viewing, it requires a smaller magriﬁcation to
achieve an identical frequency. Accordingly, it gives a poorer resolution on the
rrricrostructure of specimen surface.

Based on the image of moiré fringes, the six SEM moiré methods can be divided
into two goups, the fringe viewing and the total imaging, which include both speicmen
gatings and moire fringe patterns. Because of the signiﬁcant difference in resolution
between specimen gatings and moire fringe pattern, the images based on monitor
viewing and photogaph viewing give only moire’ fringe patterns. However, in total
imaging, which is based on recording both the initial specimen gating and the
deformation specimen gating, the moire fringes must be identiﬁed by tracing the
intersecting points of the two specimen gatings. Although the fringe-tracing procedure
is not as simple as that based on fringe viewing, it provides an opportunity to increase
sensitivity.

Based on the differences due to gating producing technique, scanning/viewing
technique, and imaging technique, details of the six SEM moiré methods are given in

Appendix B for comparisons.

5.7 DEMONSTRATIONS
Experiments based on the six SEM moire methods were performed. The
specimens used in the studies were either made of aluminum or epoxy. The aluminum

specimens were coated with a PMMA layer and were used for the LM and LT cases.

78

specimens were first coated with a gold layer and then a PMMA layer. They were used
in the LP, CM, CP and CT cases. Experimental results of moire fringe patterns based on
specimen rotation are given in ﬁgures 5.4-5.9. The comparison between the experimental
results and analytical calculations based on Equation 2.4 are also presented:

sin 4)

tan9 = (2.4)

 

pf
Pr

 

cos¢ +

where 0 and 4) are angles of specimen and moire fringes with respect to the scanning
lines, respectively, and pf and p, are pitches of moire fringes and reference gating,
respectively. The angles 0 and 6 are also shown in each ﬁgure. In all cases, the

experiment results seem to agee very well with the analytical calculations.

5.8 CONCLUSIONS

The carbonaceous gating is much easier to prepare on testing specimens than the
lithogaphic gating. In casting carbonaceous gating, there is no need to remove the
specimens from SEM chambers as needed in the lithogaphic gating technique for
chemical etching. Besides, the thickness of carbonaceous gating can be as thin as 4 nm,
compared to the 100 nm usually used in the lithogaphic gating. Hence, the
reinforcement effect on the specimens can be negligible. Although the carbonaceous
grating has been veriﬁed to be a feasible technique, more studies are needed to improve
its quality and increase its frequency.

Unlike the conventional moiré methods that only record moiré fringe patterns, the
total imaging technique records both moire fringes patterns and moire gatings. If two

real moire gatings, such as the initial specimen gating and the deformed specimen

79

 

 

90 A
on
80 g
V
70 3
0 CD
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o 5 0'
50 gr,
0 .E 0’
40 h
30 e“
80 O.
CO .
10 0 experimental
C’ . analytical
-8 -6 4 -2 0 2 4 6 8
0, specimen rotation angle (deg)
(19)

Figure 5.4(a) Moiré fringe pattern based on LM method. (b) Comparisons between
analytical calculations and experimental measurements.

80

w/

Z ' /
// "
, parse/28¢

/
.I [1% l
/ ' ' 1T1

 

 

//
(a)
A
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.0 70 g 0.
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0 40 ‘T C.
e“
30
2 .
0 0 experimental
10 0 analytical
-6 -4 -2 0 2 4 6
0, specimen rotation angle (deg)
(13)

Figure 5.5(a) Moire fringe pattern based on LP method. (b) Comparisons between
analytical calculations and experimental measurements.

81

 

 

110 ’57)
Q)
108 E
(D o
106 a
104 5 CD
“6’0
102
. C)
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0 98 e
O
96 o
94 O .
expenmental
92 o analytical
—40 -30 —20 -10 0 10 20 30

0, specimen rotation angle (deg)

(b)

Figure 5.6(a) Moire fringe pattern based on LT method. (b) Comparisons between
analytical calculations and experimental measurements.

82

243.078-

 

 

90 '-
A
”— 8"
80 “ 3 a
70 “r a
0 -_
60 —— 5
o - a C'
50 " E” C.
0 40 “ “'1
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30 ‘-
20 -- .
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10.: o analytical

 

4 -2 0 4
0, specimen rotation angfe (deg)

(b)

Figure 5.7(a) Moire fringe pattern based on CM method. (b) Comparisons between
analytical calculations and experimental measurements.

83

" ’ e gar":
" ' I . *- 7‘
it efﬁgy”?

.4:

. is?”

 

 

(a)
180
170 . 90
160
0 0 O
150 1?” °
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140 3 '°
0 o V o o
. o 130 a
e 120 5 ° 0
d)
110 E9
I o .
100 h experimental
e“ 0 analytical
.4 -2 0 2 4

0, specimen rotation angle (deg)

(b
Figure 5.8(a) Moire fringe pattern based on CP method. (b) Comparisons between
analytical calculations and experimental measurements.

84

 

 

100 -- a
Q
r E
Q)
98 ‘ ED
9
96 - g0 a
O. 94 - e“
0 _
92 " O. 0 experimental
" O analytical

 

-10 -8 —6 —4 -2 0 2 4 6 8 10
0, specimen rotation angle (deg)

(b)

Figure 5.9(a) Moiré fringe pattern based on LT method. (b) Comparisons between
analytical calculations and experimental measurements.

85

grating are cast on a specimen, a real moiré fringe pattern can be identiﬁed from tracing
the intersecting points of two moire gatings. Since the moiré fringe pattern is also a real
image, there is no limit on magniﬁcation in total imaging. Hence, the sensitivity of a
moire method based on total imaging is only dependent on the frequency of the specimen
grating. Since the frequency of the specimen gating can be made very high, such as
10,000 lines/mm, the moiré method based on total imaging can thus have a very high

sensitivity.

86

Chapter 6
APPLICATIONS OF SEM MOIRE

6.1 INTRODUCTION

Carbon ﬁber composites and two-phase polymers served as model materials to
demonstrate the ‘applicability of newly developed SEM moiré methods to measure
microscopic deformation. Two SEM moiré methods, carbonaceous gating and monitor
viewing (CM) and carbonaceous gating and total imaging (CT), were applied to rotation
angle measurements on carbon ﬁber reinforced composites. The composite specimens
were able to carry carbonaceous gatings on their surface. The moiré fringe patterns and
carbon ﬁbers were observed simultaneously, which showed the feasibility of the SEM
moiré methods for the investigation of micromechanics. The other application of the
SEM moire’ methods was the local strain measurement of each component in a two-phase
polymer material. The interface shifting was observed during the stress relaxation
experiment. The strain of the individual phase of this specimen did not remain constant
when the global strain did. An energy loss may occur due to this interface shifting, which
results in the deviation of the analytical calculation from the experimental data.
Therefore, the viscoelastic response of the two-phase polymer specimens was
investigated. The dynamic mechanical tests were conducted on the specimens with
different volume fractions in parallel and serial loading conﬁgurations. The analytical
calculations based on the rule of mixtures do not predict the dynamic experimental
testing data of two-phase polymers in serial loading configuration. On the other hand, the
dynamic experimental testing data of specimens in parallel loading conﬁguration match

very well with the analytical calculation.

87

The above applications of the SEM moiré method reveal the importance of getting

the microscopic observation and deformation measurement simultaneously.

6.2 CARBON FIBER REINFORCED COMPOSITES
6.2.1 Experimental Procedures
A. Materials and Specimen Preparation

The material used in this study was a [0°/90°]s laminated carbon ﬁber/epoxy
composite. The composite material was cut into several 5mm by 5mm specimens. They
were polished culminating with 0.05 pm alumina particles and then coated with a thin
layer of gold on the polished surfaces. Specimens were kept in the normal laboratory
environment prior to the deposition of carbonaceous gatings.
B. Grating Deposition and Veriﬁcation

Two SEM moire methods, carbonaceous gating and monitor viewing (CM) and
carbonaceous gating and total imaging (CT), were applied to composite Specimens.
Direct carbonaceous gating deposition was carried out under a CamScan 44FE scanning
electron microscope. After gun alignment and focusing, a desired electron beam current

of 1.7 nA was obtained. The SEM settings were the following:

Acceleration voltage: 15 keV Beam aperture: 50 run
First condenser lens (Cl): 6.24 mV Spot size: 9

Second condenser lens (C2): 1.48 mA Working distance: 23 mm
Objective lens (C3): 0.71 mA Electron beam current: 1.7 nA

Then, composite specimens used for SEM moire CM method were under direct electron
beam scanning for 8 minutes at the magniﬁcation factor 500 to deposit carbonaceous

grating with a frequency of 2774 lines/mm on specimen surfaces.

88

After deposition, scan coils were rotated an angle with respect to composite
specimens while the magniﬁcation factor remained unchanged, and the moire fringe
patterns were recorded accordingly. Since the SEM settings were not altered before and
after the gating deposition, a null ﬁeld of a moiré fringe pattern was observed before
scan coils were rotated. If the magniﬁcation factor changed to 480, carrier fringes would
be observed. Based on this magniﬁcation factor, another set of moiré fringe patterns,
with carrier fringes as initial fringes, was recorded as well at various rotation angles.

For the SEM moiré CT method, ﬁve gatings were deposited onto the surface of
composite specimens with same gating orientation ﬁrst. Then, the second gating was
deposited on one of the ﬁve previous gatings areas after the scan coils were rotated an
angle with respect to specimens. Five rotations were made during this experiment.

6.2.2 Analytical Calculation
The Equation 2.4 was used for analytical calculation in both CM and CT methods:

sin 4)
p_,
Pr

tan 0 = (2.4)

cos¢ +
where 0 and 6 are angles of specimen and moiré fringes with respect to the scanning
lines, respectively, and p; and p, are pitches of moire fringes and reference gating,
respectively.

6.2.3 Discussion

Figure 6.1 and 6.2 show the moiré fringe patterns along with rotation angles from
CM method at two different frequencies of reference gating: 2778 lines/mm and 2667
lines/mm respectively. Figure 6.3 shows the moire fringe patterns from CT method with

a frequency of 2774 lines/mm as a reference gating. In all cases, the experiment results

89

forced

is 2778

.m
m
r

m.
n

.m
m
c
n
O
s

be.
m.
n

.w
t
m
m
s
u

.m
v
m
m
m
a
P
We
n

Figure 6.1 Moiré fri

ng

gati

The frequency of reference

te based on CM method.

lines/mm.

COIIIpOSl

 

.w
m
. :0.
.m
. m
r
.m
ﬁ
m
m
c
n
o
5
1w
g
m
n
.w
m
m
S
u
.m
v
t
a
s
m
m
a
P
We
.n
, .m
M
o
M
2
6
m
u
.Wo
F

The frequency of reference grating is 2667

composite based on CM method

lines/mm.

 

 

Figure 6.3 Moiré fringe patterns at various rotation angles on carbon ﬁber reinforced
composite based on CT method. The frequency of reference gating is 2774
lines/mm.

92

seem to agee very well with the analytical calculations as shown in Figure 6.4 and
Figure 6.5 for CM and CT methods respectively. Based on the above demonstration, this
carbonaceous gating technique can be applied to polymer matrix composite materials.
The deformation measurement of composite materials under loading is feasible but needs

further investigation.

6.3 INTERFACE SHIFTING OF TWO-PHASE POLYMERS
6.3.1 Experimental Procedures
A. Materials and Specimen Preparation

The epoxy resin for this application was di-functional pure diglycidyl ether of
bisphenol A (DGEBA) (DER332, Dow Chemical USA). Amine terminated
poly(propylene oxide) with two different molecular weights, i.e. JEFFAMINE D230 and
JEFFAMINE D400 (Huntsman, USA), were used to crosslink epoxy resin, DGEBA.
Their chemical structures are shown in Figure 6.6.

The molar ratio of epoxide to amine was stoichiometric when mixing DGEBA
with the JEFFAMINE D series. The weight fraction of epoxy and diamines were the
following: DGEBA2D230 = 0.7473:0.2527 and DGEBA:D400 = 06734202266.
DGEBA (366.9g) was ﬁrst mixed with JEFFAMINE D230 (124.1 g) and cured at 100°C
for 24 hours and then kept in the oven for slow cooling to room temperature. This cured
DGEBA/D230 epoxy (Material E) was immersed into a mixture of DGEBA (133.6g) and
JEFFAMINE D400 (78.6g) (Material F). Then Material E and F were cured in an oven at

100°C for 24 hours and kept in the oven to cool down to room temperature.

93

p—r
J
l

‘ o
-- 0 o
0 .90 __ .
80 -~ 9,
Q)
70 -~ 3 A
A‘ 60 I" it AA
50 —~ 5
r- ?” .
‘4‘ 40 ‘” 5 A experimental-1
-. 2.. A .
30 —— 94-1 A analytical-1
20 f 648 O experimental-2
10‘» 0 analytical-2

 

 

I I I I I I I I I I I l I l

—7 -5 -3 . -1 . 1
0, specrmen rotation angle fdeg)

Figure 6.4 Comparisons between analytical calculations and experimental measurements
based on CM method. Specimen is carbon ﬁber reinforced composite.

94

 

 

120 r ’53
Q)
3 o
” .2
° 8”
110 -— ,9
ea
OE C
Q ﬂ-t
e“
100 “—
© 0 experimental
0 analytical
-60 —40 -20 0 20 40 60

0, specimen rotation angle (deg)

Figure 6.5 Comparisons between analytical calculations and experimental measurements
based on CT method. Specimen is carbon ﬁber reinforced composite.

95

AF— Cris AH
“— .._.‘,‘._a..._ 2
CH3

(a)

HzN CH

 

 

 

CH2 { 0 CH2

 

CH —]-——n NH;

CH3 CH3

(b)

Figure 6.6 Molecular structure of (a) diglycidyl ether of bisphenol A (DGEBA) and (b)
polyoxypropylenedianrine (JEFFAMINE D-230 where n=2.6, JEFFAMINE
D-400 where n=5.6).

96

This two-phase polymer was milled into a dog-bone-shaped specimen and was
drilled one hole with 3/32 inch in diameter at each end. The specimen consisted of
50.30% volume fraction of Material E and 49.70% volume fraction of Material F in serial
loading conﬁguration. The cross section area of the specimen was 6.41 mm2 (1.75 mm
by 3.37 mm) with the gage length of 10.64 mm. The interface of Material E and F was
around the middle of the gage section.

The specimen was polished culminating with 0.05 pm alumna particles. It was
immersed in distilled water subjected to ultrasonic cleaning for 30 minutes and was
blown dry with clean air. Then the specimen was annealed at 100°C for 1 hour and kept
in the oven to cool down to room temperature before being coated with a thin layer of
gold. The specimens were kept in the normal laboratory environment prior to gating
deposition.

B. Testing Method

An SEM testing stage (Fullmam USA) was installed in the SEM chamber, and the
specimen was held at each end by two pins with diameter of 3/32 inch. The specimen
grips were controlled by a screw-driven motor with a resolution of 0.001 inch. The force
was measured by a load cell with a resolution of 0.1 lb.

For local displacement measurement, the SEM moiré CM method was used in this
application. The carbonaceous gating with a frequency of 2778 lines/mm was deposited
onto the specimen surface at the interface of Material E and F.

A stress relaxation experiment was conducted in the SEM chamber. A constant
grip distance of 0.031 inch was applied to the specimen, which yielded to a strain of

7.40% resulting in a loading of 29.5 lb, which was a stress of 2969 psi (20.47 MPa).

97

Then, moire fringe patterns as well as the forces were recorded accordingly.
C. Results

The local displacement was measured both from the shifting distance of the
interface and moiré fringe patterns while the gip distance was kept constant during the
stress relaxation experiment. The shifting distance of the interface was measured from
the interface position based on the SEM images. Figure 6.7 shows the strain of Material
E and F measured from the shifting distance of interface and the moiré fringe patterns
during the stress relaxation experiment. Accordingly, the local strain did not remain
constant on either Material E or Material F. Even though the global Strain was kept
constant for the stress relaxation experiment.

6.3.2 Analytical Calculation

Since the local strain of Material E and F had changed during the stress relaxation
experiment for the two-phase polymer specimen in serial loading conﬁguration, quasi-
elastic analysis was not valid. Therefore, by assuming that the linear viscoelastic theory
holds, the Boltzmann superposition integal was utilized to analyze this two-phase
polymer specimen. For this Specimen the local strain of Material E and of Material F was
presented in terms of individual relaxation modulus and volume fractions. The detailed
derivation is shown in Appendix C.

The individual relaxation modulus of Material E and F was obtained from the
dynamic experimental data by a computer progam [61]. This computer progam written
by Bradshaw and Brinson utilized a Prony exponential series to curve ﬁt the dynamic
experimental data (storage and loss modulus) within the frequency domain. Then,

inverse Fourier transformed the Prony exponential series to the relaxation modulus. Both

98

relaxation moduli of Material E and F were used to calculate their local strain for this
two-phase polymer specimen. The results are plotted in Figure 6.7.
6.3.3 Discussion

The measurements from the SEM moiré method and the interface shifting Show
the similar results. Accordingly, the SEM moire method was a useful and reliable tool to
measure local deformation.

This interface shifting of the specimen during the stress relaxation experiment
might result in additional energy loss for the specimen. A simple analytical calculation,
such as the rule of mixtures, did not encounter this energy loss. It is of interest to study
the effect of this additional energy loss due to the mismatch of the viscoelastic response

of two linear viscoelastic materials.

6.4 MISMATCH OF VISCOELASTIC RESPONSE OF TWO-PHASE POLYMERS
6.4.1 Experimental Procedures
A. Materials and Specimen Preparation

The material used in this study was identical to the one in previous application.
This two-phase epoxy material was cut to several 6 mm x 25 mm x 2 mm strips
consisting of different volume fractions of Material E and F. The specimens were
grouped into parallel and serial specimens depending on their loading direction. Both
100 percent of Material E and F were also cut from the same two-phase epoxy material.
Therefore, there were nine different specimens for dynamic mechanical testing. Each
specimen was polished with #1200 sand paper on both sides, annealed at 100°C for one

hour, and cooled down to room temperature in an oven. Each specimen was kept at room

99

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I

Figure 6.7 Comparisons of strain obtained from the SEM moire method, from interface

position, and from analytical calculation.

100

temperature for about two hours to maintain a similar initial aging condition prior to the
dynamic mechanical thermal analysis (DMTA).
B. Testing Method

TA Instrument DMTA 2980 was used to carry out frequency sweep experiments
at each different temperature with displacement amplitude of 10 um. The data were
collected at 6le, 37Hz, 23Hz, 14Hz, 8.5Hz, 5Hz, 3H2, 2H2, le, 0.7Hz, and 0.45Hz.
The temperature steps were from 20°C to 115°C with 5°C intervals. The forces,
amplitudes of deformation and phase angles were measured during the experiments.
Along with calibration constants, forces and amplitudes were used with the phase angles
to calculate the storage and loss modulus.

C. Results

Frequency-temperature superposition was applied to dynamic experimental data
to construct a master curve for each specimen at the reference temperature of 25°C.
Figures 6.8 and 6.9 represent the master curves of storage modulus of specimens in
parallel and serial loading configurations, respectively. Figures 6.10 and 6.11 represent
the master curves of tan8 of specimens in parallel and serial loading conﬁgurations,
respectively. The shift factor is plotted in Figure 6.12.

Frequency-temperature superposition was still applicable to the dynamic
mechanical testing data with different loading configurations and different volume
fractions of these two-phase polymer specimens. Therefore, these specimens were
thermorheologically simple materials, so that the linear viscoelastic theory was applicable

to them.

101

 

 

 

 

 

 

 

 

 

*9. V.
S ES
0 O O
BEQBG
= *7 Chow:
HOWMO
X. rial
—<r-
~01
~o
~01
I
_#H
22 ~©E
: 'V
9 - >.
0.5 _oog
5i: .0
H0 * ﬂ
3:. _c><:r
2E "’3
I ”NE.
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4'4
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l
VD
”v—i
I
00
‘v—t
l
o
”‘1'
L.
N
[IlllllTl [ITTITIIﬁW‘lIITJII |ll|l<lrl N.
o o o o ._.
8 8 o "
F-t
O t—I
r—i
[(etrw).a]30'1

Figure 6.8 Master curves of storage modulus from experimental data. Specimens are in
parallel loading conﬁguration with various volume fractions.

102

50/50
0 33/67
- 0/100

E
i
x 100/0
0 75/25

H 67/33

 

 

 

 

r‘l‘
-N
-O
—e.I
0'3 ~
2: "ET:
:4) - E
DE _\r'>v
35 e 5*
‘53:. ~°9=r
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't-t
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. 'T—ﬂ‘l‘l—l—l—T—ﬁﬁ—“q
O O O I—‘
8 o "‘
F4
p—4

10000

[(eaw) .51] 301

Figure 6.9 Master curves of storage modulus from experimental data. Specimens are in
serial loading conﬁguration with various volume fractions.

103

 

 

 

 

 

 

 

 

‘0. ‘12
N E
omo o
\‘TZQBO
¢ >gbom:
u.) MOWMO
XI 0| V
F
r
—N
O
N
I
V
9'— '
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:9 .I' 9E
DE |'|I|l v
5': ‘I'I'II 0°“
a)” It}: I:
H I Hlﬂ'l Q
can: I :3
“N OU‘
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W'*‘&:& 00
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N
IIIIIrfIIIIIrrﬁIIIIQ
°9 ‘9 <1; “I "" °Q ‘0. “I N. o
—‘v—4v—1v—4 COCO
9am

Figure 6.10 Master curves of tan5 from experimental data. Specimens are in parallel
loading configuration with various volume fractions.

104

cote -
59mm o
ome a
mmkb n
QOh o
OBS

 

 

 

 

 

Rania—352534

o- w- 3.

 

anﬁuomxm-
9.50 H832

NT

3.

2-

wT

om-

 

 

105

Figure 6.11 Master curves of tan8 from experimental data. Specimens are in serial
loading conﬁguration with various volume fractions.

Shift Factor

~10

L08 [3T]

 

 

'25 l l 7 I Y T f I T 7 1 1 r [ r 7 T T T 1

O 10 20 30 40 50 60 70 80 90 100
Temperature (°C)

Figure 6.12 Shift factor at the reference temperature of 25°C.

106

110 120

However, the tan5 peak of Material E in the specimens in serial loading
configuration was shifted toward a lower frequency compared with 100 percent of
Material E. For those specimens in parallel loading configuration, tan5 peak of Material
F shifted toward a higher frequency.

The area under tan5 peak in dynamic experimental data is usually considered as
the damping energy of the material. Apparently, Material F dominated the energy
absorption during the dynamic mechanical test of the specimens in serial loading
configuration regardless of their volume fractions. Similarly, the volume fractions of
Material E do not alter the energy absorption of the specimens in parallel loading
configuration.

6.4.2 Analytical Calculation

The rule of mixtures was applied to calculate the analytical solution of these two-
phase polymer specimens at various volume fractions based on the dynamic mechanical
testing data of 100 percent of Material E and F. The detailed derivation is shown in
Appendix D. The storage modulus, loss modulus, and tan8 of these two-phase polymer
specimens in serial and parallel loading conﬁguration could be calculated based on the
experimental data of 100% Materials E and F and their volume fractions from the

following equations:

EPvszEEI+VFEFv

 

EPvtszEEn+VFEFH (6.1)
tanap _ VEEEn+VFEFn
vEEEI+VFEFv

107

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

St E! F0
E,=VEE,+VFE,
E5 E5 E"
Sn En For
__E , =vE—E , +vF——E , (6.2)

E5 E5 13‘”

E" F"

v5 EE, +VF EF,

5" E E

tan5s 2:51: E50 EFI

VE . +VF—T

EE EF’

 

 

 

where E’, E", and tan6 represented the dynamic mechanical properties of two-phase
polymer specimens. The superscript “p” and “5” represent the specimens in parallel and
serial loading conﬁguration, respectively. The superscript “E” and “F” represent the
specimens of Materials E and F, respectively. VB and VF are the volume fraction of
Material E and F in these two-phase polymer specimens, respectively.

The storage modulus and tan6 for each specimen with different volume fractions
in parallel and serial loading conﬁgurations are calculated from those of 100 percent of
Materials E and F by using Equation 6.2 and 6.3 and the calculated results are plotted in
figures 6.13-6.16.

6.4.3 Discussion

The comparisons of the experimental data and the analytical calculation for each

specimen are shown in figures 6.17—6.30. These figures show that the analytical

calculation is in a good agreement with experimental data of storage modulus, loss
modulus, and tan8 in parallel loading conﬁguration as well as storage modulus in serial
loading conﬁguration. The rule of mixtures does not predict well the experimental data

of loss modulus and tan8 in a serial loading conﬁguration.

108

 

 

 

 

 

 

50/50
0 35 .6/64.4

I 67.4/32.6
~ 0/ 100

X 100/0

 

 

 

-8 -6 —4 -2

- 1 0
Log [Frequency (Hz)]

Master Curve
-Analytical

-12

-14

 

-16

 

—18

 

~20

 

 

-22

||llllll l [lllllll l llllllll l jlllllll l

8 8 53 "‘
8 v—d

v-(

1000

[(Baw) .3130'1

Figure 6.13 Master curves of storage modulus from analytical calculation based on
parallel loading conﬁguration and various volume fractions.

109

 

x 100/0
0 75/25
0 67/33
0 50/50
A 33/67
* 0/100

 

 

 

-6 —4 —2

-8
Log [Frequency(Hz)]

  
  
  

-10

 

Master Curve
-Analytical
-18 —16 —14 -12

-20

 

 

[1 ll [lilllll l VTlTTWT |

-22

00

1000

00
10 -

1

[manual 301

Figure 6.14 Master curves of storage modulus from analytical calculation based on serial
loading conﬁguration and various volume fractions.

110

v N am.

ooze .
v.vc\©.mm o

oﬂom
QNQVSo a

CBS x

 

 

 

 

 

HAum—Kcaoaaourﬂwed

w- w- w- 2-

 

I II.‘

.8???
3.50 .3632

3-

2-

E.

mm-

T

l FTl T

l

h!
p—a

l

“I
v—4

l

‘0.
v—q

 

l

°Q
V—1

°9‘°."Z“!°
coco

e;

9
Figure 6.15 Master curves of tan8 from analytical calculation based on parallel loading

conﬁguration and various volume fractions.

111

Raymoaoauaaawcd

v N o N- .v- o- w- OT NT 3. 3. MS.

85 - .
Sam 0 ﬂaw
85w 4 .. aw... x «as
8% a . -- x a.
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92: x .. - ma

a

m 332$

3.50 .5352

ON-

 

 

Figure 6.16 Master curves of tan8 from analytical calculation based on serial loading

configuration and various volume fractions.

112

 

 

 

 

 

 

 

 

 

   

 

 

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[(BdIAILHIBO'I

Figure 6.17 Comparison of experimental data and analytical calculation in master curve
of storage modulus. Specimen is in parallel loading with volume fraction
(RIF): 67.4/32.6.

113

v N

o

25.5 55.59:: wea—

N- v- c- w- 2. NT 3-

E-

 

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114

of tan5. Specimen is in parallel loading with volume fraction (E/F)

Figure 6.18 Comparison of experimental data and analytical calculation in master curve
67.4/32.6.

 

 

 

 

 

 

 

 

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p-q

[manual 30’1

Figure 6.19 Comparison of experimental data and analytical calculation in master curve
of storage modulus. Specimen is in parallel loading with volume fraction

(F/F)=50/50.

115

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v N o N- v- o- w- 2- NT 3- 2.. wT ON- NN-

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116

of tanS. Specimen is in parallel loading with volume fraction (E/F)=50/50.

Figure 6.20 Comparison of experimental data and analytical calculation in master curve

 

 

 

 

 

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[llTTlll f {”11le l lllllllT T [lllllll T
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v-i
[(Baw).a]30'1

Figure 6.21 Comparison of experimental data and analytical calculation in master curve

of storage modulus. Specimen is in parallel loading with volume fraction
(E/F)=35.6/64.4.

117

 

 

  

 

 

 

 

 

 

Rummy 55:03.3 we‘—
v N c N- v- o- w- 3. NT 3- 2- M:- oN- NN-
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118

of tan5. Specimen is in parallel loading with volume fraction

(E/F)=35.6/64.4.

Figure 6.22 Comparison of experimental data and analytical calculation in master curve

 

 

 

 

 

   

A
m a
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8 8 S "‘
a g r

[mam-a] 30’1

Figure 6.23 Comparison of experimental data and analytical calculation in master curve
of storage modulus. Specimen is in series loading with volume fraction

(E/F)=75/25.

119

 

 

9; a
m 5 "a
a O
l‘ .
v 'C go
In a. a? \ 8
m 0 ' i
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N °‘2 ©- ‘t o; H 09
v—l H H ﬂ o
9“”

Figure 6.24 Comparison of experimental data and analytical calculation in master curve
of mud. Specimen is in series loading with volume fraction (E/F)=75/25.

120

 

 

 

 

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Figure 6.25 Comparison of experimental data and analytical calculation in master curve
of storage modulus. Specimen is in series loading with volume fraction

(E/F)=67/ 33 .

121

I
Serial (67/33)
0 Expenmental
I Analytic 3.1

100/0
x: 0/100

V “" “KO O'QO 3 O A“
‘r-z‘ x; ,. 0
is»; 3&8 8

or 0°! yﬁogsgo‘lgaosg g .

 

L08 [Frequency (Hz)]

 

 

91191

Figure 6.26 Comparison of experimental data and analytical calculation in master curve
of tan8. Specimen is in series loading with volume fraction (FJF)=67/33.

122

 

 

 

 

 

   

 

 

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Figure 6.27 Comparison of experimental data and analytical calculation in master curve
of storage modulus. Specimen is in series loading with volume fraction

(E/F)=50/50.

123

 

 

 

 

 

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of tano. Specimen is in series loading with volume fraction (E/F)

Figure 6.28 Comparison of experimental data and analytical calculation in master curve

124

 

 

 

 

 

 

 

 

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Figure 6.29 Comparison of experimental data and analytical calculation in master curve
of storage modulus. Specimen is in series loading with volume fraction

(E/F)=33/67.

125

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Figure 6.30 Comparison of experimental data and analytical calculation in master curve
of tan8. Specimen is in series loading with volume fraction (E/F)=33/67.

126

According to the strain measurement by the SEM moiré method, each component
of the specimen in serial loading conﬁguration does not undergo a constant strain
experiment even though the whole specimen does. Therefore, when calculating the
analytical solution for specimens in serial loading conﬁguration, one needs to modify the
rule of mixtures. Based on the previous observation from the SEM moiré method, a
relaxation function must employ in the analytical calculation.

In serial loading experiments the peak position of tan8 of Material E shifts toward
a lower frequency compared with that of 100 percent of Material F, which implies the
viscoelastic response of Material E in two-phase polymer specimen of serial loading
configuration is delayed. On the other hand, the viscoelastic response of Material F in

the specimens with parallel loading conﬁguration is accelerated.

6.5 CONCLUSIONS

The SEM moiré methods have been performed in measuring the deformation of
carbon ﬁber reinforced composites. Based on carbonaceous grating and monitor viewing
techniques (CM), a reference grating (either 2778 or 2667 lines/mm) interfered with a
carbonaceous grating with a frequency of 277 8 lines/mm. The angles between these two
gratings were calculated from Equation 6.1 based on the measured moiré fringe angle (4))
and moiré fringe pitch (pf) from observed moiré fringe patterns. A comparison of the
angles measured from the SEM images taken at different angle rotations with the
calculated angles from the SEM moiré CM method proves this SEM moiré CM method
to be feasible. Another SEM moiré method, carbonaceous grating and total imaging

(CT), also presented rotation angle measurements on composite specimens and the results

127

were promising as shown in Figure 6.5.

The second application of the SEM moiré CM method was to measure the local
strain of two-phase epoxy specimen in serial loading conﬁguration during its stress
relaxation experiment. In addition to the SEM moiré CM method, the local strain was
also measured based on the SEM images of interface shifting. The measurements from
these two methods were in good agreement. The shifting of the interface resulted in the
changes of local strain on both Material E and F during the stress relaxation experiment,
which kept the global strain constant. Some additional energy loss was expected in this
two-phase polymer specimen compared with the regular 100 percent single-phase
materials.

To examine this hypothesis, specimens in serial and parallel loading
conﬁgurations at different volume fractions were prepared to run the frequency sweep of
dynamic mechanical test at various temperatures. The experimental data were compared
with the analytical calculation by the rule of mixtures. The analytical calculation in
parallel loading conﬁguration predicted the experimental data very well as shown in
ﬁgures 6.17, 6.19, and 6.21. On the other hand, the experimental data from serial loading
conﬁguration was not well predicted by the rule of mixtures especially in loss modulus
and tanS. Therefore, weight functions accounting for additional energy loss due to the
mismatch of viscoelastic response between Material E and F were required to employ

while ﬁtting the experimental data of specimens in serial loading conﬁguration.

128

Chapter 7
CONCLUSIONS

Based on the concept of the SEM moire, the AFM moiré method was developed.
The viewing scanner of AFM as a reference grating interfered with the lithographic
grating as a specimen grating resulting in moiré fringes observed in AFM. Angle rotation
of two grating systems was performed to verify the feasibility of the AFM moire method.
The advantages of the AFM moire method compared to the SEM moire method are
convenience and economy. The SEM moiré method requires a vacuum environment as
well as a conductive layer to prevent charge build-up on non-conductive specimens and
to avoid possible contamination to the electron gun. However, because AFM is a surface
topographic technique and the target specimen is coated with lithographic grating, the
AFM moiré method cannot provide microscopic measurement simultaneously with
microscopic observation as can the SEM moiré method.

To simplify the grating fabrication technique and to improve the AFM moire
method, the carbonaceous grating technique was developed. Based on the contamination
in SEM chamber and testing specimens, direct electron beam deposition is utilized to
deposit carbonaceous grating on specimen surface as a specimen grating. This new
technique reduces the multiple procedures of coating and developing in lithographic
grating technique. Since the moiré fringe formation depends not only on the topographic
contrast but also on the voltage contrast for this technique, the carbonaceous grating can
be as thin as 4 nm. With the advantage of this reduced thickness, the AFM moiré method
is able to provide microscopic measurement and observation simultaneously. Compared

with the 100 nm thickness of lithographic grating, carbonaceous grating can reduce the

129

reinforcement effect to a minimum as well.

After developing the carbonaceous grating technique and the total imaging
technique, there then exist two grating-casting techniques and three fringe-viewing
techniques for the SEM moire method. With the combination of these two groups, a total
of six SEM moiré methods are available. Besides the SEM moiré LM method, which is
commonly used by many researchers, another ﬁve new SEM moire methods are
introduced. Based on these ﬁve new SEM moiré methods, the experimental procedures
of preparing specimen grating become easier and the sensitivity of measuring
deformation increases. The sensitivity of the lithographic grating and total imaging
method (LT), as well as the carbonaceous grating and total imaging method (CT), truly
depends on the frequency of specimen grating, which can be very high.

With these new developed techniques, the SEM moiré methods are applied to
measure the deformation of carbon ﬁber reinforced composites and two-phase polymers.
For carbon ﬁber reinforced composites, the carbonaceous grating and monitor viewing
method (CM) as well as the carbonaceous grating and total imaging method (CT) are
used to measure the angle between two gratings. The experimental measurements are in
a good agreement with the analytical calculation.

For two-phase polymers, the local strain is measured by the SEM moiré CM
method during the stress relaxation experiment. The interface shifting of the two-phase
polymer specimen is observed under the SEM and the local strain is measured from the
SEM images. The measurements from the moiré fringe patterns and the SEM images
agree that the strain in each phase is not constant. Accordingly, the method to analyze

the viscoelastic response of the two-phase polymer specimen requires Boltzmann

130

superposition integral instead of quasi-elastic analysis. Based on the observation from
the SEM moiré CM method, the dynamic mechanical tests are conducted to investigate
the viscoelastic response of two-phase polymers. The analytical solution is derived based
on the rule of mixtures. The rule of mixtures predicts the dynamic mechanical testing
data of the specimens in parallel loading conﬁguration. However, the rule of mixtures
does not predict the dynamic mechanical testing data of specimens in serial loading
conﬁguration. A weight function has to be employed to allow the analytical solution to

ﬁt the experimental data in serial loading conﬁguration.

131

APPENDICES

132

APPENDIX A

SEM SETTING PARAMETERS FOR ELECTRON BEAM
LITHOGRAPHY

A CamScan 44FE scanning electron microscope was used in this study. The
grating technique was based on electron beam lithography and was similar to the method
presented by Attwood and Hazzledine [37]. It utilized a built-in photograph scanner with
a scanning rate of 1250 lines/frame to perform a single scanning on an epoxy specimen
coated with gold and PMMA. In order to achieve the desired quantity and quality for the
moiré grating, the following SEM parameters were used: an acceleration voltage of 20
keV, a beam aperture of 50 pm, a spot size of 9 and a working distance of 20 mm. A
potentiometer designated as C 1 was set to 6.295 mV, resulting in 1.72 mA and 0.93 mA
for C2 and C3 readings, respectively, to achieve an electron beam current of 1.5 nA.

The alignment and the focus of the electron beam were checked at a location
away from the area of interest before performing the lithographic scanning. The electron
beam was then blocked by a beam stopper before being relocated to the desired area for
lithography. The speciﬁc magniﬁcation factor 360 was calculated from Equation (5.1)
for the desired grating frequency, i.e. 5000 lines/mm. Based on the magniﬁcation factor,
an exposure time of 21 seconds per scanning frame was found to give the right electron

dosage.

133

APPENDIX B

COMPARISONS OF VARIOUS SEM MOIRE METHODS BASED ON
SPECIMEN GRATING OF 5000 LINES/MM

 

 

 

 

 

 

 

 

 

 

SEM Moire LM LP LT CM CP CT
. scfnmng Rate 1250 1250 1250 500 500 500
Specrmen (lines/frame)
Grating Magniﬁcation
(Initial and Factor 360 360 360 900 900 900
Deformed) Scanning Area 333 x 333 x 333 x 133 x 133 x 133 x
(um x mm) 250 250 250 100 100 100
5‘3“” Rate 500 1250 1250 500 1250 500
Reference (lines/frame)
Grating or Magniﬁcation 900 360 6000* 900 360 6000*
Total Factor
Imaging Viewing Area 133 x 333 x 20 x 133 x 333 x 20 x
(um x pm) 100 250 15* 100 250 15*
M‘""““’“ 5m“ for 0.2% 0.08% 0.02%“ 0.2% 0.08% 0.02%”

One Moire Fringe

 

 

 

 

 

 

 

* based on a viewing magniﬁcation factor of 6000

# based on 5000 lines/mm

134

 

APPENDIX C

LOCAL STRAIN CALCULATION OF MATERIAL E AND F IN
TWO-PHASE POLYMER SPECIMEN

Here are the Symbols that used in the derivation:
a: stress;
a strain;
V: volume fraction
J: creep compliance of the material
E: relaxation modulus of the material
L: Laplace transformation
superscript E and F: Material E and F
superscript p and 5: parallel and serial loading conﬁguration
subscript 0: the initial magnitude

aE(t)=oF(t)

55 =vEsE(:)+stF(:)

E F
r E (18 t p (18
E t-r —dr= E t—r —dr
IO ( ) d1 IO ( ) d1

 

 

 

s daE doF
so=v51515(r-r) d1 dr+VF151F(z—r) d1 dr
E E
EE(s)eE(s)=EF(s)8F(s)=>£F(s)=E (‘28 (S)
E (s)

8_0=VEJE(s)aE(s)+VFJF(s)0F(S)
S
=VEEE(s)+VF£F(S)

E E
=VE8E(S)+VFE (8)8 (S)
E"(s)

 

E
=(VE+VF£F(—S)-)35(s)
E (s)

EF(s>
VEEF(s)+VFEE(s)
85m = L'lreE(s)]

 

ES
55(5) =._0_*
s

135

APPENDIX D

ANALYTICAL SOLUTIONS OF TWO-PHASE POLYMERS BASED
ON RULE OF MIXTURE

Here are the Symbols that used in the derivation:

L: length Al: displacement 8: strain
P: force A: area 6: stress
V: volume fraction

E', E ', E ": complex, storage, and loss modulus of the material
superscript E and F: Material E and F

superscript p and 3: parallel and serial loading conﬁguration
subscript 0: the initial magnitude

For Material E,

O. E=(I) 0.0 OEeI(a)I+6E )

 

 

 

 

Ei(air+6E )
. a t o e _a E ___Eo ..
EB“ =EE'+zEE"= E0: 0 8E eiax 2e e'5 0 —(coso'E +rsm65)
8 EU) eoe 80 £65
E E0
0 E
EE'=—gcos65=Egcos55=>E§= E
80 c086
E Eu
0 . . E
EE"=—g,srnr‘5E =E6: srn5E =>E63 = E
80 sin5

For Material F,
8 F=(I) age “DI

0. F—(t) 0.0 Fei(wt+6F )

 

 

 

EF*=EF'+iEF"= F F , F=—;:—e' 00 F(cosc3F +isin6F)
e (t)= 80 e‘“ 80 =£0F
F F.
a E
EF'=—OTcode=Egcos6F=¢E67= F
80 c056

F ”F F F F F EF"
E "=—2,sin6 =E0 sin5 =EO = F
80 sin6

 

136

For Material E and F in parallel conﬁguration,

16:15:15. AIPe iaszlEe iaszlFe I601
sgeim=egem=sFeW, spa): e E0): e E0)

P0E+P0E =P0P ,00 EAE+aE AF=06DAP, VEa§+Van E: 00”,

0P(t)=O.Pei(wt+6P) =(Vsog +VF067)ei(wt+5P)

—VEO'6:e i(ax+65+6P—6E) +VFog‘ei(an+6F+6P—5F)

oE(t)=onE(z)e‘(5P‘EE) +VEaE(t)e‘(EP‘5F)

p*_ 0 E0) _VEaE(:)e"(5P’5E) VEoE(r)e’(5P‘5F)
e E0) 5E0) + 5%)

:VE[EE *ei(6 P—aE)]+VF[EF*ei(6P-6F)]

E

 

 

EP*e—i6P =VE[EE*e-iaE]+VF[EF*e-i6EL
(EP'+iEP")(cos6P -isin6”)=VE(EE'+iEE")(cos6E —ssin6E)
+VE(EE'+iEE")(cos6E —isin5E)
EP'coerP +EP"sin6P =VE(EE'cosc‘5E +EE"sin5E)
+VE(EE'cos5E +EE"sin6E)
EP"c035P —EP'sin5P =VE(EE"cos§E —EE'sin5E)
+VE(EE"cos5E —EE'sin6E)
EP'=VEEE'+VFEF'
EPII=VEEEII+VFEFII
map =VEEE"+VEEE"

VEEEwVEEE'

 

137

For Material E and F in serial loading conﬁguration,

POE =P0E =POS,a(E =05” =05

15 :1515 Alsei‘“ =A1Ee‘w‘ +A1Ee‘w‘,

E F s Ei(c:+<:s s(ax+55 «(was )

0'0 =00 =00 2058 )=O'0Fe )=O'Oe

. S E . s F
o s_(t) Use «(was )_ aEmezw -5 ):0F(t)el(5 —6 )

o S(t)=VE a E(t)+VFaF(t)

ES 155* EF
1 _ VE + VE : 1 _ VE + W”
Es" EE*ei(¢SS-6E) EF*ei(65—6F) ES [35* E“

 

* ,

 

 

 

 

 

 

 

 

 

 

 

 

(ES'—iES")(cos55 + isino's) =VE (EE'-iEE")(cos6E + isin6E)

ES FE

 

 

 

 

VE (EE'—iEE")(cos6E +isin6E)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EF
ES'cos5S +Es"sin6$ -VE EE'cosdE +EE"sinc‘)‘E +VF EF'cosb‘F +EF"sin6F
* * *

ES EE FE
Es'srnSS —ES"cos55 -VE EE'sinr‘SE--El'g"c036E +Vp EF'sino'F -EF"c036F
ES EE FE
SI El FI S" E" F"

E
E*=VE +VFE*,E*=VEE*+VFE*
ES FE EE ES EE FE
E" F"
VE E a. +VF_E___
5.. EE EF
S E
tam; s 7 f E F
E VE E * +VE E *
EE EF

 

 

 

 

138

E/F-p and EfF-s in serial:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CI P! S!
—E . =VP—E . +Vs—E _
EC EP ES
EC" :VP EP" VS ES"
EC. El’. E5.
P" Sn
V” E ‘ +VS E ‘
P S
tanac = EC" = E E
EC! E1). E5!
VP—7+Vs 5*
E E
E/F-p and E/F-s in parallel:

ECvszEPI+VSES!
EC"=VPEP"+VSES"
P P" 5 Sn
tantsc =VpEp+V5E5
V E '+V E '

 

 

139

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