Embed Size (px)
Citation preview
University of Massachusetts Amherst University of Massachusetts Amherst
ScholarWorks@UMass Amherst ScholarWorks@UMass Amherst
Doctoral Dissertations 1896 - February 2014
1-1-1998
Pressure-volume-temperature and wave propagation studies of Pressure-volume-temperature and wave propagation studies of
polyimide films. polyimide films.
Michael John Chen University of Massachusetts Amherst
Follow this and additional works at: https://scholarworks.umass.edu/dissertations_1
Recommended Citation Recommended Citation Chen, Michael John, "Pressure-volume-temperature and wave propagation studies of polyimide films." (1998). Doctoral Dissertations 1896 - February 2014. 974. https://doi.org/10.7275/nff3-xy23 https://scholarworks.umass.edu/dissertations_1/974
This Open Access Dissertation is brought to you for free and open access by ScholarWorks@UMass Amherst. It has been accepted for inclusion in Doctoral Dissertations 1896 - February 2014 by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contact [email protected].
PRESSURE-VOLUME-TEMPERATURE AND WAVE PROPAGATIONSTUDIES OF POLYIMIDE FILMS
A Dissertation Presented
by
MICHAEL JOHN CHEN
Submitted to the Graduate School of the
University of Massachusetts Amherst in partial fulfillment
of the requirements for the degree of
DOCTOR OF PHILOSOPHY
February 1998
Polymer Science and Engineering Department
© Copyright by Michael John Chen 1998
All Rights Reserved
PRESSURE-VOLUME-TEMPERATURE AND WAVE PROPAGATIONSTUDIES OF POLYIMIDE FILMS
A Dissertation Presented
by
MICHAEL JOHN CHEN
Approved as to style and content by
Ricliani J. Farris, Cliair
Alan J. Lesser, Member
Thomas J. Lardner,-MenSCT~
Richard J. Farris, Department Head
Polymer Science and Engineering Department
ACKNOWLEDGEMENTS
I have had a truly memorable five years at the University of Massachusetts at
Amherst. Back in the fall of 1992, 1 would never have imagined all the professional and
personal experiences that would occur in my life from then until now.
First of all, I was fortunate to have Dr. Richard Farris as my advisor. I am
grateful for his guidance and patience throughout my graduate studies. Dr. Farris'
creativity and ability to generate novel ideas are truly his strengths as a mentor. His
hands-off style of managing his research group and his approach in dealing with people
in industry taught me much. I thank him tremendously for giving me the opportunity to
learn from him and his research group. In addition, I wish to thank my committee
members. Dr. Alan Lesser and Dr. Thomas Lardner, for their support and advice
throughout the years. Their review ofmy work through the various stages ofmy studies
was instrumental to the final completion of my thesis.
The research funded by NSF Contract ECS 9202696#001 was an exceptional
first project to participate on. The collaborations with Dr. Paivikki Buchwalter at IBM,
Dr. Brian Auman at DuPont, and Dr. Todd Gross and Dr. Mike Gosz at UNH were a
great experience. Beyond question, I must thank Kapil Sheth for our successful
partnership on this project and for making all of our conference travels a fun time. Many
thanks also to Dr. Paul ZoUer and Liebmann Optical for their help with the PVT
Apparatus over the years. Furthermore, I would like to acknowledge Dr. Alan Waddon
for his assistance on the x-ray studies of the polyimides. Recognition should also be
made to the PSE support staff which includes Joanne Purdy, Eileen Besse, Carol Moro,
iv
Norm Page, and John Domian for their assistance with my research and non-technical
matters. Lastly, I wish to acknowledge MRSEC and the Hewlett-Packard Grant
#31891.1 for their equipment and financial support.
Back when I was looking for a research group to join, I heard a comment that
not only is Dr. Farris' group known for good research, but they have the nicest and
friendliest people in the department. Much appreciation goes to the many past and
present Farris group members who have helped me. I would also like to recognize
members of Dr. Lesser's group and past members of Dr. Karasz's group. In addition, I
must thank my classmates of 1992, namely Darrin Pochan, Wendy Petka, Bert Chien,
Meredith White, Darius Deak, and Shalabh Tandon. We were definitely a unique group
who shared many a good times together! All the tennis matches, rollerblading
adventures, and softball games will always be part of the memorable experiences ofmy
graduate school days.
I would like to dedicate my dissertafion to my entire family. To my mother,
father, and brother for your support through my college and graduate school studies, I
thank you very much. From the bottom ofmy heart, I must also thank my wife, Sophie,
for her loving support and encouragement. Back in 1992, 1 would not have foreseen that
in 1997, 1 would be marrying in three different locafions, finishing my Ph.D., and
starting a new job! Without a doubt, my graduate degree is a great personal achievement
to me, however it would have been a much tougher accomplishment without the support
ofmy family.
V
ABSTRACT
PRESSURE-VOLUME-TEMPERATURE AND WAVE PROPAGATIONSTUDIES OF POLYIMIDE FILMS
FEBRUARY 1998
MICHAEL JOHN CHEN, B.S., NORTHWESTERN UNIVERSITY
M.S., UNIVERSITY OF MASSACHUSETTS AMHERST
Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST
Directed by: Professor Richard J. Farris
This dissertation presents an investigation of the mechanical, thermal, and
physical properties of polyimide coatings and films. In the electronics industry,
polyimide coatings are commonly found as dielectric interlayers for high density multi-
chip modules. As a film, polyimides are used as flexible printed circuit boards.
Therefore, complete understanding of their properties can be important for material
selection and reliability prediction. In addition, better comprehension of their processing
can aid in improving the properties of the polyimides.
Orthotropic linear elasticity theory has been used to characterize several thin
polyimides including novel fluorinated polyimides. Using a commercially available
Pressure-Volume-Temperature (PVT) Apparatus, the bulk compressibility and
volumetric thermal expansion of the polyimides were measured. In combination with
other techniques such as vibrational holographic interferometry, high pressure gas
dilatometry, tensile testing, and thermomechanical analyzer, the out-of-plane Young's
Modulus and out-of-plane coefficient of thermal expansion were determined. As a
result, knowledge of the in-plane and out-of-plane elasticity coefficients and coefficients
vi
of thermal expansion can help in designing finite element models that predict the
reliability of complex microelectronic devices. Similar characterization studies were
done on poly(ethylene terephthalate) and bisphenol A polycarbonate.
From the initial PVT experiments on polyimides, irreversible densification was
observed for some thermally cured polyimide films which were subjected to high
pressures and temperatures. Using optical microscopy, wide-angle x-ray diffraction, and
density measurements, studies were done to probe the changes associated with this
densification behavior. The findings suggest that polyimides used as dielectric
interlayers in multi-chip modules may crystallize under highly constrained situations
and high temperatures.
Tenter frame processing is typically used to produce highly oriented polymer
films. However, past studies have revealed that better quality polyimide films may be
achieved by controlling its stress state during the tentering process. Therefore, the
mathematics are detailed for measuring the complete state of stress in a polyimide film
using wave propagation theory. Preliminary experimental research has involved a
laboratory scale setup consisting of a means for inducing wavefront propagation, non-
contact fiber-optic displacement sensors for detecting the wavefront, and an
oscilloscope and computer for collecting and interpreting data.
vii
TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS
ABSTRACT ^
LIST OF TABLESA.1
LIST OF FIGURES^ii
Chapter
1. INTRODUCTION AND BACKGROUND 1
Introduction1
Dissertation Overview 1
Background 4
Development of Stresses in Polymer Coatings 4
Overview of Polyimides in the Electronics Industry 6
References U
2. MATERIALS 13
Introduction 13
Polyimides 13
Thermogravimetric Analysis (TGA) 20
Density Measurements 20
Attenuated Total Reflection (ATR) Fourier Transfomi Infrared (FTIR)
Spectroscopy 21
Dynamic Mechanical Thermal Analysis (DMTA) 23
Poly(ethylene terephthalate) (PET) 24
Differential Scanning Calorimetry (DSC) 25
Bisphenol A Polycarbonate 26
Differential Scanning Calorimetry (DSC) 26
viii
3. DETERMINATION OF OUT-OF-PLANE PROPERTIES OF POLYIMIDECOATINGS AND FILMS 30
Introduction 30Orthotropic Elasticity Theory 33Experimental Techniques 35
Vibrational Holographic Interferometry 36High Pressure Gas Dilatometry 44Pressure-Volume-Temperature (PVT) Apparatus 46
Results and Discussion 50
Vibrational Holographic Interferometry 50High Pressure Gas Dilatometry 52
Tensile Testing 55
Thermomechanical Analysis (TMA) 58
Pressure-Volume-Temperature (PVT) Apparatus 60
Conclusions 75
References 76
4. PRESSURE-INDUCED CRYSTALLIZATION IN POLYIMIDES 81
Introduction 81
Experimental 84
X-ray Photoelectron Spectroscopy (XPS) 84
Optical Microscopy 85
Wide Angle X-ray Diffraction (WAXD) 85
Density Measurements 85
Results and Discussion 86
Isobaric PVT Experiment 86
X-ray Photoelectron Spectroscopy (XPS) 87
Optical Microscopy 90
Wide Angle X-ray Diffraction (WAXD) 90
Density Measurements 92
Conclusions 93
References 95
ix
5. STRESS MEASUREMENT IN POLYIMIDE FILMS BY WAVEPROPAGATION TECHNIQUES 97
Introduction
Theory IIIII!IIII"I"lOOExperimental
Striker Mechanism jq5Sensors for Detection of Wave Propagation 106Collection and Analysis of Data 109
Results and Discussion
Conclusionsj 15
References
6. SUMMARY AND FUTURE WORK 118
Summary1 18
Future Work 120
References 123
APPENDIX: LOTUS 1-2-3 MACRO PROGRAMS USED FOR ANALYZINGTHE PVT DATA 124
BIBLIOGRAPHY 129
X
LIST OF TABLES
2.1 Spin speeds used to obtain polyimide coatings of 10 |im in thickness 14
2.2 Copolymer composition and molecular weights of the fluorinated
polyimides j5
2.3 Summary ofTGA results for polyimides 20
2.4 Density of polyimides 2
1
2.5 Summary ofDSC results for Kodak PET 25
3.1 In-plane Poisson's ratios for thin polymer films 52
3.2 Summary of high pressure gas dilatometry on thin polymer films 54
3.3 Out-of-plane Poisson's ratios for thin polymer films 54
3.4 Young's Moduli for thin polymer films 56
3.5 In-plane CTEs of thin polymer films 59
3.6 Summary ofPVT results on polyimides: Determination of out-of-plane
CTE and out-of-plane Young's Modulus 69
3.7 Comparison on the volumetric thermal expansion of polyimides averaged
over different temperature ranges 72
3.8 Coefficients for the Tait equation 73
3.9 Summary ofPVT results on Kodak PET and GE polycarbonate:
Determination of out-of-plane CTE 75
xi
LIST OF FIGURES
Page
1 . 1 Preparation ofPMDA-ODA polyimide by the thermal cure route 8
1 .2 Preparation ofPMDA-ODA polyimide by the chemical cure route 8
2.1 Chemical structures of dianhydrides and diamines used to prepare
polyimides j5
2.2 Chemical structure ofPMDA-ODA 17
2.3 Chemical structure of BPDA-PPD1
7
2.4 Chemical structure of FPI-135 17
2.5 Chemical structure of Upilex®R 18
2.6 Chemical structure of Upilex® S 18
2.7 TGA traces of selected polyimides 19
2.8 ATR FTIR spectra ofPMDA-ODA precursor and cured polyimides 22
2.9 DMTA trace of Kapton® 200H 23
2.10 Chemical structure ofPET 24
2. 1 1 DSC thermogram of Kodak PET 25
2.12 Chemical structure of bisphenol A polycarbonate 26
2. 1 3 DSC thermogram of GE polycarbonate 26
3.1 Generalized Hooke's Law for a linearly elastic orthotropic material 34
3.2 Components of stress tensor for a volume element of film 35
3.3 Schematic of vibrational holographic interferometry 36
3.4 Polymer coating as a 2D constrained circular membrane and ID constrained
thin ribbon 38
xii
3.5 Representative modal vibration patterns 39
3 .6 Splitting behavior of the n,i = 1 , 1 mode of vibration for Kapton® 200H 40
3.7 Polymer coating as a 2D constrained square membrane and ID constrainedthin ribbon 4j
3.8 Schematic of high pressure gas dilatometry 44
3.9 Schematic of the Gnomix Inc. PVT Apparatus 47
3.10 Determination of machine and transverse directions and 1 " principal
direction (0 clockwise from the machine direction) for a standard sheet ofpolymer film 51
3. 11 High pressure gas dilatometry on a Kapton® 200H sample cut in the 1"
principal direction 53
3.12 Tensile testing of selected polyimides 57
3.13 TMA on an Upilex® R sample cut in the 2"** principal direction 58
3.14 Isothermal mercury calibration 62
3.15 Isobaric mercury calibration at 50 MPa 62
3.16 Volumetric thermal expansion as a function of pressure for aluminum 63
3.17 Isothermal PVT run on PMDA-ODA 65
3.18 Bulk compressibility as a function of temperature for PMDA-ODA 65
3.19 Isothermal PVT run on Kapton® 200H 66
3.20 Bulk compressibihty as a function of temperature for Kapton® 50H 66
3.21 Isothermal PVT run on FPI-1 37M 67
3.22 Bulk compressibility as a function of temperature for FPI-46 67
3 .23 Isobaric PVT run at 1 0 MPa on PMDA-ODA 68
3.24 Isobaric PVT run at 10 MPa on BPDA-PPD 68
xiii
3.25 Isothermal PVT run on Kodak PET 74
3.26 Isothermal PVT run on GE polycarbonate 74
4.1 Isothermal PVT experiment on PMDA-ODA film under high pressures and
temperatures
4.2 Densification behavior in 10 ^m spin coated PMDA-ODA film under aconstant hydrostatic pressure of 100 MPa 86
4.3 XPS ofPMDA-ODA film (PVT treated): 15^ take-off angle 88
4.4 XPS ofPMDA-ODA film (PVT treated): 75° take-off angle 88
4.5 PMDA-ODA film (Original): 50X, crossed polarizers, ?i - 530 nmwavelength plate 89
4.6 PMDA-ODA film (PVT treated): 50X, crossed polarizers 89
4.7 WAXD on PMDA-ODA films 91
5.1 A typical tenter frame line for thermoplastics 97
5.2 Components of stress tensor for a volume element of film 100
5.3 Initial response of a uniformly tensioned membrane due to a single pulsed
disturbance at the center 102
5.4 Non-uniformly tensioned membrane with single pulsed disturbance at the
origin 105
5.5 Schematic of MTI-2000 Fotonic™ Sensor probe 109
5.6 Voltage output versus displacement 109
5.7 Experimental setup 110
5.8 Ball drop experiment 1 12
5.9 Wavefi*ont propagation initiated by a dropped ball 112
5.10 Using a spark plug to induce a single pulse disturbance 113
5.11 Schematic of the electrical wiring for the spark plug 1 13
xiv
5.12 Using a solenoid value to shoot a burst of water
XV
CHAPTER 1
INTRODUCTION AND BACKGROUND
Introduction
Polyimides are an important class of polymers which have found numerous
applications in the automotive, aerospace, and wire and cable insulation industries.
Because of their excellent dimensional stability, thermal stability, chemical resistance,
and dielectric properties, polyimide coatings and films are greatly superior than other
polymer materials in harsh and challenging environments. Therefore, full
comprehension of their mechanical, thermal, and physical properties are important for
determining their performance and reliability.
Dissertation Overview
Chapter 1 presents a general overview of the thesis research. The uses of
polymer coatings are discussed, and the common mechanisms of coating failure are
reviewed. Further, a summary of polyimides is given, and the two different routes of
processing are explained. Lastly, the applications of polyimide materials in the
electronics industry are highlighted.
Some common thermal and physical properties of all the materials studied are
described in Chapter 2. The thermally cured polyimides and their preparation
procedures are detailed. Commercial polyimide films have also been examined for
1
comparison purposes. Further, thermogravimetric analysis (TGA), density
measurements, and Fourier transform infrared (FTIR) spectroscopy were used to
characterize the polyimides. For commercial films of poly(ethylene terephthalate) (PET)
and bisphenol A polycarbonate, density measurements and differential scanning
calorimetry (DSC) were employed.
In Chapter 3, the difficult to measure out-of-plane Young's Modulus and out-of-
plane coefficient of thermal expansion (CTE) were determined for several polyimides
including novel fluorinated polyimides using a Gnomix Inc. Pressure-Volume-
Temperature (PVT) Apparatus in combination with other techniques such as vibrational
holographic interferometry, high pressure gas dilatometry, tensile testing, and
thermomechanical analysis (TMA). Both commercial polyimide films and thermally
cured polyimide coatings that were removed from their substrates as free-standing films
were examined. Using classical linear elasticity theory for an orthotropic material, the
bulk compressibility is shown to be related to the out-of-plane Young's Modulus. A
similar relationship is also made between the volumetric thermal expansion and the out-
of-plane CTE. As a result, detailed descriptions are given concerning the techniques
required to fully characterize anisotropic polymer films by their in-plane and out-of-
plane orthotropic elasticity coefficients and CTEs. In order to predict the reliability of
polyimides in multi-chip module (MCM) packages, it is essential to know all of these
properties for good finite element modeling in complex geometries. Similar techniques
for measuring the out-of-plane properties of polyimide films were also used on
commercial films ofPET and bisphenol A polycarbonate.
2
Chapter 4 reveals the effect of high hydrostatic stresses and temperatures on the
irreversible densification behavior in typically amorphous polyimides. This study was
developed as an offshoot of the initial PVT research on several thermally cured
polyimides subjected to high pressures up to 200 MPa and temperatures up to 315°C.
Using optical microscopy, density measurements, and wide-angle x-ray diffraction
(WAXD), an investigation of pressure-induced crystallization was performed. For
polyimides used in multilayered MCMs, this discovery is noteworthy since similar
temperature and stress conditions may exist in highly constrained situations from the
effects of the other polymer, metal, and/or ceramic layers. Therefore, these significant
changes seen in polyimides as a result of high pressures and temperatures may elucidate
the cause of dielectric interlayer cracking in MCMs.
A unique method based on classical wave propagation theory is presented in
Chapter 5 for measuring the complete state of stress in a polymer film produced on
tenter frames. Tenter frame processing permits fast continuous production of highly
oriented polymer films such as polypropylene, polyethylene, polyamide, polystyrene,
and polyimide. In the electronics industry, polyimide and PET films are often used as
flexible printed circuit boards. However, major problems such as warping, irreversible
shrinkage, and large spatial variations in properties across the width of the film are
usually found. Previous stress analyses of tentering frames by Jennings and Farris have
shown that strong processing gradients in the production line produce large in-plane
shear stresses which vary across the width of the line. [1] In turn, this results in poor
quality films in which the principal stresses and the principal directions of stress also
vary across the width of the film line. Therefore, the research goal of this work is to
3
develop the basic foundation for identifying and controlling the state of stress of a
polymer film during processing. Using wave propagation theory, experimental work
entailed a large stationary polymer membrane and the study of the physical wavefront
velocities using an array of non-contact fiber-optic displacement sensors. As a result,
better control of the stress state could lead to higher quality polyimide and PET films
with uniform physical properties across the width of the film.
In closing. Chapter 6 summarizes the research work of the entire thesis.
Discussions for future paths of study are offered.
Background
Development of Stresses in Polvmer Coatings
Polymer coatings are utilized in many significant applications such as sealants
for woods, decorative paint finishes for walls, protective coatings for corrosion
prevention, and dielectric insulating layers for high density integrated circuits. In the
printing industry, polymer coafings are commonly applied to printed paperboards to
provide cosmetic gloss and abrasion resistance. In the food science industry, polymer
coatings are important for preventing food spoilage. For photographic applications,
coatings are used to filter light in color films and as colloid protectors for the silver
halide crystals. Therefore, the reliability and performance of polymer coatings require a
careful understanding of their mechanical, thermal, and physical properties.
The common failures in polymer coatings, which may be described as cracking
and delamination, are directly attributed to the state of stress in the coating. [2] The
residual stresses of a coating are a consequence of the material properties of the coating
4
and the subjected processing conditions. Failure due to cracking happens when the
tensile stress in the plane of the coating is greater than the ultimate tensile strength of
the material. Delamination represents the failure that occurs when the elastic energy
stored in the coating is greater than the adhesion energy. Furthermore, a form of
delamination called blistering can occur when the coating is under compressive stresses.
There exists several internal mechanisms which cause coating failure. [2-4] For
example, when a typical polymer coating on a steel substrate is cooled from a high
temperature to room temperature, the coating desires to shrink much more than the
metal substrate. This results in a coating in tension with respect to the substrate because
the substrate prevents the coating from shrinking. There is simply a mismatch in the
coefficient of thermal expansion between the substrate and coating. A second
mechanism for coating failure is the mismatch in swelling coefficients between the
substrate and coating. Because of differences in the humidity expansion coefficient, the
development of strong internal stresses causes "curling" in the photographic bilayer
system of gelatin and cellulose acetate or PET. [5] Another common mechanism is the
volume change as a result of curing and/or solvent loss that may lead to stresses in the
plane of the polymer coating. If solvent is removed from a two dimensionally
constrained coating, the in-plane shrinkage of the coating on a rigid substrate produces
tensile stresses. In this particular case, the volumetric change can only occur in the out-
of-plane direction. Lastly, physical aging may also play a role. This relaxation or
rearrangement of molecules over time can lead to strong internal stresses and eventual
failure in the coating.
5
Overview of Polvimides in the Rier.tronics InHnc^tr^/
Polyimides form a class of polymers which are well known for their high
thermal stability, excellent mechanical properties, outstanding electrical properties, low
moisture absorption, good abrasion resistance, and strong chemical resistance against
organic solvents and dilute acids. Generally, polyimides have glass transition
temperatures above 300°C and are thermally stable in air at 450°C for short periods of
time. In comparison to other polymers, polyimides are commonly employed in
microelectronics applications because of their good dimensional and thermal stability.
Polyimides as free-standing films are utilized in flexible printed circuits boards due to
their soldering resistance at high temperatures. Moreover, it is not unusual to find
polyimides in temperature environments in the -270°C to 400°C range because of their
fairly constant properties over a wide range of temperatures. Generally, polyimides have
relatively low thermal expansion and good elongation properties. Their dielectric values
are typically below 3.2, and their moisture absorpfion at room temperature is between 2-
4%. Polyimides are often applied as films, coatings, matrix resins, fibers, foams, and
adhesives. [6-11]
Developed by DuPont in 1956, aromatic polyimides are typically made from an
addition reaction between dianhydrides and diamines to form long chain precursor
molecules where the heterocyclic rings are not closed. These poly(amic acid) precursors
are soluble in dipolar aprotic amide solvents such as N-methylpyrrolidinone (NMP),
N,N-dimethylformamide (DMF), N,N-dimethylacetamide (DMAc), and tetramethylurea
(TMU). The poly(amic acid) solution can easily be cast onto a smooth surface in which
the solvent is then driven off. In the thermal cure route as shown in Figure 1 . 1 , the
6
completion of the heterocyclic ring structure is achieved by a cyclizing dehydration
reaction, typically at temperatures above 120°C. Poly-[N,N' bis-phenoxyphenyl
pyromellitimide] is more commonly known as PMDA-ODA. By 200°C, complete
imidization is attained. Then, temperatures are generally brought to 300-400°C to take
advantage of ordering effects such as chain extension and crosslinking which impart
mechanical stability over a wide range of temperatures. The polyimide can be left
deposited or taken off the substrate as a free-standing film.
On the other hand, the precursor poly(amic acid) can also be made into the
heterocyclic stable structure by a chemical cure method rather than the thermal cure
method. As represented in Figure 1.2, anhydride (i.e. acetic anhydride) and amine (i.e.
pyridine) curing agents are used to allow imidization to start at room temperature. Then,
similar to the thermal cure procedure, final cure temperatures of 300-400°C are reached
to attain ordering effects. The advantage of the chemical cure method over the thermal
cure method is simply the speed of processing with the chemical cure route being much
faster. This method is commonly how commercial polyimide films are produced on
tentering frames. A more detailed description of tenter frame processing is presented in
Chapter 5. Kapton® is the DuPont tradename for PMDA-ODA prepared by the chemical
cure route.
The glass transition behavior, thermal breakdown, dielectric constant, moisture
content, adhesion, elongation, planarity, and solvent and chemical resistance of
polyimides are all important properties which are directly affected by molecular
orientation and molecular ordering. The degree of molecular orientation is related to the
7
pyromellitic dianhydride + bis(4-aminophenyl) ether
< lOI >«=~^o^.„,
O
poly(amic acid)
-2H2O
300-400°C
O
o o
poly-[N,N'-bis-phenoxyphenylpyromellitimide]
Figure 1.1 Preparation ofPMDA-ODA polyimide by the thermal cure route
o o
poly(amic acid)
o o
o oII II
H3CCOCCH3
o
N
H3CCO 0CCH3
6 0^6 o
+2H3CCO- HN
-2CH3COOH
300-400X
o o
0 0
poly-[N,N'-bis-phenoxyphenylpyromellitiinide]
Figure 1 .2 Preparation ofPMDA-ODA polyimide by the chemical cure route
8
thickness of the polymer coating. Orientation has an influence on the modulus and
thermal expansion which, in turn, contributes to the stress development during the final
stages of cure. On the other hand, the degree of ordering or crystallinity is influenced by
the chemistry and processing conditions. The chemistry is mainly dependent upon the
backbone chain stiffness, polymer-solvent and polymer-polymer interactions. The
thickness, final cure temperature, and cure route followed (i.e. chemical or thermal cure)
govern the effects of the processing conditions on formation of the final rigid polyimide.
[12]
In this thesis research, the main goals concentrate on the study of polyimide
coatings and films which are commonly used for electronic applications. For instance,
polyimides can be found as interiayer dielectrics on high density MCM packages. Since
polyimides have good thermal expansion compatibility with the other layers of ceramic
and silicon, the stresses in the structure are minimized. In comparison with printed
circuit boards of the past, today's high density MCMs allow integrated circuits to be
placed closer together and thus shortening the interconnect path between adjacent
integrated circuits. In combination with low dielectric polyimides, propagation delays
between integrated circuits are improved resulting in enhanced performance. Good
adhesion to self and substrate for metallization and ceramics is another noteworthy
property of polyimides. As a result, smaller microelectronic devices can be imagined
with increased performance. [13] On integrated circuits, polyimides also act as
passivation layers and as thermal and mechanical stress buffers. Polyimides make good
passivation layers for insulating the metal circuits between levels because they have
9
excellent dimensional and thermal stability. As stress buffers, they relieve highly
concentrated stress points and evenly distribute stress to minimize reliability problem;
Lastly, in flexible printed circuits boards, polyimides are utilized due to their solderin,
resistance and dimensional stability at high temperatures. [14-17]
10
References
1. R. M. Jennings and R. J. Farris, "Analysis of Stresses Arising During theProcessing of Polymeric Films on Tentering Frames," Polymer Engineering andScience, 32(23), pp. 1792, 1992.
2. M. A. Maden, "The Determination of Stresses and Material Properties ofPolyimide Coatings and Films Using Real Time Holographic Interferometry,"Polymer Science and Engineering Department. University of MassachusettsAmherst, Ph.D. Thesis, 1992.
3. S. G. Croll, "Internal Stress in a Solvent-Cast Thermoplastic Coating," Journal
of Technology, 50(638), pp. 33, 1978.
4. S. G. Croll, "Internal Strain in Solvent-Cast Coatings," Journal of Technology,
51(648), pp. 64, 1979.
5. J. K. Vrtis, "Stress and Mass Transport in Polymer Coatings and Films,"
Polymer Science and Engineering Department. University of Massachusetts
Amherst, Ph.D. Thesis, 1995.
6. C. E. Sroog, "Polyimides," Progress in Polymer Science, 16, pp. 561-694, 1991
.
7. R. J. Young and P. A. Lovell, Introduction to Polymers, 2 ed. London, England:
Chapman and Hall, 1991.
8. C. J. Lee, "Polyimides, Polyquinolines and Polyquinoxalines: Tg-Structure
Relationships," JM5'-7?ev. Macromol. Chem. Phys., C 29(4), pp. 431-560, 1989.
9. M. I. Bessonov, M. M. Koton, V. V. Kudryavtsev, and L. A. Laius, "Practical
Applications of Polyimides," in Polyimide: Thermally Stable Polymers. NewYork, NY: Consultants Bureau, 1987.
10. D. Likhatchev and R. Vera-Graziano, "Polyimides, High Performance Films," in
The Polymeric Materials Encyclopedia, J. C. Salamone, Ed. Boca Raton, FL:
CRC Press, Inc., 1996.
11. C. E. Sroog, "Polyimides (Introduction and Overview)," in The Polymeric
Materials Encyclopedia, J. C. Salamone, Ed. Boca Raton, FL: CRC Press, Inc.,
1996.
11
12. J. Cobum and M. Pottiger, "The Influence of Processing Condition on Structure,Properties, and Stress Development in Spin Coated Polyimide Films," presentedat Advances in Polyimide Science and Technology, 1 991
.
13. S. Sasaki and S. Nishi, "Synthesis of Fluorinated Polyimides," in Polyimides:Fundamentals and Applications, M. Ghosh and K. L. Mittal, Eds. New YorkNY: Marcel Dekker, Inc., 1996.
1 4. P. A. Flinn, "Mechanical Stress in VLSI Interconnections: Origins, Effects,
Measurements, and Modeling," MRS Bulletin, pp. 70, 1995.
15. D. E. Eastman, "Materials Science and Processing - The Foundation ofPackaging," presented at Mat. Res. Soc. Symp. Proc, 1985.
16. "Pyralin Polyimide Coatings for Stress Buffer Applications," DuPontElectronics, Wilmington, DE, 1990.
1 7. "Pyralin Polyimide Coatings for Multichip Modules and High Density
Interconnects," DuPont Electronics, Wilmington, DE, 1991.
12
CHAPTER 2
MATERIALS
Introduction
The study of thin polyimide coatings and films is the primary focus of this thesis
research. In addition, commercial films of poly(ethylene terephthalate) and bisphenol A
polycarbonate have been investigated. This chapter details the polymer materials
examined and their thermal and physical properties determined using several common
characterization techniques.
Polyimides
The polyimides, PMDA-ODA (PI-2540), BPDA-PPD (PI-581 1), PMDA/BPDA-
TFMOB/PPD (FPI-45M), 6FCDAyBPDA-TFM0B (FPI-46), 6FCDA-TFMB (FPI-
135), PMDA/6FDA-TFM0B (FPI-136), PMDA/6FDA-TFM0B/PPD (FPI-136M), and
PMDA-TFMOB/PPD (FPI-137M), were prepared by spin coating from 10-14 wt%
poly(amic acid) in NMP solution onto silicon wafer or glass substrates. Spin coating is a
common method for acquiring good coating planarization. For long-term storage, the
poly(amic acid) solutions were kept in the freezer at -15°C. Generally, 20-30 minutes of
thawing at room temperature were needed prior to spin coating. All the poly(amic acid)
solutions were supplied by DuPont.
13
Polyimide coatings and films were prepared as either a single layer or
multilayered structure with each layer having a thickness of approximately 10 )im. The
layer thickness is easily varied by changing the spin speed or the concentration of the
poly(amic acid) solution. Table 2.1 reveals the spin speeds used for preparing the
polyimides with a spin time of 30 seconds. As expected, poly(amic acid) solutions of
higher viscosity required faster spin speeds. The following describes the typical curing
procedure [1]:
1 ) Air dry on a hot plate at 85°C for 30 minutes.
2) Heating under nitrogen gas to 200°C at 2°C/min and holding for 30 minutes
at 200°C. If a multilayered coating was to be made, steps 1 and 2 would be
repeated after spin coating each additional layer.
3) The final curing step for single layer and multilayered coatings involves
heating under nitrogen gas from 200°C to 350°C at 2°C/min, then holding
for 1 hour at 350°C, and finally cooling below 100°C. The coating can be
left on the substrate or carefully removed to obtain a free-standing film.
Table 2.1 Spin speeds used to obtain polyimide coatings of 10 |im in thickness
Sample Spin Speed (rpm)
PMDA-ODA 1000
BPDA-PPD 1200
FPI-45M 1700
FPI-46 1300
FPl-135 1200
FPl-136 1650
FP1-136M 850
FPI-137M 1050
14
The monomers which comprise the studied polyimides are shown in Figure 2.1.
The names of the polyimides are normally derived from the abbreviated names of their
monomer constituents.
O O
o o
o oPMDA
O
O(
6FDA
BPDA
CF3 0CF3
TFMB TFMOB
PMDA: pyromellitic dianhydride
BPDA: 3,3',4,4'-biphenyltetracarboxylic dianhydride
6FDA: 2,2'-bis(3,4-dicarboxyphenyl)-hexafluoropropane dianhydride
6FCDA: 9,9'-bis(trifluoromethyl)-2,3,6,7-xanthenetetracarboxylic dianhydride
ODA: 4,4'-diaminobiphenyl ether
PPD or PDA: p-phenylene diamine
TFMB : 2,2'-bis(trifluoromethyl)benzidine
TFMOB: 2,2'-bis(trifluoromethoxy)benzidine
Figure 2.1 Chemical structures of dianhydrides and diamines used to prepare polyimides
15
2.2 Copolymer composition and molecular weights of the fluorinated polyimidi
Sample Chemistry
/ fx /f\^ ^ 1 \(g/mol) (g/mol)
FPI-45M PMDA/BPDA-TFMOB/PPD(90/1
221,000 446,000 2.02
FPI-46 6FCDA/BPDA-TFM0Byl ^/Zr^ i \J\J i
178,000 366,000 2.06
FPI-135 6FCDA-TFMBn 00-1 00^
FPI-136 PMDA/6FDA-TFM0B(95/5-100)
211,000 414,000 1.96
FPI-136M PMDA/6FDA-TFM0B/PPD(95/5-95/5)
216,000 418,000 1.94
FPI-137M PMDA-TFMOB/PPD(100-95/5)
116,000 241,000 2.08
The standard PMDA-ODA is regarded as a semi-rigid polyimide and has a
dielectric constant of 3.2. For microelectronic applications, a poor property of this
polyimide is its relatively high moisture absorption at 4%. BPDA-PPD is generally
considered a second generation polyimide and was specifically designed to remedy this
problem. It has a lower moisture absorption at 2%, and due to its more rigid backbone,
it also has a significantly lower in-plane coefficient of thermal expansion. BPDA-PPD
has a similar dielectric constant of 3.1. The fluorinated polyimides, which begin with
"FPI" in their abbreviated names, represent the current generation ofnew polyimides. In
Table 2.2, their copolymer composition by percentage weight and their molecular
weights are given. [2] Fluorinated groups of trifluoromethyl and perfluoroalkyl have
been incorporated to acquire better solubility, lower moisture pickup, and lower
dielectric constant. For example, FPI-135 has a dielectric constant of 2.5. In common
fluoropolymers, it is well known that there exists a strong bond between carbon and
16
fluorine atoms which promotes high chemical and thermal stability. In turn, the
electrical polarity is small and gives a low refractive index and low dielectric constant.
Low cohesive energy and low surface free energy due to low polarity result in a low
uptake of water and oil and resistance to wear and abrasion. Over the past several years,
the goal of adding highly electronegative fluorine has been to introduce these beneficial
improvements without compromising the adhesion strength, mechanical strength, and
thermal expansion of traditional polyimides. [3] In Figures 2.2-2.4, the chemical
structures of PMDA-ODA, BPDA-PPD, and FPI-135 are shown.
[-N
Figure 2.2 Chemical structure ofPMDA-ODA
[-N
Figure 2.3 Chemical structure ofBPDA-PPD
[-N
Figure 2.4 Chemical structure of FPI-135
17
In addition, commercial polyimide films of the DuPont Kapton® H series in
various thicknesses were studied. Kapton® 30H, 50H, and 200H denote film thicknesses
of 0.3 mils (7.6 ^im), 0.5 mils (12.7 ^im), and 2.0 mils (50.8 ^im) respectively. Upilex®
R (BPDA-ODA) and Upilex® S (BPDA- PDA) produced by Ube Industries were also
examined. Using a Mitutoyo thickness measurement device, their film thicknesses
respectively 46 ± 0.5 ^im and 23 ± 0.5 ^im. According to literature, Upilex® R has a
sharp glass transition temperature around 285°C. [4] Figures 2.5 and 2.6 detail the
chemical structures of Upilex® R and S.
were
[-N
Figure 2.5 Chemical structure of Upilex®R
[-N
Figure 2.6 Chemical structure of Upilex® S
18
FPM35
100
i
0 1 00 200 300 400 500 600 700
Temperature (°C)
Kapton®200H
100
90
^ 80
70
60
1 \ \ \ n ~r100 200 300 400 500 600 700 800
Temperature (°C)
Figure 2.7 TGA traces of selected polyimides
19
Thermogravimetric Analysis (TGA)
Using a TA Instruments 2920 Thermogravimetric Analyzer, the thermal stability
of the polyimides was investigated and are reported in Table 2.3. About 5-10 mg of film
sample were heated under nitrogen gas from room temperature to 700°C at a heating
rate of 20°C/min. Nitrogen flow rates of 40 ml/min for the balance and 60 ml/min for
the furnace were used. As shown in Figure 2.7, the weight as a function of temperature
was examined. As a whole, these polyimides are highly thermally stable at 400°C, and
their onset of decomposition does not occur until around 500-600°C.
Table 2.3 Summary ofTGA resuUs for polyimides
Sample Weight (%) Temperature (°C)
at 400°C at 5% Weight Loss
PMDA-ODA 99.7 569
BPDA-PPD 99.5 594
FPI-45M 99.5 602
FPI-46 99.5 518
FPl-135 99.1 513
FPI-136 99.9 575
FPI-136M 99.9 573
FPI-137M 99.8 582
Kapton® 200H 99.0 582
Upilex® R 99.1 587
Upilex® S 98.9 609
Density Measurements
The density measurement of the polyimides was carried out at using a
density gradient column [5, 6] as well as a flotation technique. In the flotation
technique, a square film sample of 1 cm^ was placed in a beaker containing a miscible
mixture of carbon tetrachloride (p - 1.583 g/cm^) and p-xylene (p = 0.858 g/cm^). The
20
composition of the mixture was varied in order to achieve flotation of the sample. Usin,
a calibrated pipette, 10 ml of solution was drawn out and weighed. Density (± 0.01
g/cm^) of the polyimide was calculated from knowing the weight and volume of the
solution. At least five different measurements for each sample were taken, and the
average value is reported in Table 2.4. For good density measurements, the chosen
solvents should be miscible with each other, must not swell the polymer sample, and
should not be highly volatile.
Table 2.4 Density of polyimides
Sample Density (g/cm^)
PMDA-ODA 1.40
BPDA-PPD 1.45
FP1-45M 1.55
FPI-46 1.56
FPl-135 1.55
FPl-136 1.55
FP1-136M 1.55
FPI-137M 1.55
Kapton® 30H, 50H, 200H 1.44
Upilex® R 1.39
Upilex® S 1.47
Attenuated Total Reflection (ATR) Fourier Transform Infrared (FTIR) Spectroscopy
Infrared spectra were acquired using a Perkin Elmer Spectrum 2000 FTIR
spectrometer equipped with a liquid nitrogen cooled mercury cadmium telluride (MCT)
detector. Spectra of the samples were obtained by co-adding 512 scans at a resolution of
2 cm"' and using a Graseby Specac horizontal ATR accessory fitted with a KRS-5
internal reflectance element (45°, six reflections). Care was taken to ensure uniform
21
contact of the polymer film with the crystal element. All spectra were recorded with
respect to a reference spectrum obtained for the empty ATR accessory. A nitrogen gas
line was used to purge the sample chamber of the spectrometer to eliminate the strong
infrared absorbances of carbon dioxide and water vapor.
CO
"cID
0)ocCO
"ECOc2I-
PMDA-ODA — Poly(amic acid)
- Cured at 350XKapton®30H
1540
1776
17161369
—I
1
]
—1800 1500 1200 900
Wavenumber (cm*'')
Figure 2.8 ATR FTIR spectra ofPMDA-ODA precursor and cured polyimides
Figure 2.8 shows the reflectance infrared spectrum obtained for three films
based on PMDA-ODA in the mid-infrared region. A PMDA-ODA poly(amic acid)
sample was prepared from spin coating on a silicon wafer and drying in an oven at 85°C
for 30 minutes. At 85''C, this temperature is hot enough to remove most of the solvent,
but it is still well below the temperature at which imidization begins. Another sample
was a spin coated PMDA-ODA fully cured at 350°C following normal curing
22
procedures discussed earlier. Lastly, a commercial PMDA-ODA film, more specifically
Kapton®30H, was analyzed. All samples were approximately 10 fim in thickness.
For the fully cured PMDA-ODA film and Kapton® film, nearly identical spectra
were found which confirm the successftil curing of the spin coated PMDA-ODA
materials in our laboratory. The characteristic vibrational bands for the aromatic imides
are clearly recognized at 1780 cm ' (strong intensity, C=0 asymmetrical stretching), at
1720 cm ' (very strong intensity, C=0 symmetrical stretching), and at 1380 cm"' (strong
intensity, C-N stretching). On the other hand, the PMDA-ODA poly(amic acid) film
showed characteristic vibrafional bands arising at 1660 cm"' (Amide I, strong intensity,
C=0 from COOH) and at 1550 cm"' (Amide II, medium intensity, C-NH). [7]
Dynamic Mechanical Thermal Analysis (DMTA^
10* -
IdQ.
LiJ
10^ -
10« -
0.0 100.0 200.0 300.0 400.0 500.0
Temperature ("C)
Figure 2.9 DMTA trace of Kapton® 200H
23
Using the Rheometric Scientific DMTA Mark IV, the dynamic mechanical
properties of Kapton® 200H films were studied in tensile mode. With a gauge length of
temperature ramp mode from room temperature to 500°C at a heating rate of 10°C/min
and at a frequency of 2 Hz. As shown in Figure 2.9, the glass transition of Kapton® can
be estimated from the maximum peak of the tan 5 curve which has been data smoothed.
Currently, the E" and tan 8 data appear with too much noise, and further optimization of
the experimental parameters are needed. Therefore, dynamic mechanical analysis should
give the ability to observe glass and sub-glass (p) transitions, as reported in the
literature, in several thermally cured polyimides including fluorinated polyimides. [8-
Biaxially oriented poly(ethylene terephthalate) films prepared by tenter frame
processing from Kodak (Tradename: Estar®) were studied. The density was measured to
be 1 .40 g/cm^ using the flotation technique, and the film thickness was determined to be
94 ± 0.5 |j.m. Furthermore, its crystallinity has been previously reported as 34.2%. [13]
20 mm and a width of 5 mm, samples were examined under nitrogen gas in a dynamic
12]
Poly(ethylene terephthalate) (PET^
O o
[—O—CH—CH—O—C C—O—
]
n
Figure 2.10 Chemical structure of PET
24
Differential Scanning Calorimetrv jn^C)
Using a TA Instruments 2910 Differential Scanning Calorimetry, the thermal
transitions ofPET were studied and reported in Table 2.5. About 5-10 mg of film
sample were heated under nitrogen gas from room temperature to 300°C at a heating
rate of 10°C/min. Samples were allowed to air cool to room temperature, and a second
heating was done. A nitrogen flow rate of 40-60 ml/min was generally used. Non-
hermetically sealed pans were used to attain good thermal contact. As shown in Figure
2.11, the heat flow as a function of temperature was examined. Values for the glass
transition temperature (T^), melting temperature (TJ, and heat of melting (AHJ agree
well with reported literature values. [14]
Table 2.5 Summary of DSC results for Kodak PET
T, rc) (°C) AH, (J/g)
r' Heating 76.7 253.8 46.8
2"' Heating 79.6 252.8 43.0
-0.8 -
-0.9
-1.0 J] \ \
\ 1 r~
50 100 150 200 250 300
Temperature (°C)
Figure 2.11 DSC thermogram of Kodak PET
25
Bisphenol A Polvcarhonate
Commercial polycarbonate films from GE Plastics (Tradename: Lexan®) were
examined. As reported in their technical data sheet, the density is approximately 1.20
g/cm\ and the film thickness is 7 mils (177.8 }im). [15]
[-0
CH3
c—oII
,0-C-]nCH
Figure 2.12 Chemical structure of bisphenol A polycarbonate
Differential Scanning Calorimetry (DS,C)
0.30
0.35
^ -0.40
I
CD
X
-0.50
0.55
2nd Heating
50
11 r~ ^
100 150 200 250 300
Temperature (°C)
Figure 2.13 DSC themiogram of GE polycarbonate
Using a TA Instruments 2910 Differential Scanning Calorimetry, the glass
transition of polycarbonate was evaluated as shown in Figure 2.13. About 5-10 mg of
26
film sample in non-hermetically sealed pans were heated under a controlled flow of
nitrogen gas from room temperature to 300°C at a heating rate of 10°C/min. Samples
were allowed to air cool to room temperature, and a second heating was done. The T
was determined at 147.5°C on first heating and 146.2°C on second heating. This agrees
well with reported literature values. [14]
27
/
References
1. P. Buchwalter, "Curing Procedures For Polyimides," IBM, Yorktown Heights,NY, personal communication, 1993.
2. A. E. Feiring, B. C. Auman, and E. R. Wonchoba, "Synthesis and Properties ofFluorinated Polyimides From Novel 2,2'-Bis(fluoroalkoxy)benzidines,"
Macromolecules, 26, pp. 2779, 1993.
3. S. Sasaki and S. Nishi, "Synthesis of Fluorinated Polyimides," in Polyimides:
Fundamentals and Applications, M. Ghosh and K. L. Mittal, Eds. New York,NY: Marcel Dekker, Inc., 1996.
4. J. Edman, "Properties of Upilex® R," DuPont Films, Circleville, OH, personal
communication, 1996.
5. B. Auman, "Density of Fluorinated Polyimides Using a Density Gradient
Column," DuPont, Wilmington, DE, personal communication, 1995.
6. "ASTM Dl 505-68: Standard Method of Test for Density of Plastics by the
Density-Gradient Technique," Annual Book ofASTM Standards, 1968.
7. T. Takekoshi, "Synthesis of Polyimides," in Polyimides: Fundamentals and
Applications, M. K. Ghosh and K. L. Mittal, Eds. New York, NY: Marcel
Dekker, Inc., 1996.
8. G. A. Bemier and D. E. Kline, "Dynamic Mechanical Behavior of a Polyimide,"
Journal ofApplied Polymer Science, 12, pp. 593-604, 1968.
9. J. K. Gillham, K. D. Hallock, and S. J. Stadnicki, "Thermomechanical and
Thermogravimetric Analyses of Systematic Series of Polyimides," Jourwa/ of
Applied Polymer Science, 16, pp. 2595-2610, 1972.
10. J. C. Cobum, P. D. Soper, and B. C. Auman, "Relaxation Behavior of
Polyimides Based on 2,2'-Disubstituted Benzidines," Macromolecules, 28(9),
pp. 3253, 1995.
11. F. E. Arnold, K. R. Bruno, D. Shen, M. Eashoo, C. Lee, F. W. Harris, and S. Z.
D. Cheng, "The Origin of p Relaxations in Segmented Rigid-Rod Polyimide and
Copolyimide Films," Polymer Engineering and Science, 33(21), pp. 1373, 1993.
28
12. J. M. Perena, "Dynamic Mechanical Relaxations in Polyimide andPo\yamidQim\de;' Die Angewandte Makromolekulare Chemie, 106 pp 61-661982.
'KF- '
13. J. K. Vrtis, "Stress and Mass Transport in Polymer Coatings and Films,"Polymer Science and Engineering Department. University of MassachusettsAmherst, Ph.D. Thesis, 1995.
14. G. Odian, Principles ofPolymerization, 3 ed. New York, NY: John Wiley &Sons, Inc., 1991.
15. "Structured Products - LEXAN® Graphic Film," GE Plastics, NY, 1 996.
29
CHAPTER 3
DETERMINATION OF OUT-OF-PLANE PROPERTIES OF POLYIMIDECOATINGS AND FILMS
Introduction
Polyimide materials are generally found as dielectric interlayers in high density
multi-chip module (MCM) packages. As these microelectronic packages become
smaller and more complex, there becomes a greater need to comprehend their reliability
and performance. In order to predict reliability, especially in complex geometries near
holes, copper vias, and vertical sidewalls, finite element modeling is a common method
of choice. [1-3] Therefore, good knowledge of the far field residual stresses and the in-
plane and out-of-plane elastic constants and coefficients of thermal expansion is
necessary. In past research by Sheth et al., the complete characterization of several
polyimides was reported. [4]
Out-of-plane properties, namely the out-of-plane Young's Modulus and out-of-
plane coefficient of thermal expansion (CTE), of thin polymer coatings and films are
very difficult quantities to measure. Due to their lack of appreciable thickness,
conventional mechanical methods do not have the ability to strain the film in the
thickness direction, nor do they have the sensitivity to detect the small thickness
changes associated with changes in temperature. For polyimides used in high density
MCMs, it has been seen that a high out-of-plane CTE can lead to interlayer
delamination and/or cracking in the multilayered structure as a result of CTE
30
mismatches. [5] Moreover, repeated thermal cycling during their fabrication can cause
significant stresses in the constrained system. [6]
Studies by Gosz and Dolbow have used finite element modeling to examine the
development of interfacial stresses during the thermal cycling of a model copper-
polyimide/silicon structure. [7] More specifically, a single layer array of square copper
vias in a polyimide insulator on top of a silicon substrate was studied. Assuming that the
polyimide is in-plane isotropic, the circumferential and normal stresses were evaluated
as the structure cools uniformly to room temperature from a stress free state at an
elevated temperature. Their work revealed that the interfacial stress components are
highly dependent on the out-of-plane CTE and out-of-plane shear modulus.
Furthermore, the out-of-plane Young's Modulus does not seem to have a great influence
on the stress of the structure. Another important finding showed that energy release
rates along pre-existing interfacial flaws are also highly sensitive to the out-of-plane
CTE and out-of-plane shear modulus. Consequently, a good comprehension of the
effects of out-of-plane properties is important for predicting material reliability. [8]
The out-of-plane CTE of thin polyimide films has been previously investigated
by Tong et al.. [9] From their published research, they describe three different
techniques. In the capacitance change method, the air spacing between two parallel
plates is examined in which the thickness of the spacing corresponds to the thickness of
the polymer film. The out-of-plane expansion and contraction of the film during thermal
cycling was determined fi-om the changes in capacitance of the parallel plate capacitor
whose electrodes are separated by the air gap. Hodge et al. have also designed
resembling electrode geometries for measurement of the tlirough the thickness thermal
31
properties of thin dielectric materials. [10] Another technique by Tong et al. is the
Fabry-Perot laser interferometric technique which also relies on measuring an air gap.
However, the experimental setup has the polymer film sandwiched between a reflective
substrate and a beamsplitter layer. Film thickness differences are measured from the
oscillations in the reflected intensity due to the changing phase difference between the
interfering reflections from the top and bottom layers. Both the capacitance change and
Fabry-Perot laser interferometric techniques are capable of detecting the very small
thickness changes of polymer films, but the design of their experimental setups
introduces small errors to their out-of-plane CTE calculations. Lasfly, Tong et al. have
utilized on polyimide films a thermomechanical analyzer with a push-rod dilatometer
attachment. The main difficulty with this technique is that much thicker samples or
stacks of film are needed to acquire any sufficient amount of signal. Studies by Sheth
have also examined this method to measure the out-of-plane CTE ofPMDA-ODA and
FPI-135 films. [1 1] A TA Instruments 2940 Thermomechanical Analyzer with silica
particles as the confining medium was employed.
Using scanning probe microscopy. Gross and Zhmurkin have observed the
changes in the relative heights of parallel copper lines and 1 |im thick spin coated
polyimide line arrays between room temperature and 97°C. [12] Out-of-plane CTE
values were estimated fi-om the change in topography of the samples due to changes in
temperature and the predictions fi-om finite element modeling. In result, they report
values for the out-of-plane CTE of FPI-135 and FPI-136 polyimides.
32
In this chapter, the out-of-plane Young's Modulus and out-of-plane CTE are
determined for several commercial and spin coated polyimide films, including novel
fluorinated polyimides. With orthotropic linear elasticity theory as the basic foundation,
the fiill characterization of a polymer film in terms of its elasficity coefficients are
discussed. Using a commercially available Pressure-Volume-Temperature (PVT)
Apparatus, direct measurements of volumetric thermal expansion and bulk
compressibility are made. In combination with other characterization techniques such as
holographic interferometry, high pressure gas dilatometry, tensile testing, and
thermomechanical analysis (TMA), the out-of-plane properties can be deduced. A
detailed description of the unique characterization techniques is presented. As a resuh, a
better understanding of the out-of-plane properties of polyimides should give valuable
insight to evaluating reliability in today's microelectronic packages. Similar
characterization of commercial films of poly(ethylene terephthalate) (PET) and
bisphenol A polycarbonate (PC) is also detailed.
Orthotropic Elasticity Theory
Most commercial polymer films are anisotropic in nature. They have different
physical and material properties in the machine and transverse directions as well as in
the out-of-plane direction. If the orthotropic axes for an anisotropic film can be
identified, the polymer film may be described by the generalized Hooke's Law for a
linearly elastic orthotropic material in matrix form as shown in Figure 3.1. For an
orthotropic material, there exists 3 mutually perpendicular planes of symmetry. [13]
33
^111 1
- a, AT"1
I 1 1
II 12 13 0 0 0 rr
- a2AT c c^21 ^22 ^23 0 0 0 ^22
833 - a3AT c c^31 ^32 ^33 0 0 0 ^33
28,2 0 0 0 r 0 0 ^12
28,3 0 0 0 0 C55 0
0 0 u u u _^23_
c,, = 1/E„ r - 1/G„c22 — 1 / F
1 / j_^22 C55 = 1 / n
c = 1/E33 Ccc = I/G23
c12 ~ = ~V|2 /E„ = -V / E21 ' ^22
c13 = ^3, =-Vi3 /E„ = -V / E?i ' ^33
c " ^32 ~ ~^23 /E22 =-v / E32 ' ^33
Ejj = orthogonal Young's Moduli
Cjj = compliances
Gjj = shear moduli
Vjj = Poisson's ratios
= normal and shear strains
= normal and shear stresses
a, = CTEsT = temperature
gure 3.1 Generalized Hooke's Law for a Unearly elastic orthotropic material
34
Since there exists symmetry in the comphance matrix, an orthotropic material need only
be described by 9 independent constants instead of 21 for an anisotropic material. These
are the 3 normal compliances, the 3 shear compliances, and the 3 compliances
associated with Poisson's ratios. A more complete characterization should also include
the two in-plane CTEs and the out-of-plane CTE. As illustrated in Figure 3.2, the 1 and
2 directions are the in-plane directions, and the 3 direction represents the out-of-plane or
through the thickness direction. Concerning notation, ct,, represents the stress acting on
the 1 face in the 2 direction.
Figure 3.2 Components of stress tensor for a volume element of film
As reported in the literature, commercial polyimide films are typically
anisotropic materials due to their precursor chemistry and processing conditions.
Anisotropy exists in their dielectric constant, index of refraction, thermal expansion, and
mechanical properties. [14] However, if a polyimide is spin coated, it may be described
as being transversely isotropic. [15] The CTEs, Young's Moduli, and principal stresses
should have the same values in all directions within the plane of the film. Thus, only 5
A ^33
11
22
35
independent constants, as opposed to 9, are now needed to characterize the material,
These constants are E,, [E„ = E,,l E33, v,^ [G,^- E,/2(l+v,,)], v,, [v,3= v,3], and G
[Gi3= G23].
13
Experimental Techniques
Vibrational Holographic Interferometry
Mirror
DCamera
Beam Splitter
Mirror
60X LensJS:^^
Mirror60X60X Lens
Shutter He-Ne Laser
7Piezoelectric Shaker
Sine WaveGenerator
Photo Plate Sample Chamber
Figure 3.3 Schematic of vibrational holographic interferometry
Developed in our research laboratory several years ago, vibrational holographic
interferometry is a useful technique for studying residual stresses in polymer coatings.
[16, 17] It has also been successfully employed to measure stresses as a function of
temperature and humidity. [1 1, 18, 19] Furthermore, principal directions of stress,
unequal biaxial stresses, and in-plane Poisson's ratios for an orthotropic polymer
coating can all be determined using this powerful tool. [20]
36
Figure 3.3 reveals a detailed schematic of vibrational holographic
interferometry. The technique basically involves a polymer membrane in a state of
tension which is vibrated sinusoidally at certain characteristic frequencies using a
piezoelectric shaker. Using a camera, unique modal patterns are observed which are
produced from the superimposition of the real-time vibrating image with the reference
image of the stationary membrane stored in the photo plate.
A polymer coating can be placed onto a hollow steel washer and removed from i
rigid substrate while the state of stress in the coating is preserved. Thus, a polymer
membrane constrained on a washer can be made for holographic interferometry studies.
For a polymer coating on a rigid substrate, there does not exist any shear stresses or
normal tractions between the coating and substrate beyond several thicknesses from the
edges of the coating. [21] Several methods can be used to remove a coating from a
substrate while maintaining its state of stress. [17]
Equation 3.1 describes the free vibration of a membrane under uniform biaxial
stress (ct,, = a22= a).
aV'u = p— (3.1)oV
a = biaxial stress (N/m^)
V" = Laplacian operator
u = out-of-plane displacement (m)
p = material density (kg/m^)
t = time (s)
37
2D ID
Washer
Polymer
coaling
Figure 3.4 Polymer coating as a 2D constrained circular membrane and 1 D constrained
thin ribbon
If the appropriate boundary conditions are used for a 2-dimensionally (2D)
constrained membrane of circular geometry as shown in Figure 3.4, the classical
solution for the free vibration of a membrane is given in Equation 3.2. [22] It should be
noted that the only material property needed to detemiine the biaxial stress is the density
of the material. Furthermore, holographic interferometry experiments require a vacuum
environment to eliminate lateral pressure effects imposed by air. If the phenomenon
called air damping could be mathematically accounted for, the capabilities of
holographic interferometry could be extended for measuring stresses of environmentally
sensitive polymer coatings which require an air, helium, or nitrogen atmosphere. [23]
a = 4p7i R 111
(3.2)
R = radius of sample (m)
f„i= resonant frequency of vibration (Hz)
Z. •= i"' zero of n"' order Bessel function
Using vibrational holographic interferometry, the residual stress in a polymer
coating can be easily measured from observations of the unique modal vibration
38
patterns and their respective resonant frequencies. The order of the Bessel function is
deduced from the type of symmetry in the vibration pattern. For example, Figure 3.5
shows the n,i = 2,1 pattern which possesses 2 degrees of axial symmetry and 1 degree of
circular symmetry. Further, the n,i = 0,1 pattern possesses no axial symmetry and only 1
degree of circular symmetry. Knowing the values for n and i, numerical values for the
Bessel function term can be found in standard mathematics textbooks. [24] For a given
polymer membrane measured by holographic interferometry, there will appear several
modes of vibration with each occurring at a specific resonant frequency. Yet, the stress
calculated at each mode of vibration would be the same value. Thus, this technique
provides a high level of redundancy and self-check in the stress measurements. Studies
by Maden have shown that the first 20 modes of vibration are observable.
n,i = 0,1 n,i = 2,1
Figure 3.5 Representative modal vibration patterns
(3.3)
ct'° = uniaxial stress (N/m^)
L = length of ribbon sample (m)
= resonant frequency of vibration (Hz)
n, = i"' node of vibration
39
In addition, holographic interferometry can be used to determine the uniaxial
stress in a 1 -dimensionally (ID) constrained thin ribbon sample as represented in Figure
3.4. Based on measurements of resonant frequency and node of vibration, the a'° can be
calculated using Equation 3.3.
As shown in Figure 3.6, holographic interferometry is also helpful for
determining the principal directions of stress in a polymer film. As discussed by Tong,
anisotropic films such as Kapton® or Upilex® will show a particular mode of vibration
occurring at a particular frequency. [16] However, at a slightly higher or lower
frequency, the same pattern appears but is rotated by 90°. The axial lines of symmetry
are in the same directions as the principal directions of stress. For commercial films, the
principal directions do not generally correspond with the machine and transverse
directions.
Figure 3.6 Splitting behavior of the n,i = 1,1 mode of vibradon for Kapton 200H
For an anisotropic material with known orthotropic axes, the principal stresses
can be determined using holographic interferometry. When a membrane is in a state of
unequal biaxial stress, observafion of the splitfing behavior of the n,i = 1,1 mode of
vibration deduces the principal directions of stress. In order to determine the principal
1144 Hz 1297 Hz
40
stresses, a membrane of square geometry must be studied because the solution to the
problem is easier to solve.
2D ID
Figure 3.7 Polymer coating as a 2D constrained square membrane and 1 D constrained
thin ribbon
As shown in Figure 3.7, square inserts are placed within the circular washer to
produce a membrane of square geometry. Further, the sides of the square are parallel to
the principal directions of stress. Using the appropriate boundary conditions, the
solution to the classical wave equation becomes Equations 3.4 and 3.5. <j]^ represents
the principal stress in the principal direction. In order to determine the second
principal stress, the delta function, 5, should be solved as shown in Equation 3.6. 5 is
the ratio of the two principal stresses and can be solved analytically by any pair of
different resonant frequencies or by averaging the results from all the resonant
frequencies. [16] Lastly, in the same manner as discussed before, the uniaxial stress for
a thin ribbon sample constrained by a square washer is calculated using Equation 3.3.
However, it should be mentioned that the ribbon sample must be cut in the appropriate
principal direction.
41
fni
Vn +5i J (3.4)
L = length of each side (m)
f„j = resonant frequency of vibration (Hz)
n, i = an integer (0, 1 ,2,3 ...
)
^2D 5:^20(3.5)
5 =f ^ - f^n'^
f2.,2_p2.2 (3.6)
The in-plane Poisson's ratios of a polymer coating can be determined by
vibrational holographic interferometry. Poisson's ratio can be described as the ratio of
lateral strain to axial strain. [25] Equation 3.7 represents the theory of incremental
elasticity for an isotropic, linearly elastic material with no concentration or solidification
effects.
E(ds,^-5„adT) = (l + v)da,j-v5,^akk (3.7)
If the coating is 2D constrained by a hollow circular steel washer as shown in
Figure 3.4, then dej^ = = 0 , da'J" = 0 , and Equation 3.8 results.
2D 2D EadT(3.8)
42
On the other hand, a coating held 1 D constrained as seen in Figure 3.4 is
basically a thin ribbon sample fixed by a circular washer. Thus, dc|'/ = 0
,
dcj22 = dCTj" =0, and Equation 3.9 follows.
da[5^ = -EadT(3 9)
Combining Equations 3.8 and 3.9 gives Equation 3.10 for determining the
Poisson's ratio for an isotropic linearly clastic material. Using holographic
interferometry on a 2D constrained circular membrane, ct^° can be calculated from
Equation 3.2. Further, a'" can be determined from Equation 3.3 using holographic
interferometry on a ID constrained thin ribbon sample.
^11)G - av= ^ (3.10)
If the material is anisotropic with known orthotropic axes, the in-plane Poisson's
ratios can be determined from Equations 3.1 1 and 3.12. As an example, the
determination of v,2 requires the evaluation of the principal stresses (Equations 3.4 and
3.5) for a 2D constrained square membrane in the 1" and 2'"' principal directions as well
as the uniaxial stress of a thin ribbon sample cut along the T' principal direction
(Equation 3.3).
V,2= 15 (3.11)
^22
43
High Pressure Gas Dilatometry
a
3
Load
Cell
Ribbon
Sample
Figure 3.8 Schematic of high pressure gas dilatometry
High pressure gas dilatometry developed by Farris Instruments was originally
designed to observe crazing and cavitation in glassy polymers. [26] However, this
instrument can also be used to help determine the out-of-plane Poisson's ratios, v,3 and
V23, of orthotropic films. [27, 28] As shown in Figure 3.8, a thin ribbon sample is held at
constant strain with one end attached to a load cell. An inert gas such as nitrogen or
helium is introduced into the chamber, and a hydrostatic pressure (P) is applied around
the sample. Observing the response from the load cell, the change in stress of the film
sample as a function of hydrostatic pressure is recorded,
44
Equation 3.13 represents the case of a uniaxially constrained ribbon sample cut
in the r' principal direction. As discussed earlier, the principal directions of a film can
be determined from holographic interferometry.
^11 = CjiGu +C,2a22 +Ci3a33 (3.13)
Substituting a,, = (a - P) and = ^^33 = -P resuh in Equation 3.14 in which a is
the stress resulting from the initially imposed constant strain.
^11 ^11 ^11
Differentiating Equation 3.14 with respect to pressure gives
(da)
UpJ ~'~^i2"^i3 (3.15)
1 I
According to Equation 3.15 for a thin ribbon sample cut along the principal
direction and held at isostrain, the slope of the stress versus hydrostatic pressure curve is
dependent upon both and V]3. Since the in-plane Poisson's ratio, Vi2, can be measured
using holographic interferometry, the out-of-plane Poisson's ratio, V13, can be solved.
Similarly, the other out-of-plane Poisson's ratio, V23, can be determined as shov^n in
Equation 3.16 from high pressure gas dilatometry on a thin ribbon cut along the 2'
principal direction.
45
C22
Pressure-Volume-Temperature CPVT) Apparatus
As shown in Figure 3.9, the principal tool used to help determine the out-of-
plane CTE and out-of-plane Young's Modulus is the Gnomix Inc. PVT Apparatus. This
instrument allows one to measure the volume change of a sample as a function of
temperature and hydrostatic pressure. [29-32] In their design, a rigid sample cell having
a total volume space of approximately 7.45 cm^ is sealed at one end with the other end
having a flexible stainless steel bellows. Typically, a sample weight of 0.5-2.0 g is used
with mercury as the confining fluid. Mercury is normally used because of its unreactive
nature to polymers. Sample preparation is of the utmost importance because one must
take great care to minimize the air in the sample cell. With the sample cell surrounded
by a pressure vessel, an Enerpac P-2282 high-pressure hand pump is used to attain
pressures from 10 MPa to 200 MPa (-29,000 psi). A heating jacket surrounds the
pressure vessel and is connected to a temperature controller which can vary temperature
from 30°C to 400°C. The change in volume of the sample is measured by the deflection
of the bellows which is attached to a linear variable differential transducer (LVDT).
Lastly, a computer records the elapsed time, sample temperature, and signal response
from the LVDT. According to its technical specifications, the PVT Apparatus has a
sensitivity of <0.0005 cmVg and an accuracy of ±0.002 cmVg at temperatures less than
250°C and up to ±0.004 cmVg at higher temperatures. [33]
46
Ram
Thermocouple Pressure Vessel with
Heating Jacket
Thermocouple
Sample
3
Bellows
Piezometer
Base
High Pressure
Hand Pump
LVDT 0Gauge
Figure 3.9 Schematic of the Gnomix Inc. PVT Apparatus
The PVT Apparatus has mainly been used on soHd and molten polymers,
however liquids such as water have also been tested. [34-36] Extensive research studies
by Zoller have examined the phase separation of polymer mixtures and the heat of
fusion and crystallization kinetics of numerous polymers. [37-39]
Several different theories for the equation of state of polymers have been
detailed in the literature. [3, 40] One of the more common theories is the empirical Tait
equation which is typically applied to the PVT behavior of polymer melts and glasses
along isotherms. As shown in Equation 3.17, the Tait equation represents the pressure
and temperature dependent specific volume, V(P,T), in terms of a specific volume at
zero pressure expression, V(0,T), and a Tait parameter expression, B(T), which is
temperature dependent.
47
V(P,T) = V(0,T) 1-0.0894 1 +P
V B(T)
;
(3.17)
Generally, the specific volume behavior at zero pressure is expressed by a 2"" order
polynomial as shown in Equation 3.18.
Further, the Tait parameter expression is denoted by an exponential temperature
dependence.
As a result, the PVT equation of state for a polymer is represented by five independent
constants (V„, V,, Vj, B,, and Bj). Research by Pottiger and Cobum has explored the
PVT behavior of a few thermally cured and commercial polyimides. In addition, values
have been reported for their bulk compressibility, volumetric thermal expansion, and
Tait equation parameters. [5]
The relationship between the normal stresses and normal strains for an
orthotropic linearly elastic material can be written as
V(0,T) = V„ + VJ + V2T2 (3.18)
B(T) = B,exp(-B2T) (3.19)
Sii -aiAT = CiiOii +Ci2a22 +C13O33
S22 - a2AT = C2iai 1 + €22^^22 + C23(^33
S33 - a3AT = C3iaii + C32a22 + C33a33(3.20)
48
Furthermore, shear moduU are not required in this particular analysis, and C^j = q, due
to symmetry. For a film under hydrostatic pressure (P), the relationship a,, = g,, = a,, =
-P exists. Therefore, the dilatation, which is the sum of the strains in the three principal
directions, can be represented as a function of pressure and temperature.
AV 3^ = (ai + a2 + a3)AT - P SC. (3-21)
As shown in Equations 3.22 and 3.23, the out-of-plane Young's Modulus, E33,
can be determined from an isothermal set ofPVT experiments.
"Z^ij (3.22)T ij=l
where
XCi^ = C„ +C,, +C33 +2(C„ +C,3 +C,3) (3.23)
'J=i
As shown in Equation 3.22, the left hand side denotes bulk compressibility and is equal
to the sum of the coefficients of the compliance matrix. If all the compliances on the
right side of Equation 3.23, except C33, are known from other techniques, C33 and hence
the out-of-plane tensile modulus, E33, can be calculated. Both C,, and C,, can be
obtained from standard tensile testing to determine the two in-plane Young's moduli,
E,i and Ejj. As discussed earlier, C,2 can be detennined from either in-plane Poisson's
rafios, v,2 and Vj,, using vibrational holographic interferometry. Lastly, C,3 and C23 can
49
be found using high pressure gas dilatometry in which the two out-of-plane Poisson's
ratios, v,3 and V23, are measured.
On the other hand, the volumetric thermal expansion, a„ can be found from an
isobaric set of PVT experiments. Thus, the out-of-plane CTE, a„ can be calculated from
All the spin coated polyimides studied in this chapter were thermally cured at
350°C following normal curing procedures outlined in Chapter 2. After removal from
their substrates, free-standing films of approximately 10 \xm in thicknesses were
obtained. Further, the commercial polyimide films were tested as received.
Vibrational Holographic Interferometry
For the spin coated polyimide films, the in-plane Poisson's ratios, v,2and V21,
were determined by measuring the residual biaxial stress in a circular membrane
(Equation 3.2) and the uniaxial stress in a thin ribbon sample (Equation 3.3). Thus, the
calculation for Poisson's rafio is made using Equafion 3.10. Since these polyimides are
transversely isotropic, the values for Vj^and V2, should be identical. The data for the spin
coated polyimides was obtained from studies by Sheth. [11]
knowing the two in-plane CTEs, a, and a^, which are commonly measured using a
thermomechanical analyzer.
(3.24)
Results and Discussion
50
Membrane samples prepared for holographic interferometry were made by
gluing steel washers onto fully cured polyimide coatings on glass or silicon wafer
substrates. Shell Epon® 828 resin with Epon® V-40 curing agent was used as the
adhesive in a 3:1 ratio and cured at 85°C for 45 minutes. Super Glue® was often used as
an effective adhesive as well. In result, the polyimide coating constrained on the washer
could then be carefully removed off the substrate, and the original state of stress is
On the other hand, commercial polyimide films are anisotropic in nature, and
their principal directions of stress need to be first determined in order to obtain the in-
plane Poisson's ratios. Concerning sample preparation, steel or copper washers were
glued onto flat polymer films at room temperature. After placing the samples in an oven
at 350°C for 2 minutes, the membranes appear in a state of tension upon cooling to
room temperature due to residual shrinkage effects.
Figure 3.10 Determination of machine and transverse directions and T' principal
direction (G clockwise fi-om the machine direction) for a standard sheet of polymer film
preserved.
Machine
Transverse
51
As represented in Figure 3.10, the machine direction of the film is the length
direction of a sheet of film. Thus, the transverse direction is the width direction of a
sheet of film. From the splitting behavior of the n,i = 1,1 mode of vibration, the
principal directions for Kapton® 200H and Upilex® R films were observed using
holographic interferometry. A light amount of talc powder was often applied on the
surface of the polymer membranes so that the resonant vibration patterns could be seen
more easily. For consistency, the V principal direction is taken from the splitting
pattern which occurs at the lower resonant frequency. As a result, the T' principal
direction for Kapton® 200H was found at 32° clockwise from the machine direction. For
Upilex® R, the T' principal direction was found at 12° clockwise from the machine
direction. Knowing the principal directions, the determination of and V2, (Equations
3. 11 and 3.12) can be accomplished by examining the stress in a 2D constrained square
membrane (Equations 3.4-3.6) and ID constrained thin ribbon (Equation 3.3).
Table 3.1 In-plane Poisson's ratios for thin polymer films
Sample V,2 V21
PMDA-ODA 0.34 0.34
BPDA-PPD 0.30 0.30
FPI-135M 0.31 0.31
Kapton® 200H^ 0.39 0.52
Upilex® R^ 0.36 0.23
^Data on Kapton* 30H and Upilex* R [17]
High Pressure Gas Dilatometrv
The out-of-plane Poisson's ratios, v,3 and V23, (Equations 3.15 and 3.16) for
several commercial and thermally cured polyimides were evaluated from high pressure
52
gas dilatometry experiments in combination with in-plane Poisson's ratio results from
holographic interferometry. Using thin ribbon samples of 5 mm in width and 6-8 cm in
length, the change in stress as a function of hydrostatic pressure was examined from
atmospheric pressure to 7 MPa under helium gas. The time interval between data points
was 6 minutes, and good reproducibility in the data was achieved. All data was
corrected for the response of the load cell to helium gas as a function of pressure. For
the anisotropic commercial films, thin ribbon samples were examined along their
principal directions. As shown for Kapton® 200H in Figure 3.11, good linearity is seen
in the stress versus hydrostatic pressure plot. Table 3.2 summarizes for several
polyimides the calculated slopes of the stress versus hydrostatic pressure curves and
their r^ values. The data for the spin coated polyimides was obtained from work by
Sheth. [11]
20 -11
18 -
12 -
10 -|1 \ 1 1 \ 1
\012345678Pressure (MPa)
Figure 3.11 High pressure gas dilatometry on a Kapton® 200H sample cut in the 1
principal direction
53
3.2 Summary of high pressure gas dilatometry on thin polymer films
Sample
UpJ
r^
Kd?)
r
FPI-45M 0.83 0 984 \J.OJ U.yo4FPI-46 0.47 0.992 0.47 0 992
FPI-137M 0.24 0.950 0.24 0.950
Kapton* 200H 0.40 0.998 0.28 0.940Upilex*' R 0.51 0.975 0.64 0.997
Table 3.3 Out-of-plane Poisson's ratios for thin polymer films
Sample V,3 V23
PMDA-ODA 0.39 0.39
BPDA-PPD 0.23 0.23
FPI-135M 1.39 1.39
Kapton* 200H 0.21 0.20
Upilex® R 0.13 0.13
It should be noted that the out-of-plane Poisson's ratios determined in Table 3.3
for the two commercial polyimide films are most likely inaccurate since the in-plane
Poisson's ratios used in the calculations were taken from that reported by Maden. [23]
Due to slight difference between our materials, it is expected that slight errors in
calculations are produced. The goal for future work is to determine the in-plane
Poisson's ratios for our batch of commercial polyimides. For Kapton® 200H, it is
expected that the v,3 and V23 values would differ due to the strong anisotropic behavior
seen in typical Kapton® films. On the other hand, Upilex® R is generally not too
anisotropic as exhibited in their similar in-plane CTEs and in-plane Young's ModuU.
54
aThe out-of-plane Poisson's ratios for the fluorinated polyimide, FPI-135, has
value of 1.39. This means that the stress decreases as the hydrostatic pressure increases.
Normally, isotropic linear elasticity theory states that the Poisson's ratio should have a
value of -1< V < 0.5. For an isotropic material, the restrictions on Poisson's ratio are
due to a positive strain energy requirement. This means that if the material is in a
deformed state, it must also have a finite positive strain energy density. [41] Therefore,
the compliance matrix must be positive definite. Since this condidon is satisfied, a v,3 =
V23 = 1.39 for FPI-135 is theorefically possible. In addifion, for an anisotropic linearly
elastic material, the out-of-plane Poisson's ratio could take any value as long as the
compliance matrix is positive definite. [42]
Tensile Tesdng
Using an Instron® Tensile Tester Model 5564, the Young's Modulus, tensile
strength, and elongation at break were examined at room temperature. Following ASTM
D882-88 guidelines [43], rectangular samples of 5 cm in length by 5 mm in width were
tested with a cross-head speed of 5 mm/min (strain rate = 10%/min). Further, a 1 kN
load cell was used. As given in Table 3.4, results are typically an average of 7-10
specimens. Sample preparation involved adhering with Krazy Glue® the ends of the
samples to small tabs made firom manila folders. For the commercial polyimides,
samples were cut along their orthotropic axes. Thus, E,, and £,2 were determined from
samples cut respectively along their 1" and 2'"* principal directions. Lastly, compressed
air was set at 55 psi in order to prevent slippage of the samples from the pneumatic
55
grips. The data for the transversely isotropic spin coated polyimides was obtained from
work by Sheth. [11]
In Figure 3.12, load versus displacement curves are shown for Kapton® 200H
and Upilex^R. Knowing the cross-sectional area of the sample, a stress versus strain
curve can be produced. For most of the polyimide samples, the stress versus strain
behavior of Kapton® 200H is the norm. With increasing strain or displacement, the
stress or load in the sample increases sharply until eventual breakage. The Young's
Modulus of a material is determined from the slope of elastic region in the stress versus
strain curve. For Upilex®R, an interesting note about its stress versus strain behavior is
the yield point which develops. [25] In comparison to the traditional spin coated
polyimides, the new fluorinated polyimides seem to have higher in-plane Young's
moduli due to their higher degree of in-plane orientation.
Table 3.4 Young's Moduli for thin polymer films
Sample En(GPa) (GPa)
PMDA-ODA 3.1 3.1
BPDA-PPD 10.1 10.1
FPI-45M 11.3 11.3
FPI-46 8.0 8.0
FPI-135 7.7 7.7
FPI-136 11.5 11.5
FPI-136M 10.7 10.7
FPI-137M 13.0 13.0
Kapton® 200H 2.6 2.9
Upilex® R 3.8 3.9
Upilex® 6.6 7.5
GE PC^ 1.6 1.8
^ Tested only in the machine and transverse directions,
56
Kapton'^200H
Upilex® R
Figure 3.12 Tensile testing of selected polyimides
57
Thermomechanical Analysis ^TM A)
The in-plane CTEs, a, and a^, were measured on thin films using a TA
Instruments 2940 Thermomechanical Analyzer. A force of 0.01 N was applied to 5
wide by 25 mm long samples. A nitrogen flow rate of 100 ml/min was used. For the
mm
runpolyimide samples, an average linear CTE was determined from the second heating
from 50°C to 200^C at a heating rate of 5X/min. Figure 3T3 reveals a plot for Upilex®
R showing the change in length of the sample as a function of temperature. As discussed
earlier, the determination of the in-plane CTEs for the commercial polyimide films
requires that their principal directions need be first measured using holographic
interferometry. Data for the spin coated polyimides was obtained from the work by
Sheth. [11] Because these films are in-plane isotropic, their in-plane CTEs should be
identical.
180
160
^ 140
^ 120D)C_2 100 ^
oC 80gCO
S 60
iQ 40
20
2nd Heating
1
—~i \ I \
i ] I
20 40 60 80 1 00 1 20 1 40 1 60 1 80 200 220
Temperature (X)
Figure 3.13 TMA on an Upilex® R sample cut in the 2""^ principal direction
58
Table 3.5 In-plane CTEs of thin polymer films
Sample a, iv>xm\l'^C\1 VHH / ^1 ippni/ \^ )
PMDA-ODA 27 1 LI ABPDA-PPD 1 1 1D. 1
FPI-45M' -4 S -4. J
FPI-46' -0 4
FPI-135 6 1 0. i
FPI-136*
FPI-136M* -2 2 7 9
FPI-137M* -2 0
Kapton® 30H^ 33 8 94 9
Kapton® 50H^ 32 2 91 (\
Kapton® 200H 31.4 22.0
Upilex® R 37.8 36.2
KODAK PET^ 18.3
GE PC^ 85.0
Tested only in the machine and transverse directions,
(ai^otmachmc and a2 ^transverse)
* Averaged in the range 50°C-100''C.
Examining the spin coated polyimides in Table 3.5, it is revealed that BPDA-
PPD has a significantly lower in-plane CTE than that ofPMDA-ODA. The reasoning is
clearly due to the greater degree ofbackbone rigidity in BPDA-PPD. Furthermore, a
comparison ofPMDA-ODA to the fluorinated polyimides shows that the fluorinated
polyimides have lower in-plane CTEs with some values which are even negative. These
fluorinated polyimides have a very high degree of in-plane orientation and therefore
tend to have low in-plane CTEs. In addition, studies by Sheth have seen slight, yet
noteworthy, deviations from linearity in the TMA traces for the fluorinated polyimides.
[1 1] As a result, two values for the in-plane CTEs of these fluorinated polyimides were
reported averaged over the temperature ranges 50°C-100°C and 150^C-200X.
59
For both the Kodak PET and the GE polycarbonate films, a heating rate of
5°C/min was used, and the average linear CTE was analyzed in the temperature range
between room temperature and their respective glass transition values.
Pressure-Volume-Temperature rPVT) Apparatus
The sample cell configuration used for all the PVT experiments is bellows #4,
long tube #24, partition #44, and sample container #64. The cross-sectional area of
bellows #4 is 1.209 cm'. [33] Knowing this area and the vertical displacement of the
bellows, the volume change of a sample can be determined.
For transmitting the pressure to the sample via the flexible bellows, a special
high temperature silicon oil (Dow Coming Corporation 21 OH Silicon Fluid) is required.
The hydrostatic pressure of silicon oil which surrounds the sample cell is applied by the
high pressure hand pump. Further, because high temperatures over long periods of time
tend to degrade the oil, fresh silicon oil is used for each sample run.
All experiments used pre-purified instrument grade triple distilled mercury from
D.F. Goldsmith Chemical and Metal Corp.. About 6-7 ml of fresh liquid mercury are
used for a typical sample experiment. The filling of the sample cell with mercury is
done using a special mercury filling apparatus under vacuum. Generally, the total
volume occupied by the polymer sample and mercury is no less than 0.1 cm^ from the
total volume of a completely filled sample cell containing only mercury.
Isothermal and isobaric calibrations were done to account for the volume change
of mercury due to pressure and temperature as well as any dimensional changes of the
sample cell and LVDT assembly. In the isothermal mercury calibration, the
60
displacement (Dl) of the LVDT rod is observed at several temperatures as a function of
pressure up to 200 MPa at 10 MPa intervals. From the data, a calibration curve equation
is produced with the variables temperature (T) and pressure (P). For a typical isothermal
calibration as shown in Figure 3.14, Dl(mm) = -2.2179 - 2.3562E-3*P - 3.9481E-7*P^ +
(7.8208E-3-5.051 1E-6*P+9.434E-9*P^)*T. On the other hand, the isobanc mercury
calibration observes the displacement of the LVDT on heating and on cooling at a rate
of 2.5°C/min as a function of temperature at constant pressure. As shown in Figure
3.15, Dl(mm) = -2.346 - 7.953E-3*T on heating, and Dl(mm) = -2.378 - 8.176E-3*T
on cooling. It should be noted that isobaric experimental data is usually not taken below
100°C on cooling runs because of difficulties in maintaining a constant cooling rate.
Lastly, the starting conditions for all PVT experiment are Dl (mm) = -2.000, P = 10
MPa, and T = 30°C.
In Figure 3.16, the volumetric thermal expansion as a function of five different
pressures are shown for a small rod of standard aluminum. Isobaric sample runs were
done from room temperature to 200°C, and the change in volume as a function of
temperature determines the volumetric thermal expansion. If the volumetric thermal
expansion was extrapolated to atmospheric pressure, a ay = 22.1 ppm/°C is calculated.
Values for the linear CTE of several common metals are published in the CRC Press
Handbook of Chemistry and Physics. [44] For example, the linear CTE for an Al alloy,
stainless steel 304, brass, and iron are around 9-12 ppm/°C. Assuming that the linear
CTE is 1/3 the value of the volumetric thermal expansion, the volumetric thermal
expansion experimentally determined for our aluminum sample is a reasonable value.
61
EE
c0)
E8TO
b
1 I I I1 ( r
0 50 100 150 200 250 300 350
Temperature (°C)
Figure 3,14 Isothermal mercury calibration
(Data points arc only shown for P = 10, 60, 1 10, and 160 MPa)
"1r r-
—~t— n
0 50 1 00 1 50 200 250 300 350
Temperature (°C)
Figure 3.15 Isobaric mercury calibration at 50 MPa
(Data points are plotted at 5 minute intervals: A heating run, • cooling
62
38.0
0 20 40 60 80 100 120
Pressure (MPa)
Figure 3.16 Volumetric thermal expansion as a function of pressure for aluminum
Over the past five years, our PVT Apparatus has been successfully used on
polyimide, polyethylene, poly(ethylene terephthalate), polycarbonate, polypropylene
[45], polyamide, rubber [18], and epoxy samples. From our experiences, solid pellets
are clearly the easiest samples to examine. Samples such as Kelvar® or Spectra® fibers
are difficult, if not impossible, to analyze using the PVT Apparatus.
In this thesis research, film samples were investigated using the PVT Apparatus.
For a typical sample run of a 10 ^im thick polyimide film, at least one sheet of film with
dimensions of 8.5" x 11" would be required. In addition, it was found that thinner films
had greater static attraction. Thus, the sample preparation of films thimier than 10 |im
was often a challenge. For the PVT experiments, polymer films were cut as long strips
having a width of 1 cm which were stacked together and then rolled into the sample
cell. This allows one to acquire enough sample and to minimize the amount of air in the
63
cell. In order to remove moisture, films were dried overnight under vacuum at 100°C
prior to the PVT analysis.
For the polyimide materials, the bulk compressibility was found by observing
isothermally the specific volume as a function of pressure. At a constant temperature,
the specific volume was studied as pressure was varied from 10 MPa to 100 MPa at 10
MPa increments. As a result, the bulk compressibility was measured at various
temperatures between 50-200°C, and by extrapolation, the bulk compressibility could
be determined at 25°C. In Figure 3.17, the isothermal PVT data for thermally cured
PMDA-ODA is shown. After reinterpreting the same isothermal data, Figure 3.18
shows the temperature dependence of bulk compressibility determined from the slope of
the specific volume versus temperature curves. Therefore, the bulk compressibility of
PMDA-ODA at 25°C can be calculated by extrapolation. Figures 3.19-3.22 illustrate the
isothermal PVT behavior of some Kapton® and fluorinated polyimides.
On the other hand, the determination of the volumetric thermal expansion, ay,
was accomplished by observing the specific volume at constant pressure as a function of
temperature. In this isobaric mode, the specific volume is measured for a constant
pressure as the temperature is increased at a rate of 2.5°C/min. from 50°C to 200°C. By
determining the volumetric thermal expansion at various pressures, the volumetric
thermal expansion at atmospheric pressure (P = 0) can be found by extrapolation. This
provides a good method because air effects on the PVT measurements are minimized at
higher pressures. As shown in Figures 3.23 and 3.24, the isobaric PVT behavior of
thermally cured PMDA-ODA and BPDA-PPD polyimides are represented. From the
64
0.725
0.720 -
^ 0.715
CD
E
o>o•MaoQ.w
0.710 -
0.705 -
0.700 -
0.695 -
0.690
• 20MPaV 40MPa
60 MPaA 80MPa
100 MPa
V
• V
^A A
A
• •V
V
• •• V
AA
• • V A
V V V A AV A A
A A A
A A
\I I
\ \\ 1 \
40 60 80 1 00 1 20 1 40 1 60 1 80 200 220
Temperature fC)
Figure 3.17 Isothermal PVT run on PMDA-ODA
0.400
^ 0.380
I
CO
CL
(J 0.360
OO
CO
0.340 -
0.320
0.300
0.280
0.260 \ 1 1 \ 1 1 1
\
40 60 80 100 120 140 160 180 200 220
Temperature (°C)
jure 3.18 Bulk compressibility as a function of temperature for PMDA-ODA
65
0.720
0.715
0.710
CD
E
o>oIE"o0)ClCO
0.705
0.700 -
0.695
0.690
0.685
20 MPa40 MPa60 MPa80 MPa100 MPa
V
A
V
A
V
A
• VV
V _A
V
A
V
A
V
A
A
I
^ \ \ \ \ \ \
40 60 80 100 120 140 160 180 200 220
Temperature fC)
Figure 3.19 Isothermal PVT run on Kapton® 200H
0.220
40 60 80 100 120 140 160 180 200 220
Temperature (°C)
Figure 3.20 Bulk compressibility as a function of temperature for Kapton® 50H
66
40 60 80 1 00 1 20 1 40 1 60 1 80 200 220
Temperature (°C)
Figure 3.21 Isothermal PVT run on FPI-137M
0.400
0.150I
1 \ \ \ r
40 60 80 1 00 120 1 40 1 60 1 80 200 220
Temperature (°C)
Figure 3.22 Bulk compressibility as a function of temperature for FPI-46
67
0.745
CO
0.740
§ 0.735
CD
E2 0.730O>o^ 0.725
0)
w0.720
0.715I
^T ] 1 1 1
40 60 80 100 1 20 140 1 60 1 80 200 220
Temperature (°C)
Figure 3.23 Isobaric PVT run at 10 MPa on PMDA-ODA
CO
E
0)
E
O>o
'o0)Q.C/)
0.708
0.704
0.700 -
0.696
0.692
0.688
40 60 80 100 1 20 140 1 60 1 80 200 220
Temperature (°C)
Figure 3.24 Isobaric PVT run at 10 MPa on BPDA-PPD
68
curve
was
specific volume versus temperature plot at constant pressure, the slope of the
allows one to calculate the volumetric thermal expansion.
In our analyses for the polyimides, the minimum temperature examined
50°C. In the published literature, it has been said that polyimides in the presence of
moisture tend to shrink at temperatures below 50°C. Therefore, it is common to see
published data on polyimides with 50°C as the minimum temperature of analysis. [5]
Table 3.6 Summary of PVT results on polyimides: Determination of out-of-plane CTEand out-of-plane Young's Modulus
Sample
(ppm/°C)
a,
(ppm/°C)f 1 av^i
lv„ d?)° T=25''C
(GPa-')
E33
(GPa)
PMDA-ODA 199.5 145.3 0.248 3.1
BPDA-PPD 145.7 139.5 0.212 6.1
FPI-45M 287.4 296.4 0.158
FPl-46 220.8 221.6 0.157
FPl-135 127.8 115.6 0.185 1.4
FPI-136 244.9 251.9 0.149
FPI-136M 122.2 126.6 0.144
FPI-137M 303.2 307.2 0.155
Kapton® 30H 171.6 113.6 0.173 3.7
Kapton® 5OH 177.4 123.6 0.150 4.1
Kapton® 200H 176.4 123.0 0.144 4.2
Upilex® R 148.5 74.5 0.135
Upilex® S 0.107
Kapton" H:v = 0.39, v = 0.52, v =v =0.34 [17]^ 12 :i 13 31
A summary of the all the PVT experiments on polyimides is given in Table 3.6.
The bulk compressibility at 25°C and the volumetric thermal expansion have been
69
measured for several commercial and thermally cured polyimides. For a given
polyimide, the variability m the PVT data among multiple sample runs is less than 5%.
This can be attributed to slight differences in the polyimide curing conditions as well as
the quality of loading the films into the PVT sample cell. Using values for the in-plane
Young's Moduli and the in-plane and out-of-plane Poisson's ratios, the out-of-plane
Young's Modulus is determined (Equations 3.22 and 3.23). On the other hand,
volumetric thermal expansion values were evaluated on isobars at 10 MPa. These values
should give a fair approximation to the volumetric thermal expansion at atmospheric
pressure. Using the values reported for the in-plane CTEs, the out-of-plane CTE is
calculated (Equation 3.24). As observed, the out-of-plane CTE can be many times
greater than the in-plane CTEs for a given material.
In comparison to PMDA-ODA, the Kapton® H has a lower bulk compressibility
and lower volumetric thermal expansion due to its higher crystalline order and greater
in-plane orientation. Although Kapton® is the chemically cured version ofPMDA-ODA,
the dissimilarity in properties can be attributed to differences in curing and processing
conditions. Among the Kapton® H films of various thicknesses, no apparent thickness
dependence on properties exists. The variability in bulk compressibility values can be
credited to differences in processing by tentering frames. In comparison to PMDA-
ODA, BPDA-PPD has a lower volumetric thermal expansion and a lower bulk
compressibility. This is due to the greater backbone rigidity and higher degree of planar
molecular orientation found in BPDA-PPD.
In addition, among the fluorinated polyimides, bulk compressibility values
appear rather similar. However, there exists differences in the volumetric thermal
70
expansion among the different fluorinated polyimides. Considering that the fluorinated
polyimides are typically described as rigid rods, no definitive correlation between
volumetric thermal expansion and the degree of rigidity in the chemical structure can be
accessed at this time. Among all the thermally cured polyimides, FPI-135 and FPI-
136M have one of the lowest out-of-plane CTEs. This finding may be of interest to
designers of microelectronic devices who use polyimide as the dielectric interlayer.
From the PVT data for the thermally cured polyimides, noticeable deviafions in
linearity are often seen in the specific volume versus temperature curves. As discussed
earlier, TMA studies by Sheth have seen similar behavior in fluorinated polyimides. The
reasoning for this unusual behavior can be attributed to p relaxations in polyimides. P
transitions are often found in amorphous polymers due to localized main chain motions
and side chain motions. Usually, differential scanning calorimetry does not have the
sensitivity to detect these secondary transitions, and techniques such as dilatometry,
dynamic mechanical analysis, dielectric relaxation, and NMR are required. [46] In past
research, dynamic mechanical relaxation studies on PMDA-ODA have observed a p
transition at ~80°C due to the coupled oscillations of the p-phenylene rings. [47]
Recently, studies on novel fluorinated polyimides have observed secondary transitions
ranging from 138°C to 302°C depending on the chemical structure. [48, 49] Further, P
transitions were found to be more pronounced for the fluorinated polyimides than for
traditional polyimides. Since the P relaxation is primarily a result of rotational motions
localized within the diamine segments, the addition of large fluorinated groups to the
rings of the benzidine structure generally increases the temperature of the p transitions.
71
In Table 3.7, a study of the volumetric thermal expansion averaged over two different
temperature ranges is presented. The break temperature of 125°C was picked arbitrarily.
As shown, the volumetric thermal expansion for the spin coated polyimides can have
widely different values depending upon the temperature range of analysis.
Table 3.7 Comparison on the volumetric thermal expansion of polyimides averagedover different temperature ranges
Sample (50-200°C)
(ppm/°C)
a, (50-125°C)
(ppm/°C)
a,(125-200°C)
(ppm/°C)PMDA-ODA 199.5 142.9 245.8BPDA-PPD 145.7 103.3 180.3
FPI-45M 287.4 187.4 367.5
FPI-46 220.8 175.6 269.6
FPI-135 127.8 53.8 204.3
FPI-136 244.9 203.3 296.9
FPI-136M 122.2 93.7 165.1
FPI-137M 303.2 230.1 344.0
Kapton"" 5OH 177.4 155.5 198.8
Kapton® 200H 176.4 149.7 216.7
Upilex® R 148.5 141.9 180.3
In Table 3.8, the Tait parameters for the polyimide materials are presented. The
values for spin coated PMDA-ODA, Kapton®, and Upilex® R are in agreement with
literature reported values. [5] Using the isothermal experimental data from 10 MPa to
50 MPa, the V(0,T) was determined by extrapolation to zero pressure. V^, Vj, V2
(Equation 3.18) could then be evaluated by fitting the V(0,T) data to a 2"^^ order
polynomial. Lastly, and Bj (Equation 3.19) were determined from fitting the
complete specific volume data to the Tait equation.
72
Table 3.8 Coefficients for the Tait equation
Sample V0 V Bi B,PMDA-ODA 0 7138 0. loJn- / 251.3 2.649E-3BPDA-PPD 0.6883 1 14QF-4 Z./Z /li- / 728.6 3.136E-3FPI-45M 0.6476 0. / 1 Oli- / jU7.0 4.91 OE-3FPI-46 0.6403 6 OO'^F-S\j - yj^ ^ u jUo.z 4.877E-3FPI-136 0.6447 A 1 AST? 7 A 07 /I4v /.4 5.532E-3FPI-136M 0 6473 1 1 Q'^P 7 ^77 A
5.377E-3FPI-137M 0.6439 9 022F-S A AQAV 7 jUo.4 4.93 lE-3
Kapton* 5OH 0.6936 7.818E-5 1.825E-7 555.5 2.216E-3Kapton* 200H 0.6964 5.318E-5 2.797E-7 595.7 1.700E-3Upilex* R 0.7189 6.367E-5 1.743E-7 616.1 2.136E-3Upilex* S 0.6813 3.372E-5 9.275E-8 788.4 1.764E-3
Similar PVT measurements have also been made on commercial PET and
polycarbonate films. In Figure 3.25, the glass transition (Tg ~ 80°C) and melting
transition (T„ ~ 250°C) ofPET can be observed. In Figure 3.26, the glass transition of
polycarbonate can be seen around 140°C. The onset of these transitions agrees well with
that measured by differential scanning calorimetry in Chapter 2. In comparison to PVT
studies by Zoller on PET and polycarbonate materials, the results appear quite similar.
Furthermore, if our results had been taken with greater detail, the observation of the
pressure dependence on the glass transition temperature may have been more apparent.
[50-52] As a result, volumetric thermal expansion and bulk compressibility for PET and
polycarbonate films have been measured and are reported in Table 3.9. In combination
with their in-plane CTE values using TMA, the out-of-plane CTE can be approximated.
73
0.840
0.820
0.800CO
Eo— 0.7800)
E-5 0.760 -
O>^ 0.740
*oCD
^ 0.720 ^
0.700
0 680
• 20 MPaV 60 MPa
100 MPaA 140 MPa
180 MPa
Vs
V
A
V
A
V
A
50 100
••
•
V V V
A A A
A
150 200
Temperature fC)
250 300
Figure 3.25 Isothermal PVT run on Kodak PET
Eo
0.960
0.940 H
0.920
0.900
0)
£ 0.880 -
o>o
0.860
0.840 HO0)Q.</) 0.820
0.800
0.780
• 20 MPaV 60 MPa
100 MPaA 140 MPa
180 MPa
V
A A
V
A
VV
A
V• V
• V
• V A• V A
• V AV
V
AA
A AA
50 100 150 200
Temperature CC)
250 300
Figure 3.26 Isothermal PVT run on GE polycarbonate
74
Table 3.9 Summary ofPVT results on Kodak PET and GE polycarbonate:Determination of out-of-plane CTE
Sample Temperature
Range (ppm/°C)
a,
(ppm/°C)f 1
T=25''C
(GPa')Kodak PET T<T
T <T<T323.9
426.3
287.3 0.14
GE PC T<T,
T>T,432.9
746.1
262.9 0.20
Conclusions
In this chapter, the out-of-plane properties of several thin polyimide films were
investigated. Vibrational holographic interferometry was used to determine the principal
directions of stress and in-plane Poisson's ratios. The out-of-plane Poisson's ratios were
measured using high pressure gas dilatometry. The in-plane Young's Moduli were
found from standard tensile testing, and the in-plane CTEs were acquired from
thermomechanical analysis. Combining the above experimental results with bulk
compressibility and volumetric thermal expansion measurements from the PVT
Apparatus, the out-of-plane coefficient of thermal expansion and out-of-plane Young's
Modulus could be determined. As a result, an understanding of out-of-plane properties
of polyimides is important for predicting reliability in multilayered microelectronic
packages. In addition, similar studies have been achieved on commercial PET and
polycarbonate films.
75
References
1. P. A. Flinn, "Mechanical Stress in VLSI Interconnections: Origins, Effects,Measurements, and Modeling," MRS Bulletin, pp. 70, 1 995.
2. R. Larson, "Back to Basics is Necessary for Viable FEA Modeling," PlasticsEngineering, pp. 29, 1992.
3. J. Bicerano, Prediction ofPolymer Properties, 2 ed. New York, NY: MarcelDekker, Inc., 1996.
4. K. C. Sheth, M. J. Chen, and R. J. Farris, "Characterization of Elastic Constantsand Stress in Low Thermal Expansion Polyimides," presented at 5^^
International Conference on Polyimides - New Trends in Polyimide Science andTechnology, Ellenville, NY, 1994.
5. M. T. Pottiger and J. C. Cobum, "Out-of-plane Expansion Measurements in
Polyimides Films," presented at ACS Symposium Series, pp. 282, 1993.
6. M. T. Pottiger and J. C. Cobum, "Modeling Stresses in Polyimide Films,"
presented at Mat. Res. Soc. Symp. Proc, pp. 527, 1993.
7. J. Dolbow and M. Gosz, "Effect of Out-of-plane Properties of a Polyimide Film
on the Stress Fields in Microelectronics Structures," Mechanics ofMaterials,
23(4), pp. 311, 1996.
8. S. G. H. Anderson and P. S. Ho, "Chemistry, Reactivity, and Fracture of
Polymer Interfaces," Characterization ofPolymers, H. Tong, S. P. Kowalczyk,
R. Saraf, and N. J. Chou, Eds. Stoneham, MA: Butterworth-Heinemann, 1994.
9. H. M. Tong, K. D. Hsuen, K. L. Saenger, and G. W. Su, "Thickness-Direction
Coefficient of Thermal Expansion Measurement of Thin Polymer Films," Rev.
Sci. Instrum., 62(2), 1991.
10. T. C. Hodge, S. A. Bidstrup, P. A. Kohl, J. B. Lee, and M. G. Allen, "In-situ
Determination of Thickness Direction Thermal Strain of Spin-coated Polymer
Films," presented at International Symposium on Advanced Packaging
Materials, Atlanta, GA, 1995.
IL K. C. Sheth, "Stress, Mechanical and Thermal Characterization of Anisotropic
Polyimide Thin Films and Coatings," Polymer Science and Engineering
Department. University of Massachusetts Amherst, Ph.D. Thesis, 1996.
76
12. T. S. Gross, D. V. Zhmurkin, L. P. Buchwalter, and F. B. Kaufman,"Thermomechanical Deformation of 1 ^im Thick Cu-Polyimide Line ArraysStudied by Scanning Probe Microscopy," Journal ofElectronic Materials,submitted for publication, 1995.
13. L. E. Malvern, Introduction to the Mechanics ofa Continuous Medium.Englewood Cliffs, NJ: Prentice-Hall Inc., 1969.
14. B. F. Blumentritt, "Anisotropy and Dimensional Stability of Polyimide Films,"Polymer Engineering and Science, 1 8( 1 6), pp. 1 2 1 6, 1 978
.
15. J. M. Whitney and R. L. McCullough, "Introduction to Anisotropic Elasticity,"
in Micromechanical Materials Modeling, 2, L. A. Carlsson and J. W. Gillespie,
Eds. Lancaster, PA: Technomic Publishing Co., 1992.
1 6. Q. K. Tong, "A Structure Property Investigation of a Multi-ComponentPolyacrylate Photoresist," Polymer Science and Engineering Department.University of Massachusetts Amherst, Ph.D. Thesis, 1993.
17. M. A. Maden, "The Determination of Stresses and Material Properties ofPolyimide Coatings and Films Using Real Time Holographic Interferometry,"
Polymer Science and Engineering Department. University of Massachusetts
Amherst, Ph.D. Thesis, 1992.
18. D. Macon, "Thermal and Mechanical Behavior of Rubber Systems," Polymer
Science and Engineering Department. University of Massachusetts Amherst,
Ph.D. Thesis, 1996.
19. J. K. Vrtis, "Stress and Mass Transport in Polymer Coatings and Films,"
Polymer Science and Engineering Department. University of Massachusetts
Amherst, Ph.D. Thesis, 1995.
20. R. J. Farris, J. K. Vrtis, C. Jou, M. J. Chen, and K. C. Sheth, "Experimental
Stress Analysis Methods for Coatings," presented at Advanced Coatings
Technology Conference - Engineering Society, 1 994.
21 . M. S. Hess, Journal ofComposite Materials, 3(10), pp. 630, 1969.
22. F. Bowman, Introduction to Bessel Functions. New York, NY: Dover
Publications, Inc., 1958.
77
23. M. A. Maden, K. Tong, and R. J. Farris, "Measurement of Stresses in ThinFilms Using Holographic Interferometry: Dependence on AtmosphericConditions," Material Research Society Symposium, 188, pp. 29, 1990.
24. M. Abramowita and I. A. Stegun, Handbook ofMathematical Functions NewYork, NY: Dover Publications, Inc., 1964.
25.
W.D.J. Callister, Materials Science and Engineering - An Introduction NewYork, NY: John Wiley & Sons, Inc., 1985.
26. R. J. Farris and R. Falabella, "The Influence of Cavitation in the MechanicalBehavior of Filled Polymers and Heat Build Up in Nonhysteretic Elastomers,"presented at Elastomers and Rubber Technology, pp. 197, 1987.
27. C. L. Bauer, "The Determination of Mechanical Behavior of PolyamicAcid/Polyimide Coatings," Polymer Science and Engineering Department.University of Massachusetts Amherst, Ph.D. Thesis, 1988.
28. C. L. Bauer and R. J. Farris, "Determination of Poisson's Ratio for PolyimideFilms," Polymer Engineering and Science, 29(16), pp. 1 107, 1989.
29. P. Zoller, P. Bolli, V. Pahud, and H. Ackermann, "Apparatus for MeasuringPressure-Volume-Temperature Relationships of Polymers to 350°C and 2200kg/cm2," 7?ev. Sci. lustrum., 47(8), pp. 948, 1976.
30. P. Zoller, "Dilatometry," in Encyclopedia ofPolymer Science and Engineering,
5, H. Mark, N. Bikales, and C. Overberger, Eds., 2 ed. New York, NY: WileyInterscience, 1986.
31. Y. A. Fakhreddine and P. Zoller, "Pressure-Volume-Temperature Studies: AVersatile Analytical Tool for Polymers," presented at SPE ANTEC, Boston,
MA, pp. 1642, 1991.
32. T. Wiegmann and F. Oehmke, "Measuring the PVT Behavior of Polymers,"
presented at SPE ANTEC, Boston, MA, pp. 1646, 1991.
33. P. Zoller, "PVT Manual (Version 2.01)," Gnomix Inc., Boulder, CO, 1987.
34. Y. A. Fakhreddine and P. Zoller, "The Equation of State of Solid and Molten
Poly(butylene terephthalate) to 300°C and 200 MPa," Journal ofPolymer
Science: Part B: Polymer Physics, 29, pp. 1 141-1 146, 1991.
78
35. P. Zoller, "Pressure-Volume-Temperature Relationships of Solid and MoltenPolypropylene and Vo\y{hniQnQ-\)r Journal ofApplied Polymer Science 23 pp1057-1061,1979. ' '
i^F-
36. J. He and P. Zoller, "The Equation of State of Water to 250°C and 200 MPaObtained from a High Pressure Dilatometer," Rev. Sci. Instrum., 62(5) pp 13041991.
37. P. Zoller and H. H. Hoehn, "Pressure-Volume-Temperature Properties of Blendsof Poly(2,6-dimethyl-l,4-phenylene ether) with Polystyrene," Jowrwa/ ofPolymer Science: Polymer Physics Edition, 20, pp. 1385-1397, 1982.
38. H. W. J. Starkweather, P. Zoller, and G. A. Jones, "The Heat of Fusion ofPoly(ethylene terephthalate)," Journal ofPolymer Science: Polymer PhysicsEdition, 21, pp. 295-299, 1983.
39. J. He and P. Zoller, "A Dilatometric Study of the Crystallization Kinetics ofPolypropylene at Pressures to 200 MPa," presented at SPE ANTEC, Boston,
MA, pp. 1723, 1991.
40. P. Zoller, "PVT Relationships and Equations of State of Polymers," in PolymerHandbook, J. Brandrup and Immergut, Eds., 3 ed. New York, NY: Wiley and
Sons, 1989.
41. S. G. Lekhnitskii, "Theory of Elasticity of an Anisotropic Body," MIR, 1981.
42. R. J. Farris, R. Falabella, and Y. D. Tsai, presented at ACS Symposium Series,
1979.
43. "ASTM D882-88: Standard Test Method for Tensile Properties of Thin Plastic
Sheeting," Annual Book ofASTM Standards, 1 988.
44. R. C. Weast, CRC Handbook of Chemistry and Physics, 66 ed. Boca Raton, FL:
CRC Press, Inc., 1986.
45. S. Tandon, "Modeling of Stresses in Cylindrically Wound Capacitors:
Characterization and Influence of Stress on Dielectric Breakdown of Polymeric
Film," Polymer Science and Engineering Department. University of
Massachusetts Amherst, Ph.D. Thesis, 1997.
46. J. J. Aklonis and W. J. MacKnight, Introduction to Polymer Viscoelasticity, 2
ed. New York, NY: John Wiley & Sons, Inc., 1983.
79
47. J. M. Perena, "Dynamic Mechanical Relaxations in Polyimide andPolyamideimidQ," Die Angewandte Makromolekulare Chemie, 106, pp. 61-66,1 9S •
48. F. E. Arnold, K. R. Bruno, D. Shen, M. Eashoo, C. Lee, F. W. Harris, and S. Z.D. Cheng, "The Origin of p Relaxations in Segmented Rigid-Rod Polyimide andCopolyimide Films," Polymer Engineering and Science, 33(21), pp. 1373, 1993.
49. J. C. Cobum, P. D. Soper, and B. C. Auman, "Relaxation Behavior ofPolyimides Based on 2,2'-Disubstituted Benzidines," Macromolecules 28(9)pp. 3253, 1995.
50. P. Zoller and P. Bolli, "Pressure-Volume-Temperature Relationships of Solidand Molten Poly(ethylene terephthalate)," J. Macromol. Sci. - Physics B18(3)
pp. 555-568, 1980.
51. P. Zoller, "A Study of the Pressure-Volume-Temperature Relationships of FourRelated Amorphous Polymers: Polycarbonate, Polyarylate, Phenoxy, andPolysulfone," Journal ofPolymer Science: Polymer Physics Edition, 20, pp.1453-1464, 1982.
52. H. A. Schneider, B. Rudolf, K. Karlou, and H.-J. Cantow, "Pressure Influence
on the Glass Transition of Polymers and Polymer Blends," Polymer Bulletin, 32,
pp. 645-652, 1994.
80
CHAPTER 4
PRESSURE-INDUCED CRYSTALLIZATION IN POLYIMIDES
Introduction
Although most aromatic polyimides have highly regular chemical structures,
they are generally amorphous or have low degrees of crystallinity. The primary
reasoning lies in the extremely slow rate of crystallization for polyimides. During curing
in the precursor state, there is a lack of molecular mobility required for packing and
crystallization due to steric hindrance and high viscosity. In the literature, investigations
into the crystallinity of aromatic polyimides have usually been established by wide x-
ray diffraction (WAXD) on oriented polyimide fibers or on polyimide films oriented by
high temperature stretching. [1,2] Further, research studies by Wang et al. have
explored the solvent-induced crystallization of aromatic polyimides at elevated
temperatures. [3] Lastly, the development of crystallinity for an aromatic polyimide
precipitated from solution has also been reported. [4]
For polymer materials, characterization techniques to study the degree of
crystallinity usually involve WAXD, differential scanning calorimetry, density
measurements, infrared spectroscopy and nuclear magnetic resonance. [5] In the early
1970's, significant x-ray analyses by Kazaryan et al. looked at the crystalline structure
in oriented fibers of PMDA-ODA. [6] From the x-ray patterns taken, the periods along
the chain axis were determined, and the 3-dimensional cell dimensions were calculated.
81
Moreover, the density of the PMDA-ODA crystaUites was estimated to have a value of
1.56 g,W.
In past research by Jennings and Farris, the production of a highly crystalline
aromatic PMDA-ODA polyimide has been detailed. [7, 8] Using a special high pressure
thermal curing technique on the poly(amic acid) solution ofPMDA-ODA, a highly
crystalline polyimide powder was prepared. The experimental conditions included
pressures up to 650 psi (-4.5 MPa) and temperatures up to 260°C under nitrogen gas for
several hours. From WAXD studies, one of the sharpest scattering patterns for a
polyimide was observed which is indicative of a high degree of crystallinity and long
range order. In support of their discovery, density measurements of this polyimide
powder revealed a density of 1 .46 g/cm^ as opposed to 1 .40-1 .42 g/cm^ for typical
polyimide films. The existence of birefringence was also noted using optical
microscopy with cross polarizers. From differential scanning calorimetry and
thermogravimetric analysis, an estimated melting temperature of 594°C was determined
as predicted for PMDA-ODA by Bessonov. [9] Similar research on the high pressure
polycondensation of aliphatic and aromatic polyimides has also been reported. [10]
However, these highly crystalline polyimides were prepared from their salt monomers
in a 200-600 MPa piston-cylinder type hot pressing apparatus at temperatures of 280°C
for 3-30 hours.
From our initial research on the PVT properties of polyimides as discussed in
Chapter 3, a rather interesting finding was discovered. Under relatively high hydrostatic
pressures and temperatures, several thermally cured polyimides exhibited an irreversible
82
0.750
0.740
CO
i 0.730
E-2 0.720 -
O>O^ 0.710
<DQ.CO
0.700
0.690
• 20 MPaV 60MPa
100 MPaA 140 MPa
180 MPa
VVVV
V
V
V
VV
A
V
aA^
A
AAA^A
0 50 100 150 200 250 300 350
Temperature (°C)
Figure 4.1 Isothermal PVT experiment on PMDA-ODA film under high pressures and
temperatures
densification behavior. As shown in Figure 4.1, a PMDA-ODA film fully cured at
350°C was subjected to an isothermal PVT experiment in which a maximum
temperature of 3 1 5°C and a maximum pressure of 200 MPa were attained. The results
illustrate a significant specific volume decrease in the polyimide beginning around
270°C. It should be noted that the PVT experiments done on polyimides (i.e. Figure
3. 17) in the previous chapter were performed up to a maximum pressure of 100 MPa.
Furthermore, similar densification behavior was also seen experimentally in thermally
cured BPDA-PPD and FPI-135 films, but not in commercial films of Kapton®.
Therefore, various characterization techniques such as optical microscopy, density
measurements, and WAXD have been used to probe the microstructural and physical
property changes in polyimides exposed to high pressures and temperatures. If
83
significant densification m polyimides occurs due to high pressures and temperatures,
this fact may explam why dielectric interlayer delammation or cracking in muhi-chip
module packages is occasionally seen for polyimides under highly constrained
conditions.
Experimental
Four different batches of spin coated PMDA-ODA films have been observed to
irreversible densify as a result of high pressures and temperatures using the PVT
Apparatus in the isothermal run mode. Comparisons between the original and the PVT
treated polyimide films were studied. All films were fully cured at 350°C following the
normal curing procedures outlined in Chapter 2. All PVT treated films were exposed to
temperatures slightly above 300°C and hydrostatic pressures up to 200 MPa. It should
be mentioned that the glass transition temperature ofPMDA-ODA has a reported value
of 400°C at atmospheric pressure. [11] Thus, the highest temperatures that the PVT
treated polyimide films experience are lower than their final cure temperature as well as
their glass transition temperature.
X-ray Photoelectron Spectroscopy fXPS^
Surface analysis by x-ray photoelectron spectroscopy (XPS) or more commonly
known as Electron Spectroscopy for Chemical Analysis (ESCA) is a good technique for
determining if the element mercury exists near the surface or within the PVT treated
PMDA-ODA film sample. XPS involves the irradiation of a solid sample in vacuum
with monoenergetic soft A1K„ x-rays (1486.6 eV) and then sorting out the emitted
84
electrons by energy. Each element has its own characteristic energy spectrum, and
mercury gives distinctively sharp and strong intensity peaks which make it an easy
element for detection.
Optical Microscopy
To check for any preferential in-plane chain orientation, an Olympus® BH-2
optical microscope with cross polarizers and a full wavelength plate (X = 530 nm) were
used. For normal spin coated PMDA-ODA films, there is a high degree of in-plane
isotropy, and no birefringence should appear. [12, 13] In comparison, Kapton® films
have been seen under cross polarizers to be birefringent with oriented patterns of fine
bright or dark lines. [2]
Wide Angle X-ray Diffraction (WAXD^
WAXD studies were accomplished to probe the degree of crystalline order in the
original and PVT treated PMDA-ODA films. [14] These experiments were done in
transmission mode using the Siemens Diffractometer D500 with a Ni filtered CuK„
radiation source (A, = 1.5418A). The x-ray generator operated at 40 kV and 30 mA, and
data was taken at a scan rate of 0.2°/min from 20 = 2° to 30°.
Density Measurements
All density measurements for the polyimides were done using the flotation
technique as described previously in Chapter 2.
85
Results and Disciissinn
Isobaric PVT Experiment
0.725
0 50 100 150 200 250 300 350
Temperature (°C)
Figure 4.2 Densification behavior in 10 |im spin coated PMDA-ODA film under a
constant hydrostatic pressure of 100 MPa
To elucidate the effects of a constant high pressure on PMDA-ODA films, an
isobaric PVT experiment was performed. In contrast, the isothermal PVT experiments
expose a sample to a given temperature, but the hydrostatic pressure is applied
incrementally from 10 MPa to 200 MPa within a 3-5 minute period. As shown in Figure
4.2, a 10 (j.m spin coated PMDA-ODA film under a constant hydrostatic pressure of 100
MPa was heated from room temperature to approximately 300°C, held for 1 hour, and
then cooled to 30°C. Examining the region during headng between 170-200°C, the
86
specific volume of the polyimide rapidly dropped to a point, and then increased again.
On cooling, the specific volume versus temperature behavior followed a different path
from the heating run and indicates that the polyimide film is smaller than its original
size. Comparisons at 25°C between the original specific volume (V„ = 0.709 cmVg) and
final specific volume (V, = 0.683 cmVg) reveal a 3.7% specific volume decrease in the
polyimide film. On second heating, the specific volume versus temperature behavior did
not exhibit any densification, and the second cooling run followed the previous heating
run fairly well. Further, comparisons at 25°C between the original density (p„ = 1.40
g/cm') and final density (p^^ 1.45 g/cm') show a 3.6% increase in density.
X-rav Photoelectron Spectroscopy rXPS)
From Figures 4.3 and 4.4, XPS measurements indicate that no mercury existed
within the PVT treated polyimide films. The spectra plots obtained show the number of
emitted electrons per energy interval versus their kinetic energy. Peaks corresponding to
the atomic orbitals of specific elements have been labeled. As indicated in the literature,
mercury would exhibit highly intense peaks due to the electrons from their 4f orbitals.
[15] Both take-off angles of 15° and 75° were studied which correspond to a sampling
depth of 1 5 A and 45 A respectively. This qualitative technique provides us with the
assurance that the liquid mercury used in the PVT experiments did not penetrate nor
chemically react with the sample. Further, the existence of mercury within the film
sample would certainly affect density measurements on the PVT treated films.
87
Hi
Figure 4.3 XPS ofPMDA-ODA film (PVT treated): 15° take-off angle
1000.0 900.0 800.0 700.0 GOO.O 500.0 mO 300.0 200.0 100.0 0 0
BINDING ENERGY. eV
Figure 4.4 XPS ofPMDA-ODA film (PVT treated): 75° take-off angle
88
Figure 4.5 PMDA-ODA film (Original): SOX, crossed polarizers, Xwavelength plate
Optical Microscopy
On direct visual and physical inspection, the PVT treated PMDA-ODA films
appeared significantly darker and very bnttle in comparison to the original films. Upon
removal from the PVT sample cell, the PVT treated films are very stiff and take the
shape of the cylindrical sample chamber.
Using optical microscopy, the original spin coated PMDA-ODA films have a
dark and uniform appearance under cross polarizers. Polarization colors are constant
over the extended areas when a fiill wavelength plate (I = 530 nm) is inserted at 45° to
the polarizers as shown in Figure 4.5. With the full wavelength plate, the wave
retardation is exactly one wavelength if the incident light is 530 nm. On the other hand,
as revealed in Figure 4.6, the PVT treated films exhibit Maltese cross-like patterns. It
could be suggested that crystallization may be induced near small voids or dust particles
within the film. However, the patterns may solely represent stressed regions around
voids. Using a full wavelength plate, regions of orange colors and regions of blue colors
appear which are indicative of birefringence and orientation in the PVT treated PMDA-
ODA films.
Wide Angle X-ray Diffraction rWAXD)
As shown in Figure 4.7, WAXD studies of the PVT treated PMDA-ODA films
show a highly sharp distinctive peak in the scattering pattern at 20 = 5.6°. Density
measurements also confirm an increase in density of the PVT treated polyimides. Using
Bragg's law, nA, = 2dsin0, a repeat distance of 16 A is calculated. Published literature on
90
(002)
Original Sample (p=1.40 g/cc)
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0
20
Figure 4.7 WAXD on PMDA-ODA films
PMDA-ODA films indicate that this particular d-spacing is typically referred to as the
intrachain repeat distance and is defined as the periodically repeating structure within
the polymer chains. More importantly, this (002) diffraction peak at 20 = 5.6° is
associated with crystalline ordering. From WAXD studies by Cobum et al. on spin
coated PMDA-ODA films prepared at curing temperatures of 250°C, 300°C, 400°C,
and 450°C, the intensity of the (002) diffi-action peak increases with higher curing
temperatures. [16-18] Furthermore, additional diffraction peaks such as the (004) peak
begin to appear with PMDA-ODA films cured at 450°C. Polyimides tend to have higher
crystallinity when cured at higher temperatures due to greater chain extension and
ordering effects. Since the (004) diffraction peak is also seen in our PVT treated
91
PMDA-ODA films at 26 = 1 1.0°, there is even greater evidence of higher crystalline
ordering.
Density Measurements
One method to estimate the degree of crystallinity in a polymer material is based
on density measurements. [12]
f _ P~Pa^ n -n (4.1)
fg = volume fraction crystallinity
p = density of total material
p, = density of crystalline phase
Pa = density of amorphous phase
According to Equation 4.1, the volume fraction crystallinity can be calculated
knowing the density of the material in question, the density of the crystalline phase, and
the density of the amorphous phase. Usually, WAXD is used to calculate the density of
the crystalline phase from unit cell parameters. As mentioned previously, the value of p,
was calculated to be 1.56 g/cm^ based on research by Kazaryan. [6] According to Perez,
fully cured PMDA-ODA films typically have a crystallinity of about 10%. [8] If p =
1.40 g/cm\ then p^ should equal 1.38 g/cm\ This value definitely appears as a
reasonable density for a PMDA-ODA polyimide which is fully imidized yet only
exposed up to a maximum temperature of 200°C. Therefore, the calculafion for the PVT
treated PMDA-ODA film in Figure 4.7 results in an esfimated degree of crystallinity of
33%.
92
Conclusions
With the use of optical microscopy, density measurements, and wide-angle x-ray
diffraction, pressure-induced crystallization of thin thermally cured PMDA-ODA
polyimide films were studied and validated. The importance of this finding is great
when one considers that similar temperature and stress conditions may exist for
polyimides in multi-chip modules. During fabrication of these muldlayered
microelectronic devices, polyimides are exposed to high temperatures and repeated
thermal cycling. Further, the effects from the other layers of polymers, metals, and/or
ceramics in a highly constrained situation can lead to significant pressures. Therefore,
any appreciable amount of densification and microstructural change in polyimides may
result in material delamination or cracking.
A simple estimate can be made concerning the amount of stress which could
develop for a polyimide in a highly constrained region. As expressed in the previous
chapter, the relationship between the normal stresses and normal strains for an
orthotropic linearly elastic material can be written as
8,1 -aiAT = C,,CT]| +€,2^22 +C,3CT33
822 - a2^T - C2ian + C22CJ22 + ^23(733
833 -a3AT = C31CT11 +C32a22 + C33a33(4 2)
8ij= normal and shear strains
ttj = coefficients of thermal expansion
T = temperature
Cjj = compliances
= normal and shear stresses
93
After adding together the three equations and substituting the relationships
= ^22 = C733 = -P and 8 11= = £33 = 0 for a material which is 3-dimensional
constrained such as at a comer, Equation 4.3 results. P represents the pressure which
arise due to the volumetric thermal expansion in a constrained situation.
Using PMDA-ODA as an example, P = (0.8 MPa)AT/°C when the volumetric
thermal expansion, a^, is 200 ppm/°C and bulk compressibility (Equation 3.22) is 0.25
GPa"'. Therefore, if the polyimide is subjected to a typical thermal treatment up to
300°C, pressures as high as 240 MPa are possible. However, it should be clarified that
this analysis does not account for the relaxation of the sample over time in response to
the high stress. In the real case scenario, the pressure is probably not a constant value
and may diminish to a degree upon densification of the sample.
a,,AT
(4.3)
94
References
1.
G. Conte, L. Dllario, and N. V. Pavel, "An X-ray and Conformational Study ofKapton® H," Journal ofPolymer Science: Part B: Polymer Phvsics 14 nn1553-1560, 1976. '
'
2. R. F. Boehme and G. S. Cargill, "X-ray Scattering Measurements DemonstratingIn-plane Amsotropy m Kapton Polyimide Films," in Polyimides: SynthesisCharacterization and Applications, 1, K. L. Mittal, Ed. New York NY" PlenumPress, pp. 461, 1984.
J. Wang, T. Dibenedetto, J. F. Johnson, S. J. Huang, and J. L. Cercena, "Solvent-induced Crystallization of Aromatic Polyimide," Polymer, 30(4), pp. 718, 1989.
4. A.J. Waddon and F. E. Karasz, "Crystalline and Amorphous Morphologies ofan Aromatic Polyimide Formed on Precipitation From Solution " Polymer33(18),pp. 3783, 1992.
3.
5 Z. Mo and H. Zhang, "The Degree of Crystallinity in Polymers by Wide-angleX-ray Diffraction (WAXD),"y.M5'.-/?ev. Macromol. Chem. Physc
, C35(4) pp555-580, 1995.
6. L. G. Kazaryan, D. Y. Tsvankin, B. M. Hinzburg, S. Tuichiev, L. N. Korzhavin,and S. Y. Frenkel, "X-ray Diffraction Study of the Crystalline Structure ofAromatic Polyimides," Vysokomol. soyed, A14, pp. 1199, 1972.
7. R. M. Jennings and R. J. Farris, "Formation of a Highly Ordered Poly(N, N'-Bis-
Phenoxyphenylpyromellitimide) Powder Using a High Pressure Curing
Technique," Journal ofPolymer Science: Part B: Polymer Physics, 32, pp.
1457-1464, 1994.
8. M. Perez, Y. Ren, R. J. Farris, and S. L. Hsu, "Characterization ofPMDA-ODAPolyimide Films by External Reflectance Infrared Spectroscopy,"
Macromolecules, 27, pp. 6740, 1994.
9. M. I. Bessonov, M. M. Koton, V. V. Kudryavtsev, and L. A. Laius, "Practical
Applications of Polyimides," in Polyimide: Thermally Stable Polymers. NewYork, NY: Consultants Bureau, 1987.
10. Y. Imai, "High Pressure Polycondensation (For High Temperature Polymers),"
in The Polymeric Materials Encyclopedia, J. C. Salamone, Ed. Boca Raton, FL:
CRC Press, Inc., 1996.
95
11. C. E. Sroog, "Polyimides," Progress in Polymer Science, 1 6, pp. 56 1 -694, 1 99
1
12. D. Campbell and J^R. White, Polymer Characterization: Physical Techniques.London, England: Chapman and Hall Publishing Co., 1989.
F W. J. Billmeyer, Textbook ofPolymer Science, 3 ed. New York, NY- JohnWiley & Sons, Inc., 1984.
13
on14. J. H. Magill, "Morphogenesis of Solid Polymer Microstructures," in Treatise
Materials Science and Technology: Properties ofSolid Polymeric Materials -
Part A, 10, J. M. Shultz, Ed. New York, NY: Academic Press, 1977.
15. "Handbook of X-ray Photoelectron Spectroscopy," Perkin-Elmer.
16. J. C. Cobum and M. T. Pottiger, "The Relationship of Morphology to Propertiesm Spm Coated Polyimide Films," presented at SPE ANTEC, pp. 656, 1993.
17. J. Cobum and M. Pottiger, "The Influence of Processing Condition on Structure,Properties, and Stress Development in Spin Coated Polyimide Films," presentedat Advances in Polyimide Science and Technology, 1991.
18. J. C. Cobum and M. T. Pottiger, "Thermal Curing in Polyimide Films andCoatings," in Polyimides: Fundamentals and Applications, M. Ghosh and K. L.
Mittal, Eds. New York, NY: Marcel Dekker, Inc., 1996.
96
CHAPTER 5
STRESS MEASUREMENT IN POLYIMIDE FILMS BY WAVEPROPAGATION TECHNIQUES
Introduction
Tenter frame processing is a fast continuous means of polymer film production
in which the degree of drawing can be varied. Generally, polymer films begin either as
melt cast film in the case of Estar® poly(ethylene terephthalate) (PET) or as a solvent
cast film in the case of Kapton® polyimide. As shown in Figure 5.1, both edges of the
line through various stages of thermal or chemical treatments. Stretching of the film
may occur in the transverse direction as well as the machine direction in a one-stage or
two-stage process. Especially in Kapton® film lines, it should be noted that a drawing
effect in the film also occurs from large shrinkages due to solvent removal. The speed of
these tenter frame lines normally may reach 10-50 ft/min, and the width of the lines may
be as large as several meters. [1,2]
film are held tightly by a series of tenter clips, and the sheet moves down the production
Coolingrolls
Heated zones
Accelerating tenter clips
Wind-up
Figure 5.1 A typical tenter frame line for thermoplastics
97
Commercial production of polyimide and poly(ethylene terephthalate) films for
electronic applications such as flexible printed circuit boards is commonly
accomplished by tenter frame processing. However, studies have shown that significant
problems exist with polymer films processed on tentering frames. For instance, warping
may appear after the film is removed from the tentering frame. In another case, the
polymer film may appear initially flat, but upon heating, the film changes shape and
warps permanently. For polyimide films used as substrates for metallizafion, warping
would have drastic effects. If multilayered laminates of polyimide films are constructed,
the warping effects become amplified and may cause eventual structural failure. In
addition, large spatial variations in properties such as moduli, birefringence, and thermal
expansion across the width of the film are common problems. There exists distinctive
in-plane orientation in which the maximum orientation does not appear in the machine
nor transverse directions but at ± 45° to the machine direction. Studies by Blumentritt
on 1,3, and 5 mils thick Kapton® films revealed that significant property variations
exist within the plane for modulus, ultimate strength, ultimate elongation, and thermal
expansion and hygroscopic expansion coefficients. [3] This preferred orientation in the
polyimide films is a result of tenter frame processing. Similar findings have also been
reported by Sakamoto and others on PET films manufactured on a tenter frame. [4, 5]
Jennings and Farris performed what is believed to be the first ever mathematical
stress analysis of polymer films during the tenter frame process. [6, 7] The model was
accomplished using certain assumptions about the material and processing conditions.
For instance, the material is assumed to follow linear elasticity behavior. Any external
98
strains placed on the polymer film is represented by small strain theory. And lastly,
temperature and solvent concentration gradients may only occur in the machine
direction. The results of their findings showed that strong thermal, solvent, and stretch
gradients in the processing line produce variations in the normal stresses causing large
in-plane shear stresses. These shear stresses that vary across the width of the film
promote the non-uniformity problems in the film. Poor quality films are produced
because the principal directions of stress and principal stresses vary across the width of
the film line. Because the state of stress is different for every width posifion,
orientational anisotropy and residual shrinkage would exist. For instance, warping often
occurs in bilayer laminates of polyimide films because their orthotropic axes are
oriented differently in the two layers. An additional finding was that the magnitude of
anisotropy varies transversely across the line, becoming planar isotropic at the center
and reaching its maximum values at the edges of the line. Therefore, wide film lines as
opposed to narrow lines are expected to produce the greater spatial variations in
properties. In result, it was suggested that by minimizing processing gradients and
controlling the stress, higher quality polymer films may be attained.
If the model by Jennings and Farris was to be extended to better represent a real
tenter frame processing line, large deformations and material non-linearities such as
viscoelasticity would need to be included. However, this would require a considerably
significant finite element modeling effort, and the material properties required for such
an analysis are largely unknown. The solution to the problem may exist in devising a
method for measuring the state of stress as a function of the transverse and machine
positions during production. Therefore, the research objective of this chapter is the
99
development of a new unique technique based on wave propagation theory for
determining the total state of stress in thin polymer films. [8]
Theory
The ability to produce high quality polyimide and poly(ethylene terephthalate)
films should be possible by identifying and controlling the state of stress in polymer
films during the tentering process. Further, it is believed that wave propagation theory
may offer a good solution to the problem. In summary, this research study hopes to
provide the foundation for developing a scanning online tool for state of stress
measurements during tenter frame processing. As a result, better quality polyimide and
PET films would influence improved production, performance, and reliability of
numerous electronic devices.
yy
Figure 5.2 Components of stress tensor for a volume element of film
As shown in Figure 5.2, an orthotropic volume element has a total of 9
components of stress. There are 3 normal ones which are perpendicular to the face and 6
shear stresses which are parallel to the face of a typical volume element. As a result of
100
symmetry, the shear stresses are reduced to only three shear components. In a two
dimensional constrained system such as a coating, the out-of-plane normal stress, is
zero. Also, the shear stresses, a,, and are zero away from the edges of the coating.
Therefore, the state of stress need be only described by the two in-plane normal stresses,
a,, and a^^, and the single in-plane shear stress a.^. To avoid confusion with the
notation used in Chapter 3, the m-plane directions, 1 and 2, are now represented by x
and y. Further, the out-of-plane direction, 3, is now represented by z.
aV u = p—
-
(5.1)
a = biaxial stress (N/m^)
= Laplacian operator
u = out-of-plane displacement (m)
p = material density (kg/m^)
t = time (s)
Identical to Equation 3.1 which describes the free vibration of a membrane in
holographic interferometry, Equation 5.1 also governs the wave propagation in a
uniformly tensioned membrane. The mathematical solution for the classical case of a
membrane uniformly tensioned with a single pulsed disturbance at some origin has been
previously detailed in the applied mathematics literature and is shown below. [9]
0<r<rt u(r,t)Cot
27ir"^[c„V-r^]3/2
Cot<r<~ u(r,t) = 0(5.2)
Wave Velocity C_ = J~P
Position ofj- = c t
Wavefront^
101
The results indicate that if one induced a singular sharp pulse at some point of
origin on a uniformly tensioned membrane, a wave which is circular in shape should
propagate outwards as shown in Figure 5.3. Any method to determine the wave
velocity, Q, of the wavefront should give the state of stress. It should also be noted that
density is the only material property needed to calculate the stress. In an effort to
measure the wave characteristics, an arrangement of highly sensitive displacement
sensors at known distances from the origin could be used to detect the motion of the
wavefront. By knowing the time of flight of the wavefront, the wave propagation
velocity and then the state of stress at a point can be calculated. An estimated
calculation of the wave velocity can be made for a typical polyimide film. If the density
of the polyimide film is equal to 1 .4 g/cm\ and the biaxial stress is equal to 10 MPa, the
wavefront should travel around 84.5 m/s or 1 mm in 1 1 .8 fis.
t=t
t=t,>t„
t=t,>t,
Figure 5.3 Initial response of a uniformly tensioned membrane due to a single pulsed
disturbance at the center
102
As a scientific note of interest, the two dimensional solution of the out-of-plane
wave behavior in a tensioned membrane is quite unique. The wavefront travels in a well
defined fashion and is circular in the case of a uniformly tensioned membrane.
However, the two dimensional case can also be described as having residual motion.
This means that there will be a "wake" or "tail" left behind after the wavefront passes.
Basically, energy is left behind after the wave passes. This assures that the membrane
waves will quickly die out and not cause any unwanted vibrations in the line. In
comparison to the case of the one dimensional solution (i.e. wave propagation in a
string) and three dimensional solution (i.e. wave propagation in a volume of gas), the
material in front of the wave is motionless, and the material after the wavefront passes is
motionless too. No energy is lost in the ideal one dimensional or three dimensional
cases. [9]
For a polymer membrane that is non-uniformly tensioned, Equation 5.3 for a
state of stress containing two normal stresses and one shear stress must be used in this
analysis. The x and y axes refer to the machine and transverse directions in the tenter
frame line.
d'u d'u d'u d'u
As shown below, a coordinate transformation of the form x' = XC0S9 + ysincp and
y* = -xsincp + ycoscp can be used to simplify Equation 5.3 in terms of the principal
stresses and principal directions.
103
where
= a,cos^(p + a2sin^(p
- a,sm (p + CT2C0S (p
= -(a,a2)cos(psincp
tan2(p
(5.4)
To represent a non-uniformly tensioned membrane, one of the coordinates can
be made to stretch by another coordinate substitution : x" = x' and y" = yXa^/a^f^
As a result, when one returns back to the original equation that represents the
wave motion for a uniformly tensioned membrane, the solution for the more
complicated stress state can be deduced. Therefore, the description of the wavefront in
terms of the principal stresses and the non-uniformly tensioned coordinate system is
given as
(X")' (y")t^ =
2v+
2v:(5.5)
GV2 =
a(5.6)
The mathematical solution reveals an elliptical wave shape for a single pulsed
disturbance in a non-uniformly tensioned film as illustrated in Figure 5.4. Further, as
shown in Equations 5.5 and 5.6, there would exist two characteristic velocities, Vj and
V2, corresponding to the major and minor axes of the elliptical wave shape. In tum, by
104
knowing the state of stress in the film in terms of the two principal stresses and their
orientation, the two normal stresses and in-plane shear stress can be determined from
Equation 5.4.
V.
Elliptical Wave Propagation Profile
Figure 5.4 Non-uniformly tensioned membrane with single pulsed disturbance at the
origin
Experimental
A custom-made two-piece heat-treated steel frame was constructed for holding a
polymer film (25.4 cm x 25.4 cm) in a state of tension. A large membrane of Kapton®
200H polyimide was prepared by firmly sandwiching the film between the bottom and
top steel frames. To place the film in tension, the whole structure was placed in an oven
at 400^C for five minutes and then allowed to cool at room temperature. Belleville
washers were used to tightly hold the shrinking film during cooling. Therefore, an
opportunity exists to evaluate different methods for inducing and detecting wavefi-ont
105
propagation on the tensioned polymer membrane. Any means to observe the wavefront
velocity and wave shape would enable the determination of the stress state at the point.
There exists three main issues for measuring the state of stress using wave
propagation techniques. First of all, the striking mechamsm must produce the sharp
single pulsed disturbance. Secondly, a good technique for detection of the wavefront
must be employed. And lastly, the acquisition of the wavefront velocities and
calculation of the state of stress must be done in a fast and efficient manner.
Striker Mechanism
The striker should be quick and reproducible and only hit the polymer
membrane with a single pulse at the origin. A simple method that was attempted was to
use a small metal probe attached to a relay which causes a small displacement into the
film upon application of a voltage. [10] However, it was realized that a faster striker
mechanism was needed. Other techniques such as an air pulse, a spark plug, or a
piezoelectric device are discussed in the following section.
Sensors for Detection of Wave Propagation
Several ideas for detecting wavefront propagation were pursued. Early studies
involved an array of bi-radial elliptical diamond tip phonograph cartridges as contact
sensors. [1 1] In the experimental design, a phonograph cartridge was located at the
origin while the other three cartridges were located at known distances away. The
sensor at the origin revealed when the striker mechanism would hit the polymer, and the
other three sensors detected the passing of the wavefront. However, it was discovered
that these phonograph cartridges did not have the necessary response time. In any case,
106
sensors which are non-contact would obviously be more beneficial for appHcation on a
tenter frame processing line.
The possibility of using high speed photography and video were also
investigated. The new Kodak EKTAPRO 4540 high speed motion camera has the
ability to capture events at 40,500 frames/second. [12] Furthermore, CCD technologies
by Xibion Corp. and Cooke Corp. advertise ultrahigh shutter speeds as low as 1 ^im. In
conjunction with some combination of strobe lights, optical choppers, backlighting or
image intensifiers, the detection of the small out-of-plane displacements of the
wavefront may be possible.
In addition, laser displacement sensors were examined for feasibility. For
example, the dual channel MTI Microtrak™ 7000 offers high resolution up to 0.0127
|im and standoff distances up to 25.4 mm. However, difficulties may arise with
detecting the wavefront in a smooth, transparent polymer film. To date, the Microtrak'^^^
7000 laser displacement sensors have been mainly successful on highly reflective,
mirrored surfaces and on semi-reflecfive, matted surfaces. [13]
The MTI-2000 Fotonic™ Sensor by MTI Instruments is a high-resolution, non-
contact, fiber-optic system for measurement of vibration and displacement. [14] It has
dual channel capability so that simultaneous measurements from two fiber-opfic probes
are permitted. Some real applicafions of the MTI-2000 in industry have included
measuring the vibration amplitude of an ultrasonic welder tip, studying the
displacement and phase of magnetic and optical disk-drive read/write heads, and
observing the displacement and wave shape of mechanical shock pulses. Furthermore,
107
fiber-optic technology is not affected by magnetic or electnc fields. For this research, a
minimum of two MTI-2000 units and four fiber-optic probes would be required. With
additional probes, the complete mapping of the propagating wave shape should be
possible.
Despite the yellowish-orange color and transparency of typical polyimide films,
the MTI-2062R probes work well in our application. As shown in Figure 5.5, they
contain numerous randomly distributed optical fibers in which half are transmitting light
and half are receiving light. Based upon the amount of light received off the reflected
target surface, an electric signal is produced which is proportional to the distance
between the probe tip and target surface. In Figure 5.6, two operating ranges of
displacement exist. The front slope represents the highest degree of sensitivity where
very small displacement changes correspond to large voltage changes. According to
their technical specificafions, the MTI-2062R probes have a resolufion up to 0.03 )iim
and a frequency response up to 130 kHz. They can detect small displacements within a
linear range of 0.14 mm, and a maximum standoff of 1.47 mm can be achieved. With
the KD-LS-2A optical extenders, the probes can be used at a greater distance (<1 cm)
from the target while not affecting the fi-equency response. In addition, the spot size is
reduced, and the sensitivity is increased by a factor of 4. [15] Research by Jagota et al.
have used MTI- 1 000 Fotonic''"'^ sensors to help measure stresses in polymer and metal
membranes by vibrational analysis techniques. [16]
108
From Ught Source To Pholocell
Light TransmittingFiber Optic Filament
Light ReceivingFiber Optic FllamenC
Probe-to-Target
Displacement
Figure 5.5 Schematic of MTI-2000 Fotonic™ Sensor probe
Front Slope
Back Slope
Distance of Probe Surface
(Displacement)
Figure 5.6 Voltage output versus displacement
Collection and Analysis of Data
The collection and analysis of signals from the sensors are accomplished using
an oscilloscope and computer. A color digitizing 4-channel Hewlett-Packard 54540C
oscilloscope with large memory capabilities and high sampling rate has been used in
this research. [17] It also has a 32K/channel acquisition memory and 125 MHz single-
shot bandwidth/channel. By triggering the oscilloscope at the same time as the initial
pulsed disturbance, the time difference from the initial pulsed disturbance to the passing
of the wavefront at some known distance can be obtained. Using the HP 3481OA
109
BenchLink Scope software, the HP Vectra XU Pentium Pro 200 MHz computer was
directly interfaced with the oscilloscope. Therefore, data from the oscilloscope could be
transferred and stored on the computer and quickly manipulated to determine the total
state of stress of the polymer film. With additional sensors and a second 4-channel
oscilloscope linked through the HPIB interface, it would be possible to more completely
map out the wave shape of the propagating wave. For the case of a moving film on a
tenter frame line, more than four channels would definitely be advantageous.
Furthermore, the HP VEE 3.2 for Windows 95/NT software could be used to control the
two oscilloscopes from the computer and permit simultaneous triggering and data
collection at all eight channels.
Results and Discussion
Top View
m iNilll
Polymer
Film
o
t
Frame
MTl-2000 Fotonic™ Sensors
HP 54540C 4-channel
color digitizing oscilloscope
HP Vectra XU 6/200 MHz computer
Figure 5.7 Experimental setup
110
In this research, the experimental setup was focused on a 50.8 ^im thin Kapton
H® polyimide membrane tensioned on a stationary frame. Using an array of non-contact
fiber-optic MTI-2000 Fotonic™ displacement sensors, studies of the physical wavefront
velocities were made. CAJON Ultra-Torr fittings with nylon washers were used to help
fix the probes slightly above the surface of the polymer. The outputs of the sensors were
read by the oscilloscope which was directly interfaced with the computer. In the back
slope region for the MTl Fotonic™ sensors, an excellent linear range of -50 milli-
inches (1 .27 mm) was experimentally observed. Since both wavefront detection and
data collection have been successfully established, the major concern in the present
research is the striker mechanism. Currently, several different ideas have been
evaluated.
In the ball drop experiment as shown in Figure 5.8, each of the sensors (O, ©,
©, O) are placed about 1 inch (2.54 cm) apart along a straight line. A small metallic ball
of 0.564 g is dropped from an approximate height of 1 inch (2.54 cm) at a point on the
film that is 1 inch (2.54 cm) away from sensor O. In Figure 5.9, the oscilloscope
observes the motion of the wavefront as it passed under each of the sensors. Analysis of
the data shows that the wave velocity is fairly constant having an average value of 29.6
m/s. Knowing the density of the polyimide film, an estimate stress value of 1.3 MPa
was calculated. However, the problem with this experiment is when the ball makes
contact with the film, it does not immediately leave the film at the point of contact.
Thus, the striker mechanism does not displace the film with a single pulsed disturbance
quick enough.
Ill
Side View
oeeoPolymer
Film
1
BallFrame
Figure 5.8 Ball drop experiment
hp STOPPED
\
o
o
900.0 us 1 . 6000 ms 4 . 1000 ms500 us/Diy REALTIME
1 100.0 my/D 7 100.0 fnV/D 3 100.0 m'^^O 4 100. <) mV^ii7.7? 100 y 7.21-100 K- 7 ,^-\-:><'}<:^ V 7.87-I00 V
Distance (mm) Traveled by Wave Wave Velocity
(m/s)
74.46 (Sensor G to Sensor O) 29.1
49.56 (Sensor O to Sensor 0) 30.0
24.83 (Sensor O to Sensor ©) 29.6
Average (m/s) 29.6
Estimated Stress (MPa) 1.3
Figure 5.9 Wavefront propagation initiated by a dropped ball
112
Another possible striker mechanism was a modified spark plug as shown mFigure 5.10. By completely confmmg the space around the spark and puttmg a small
needle wide opening, it was believed that a large enough spark would be able to
displace the air within the restricted space. Thus, if a polymer membrane was placed
near the opening, a small air burst may initiate the single pulsed disturbance. As shown
in Figure 5.11, a 12 V (2.5 A) power supply was comiected to a typical automobile's
ignition coil and condenser. [11]
Polymer
Film Frame
Ii
\l/
Spark Plug
Figure 5.10 Using a spark plug to induce a single pulse disturbance
12 V +
Power
Supply"
Ignition Coil
Spark
Plug
Figure 5.1 1 Schematic of the electrical wiring for the spark plug
113
A high speed solenoid valve (INKX0503950A) from the Lee Company was also
exammed as a striking mechamsm. According to its technical data, it has a maximum
operating frequency of 1 OOOHz at a 40 V pulse voltage and a response time of 0.25
milliseconds. [18] Furthermore, it has been rated to provide a -15 ^1 burst of air for a
compressed air source of 10-20 psi and 8 V pulse voltage. The outlet diameter measures
1 .25 mm. Typically, these high speed valves are used for ink jets and medical devices
such as tonometers which require precision microdispensing capabilities of liquids or
gases. In our experimental setup, a 7 ms voltage pulse of~6 V shot a burst of pressured
water (1 8 psi) at a tensioned polyimide membrane. As shown in Figure 5.12, sensor O
which represents a position about 0.5 cm from the point of impact does detect the
propagating wavefront. As a result, solenoid or piezoelectric valves which dispense
compressed gas or liquid may offer the best potential as a striker mechanism.
hp STOPPED
. . .
Voltage supplied
to valve
O€)
25.000 ms 0.000 55.00 ms/Diy
1 5.000 'J/D 2 ^'JOO.O mU/O 3 200.0 D0.00000 0 0.00000 0.00000 I.'
25.000 msREALTIME
Figure 5.12 Using a solenoid value to shoot a burst of water
114
Conclu.siong
In this chapter, we have detailed a new, unique, and powerful method for
determining the state of stress in thm polymer films usmg wave propagation theory. It
is believed that online identification and control of the stress state in polymer films
during the tentering process would be greatly beneficial for producing high quality
polyimide and PET films. It is anticipated that flatter films and more uniform spafial
properties will contribute to better reliability and durability ofnumerous electromc
devices. In addition, this technique may also be applicable for measuring the complete
state of stress of other polymer films on typical film lines and on pellicles.
115
Referenres;
J. H. Briston, Plastic Films, 2 ed. New York, NY: Longman Inc., 1983.
W. K. Park, Plastic Film Technology. New York, NY: Van NostrandReinhold Company, 1969.
B. F. Blumentntt, "Anisotropy and Dimensional Stability of Polyimide Films"
Polymer Engineering and Science, 18(16), pp. 1216, 1978.
K. Sakamoto, "Anisotropic Properties of Biaxially Oriented Poly(ethvleneterephthalate) (PET) Films manufactured by a Tenter and Their TheoreticalTreatments," Kobunshi Ronbunshu, 48(1 1), pp. 671-678, 1991.
T. Yamada and C. Nonomura, "Attempt to Reduce Bowing Distortion my^^tenng of Film,'VoMrna/ ofApplied Polymer Science, 52, pp. 1393-1403,
R. M. Jennings, "An Investigation of the Effects of Curing Conditions on theResidual Stress and Dimensional Stability in Polyimide Films," Polymer Scienceand Engineering Department. University of Massachusetts Amherst Ph DThesis, 1993.
R. M. Jennings and R. J. Farris, "Analysis of Stresses Arising During theProcessing of Polymeric Films on Tentering Frames," Polymer Engineering andScience, 32(23), pp. 1792, 1992.
R. J. Farris, "Development of an On-line Method for the Measurement of Stress
State of Films Being Produced in Tenter Frames," University of MassachusettsAmherst, 1995.
K. F. Graff, Wave Motion In Elastic Solids. London, England: OxfordUniversity Press, 1975.
V. C. Lo, "Synergistic Properties of Poly(ethylene 2,6-naphthalate) Fibers
Blended with Novel Thermotropic Liquid Crystalline Copolyesters," Polymer
Science and Engineering Department. University of Massachusetts Amherst,
Ph.D. Thesis, 1996.
D. Macaulay, The Way Things Work. Boston, MA: Houghton Mifflin Company,
1988.
116
12. "Kodak EKTAPRO 4540 High Speed Motion Camera," Eastman KodakCompany - Motion Analysis Systems Division, San oiego, CA 1996
13. "Microtrak 7000 - Specifications," MTI Instruments, Latham, NY, 1996.
14. "MTI-2000 FotonicTM Sensor," MTI Instruments, Latham, NY, 1996.
"KD-LS-2A Optical Extenders," MTI Instruments, Latham, NY, 1996.15.
16.
17.
18.
A. Jagota, S. Mazur, and R. J. Fams, "A Vibrational Technique for StressMeasurement m Films," presented at Mat. Res. Soc. Symp. Proc, 1990.
Test & Measurement Catalog. Santa Clara, CA: Hewlett-Packard Company,
Electro-Fluidic Systems Technical Handbook," The Lee Company TechmcalCenter (http://www.theleeco.com), Westbrook, CT, 1994.
117
CHAPTER 6
SUMMARY AND FUTURE WORK
Summary
The mechanical, thermal, and physical properties of polyimide coatings and
films have been studied in this thesis research. Using a Pressure-Volume-Temperature
(PVT) Apparatus, the bulk compressibility and volumetric thermal expansion were
obtained for several polyimides including novel fluorinated polyimides. From
orthotropic elasticity theory, the relationship between these properties and the out-of-
plane Young's Modulus and out-of-plane coefficient of thermal expansion were
revealed. Thus, the important and largely unknown out-of-plane properties of
polyimides were determined. In addition, knowledge of the anisotropic elasticity
coefficients and coefficients of thermal expansion provides the necessary information to
use sophisticated finite element analysis for designing complex microelectronic devices.
Using stress based failure criteria, proper selection of materials could be made fi-om
good property understanding of the polyimides. Lastly, similar characterization
techniques were also used on poly(ethylene terephthalate) and bisphenol A
polycarbonate films.
As an offshoot of the initial PVT studies, several thermally cured polyimides
were shown to irreversibly densify when subjected to high pressures and temperatures.
As the trend in the microelectronics industry moves toward microminiaturization in
118
wh,ch .uuneve. copper/pCyi.ide„es .e,uire vertioai sidewal.s, ,h,n ,
insulaUon. and sub^icron features, i. is i.ponan. to e„«„d how po,y™ides ^aybehave unde. these conditions. Using optica, nt,„oscopy, density nteasure^ents, and
wide-angle x-tay diffraction, it was shown that pressure-induced ctystai.i.tion in
polytmides can occur. Therefore, under sintdar temperature and stress condr.ions in a
constrained situation, polyintides n,ay noticeably densify ,n real applicat.ons in ntulti-
chip module packages.
The problems associated with commercial polymer films produced on a tenter
frame were discussed. The basic reasonmg deals with longitudinal stress gradients due
to temperature, concentration, or stretch gradients which produce a very inhomogeneous
stress state and similar vanations in properties. The goal of this research was to remedy
the problem by achieving a more uniform stress state in the polymer film. Therefore,
wave propagation theory was proposed to measure the complete stress state of a
polymer film during processing. Experimental research has entailed the use of non-
contact fiber-optic displacement sensors, an oscilloscope, and computer. Further studies
into a good striker mechanism are an ongoing effort. Therefore, if the stress state
distribution in a commercial film line can be mapped out, film line operators could learn
to adjust the process to form a uniform stress profile and thus make better polymer
films. Without a doubt, more uniform properties would be greatly beneficial to Kapton®
and Upilex® films used as base film for flexible printed circuit boards and as carrier tape
for tape automated bondings.
119
Future Work
In Chapter 3, the Poisson's ratios were not determined for the majority of the
fluonnated polyimides. Smce these polyimides have negative in-plane coefficients of
thermal expansion, the normal methods of preparing samples for holographic
interferometry gave membranes which appear buckled and indicate compressive
stresses. Flexus measurements have confirmed compressive stresses in these fluorinated
polyimides. [1] Because holographic interferometry requires tensile residual stresses,
the technique can not be used to measure their in-plane Poisson's ratios. Thus, the out-
of-plane Poisson's ratios can not be determined since the in-plane Poisson's ratios are
required in our calculations. In order to prepare these materials in a state of tension,
several concepts have been pondered. One idea is to cool a film sample using liquid
nitrogen, and then clamp the sample with a steel washer. Upon returning to room
temperature, the fluorinated polyimide would desire to shrink and thus appear in a state
of tension. Another idea is to biaxially stretch the film and then tightly clamp it to
washer. Thus, holographic interferometry may be used to deduce the in-plane Poisson's
ratios, and then the out-of-plane Poisson's rados may be determined from high pressure
gas dilatometry experiments.
As a comparison to polyimides, an interesting study would be to examine the
out-of-plane properties of other competitive polymer materials used in the
microelectronics industry. For example, Dow Chemical's Cyclotene 3022 is a divinyl
siloxane bisbenzocyclobutene thermoset resin which can be spin coated and thermally
cured from mesitylene solutions. Benzocyclobutene (BCD) polymers are intended for
120
thin film advanced electronic devices as an alternative to polyimides used as dielectric
interlayer coatings in multi-chip modules. Some unique properties of Cyclotene
materials are that they are typically ^60o/o solid, cure rapidly in about 5 minutes, and are
considered fairly isotropic. They have a comparable dielectric constant of 2.6 at 1 MHz.
Furthermore, 90-100% penalization can be achieved with just one 12-24 ^m thick coat
of Cyclotene rather than 2 or more coats of polyimide. [2]
Additional studies into the pressure-induced crystallization of thermally cured
polyimides should be extended to the other fluorinated polyimides. Further, the
minimum temperatures and pressures required to induce crystallization should be
examined in greater detail. In effect, a complete mapping of the irreversible
densification behavior found in polyimides as a function of pressure and temperature
should be pursued.
In Chapter 5, one concern about implementing the wave propagation theories to
real application is air impedance effects on the wave propagation. This is a common
phenomenon which is seen when measuring stresses by vibrational techniques. [3] The
possibility does exist that air impedance effects may be negligible. However, if not,
mathematical corrections may be incorporated to attain the desired state of stress
measurements.
Comparisons of the measured stress state by wave propagation techniques can
be made with a membrane deflection technique and time-averaged vibrational
holographic interferometry. [4, 5] These are two successful methods for studying
stresses in polymer coatings and films, yet require special time consuming sample
121
preparauon methods which thus prevent them from working on a moving tenter frame
line.
After successful design of the wave propagation expenmentation on a stationar>^
polymer membrane, the next stage of the project should mvolve usmg similar detection
techniques to measure the stress state on a moving tensioned polyimide film. Thus, the
construction of a small laboratory scale model of the tenter frame system should be
made. The last stage of the research would finally be the application of the
propagation techniques to a polymer film during tenter frame processing. The mam
problem that can be foreseen is that the detection method must be able to withstand the
harsh solvent and high temperature conditions during the processing. Also, significant
vibrations on the processing line may make wavefi-ont detection more difficult. The full
completion of this research work should ignite the building of simple low-cost devices
for measuring the state of stress ofpolymer films during the tentering process.
wave
122
Rcfercngff;
1. P Buchwallcr.-Flexus Results on FPl,"ll!M,York,ow„ Heights NY „as„,v,lcommunication, 1995.'n r
, ptisonal
2. E. Shaffer, "Ben/ocyclobt.tcnc (IK'B) Polymers," Dow Chemical Midland Mlpersonal communication, 1997iviuiiand. Ml,
3.
4.
M. A. Madcn K. long, and R. J. Farris, "Measurement of Stresses in ThinF.lms Using Holographic Interferometry: Dependence on AtmosphericConditions, Material Research Society Symposium, 1 88, pp. 29, 1 990.
M A. Maden, "The Determination of Stresses and Material Properties ofPoly.mide ( oatings and iMlms Using Real Time Holographic Interferometry
"
Folymer Science ami Engineering Department. University of Massachusetts'Amherst, Ph.D. fhcsis, 1992.
5. R. M. Jennings, "An Investigation of the Effects of Curing Conditions on theResidual Stress and Dimensional Stability in Polyimide films," Polymer Scienceand Engineering Department. I Jniversity of Massachusetts Amherst Ph DThesis, 1993. '
'
"
123
APPENDIX
LOTUS 1-2-3 MACRO PROGRAMS USED FOR ANALYZING THE PVT DATA
Both isothermal and isobaric data from the Gnomix Inc. PVT Apparatus were
:^lTzzT^^^^^ '-'-'r'''~- ^"^^ ^^^^^^^^^^^
n^n^r! ff' parameters are calculated. Furthermore, data ismodified for easy exporting into the SigmaPlot graphing software.
ISOTHERM {SELECT Original Data:Al|
i MLh-lMPURT "COMMA";"C:\data.XXX"-WINDOWS"}{EDI 1-CU
1
}
Modifies data with
correct temperature{bbLblh-ROWS}
ikiUMl 2nuuWN}^bUll-PASTE}
{JiELECl-DOWN 19}
ibUl l -CUPY-MLL "DOWN"}{CELL-ENTER "P";Original Data:Bl}
{CELL-ENTER "Temp";Original Data:Cl
}
{CELL-ENTER "Sp_Volume";Original Data:Dl
}
{CELL-ENTER "Vol_Change";Original Data:El}
{CELL-ENTER "Dilatation";Original Data:Fl}
{GET-NUMBER "What is the density (g/cc) of the
polymer?" ;Macro Info:D200;1.40}
{SELECT Onginal Data:F2} Dilatation
calculated{CELL-ENTER "+E2*$Macro Info:$D$200"}
{SELECT-DOWN 19}
{EDIT-COPY-FILL "DOWN"}{SELECT Original Data:A 1..Original Data:F8192}
{COLUMN-WIDTH-FIT-WIDEST
}
{SELECT Original Data:Bl.. Original Data:Fl}
{STYLE-ALIGN-HORIZONTAL "CENTER"
}
{SELECT Original Data:Gl
}
{DELETE-COLUMNS}{DOWN} {LEFT}
{REGRESS} Goto K, Tait
{BRANCH LOOP}
124
REGRESS {SELECT-DOWN 9}
^ R A Mr^Tn XT A A AC? r^n r'A-TT-'nT^ '
^iv/^iNun-iNAJVlb-CREATE K DTLS"*{LEFT 2}
Kfrom P=l 0-100 MPa
{SELECT-DOWN 4}
{IvAHLrb-NAME-L-kbA l E "TAIT VS"} Sp. Vol. from P= 10-50 MPa{LEFT}
tiv/AiNut^-iNAMb-CREATE K TEMP"}t/\rrtiiNUBbL(JW K#TEMP;K TEMP} Records temperature{Arrt^iNUBbLUW TAIT#TEMP;K TEMP}n FFTl
{KAlNUb-NAME-CREATE K PS"}
ISELECT-R ANnF PPT ATr\/n ...r\ a m( Lji^L^i^v^ 1 iv/Ai>ivjc-iviz,i^A live ;j;(J;(J^U
}
ISELECT-DOWNJ 41
^KAiNUb-iNAMb-LRhATE TAIT PS }
ISEI FCT-RANHP PPT atf\/t7 ...c a a»>i i\/\iNvjn-KbbA 1 1 Vb ;;;j;0;0}
IRECiRFSSION T<r P^ v T^TTQ*Regression for K(T)
\u/\ 1 A-KbUKboolUN-RESET
}
/ ^P I PPT D A M/^ t7 DOT A '-rj\ 71-* A r\ r^^j^bbbL. 1 -KAINOb-RbLATIVE ;;;4;0;0}
1 R FHR F^^FOKT T A TT DC A tt^ \/c »
Regression for V(0, T)/DATA-PPnPPQQTOM DnecT"*
IR ANHF-KJ A IV/fP PPPATT7 "xatx \nn\Jv^iN vJC-iN A.iviiz.-L.Ki:I/A lb 1 Al 1 V J
I APPFMHRPT OW T A TT^\/.x A TT^ \ /
1
^ y-\rr GiNUDCL^W W lAllffV,lAll V[ Makes Vvs. Tplot/r^OWXT Al / T CFT ^»{L/VJ WIN 0/ {bbr 1 j|
IRANGF-NAMF-PRF ATP "]<r "i
{APPENDBELOW K#;KJ Makes K vs. Tplot{LEFT 8} {DOWN 13}
{RETURN}
LOOP {EDIT-CUT} Modifies data with
correct temperature{SELECT-DOWN}{DELETE-ROWS}
{RIGHT 2}
{EDIT-PASTE}
{SELECT-DOWN 19}
{EDIT-COPY-FILL "DOWN"}{UP} {RIGHT 3} Dilatation
calculated{SELECT-DOWN 20}
{EDIT-COPY-FILL "DOWN")
125
LAST IR S nil 11 1
{SELECT-HOME}/T? A XT/^Th XT A A yfc r> r? a t^t^ in-'/^rr-. * , 17^ ^
^iv/viNOt-lNAlvlh-CKhAlh lUl AL }
(SELECT Original Data- A 1
1
{DELETE-COLUMNS}{EDIT-GOTO Compressibility:B2}
{CELL-ENTER "+C2*- 1 000"
}
{BEEP}
{ALERT "REMINDER : COPY DOWN THE REST OFTHE FORMULAS!!!!";!}
{MENUBRANCH QUERY P}
QUERY P Maximum Pressure = 100 MPa Maximum Pressure = 200 MPaSet Query for P=10-100 MPa ONLY Set Query for P= 10-200 MPa ONLY{EDIT-GOTO Original Data:A2} {EDIT-GOTO Sigma Plot IT:A1
}
{BRANCH SPWJT P=100} {BRANCH SPW IT P=200}
SPW ITP=100 {IF @CELLPOINTER("type")="v"} {BRANCHLOOP D P=100}
{EDIT-GOTO Sigma Plot IT:A1
}
{SELECT "Query 1";"";"QUERY"}
{QUERY-REFRESH}
{SELECT "Query 2";"";"QUERY"}
{QUERY-REFRESH}
{SELECT "Query 3";"";"QUERY"}
{QUERY-REFRESH}
{SELECT "Query 4";"";"QUERY"}
{QUERY-REFRESH}
{SELECT "Query 5";"";"QUERY"}
{QUERY-REFRESH}
{SELECT "Query 6";"";"QUERY"}
{QUERY-REFRESH}
{SELECT Farris Eq.:Al}
{QUERY-NEW total;D:Al;;;;"P";"+Temp-
SOriginal Data:$B$2";"Dilatation";"Temp"}
{QUERY-SHOW-FIELD "+Temp-$Original
Data:$B$2";"Dtemp"}
Sets up P=20, 40, 60,
80,100 MPa
126
{QUIT}^
{LAUNCH "C:\SPW\SPW.EXfT
SPW IT P=200 {SELECT "Query 1";"";"QUERY"}
{QUERY-CRITERIA "(P=20)"}
{QUERY-REFRESH}{SELECT "Query 2";"";"QUERY"|
{QUERY-CRITERIA "(P=60)"}
{QUERY-REFRESH}{SELECT "Query 3";"";"QUERY"}
{QUERY-CRITERIA "(P=100)"}
{QUERY-REFRESH}{SELECT "Query 4";"";"QUERY"}
{QUERY-CRITERIA "(P=140)"}
{QUERY-REFRESH}{SELECT "Query 5";"";"QUERY"}
{QUERY-CRITERIA "(P=180)"}
{QUERY-REFRESH}{SELECT "Query 6";"";"QUERY"}
{QUERY-REFRESH}{SELECT Farris Eq.:Al}
{QUERY-NEW total;D:Al ;;;;"P";"+Temp-
SOriginal Data:$B$2";"Dilatation";"Temp"
}
{QUERY-SHOW-FIELD "+Temp-$Original
Data:$B$2";"Dtemp"}
{QUIT}
{LAUNCH "C:\SPW\SPW.EXE"}
Sets up
P=20,60,I00,
140,180 MPa
LOOP DP=100 {DOWN 10}
{SELECT-DOWN 9}
{DELETE-ROWS}
{BRANCH SPWJT P=100}
ISOBAR {SELECT Original Data:Al}
{FILE-IMPORT "COMMA";"C:\XXXfl .CPR";
"WINDOWS"}{SELECT Original Data:Bl.. Original Data:E8192;
Original Data:Bl}
{COLUMN-WIDTH-FIT-WIDEST}{GET-NUMBER "What is the density (g/cc) of the
polymer?";Macro Info:D200;1.40}
127
{SELECT Original Data:Al}
{DELETE-COLUMNS
}
{DELETE-ROWS}{RIGHT 3}
{BEEP}
{ALERT "REMINDER : COPY DOWN THE RESTOF THE FORMULAS !!!!"; 1
}
{SELECT Sigma Plot IT:Al
}
{DELETE-SHEETS}
{SELECT Compressibility:Al
}
{DELETE-SHEETS}
(SELECT Tait Eq.:Al}
{DELETE-SHEETS}
{SELECT Farris Eq.:Al}
{DELETE-SHEETS}
{SELECT Original Data:Al}
{QUIT}
{LAUNCH "C:\SPW\SPW.EXE"}
Dilatation
calculated
128
BIBLIOGRAPHY
"Handbook of X-ray Photoelectron Spectroscopy," Perkin-Elmer.
"ASTM D1505-68: Standard Method of Test for Density of Plastics by the Density-Gradient Technique," Annual Book ofASTM Standards, 1968.
"ASTM D882-88: Standard Test Method for Tensile Properties of Thin PlasticSheeting," Annual Book ofASTM Standards, 1988.
"Pyralin Polyimide Coatings for Stress Buffer Applications," DuPont ElectronicsWilmington, DE, 1990.
"Pyralin Polyimide Coatings for Multichip Modules and High Density Interconnects,"DuPont Electronics, Wilmington, DE, 1991.
"Electro-Fluidic Systems Technical Handbook," The Lee Company Technical Center(http://www.theleeco.com), Westbrook, CT, 1994.
"MTI-2000 FotonicT"^ Sensor," MTI Instruments, Latham, NY, 1 996.
"MTI Microtrak^M 700O - Specifications," MTI Instruments, Latham, NY, 1996.
"Structured Products - LEXAN® Graphic Film," GE Plastics, NY, 1996.
"KD-LS-2A Optical Extenders," MTI Instruments, Latham, NY, 1996.
"Kodak EKTAPRO 4540 High Speed Motion Camera," Eastman Kodak Company -
Motion Analysis Systems Division, San Diego, CA, 1996.
Test & Measurement Catalog. Santa Clara, CA: Hewlett-Packard Company, 1997.
Abramowita, M. and I. A. Stegun, Handbook ofMathematical Functions. New York,
NY: Dover Publications, Inc., 1964.
Aklonis, J. J. and W. J. MacKnight, Introduction to Polymer Viscoelasticity, 2 ed. NewYork, NY: John Wiley & Sons, Inc., 1 983.
Anderson, S. G. H. and P. S. Ho, "Chemistry, Reactivity, and Fracture of Polymer
Interfaces," Characterization ofPolymers, H. Tong, S. P. Kowalczyk, R. Saraf,
and N. J. Chou, Eds. Stoneham, MA: Butterworth-Heinemann, 1994.
129
Arnold, F. E., K. R. Bruno, D. Shen, M. Eashoo, C. Lee, F. W. Harris, and S. Z DCheng, "The Origin of p Relaxations in Segmented Rigid-Rod Polyimide andCopolyimide ^i\ms" Polymer Engineering and Science, 33(21), pp. 1373, 1993.
Auman, B., "Density of Fluorinated Polyimides Using a Density Gradient Column,"DuPont, Wilmington, DE, personal communication, 1995.
Bauer, C. L., "The Determination of Mechanical Behavior of Polyamic Acid/PolyimideCoatings," Polymer Science and Engineering Department. University ofMassachusetts Amherst, Ph.D. Thesis, 1988.
Bauer, C. L. and R. J. Farris, "Determination of Poisson's Ratio for Polyimide Films,"Polymer Engineering and Science, 29(16), pp. 1 107, 1989.
Bemier, G. A. and D. E. Kline, "Dynamic Mechanical Behavior of a Polyimide,"Journal ofApplied Polymer Science, 12, pp. 593-604, 1968.
Bessonov, M. I., M. M. Koton, V. V. Kudryavtsev, and L. A. Laius, "Practical
AppHcations of Polyimides," in Polyimide: Thermally Stable Polymers. NewYork, NY: Consultants Bureau, 1987.
Bicerano, J., Prediction ofPolymer Properties, 2 ed. New York, NY: Marcel Dekker,
Inc., 1996.
Billmeyer, F. W. J., Textbook ofPolymer Science, 3 ed. New York, NY: John Wiley &Sons, Inc., 1984.
Blumentritt, B. F., "Anisotropy and Dimensional Stabihty of Polyimide Films,"
Polymer Engineering and Science, 18(16), pp. 1216, 1978.
Boehme, R. F. and G. S. Cargill, "X-ray Scattering Measurements Demonstrating In-
plane Anisotropy in Kapton Polyimide Films," in Polyimides: Synthesis,
Characterization and Applications, 1, K. L. Mittal, Ed. New York, NY: Plenum
Press, pp. 461, 1984.
Bowman, F., Introduction to Bessel Functions. New York, NY: Dover Publications,
Inc., 1958.
Briston, J. H., Plastic Films, 2 ed. New York, NY: Longman Inc., 1983.
Buchwalter, P., "Curing Procedures For Polyimides," IBM, Yorktown Heights, NY,
personal communication, 1993.
130
Buchwalter, P., "Flexus Results on FPI," IBM, Yorktown Heights, NY, personalcommunication, 1995.
Canister, W a J., Materials Science and Engineering - An Introduction. New YorkNY: John Wiley & Sons, Inc., 1985.
Campbell, D. and J. R. White, Polymer Characterization: Physical TechniquesLondon, England: Chapman and Hall Publishing Co., 1989.
Cobum, J. and M. Pottiger, "The Influence of Processing Condition on StructureProperties, and Stress Development in Spin Coated Polyimide Films," presentedat Advances m Polyimide Science and Technology, 1 99 1
.
Cobum, J. C. and M. T. Pottiger, "The Relationship of Morphology to Properties inSpin Coated Polyimide Films," presented at SPE ANTEC, pp. 656, 1993.
Cobum, J. C, P. D. Soper, and B. C. Auman, "Relaxation Behavior of PolyimidesBased on 2,2'-Disubstituted Benzidines," Macromolecules, 28(9) pp 32531995.
Cobum, J. C. and M. T. Pottiger, "Thermal Curing in Polyimide Films and Coatings,"in Polyimides: Fundamentals and Applications, M. Ghosh and K. L. Mittal, Eds.New York, NY: Marcel Dekker, Inc., 1996.
Conte, G., L. D'llario, and N. V. Pavel, "An X-ray and Conformational Study ofKapton® H," Journal ofPolymer Science: Part B: Polymer Physics, 14, pp.1553-1560, 1976.
Croll, S. G., "Intemal Stress in a Solvent-Cast Thermoplastic Coating," Jowrna/ o/Technology, 50(638), pp. 33, 1978.
Croll, S. G., "Intemal Strain in Solvent-Cast Coatings," Journal of Technology,
51(648), pp. 64, 1979.
Dolbow, J. and M. Gosz, "Effect of Out-of-plane Properties of a Polyimide Film on the
Stress Fields in Microelectronics Structures," Mechanics ofMaterials, 23(4), pp.
311, 1996.
Edman, J., "Properties ofUpilex® R," DuPont Films, Circleville, OH, personal
communication, 1996.
Fakhreddine, Y. A. and P. Zoller, "Pressure-Volume-Temperature Studies: A Versatile
Analytical Tool for Polymers," presented at SPE ANTEC, Boston, MA, pp.
1642, 1991.
131
Fakhreddine Y. A. and P. Zoller, "The Equation of State of Solid and MoltenPoly(butylene terephthalate) to 300°C and 200 MPa," Journal ofPolymerScience: Part B: Polymer Physics, 29, pp. 1 141-1 146, 1991
.
Farris, R. J., R. Falabella, and Y. D. Tsai, presented at ACS Symposium Series, 1979.
Farris, R J. and R. Falabella, "The Influence of Cavitation in the Mechanical Behaviorof Filled Polymers and Heat Build Up in Nonhysteretic Elastomers," presentedat Elastomers and Rubber Technology, pp. 197, 1987.
Farris, R. J., J. K. Vrtis, C. Jou, M. J. Chen, and K. C. Sheth, "Experimental StressAnalysis Methods for Coatings," presented at Advanced Coatings TechnologyConference - Engineering Society, 1994.
Farris, R. J., "Development of an On-line Method for the Measurement of Stress Stateof Films Being Produced in Tenter Frames," University of MassachusettsAmherst, 1995.
Feiring, A. E., B. C. Auman, and E. R. Wonchoba, "Synthesis and Properties ofFluorinated Polyimides From Novel 2,2'-Bis(fluoroalkoxy)benzidines,"
Macromolecules, 26, pp. 2779, 1993.
Fleischer, C. A., C. L. Bauer, D. J. Massa, and J. F. Taylor, "Film as a CompositeMaterial," MRS Bulletin, 21(7), pp. 14, 1996.
Flinn, P. A., "Mechanical Stress in VLSI Interconnections: Origins, Effects,
Measurements, and Molding," MRS Bulletin, pp. 70, 1995.
Gillham, J. K., K. D. Hallock, and S. J. Stadnicki, "Thermomechanical and
Thermogravimetric Analyses of Systematic Series of Polyimides," Jowrwa/ ofApplied Polymer Science, 16, pp. 2595-2610, 1972.
Graff, K. F., Wave Motion In Elastic Solids. London, England: Oxford University Press,
1975.
Gross, T. S., D. V. Zhmurkin, L. P. Buchwalter, and F. B. Kaufman,
"Thermomechanical Deformation of 1 |Lim Thick Cu-Polyimide Line Arrays
Studied by Scanning Probe Microscopy," Journal ofElectronic Materials,
submitted for publication, 1995.
He, J. and P. Zoller, "The Equation of State of Water to 250°C and 200 MPa Obtained
from a High Pressure Dilatometer," Rev. Sci. Instrum., 62(5), pp. 1304, 1991.
132
He, J. and P. Zoller, "A Dilatometric Study of the Ctystallization Kinetics of
Hess, M. S., Jowr«a/ ofComposite Materials, 3(10), pp. 630, 1969.
Hodge, T. C, S. A. Bidstrup, P. A. Kohl, J. B. Lee, and M. G. Allen "In-situDetermination of Thickness Direction Thermal Strain of Spi^-coated PolymerFilms, presented at International Symposium on Advanced PackagingMatenals, Atlanta, GA, 1995.
Imai, Y "High Pressure Polycondensation (For High Temperature Polymers) "in The
Polymeric Materials Encyclopedia, J. C. Salamone, Ed. Boca Raton FL- CRCPress, Inc., 1996.
Jagota, A., S. Mazur, and R. J. Farris, "A Vibrational Technique for StressMeasurement in Films," presented at Mat. Res. Soc. Symp. Proc, 1990.
Jennings, R. M. and R. J. Farris, "Analysis of Stresses Arising During the Processing ofPolymeric Films on Tentering Frames," Polymer Engineering and Science32(23), pp. 1792, 1992.
Jennings, R. M., "An Investigation of the Effects of Curing Conditions on the ResidualStress and Dimensional Stability in Polyimide Films," Polymer Science andEngineering Department. University of Massachusetts Amherst, Ph D Thesis1993.
Jennings, R. M. and R. J. Farris, "Formation of a Highly Ordered Poly(N, N'-Bis-
Phenoxyphenylpyromellitimide) Powder Using a High Pressure CuringTechnique," Journal ofPolymer Science: Part B: Polymer Physics, 32, pp.1457-1464, 1994.
Kazaryan, L. G., D. Y. Tsvankin, B. M. Hinzburg, S. Tuichiev, L. N. Korzhavin, and S.
Y. Frenkel, "X-ray Diffraction Study of the Crystalline Structure of Aromatic
Polyimides," Vysokomol. soyed, A14, pp. 1199, 1972.
Larson, R., "Back to Basics is Necessary for Viable FEA Modeling," Plastics
Engineering, pp. 29, 1992.
Lee, C. J., "Polyimides, Polyquinolines and Polyquinoxalines: Tg-Structure
Relationships," JM5-i?ev. Macromol. Chem. Phys., C 29(4), pp. 431-560, 1989.
Lekhnitskii, S. G., "Theory of Elasticity of an Anisotropic Body," MIR, 1981.
133
Likhatchev, D. and R. Vera-Graziano, "Polyimides, High Performance Films "in The
Polymeric Materials Encyclopedia, J. C. Salamone, Ed. Boca Raton FL- CRCPress, Inc., 1996.
Lo, V. C, Synergistic Properties of Poly(ethylene 2,6-naphthalate) Fibers Blendedwith Novel Thermotropic Liquid Crystalline Copolyesters," Polymer Scienceand Engineering Department. University of Massachusetts Amherst Ph DThesis, 1996. '
"
"
Macaulay, D., The Way Things Work. Boston, MA: Houghton Mifflin Company, 1988.
Macon, D., "Thermal and Mechanical Behavior of Rubber Systems," Polymer Scienceand Engineering Department. University of Massachusetts Amherst Ph DThesis, 1996.
Maden, M. A., K. Tong, and R. J. Farris, "Measurement of Stresses in Thin Films UsingHolographic Interferometry: Dependence on Atmospheric Conditions," MaterialResearch Society Symposium, 188, pp. 29, 1990.
Maden, M. A., "The Determination of Stresses and Material Properties of PolyimideCoatings and Films Using Real Time Holographic Interferometry," PolymerScience and Engineering Department. University of Massachusetts Amherst,Ph.D. Thesis, 1992.
Magill, J. H., "Morphogenesis of Solid Polymer Microstructures," in Treatise onMaterials Science and Technology: Properties ofSolid Polymeric Materials -
Part A, 10, J. M. Shultz, Ed. New York, NY: Academic Press, 1977.
Malvern, L. E., Introduction to the Mechanics ofa Continuous Medium. EnglewoodCliffs, NJ: Prentice-Hall Inc., 1969.
Mo, Z. and H. Zhang, "The Degree of Crystallinity in Polymers by Wide-angle X-ray
Diffraction QNAXD);' J.M.S.-Rev. Macromol. Chem. Physc, C35(4), pp. 555-
580, 1995.
Odian, G., Principles ofPolymerization, 3 ed. New York, NY: John Wiley & Sons, Inc.,
1991.
Park, W. R. R., Plastic Film Technology. New York, NY: Van Nostrand Reinhold
Company, 1969.
Perena, J. M., "Dynamic Mechanical Relaxations in Polyimide and Polyamideimide,"
Die Angewandte Makromolekulare Chemie, 106, pp. 61-66, 1982.
134
Perez, M. Y. Ren, R. J. Farris, and S. L. Hsu, "Characterization ofPMDA-ODAPolyimide Films by External Reflectance Infrared Spectroscopy "
Macromolecules, 27, pp. 6740, 1994.
Pottiger M. and J. C. Cobum, "Out-of-plane Expansion Measurements m Polyimideshilms, presented at ACS Symposium Series, pp. 282, 1993.
Pottiger M. T. and J. C. Cobum, "Modelmg Stresses m Polyimide Films," presented atMat. Res. Soc. Symp. Proc, pp. 527, 1993.
Sakamoto, K., "Anisotropic Properties of Biaxially Oriented Poly(ethyleneterephthalate) (PET) Films manufactured by a Tenter and Their TheoreticalTreatments," Kohunshi Ronbunshu, 48(1 1), pp. 671-678, 1991.
Sasaki, S. and S. Nishi, "Synthesis of Fluorinated Polyimides," in Polyimides:Fundamentals and Applications, M. Ghosh and K. L. Mittal, Eds New YorkNY: Marcel Dekker, Inc., 1996.
Shaffer, E., "Benzocyclobutene (BCB) Polymers," Dow Chemical, Midland, MI,personal communication, 1997.
Sheth, K. C, M. J. Chen, and R. J. Farris, "Characterization of Elastic Constants andStress in Low Thermal Expansion Polyimides," presented at 5^^ International
Conference on Polyimides - New Trends in Polyimide Science and TechnologyEllenville,NY, 1994.
Sheth, K. C, "Stress, Mechanical and Thermal Characterization of Anisotropic
Polyimide Thin Films and Coatings," Polymer Science and Engineering
Department. University of Massachusetts Amherst, Ph.D. Thesis, 1996.
Sroog, C. E., "Polyimides," Progre^^ in Polymer Science, 16, pp. 561-694, 1991.
Sroog, C. E., "Polyimides (Introduction and Overview)," in The Polymeric Materials
Encyclopedia, J. C. Salamone, Ed. Boca Raton, FL: CRC Press, Inc., 1996.
Starkweather, H. W. J., P. Zoller, and G. A. Jones, "The Heat of Fusion of
Poly(ethylene terephthalate)," Journal ofPolymer Science: Polymer Physics
Edition, 21, pp. 295-299, 1983.
Takekoshi, T., "Synthesis of Polyimides," in Polyimides: Fundamentals and
Applications, M. K. Ghosh and K. L. Mittal, Eds. New York, NY: Marcel
Dekker, Inc., 1996.
135
Tandon, S., "Modeling of Stresses in Cylindrically Wound Capacitors: Characterizationand Influence of Stress on Dielectric Breakdown of Polymeric Film," PolymerScience and Engineering Department. University of Massachusetts AmherstPh.D. Thesis, 1997.
Tong, H. M., K. D. Hsuen, K. L. Saenger, and G. W. Su, "Thickness-DirectionCoefficient of Thermal Expansion Measurement of Thin Polymer Films " RevSci. Instrum., 62(2), 1991.
Tong, Q. K., "A Structure Property Investigation of a Multi-Component PolyacrylatePhotoresist," Polymer Science and Engineering Department. University ofMassachusetts Amherst, Ph.D. Thesis, 1993.
Vrtis, J. K., "Stress and Mass Transport in Polymer Coatings and Films," PolymerScience and Engineering Department. University of Massachusetts AmherstPh.D. Thesis, 1995.
Waddon, A. J. and F. E. Karasz, "Crystalline and Amorphous Morphologies of anAromatic Polyimide Formed on Precipitation From Solution," Polymer, 33(18)
pp. 3783, 1992.
Wang, L., C. L. Choy, and R. S. Porter, "Thermal Expansion of Oriented Poly(Methyl
Methacrylate)," Journal ofPolymer Science : Polymer Physics Ed., 21, pp. 657-
665, 1983.
Weast, R. C, CRC Handbook of Chemistry and Physics, 66 ed. Boca Raton, FL: CRCPress, Inc., 1986.
Whitney, J. M. and R. L. McCullough, "Introduction to Anisotropic Elasticity," in
Micromechanical Materials Modeling, 2, L. A. Carlsson and J. W. Gillespie,
Eds. Lancaster, PA: Technomic Publishing Co., 1992.
Wiegmann, T. and F. Oehmke, "Measuring the PVT Behavior of Polymers," presented
at SPE ANTEC, Boston, MA, pp. 1646, 1991.
Yamada, T. and C. Nonomura, "Attempt to Reduce Bowing Distortion in Tentering of
Film," Journal ofApplied Polymer Science, 52, pp. 1393-1403, 1994.
Young, R. J. and P. A. Lovell, Introduction to Polymers, 2 ed. London, England:
Chapman and Hall, 1991.
ZoUer, P., P. Bolli, V. Pahud, and H. Ackermann, "Apparatus for Measuring Pressure-
Volume-Temperature Relationships of Polymers to 350°C and 2200 kg/cm^,"
Rev. Sci. Instrum., 47(8), pp. 948, 1976.
136
Zoller, P. "Pressure-Volume-Temperature Relationships of Solid and Molten
lot7To6U97"'^'^^^'"^^"^-1)'" ofAppUed Polymer Science, 23, pp.
Zoller, R and P^Bolli, ''Pressure-Volume-Temperature Relationships of Solid and
^5^568 191^^^^terephthalate)," J. Macromol. Sa. - Physics, B18(3), pp.
Zoller, P. and H. H. Hoehn, "Pressure-Volume-Temperature Properties of Blends ofPoly(2,6-dimethyl-l,4-phenylene ether) with Polystyrene," yo^.r«a/o/Po/vmerScience: Polymer Physics Edition, 20, pp. 1385-1397, 1982.
Zoller, P., "A Study of the Pressure-Volume-Temperature Relationships of Four RelatedAmorphous Polymers: Polycarbonate, Polyarylate, Phenoxy, and Polysulfone,"Journal ofPolymer Science: Polymer Physics Edition, 20, pp. 1453-1464, 1982.
Zoller, P., "Dilatometry," in Encyclopedia ofPolymer Science and Engineering, 5, H.Mark, N. Bikales, and C. Overberger, Eds., 2 ed. New York, NY: Wiley'Interscience, 1986.
Zoller, P., "PVT Manual (Version 2.01)," Gnomix Inc., Boulder, CO, 1987.
Zoller, P., "PVT Relationships and Equations of State of Polymers," in PolymerHandbook, J. Brandrup and Immergut, Eds., 3 ed. New York, NY: Wiley andSons, 1989.
137
