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THESIS

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31293 017019211

This is to certify that the

thesis entitled

STRESS EVOLUTION DURING ISOTHERMAL AND ISOCHRONAL ANNEALING
OF SfUTTERED NiTi THIN FILMS ON (100) - Si

presented by

Jinping Zhang

has been accepted towards fulﬁllment
of the requirements for

Master's degree in Materials Science

 

 

 

 

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STRESS EVOLUTION DURING ISOTHERMAL AND ISOCHRON AL
ANNEALING OF SPU'ITERED NiTi THIN FILMS ON (100) - Si

By

Jinping Zhang

A THESIS

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

MASTER OF SCIENCE

Department of Materials Science and Mechanics

1997

ABSTRACT

STRESS EVOLUTION DURING ISOTHERMAL AND ISOCHRONAL
ANNEALING OF NiTi THIN FILMS ON (100) - Si

By

J inping Zhang

The goal of this research has been to investigate the intrinsic stress resulting from
sputtering, extrinsic thermal stress resulting from the temperature change in NiTi on
(100)Si, stress evolution behavior during isochronal and isothermal annealing of as-
sputtered ﬁlms, and the interaction between stress and phase transformations in crystallized
ﬁlms. The latter may eventually lead to application of NiTi ﬁlms as actuator materials in
microelectromechanical systems (MEMS). Near-equiatomic Ni—rich NiTi ﬁlms were
fabricated by planar d.c. magnetron sputtering using N i-rich NiTi cathodes, and near-
equiatomic Ti-rich NiTi ﬁlms were fabricated using a composite cathode. Thin ﬁlm stress
measurements by the wafer-curvature method showed that compressive intrinsic stresses
resulted from the deposition parameters used, and the magnitude of the intrinsic stress
depended on the working gas density as well as the ﬁlm thickness. Both isothermal and
isochronal annealing experiments showed that the residual stresses were stable below the
deposition temperature. When the annealing temperature exceeded the deposition
temperature, stress was relaxed by a two-stage process for crystalline ﬁlms, and by a one-
stage process for amorphous ﬁlms. For both near-equiatornic Ni-rich N iTi ﬁlms on Si and
near-equiatomic Ti-rich NiTi on Si02/Si, extrinsic thermal stresses as high as 700 MPa
were obtained by cooling the sample from a nearly stress-free state at a high annealing
temperature, but were relaxed to nearly zero by R-phase and martensitic transformations.
The stress was recoverable by reverse transformations taking place during heating. The
reversibility of stress relaxation may be exploited to produce cyclic displacements useful in

microelectromechanical systems.

ACKNOWLEDGMENTS

This project has been sponsored by the US. National Science Foundation and the
Center for Fundamental Materials Research at Michigan State University.

I would like ﬁrst to express my gratitude to my major advisor Professor David
Grummon for his guidance and ﬁnancial support. Special thanks to my committee
members Professor Thomas Pence and Professor Martin Crimp for their valuable
suggestions and comments to this thesis.

My appreciation is also extended to Reza Loloee, Li Hou, Zhibao Zhao, Tom
Lagrange and Kuanbao Wang for their valuable help.

Finally, a special appreciation to my wife Fenglian, who has been understanding

and supportive during my study in this period.

TABLE OF CONTENTS

LIST OF TABLES .......................................................................................................... vii
LIST OF FIGURES ........................................................................................................ viii

CHAPTER 1
INTRODUCTION ............................................................................................................. 1

CHAPTER 2
LITERATURE REVIEW .................................................................................................. 4
2.1. The Shape Memory Effect and Near-Equiatomic NiTi Based Alloys ....................... 4
2.1.1. SME and Related Phenomena .......................................................................... 5
2.1.1.1. Thermoelastic Martensite vs. Non-Thermoelastic Martensite ............. 5

2.1.1.2. Structure and Microstructure Aspects of Martensitic
Transformation in SMAs ...................................................................... 6

2.1.1.3. Deformation Behavior of Martensite

and One-Way SME ............................................................................... 8

2.1.1.4. Two-Way SME ................................................................................... 10
2.1.1.5. Deformation Behavior of the Parent Phase

and Superelasticity .............................................................................. 11

2.1.1.6 Other Properties of SMAs ................................................................... 12

2.1.2. Equiatomic NiTi and N iTi-based SMAs ........................................................ 13

2.1.2.1. SME and Displacive Transformations in

Near-Equiatomic NiTi Alloys ............................................................. 14

2.1.2.2. Diffusive Transformations in Near-Equiatomic NiTi Alloys ............. 16

2.1.2.3. NiTi-Base Ternary Alloys .................................................................. 18

2.2. Thin Film: Fabrication, Microstructure and Stresses ............................................... 20

2.2.1. Thin Film Fabrication: Sputtering .................................................................. 21

2.2.2. Composition, Structure, Microstructure and
Properties of Sputtered Films ......................................................................... 22

iv

2.2.2. 1 . Compositions ....................................................................................... 23

2.2.2.2. Structure and Microstructure ............................................................... 24

2.2.2.3. Adhesion and Surface Roughness ....................................................... 25

2.2.3. Stresses in Thin Films ........................................................................................... 26

2.2.3.1. Classiﬁcations of Stresses ................................................................... 26

2.2.3.2. Thermal Stresses .................................................................................. 28

2.2.3.3. Intrinsic Stresses .................................................................................. 29

2.2.3.4. Stress Evolution ................................................................................... 34

2.3. NiTi Thin Films ........................................................................................................ 36

2.3.1. Fabrication of NiTi Thin Films ...................................................................... 36

2.3.2. Structure, Microstructure and Transformations

of NiTi Thin Films .......................................................................................... 38

2.3.3. Current Application-Oriented Work ............................................................... 4 1
CHAPTER 3

EXPERIMENTAL METHODS ...................................................................................... 45

3.1. Thin Film Fabrication ............................................................................................... 45

3.2. Thin Film Characterization ....................................................................................... 4 7

3.2.1. Thickness Measurement ................................................................................. 47

3.2.2. Stress Measurement ........................................................................................ 47

3.2.3. Thermal Treatment ......................................................................................... 49

3.2.4. Transformation Temperature Measurement ................................................... 50

3.2.5. Composition Analyses .................................................................................... 51

3.2.6. Structure and Microstructure Analyses .......................................................... 51
CHAPTER 4

RESULTS AND DISCUSSION ..................................................................................... 53

4.1. Stresses and Stress Evolution Behaviors of As—Deposited NiTi on Si ..................... 53

4.1.1. Stress Evolution of NiTi on Si During Isochronal Heating ............................ 53

4.1.1.1. Extrinsic Thermal Stresses .................................................................. 54

V

4.1.1.2. Stress Development from Crystallization ............................................ 55

4.1.1.3. Dynamic Stress Relaxation ................................................................. 56
4.1.2. Stress evolution of NiTi on Si During Isothermal Annealing ........................ 57
4.1.2.1. Stress Relaxation in Fully Crystalline NiTi on Si ............................... 57
4.1.2.2. Stress Relaxation in NiTi on Si with Initially Mixed Structure ........... 6 3
4.1.2.3. Stress Relaxation in Fully Amorphous NiTi on Si .............................. 65
4.1.2.4. Stress Relaxation Behavior of NiTi on Si
During Isochronal Annealing ............................................................... 66
4.1.3. Stress Relaxation Evolution of Amorphous NiTi on Si
During and After Crystallization .................................................................... 67
4.1.4. Crystallization Temperature of Amorphous NiTi ........................................... 6 9
4.1.5. Intrinsic Stress vs. Deposition Parameters ...................................................... 72
4.1.6. Discussion on Stresses and Stress Evolution in As-Sputtered NiTi ............... 76
4.2. Displacive Transformation Induced Stress Evolution in
SMA NiTi Films on Si .............................................................................................. 76
4.2.1. Displacive Transformation Induced Stress Evolution
of a Ni-Rich NiTi Film on Si .......................................................................... 77
4.2.2. Displacive Transformation Induced Stress Evolution
of a Ti-Rich N iTi Film on SiO2/Si .................................................................. 81
4.2.2.1. Stress-Temperature Hysteresis Loop After Annealing at 723 K .......... 82
4.2.2.2. Stress-Temperature Hysteresis Loop After Annealing at 873 K .......... 82
4.2.3. Discussion about the Potentials of Transformation
Induced Stress Relief of NiTi on Si ...... 85
CHAPTER 5
CONCLUSIONS ............................................................................................................. 87
BIBLIOGRAPHY ............................................................................................................ 9 0

vi

LIST OF TABLES

Table l. A comparison of NiTi SMA with piezoelectric, electric,
and bimetal actuators (after Johnson, 1991) .................................................. 100

vii

LIST OF FIGURES

Figures

2-1 A schematic of martensitic transformation showing four
characteristic transformation temperatures and structure
within certain temperature intervals ........................................................................ 101

2-2 Deformation behavior of a martensite material ....................................................... 102
2-3 A schematic of SME in two-variant martensite.

The left side shows the macroscopic change of an SMA material
by heating/cooling and applied stresses, the right side shows

the corresponding microscopic response ................................................................. 103
2-4 Deformation behavior of an austenite material at different temperatures ............... 104
2-5 Binary Ni-Ti phase diagram [Massalski, 1987] ...................................................... 105
3-1 A schematic showing the dc. megnetron sputtering apparatus ............................... 106
3-2 Sketch of apparatus for stress measurement by wafer-curvature method ............ 107

3-3 Optical paths for stress measurement by wafer-curvature method
under (a), stress-free, (b), tensile stress and (c), compressive
stressconditions................. ................................................................................ 108

3-4 Schematic drawing showing apparatus for transformation temperature
determination by electrical resistivity measurement .............................................. 109

4-1 Stress - temperature curves of as-sputtered NiTi ﬁlms on Si
deposited at different temperatures. Deposition temperature Td
and crystallization temperature Tc are indicated by arrows in
each ﬁgure ................................................................................................................ 110

4-2 (a, b) Stress variation of two crystalline N iTi ﬁlms on Si deposited
at 693 K during thermal treatments with time starting at the ﬁrst
isothermal annealing ............................................................................................... 111
(c) Stress relaxation in as-sputtered NiTi ﬁlms on Si deposited
at 693 K during the ﬁrst 25 ks isothermal holding at different
temperatures. Tinting started at each temperature .................................................. 112

4-3 Plots of ln(k(0', T) ) vs. 0' from stress relaxation curves for the crystalline

ﬁlms deposited at 693 K and isothermally annealed at different
temperatures ............................................................................................................. 113

viii

4-4 (a) Calculations of activation volume and activation energy based on
the intercepts and slopes in Fig. 4-3 for the ﬁrst stage of stress

relaxation in fully crystalline ﬁlms .................................................................

(b) Calculations of activation volume and activation energy
based on the intercepts and slopes in Fig. 4-3 for the second

stage of stress relaxation in fully crystalline ﬁlms .........................................

4-5 (a) Stress variation of an initially partially crystalline NiTi on Si
deposited at 623 K during thermal treatment with time starting

at the ﬁrst isothermal annealing ......................................................................

(b) Stress relaxation curves of the NiTi ﬁlm on Si deposited at
623 K during the ﬁrst 15 ks of isothermal holding at different
temperatures after the ﬁlm became fully crystalline. Timing

started at each temperature .............................................................................

4-6 Plots of ln(k(o; T) ) vs. O'from the stress relaxation curves for
the initially partially crystalline ﬁlm deposited at 623 K and

isothermally annealed at different temperatures .............................................

4-7 (a) Calculations of activation volume and activation energy based
on the intercepts and slopes in Fig. 4-6 for the ﬁrst stage of stress

relaxation after crystallization of partially crystalline ﬁlm ............................

(b) Calculations of activation volume and activation energy
based on the intercepts and slopes in Figure 4-6
for the second stage of stress relaxation after crystallization

of the initially partially crystalline ﬁlms .........................................................

4-8 (a) Stress relaxation of an amorphous NiTi ﬁlm on Si
deposited at 573 K during thermal treatment with time starting

at the ﬁrst isothermal annealing ......................................................................

(b) Stress relaxation curves of the amorphous NiTi on Si
deposited at 573 K during isothermal holding at different

temperatures with time starting at each isothermal annealing ........................

4-9 Plots of ln(k(o; T) vs. 0' for an as-sputtered amorphous N iTi on Si

deposited at 573 K during annealing at various temperatures ........................

4-10 Calculations of actication volume and activation energy
for amorphous NiTi on Si based on the intercepts and slopes

in Fig. 4-9 for stress relaxation in fully amorphous ﬁlms .............................

4-11 (3) Stress evolution of a NiTi ﬁlm deposited at ambient temperature
during isothermal annealing at 723 K. TEM shows that the

microstructure of the aged ﬁlm is free of precipitates ..................................

(b) Stress evolution of an amorphous ﬁlm deposited at 573 K
during isothermal annealing at 713 K. TEM after annealing
shows that the microstructure of the aged ﬁlm contains

numerous N i4Ti3 precipitates ........................................................................

4-12 TEM micrographs showing the microstructures of the annealed ﬁlms
with two kinds of stress evolution behaviors during annealing at
crystallization temperature:

(a) Microstructure is free of precipitates, corresponding to the ﬁlm

with a relatively lower relaxation rate after crystallization ..........................

ix

........ 115

........ 116

........ 117

........ 118

119

........ 121

........ 121

........ 122

........ 123

........ 124

........ 125

........ 126

........ 127

........ 128

(b) Large number of precipitates, corresponding to the ﬁlm with a
relatively higher relaxation rate after crystallization ............................................ 128

4-13 Constrained annealing effect on precipitation and intrinsic
two-way memory effect mechanism in Ni-rich NiTi alloys

proposed by Nishida et al. [Nishida et al., 1987] .................................................. 129
4-14 (3) Stress variation monitoring crystallization during annealing

of amorphous NiTi ﬁlms deposited at ambient temperature on Si ....................... 130

(b) Calculation of activation energy of crystallization for

amorphous NiTi ﬁlm by linear ﬁtting ................................................................... 131

4-15 Intrinsic stress vs. working gas pressure for NiTi ﬁlms on Si
deposited at ambient temperature (T d ~ 400 K) with ﬁlm
thicknesses ~15 to 2.5 microns ............................................................................. 132

4-16 Intrinsic stress vs. deposition temperatures for NiTi ﬁlms on Si
deposited at constant working gas pressure of ~ 5.1 mTorr with
thickness 1.5 to 2.5 microns ................................................................................... 133

4-17 Intrinsic stress for as-sputtered NiTi on Si vs. the ratio of working
gas pressure to deposition temperature, and ratio of working
distance (Wd) to mean free-path of Ar (M), Ni (Mi) and
Ti (ATi) atoms. (combined Fig. 4-15 and 4-16) ..................................................... 134

4-18 Intrinsic stress vs. ﬁlm thickness for NiTi on Si deposited at
ambient temperature Td ~400 K and constant Ar pressure (5.1 mTorr) ................ 135

4-19 Stress relief and recovery during the ﬁrst cooling/heating cycle
of a Ni rich NiTi/Si composite after annealing for 2 hours at
723 Kwith X-ray diffraction spectrum at room temperature
(left-upper corner) and resistivity curve for free-standing ﬁlm ............................. 136

4-20 Stress relief and recovery during heating/cooling cycles
of a Ti-rich N iTi/SiOz/Si composite after different heat treatments ...................... 137

4-21 Resistivity~temperature curves of free-standing Ti-rich NiTi
ﬁlms that was annealed 2 hours at 723 K (upper) and additional
2 hours at 873 K (lower) ........................................................................................ 138

4-22 Stress variation with temperature during the second heating/cooling
cycle of a Ti-rich N iTi/SiOz/Si composite that has been annealed
at 723 K for 2.5 hours followed by anneals at 873 K with
accumulative time of 8.5 hours. In-situ resistivity measurement
was used to monitor phase transformation ............................................................ 139

4-23 (3) Resistivity - temperature curves of Ti-rich NiTi ﬁlms annealed
at 873 K for varying time during thermal cycles at stress-free states;
(b) R-phase transformation temperatures are stable;
(c) martensitic transformation temperatures increase with increased
annealed time at 873 K .......................................................................................... 140

4-24 Calculation of displacement of a cantilever deposited a NiTi layer
resulting from stress relaxation by phase transformations ..................................... 141

X

Chapter 1

INTRODUCTION

Shape Memory Alloys (SMAs) undergo a reversible displacive transformation
between a low-temperature martensite phase and a high-temperature austenite parent phase
[Wayman and Duerig, 1990]. It is characteristic of SMAs that large amounts of strain that
are induced at relatively low flow stresses in the martensite can be recovered when the
reverse martensitic transformation is completed, yielding a large force and/or displacement
output [Otuska and Shimizu, 1986]. Alloys such as InTl, CuZnAl, CuAlNi, CuSn, Aqu,
NiTi, and some ferrous materials have been found to exhibit this effect.

Near-equiatomic NiTi alloys have been the most technically important of the shape
memory materials because of their high strain output and austenite toughness. It is well
accepted that the displacive transformation underlying the Shape Memory Effect (SME) in
NiTi is between a low-temperature B 19’ monoclinic phase and an ordered B2 phase (CsCl
structure) [Goldstien, Kabacoff and Tydings, 1987; Wayman and Duerig, 1990]. In
addition, a premartensitic transformation that forms a rhombohedral phase (R-phase)
sometimes occurs which also exhibits a SME [Miyazaki and Otuska, 1986; Otsuka, 1990].

Martensitic transformation in near-equiatomic N iTi can produce a fully recoverable
strain of up to 10% [Wasilewski, 1972], exceeding that of other known SMAs. In
addition, near-equiatornic NiTi has a low martensite ﬂow stress (~ 100 MPa), high austenite
strength (>500 MPa) [Ford and White, 1996], excellent corrosion resistance [Beuhler and
Wang, 1967], excellent fatigue properties [Melton and Mercier, 1979; Miyazaki, Sugaya

and Otsuka, 1989] and excellent biocompatibility [Lu, 1990], making it the ﬁrst choice for
many applications. Furthermore, ternary additions such as Cu, Nb, Fe, Hf, Pd and Pt can
be readily added to modify transformation properties without destroying shape memory
properties, allowing considerable ﬂexibility for material system design.

There has been an increasing interest in developing themal microactuators with
high energy-density output. Crystalline N iTi thin ﬁlms, which have larger energy-density
output than any thermal actuator materials currently available [Johnson, 1991; Kim, 1994],
have been demonstrated to possess shape memory properties comparable to those of their
melt-solidiﬁed counterparts [Busch, Johnson, Hodgson, Lee and Stevenson, 1990; Busch,
Johnson, Lee and Stevenson, 1990; Ikuta, Fujita, Ikeda and Yarnashita, 1990; Walker,
Gabriel and Mehregany, 1990; Chang and Grummon, 1992; Ishida, Takei and Miyazaki,
1993; Miyazaki and Ishida, 1994; Hua, Su, and Wuttig, 1995; Chang and Grummon,
1997]. Thermally driven Si-based NiTi microgrippers [Lee et al., 1995] and various
microactuators [Walker et al., 1989; Kuribayashi et al., 1990; Johnson, Busch, Ray and
Charles, 1992; Grummon, Hou, Zhao and Pence, 1995; Kmlevitch et al., 1997] have
been realized.

In order to achieve cyclic displacement output in microactuators, NiTi thin ﬁlms
must have biasing stresses, which can be internal or external, to deform the martensite
during the cooling transformation. Thin ﬁlm fabrication will often introduce intrinsic
stresses, and also, temperature changes may result in extrinsic stresses. How to efﬁciently
use those stresses to bias martensite is an important issue for actuators. Also of interest are
the relations between the intrinsic stresses and process parameters, thermal stability of the
stresses and the way that the stresses affect the martensitic transformation. Theses issues
constitute the main objects of this thesis work.

In this thesis, the shape memory effect (with emphasis on that in NiTi alloys), thin
ﬁlm sputtering technology, stresses in thin ﬁlms and current work on SMA NiTi thin ﬁlms

are reviewed in the literature survey chapter. Experimental techniques used in this research

work are illustrated in the Experimental Methods chapter. The experimental results on the
stress and stress evolution during annealing and phase transformation of NiTi on Si are
presented and discussed in the Results and Discussion chapter. The major results of this

research are summarized in the Conclusions chapter.

Chapter 2

LITERATURE REVIEW

In this chapter, the fundamentals of, and experimental ﬁndings on SME and related
phenomena, particularly in near-equiatomic N iTi alloys, are reviewed. Also, fabrication
techniques, microstructural characterization and properties of thin ﬁlms are discussed with
an emphasis on NiTi SMA ﬁlms. The present applications and possible future work of
NiTi thin ﬁlms are discussed.

2.1. The Shape Memory Effect and Near-Equiatomic NiTi Based Alloys
Since Chang and Read ﬁrst discovered SME in Au-Cd alloy in 1951 [Chang and Read,
1951], it has been extensively studied by many groups, and a number of alloys have been
found to be shape-memory materials. The list includes NiTi, Cu-Zn [Schroeder and
Wayman, 1979], Au-Cd [Chang and Read, 1951], Cu-Zn-Al [Delaey et al., 1981], Cu-Al-
Ni [Arbuzova and Khandros, 1964], Ni-Al [Smialek and Hehemann, 197 3], Fe-Mn-Si
[Miyazaki and Otuska, 1989] Pd-Ti [Donkersloot and van Vucht, 1970] and others. Even
some ceramics [Muddle and Trail], 1994] and polyirnides [I-Iayashi, 1993] have been found
to exhibit SME. Among those materials, NiTi-based alloys are the most important due to
their superior properties. In this section a review including the fundamentals of SME,
SME-related phenomena, and phase transformation, microstructure and alloying properties

of NiTi is presented.

2W
SME is a shape recovering effect activated by temperature changes. In more detail,

a plastic deformation produced when the materials are in the low-temperature phase can be
recovered on heating. In metals, the shape recovery starts at the austenite start temperature
(A) and completes at the austenite ﬁnish temperature (A,). In the absence of stress, no
overall shape change is associated with the martensitic transformation, which starts at the
martensite start temperature 0%,) and is completed at the martensite ﬁnish temperature (M,).
The four characteristic temperatures M,, MP A, and Af are illustrated in Fig. 2-1. Besides
SME, other phenomena such as superelasticity of SMAs are also related to the martensitic
transformation. In the following, the martensitic transformation in SMAs, martensite
structure characteristics, one-way SME, two-way SME, superelasticity and other related

properties of SMAs are described.

2.1.1.1. Thermoelastic Martensite vs. Non-Thermoelastic Martensite

The martensite in SMAs is thermoelastic and is characterized by a small
transformation hysteresis and mobile martensite/austenite interfaces. Upon cooling,
martensite plates continuously grow and new plates nucleate. If the cooling process is
stopped, growth and nucleation cease, but if the cooling is resumed, growth and nucleation
continue until the plates impinge with an obstacle such as a grain boundary or another plate.
When the sample is heated, the reverse transformation occurs by the ‘backwards’
movement of the martensite/parent interface. The martensite plates revert completely to the
parent phase and to the original lattice orientation, i. e. , complete crystallographic
reversibility. Although martensitic transformations also occur in steels and carbonless
ferrous alloys, there are distinct differences among the martensite in steels, in carbonless
ferrous alloys and in shape-memory alloys. In steels, when the martensite is heated it
undergoes tempering and eventual decomposition into equilibrium phases, i. e. , ferrite and

carbide [Reed-Hill and Abbraschian, 1992]. In carbonless ferrous alloys such as Fe-Ni,

the martensitic transformation is reversible but the transformation hysteresis is as high as
420 K. In addition, during cooling, a martensite plate usually springs full size into
existence, and then the interface between the martensite and parent phase becomes
disarrayed and sessile. Such martensite plates do not exhibit ‘backwards’ movement when
the specimen is heated. Instead, the parent phase (austenite) is nucleated as platelets within
the martensite plates. Since several variants of the parent with different orientations are
usually nucleated within a single martensite plate, the martensite plate as a whole does not
revert to its original austenite orientation [Kessler and Pitsch, 1965]. The martensite in Fe-
Ni alloys is thus non-thermoelastic [Kaufman and Cohen, 1958].

The thermoelastic martensitic transformation giving shape memory is characterized
by several common features [Wayman, 1992]:

(1) The transformation has deﬁnite hysteresis, which means that there exists a
temperature region at which the microstructure of the materials depends on the
thermal history;

(2) The transformation is athennal, which means that phase fraction is only a function of
temperature, and independent of isothermal holding time. This is due to the
displacive nature of the transformation;

(3) The martensite usually has lower crystallographic symmetry than the parent phase;

(4) Martensite is often internally faulted by lattice imperfections such as twin boundaries
and stacking faults;

(5) Plastic deformation of the martensite phase may be accomplished by twinning-type

mechanism rather than dislocational slip.

2. 1.1.2. Structure and Microstructure Aspects of the Martensitic Transformation in SMAs
Martensitic transformations are accompanied by a lattice distortion that resembles a
simple shear, but in general is not exactly a shear, rather, an invariant-plane strain, and a

lattice invariant plane exists during the transformation. Mathematically, an invariant-plane

strain is a homogeneous distortion such that the displacement of any point is in a common
direction and proportional to the distance from the invariant plane. In most martensitic
transformations, 3 volume change accompanies the structure which produces a normal
component to the invariant-plane strain [Wayman, 1983].

A deﬁnite orientation relationship between the parent phase and martensite is found
in the martensitic transformation in SMAs. However, due to the crystal symmetry of the
parent phase, a number of martensite plates with different orientations may form even from
a single-crystal parent phase. One martensite plate with a deﬁnite orientation is called a
martensite variant. Since martensite can nucleate at different places, multi-variant
martensite is expected to form upon cooling of austenite.

The martensite formed in SMAs is usually self-accommodating, which means the
variants from in groups such that macroscopically the shape-strain is minimized, and
microscopically intervariant junction planes are crystallographically reasonable [Miyazaki,
Otuska and Wayman, 1989]. The self-accommodating morphology of martensite was
observed from the optical microscopic observation of martensitic transformation induced
surface relief of a ﬂat surface prepolished prior to the formation of martensite in a Cu-
40%Zn alloy. The invariant plane strain surface tilt gives an overall diamond-like
morphology, with each diamond consisting of four crystallographic variants of martensite.
Scratch observation indicates that although a straight scratch is locally deviated across the
width of the individual plates of martensite, it still appears on the whole as a straight line.
In more detail, if a given plate produces an ‘up’ displacement, its adjacent neighbor
undergoes a ‘down’ displacement to annul the ﬁrst, and the two plates thus self-
accommodate each other. Electron diffraction investigation in TEM shows that the
martensite plates in a single self-accommodation group are twin-related. Detailed analyses
by invariant strain matrix indicate that the martensite variants form in self-accommodating
groups because in doing so, the average deformation resulting from the transformation is

l.

Thermoelastic martensitic transformations are found exclusively in ordered alloys,
where an ordered parent phase is transformed into an ordered martensite. In such a case,
ordering promotes crystallographic reversibility because the reverse transformation path in
ordered alloys is unique, in contrast to multiple paths possible for disordered alloys
[Otsuka and Shimizu, 1972]. Ordering also promotes a higher ﬂow stress in the parent
phase, making it less likely for the martensite parent interface to become damaged and then
immobile as the plate grows [Dunne and Wayman, 1973].

Crystallographically, there is a lattice correspondence for the martensitic
transformation. Wechesler, Liebermann and Read [1953, 1955] developed a theory, which
is called WLR theory, that can phenomenologically explain structural and rnicrostructural
characteristics of the martensite. The basic assumption of WLR theory is that in order to
minimize the transformation elastic strain energy, there exists a lattice invariant plane during
the transformation. The transformational displacement may be analyzed as consisting of
three components:

(1) A Bain distortion, which describes the lattice correspondence between the parent
phase and the martensite phase but does not necessarily produce an invariant plane;

(2) A lattice invariant shear, which is realized by twinning or dislocation slip, which does
not change the lattice symmetry but yields an undistorted interface plane;

(3) A rigid body rotation, which makes the undistorted plane that has been produced by

the ﬁrst two operations coincide in both martensite space and parent lattices.

2.1.1.3. Deformation Behavior of Martensite and One-Way SME

As shown in Fig. 2-2, deformation of martensite involves an elastic stage followed
by a plastic stage. While the elastic stage is the same as that in non-SMA materials, the
plastic stage involves a different mechanism. From the discussion in last section, cooling a
single-crystal SMA from austenite results in a multi-variant martensite plates appearing in

self-accommodated groups with no macroscopic shape strain. Because the variants in a

group are twin-related and the twin interfaces of thermoelastic martensite are mobile, and if
the stress to activate dislocation movement is high enough, plastic deformation is realized
by twin boundary movement, i. e. , in one self-accommodating variant group, one variant
grows at the expense of others, in a process called detwinning. The deformation continues
until only one variant in the sample is persisted. At this point the specimen surface is
featureless. The surviving variant is that whose shape strain direction is most nearly
parallel to the highest shear stress component. It is noted that though one self-
accormnodating group of variants eventually becomes a single variant by detwinning,
coalescence of the variants from different self-accommodating groups must occur before
single-variant martensite is formed. It is found that all the variants are capable of
combining in a twin or pseudo-twin relation, as occurs in a 18R Cu-Zn-Al martensite
[Adachi et al., 1988]. Upon further loading of the single-variant martensite, it undergoes
elastic deformation followed by plastic deformation by slip until the sample eventually fails,
which is the same as that in non-SMA materials.

Because the twin-related variants are crystallographically identical, they are energetically
equivalent and will not move back when the specimen is unloaded. Therefore, the
deformation realized by detwinning is plastic in nature. When the detwinned martensite is
heated between A, and A,, the original specimen shape and parent single crystal are
regenerated. This is the shape memory effect.

SME is realized by the reverse transformation of thermoelastic martensite. Because
of crystallographic restrictions and the necessity to maintain ordering, the detwinned
martensite has only one way to undergo the reverse transformation. In other words, there
are numerous variants of the Bain strain during the forward transformation but only one in
reverse. It is to be noted that the ‘one-way’ memory just described is a one-time-only
occurrence, but can be repeated by retransforming to the martensite, deforming it, and

reheating it. Completely recoverable strains of over ten percent have been observed. The

10

shape memory process in a simpliﬁed two-variant model is schematically described in Fig.
2.3.

In polycrystalline SMAs, the deformation of martensite and the shape memory
effect occur by the same mechanism as in single-crystal austenite. The only difference is
that the grain boundaries are irrunobile, so each grain must be treated separately. The
maximum recoverable strain is the average strain of all grains, and depends on the texture

of the austenite grains.

2.1.1.4. Two-Way SME

In the one-way SME, the cooling from the parent phase does not generally give a
macroscopic shape change due to the self—accommodating ability of martensite. However,
shape memory materials can also be processed to give shape-strains on both heating and
cooling transformation, in which case the SME is called two-way SME. Generally there
are two ways to do this. One way is to use external biasing stress [Ditrnan and Bergman,
1994]. In that case, materials spontaneously switch between a low-temperature shape,
which is formed by de-twinning the martensite at low ﬂow stresses, and a high-temperature
shape, which is restored by reverse martensitic transformation', upon heating. The other
employs an intrinsic biasing stress. The intrinsic biasing stress may be created by SME
cycling or loading-unloading cycling [Schroeder and Wayman, 1977], which introduces
stabilized defects [Perkins and Sponholz, 1984; Liu and McCormick, 1990; Filip and
Mazanex, 1996], or by constrained annealing, which introduces coherent/semicoherent
second phases [Nishida and Honma, 1984]. In each case, the thermally induced martensite
is not fully self-accommodated, but biased by the internal stress ﬁelds of the defects or

second phases. The biased martensite microstructure may realize a different macroscopic

 

‘ If properly chosen, external biasing stress will produce only a small amount of elastic
deformation at austenite, since it has a much higher plastic flow stress than martensite.

ll

conﬁguration with that of austenite. Up to 2% ~ 3% two-way memory strain is observed

in cyclically trained samples.

2.1.1.5. Deformation Behavior of the Parent Phase and Superelasticity
At temperatures above M,, martensite can also be stress induced, in which case the
martensite is called stress induced martensite (SIM). According to Clapyron’s equation in

the strain-stress version:

da_ AH

___ 2.1
dT T-A£ ( )

where o; T, AH and A8 are the stress, transformation temperature, transformation enthalpy
and resolved transformation strain in the direction of applied stress, respectively [Otsuka
and Shinrizu, 1986]. Since the martensitic transformation is exothermic (AH is positive)
[Ortin and Planes, 1990] and A8 is also positive if a is positive, the transformation
temperature is expected to increase when an external stress is applied.

Due to the transformation hysteresis in temperature, the deformation behavior of
austenite is different for different deformation temperatures, as shown in Fig. 2-4. When
stresses are applied to an austenite material, it deforms elastically until either the critical
stress for stress-induced martensitic transformation or dislocation movement related slip is
reached, both of which are temperature dependent. If the critical stress for slip is higher at
the deformation temperature (Td),2 stress induced martensitic transformation takes place
prior to slip and the material may continue to deform by the formation of stress induced
martensite, until the structure is fully martensitic [Wayman, 1992]. Unloading at this

period of deformation, the material behaves differently depending on the deformation

 

2 The temperature at which the critical resolved stress for dislocation slip equals that for stress
induced martensite transformation is deﬁned as the upper bound of temperature for
superelasticity and is represented by M,t

12

temperature. If Td < A,, the martensite is stable when the stress is released, so almost all
strain is retained. If A, < Td < A, the martensite is partly retained upon unloading and
hence only a part of the deformation is retained. In these two situations, only when
reheated to Ar or above, can the material fully recover the deformation strain. If Td > Af,
upon unloading, the martensite is no longer stable, and it spontaneously transforms back to
austenite. Therefore, all the strain is recovered. This phenomenon is called superelasticity
(SE), another well-known property of SMAs. More than 10% superelastic strain is
observed in NiTi materials.

It is noted that stress induced martensite (SIM) is not a self-accommodated multi-
variant martensite, but single-variant martensite in a given austenite grain. The variant
chosen by the stress induced martensitic transformation is the one which experiences the
maximum resolved shear stress. Further deformation results in the nucleation of numerous
parallel variants, which eventually coalesce as the elongation approaches the maximmn
recoverable strain. Upon unloading, the inverse process occurs, whereby plates of the
parent nucleate, coalesce, etc., restoring the parent grains in their original orientations, as

occurs in SME.

2.1.1 .6. Other Properties of SMAs

Among the properties of SMAs other than SME and PE, the rubber-like ﬂexibility
[Olander, 1932] and damping effects [Lin, Wu and Chang, 1994; Yeh et al., 1994] are
also observed. Rubber-like behavior is a spontaneous strain recovery upon loading
occurring in fully martensitic materials, and was observed in Au-Cd alloy [Olander, 1932;
Chang and Read, 1951], Cu-Al-Ni [Sakamoto, Otsuka and Shimizu, 1977], Cu-Au-Zn
[Miura, Meada and Nakanishi, 1974], and Cu-Zn [Schroeder and Wayman, 1979].
Interestingly the rubber-like behaviors is found only after the martensite is aged for at least
a few hours. Freshly transformed specimens exhibit only shape memory behavior. Based
on microscopic observation, Chang and Read [1951] attributed the rubber-like behavior to

13

favorably oriented ‘regions’ growing at the expense of others, but did not explain the
driving force for the springback. A number of mechanisms were proposed such as
interaction between twinning dislocations and order faults inherited from the parent phase
[Birnbaum and Read, 1961] and twinning shufﬂes which were time dependent [Lieberman
et al., 1975], but neither was experimentally supported [Ohba, Otsuka and Sasaki, 1990].
More recently, Japanese scientists [Cahn 1995] showed that a short-range order transition
occurs during the aging of the deformed martensite which is conelated the transition to the
rubber-like phenomenon. However, the driving force is yet not convincingly clariﬁed.
Unusual damping properties are also found in SMAs. Good damping capacity is
demonstrated when the SMA is in the martensitic form. Energy dissipation is realized by
the movement of planar defects such as twin boundaries and variant interfaces. However,
the best damping capacity is always found when the temperature is in the martensitic
transformation temperature region. In this case, most of the energy is dissipated through
the movement of martensite/parent phase interfaces. The damping effect of SMAs have

found various applications in sports supplies[Yeh et al., 1994].

2.12 E . . II'I' INT-E 1511!
Although SME was found as early as 1951, it did not become of engineering

signiﬁcance until 1965, when Buehler, Gilfrich and Wiley at the US Naval Ordnance
Laboratory found SME in near-equiatomic TiNi, and named this alloy as Nitinol. Since
then, considerable work in understanding of the transformation physics and in developing
practical engineering application has been done. The development of NiTi alloy has been
so successful that almost all the current SME applications are based on NiTi or TiNi-based
ternary alloys.

Compared to other shape memory alloys, near-equiatomic NiTi alloy has the
following advantages: (1) Better shape memory effect. Although it depends on the crystal

orientation, a theoretically perfectly recoverable strain of up to 10% for single-crystal NiTi,

14

and 8.4% for polycrystalline NiTi have been found [Miyazaki, Nomura and Ishida, 1995],
which are the best among all of the SMAs currently available; (2) Better fatigue properties
and thermal stability. NiTi can work for more than 108 cycles at a recovery strain as high
as 2% without serious SME degradation [Miyazaki, Sugaya and Otuska, 1989]; (3)
Excellent mechanical properties. The alloys have an austenite strength > 620 MPa,
martensite strength > 103 MPa, and room-temperature ductility of up to 60% [Buehler and
Wang, 1968; Cross et al., 1969]; (4) Excellent corrosion resistance [Vicentini et al., 1986],
which allows the products to work in severe conditions such as saline environments; (5)
Biocompatibility [Lu, 1990], which allows the SMAs to work in the human body. The
majority of the current applications of SMAs are biomedically related [Fukuyo et al. ,
1990].

While the displacive transformations are the basis of SME, the diffusive
transformations that take place at higher temperatures modify the microstructure of the
material, thereby the mechanical properties and transformation temperatures can be
modiﬁed, and the SME can be improved. The following describes the transformation

aspects of near-equiatomic NiTi and ternary alloys.

2.1.2.1. SME and Displacive Transformations in Near-Equiatomic NiTi Alloys

The high-temperature equilibrium phase of equiatomic NiTi is the CsCl-type
ordered structure (B2 structure) with a lattice parameter of 0.301 nm [Knowles and Smith,
1981, Matsurnoto et al., 1987]. Upon cooling, the material is subject to the following
displacive transformation: B2 -> Incommensurate phase (IC) —> Commensurate Phase
(CP) —) martensite phase (M) [Hng et al., 1983; Wayman, 1983]. The B2 parent phase
also transforms directly to martensite without the intermediate phases if certain free energy
criteria are satisﬁed [Liu and McCormick, 1996]. Upon heating, the martensite can
transform to the B2 parent phase with or without intermediate phases, also according to the

thermodynamic conditions.

15

In the incommensurate phase, atoms move slightly away from the rational
positions, creating diffuse features in electron diffraction patterns. The B2 -) IC
transformation is a second-order transformation and it is accompanied by a sharp increase
of resistivity. The CP is formed from IC when the atoms are locked at the exact rational
positions and a rhombohedral angle is achieved. Therefore, the CP is called the R phase.
The rhombohedral angle further deviates away from a right angle when the temperature is
decreased [Ling and Kaplow, 1981; Meichle et al., 1981]. The B2 -> R transformation
(R-phase transformation) is a ﬁrst-order transformation which is accompanied by an
internal friction peak and a decrease in elastic modulus. The R phase is characterized by
1/3 superlattice reﬂections along major directions such as <110> and <111> in reciprocal
space [Wu and Wayman, 1989] and by weave-like domains in the microstructure [Xie et
al., 1990]. Since the rhombohedral angle is achieved by lengthening one of the <111>
direction of the B2 unit cell, there are a total of 8 possible R-phase variants.

The formation of martensite, regardless of whether it comes from the R phase or
directly from the B2 parent phase, is a ﬁrst order transformation. The martensite of NiTi
has a monoclinic structure with lattice parameters a = 0.2889 nm, b = 0.4120 nm, c =
0.4622 nm and 7 = 98.6" [Matsumoto et al., 1987]. The orientation relationship between
martensite and austenite is [Otsuka, Sawarnura and Shimizu, 1971]

[111],,//[ii1],,2

~6.5

(001)” // (101)32

(2.2)

Due to lattice symmetry of the parent phase, there are 12 lattice correspondences satisfying
the orientation relationship, and these 12 lattice correspondences further form 24 habit
plane variants when internal twinning is considered [Matsumoto, Miyazaki, Otsuka and
Tamura, 1987].

For solution-treated binary NiTi, the B2 —) R transformation and the R -> M

transformation are so close that no temperature interval is detected. By adding a third

l6

element such as Fe into the binary alloy, or annealing Ni-rich NiTi alloys at intermediate
temperatures, the martensitic transformation can be depressed and the R-phase
transformation can be separated from the martensitic transformation. Both the R-phase
transformation and the martensitic transformation exhibit SME and PE by the mechanism
described in 2.1.1. The SME and PE associated with the martensitic transformation in
NiTi exhibit a fully recoverable strain of up to 10%, while those associated with the R-
phase transformation exhibit a fully recoverable strain near 1% [Ling and Kaplow, 1980].
The R-phase transformation is unique in that the transformation hysteresis is as narrow as 1
K [Hwang et al., 1983], which is particularly useful for developing snap performance in

thermal actuators.

2.1.2.2. Dtﬂusive Transformations in Near—Equiatomic NiTi Alloys
Although Koskimaki et a1. [1969] reported a eutactoid transformation

[3(NiTi) —.> Ni3Ti + TizNi (2.3)

occurred when a near-equiatomic NiTi alloy was annealed at intermediate temperatures
(0.3Tm to 0.6 Tm), no other independent experiments conﬁrmed this kind of decomposition
[Wasilewski et al., 1971]. Thus, it has been generally accepted that the B2 structure is a
stable phase at high temperature. Whether the alloys are Ni rich or Ti rich is important for
diffusive solid state reactions. According to the equilibrium phase diagram (Fig. 2-5),
stoichiometric NiTi can dissolve almost no excess Ti, but can dissolve up to a few percent
of excess Ni at solution temperatures. In most Ti-rich NiTi alloys (with atomic
compositions more than 50at.% Ti but less than 67at.% Ti), the equilibrium microstructure
would be a mixture of B-NiTi and the interrnetallic compound TizNi, which has a B2
structure with a = 0.301 nm, and hexagonal structure with lattice parameters a = 0.2549 nm

and c = 4.3648 nm [Bhan, 1971], respectively. For near-equiatomic Ti-rich NiTi alloys,

17

the matrix essentially is B-TiNi, so the transformation temperatures changes little even
though the intermetallic compound TizN i, which tends to appear near grain boundaries, has
negative effects on the mechanical properties of the materials.

Diffusive intermetallic reactions in Ni-rich near-equiatomic NiTi are much more
signiﬁcant than those in Ti-rich NiTi alloys. Firstly, there are a number of metastable
intermetallic compounds such as N i3Ti, N i3Ti2 and Ni4Ti3 that may appear when the
materials are annealed at intermediate temperatures (673 K ~ 973 K). The Ni3Ti phase has
a hexagonal structure with lattice parameters a = 0.5109 nm and c = 0.8310 nm [van
Vucht, 1966], the Ni3Ti2 has a hexagonal structure with lattice parameters a = 0.44028 nm
and c = 1.3525 nm [Nishida, Wayman and Honma, 1987], while the Ni4Ti3 has a
rhombohedral structure with lattice parameters of a = 0.661 nm and a = 113.65° [Kinuma,
Matsumoto and Honma, 1986], or equivalently, a hexagonal structure with lattice
parameters of a = 1.124 nm, c = 0.5077 nm [Saburi, Nenno and Fukuda, 1986]. A
sequence of precipitation was obtained by Nishida et al. [Nishida Wayman, Honma, 1986;
Nishida and Wayman, 1987] when they worked on a Ti,,,Ni52 alloys:

[30 —) A + Ni4Ti3 —) [32 + Ni3Ti2 -—) [33 + Ni3Ti (2.4)
where [30 represents the structure of the as—solution treated alloys, and B], B2 and [33
represent the structures of the matrix after the precipitates Ni4Ti3, Ni3Ti2, Ni3Ti are formed.
Independent work by Beyer et al. [1986] on N iTi-Ni diffusion couples supported these
results.

Secondly, metastable phases exert important effects on the R-phase and martensitic
transformations. The most signiﬁcant metastable phase is N i4Ti3. It is lenticular in
appearance and can be obtained by annealing the N i-rich NiTi at temperature between 673
K and 873 K. The orientation relationship between the precipitates and the B2 matrix is

[Nishida Wayman, Kainuma and Honma, 1986]:

18

(100),,m, //(142)B2

_ (2.5)
[001]~,,T.-, //[01 2 132

The habit plane of the precipitation is {111}, and because of the symmetry of the matrix,
there are 8 variants of precipitates in total.

N i4Ti3 precipitates affect the R-phase and martensitic transformations differently
according with the precipitation stage. When the precipitates are small, a coherent interface
with the matrix is maintained. The martensitic transformation is seriously delayed, and the
interface stress of the precipitates tends to encourage a single—variant martensite [N ishida
and Honma, 1984; Xie et al., 1990], by which biased nrartensite is formed if the material
is sufﬁciently cooled.

As the precipitates grow, the coherent interface becomes semi-coherent even
incoherent, and it becomes a favorable nucleation site for martensite instead [Xie et al. ,
1990]. By selectively encouraging the growth of Ni,,Ti3 variants through constrained
annealing of Ni-rich [3 solid solution at intermediate temperature, Nishida et al. [1984]
found that the two-way SME was realized. The stress biasing effect on the growth of the
precipitates was recently proved by Li and Chen [1997] in Ni-rich NiTi under uniaxial

stress conditions.

2.1.2.3. NiTi-Base Ternary Alloys

Although near-equiatornic binary NiTi alloys exhibit excellent SME and PE, these
alloys have a number of disadvantages. The transformation temperature is very
composition-sensitive and the servicing temperature can not be higher than 373 K.
Alloying has proven to be an efﬁcient way to modify the properties of the material. The
following section brieﬂy describes the most popular ternary NiTi base alloys.

19

Ni Ti- Cu SMAs. Transformation temperatures in binary near-equiatomic NiTi are
very sensitive to composition. 1 atomic percent excess Ni can decrease M by 100 K if all
the excess Ni atoms are dissolved into the matrix. Up to 30 at.% addition of Cu substituted
for Ni considerably decreases the sensitivity of the transformation temperature on
composition [Vanloo, 1978; Mercier and Melton, 1979], making it easier to control the
transformation temperature by composition adjustment In addition, NiTi—Cu has a number
of other advantages over binary NiTi. For example, the martensite de-twinning stress is
lowered, the hysteresis is narrowed, and fatigue properties are improved [Proft, Melton
and Duerig, 1987]. Another feature of NiTi-Cu is that typically the A, is just above human
body temperature, which is convenient for use in biomedical applications [Krulevitch,
1996]. Crystallographically, the lattice parameters of martensite change with increasing Cu
addition, and if the Cu content is more than 10 at.%, an orthorhombic martensite may
appear before the monoclinic martensite does, yielding a two-step martensitic

transformation [Moberly and Melton, 1990].

NiTi-Nb SMAs. Narrow hysteresis is useful for thermal actuation, but wide
hysteresis is useful in some other applications such as pipe couplings, where it is desirable
for the opened SMA component not to shrink upon a slight temperature increase, and once
it shrinks, it does not loosen from transformation while in service. Addition of Nb near 10
at.% works well in widening the transformation hysteresis. It has been reported that in
NiTiNb9 alloys, the hysteresis is as large as 130 K [Melton, 1986]. Microstructurally,
Additional Nb is not miscible in either the parent phase or the martensite. It exists as pure
Nb islands distributed in the matrix, but it does change the deformation behavior of the
martensite. The deformation of a N iTiNb material occurs in the martensite as well as the
pure Nb islands since Nb is very easy to deform. When heated, the deformed Nb delays
the reverse transformation by elastic interactions, therefore, the transformation hysteresis is

widened [Zhang et al., 1990].

20

Ni( Til-1f) and Ti(NiPd) SMAs. Hi gh-temperature SMAs are needed in automotive
and spacecraft applications. Because the M8 temperature of binary NiTi is less than 373 K
[Thoma et al., 1991], no SME applications over 373 K can be made with binary NiTi.
However, by substituting Zr or Hf for Ti, or by substituting Pd or Pt for Ni, the
transformation temperatures can be substantially increased. Although the ﬁrst few percent
of Hf or Pd actually lowers transformation temperatures slightly, if the Hf addition is more
than 5 at.% [Angst, Thoma and Kao, 1995], or Pd more than 10 at.% [Lotkov et al.,
1982], the transformation temperatures increase very rapidly. 15% of Hf addition or 30%
of Pd can raise the M, temperature to as high as 473 K. In addition, these new ternary
alloys have a recoverable strain of up to 3% and satisfactory thermal stability, making them
feasible for high-temperature SME applications [Pu et al. , 1994]. Crystallographically,
there also exist monoclinic martensite and orthogonal martensite, the latter of which appears

as the ternary additions increase [Sivokha et al., 1983; Han et al., 1996].

2.2. Thin Film: Fabrication, Microstructure and Stresses

Thin ﬁlm science and technology plays an important role in industry. While the
major exploitation of thin ﬁlms has been in microelectronics, there are also increasing
applications in communications, optical electronics, coatings of all kinds, and in energy
generation and conservation strategies, which are also of great interest. Since this thesis
work is on N iTi thin ﬁlms, a review on thin ﬁlm fabrication and characterization is useful.
In the following, the sputtering technique, which is an extensively used method for making
thin ﬁlms and is the major method for NiTi thin ﬁlm fabrication, is described in detail.
Structural characteristics of sputtered ﬁlms and stress development in thin ﬁlms are

reviewed.

21

Z-ZIIIE'I El' . .5 .

There are numerous methods of making ﬁlms, but there basically are two
categories, Chemical Vapor Deposition (CVD) and Physical Vapor Deposition (PVD),
according to whether chemical reactions are involved during the deposition. The sputtering
method, one of the PVD methods, has a high deposition rate and a high ﬂexibility of target
material selection, thus has been favored for small-area deposition.

A sputtering system is composed of a vacuum chamber, which is usually ﬁlled to low
pressure with an inert working gas (usually argon), a cathode, which is the ‘target’ material
which is connected to a negative voltage supply, and a substrate holder forming the anode
and facing the target. Ionized gas atoms (usually Ar) gain kinetic energy through the
electric ﬁeld and accelerate toward the cathode. Atoms in the cathode are ejected from the
surface by the knock-on effects of the incoming ions, and deposit on a substrate, forming a
continuous ﬁlm. The collision cascades between the ions and target atoms not only yield
neutrals of the target material, but also yield Auger electrons, secondary electrons, and
reﬂected neutral species of the working gas. The secondary electrons are critical for the
maintenance of the plasma, which is primarily determined by the working gas pressure. If
the working gas pressure is too high, insufﬁcient secondary electrons are produced since
the ions lose most of their energy in collisions on the way to the cathode. If the working
gas pressure is too low, even if there are enough secondary electrons in the initial period,
the ion ﬂux keeps diminishing because not enough working gas atoms are ionized. Both of
the situations eventually lead to loss of the plasma and termination of the deposition
[George, 1992].

What was described above is essentially glow discharge d.c. sputtering, which uses
a dc. electric ﬁeld to accelerate the ions and the plasma is self-sustained. As described in
the last paragraph, the sputtering must operate with a limited range of working gas pressure
(usually >10 mTorr). The most serious drawback of the self-sustained glow discharge as a

technique for the sputter deposition of ﬁlms is contamination of the deposited ﬁhn by the

22

inert gas used to produce the discharge. But concentration of this trapped inert gas in the
ﬁlm can be lowered if the sputtering is done at low pressure. Another advantage that might
be expected from sputtering at low pressure is the higher mean energy of the sputtering
particles when they strike the substrate, resulting in better adhesion and more compact
ﬁlms.

There are several ways to realize sputtering at low pressure. One is triode
sputtering. In triode sputtering systems, an independent thermionic source is used to
supply additional electrons for the maintenance of the discharge glow at low working gas
pressure. The anode of the thermionic source is biased positively with respect to the
substrate to avoid the collection of electrons at the substrate, which may result in gross
inhomogeneities in plasma density at the target. Triode sputtering allows operation at much
lower pressures (<10’3 Torr) than in a conventional diode glow discharge system. Another
way to enable the sputtering to work at low working gas pressure is magnetron sputtering.
The permanent magnets backing the planar cathode in a magnetron sputtering gun make the
secondary electrons move in orbits so that the probability of working gas ionization is
promoted because the path of secondary electrons becomes much longer. Most magnetron
sources operate in the pressure ranging of 1 to 20 mTorr and with a cathode potential of
300 ~ 700 V. In comparison to the conventional diode sputtering, magnetron sputtering
gives high deposition rates at lower working-gas pressure and also high-quality ﬁlms at

low substrate temperatures.

Hurt.” , .r. r.-‘ u, 0 tr. Ll‘ -._u ’1 H.113 0 0-1;” '11.

There are a number of parameters involved in a sputtering process such as working
gas species, working gas pressure, working distance (cathode-to-substrate distance),
deposition power and substrate temperature. The compositions, microstructure and
physical properties of the as-sputtered ﬁlms depend on the processing parameters chosen,

which issues are discussed next.

23

2.2.2.1. Compositions

It is obvious that a pure-element target produces pure-element ﬁlm by sputtering
even though ﬁlm growth rate may constantly change with time due to the topographical
changes in the target. For alloy cathodes, because the sputter yields of different species are
different, preferential sputtering effects may exist. 80 it is expected that when the
deposition is started, the composition of the mass ﬂux will deviate from that of the target
material. However, for a well cooled cathode where diffusion is negligible, as the
sputtering process progresses, the composition at surface and sub-surface changes such
that preferentially sputtered atom species decreases while the other species increases.
Eventually, a steady-state mass ﬂux of the same composition as the target material will be
achieved. Of course, it can be imagined that an over-worn target will produce ﬁlms of an
unpredictable composition since at that time the geometric conﬁguration of the target has
changed substantially.

Although eventually the mass ﬂux of the sputtered neutrals reaches a steady state
with the same composition as the target, the resulting ﬁlm does not necessarily do so. This
is primarily because (1), stereo angular distribution of each sputtered species may not be
the same, therefore, the composition of the ﬁlm may vary from site to site, (2) more
importantly, a preferential re-sputtering effect may occur on the ﬁlm. Resputtering is a
process whereby some atoms in the growing ﬁlms are sputtered off by bombardment with
the incoming species. Some of the atom species are thus preferentially back-sputtered due
to the difference of sputter yielding rates among different species, and no steady state
evolves. In general, lighter atoms preferentially re-sputter, but some other effects such as
bond energies and saturated vapor pressure are also important in determining the
preferential sputtering sequence. Biasing voltage on the substrate, as well as low working
gas pressure and off-axis deposition conditions may increase the extent of preferential

resputtering.

24

2. 2.2. 2. Structure and Microstructure

The structure of the as-sputtered ﬁlm is strongly dependent on the process
parameters such as working gas pressure, working distance, deposition rate, off-axis
conditions and substrate temperature, among which the substrate temperature is the most
important. Thornton [1977] developed a zone structure model for sputtered ﬁlms which
was extended from the work by Movchan and Demchishin [1969] on electron beam
evaporated ﬁlms. It states that the microstructure of the sputtered ﬁlms are divided into
basically three ‘zones’ depending on the homologous deposition temperature Tﬂ‘,I (where
T, is substrate temperature during deposition, TM is the melting temperature of the ﬁlm):

Zone I (Tﬂ'm < 0.3): Characteristic microstructure of the ﬁlms is either amorphous,
dentrite or noncrystalline. In each case the structure is extended in the growth
direction. The ﬁlms are rather porous, and possess very poor mechanical
properties.

Zone I (0.3 < T/Tm < 0.5): The most characteristic feature of the microstructure is
largely uniform columnar structure with high compactness. The grain diameter, (1,
extends throughout the thickness of the ﬁlm, I, but the grain aspect ratio d/h usually
less than one.

Zone I (T/I‘m > 0.5): metallic ﬁlms have a columnar structure with a grain diameter
greater than the thickness of the ﬁlm. The texture of the ﬁlms is very strong. At
extreme conditions, the grain growth behaves like epitaxial growth.

Although it is suggested that there is a regime between Zone I and Zone II where the grain
structure changes smoothly from characteristics of one zone to those of the other as the
substrate temperature changes ['Thornton, 1977], later experiments showed that the grain
structure underwent a discontinuous evolution characterized by the formation of a bimodal

grain structure [Smith and Ibrahim, 1984].

25

The zone structure itself can be explained to some extent in terms of self-
shadowing, surface diffusion, bulk diffusion, which, along with adsorption of adatoms,
constitute four basic processes of ﬁlm formation ['Thornton, 1977; Chopra, 1979; Ohring,
1992]. In the ﬁrst regime, both adatoms and inner atoms have very poor mobility. Due to
self-shadowing effect, porous structures are usually developed. Intermediate substrate
temperature allows sufﬁcient surface diffusion of the adatoms but sluggish bulk diffusion
of the inner atoms. At this time, more compact ﬁlms result, but meanwhile, numerous
grain boundaries exist. High substrate temperature allows both sufﬁcient surface diffusion
and bulk diffusion, therefore, large grain size will result.

For sputtering, working gas pressure is another important parameter since it
evidently affects the zone structure. The momentum exchange of the incoming species with
the adatoms provide more energy for movement to stable low—energy sites. The kinetic
energy of the incoming species diminishes during transport to the substrate if collisions
with working gas molecules occur. Low working gas pressure decreases the probability of
such collisions, and thus, help to preserve the kinetic energy of the incoming species. As a
consequence, lowering working gas pressure is similar in a sense to increasing the
deposition temperature [Hoffman and Thourton, 1979; Hoffman, 1983], making the

whole zone structure move toward lower temperature regime.

2. 2.2.3. Adhesion and Surface Roughness

Interfacial adhesion at the ﬁlm/substrate interface depends on both the nature of the
electronic bonding at the interface and other factors such as substrate morphology, chemical
diffusion, contamination, and defects. Strong adhesion of thin ﬁlms is associated with
enhanced substrate-adatom bonding, small local stress, uniform ﬁlm thickness, and
absence of an easy deformation or fracture path [Mattox, 1978]. In practice, adhesion may
be improved by means such as substrate cleaning, reduced pressure during deposition,

removal of surface oxides and reduction of ﬁhn thickness. High energy ion bombardment

26

before or during sputter deposition has been also used to improve the adhesion of thin ﬁlms
[Baglin, 1987].

The surface morphology of thin ﬁlms evolves in both the deposition process and
during post-deposition processes. During deposition, while the surface diffusion
potentially makes the ﬁlm smoother [Chason et al., 1984], resputtering resulting from
bombardment by incoming species tends to make the ﬁlm rougher [Keste and Messier,
1993]. It has been observed that the etching effect induced by resputtering causes
considerable non-uniform thickness in the ﬁlm, which is aggravated by increasing
sputtering power, prolonged deposition time, decreasing the working gas pressure,
decreased working distance and increased 02 levels. Microscopically, resputtering causes
the formation etch pits, ripples, cones, and craters at the micron scale on the surface of the
ﬁlms [Keste and Messier, 1993]. During post-deposition annealing, hillocks may formed
by stress relaxation processes associated with grain sliding and grain boundary diffusion if
the annealing ﬁlm is under stress [Nix, 1989].

2 2 3 S . 11' El
Stresses are often introduced from thin ﬁlm fabrication processes and post-

fabrication treatment. Stresses in thin ﬁlms have important effects on many phenomena
such as decohesion, defect generation and surface morphology evolution [Drory, Thouless
and Evans, 1988; d’Heurle, 1989]. In the following, a review on stress classiﬁcation,

stress formation and stress evolution during post-deposition annealing is presented.

2. 2.3.1. Classiﬁcations of Stresses

According to how they are created, stresses in thin ﬁlm can be divided into two
general categories: Extrinsic stresses and intrinsic stresses. While extrinsic stress results
from differential thermal expansion coefﬁcients, intrinsic stress is simply the rest, which is

developed during the ﬁlm growth process. In addition, stresses can also be divided into

27

three types according to their spatial homogeneity [Macherauch and Kloos, 1987]. The
ﬁrst, called macro stress, is nearly homogeneous across a large area (say, several grains) of
a material, and are equilibrated within the whole body. The second kind of stress is nearly
homogeneous across microscopic area (say, one grain or parts of a grain) of a material, and
are equilibrated across a number of grains; The third kind of stress is inhomogeneous
across submicroscopic area (several atomic distances within a grain) of a material, and are
equilibrated across a small part of a grain.

Macroscopic stress generates by numerous ways. Any mechanical, thermal and
chemical treatments, including elastic-plastic loading, machining, joining, forming, heat
treatment and coating, cause macroscopic stress. In all cases, the resulting stress states
strongly depends on the existing geometrical conditions and on the parameters of the
treatments and processes applied. In elastic-plastic loading, some of the stress is vanished
if the loading is released. However, residual stress may exist if an inhomogeneous
deformation has undergone. In welding, the shrinkage of seams produces biaxial residual
stress. As a special forming method, shot peening is widely used to produce compressive
stress near the surface of the material, thereby to improve the hardness of material’s
surface.

Residual stress states of the second kind exist in both homogeneous and
heterogeneous materials. For example, homogeneous materials with a pronounced
anisotropy of the yield strength of their grains show residual grain stresses of different
magnitudes after uniaxial elastic-plastic tensile deformation [Macherauch and Kloos, 1992].
Similar effects will occurs in heterogeneous materials composed of two phases with
different yielding strengths.

The third kind of residual stresses is produced by lattice imperfections including
dislocations, interstitial atoms, substitutional atoms, vacancies, microcracks, grain
boundaries and phase boundaries. The submicroscopic stresses are associated with

strongly inhomogeneous lattice strains. Very complicated stress states occur when stress

28

ﬁelds resulting from different types of lattice imperfections overlap. Experimentally it is
hard to separate the third kind of stress from the others.

2.2.3.2. Thermal Stresses

Generation of thermal stresses are easy to understand. In general, thermal stress
can be created by either non-uniform temperature change or uniform temperature change in
the presence of differential thermal expansion coefﬁcients. Rapid solidiﬁcation of a liquid
material, which results in a large temperature difference across the material during the
process, creates considerable thermal stress even if the thermal expansion coefﬁcient is the
same across the material. The stress is generally inhomogeneous due to the complexity of
the temperature ﬁeld. For a thin ﬁlm on a substrate, considering the situation that at a given
time, the temperature is the same across the whole material, thermal stress is the same
across the material and it can be quantitatively calculated if the temperature change and the

difference in thermal expansion coefﬁcient between ﬁlm and substrate are known:

 

r
’ E

Aowma, =f1__{’ -(af -a,)dT (2-6)
T, I

Here T, and T, are starting temperature and ﬁnishing temperature, respectively; B, is the
elastic modulus of the ﬁlm, vfis the Possion’s ratio of the ﬁlm, and a, and a, are thermal
expansion coefﬁcients of the ﬁlm and the substrate, respectively. It is assumed that the
stresses are biaxial, the substrate is rigid and much thicker than the ﬁlm, and the ﬁlm and
substrate are elastically deformed. Because the temperature is the same anywhere in the
sample, the stress is uniform across the sample. Therefore, thermal stress is basically

macroscopic stress.

29

2.2.3.3. Intrinsic Stresses

While the origin of extrinsic stress is quite clear, that of intrinsic stress is much
more complicated. No single model can explain how the intrinsic stress is created.
Nevertheless, it is found that a number of mechanisms, such as nonequilibrium growth,
defect evolution, interfacial constraint, in-situ phase transformation and in-situ stress
relaxation are related to the sign and magnitude of the intrinsic stress. Each process is

reviewed in the following.

Nonequilibrium Film Growth Intrinsic stresses observed in continuous metal
ﬁlms, if no bombardment-like process is involved during the ﬁlm fabrication process, are
generally tensile. Klokholm et al. [1968] and Buckel [1969] considered that the material
was deposited in a metastable state and that subsequent atomic rearrangement (which would
result in a shrinkage of the ﬁhn if it were not attached to the substrate) generated the
observed tensile stress. However, the as-deposited material need not be amorphous or
have a metastable crystal structure. Other departures from the equilibrium can lead to
stresses. For example, an excess vacancy concentration can result in tensile stresses by
diffusion of the vacancies to the grain boundaries and annihilation there. It is noted that the
stress results from the rearrangement of the depositing atoms after they arrive to the
substrate. If the ﬁhns is not allowed to change structurally, but maintains its ‘frozen-in’
structure, no stress is expected to develop.

In order to predict the stress generation in thin ﬁlms at various substrate
temperatures, it is important to consider the kinetic process involved. There are three major
aspects of stress generation wherein the kinetics of atomic motion should be considered.
The ﬁrst involves the rate of atomic rearrangement on the growing surface. It this occurs
rapidly compared to the rate of arrival of depositing atoms then an equilibrium structure will
be formed and the ﬁlm will grow in a stress-free state. Conversely, if the depositing atoms

arrive more rapidly than they rearrange, a nonequilibrium structure will be formed.

30

Subsequent rearrangement of the structure leads to stress in the ﬁlm. In this case, the
kinetics of the atomic rearrangement must be considered, and deposition temperatme seems
to be crucial. Buckel [1969] showed stress-free growth of amorphous Ga and Bi below 20
K. At these low temperatures, stress generation is limited by the low atomic mobility.
Klokholm [1969] and Rottrnayer and Hoffman [1971] showed an increasing stress with
increased deposition temperature.

The third aspect of stress generation that requires kinetic considerations involves
stress relaxation, i.e., in-situ relaxation. Since stresses as high as the ﬂow stress are
observed during thin ﬁlm growth [Klokholm and Berry, 1968; Plunkett et al., 1979],
dislocation motion as well as diffusional process can operate to reduce the stress. The
observed stress depends on the rate of stress generation associated with atomic
rearrangement relative to the rate of stress relaxation rate. Since diffusional stress
relaxation involves the mass transport of material from surface or the substrate/ﬁlm
interface to the interior, stress generation due to local atomic rearrangement is likely to
proceed faster than stress relaxation. However, if the stresses are high enough, stress

relaxation may occur rapidly through dislocation motion.

Grain Growth One type of atomic rearrangement that can be responsible for
generating tensile stresses is grain growth [Chaudhari, 1972]. It is believed that the grain
boundary density is less than that of the perfect lattice and a strain in the ﬁlm due to the
elimination of grain boundaries will result. Doemer and Nix [1989], based on the
observation that the grain growth decreased the grain boundary energy but at the same time,
increased the elastic energy, kinetically analyzed the grain growth and grain-growth
induced stress evolution. They concluded that the grain growth stops when the grain size
reaches a critical size, and the smaller the initial grain size is, the more signiﬁcantly the
stress changes by grain growth. According to their calculation for Ni ﬁlms, when the
initial grain size is less than 20 am, more than 20 MPa stress can be developed before the

31

grain size reaches the critical size. Nearly 2 GPa tensile stress can develop when the initial
grain size is 2 nm. However, such high stress was rarely observed because stress

relaxation becomes signiﬁcant at this time.

Excess Vacancy Annihilation Another source of stress generation in thin ﬁlms
involves the annihilation of excess vacancies. In general, volume changes are associated
with the annihilation of vacancies and these volume changes lead to stresses in the ﬁlm
when the ﬁhn is attached to a substrate. The sign and magnitude of the stress produced
depend both on the vacancy volume and on the site of vacancy annihilation. If the
vacancies annihilate at the free surface of the ﬁlm, or at the surfaces of internal cavities, no
additional stress is expected because the planar dimension of the ﬁlm does not change.
However, if the vacancies annihilate at grain boundaries perpendicular to the plane of the
ﬁlm, a biaxial tensile stress develops within the ﬁlm. The initial vacancy fraction, average
grain size and the temperature determine how much stress can result. According to the
calculation results by Doerner and Nix [1989], if the initial vacancy fraction of 1% and a
grain size of 30 nm are assumed for Ni ﬁlm, the stress magnitude in the MPa range is not
observed for holding time as long as ~103 seconds at temperature below 473 K. Therefore,
it appears unlikely that vacancy diffusion contributes signiﬁcantly to stress generation for

low temperature deposition.

Grain Boundary Relaxation One of the most widely quoted models of intrinsic
stress is Hoffman’s grain-boundary relaxation model [Hoffman, 1966, 1976; Doljack and
Hoffman, 1972; Pulker, 1982]. According to the model, tensile stresses are created in thin
metal ﬁlms because the crystallites that form on the substrate are never located in the correct
positions to produce equilibrium grain boundaries when the crystals grow together. It is
argued that, on average, the atoms in the grain boundary are more widely spaced than they
would be if the crystals were free to form an equilibrium boundary. As the atoms relax

32

toward their equilibrium positions, an elastic strain and a corresponding intrinsic tensile
stress develops in the ﬁlm. Under these conditions the equilibrium state of the ﬁlm is not a
stress-free state. Rather, the total free energy of the system, including both interfacial ands
elastic strain energy, reaches a minimum at a ﬁnite elastic strain.

Even though some ideas from Hoffman’s model are open to question [Doerner and
Nix, 1989], it is clear that, on average, an atomic deﬁciency will exist in the grain
boundaries due to the arbitrary location of the crystallites on the substrate. Atoms will be
added to each growing crystal until they grow together. When the spacing between the
surfaces of two separately growing crystals approaches an atomic dimension it becomes
more and more difﬁcult for arriving atoms to reach sites between the two crystals. This
naturally leads to the porosity of the ﬁlm. Even the porosity in the grain boundary does not
automatically lead to elastic strains in the ﬁlm, subsequent relaxation process may result in

the development of stress.

Impurity Eﬁects The effect of impurities on the stress is not well understood.
However, oxygen incorporation is thought to be probably the most signiﬁcant in changing
ﬁlm stresses. In ﬁlms deposited by vacuum evaporation, intrinsic compressive stress were
observed when the vacuum conditions were poor [Priest et al., 1962; d’Heurle et al. ,
1968], and the intrinsic stress can change from tensile to compressive if the oxygen level is
increased [d’Heurle, 1989]. The mechanism appears to be that the impurity atoms are ﬁrst
absorbed at the surface of the ﬁlms being deposited and diffuse to the interior. Clearly, this
process could happen with materials which have a high afﬁnity for carbon, oxygen, and
high solubility limits for these elements. Moreover, these elements occupy interstitial
positions, causing an increase in lattice parameter, and diffuse readily. Another possible
process is that the impurity atoms are adsorbed on the ﬁlm surface and get buried under an

upper layer of metal, thereby swelling the lattice and causing compressive stress.

33

Phase Transformation and Precipitation Volume changes associated with phase
transformation and particle precipitation also lead to stress generation in thin ﬁlms. For
example, amorphous-to—crystalline transformation often results in a l to 2% increase in
density [Davis, 197 8], it is expected that large tensile stress can develop by crystallization.
This effect is observed for a number of materials [Horikoshi et al., 1963; Pan and Belch,
1984]. Stress associated with the precipitation of additional phases have been observed
although the effect is smaller [Zingu and Mofokeng, 1993].

Epitaxy Strain can be introduced into a growing ﬁlm if the ﬁlm grows with an
epitaxial relationship to the substrate and a mismatch between the lattice spacings of the two
materials exist. As the thickness of the epitaxial layer increases, the strain energy in the
ﬁlm increases until it becomes more energetically favorable for a series of misﬁt
dislocations to form at the interface. A critical thickness thus exists, below which the
coherent strained ﬁlm is stable and above which an array of misﬁt dislocations forms to
accommodate the lattice mismatch. In this consideration, stress in ﬁlms quickly decrease

when the thickness reaches the critical thickness.

Stress in Sputtered Films In contrast with ﬁlms deposited by evaporation which
usually display tensile stresses, compressive intrinsic stresses are often observed in
sputtered ﬁlms [Blachman, 1974; Thourton and Hoffman, 1977 (a, b); 1980; 1982].
Because such ﬁlms also contain some amount (~1.0 at% or less) of incorporated gas, many
references imply that this incorporated gas is the cause of the unexpected (compared with
ﬁlm deposition by evaporation) compressive stress. But it is not the actual case. It was
ﬁrst pointed out in a study of aluminum ﬁlms deposited by dc. sputtering that [d’Heurle,
1970], while in evaporation the deposited atoms are nearly in thermal equilibrium with an
energy equal to a few kTs, in a sputtering process, a ﬂux of depositing atoms and the ion

gas atoms reﬂected from the sputter cathode arrive on the substrate with an energy of

34

several electron volts, so that the already deposited layers are subjected to a bombardment
which in an atomic scale is similar to the ‘shot peening’ effect which in metallurgical
fabrication is used to put surfaces into compression. It does not matter so much that the
energy should be so small since the damage is immediately buried under newly deposited
layers, but rather that the damage is accumulated. The effect is increased under conditions
of bias sputtering when the substrate is deliberately bombarded with energetic gas ions. In
addition, the compressive stress generated in the deposited ﬁlms is dependent on other
sputtering condition such as sputtering gas pressure, power, geometry of the relative
atomic mass of the target material to the atomic mass of the working gas [Thomton, Tabock
and Hoffman, 1979; Hoffman and Thornton, 1980]. It is particularly noted that this
peening effect mechanism is predominant only when working-gas pressure is low, since
over-dense working gas can dissipate the kinetic energy of the gas atoms reﬂected from the
sputter cathode.

2.2.3.4. Stress Relaxation

Stress relaxation may occur during deposition, in which case it is referred to as in-
situ relaxation, or it may occur during post-deposition annealing. All the relaxation
processes happening during the deposition such as structure relaxation, grain growth,
excess vacancy annihilation, grain boundary relaxation and phase transformation, can also
occur during post-deposition annealing. However, because the holding time can be very
long during post-deposition annealing, some mechanisms unavailable during in-situ
relaxation can also happen by post-deposition relaxation and have signiﬁcant effects on
morphology, microstructure and properties of ﬁlms.

Grain boundary slide is well observed mechanism for stress relaxation. It occurs
when ﬁlms are under compressive stresses. By this mechanism, grains can be extruded
from the ﬁlm surface, whereby hillocks are formed. The formation of hillch stop when

the compressive stress is completely relaxed. When the ﬁlm is under tensile stress,

35

hillocks can slide back into the ﬁlm by which the tensile stress is relaxed. Therefore, to a
limited degree, hillock formation is reversible.

It is pointed out that stress relaxation in thin ﬁlms can proceed along different
pathways [Gangulee, 1974]. Dislocation motion can take place and be observed at the
surface through the formation of visible slip lines [Caswell, Priest and Budo, 1963].
Creep either by lattice diffusion model (Nabarro and Herring creep) or by grain boundary
diffusion (Coble creep) is also a means of relaxing film stresses. Based on the level of
stress and the temperature, it can be deﬁned which process will be operative [Murakami,
1984]. According to the model proposed by Murakami, dislocation glide and climb occur
at high stress (~ 10'2G, where G is shear modulus) and high temperature (Tle >05), and
gives a strain rate as high as 0.1 5". Grain boundary diffusion occurs at an homologous
temperature (TIT m) above 0.4 and gives a strain rate of 10’2 to 10‘” s“.

For bulk materials, stress relaxation by grain boundaries dominates over bulk
diffusion (lattice diffusion) for small grain sizes and in an intermediate temperature range
(0.3 ~ 0.6 TIT”). Since the grain sizes in thin ﬁlms are typically small, grain boundary
diffusion is an important mechanism in thin ﬁlm deformation. However, both the
constraint of the substrate and the columnar microstructure of thin ﬁlms place signiﬁcant
limitations on the grain boundary diffusion process [Jackson and Li, 1982]. Once the
normal stress on the grain boundaries have been completely relaxed, grain boundary
diffusion related stress relaxation stops. Therefore, In the absence of bulk diffusion or
dislocation motion, stress within the grains will remain due to the substrate constraint.

In summary, for thin ﬁlms on substrate, while extrinsic stress is easy understood,
origin of intrinsic stress is much complicated. A number of mechanisms may contribute to
the development of intrinsic stress. Stress relaxation in thin ﬁlms is also determined by
several processes. Which one is operative depends on the stress level and temperatures.
Stress relaxation in thin ﬁlm may differ from that in bulk materials because of the constraint

of the substrate.

36

2.3. NiTi Thin Films

Based on the remarkable performance of melt-solidiﬁed NiTi alloy, thin ﬁlm NiTi
has been regarded as a promising material for high-energy-output microactuators for use in
microelectromechanical system and has been extensively studied. Considerable progress
toward engineering application has been achieved. Below is presented a review on NiTi
ﬁhn fabrication, microstructure, phase transformations, shape-memory effect of sputtered

NiTi, and current research interests of NiTi thin ﬁlms.

2.3.] E! . . [11.1.1]. Eil
While some work of NiTi thin ﬁlms were mainly directed at studies of solid state

reaction between Ni and Ti, in which case multilayer NiTi was made by sputtering
[Clemens, 1986; Jongste et al., 1988; Scineider et al., 1989], or electron beam
vaporization [Meng et al., 1987], most work aimed at the preparation of SMA NiTi thin
films. Physical vapor deposition techniques, such as sputtering [Kim, Moine and
Stevenson, 1986; Rai and Bhattacharya, 1987; Busch, Johnson, Hodgson, lee and
Stevenson, 1990 (b)], thermal evaporation [Gabraud and Delage, 1991; Moine, Delage,
Petton and Sinclair, 1992], ion mixing [Zheng and Dodd, 1994; Krulevitch et al., 1996]
and ion-beam assisted deposition [Walles, Chang and Grummon, et al., 1992] have been
used to make NiTi ﬁlms. Due to the ﬂexibility of target materials, sputtering, including
d.c. magnetron sputtering, r.f. sputtering, triode sputtering, and ion-assisted sputtering,
have been widely used in the preparation of near-equiatomic NiTi ﬁlms.

The composition of resultant ﬁlnrs is of concern because it is very important for
SME and transformation temperature control. It has been repeatedly shown that the
composition of sputtered NiTi ﬁlms may deviate from that of the sputter cathode material.
For example, when an equiatonric NiTi target is used, the as-sputtered ﬁlms have roughly a

composition 51~54 at.%Ni [Johnson, Martynov and Minners, 1995]. The reason is,

37

compared to Ni, Ti is a preferentially resputtered species. The actual composition of ﬁlms
depends on processing parameters such working gas pressure, working distance, plasma
energy and off-axis orientation, as well as target geometric conﬁguration that may change
as sputtering proceeds. Iee [1994] tentatively established the relationship between the
composition of ﬁlm and some of the process parameters. According to Lee, at 200 W
deposition power, steady-state composition of ﬁlms can be achieved only after one-hour’s
presputtering and is lost if the deposition time exceeds 3 hours. In addition, higher plasma
energy makes the ﬁlm more Ni rich, and the composition at off-axis site (1” from the
center) in the ﬁlm is less prone to change with the deposition power than on-axis
composition. More recently, Bendahan et al. [1995], having demonstrated that the ﬁlm
composition was sensitive to the product of sputtering gas pressure and the working
distance, invented a method to control the composition by changing the pressure, which is
directed by the in-situ measurement of sputtering plasma composition by optical emission
spectroscopy. Another method to realize composition control is dual-source sputtering.
By making multilayer Ti-rich ﬁlms, Chang and Grummon [1992, 1997] were able to
control the composition by alternating exposure of the substrate to two cathodes (N iTi and
Ti). For the multilayer ﬁlms, good composition homogeneity can be achieved by post-
deposition annealing. However, a popular and easy way to roughly compensate the
preferential re-sputtering effect is to put a few additional small plate pieces of the pure
element to be augmented on the surface of sputtering cathode [Kawamura et al. , 1995;
Ishida et al. , 1995]. No quantitative composition compensation can be expected by this
method.

Other qualities such as compactness and brittleness also depend on the deposition
parameters used. The most important paranreters are working-gas pressure and substrate
temperature during deposition. It seems that lower working gas pressure (<10 mTorr) and
higher substrate temperature are beneﬁcial to improve the compactness and ductility of the

ﬁlms. However, the compactness and mechanical properties of the ﬁlms are related to the

38

structure and microstructure, which may be also modiﬁed by post-deposition treatment.

The following discuss the structure, microstructure and transformations of NiTi ﬁlms at as—

deposited state and by post-deposition annealing.

 

In spite of different fabrication methods, NiTi thin ﬁlms prepared without additional
substrate heating are usually amorphous. This is probably due to the limited diffusion rate
at ambient temperature since crystalline TiN i is highly ordered and atomic rearrangement is
needed to produce crystalline structure. In crystalline B2 NiTi, the diffusion rate of T1
atoms is approximately one order of magnitude lower than that of Ni atoms [Bastin and
Rieck, 1974]. Although at present there is no diffusion rate data of Ti in amorphous TiNi,
it can be deduced, from the studies in Ni-Zr system [Johnson, 1988] due to the similarity
between Ni-Ti and Ni-Zr, that Ti is a relative immobile species in amorphous N iTi, too.
Due to the small free energy gap between amorphous and crystalline phase [Schwarz et al. ,
1985], and the sluggish diffusion of Ti, The amorphous structure stays stable until
crystallization temperature.

Amorphous-to-crystalline transformation of NiTi ﬁlms occurs at temperatures 673
K [Nakata et al., 1995] or above [Johnson, 1990], depending on ﬁlm composition
[Buschow, 1984; Kim, Moire and Steveson, 1986; Chang and Grummon, 1997], and the
heating rate of isochronal annealing [Kissinger, 1957; Chang and Grummon, 1997], with
a crystallization enthalpy as low as 1.9 kJ/mol [Busch, Johnson, Hodgson, lee and
Stevenson, l990(b)]. It is also reported that cold-work of the amorphous NiTi ﬁlms can
lower the crystallization temperature to 623 K [Madsen and J ardine, 1993]. Since atomic
rearrangement is needed for transformation of disordered structure to ordered structure, the
crystallization is an activated process. Chang and Grummon obtained crystallization
activation energies of 385 :1: 6 kJ/mol and 501 i 6 kJ/mol for Ti5,Ni44,4Cu4,6 and

Ti,.,,,.,Ni4,,5Cu6,l ﬁlms, respectively.

39

The crystallization of amorphous NiTi ﬁlms results in B2 structure and some
second phases, depending on whether the ﬁlm is Ti-rich or Ni-rich. Kim et al. [Kim,
Moire and Steveson, 1986] studied the crystallization behaviors of magnetron sputtered
Ni,,,Ti44 by Differential Scanning Calorimetry (DSC) and Transmission Electron
Microscopy (TEM), concluding that the crystallization temperature was 791 K and the

crystallization sequence was:
NiTi(Amorphous) —> Ni4Ti3 -—> [3,(NiTi) + Ni4Ti3 -) [32 (NiTi)+ Ni3Ti2 (2.7)

where B phases are the equilibrium crystalline B2 phases when the precipitates exist.

Ishida et al. observed the microstructure of 523 K-deposited Ti5,_,,Ni4,,_2 ﬁlms
annealed at different temperatures. When the ﬁlms were annealed at temperatures lower
than 97 3 K, the lower-temperature annealed samples contained TiZN i precipitates inside the
B2 grains, which was signiﬁcantly different from the melt-solidiﬁed Ti-rich NiTi, where
for as-cast and as-solution-treated samples the T12N i precipitates appeared along grain
boundaries. The ﬁne in-grain precipitates signiﬁcantly affect the shape memory effect of
Ti-rich ﬁlms [Ishida, Sato, Takei and Miyazaki, 1995].

Hot-substrate sputtering is a way to obtain crystalline NiTi ﬁlms directly. It has
been showed that when the substrate temperature is higher than 673 K, the as-deposited
ﬁlms are composed of B2 NiTi and some second phases [lkuta et al., 1990; Hou, 1997].
By observing the microstructure of the NiTi ﬁlms deposited at various temperatures on
quartz, Hou established the relationship between the microstructure of the ﬁlm and the
deposition temperature (T,). When Td < 573 K, the ﬁlm usually is amorphous with
columnar structure. At 573 K< T, < 673 K, the ﬁlm usually has a mixed structure
containing both amorphous structure and B2 crystalline structure, and possibly with some
ﬁne Ni4Ti3 precipitates. At Td > 673 K, the ﬁlm is almost fully crystalline with large Ni4Ti3

precipitates, and the grains become larger. Hou also discovered that a thin layer of

40

amorphous NiTi, near which is nanoscale B2 grains in the NiTi side, exists at the interface
between the quartz substrate and the crystalline NiTi even when the deposition temperature
exceeds 723 K, and a strong (110) texture in the as-deposited crystalline ﬁlm. Later work
by Chang [1997] indicated that the stiffness of the substrate may affect the minimum
substrate temperature for fully crystalline NiTi, and working gas pressure also affect the
texture of the as-deposited ﬁlm. According to Chang, with Kapton polyinride substrates,
whose elastic modulus is only ~ 1 .4 GPa [Product Bulletin, Du Pont Co.] in contrast to ~72
GPa for quartz [Engineered Materials Handbook, 1993], fully crystalline NiTi ﬁlms can be
obtained at substrate temperature as low as 560 K. At deposition conditions of lower
working gas pressure (~4.5 mTorr) with high deposition power ( 200 W for 2” gun), or
high pressure (~6.0 mTorr) with low deposition power ( <100 W), strong (110) texture
was observed in as.deposited N iTi on Kapton.

Near-equiatomic crystalline NiTi ﬁlms, obtained either by post-deposition annealing
or by hot-substrate deposition, have been demonstrated to undergo the B2 -) R and R —->
B19’ or B2 -> 319’ transformations upon cooling and the martensite transforms back to
austenite upon heating, which is basically the same processes as occur in melt-solidiﬁed
N iTi SMAs, and therefore, the crystalline ﬁlms have SME and PE comparable to those in
melt-solidiﬁed NiTi [Busch, Johnson, Iee and Stevenson, 1990; lkuta et al., 1990;
Kuribayashi et al., 1990; Walker et al., 1990; Johnson, 1991; Chang and Grummon,
1992; Ishida et al., 1993; Miyazaki and Ishida, 1994; Hou and Grummon, 1995; Hua,
Su and Wuttig, 1995]. Both the R—phase and martensitic transformations are observed by
resistivity measurement and DSC measurement. It has been shown that free-standing
crystalline BZ NiTi ﬁlms have comparable SME and PE with their melt-solidiﬁed
counterpart. Ishida et al. [1996] studied the annealing effect of Ni-rich NiTi on the
recoverable strain from the martensitic transformation and austenite critical stress for slip
deformation, and concluded that coherent Ni4Ti3 precipitates, which may be lost by

elevated annealing temperature( > 623 K) or prolonged time, help to maintain high stress

41

(> 580 MPa) for inducing slip deformation and larger recoverable strain ( ~5%). The same
group [1995] also found that ﬁne TizNi precipitates may exist inside the grains of annealed
ﬁlms with annealing temperature lower than 973 K, therefore, the mechanical properties of
the ﬁlms were improved. TizNi precipitates depressed the martensitic transformation so the
R—phase transformation was separated, making a two-stage transformation during cooling
from austenite. Hou and Grummon [1995] demonstrated that crystalline NiTi ﬁlms also
have superelasticity resulting from stress induced martensitic transformation, which is the
same as occurring in melt-solidiﬁed NiTi alloys.

The martensitic transformation in NiTi/Si composite has been studied by Kim
[1994]. It was shown that substrate constraint may suppress the martensitic
transformation. The martensitic transformation can be completely suppressed if the
thickness ratio between the ﬁlm and Si substrate is too small. The stress output for reverse
martensitic transformation is also related to the thickness ratio as well as substrate rigidity

[Mathews et al., 1996]. This result is useful in design of NiTi/Si nricroactuators.

Melt-solidiﬁed N iTi SMAs have found many successful applications in industry as
well as in biomedical practice. Some of the applications use SME while others use their
superelasticity. However, major work on NiTi thin ﬁlms has been aiming at the
development of Si-based SMA microactuators. The new microactuators will have
advantage over many of the actuators currently available, which are based on piezoelectric
or electrostatic principles [Fan et al., 1989; Kim, Katsurai and Fujita, 1989], in that their
energy density output is one or more orders of magnitude larger (see Table 1- 1). Si
substrates are used because they compatible with other electronic fabrication processes, and
more important, it serves as a good heat sink to allow the SMA actuators operate at higher
frequency (> 1 kHz) [Kim, 1994]. Busch and Johnson [1990] proposed the ﬁrst NiTi
SMA microactuator. Ray and his coworkers [Ray et al., 1992] invented a SMA microvalve

42

made from thin ﬁlm NiTi. More recently, Krulevitch et al. [1996], having demonstrated
the reversibility of ~500 MPa stress relief/recovery of N iTiCu on Si, proposed a Si-based
microgripper model and a Si-based electromicroactuator model [Ashley, 1996]. Also,
latest work in our laboratory demonstrated that N i-rich binary ﬁlms on Si may relieve as
large as 700 MPa stress upon the R-phase and martensitic transformations and the stress
may perfectly recovered by the shape memory effect, which results in useful cyclic
displacement [Zhang and Grummon, 1996].

Another novel application of SMA NiTi thin ﬁlms was suggested by J ardine
[J ardine, 1990; Mercado and J ardine, 1995]. It is a ferroelastic -SMA heterostructure
produced by depositing of BaTiO3 onto NiTi free standing ﬁlm This heterostructure is
expected to be able to perform sensing and actuation simultaneously. Recently, Alarn et al.
[1997] prepared a TiN i ferroelastic-ferroelectric thin ﬁhn heterostructure by hot depositing
NiTi on Si with BaTiO3 and PZT buffer layers. The buffer layers improved the
crystallinity of N iTi ﬁlms.

A number of other heterostructures are of industrial interest. One of them is to
fabricate SMA NiTi on Kapton, a base material widely used in electronics. Depositing
SMA ﬁlms on Kapton is potentially useful to realize shape change or displacement driven
by temperature change and the biasing force of Kapton layer. The difﬁculty is that
although the ﬁnal decomposition temperature of Kapton is 833 K, which is higher than the
crystallization of amorphous NiTi, when annealed at temperature as low as 7 23 K in
vacuum Kapton become unstable. Therefore, post-deposition annealing may not suitable to
produce crystalline NiTi/Kapton bilayer structure. Hot-substrate deposition may be a
solution. Grummon et al. [Grummon, Hou, Zhao and Pence, 1995] demonstrated that
NiTi ﬁlms deposited at elevated temperatures (~673 K) on Kapton was capable of
performing SME with the polyinride left intact. However, there arise other problems such
as transformation temperatures which are too low for most practical applications, which is

probably due to the nanoscale grain size. Thus it would be interesting to deposit SMA NiTi

43

ﬁlms on Kapton that have an M, near room temperature, which is possible by making Ti-
rich or stoichiometric NiTi ﬁlms. Another interest arising from the NiTi/polyimide
heterostructure is that the polyimide is a good elastic layer which can offer large
displacements due to its good ductility (~40%) and small elastic modulus (~1.4 GPa).

Just like binary melt-solidiﬁed NiTi, binary NiTi thin ﬁlms also suffer from low
transformation temperatures. High-transformation-temperature SMAs are of interest.
Johnson et al. [Johnson, Valery, Martynov and Shahoian, 1995] compared three high-
temperature SMA ﬁlms, CuAlN i, FeNiCoTi and TiNi-Hf, and concluded that, of these
candidates, TiNi-Hf had the best SME and the best mechanical properties. By substituting
15% of Hf for Ti, the M, temperature increased to 473 K, but the recoverable strain was
still kept at 4%. Almost concurrently, Miyazaki’s et al. [Miyazaki, Hashinoga, Yumikura,
Hirikawa, Ueki and Ishida, 1995] reported their results of r.f. sputtered TiNi-Pd ﬁlms and
Quandt et al. [1995] reported theirs of d.c. magnetron sputtered TiNi-Pd ﬁlms, and they
independently showed that the M, temperature reached 473 K by substituting 20 at.% to 30
at.% Pd for Ni and concluded that the NiTiPd ﬁlms were also a promising high-
temperature SMA candidate. However, it has also been indicated that the transformation
temperature is sensitive to a small composition deviation, especially when the composition
falls on the Ni-rich side [Angst et al., 1995]. How to precisely control the composition to
ensure precise control of transformation temperature remains a challenging work.

Sputtering has been favored for creating a small-area NiTi ﬁlms. However, thermal
evaporation makes lower cost ﬁlms over large areas. The problem is, although it is
possible to use hot substrates to create crystalline N iTi, which is analogous to sputtering
deposition, the composition can be even harder to predict due to the large vapor pressure
difference between Ni and Ti. Using equiatomic NiTi as parent alloy may produce
composition far away from stoichiometry. Furthermore, and diffusion at high temperatures

in the parent alloy makes the frontier composition change with the time. Possible solutions

44

include the use of parent alloy composition adjustment and the ﬂash evaporation method.
No attempts have been published using these methods.

Slow response remains a big problem for thermal induced actuation using SMA
even though thin ﬁlm components on Si can considerably shorten the response time. A
novel idea is to develop magnetically induced SME, which allows actuation frequency to
reach MHz. While James et al. [1997] have claimed success in searching for this kind of
material and have developed a theory regarding the magnetically induced martensitic
transformation, Ullakko et al. [1997] have reported that a recoverable strain of 0.15%
produced by the reorientation of magnetically induced martensite variants occurred in
N izMnGa. However, much work needs to be done to increase the magnitude of reversible
strain.

Despite all difﬁculties and limitations, Si-based SMA microactuators remain an
exciting and promising application of N iTi thin ﬁlms. In fabricating this kind of
microactuator, stresses, either intrinsic or extrinsic, will play an important role in reversible
action. This thesis research encompasses stress development during thin ﬁlm fabrication,
stress evolution in response to temperature changes, stress stability during annealing and
stress relaxation during the R-phase and martensitic transformations for NiTi thin ﬁlms on

Si.

Chapter 3

EXPERIMENTAL METHODS

Work reported in this thesis includes ﬁlm fabrication, stress analysis, phase
transformation analysis and relevant structure and microstructure investigation. Various
experimental methods have been used. In this section, the experiment procedures are
detailed.

3.1. Thin Film Fabrication

NiTi thin ﬁlms were made by the planar d.c. magnetron sputtering method using
deposition apparatus constructed in our research laboratory at MSM department of
Michigan State University [Hou, 1997]. A schematic representation of the apparatus is
shown in Fig. 3- 1. It is composed of a 2-inch magnetron gun, substrate holder and
external heating devices, housed in a deposition chamber that can be evacuated to 10'7 torr
by a Welch 1397 rotary pump and a 4000 Us Varian HS - 10 diffusion pump. Pure Ar
was used as the working gas. Pressure was controlled by an MKS 246 mass-ﬂow
controller and measured by an MKS Baratron capacitance manometer.

Two target alloys, Ni-rich and Ti-rich near-equiatomic TiN i ingots, were supplied
by Special Metals in New York. The Ni—rich ingot had a nominal composition of 51.3%Ni
- 48.7% Ti in atomic percent, while the Ti-rich alloy was 49.6%Ni - 50.4%Ti, the former
having a nominal M, of 263 K and latter having a nominal A, of 366 K, respectively. The
targets, which had a diameter of 2 inches and a thickness of 0.25 inches, were cut by

Electro Discharge Machining (EDM) from the as-supplied ingots. In addition, a composite

45

46

target was used to produce Ti-rich ﬁlms. It was made by evenly inserting four 0.125 inch
pure Ti rods within the wear track of a new Ti-rich target.

Two substrate materials were used in this study. One was single crystal Si with
(100) orientation, single-side polished, 5.1 mm (2 inches) in diameter and 0.3 mm in
thickness, supplied by Virginia Semiconductors; the other was microscope glass slides
with dimensions of 1 mm x 25 mm x 76 mm. The main purpose of using glass substrates
here was to produce free-standing ﬁlms since the ﬁlms are easily peeled off from the glass
substrates, especially when the ﬁlm/substrate sample was thermally shocked by repeatedly
immersing in liquid nitrogen.

Films have been made both with and without external heating. When external
heating was used, two separate heating elements were placed with one on each side of the
substrate. Substrate temperature was monitored by two thermocouples placed on each side
of the substrate. Temperature was regarded to be in equilibrium when both thermocouple
readings were stable and very close (difference < 2 K).

Deposition was started with a base vacuum pressure better than 5 x 10" torr. In
order to ensure a mass ﬂux with stable composition, each new target was wom—in for
approximately 7 hours before sputtering onto the substrate. 20 nrin full-power pre-
sputtering was also performed at the beginning of each run before the substrate was
exposed. For all depositions, the working distance was 65 mm, Ar pressure was set at a
carefully controlled level between 3.5 mTorr to 7 mTorr, and the deposition power was set
at level between 50 W to 200 W. In the case of hot-substrate deposition, the system was
outgassed at 50 K above the planned deposition temperature for 12 hours prior to
deposition. As-sputtered ﬁlms usually experienced furnace cooling at a rate of 20 ~ 40

K/min.

47

3.2. Thin Film Characterization
3.2.1 . Thickness Measurement

Film thickness was initially measured by scanning over deposition steps created by
masking (usually near the edge) using a Dektak IIA proﬁlometer at Department of Physics
and Astronomy of Michigan State University. Since there was no ﬁlm in the masked
region, the step heights were regarded as the ﬁlm thickness. To ensure the best accuracy,
the slowest scanning speed (~ 1 mm/min) was always used.

The deposition rate is nearly proportional to power used in sputtering, while high
deposition temperature or lower working gas pressure tends to decrease the deposition rate.
Based on the thickness measured by proﬁlometry, at 200 W, 5.0 mTorr pressure and

ambient deposition, a typical sputtering rate was ~1 nm/sec.

3.2.2. Stress Measurement
Stresses in ﬁlms fabricated under different conditions were evaluated by the wafer-
curvature method using Stoney’s equation [Hoffman, 1966; Ohring, 1992] which gives the

ﬁlms stress, a}, as:

af=W-t—-— (3.1)
wherezE, is the elastic modulus of substrate;
V, is the Poisson’s ratio of the substrate;
t, and t, are the thicknesses of substrate and ﬁlm, respectively, and
R is the curvature radius of the ﬁlm-substrate composite.
This equation is valid if t, » t, for a wide variety of shapes of the ﬁlm-substrate composite
[von Preissig, 1989].

48

The stress measurement system, which is schematically shown in Fig. 3-2, was
designed and constructed in our laboratory at MSM department of Michigan State
University [Zhao, 1995]. The system was composed of a laser scanning system driven by
an Omega PLC 812-PG card which was installed on a CompuAnd 333 computer, a quartz
bell-jar that was evacuated down to 10'8 torr by an Alcatel TM800 turbomolecular pump
and a Franklin Electric roughing pump, and an external furnace that was controlled by a
CN 8600 Omega temperature controller. The temperature was monitored by a thermocouple
which was placed near the wafer. A pure Ti getter was used in order to minimize oxidation
at high temperature. Heating was performed at rates ranging from 1.5 K/min to 3.0 K/min
by programming the Omega controller and adjusting the power input of the furnace, while
cooling was performed at rates lower than 5 K/min to ensure the homogeneous temperature
ﬁeld inside the chamber by slowly introducing cold nitrogen gas into the chamber.

A laser scanning system was used to measure the curvature of ﬁlm—substrate
composite. The optical diagram is shown in Fig. 3-3. The curvature, C, was calculated
from the linearly ﬁtted displacement for one scan step by

% (3.2)
where d is the beam displacement for one scanning step measured by Position Sensitive
Detector (PSD), D is the beam displacement for one scanning step at the sample surface,
and f is the focal length of the lens, which was 1,000 mm in this experiment.

The curvature values from the optical method were compared with that obtained
from the height-measurement method by proﬁlometry. Two samples were used to perform
calibration. By proﬁlometry, the ﬁrst one was measured to have a positive curvature radius
of 18.71 m, and the other has a negative curvature radius of -15.25 m. The calibration of
the laser scanning apparatus was completed by adjusting the gains of the ampliﬁers for the
signals from PSD and the distance between the optical lens and the pedestal on which

49

rotating nrirror and PSD were placed. After calibration, the curvature radii obtained by
laser scanning apparatus were 19.03 m and -14.95 m for the positively curved and
negatively curved samples, respectively.

Because the wafers were not perfectly ﬂat in the as-supplied condition,3
considerable error may result from the extra curvature, especially when the stress is low.
Therefore, the initial curvature of each as-supplied wafer was measured. When calculating
the stress, the curvature of the original wafer was subtracted.

Error in stress measurement may also partly result from the non-uniformity of ﬁlm
thickness, which produces an additional convex curvature. Since the ﬁlm is usually thicker
at the center than at the rim, negative curvature usually results (which corresponds to a

compressive stress). This corresponding curvature CM, can be calculated by

 

(3.3)

wafer

where R is the curvature radius resulting from the non-uniformity of ﬁlm thickness, Rm,"
is the radius of wafer (25.4 m), t, is the average thickness of the ﬁlm, and x is the
thickness deviation between that at the center and the rim (approximately 3% according to
the manufacturer for 2” gun depositing on a 2” substrate). The stress error can be
calculated by combining equations (3.1) and (3.3) and gives 0.25 MPa, which is
comparable to the sensitivity of the laser apparatus [Zhao, 1995]. Therefore, the error from

the non-uniformity of ﬁlm thickness is negligible.

3.2.3. Thermal Treatment
Post-deposition thermal treatment was sometimes necessary to acquire the shape
memory effect, to get better nechanical properties, and to modify phase transformation

characteristics of as-sputtered NiTi ﬁlms. All the post-deposition anneals were conducted

 

3 Polishing usually introduces slight doming of the wafer.

50

in the vacuum bell-jar used for stress measurement. The system was evacuated to 10'3 torr.
The heating rate usually 2 K/min. As-annealed samples usually experienced furnace
cooling, which typically was of a rate 10 ~ 20 K/min at temperatures above 573 K, or
vacuum (radiative) cooling by removing the furnace, which typically was of a rate of 100 ~
50 K/min at temperatures above 573 K. Pure Ti getters were also used to decrease residual

oxygen level.

3.2.4. Transformation Temperature Measurement

Transformation temperatures were obtained by four-probe electric resistivity
measurement. A schematic diagram of the apparatus used in this experiment is shown in
Fig. 3-4. 0 ~ 15 V voltage ( 0 ~ 6 W in power, 0 ~ 0.4 A in current) was supplied by an
HP 6010A DC supply to a 38 Q heating tape to heat the ﬁlms while cold nitrogen gas was
introduced to cool the sample. Two 12 V alkaline batteries and a 3 k9 resistor connected in
series with the tested sample ( ~l mm wide, ~10 mm long) were used to form a closed
circuit. The voltage drop across the sample, which was proportional to the resistance, and
output of the thermocouple, which gave temperature readings, were recorded on an HP
17171A chart recorder. The transformation temperatures were derived from resistivity-
temperature curves by the tangential-line method. In order to achieve good temperature
homogeneity and to obtain reliable temperature readings, both heating and cooling rates
were less than 1 K/min.

In some experiments, the resistivity of NiTi ﬁlms on Si was measured in-situ
during the stress measurement. In this case, two «300 nm thick gold squares (3 mm x 3
rmn) were sputter-deposited on NiTi side using a pure gold cathode to ensure a good
electric contact. The wafer was connected in series with a 3 k0 resistor and 20 V DC
supply through the two gold-layer squares. The voltage between the two gold layer
squares was send to an Omega OMNI AMP1M I instrumentation ampliﬁer (x10 ~ 1000)
followed by an AID conversion by an Omega PLC 812-PG card. As a result, the voltage

51

of the sample, which was proportional to the resistivity, was recorded in digital form
(0~4096). By a QuickBasic program, the resistivity and the curvature of NiTi/Si samples
were recorded simultaneously, making it possible to relate stress variation to phase

transformations.

3.2.5. Composition Analyses

The chemical composition was analde by a LINK AN - 10000 X-ray EDS
(Energy Dispersive Spectrum) system on a JEOL S - 2500 Scanning Electron Microscope
(SEM) operated at 20 kV. Gain calibration was made on Co-Ka radiation and bulk
calibration was made using LINK ZAF4 code. The test ﬁlms were usually ~ 5 um thick,
and were attached to Si wafers or glass substrates. Since no Si X-ray peaks were
observed, the substrate was taken to have no interaction with electrons, and thus the spectra
could be processed by a ZAF correction. The composition was recorded as the average of
at least 5 nearby points.

3. 2. 6. Structure and Microstructure Analyses

Phase identiﬁcation was conducted by X-ray diffraction using a SCINTAG-2000
diffractometer with accelerating voltage of 35 kV, tube current of 25 mA, Cu-K,ll radiation,
and 20 scanning mode. The scan step was 0.03 °/step, scan rate was 2 °/min and scan
range (20) is 20 ° ~ 80 °. Glass substrates were usually used in order to avoid extraneous
X-ray peaks. However, it was found that when ﬁlms were thicker than 3 um, no substrate
peaks were observed. Most X-ray diffraction experiments were performed at ambient
temperature. In some special cases, resistive heating was used to the elevate sample
temperature, which was monitored by a thermocouple.

In-plane microstructure and electron diffraction of TiN i ﬁlms were observed on a
Hitachi H - 800 Transmission Electron Microscope (TEM) operated at 200 kV using a
double-tilting specimen holder. Free-standing ﬁlms obtained by mechanical peeling from

52

the substrate were glued with acid-resistant lacquer on 3 mmer nickel grids with 2
mm hole. Electron transparency was achieved by twin-jet electropolishing method using a
fresh electrolyte containing 20% nitric acid and 80% methanol in volume percentage. The
electropolishing apparatus was operated at 8 v to give a current density of 12 mA/mmz, and
the electrolyte temperature was kept between 233 K and 243 K. Better samples were

obtained when the initial thickness of the sample was greater than 3 microns.

Chmr4

RESULTS AND DISCUSSION

In this chapter, experimental results will be presented in two sections. The ﬁrst
section concerns stress and stress evolution behavior in as-deposited ﬁlms on Si during
both isochronal and isothermal anneals, while the second deals with the stress evolution of
SMA NiTi ﬁlms on Si during displacive transformations.

4.1. Stresses and Stress Evolution Behavior of As-Deposited NiTi on Si
Stresses are often introduced from the fabrication process of thin ﬁlms. Stresses in
NiTi ﬁlms are of particular interest because they are potentially useful in developing two-
way shape memory effect by biasing martensite formation. In this section, results from
experiments which show the magnitude of stresses that can be introduced into NiTi on Si
by d.c. magnetron sputtering, and their evolution behavior during the isochronal and

isothermal annealing process, are presented and discussed.

4. W l, , . -” . . .” Ht“, 7,. _km .._H 7, h, H, .3.-R-

The variation of stress with temperature during isochronal heating at a heating rate
from 1.5 to 2.5 K/min for as-sputtered NiTi ISi was measured by the wafer-curvature
method using equation (3.1). Four representative stress-temperature curves distinguished
by the deposition temperatures of the samples are shown in Fig. 4.1. It can be seen that

(1), for all samples, upon isochronal heating from room temperature, stresses change at a

53

54

rate about -1.5 MPa/K until the temperature reaches the deposition temperature (T,),‘ where
the maximum compressive stress is obtained (for later reference, this stress decrease
occurring from RT to T, is labeled as R-I). (2), When the heating temperature exceeds T,,
the stresses start to relax at rate dependent on the maximum stress. The larger the
maximum stress is, the higher the relaxation rate. This stress relaxation occurring starting
from T, is labeled as R-II. (3), Except for the samples deposited at temperatures higher
than 673 K, a stress spike with a magnitude of 50 ~ 120 MPa occurs at approximately 723
K (this stress spike at Tc is labeled as R-ll). For samples with stress spikes, the stress
changes again at a rate of -1.5 MPa/K after the stress spike is established (this stress
decrease after Tc is labeled as R-IV); For samples deposited at temperatures higher than
673 K, no stress spike is observed, and the stress remains near zero beyond 873 K on
heating (this steady-state stress is labeled as R-V); (4), On cooling at a rate of 30 - 60
K/min, a tensile stress is developed at a rate of 1.5 MPa/K (this stress increase during
cooling is labeled as R-VI). In the following section, the origin of each of these stress

evolution features is discussed in detail.

4.1.1.1. Extrinsic Thermal Stresses
For a thin ﬁlm/substrate composite, when the temperature changes, the thermal stress is
introduced if their thermal expansion coefﬁcients are different. For N iTi on Si, the linear

thermal strain .6me, is determined by

Ethermal = (as ' arvm ) ' AT (4-1)

 

‘ High stress developed from cooling from annealing temperatures may result in delamination
of the NiTi ﬁlms, or fracture of the substrate, especially when the annealing temperature was
higher than 923 K. Sometimes the sample was broken into parts upon cooling. In most
cases, however, the ﬁlm was still perfectly kept on the substrate when sample was cooled
down to room temperature.

If the ﬁhns were still on the substrate and when the temperature got close to room
temperature, there is a stress relief, which is identiﬁed as the result of R-phase or martensitic
transformation and is presented in a separate section (4.2) because of its importance.

55

where as, and am, are thermal expansion coefﬁcients of Si and NiTi, respectively; AT is
the temperature change.

Assuming that the substrate remains undeforrned and the ﬁlm is deformed
elastically by a strain e,,,,,,,,,, which is the very close case to our experiment where the
thickness ratio between Si substrate and NiTi ﬁlms is typically more than 100 times, a
biaxial thermal stress 0'

therma

,can be obtained as:
ENiTi
athermal = m ' (as; - aNiTi ) ' AT (42)

where v is Poisson’s ratio of the ﬁlm, EMT, is the elastic constant of NiTi, as, and am, are
the thermal expansion coefﬁcients of the Si substrate and the NiTi ﬁlm, respectively, AT is
temperature change. Taking am, = 15.4 x 10" [Zhao, 1995], as, = 3x1045 [Goldsmith,
1961], Em: = 83 GPa [Cross et al., 1969; Metals Handbook, 1990] and V = 0.33 [Beuhler
and Wang, 1968], we come a stress slope with temperature during isochronal annealing at
~1.53 MPa/K, which is close to the characteristic stress slope in R-I, R-IV and R-VI.
Therefore, it may be concluded that, during the isochronal heating, at temperature lower
than T,, or right after the stress spike (T,), the extrinsic thermal stress development solely
accounts for the stress change, while the intrinsic stress is stable. On cooling at a relatively
high rate, the extrinsic thermal stress does not relax appreciably. Further conﬁrmation of

the stability of the stress state at temperatures below T, will be presented below.

4.1 .12. Stress Development from Crystallization

The stress spike (R-Il) occurring at nearly 723 K results from the crystallization of
the amorphous ﬁlms. Previous studies [Ikuta, Fujita, Ikeda and Yamashita, 1990; Hou
and Grummon, 1995] showed that crystallinity of sputtered near-equiatomic NiTi was
determined to large extent by deposition temperature: at deposition temperatures above 723

K, the as-sputtered NiTi ﬁlms usually had a fully crystalline structure, while at deposition

56

temperatures below 573 K, the as-sputtered NiTi ﬁlms had glassy structure, and at
deposition temperatures in between, the as-sputtered N iTi contained partial glassy
structure. Crystallization results in a more compact structure so tensile stress development
is expected. The reason that the 693 K—deposited ﬁlms did not show stress spike simply is
that no amorphous structure existed in the initial microstructure. Detailed discussion on
stress development from crystallization and crystallization temperature is presented in

section 4.1.4.

4.1.1 .3. Dynamic Stress Relaxation

The continuous stress decrease occurring at temperatures above T, (R-lI) is a stress
relaxation phenomenon. During this isochronal annealing period, the stress appears to
decrease linearly until it approaches a zero-stress state. The stress decreasing rate varies
with different deposition temperatures and the maximum stress at T,. For the ﬁlm
deposited at 423 K, the stress relaxation rate is 1.2 MPa/K, for the ﬁlm deposited at 543 K,
the stress relaxation rate is 3.7 MPa/K; for ﬁlm deposited at 623 K, stress relaxation is 2.2
MPa/K, for ﬁlm deposited at 723 K, the stress relaxation rate is 7 MPa/K.

The stress decreasing rate in R-II results from two opposite processes. One is the
continuous increase of compressive thermal stress, the other is stress relaxation. The
observation that stress decreases continuously during isochronal heating in RI] indicates
that the rate that thermal stress increases is unable to compete with the dynamic stress
relaxation rate, therefore, overall stress decreases. Isothermal annealing, which does not
result in thermal stress change and allows much more time to observe the stress relaxation,
has been used in this study to conduct relaxation kinetic analysis. In the next section,
detailed kinetic analyses of the stress relaxation, together with further evaluation of the

stress stability observed at the temperatures below T, are presented.

 

It was shown in last section that stress in as-sputtered NiTi ﬁlms on Si relaxes at an
appreciable rate only when the temperature exceeds the deposition temperature, T ,.
However, isochronal data obtained at heating rates from 1.5 K/min to 3.0 K/min used in
this study do not lead themselves to adequate kinetic analysis. Both the stress stability
below T, and the stress relaxation behavior above T, need to be evaluated under isothermal
conditions over more prolonged times. The variation of stress with time during isothermal
annealing for NiTi ﬁlms with initial microstructures which are fully crystalline, fully

amorphous, or partly amorphous and partly crystalline, are presented in the next sections.

4.1 .2.]. Stress Relaxation in Fully Crystalline NiTi on Si

Results Figs. 4-2(a) and (b) show the stress relaxation during isothermal
annealing for two NiTi ﬁlms deposited at 693 K on Si. Fig. 4—2(c) shows detailed stress
relaxation behavior during the ﬁrst 25 ks at each isothermal holding temperature with zero-
time corresponding to the beginning of each anneal. It can be seen from the curves that, at
temperatures lower than T,, stress remained stable even when holding time was as long as
40 ~ 60 ks, consistent with the behavior observed in isochronal annealing. In addition,
stress tended to relax at an appreciable rate only when the sample was annealed at
temperatures higher than T,, with stress relaxation rates depending on the annealing
temperature, initial stress and the time. The higher the initial stress or the higher the
annealing temperature, the larger the absolute stress drop during the ﬁrst few seconds of
the isothermal annealing. In the following kinetic analysis, it will be apparent that stress

relaxation above T, occurred by two distinct mechanisms.

Kinetics Analyses Stress relaxation is a process in which total strain, composed
of plastic and elastic components, is constant, while elastic strain is continuously converted

to plastic strain, causing the stress to decrease as the holding time is prolonged [Oding,

58

1965]. Maxwell [1868] proposed a dash pot - elastic spring model to describe it. The

basic assumption is that the stress relaxation rate is proportional to the stress, i. e.,

m = —k .o(t) (4.3)
d:

and if the stress relaxation parameter k, which must be positive, is not a function of the

stress 0', the stress at time t is:
l
o( t) = a, -exp(-kt) = a, ~exp(—;) (4.4)

where 0’, is the initial stress and t, the inverse of k, is called the relaxation time.
The above equations essentially describe a viscoelastic process [Oding, 1965]. For
crystalline materials, k is also a function of stress, 0', annealing temperature, T, and t.

Thus we start from:

da(t) =

-k(o, T, r) - O'(t) (4.5)
dt

If a ﬁrst-order-of-time process is assumed [Reed-Hill and Abbraschian, 1992], the

parameter k(o; T, t) is not a function of time, and can be obtained as

don) _ __ dln(0'(t))

k(O'T)=—o(t)-dt _ dt

(4.6)
For a diffusional stress relaxation process, k(a, T) can be expressed as a function of
diffusivity, D, as [Kato et al., 1990; Shute and Cohen, 1992]:

£08 A Q

k ,T= -D-B ,T =—-D ——-B ,T .
(0 ) 6,102,,sz (0 ) T oeXP( RT) (0 ) (47)

59

where E is the elastic modulus, .Q is the atomic volume, S is the cross-sectional area for the
diffusion process, k is Boltzmann’s constant and a,, a2 and A are grain size parameters.
This value for k( 0', T) is derived for diffusion within a volume represented by a
parallelepiped shaped grain with sides 2a, x2a2 XII. The cross-sectional area term factor S
is a function of the diffusion path, and A a Em/(aIazlzk), which is determined by
microstructural details and diffusion path. D, is the frequency parameter of diffusivity, Q
is the activation energy, R is the universal gas constant (= 8.314 J/mol), and B(O', T) is
related to the stress and temperature, and can be called a stress induced factor.

Evaluation of B(o; T) is based on the observation that an applied stress can reduce
the activation energy by an amount equal to AV- 0' [Fargeix and Ghibaudo, 1984; Brotzen
et al., 1990; Zingu and Mofokeng, 1993], where AV is called the activation volume, and 0'
is taken as the absolute value, which means both tensile stress and compressive stress

reduce the activation energy. Thus, k(o, T) can be rewritten by

 

 

dln(O'(t)) A Q AV-O’
k ,r =-—————=—-D -—- .
( ) d, T oexp( RT) exp( RT ) (4 8)
or, lnk(O',T)=lnA-lnT+lnDo—£+AV.G (49)
RT RT

For an isothermal process at temperature T, ln( k( 0', T) ) should be linearly dependent on
stress 0'. Assuming ln(k(o; T)) = m(T)- 0' + b( T), The slope of the line m( T) is AV/RT,
while the intercept of the line b( T) is the sum of the ﬁrst four terms in (4.9). Also, if
several stress relaxation curves at different temperatures are available, the diffusion volume
can be calculated by ﬁnding the slope of curve m( T) vs. Iﬂ' for which the slope should be
AV/R, and the activation energy is obtained by ﬁnding the slope of curve b( T)+ln( T) vs.
1/1’ for which the slope should be -Q/R.

60

Kinetic Parameter Calculation Figure 4-3 show curves of ln(k(o; t)) vs. stress 0'
(at absolute value), at different annealing temperatures for the data plotted in Fig. 4—2 (a -
c). These ﬁgures indicate that generally there are two distinct stages of stress relaxation
when the isothermal annealing temperature was below 843 K. The ﬁrst stage (at high
stress and short time) is characterized by a steep slope in curve ln(k(0', T))~O’, while the
second one is characterized by a shallow slope, which means in the ﬁrst stage, stress
relaxation rate is more dependent on the applied stress.

It is possible to calculate both activation volumes and activation energies for stress
relaxation for both relaxation stages from ln(k(o; T) )~O' plots at different temperatures (Fig.
4-3) using the method described above (slope ﬁtting method). In addition, for a given
ln(k(O'. T))~0' plot (at a given temperature), the slope m( T) corresponds to AV/RT,
therefore, AV can be calculated by m( T)-RT, and averaging all the AVs at different
temperature gives a value of AV (this method is called averaging method hereafter).
Results are shown in Fig. 4—4 (a) and (b). For the ﬁrst stress relaxation stage, the
activation energy is 718:1:12 kJ/mol, and the activation volume arrives at (8.27:1:0.33)x10’28
and (1.12:l:0.29)x10°28 m3, depending on whether the slope ﬁtting or the averaging
methods are used. For the second stress relaxation process, the activation energy is
309112 kJ/mol, and the activation volume is ( 1.34:1:0.93)><10'29 m3 by the averaging
method. The activation volume is apparently unavailable from slop ﬁtting method because
m( T) appears rather scattered.

It is noted that there is considerable error in determining the activation volume for
the first stress relaxation stage, and because the intercepts depend on the slopes, the
corresponding activation energy is also considered unreliable. The activation volume for
the second stress relaxation is also suspect. However, it is apparently one order of
magnitude smaller than that for the ﬁrst relaxation stage. In addition, the magnitude of
stress is smaller for the second stage of stress relaxation than that for the ﬁrst one. Since

the deviation of intercept b( T) is m( T)-0' if the stress effect on the activation energy is not

61

considered, the activation energy obtained by linearly ﬁtting b( T)+ln( T) vs. 1/1' for stress
relaxation during the second stage is much more reliable. Actually, the intercept data is
ﬁtted well except for the one obtained from annealing at 723 K, the ﬁrst stop above T,.

The uncertainty in calculating the diffusion volume and activation energy of the ﬁrst
relaxation stage by equation (4.9) suggests that the relaxation behavior may not be
adequately described by equations (4.6) and (4.7), and that other mechanisms, such as
microstructural instabilities, may operate when the annealing temperature exceeds the
deposition temperature.’ For near-equiatomic NiTi, grain growth, precipitate growth and
precipitation reactions are pronounced upon annealing at temperatures between 673 K to
873 K [Kim et al., 1986; Xie et al., 1990]. The volume change and stress localization
brought by these processes inﬂuence the evolution of overall stress in ways which are not
properly described by equations (4.6) and (4.7). This is because the stress may never fall
to zero as time goes to inﬁnity, and because the growth kinetics of second phase formation
or grain growth do not necessarily conform to equation (4.1). It may be thus difﬁcult to
model,‘5 and no successful quantitative analyses have been made at this point.

The second stress relaxation stage at each temperature stop is a diffusion-related
relaxation phenomenon. The activation energy for diffusion determines the stress
relaxation rate, while stress in turn reduces the activation by an amount equal to AV- 0'
[Fargeix and Ghibaudo, 1984; Brotzen et al., 1990; Zingu and Mofokeng, 1993]. Thus,
failure to consider the stress induced term may result in several percent error in the
calculation of activation energy [Shute and Cohen, 1992]. Sullivan [1989] arrived at a
value of AV = .0/3 for one-dimension diffusion, where .Q is the atomic volume of the

 

5 We might be able to show the structure/microstructure instability of sputtered NiTi at
temperature higher than the deposition one by comparing the transformation temperatures of
hot-deposition as-sputtered ﬁlms and those of ﬁlms which experienced annealing at a higher
temperature than T,, since transformation temperatures are sensitive to the microstructure.
Data shows that the M, temperature of as-sputtered crystalline NiTi ﬁlms is 30 ~ 40 K lower
than that of the post-deposition annealed samples.

6 Later result that stress gradients exist in as-sputtered ﬁlms which also complicates the modeling.

62

diffusant. For biaxial stress, a factor of 2 must be to be introduced [Shute and Cohen,
1992]. Even though the data are rather scattered in the activation volume calculation, it
appears that the activation volume in the second stress relaxation stage is in the same order
of magnitude with the atomic volume of Ti (AV = 2.23x10‘29 m3) or Ni (AV = 1.21x10‘29
m3), while that in the ﬁrst stress relaxation is one order of magnitude larger.

The activation energy for the second stage of the stress relaxation suggests bulk
diffusion rather than the grain-boundary diffusion controls the stress relaxation, since the
activation energy for the latter case is typically less than 1 ev. However, the comparison
between the activation energy obtained here with those obtained by other authors casts
some uncertainty. The chemical activation energy for diffusion in N i/N i, NiTi/Ni and
TiNi/Ti diffusion couples has been measured by Bastin and Rieck [1974]. They obtained a
value of 142 kJ/mol (0.89 ev), which is substantially smaller than the data we have
obtained here. The difference is probably because the diffusion in diffusion couples was
grain boundary diffusion. Furthermore, stress relaxation processes are controlled by the
slowest diffusion species, while the chemical activation energy for intermetallic reactions is
controlled by the faster diffusing species. In this context, it is interesting to note that the
activation energy of 255 kJ/mol for Ti diffusion in Ni base superalloy [Reed-Hill and
Abbraschian, 1992] is comparable to the data we have obtained here.

It is not clear whether grain boundary diffusion related stress relaxation occurs
during the annealing, but very likely it occurs because grain boundary diffusion dominates
over lattice diffusion where the grain sizes are small. It was proposed that grain-boundary
diffusion stops when the normal stresses on the grain boundary have been completely
relaxed due to the constraint of the substrate and the columnar microstructure of the ﬁlms
[Jackson and Li, 1982], therefore, stress relaxation by grain boundary diffusion only
occurs at an initial stage of relaxation [Oding, 1965], and grain-boundary diffusion alone is

unable to completely relax all the stress in thin ﬁlms. In this experiment, however, because

63

there is no way to separate the stress relaxation rate by grain boundary diffusion from other
mechanisms, the corresponding kinetics parameters were difﬁcult to specify.

The calculation of the activation energy using equation (4.9) is based on the
assumption that the parameterA is a constant. Since A is related to the grain size, it must
be assumed that the grains do not change during annealing. However, the data from the
ﬁrst annealing at 723 K deviates far from the ﬁtted line, i.e., k is higher than it should be
for the ﬁrst anneal, as shown in Fig. 4-4. This anomaly suggests a microstructural
instability. Since k is higher when grain size is smaller [Kato et al., 1990], this suggests
that larger grains have resulted after the ﬁrst annealing. Also, the good reliability of the
linear ﬁtting for data above 773 K suggests that the grain size stabilizes after the ﬁrst
annealing excursion.

In summary, it is observed that as-sputtered NiTi ﬁlms with fully crystalline
structures undergo stress relaxation during isothermal annealing above the deposition
temperature due to the structure/microstructure instabilities, and by bulk diffusion with an
activation energy of 310 kJ/mol. In view of the apparent initial instability of the
microstructure, it is interesting to consider stress relaxation of as-deposited ﬁlms that are
initially not fully crystalline. In the following section, presented is the results and
discussion of NiTi ﬁlm deposited at 623 K, which has an initially mixed crystalline and

amorphous structure.

4.1.2.2. Stress Relaxation in NiTi on Si with Initially Mixed Structure.

Figure 4-5(a) shows the stress change of a 623 K-deposited ﬁlm, which is initially
partially amorphous and partially crystalline, during isothermal anneals at different
temperatures, with time starting at the beginning of the ﬁrst isothermal annealing at 593 K.
Also, the stress was stable at 593 K for an annealing as long as 30 ks, conﬁrming the
stress stability at temperatures below T,. Stress relaxation occurs during annealing at 633

K, and an stress increase of ~150 MPa, which results in the ﬁlms in 50 MPa tensile stress,

64

occurs at 673 K due to stress relaxation and crystallization. The ﬁlm becomes fully
crystalline after the annealing at 673 K. Further increases in the temperature brings more
compressive stress, which tends to relax at isothermal annealing. The isothermal annealing
at temperatures at 773 K or above,7 and the stress relaxation curves during the ﬁrst 15 ks at
each temperature is shown in Fig 4-5(b).

In order to obtain stress relaxation kinetics, the stress relaxation rate ln(k(o; T)) is
plotted as a function of stress, following the same procedure used in analyzing stress
relaxation behavior in 693 K-deposited ﬁlms. Fig. 4-6 are the plots of ln(k(o; D) vs. a
which also show two-stage stress relaxation process during annealing at temperatures
above the crystallization temperature. For the ﬁrst relaxation stage, the activation energy is
794i66 kJ/mol, and the activation volume is at 11.401135 x10‘28 and 6031528 x10'28
m3 by slope ﬁtting and averaging methods, respectively. For the second relaxation stage,
the activation energy is 304:1:14 kJ/mol, and the activation volume is found to be
7.62:|:4.26x10‘29 m3 by the averaging method, but it is apparently not available by the linear
ﬁtting method because the data appears rather scattering. Similarly, because of the errors,
it seems that activation energy for both the ﬁrst relaxation stage, and the activation volumes
for the ﬁrst and second relaxation stage are suspect, while the activation energy for the
second relaxation is reliable. Structural instabilities may be responsible for the ﬁrst
relaxation process, and bulk diffusion may be responsible for the second relaxation
processes. The activation energy for the second relaxation of fully crystalline NiTi on Si is
seen to be very close to that of fully crystallized NiTi on Si with initially partially crystalline
structure.

Comparing Fig. 4-4(b) and Fig. 4-7(b), it may be noted that, despite the activation

energy is very close, more annealing excursions and high annealing temperature were

 

7 Stress at temperatures between 673 K to 773 K is so low that considerable error may be introduced in
analysis the stress relaxation behavior. Therefore, no isothermal annealing was applied at this
temperature range.

65

needed before the data aligns well along the ﬁtted line, and the ﬁtted line for 723 K—
deposited has been shifted to higher temperature, i.e., at a given temperature, k value is
larger for the sample deposited at 693 K. Considering the k value increases as grain size
decreases [Kato et al., 1990], these features may suggest that the 693 K-deposited ﬁlm has
a small average grain size, or the 623 K—deposited ﬁlm has experienced more grain growth.

It is noted that the stress relaxation behavior of NiTi ﬁlm with fully crystalline and
that of crystallized ﬁlm with initially mixed structure is quite similar. This is expected
because in both cases the stress relaxation occurs within the crystalline structure. Stress
relaxation in amorphous NiTi may be different. This is of interest since amorphous NiTi is
prone to form at lower deposition temperature. In the next section, a kinetic analysis of

stress relaxation in amorphous NiTi on Si is presented and discussed.

4.1.2.3. Stress Relaxation in Fully Amorphous NiTi on Si

Fig. 4-8(a) shows the stress change with time starting at the beginning of the ﬁrst
isothermal annealing (453 K) of an as-sputtered ﬁlms deposited at ~473 K, which has a
fully amorphous structure. Fig. 4-8(b) shows each stress relaxation curve with time
starting at the beginning of each isothermal holding. Once again, stress remained stable
during the annealing at 453 K with annealing time as long as 90 ks, conﬁrming that the
stress is stable at temperature below T,. At each anneals, the stress relaxation rate changes
with the annealing time. At higher annealing temperature the stress relaxes to zero more
quickly.

In analyzing the stress relaxation kinetics, following the same procedure used in
analyzing stress relaxation behavior in crystalline or partially crystalline NiTi on Si, the
stress relaxation rate is plotted as a function of stress. Fig. 4-9 are the plots of ln(k(o; T) )
vs. 0', which show one-stage stress relaxation process during annealing at temperature
above T,. Unlike those of the crystalline ﬁlms and partially crystalline ﬁlms, plots ln(k(o,

T) ) vs. 0' show a one-stage stress relaxation process. The activation energy for stress

66

relaxation is 246i10 kJ/mol, and the diffusion volume arrives at 352132 x10‘28 m3 and
7.59:l:3.91 x10‘29 m3 by slope ﬁtting and averaging methods respectively, as shown in Fig.
4-10.

The activation energy for stress relaxation in amorphous NiTi is obvious lower than
that for the second-stage stress relaxation in fully crystalline NiTi. If the stress relaxation
in amorphous is also related to diffusion process, this result is reasonable. Amorphous
structure is comparably less compact that the crystalline structure, and diffusion process in
amorphous materials should be thus easier. Although there is no activation data available
for amorphous N iTi, Cotts and his coworkers [1986] obtained the activation energy for
interdiffusion in Ni,.,,Zr32 amorphous phase to be 1.0 ~ 1.1 ev, which is comparable to the
activation energy data from our stress relaxation experiment (1.5 ev). Once again, the
difference may arise from that the stress relaxation process is primarily determined by the
most sluggish diffusant.

4.1.2.4. Stress Relaxation Behavior of NiTi on Si During Isochronal Annealing

The stress relaxation behavior in R—II during isochronal heating of NiTi ﬁlms on Si
is understandable from the stress relaxation behaviors during isothermal annealing. During
the isochronal heating beyond T,, while extrinsic thermal stress development built more
compressive stress, stress relaxation caused continual decrease in compressive stress. In
addition, stress relaxation rate was controlled by two processes: on one hand, when the
stress (in absolute value) went down, the stress relaxation rate (absolute stress drop in unit
time) was decreased since it was proportional to the stress. On the other hand, the stress
relaxation rate increases with increased annealing temperature. It is observed that at
temperatures above T,, the overall stress kept decreasing, indicating that the stress
relaxation process dominated. Furthermore, since the stress relaxation rate was stable
within a fairly long of temperature interval for both amorphous and crystalline ﬁlms, it is

suggested that the stress relaxation rate changes resulting from the decreased stress and

67

increased temperature were almost canceled out during this period. Ultimately, however,
when the temperature went high enough, the stress relaxation rate became so fast that the
thermal stress was relaxed very quickly, therefore the stress remained low, as was
observed when the temperature approached the crystallization temperature for amorphous
ﬁlms and beyond 893 K for crystalline ﬁlms.

4 rr' , o .n 0_ urn-u _' or '0 cu? AM a 1;. as 1.- Jun,

In section 4.1.2 it was shown that the diffusion process as well as
structure/microstructure instability may result in the stress evolution in as-sputtered ﬁlms of
fully crystalline, partially crystalline and fully amorphous structure. As will be shown
below, for an as-sputtered ﬁlms with fully amorphous structure, crystallization may also
produce a non-equilibrium microstructure. Microstructural evolution during the extended
annealing after crystallization of amorphous NiTi ﬁlm may result in stress relaxation stress

in ways which depend on the composition of the ﬁlm.

Results Figures 4-11 (a) and (b) show two representative stress-time curves of
NiTi ﬁlms deposited at ambient temperature on Si, during isothermal annealing at the
crystallization temperature. Both of the curves demonstrate a quick stress drop from
compressive stress levels to zero stress due to relaxation in amorphous N iTi, and a quick
stress climb of about 170 MPa due to densiﬁcation during crystallization of the amorphous
structure. What distinguishes them from each other is the stability of the 170 MPa tensile
stress during extended annealing after crystallization. The ﬁrst ﬁgure (Fig 4-11 (a)) shows
a slower stress drop (30 MPa in 4.5 ks) while the second one (Fig. 4-11 (b)) shows a
steady-state stress followed by a quicker stress relaxation (70 MPa in 0.5 ks).

TEM observation has been made for each of the aged samples exhibiting different

stress variation behavior. As shown in Figs. 4-12 (a) and (b), the sample that has

68

experienced fast stress relaxation contains numerous N i,Ti3 precipitates while the sample

that has experienced no fast stress relaxation is precipitate-free.

Discussion The fact that the sample undergoing a fast stress relaxation contains
lots of precipitates while the one undergoing no fast stress relaxation is precipitate-free
during the prolonged annealing after crystallization leads to a conclusion that the
precipitation is associated with the fast stress relaxation process. 8 It is plausible that the
steady stress period corresponds to the incubation and the early growth of precipitates,
based on the observation of stress relaxation in (Ti, Nb) high strength low alloy steel [Park
et al., 1992; Djahazi et al., 1992]. In an annealing process of a stressed (Ti, Nb) high
strength low alloy steel, the stress relaxation rate was reduced when the coherent
precipitates start to appear and when they are small. But when the precipitates grew so
large that the interfacial coherency between them and the matrix was lost, they have little
effect on stress relaxation rate. The authors accounted the dislocation movement and/or
diffusion is severely suppressed by the presence of the coherent precipitates. The situation
of precipitation in Ni-rich NiTi ﬁlms is similar. Metastable lenticular precipitates Ni4Ti3 are
subject to form at an intermediate-temperature annealing. They are coherent with the B2
matrix when they are small, and as they grow, coherent interfaces become semi-coherent,
even incoherent [Xie et al., 1990].

Applied stress can induce preferential growth of the precipitate. For example,
preferential site for precipitation may exist under applied stresses. In studying stress
effects on second phase in Cu-Cd alloys, Sulonen [1964] found that the second phases

grew preferentially at grain boundaries that were perpendicular to the applied stress axis,

 

‘ TEM micrographs in Fig. 4.12 suggest that the ﬁlms showing no fast sness relaxation is very likely
close to stoichiometry while the other is one Ni-rich. The composition deviation from ﬁhn to ﬁlm
arose from target conﬁguration when the ﬁlms were deposited [Lee, 1994]. Even when all the ﬁlms
are deposited by the targets of same composition, the target wear affects the composition of the ﬁlm:
a newly replaced target tends to produce Ni-rich ﬁhns, while an over-worn one tends to produce Ti-
rich ﬁlms.

69

and asymmetric strain was attributed to this phenomenon [Sulonen, 1964; Dryden et al.,
1990; Guo et al., 1993]. More relevantly, stress can induce preferential growth of selective
precipitate variants, as Ni4Ti3 precipitates in Ni-rich NiTi. The preferential growth of
Ni4Ti3 was proposed by Nishida et al. [1986] and confnmed by Li and Chen [1997] under
uniaxial stress condition.” Since uniaxial stress makes the precipitate variant selective,
there is no reason that biaxial stress used in this experiment does not. However, no
evidences to support this prediction have been found from the in-plane TEM observations
at this point.

Preferential growth of selective precipitate variants may result in a quicker stress
relaxation process. In the constrained annealing experiment conducted by Nishida et al.
[1986], the ﬁxed curvature was formed when the constrained annealing was completed
because the elastic strain had been converted to plastic strain, which was a stress relaxation
process. The driving force to do so was the reduction of elastic strain energy. By forming
topotaxial precipitates, elastic strain energy was reduced in the most efﬁcient way, and
therefore, stress relaxation process is quicker. Another In comparison to the precipitate-
free sample, the relaxation rate in the precipitate-free sample is determined by the diffusion
of sluggish species Ti, while the precipitation of Ni,Ti3 is determined by the diffusion of Ni

atoms. In this sense, it can also be expected that stress relaxation in Ni,Ti3-containing

sample is quicker.

 

It has been repeatedly demonstrated that, without additional substrate heating,
sputter-deposited NiTi is amorphous, and in order to acquire SME, crystallization is
necessary [Kim et al., 1986; Busch et al., 1990]. However, how high the crystallization

temperature has to be is of concerns, especially in circumstances where interdiffusion

 

9 The preferential growth of N i4Ti3 was believed to create intrinsic two-way shape-memory effect by
biasing the martensitic formation [Fig 4-14].

70

between the substrate and the ﬁlms or decomposition of the substrate may occur. For
example, Kapton polyimide, a potentially useful substrate, may decompose when exposed
to temperatures higher than 723 K even in an inert atmosphere. So there have been efforts
aimed at lowering the crystallization temperature of NiTi [Madsen and Jardine, 1993].

As shown in last sections, the completion of crystallization of fully amorphous

results in a biaxial stress of ~ 170 MPa increase, which corresponds to a strain of

e =Aa.1"" =170x106- 1'0'33

crystallization E 9 = 0 0013 7
Min 83 X 10

 

 

and a volume change of AV/V = 30.00137 = 0.0041. Taking advantage of the stress
development, the crystallization process can be monitored by measurement of the stress
variation during the isothermal annealing of the NiTi/Si composite, which in turn can yield
estimates for the kinetic parameters controlling the crystallization event.

Results Figure 4-14(a) shows stress variation with time of NiTi ﬁlms deposited at
ambient temperature on Si during isothermal annealing at 673 K to 723 K. It is apparent
that crystallization occurs at annealing temperatures as low as 673 K. In addition, as the
isothermal annealing temperature increases, the annealing time to reach the maximum
tensile stress sharply increases, which means the crystallization takes longer. Also evident
is that the incubation time is generally needed for the occurrence of the crystallization. For
example, when annealing at 708 K, about 0.8 ks of incubation time is needed, However, if
the annealing temperature decreases to 673 K, about 25 ks of incubation time is needed.

Discussion Previous reports on crystallization temperature of amorphous N iTi
have been inconsistent. It is usually believed that amorphous N iTi will not crystallize until
the annealing temperature is higher than 773 K [Johnson et al., 1990]. But other reports
indicate the crystallization temperature is lower than 773 K [Nakata et al., 1995; Zhang and
Grummon, 1996]. The inconsistency probably arises from the fact that most of the

crystallization temperatures have been determined by isochronal heating with heating rates

Cl0:

71

as high as 20 K/min. Since incubation time is needed for crystallization, the higher the
heating rate is, the higher the apparent temperature of crystallization. Isothermal annealing
has provided more precise information about how low the crystallization temperature can
be.

Considering that the incubation time for crystallization is necessary, it is possible to
decrease the crystallization temperature or shorten the crystallization time of NiTi ﬁlm by
deliberately producing crystalline embryos, which can be realized by setting the deposition
temperature just slightly above 573 K. Crystallization time of a ﬁlm deposited at 623 K
supports this prediction. As shown in Fig. 4.5 (a), the ﬁhn deposited at 623 K which is
expected to be partially crystalline, is fully crystallized in about 3 ks at 673 K, which is
much shorter than 103 ks, the time required for full crystallization of the ﬁlm deposited at
ambient temperature and annealed at 673 K.

Since the crystallization is a thermally activated process, it has a corresponding
activation energy. Chang [1992] observed that crystallization which took place during
isochronal heating of triode sputtered NiTi and N iTi-Cu multilayer ﬁlms. Using
Kissinger’s method [Kissinger, 1957], Chang obtained the activation of 485 kJ/mol for
crystallization of single-layer NiTi ﬁlms deposited by triode sputtering using a TimNiwg
target.

For isothermal annealing in this experiment, the activation energy for crystallization
can be calculated by measuring the crystallization time r from the stress—time curves. In
this calculation, we ignore the incubation time for crystallization, assume that the crystalline
phase fraction is proportional to the stress, and the crystalline phase fraction 17:1 -exp(-t/t).
Therefore, the crystallization time tconesponds to the time when the stress reaches 1-1/e,
i.e., 63.2% of the maximum level. Since 1' = Aexp(Q/RT), the activation energy Q may be
obtained by linear-ﬁtting ln(t) vs. 1ﬂ’ with the slope corresponding to Q/R. Fig. 4-14(b)
shows the linear-ﬁtting result and gives an activation energy of ~477 kJ/mol, which is very

close to Chang’s result.

72

In our experiments, crystallization never occurred in NiTi ﬁlms deposited at
ambient temperature if the annealing temperature was lower than 673 K, which is thus the
low-temperature limit for the crystallization for amorphous NiTi on (100)Si by post-
deposition annealing. By hot deposition, at least partially crystalline structure in as-
deposited ﬁlms may be obtained at deposition temperatures as low as 373 K. For T, = 673
K, as-sputtered ﬁlms are fully crystalline within a deposition time of just tens of minutes.
This difference may result from the different diffusion mechanism. As we know,
crystallization produces an ordered B2 structure, which requires short-range diffusion.
Surface diffusion plays a major role in the in-situ crystallization process during the
deposition, and also, energetic collision events with reﬂected working gas atoms, incoming
neutrals and secondary electrons provide diffusants with additional kinetic energy. Since
surface diffusion is a faster mechanism than the bulk diffusion, a lower temperature to
produce fully crystalline ﬁlms is expected where in-situ crystallization is involved. Since
hot-deposition can produce fully crystalline NiTi at relatively low temperature, it offers an
alternative method to produce crystalline NiTi at the situation where high temperature

annealing is not practical due to substrate instability.

I.IEI"S 12 ..E

It has been indicated that both intrinsic and extrinsic stresses were stable at
temperature below T,. Intrinsic stresses result from sputtering at T,. Therefore, their
magnitudes can be inferred from the stress-temperature curve of NiTi/Si composites during
isochronal heating: the peak stress as the annealing temperature approaches the deposition

temperature equals the intrinsic stress.

Results Figs. 4-15 through 4-18 show the intrinsic stress variation with the
deposition parameters. It can be seen that, (1) Under the deposition conditions used in this

experiment (Ar pressure: 3.6 ~ 5.8 mTorr; T,: ambient to 723 K), the intrinsic stresses in

73

NiTi are compressive without exception”; (2) higher deposition temperature generates
higher compressive stresses. For ﬁlms deposited at constant Ar pressure, compressive
intrinsic stresses was increased from 240 MPa to 700 MPa when the deposition
temperature was increased from 373 K to 723 K; (3) lower working gas pressure leads to
higher compressive stresses. For ﬁlms deposited at ambient temperature (T, = 400 K),
compressive intrinsic stress was increased from 380 MPa to 570 MPa when Ar pressure
was decreased from 5.2 mTorr to 3.6 mTorr; (4) Thinner ﬁlms supported more
compressive stresses. For ﬁlms deposited at ambient temperature with a constant Ar
pressure of ~5.0 mTorr, compressive intrinsic stress was decreased from 460 MPa to 250

MPa when ﬁlm thickness was increased from 1.3 um to 4.4 pm.

Discussion Intrinsic stresses in thin ﬁlm depends on many processes. In-situ
condensation and growth make the ﬁlm more compact, so they usually make the ﬁlms more
tensile or less compressive; incorporation of working gas makes ﬁlms more compressive or
less tensile; In-situ stress relaxation makes the ﬁlms less stressed. But the predominant
process by far in sputtered ﬁlms is the peening effects of the energetic reﬂected working
gas ions, neutrals and electrons on the atoms on the surface and at sub-surface of the ﬁlms
[Hoffman and Thornton, 1977 (a) and (b); 1980; 1982; Thornton and Hoffman, 1985],
which produces compressive stress. The more kinetic energy the incoming species have,
or the greater the magnitude of the ﬂux, the more compressive stress will be produced.
Kinetic energy may be lost if the incoming species collide with working gas atoms. Lower
working gas pressure preserves the kinetic energy of the bombarding species since fewer
collision events will happen in transit from the cathode. Consequently, low working gas

pressure makes the ﬁlm more compressive.

 

'0 This could be qualitatively veriﬁed by observing the reﬂection of the sputter cathode through
a window on the sputtering system. The gun image appeared smaller than it actually is,
which means the sample surface is concave, consistent with the thin ﬁlm being under
substantial compressive stress.

74

The probability that one incoming species collides with the working gas molecules
is proportional to the density of the working gas density if the working distance is held
constant.” Thus, the key parameter is the volume density, W, of the working gas.
According to the ideal gas equation

P
=— 4.11
RT ( )

<l=

Thus, increasing the temperature while keeping the pressure unchanged decreases the
volume density of the working gas, resulting in more compressive stress. In order to show
experimentally how the intrinsic stress was related to the working gas density, we combine
Fig. 4-15 and Fig. 4-16 into Fig. 4-17 by expressing the stress as a function of RH” for
both constant temperature and constant pressure experiments. Plotted this way, constant
temperature and constant pressure data collapse onto a single master curve. If treated
linearly, the data gives a slope of ~52.6 GPa-mTorr"-K. In Fig. 4-17, the intrinsic stress
is also expressed as a function of the ratio of working distance to free-path length. If
treated linearly, the data gives a slope of ~950 MPa per mean free-path length.

Under the same deposition conditions with Ar pressure of 5.1 mTorr and T, of 400
K, intrinsic stress in the sputtered NiTi ﬁlm was also found to vary with ﬁlm thickness, as
shown in Fig. 4-18. If treated linearly, the data gives a slope of ~66 MPa-um". Many
factors may contribute this effect. First, it is reasonable to consider that the strength of thin
ﬁlm is related to ﬁlm thickness. Thinner ﬁlms usually have higher strength [Murakami,

M., 1979], and lower ﬂow stress in thicker ﬁlms places a limit on intrinsic stress.

 

” The mean free path, 11, for foreign atoms passing through a space populated with Ar can be calculated
as
R ' T
)1 = 2 (4.10)
N, ~P-rt(r,, +r,)
where T is the temperature in Kelvin, R is universal gas constant (=8.314 J -mol"-K"), N, is

Avgadro’ constant (6.022x1023 moi“), P is Ar pressure in Pascal, and r,, and r, are atomic radius of
Ar and exotic atoms, respectively. I. is proportional to the ratio of T/P.

 

75

Second, in-situ stress relaxation may help preserve more compressive stress. As
shown in Fig 4-2(b), a post-deposition annealing at the deposition temperature cause a
slight stress relaxation, which is a thenmlly activated process. However, the depositing
species have a kinetic energy of up to several electron volts, and the energy exchange
between the adatoms and interior atoms could be signiﬁcant to enhance diffusion related
stress relaxation. It is thus expected that in-situ stress relaxation results in a faster
relaxation rate than the stress relaxation during post-deposition annealing at the deposition
temperature. Thicker ﬁlms have longer time for in-situ stress relaxation or densiﬁcation, so
there should be less compressive stresses in the ﬁlms.

Third, interfacial stress may be neutralized as the ﬁlm grows. Considering that
there exists a certain amount of interfacial strain, which corresponds to certain constraint
force. As the thickness of ﬁlms is increased, the average stress is decreased. In this
consideration, it is suggested that a stress gradient may exist along the thickness of ﬁlms.

Finally, substrate rigidity may affect the intrinsic stress. Assuming that the intrinsic
strain produced by energetic ion bombardment is limited for ion ﬂuxes with a given energy
level and density, and the strain is also limited within a layer with a certain thickness,
therefore, the more rigid the strained layer is, the more the intrinsic stress is produced. For
thinner ﬁlms, the elastic modulus of Si (~126 GPa) mainly contributes to the effective
modulus of the strained layer, and as the ﬁlm grows, the modulus of NiTi ﬁlm (~83 GPa)
contributes more and more to the effective modulus of the strained layer, and cause it
decreasing monotonously. As a result, the intrinsic stress decreases as the ﬁlm thickness
increases. The observation [Chang, 1997] that the intrinsic stress is very small in NiTi
deposited on Kapton polyinride, which has an elastic modulus as low as 1.4 GPa, supports
the substrate modulus effect described above. However, clariﬁcation needs to be made
using more rigid substrates, such as sapphire (E = 434 GPa), before a positive conclusion

may be drawn.

76

4. . 0', 1111.1'-1'se L11, 1‘ __V1_ -111: -.1 111

It has been shown above that (1), large compressive stress, the amount of which
was controllable through changing deposition parameters, can be developed from sputtered
NiTi ﬁlms; (2) this stress was stable during isochronal ramping and isothermal holding at
temperatures lower than T,. These results are potentially useful when we want the intrinsic
stress to bias martensitic formation, by which cyclic two-way SME can be realized. Since
the intrinsic stress is stable until the temperature reaches T,, it can work under a wide range
of temperature. To preserve this stress when temperature changes, however, the thermal
expansion coefﬁcients of substrate and the ﬁlms have to be very close, otherwise, the
intrinsic stress may be neutralized by the extrinsic thermal stresses developed from cooling
from deposition temperature, as was observed in the present study.

Another implication from the present experiment is extrinsic thermal stress can be
used to bias the martensitic transformation to realize two-way SME for N iTi/substrate
composites. It has been shown that when the sample is annealed at temperatures higher
than T,, intrinsic stresses may be readily annealed out. In this case, the stress in ﬁlms
arises from the extrinsic stress developed by cooling from the annealing temperature. To
get large stress, the thermal expansion coefﬁcients of substrate and the ﬁlms has to be
large. Below will be described experiments which illustrate how high extrinsic tensile
stresses can interact with displacive transformations to produce cyclic stress relief and

recovery.

4.2. Displacive Transformation Induced Stress Evolution in SMA N iTi Films
on Si
Due to the structure difference between martensite and austenite of an NiTi SMA,
the martensitic transformation is accompanied by a volume shrinkage of 0.34%, shear
strain of 13.07% [Knowles and Smith, 1981], and an elastic constant drop by typically
~50% [Metals Handbook, 1990], any one of which should result in a stress change in a

77

NiTi ﬁlm which is attached to a substrate. However, the most important feature for stress
evolution in SMA NiTi/Si is the formation of detwinned R phase or detwinned martensite,
by which the stress relaxes in a unique way. This section deals with the relaxation of
extrinsic thermal stresses in both Ni-rich NiTi/Si and Ti-rich NiTi/Si composites by the R—

phase and martensitic transformations, and stress recovery by reverse transformation.

4.. ,. . _-'- .1 1111-1'11'11 -.1_11- , 1-711'.u.,i-'1' . '1111.

Figure 4-19 show the stress-temperature curve of a 1.3 pm thick Ni-rich NiTi ﬁlm
on Si substrate during a thermal cycle from 253 K to 363 K. The sample used in this
experiment was deposited at ambient temperature on Si and had been annealed at 723 K for
2 hours. The stress-temperature curve was obtained right after the annealing. So it is
essentially the ﬁrst thermal cycle after the annealing.

by annealing at 723 K, part of the intrinsic stress is relaxed, and cooling from the
annealing temperature, extrinsic tensile stress is introduced at a rate of ~1.5 MPa/K, as
discussed in section 4.1.1.1. As the cooling continues, the tensile stress continues
increasing until temperature reaches 348 K, at which a maximum stress of ~700 MPa is
achieved. Further cooling from 348 K, the stress sharply decreases at a rate of ~10.5
MPa/K during the ﬁrst ten Kelvin and followed by a rate of ~5.8 MPa/K until the
temperature reaches 253 K,12 where the stress has fallen to ~80 MPa. When the sample is
subsequently reheated from 253 K, the stress ﬁrst decreases at a very shallow slope (~0.85
MPa/K) until 318 K, then climbs sharply to 700 MPa at a rate of ~36 MPa/K. After the
stress is fully recovered at 343 K, further heating results in tensile stress decreasing by -1.5
MPa/K. Two features clearly shown in the ﬁgure are (1), 700 MPa biaxial stress is relaxed
upon cooling is fully recoverable upon heating, so the stress-temperature curve forms a
close loop during a cooling/heating cycle; (2), the slope of the stress recovery upon heating

is almost 7 times larger than that of the stress relaxation upon cooling.

 

‘2 Further cooling is not available from the apparatus used in this experiment.

78

The X-Ray diffraction spectrum of the sample at ambient temperature is shown at
the left-upper comer of Fig. 4-19. It indicates that the structure of the sample at 298 K is
martensite. It might be thought that the volume change and elastic constant drop associated
with the B2 -> B 19’ transformation account for the stress relaxation [Jardine et al., 1990].
However, the martensitic transformation is accompanied by a volume shrinkage of
~0.34%, which should cause an increase in tensile stress. According to self-
accommodating theory, even if the elastic constant decreased by 50%, the residual stress,

0;, would be

700 0.0034 83000
a =—+

, - = 350+ 140 = 490 MPa
2 3 2(1-0.33)

 

upon the completion of the martensitic transformation, or, more than 350 MPa should be
maintained during the martensitic transformation. However, the stress was in fact relaxed
to a value close to zero (~80 MPa), therefore, there must be other reasons for the stress
relaxation behavior. The formation of detwinned martensite induced by thermal stress may
be the answer. Under the thermal stress, the martensite variants were selectively formed,
i.e., the detwinned martensite is formed. The actual martensite variant combination must
result in a net macroscopic biaxial strain to cancel the biaxial thermal strain. Thus, the
stress is decreased, and the overall energy therefore is decreased. In this aspect, the
martensite formation during cooling of an SMA NiTi/Si composite is similar to that in a
tensile test of an austenite N iTi at a constant temperature.

However, there may exist differences between the elongating of austenitic NiTi at a
constant temperature and the cooling of a stressed SMA NiTi/Si. In the former case, only
the variant that experiences the maximum resolved shear stress and thus gives the
maximum strain in the stress axis direction, is formed. The material is fully martensitic
only when the maximum SE elongation is reached. At that time, the martensite exists as a

single variant, and is fully detwinned. In the latter case, however, the martensite does not

79

have to be single-variant. This is because in NiTi/Si, the observed strain is much smaller
than the maximum SE strain. For example, cooling NiTi/Si from 723 K to 273 K creates a
strain em“, = AT - (mg-am“) = 450-(15.4 - 3)x10*’ = 0.56%, which is one order of
magnitude smaller than 8.4%, the theoretical maximum recoverable strain for
polycrystalline NiTi [Miyazaki, Nomura and Ishida, 1995]. When the temperature reaches
Mp NiTi ﬁlm is fully martensitic. Therefore, the martensite is in a partially detwinned
multi-variant condition. Since martensite has a low ﬂow stress of < 100 MPa [Ford and
White, 1996; Krulevitch et al., 1996], low residual stress is expected at temperatures
lower than M,.

Ambient X-Ray diffraction indicated that B 19’ martensite exist at room temperature.
Therefore, the formation of martensite, at least partly, contributes to the stress relaxation
during cooling. But it is not clear if the R-phase transformation has been taken place prior
to the formation of martensite. From the observation that the stress/temperature slope is
apparently steeper stress slope (10.5 MPa/K) during the ﬁrst ten Kelvins of stress
relaxation, it is likely that the B2 —) R transformation has occurred. However, according
to Nishida et al.’s data [1996], the start temperature of the B2 —> R transformation increase
at a rate of ~0.046 K/MPa under uniaxial applied stress, therefore, the corresponding stress
relaxation slope should be (0.046)"/(1-v) = 33 MPa/K, which is two times larger than the
ﬁrst slope (10.5 MPa/K) during cooling. On the contrary, for start temperature of R ->
819’ transformation, the expected stress/temperature slope is (0.2)"/(1-v) = 7.5 MPa/K,
which is more comparable to the second slope (5.8 MPa/K) of stress relaxation observed
during cooling. The major difference between the expected and observed stress relaxation
slopes associated with the B2 -) R transformation may arise from that the rhombohedral
angle of R phase is not acute enough to create as much shape strain as needed to relax
stresses. Other reasons include that there may exist deviation between the actual
temperature-stress data and that quoted from N ishida’s results. It is noted that according to

Clausius-Clapeyron’s equation, the transformation temperature under stress is related to the

80

transformation enthalpy, which is not available for this particular sample. Nevertheless, if
the compositions are close (both are Ni-rich), the estimation generally holds satisfactorily.

The recovery of the stress upon heating results from SME by reverse martensitic
transformation. Since the strain associated with the formation of detwinned martensite is
recovered, the stress is recovered. Since the recovery is perfect, it is apparent that no slip-
related plastic strain, which is unrecoverable by heating, has been introduced. The perfect
recovery also suggests that the biaxial strength of austenite Ni-rich NiTi ﬁlms is at least 700
MPa, which corresponds to a uniaxial strength of 470 MPa. This value is better than the
one obtained by Ishida et al. [1996], who reported the critical stress for inducing slip
deformation of 8 pm Ti,,,,Ni5L3 ﬁlms annealed at 723 K was < 400 MPa. Difference may
be expected because of the ﬁlm thickness and the substrate constraint. Thinner ﬁlms (1.3
11m in our experiment) may be stronger than free-standing thicker ﬁlms because the grain
size is expected to be smaller, and the substrate constraint makes the dislocation motion
more difﬁcult to occur [Nix, 1989].

It appears puzzling that the slope of stress recovery upon heating is considerably
steeper than that of stress relief upon cooling. For stress induced transformation, the onset
of the stress drop corresponds to M, at stress cm and the ﬁnish temperature of the stress
drop corresponds to M, at stress am, just as what we have stated before. In a similar
fashion, the onset temperature of stress recovery corresponds to A, at stress am and the
ﬁnish temperature of stress recovery corresponds to A, at stress om. Since stress
relaxation and recovery are based on reverse transformations and A,-A, is usually small (<
5 K), the slopes of stress vs. temperature at heating and cooling should be very close.

The difference in stress change slope between cooling and heating may be
explainable considering a two-step reverse transformation during heating. From the electric
resistivity-temperature curve of free-standing ﬁlm, both B19’ —) R and R —) B2 occur
during the heating. It may be assumed that the two-step reverse transformation occurs in

NiTi/Si since the stress is very low. However, R phase, like martensite, has a low ﬂow

81

stress, therefore, it will not contribute any remarkable stress recovery. Instead, because B2
phase is strong, R -> B2 transformation is mainly responsible to the stress recovery. The
increasing rate of biaxial stress in NiTi/Si can also be inferred from Ishida et al.’s
experiment [1996]. It gives a rate of 1/0.046/(1- v) = 33 MPa/K, which is close to 36

MPa/K, the slope observed in the present experiment.

4 ,D'1...' _ .1 . 111..--°11 -11- _A. I v _'1,1_1-_ ._. . . . 71111

$102151

Figure 4-20 shows the stress vs. temperature curves of a Ti-rich NiTi/SiO/Si
composite which experienced different annealing treatments between thermal cycles from
283 K to 383 K. The sample was obtained by 473 K-deposition of NiTi on SiO2
passivated Si substrate'3 using a Ti/NiTi composite target (see Chapter 3 for detail). The
sample experienced four thermal treatments after each the sample was thermally cycled in
order to get a stress—temperature curve. The four treatments were: the 1st, 2 hours at 723
K; the 2nd, 1 hour at 873 K; the 3rd, 4 hours at 873 K and the 4th, 3.5 hours at 873 K.
Except for the 4th stress-temperature curve, each curve was obtained directly after the
annealing, so essentially the stress-temperature data come from the fast cooling/heating
cycle after each anneal. The 4th curve was from the second thermal cycle after the
annealing, because before conducting stress measurement, two 0.3 um thick 3 mm x 3 mm
gold squares were coated at the edge of the sample in order to perform in-situ resistivity

measurement. During the gold-coating process, the temperature reached 37 3 K.

 

‘3 The purpose of using 8102 here was to avoid interdiffusion between Si and NiTi because high
annealing temperature was used. The $10, layer was only 0.2 micron and was just 1/8 of NiTi layer
and 1/ 1500 of the Si substrate thickness. It did not signiﬁcantly affect the stress measurement but
did provide a good diffusion barrier since experiments demonstrated that annealing at temperature
higher than 873 K may destroy the interface between the unpassivated Si and NiTi.

82

4.2.2.1 . Stress-Temperature Hysteresis Loop After Annealing at 723 K

Figure 4-20 shows the stress-temperature hysteresis loops during thermal cycling
from 283 K to 383 K. The ﬁrst hysteresis loop has A6 = 100 MPa, AT < 3 K, and may be
from the R-phase transformation occurring in a limited volume ﬁaction of material. The
electric resistivity-temperature curve (Fig. 4.21) for a similar free-standing ﬁlm which
experienced the same annealing treatment also suggests that the R-phase transformation is
responsible to the stress-temperature hysteresis loop. As shown in Fig. 4-21, after
annealed 723 K for 2 hours, the Ti-rich ﬁlm (at zero stress) had a very low martensite start
temperature (240 K). If a slope of 0.2 K/MPa for M, increase by applied stress is assumed
[Nishida et al., 1996], the M, under 600 MPa biaxial stress is 320 K, which is somewhat
lower than the onset temperature of the stress relief (~340 K). From the resistivity data of
free-standing ﬁlm, the R phase start temperature without applied stress was at 333 K, and
considering the applied stress can also increase the R-phase transformation temperature, it
is plausible that the R-phase transformation alone accounted for the stress relief.
Noticeably, upon the completion of the R-phase transformation, only 100 MPa out of 600
MPa stress was relaxed, suggesting that only a limited volume fraction was transformed. It
may be concluded that there are non-transforming material present, possibly in a form of

amorphous or highly defected N iTi resulting from incomplete crystallization .

4.2.2.2. Stress-Temperature Hysteresis 1.00ps After Annealing at 873 K

Three larger stress-temperature hysteresis loops (A0 = 450 ~ 800 MPa, AT = 10 ~
25 K) were obtained after the sample was annealed at 873 K for 1 hour, accumulatively for
5 hours and accumulatively for 8.5 hours, respectively. As shown in Fig. 4-20, the loop
obtained after the sample experienced the ﬁrst 87 3 K annealing, which has a maximum
stress of 850 MPa, is not closed while the other two are closed. Since the non-closed loop
indicated that non-recoverable strain has been introduced, the austenite yield strength is

apparently lower than 850 MPa. In addition, at the very initial stage of cooling, the stress

83

is apparently steady, instead of increasing at the expected 1.5 MPa/K slope, also indicating
the ﬁlm is yielding. Similarly, the closed loops occurring when the sample experienced
more anneals at 873 K indicate that the ﬁlm has a yielding strength is higher than or equal
to 780 MPa.

Stress Relaxation on Cooling After annealing at 873 K, stresses resulting cooling
from annealing temperature can be relaxed to almost zero stress upon cooling. The stress
relaxation paths is composed of two segments, the ﬁrst segment has a steeper slop (~50
MPa/K) while the second segment has a more shallow slop (~11 MPa/K). For all the
stress relaxation paths, while the onset temperatures for stress relaxation change little, the
ﬁnish temperatures for stress relaxation change signiﬁcantly. After annealing 1 hours at
873 K, the stress relaxation ﬁnish temperature is 288 K. When the annealing time at 873 K
increases to accumulatively 5 hours, the stress relaxation ﬁnish temperature becomes 310
K. With accumulatively 8.5 hours at 873 K, the stress relaxation ﬁnish temperature
increases to 318 K.

The change of stress-temperature slope on cooling suggests the mechanism changes
during the stress relaxation. In order to get the transformation information during stress
relaxation and recovery, electric resistivity has been measured in-situ during stress
measurement. The stress-temperature curve together with a resistivity-temperature curve
acquired during a cooling/heating cycle from 300 K to 290 K for the NiTi/SiO,/Si
composite, which was annealed 2 hours at 7 23 K and accumulatively 8.5 hours at 873 K,
are shown in Fig. 4-22. According to the traditional resistivity change with transformation
in NiTi SMA ['Thomburg, Dunne and Wayman, 1971], it is clearly indicated that the R-
phase transformation is responsible for the ﬁrst segment of the stress relaxation, while the
martensitic transformation is responsible for the second segment of the stress relaxation
during continued cooling. The stress bump occurring when the martensitic transformation

started suggests that there is a volume shrinkage, which is in agreement with the theoretical

84

calculation from lattice parameters [Knowles and Smith, 1981]. However, it is not
possible to relate the stress bump with exact volume change, since the stress reﬂects the
detwinning stress ﬂow of the martensite.

Because the conﬁgurations of stress-temperature curves after the sample was
annealed at 873 K with varying time are similar, it is suggested that the two—step
transformation is responsible for the stress relaxation behavior during cooling after the
sample was annealed at 873 K. The stress relaxation in the ﬁrst segment upon cooling
corresponds to stress induced B2 —) R transformation, by which the stress was decreased
at a rate of ~55 MPa/K. This stress decreasing rate in Ti-rich ﬁlm is apparently larger than
the one observed in Ni-rich ﬁlms (~36 MPa/K), which is expected because Ti-rich NiTi
usually has a larger transformation enthalpy than N i-rich alloys[Lo et al., 1990]. For the
same reason, it is expected the rate of stress decrease by stress induced martensitic
transformation in Ti-rich ﬁlm (11 MPa/K) is also larger than that in Ni-rich ﬁlm (~5.8
MPa/K).

It is noted that the onset temperature for stress relaxation corresponds to R, under
the stress. According to the transformation temperature data for similar free-standing ﬁlm
that experienced annealing at 873 K (Figure 4-23), R, remains stable as the annealing time
at 873 K is prolonged. Since R, is rather insensitive to the stress (0.046 K/MPa for
uniaxial stress), reasonably the onset temperature for stress relaxation does not change
signiﬁcantly. The stress relaxation ﬁnish temperature, however, corresponds to M, under
zero stress. According to the transformation data of annealed free-standing ﬁlm (Fig. 4-
23), it increases evidently as the annealing time at 873 K increases. Therefore, it is
expected that the stress relaxation ﬁnish temperature increases with increased annealing

time.

Stress Recovery on Heating For therrnocycles after the sample was annealed at
873 K, the stress that relaxed upon cooling can be recovered by reheating. From Fig. 4—20

85

it can be seem that the onset temperature for stress recovery increases with increased
annealing temperature, and the stress recovery slope on heating is very close to the stress
relaxation rate by stress induced B2 -—) R transformation. This suggests that the stress
recovery primarily results from the corresponding reverse transformation, i.e., R —) B2
transformation. Since B 19’ phase has formed when the sample is cooled down, During
reheating, B 19’ —-) R transformation must have occurred before the quick stress recovery
begins. The reason that no obvious stress change for B19’ R transformation is that the
ﬂow stress of R phase is because R phase has a ﬂow stress as low as 40 MPa [Miyazaki,
Kimura and Otsuka, 1988]. Stress is limited within the ﬂow stress by forming biased R
phase variant.

The onset temperatme for stress recovery during heating corresponds to A,
temperature at zero stress. From the transformation temperature data of annealed free-
standing ﬁlm (Fig. 4-23), it is expected that the onset temperature for stress relaxation

increases as the annealing time at 873 K is prolonged.

,. '11 11,1- 1- P 1,: 11 r 1111.1'11 14.1-11: ,, . . ..
$1151.

The stress relaxation and recovery of SMA NiTi/Si demonstrated in the last two
sections may be useful for actuation in microelectromechanical system. Characteristics of
the stress-temperature hysteresis loops include:

1. Stress relaxation and recovery is reversible at biaxial stress as high as 780 MPa;
2. Stress may be relaxed to nearly zero state on cooling;
3. Stress relaxation and recovery are driven by temperature change;
4. The onset temperatures for stress relaxation and recovery may be controllable in a
limited range by thermal treatment as well as stress;
The stress relaxation and recovery can produce cyclic displacements. If a 700 MPa biaxial

stress in 3 pm NiTi on 2” diameter 300 pm thick Si is achieved before stress relaxation,

86

according to Stoney’s equation (3.1), the composite has a curvature radius of ~1.3 m.
Upon cooling when the stress is fully relaxed, the curvature radius becomes inﬁnite. If the
center of the composite is secured, a displacement of 250 pm is produced at the rim of the
composite. Or for a 2” long cantilever, if one end is secured, a displacement of nearly 1
mm is produced at the other end (Fig. 4-24). According to Stoney’s equation, the
curvature radius of the composite is proportional to ﬁlm thickness, substrate modulus and
inverse of square of substrate thickness, larger displacement is available when thirmer
substrates or less rigid substrates is used [Krulevitch et al., 1995].

Although the stress output was large, strain output was far less than the maximum
available from NiTi SMA ﬁlms. Again assuming 700 MPa stress is achieved before stress
relaxation, which can be relaxed out on cooling and recovered completely on heating, the

reverse martensitic transformation produces a strain in NiTi of

l-v =7001-0.33

- = 0.0056
E MT.‘ 83000

Ae=Aa-

 

 

which is almost one order of magnitude smaller than the typical fully recoverable strain in
NiTi ﬁlms [Ishida, 1996]. Therefore, the transformation energy output density is far less
than the optimum. The reason for this is that the detwinning strain of martensite is preset
by the substrate. Further cooling results in multi-variant self-accommodating martensite,
which is unable to generate directional energy output. One way to maximize the energy
density output is pre-deform the free-standing SMA NiTi ﬁlms by the maximum fully
recoverable strain, which corresponds to fully detwinned martensite in microstructure, then
deposit an elastic layer. A robust SME will be produced by the reverse martensitic
transformation and the fully dewinned martensite may be restored by the elastic layer upon

cooling. Research in this direction is currently in progress.

Chapter 5

CONCLUSIONS

From experiments on stress evolution in as-deposited and annealed NiTi on Si
during isochronal and isothermal anneals, and based upon structure and microstructural

analyses, the following conclusions may be drawn:

1. Compressive intrinsic stresses were obtained without exception in magnetron
sputtered NiTi ﬁlms when deposition temperatures from ambient to 723 K and argon
pressures from 3.6 to 5.8 mTorr were used. The magnitude of the intrinsic stress
increased with decreasing working gas pressure, increased deposition temperature
and decreased ﬁlm thickness. The ratio of the argon pressure to the deposition
temperature, which is proportional to the working gas density, apparently
determines the magnitude of the compressive stress, giving a rate of ~52.6
GPa-K-mTorr“.

2. Irrespective of the deposition temperatures or the degree of crystallinity in as-
deposited ﬁlms, the stress decreased at a rate of ~1.5 MPa/K during heating between
ambient temperature and the deposition temperature, which is the characteristic slope
of thermal stress development of NiTi on Si based on differential thermal expansion
coefﬁcients. Isothermal annealing experiment conﬁrmed that both intrinsic stress
and thermal extrinsic stresses were stable at temperatures below the deposition
temperature, and they were subject to relaxation at temperatures higher than the

deposition temperature. Kinetics analysis indicated that a two-stage relaxation

87

88

process occurred during isothermal annealing of crystalline or partially crystalline as-
deposited ﬁlms at temperatures higher than the deposition temperature. The ﬁrst
was characterized by relaxation rates more strongly dependent on stress, while the
second was characterized by lower relaxation rates, less dependence of stress, and
an activation energy of ~310 kJ/mol. One-stage stress relaxation was observed for
as-deposited amorphous ﬁlms characterized by an activation energy of ~248 kJ/mol.

3. Amorphous ﬁlms on (100)Si can be crystallized at temperatures as low as 673 K
during isothermal annealing. The activation energy for crystallization of amorphous
ﬁlms was 477 kJ/mol. Crystallization of fully amorphous ﬁlms produced a tensile
stress of ~ 170 MPa during isothermal annealing.

4. Stress relaxation behavior during and immediately following depends on
composition and microstrutural stability. The precipitation of Ni4Ti3 leads to a
constant stress nucleation period followed by an obviously faster stress relaxation
process than that was observed in precipitate-free samples.

5. Reversible stress relief and recovery during thermal cycling was observed in
crystallized Ni-rich NiTi/Si composites. the maximum fully recoverable stress was
greater than 700 MPa. As the temperature was decreased from high temperature to
subambient temperature, stress in the ﬁlm was relaxed to nearly zero stress, and the
stress was recovered by a slope obviously steeper than that of stress relaxation
during cooling when the sample was heated. By analyzing the stress relaxation and
recovery slopes, X-ray diffraction and transformation temperatures, stress induced
R-phase or martensitic transformation was responsible for the stress relaxation on
cooling, while R —) B2 transformation was mainly responsible for the stress
recovery on heating.

6. Reversible stress relief and recovery during thermal cycles around room temperature
was also found in crystallized Ti-rich TiNi/SiO/Si composites. The maximum fully
recoverable stress was between 780 MPa to 850 MPa. Stresses above 850 MPa

89

apparently caused plastic ﬂow in the austenite phase. When a sample deposited at
473 K was annealed at 723 K, the R-phase transformation resulted a small narrow
stress-temperature loop between 328 K and 338 K, and 500 MPa residual stress still
remained upon the completion of the R-phase transformation. When the sample was
annealed at 873 K, stress could be relaxed to less than 100 MPa, and both the B2 —9
R and R —9 319’ transformations contributed to the stress relaxation on cooling,
while R -) B2 transformation was mainly responsible for the stress recovery on
heating. Thermal treatment at 873 K may affect the onset temperatures of stress

relaxation on cooling and stress recovery to a limited extent.

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R.W. and Haasen, P., 3rd Edition, p1035, Elsevier Sceince Publishers BV, 1983;

The International Symposium on Shape Memory Alloys, ed. Chu, Y.Y., Guilin,
China, p59, 1986; Progress in Materials Sciences, 36, 203, 1992

99

Wayman, CM. and Duerig, T.W., in Engineering aspects of Shape Memory Alloys, eds.
Duerig, T.W., Melton, K.N., Stockel, D., and Wayman, C.M., Buttherworth-
Heinemann Ltd., Boston, 1990

Wu, SK. and Wayman, C.M., Acta Metall., 37, 2085, 1989

Wu, S.K., Lin, H.C. and Chou, T.S., Acta Metall. Mater., 38, 95, 1990

Wechesler, M.S., Liebermann, BS. and Read, T.A., Trans. AIME, 197, 503, 1953

Xie, C., Zhao, L. and Tel, T., Scripta Metall., 24, 1753, 1990

Yeh, M.T., Kao, HP. and Hsu, SE, in Shape Memory Materials ’94, ed. Chu Y. and
Tu, H., p561, International Academic Publishers, Beijing, 1994

Zhang, J. and Grummon, D.S., MRS Fall Meeting, 1996, Boston, MA.

Zhang, C., Zhao, L, Duerig, T.W. and Wayman, C.M., Scripta Metall., 24, 1807, 1990
Zhao, 2., MS. Thesis, Michigan State University, 1995

Zheng, X. and Dodd, R.A., Nuclear Instrument Methods, 1994

Zingu, EC. and Mofokeng, B.J., MRS Symposium Proceedings, 308, 85, 1993

100

 

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101

 

T.
._ -./../-

    

 

apnoea/ea;

/ 100% Austenite ,x/

    

Physical Property

 

 

 

 

 

\ x X '1

 

V

 

Temperature

Figure 2-1 A schematic of martensitic transformation showing four
characteristic transformation temperatures and structure within certain

temperature intervals.

102

 

Stress

 

 

Strain

Figure 2-2 Deformation behavior of a martensite material.

AB: elastic deformation of multi-variant martensite;

BC: plastic deformation of martensite by reorientation of the martensite variants;
CD: elastic deformation of fully detwinned martensite;

DE: plastic deformation of fully detwinned martensite by slip

103

 

COOL l COOL

av
W\.

Intervariant boundary movement under stress

DEFORM 3‘?" ' “’i
.' 5 DEFORM:

4—

 

      

-&
l HEAT

 

Figure 2-3 A schematic of SME in two-variant martensite. The left side
shows the macroscopic change of an SMA material by heating/cooling and
applied stresses, the right side shows the corresponding microscopic response.

104

Td<AS As<Td<Ar

Stress
Stress

 

 

 

 

 

 

 

> . >
Strain
(b)
A A
Af<Td<Md Td>Md
a 2”":
3?. 5'.
D b

 

 

 

Strain

 

(C)

Figure 2-4 Deformation behavior of an austenite material at different temperatures:
(a) Td < As, all the strain is recovered by heating the material to above Ar,
(b) As < Td < Ar, part of the strain is recovered spontaneously upon
unloading, while the rest is recoverable by heating the material to above Ar,
(c) Ar < Td < Md, all the strain is recovered spontaneously upon unloading, which is
perfect psuedoelasticity;
(11) Td > Md, permanent strain is introduced by slip.

Transformation Temperature (°C)

105

Atomic Percent Nickel

 

0 1.0 210 3.0 49 5.0 6.0 79 89 99 100
l 800 ,
g 1670 °c
1600-: i-
: L ,
. 1455 °c,
1400‘: 1380 °c ,_

 

 

 

 

 

 

 

 

 

 

 

 

 

Weight Percent Nickel Ni

Figure 2-5 Binary Ni-Ti phase diagram [Massalski, 1987]

106

 

  
  
 

 

Bell Jar Vacuum
System

 

 

 

 

 

 

 

 

 

 

...... , Substrate
Holder

  

 

 

 

 

 

 

 

Shutter
Movement
HT
1
LI 1‘
Diffusion Pump 3
Rough Pump

 

 

Figure 3-1 A schematic showing the d.c. megnetron sputtering apparatus.

 

107

<— Furnace

  
   

" ‘_______._— Glide posts

Quartz bell jar
Sample
Quartz pillars

Heating shield

/ Furnace chasis

Feed throughs

T - cross

 

Optical window

Rotation mirror

PSD
aser generator
Rough Desk
pump

<— Feet

Figure 3-2 Sketch of apparatus for stress measurement by, wafer-curvature method.

 

108

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Temperature (K)

Figure 4-1 Stress - temperature curves of as-sputtered NiTi ﬁlms on Si deposited at

different temperatures. Deposition temperature Ta and crystallization temperature To

are indicated by arrows in each ﬁgure.

R-I: From RT to Td, thermal Stress development;

R-II: From Td to Tc for amorphous or partially amorphous ﬁlms, or Td to ~893 K for
fully crystalline ﬁlms, stress relaxation;

R-III: Stress development due to crystallization;

R-IV: Thermal stress development after crystallization;

R-V: Steady-state stress when temperature exceeds 893 K for fully crystalline ﬁlms;

R-VI: Thermal stress development due to fast cooling.

 

Stress (MPa)

Figure 4-2 (a,b) Stress variation of two crystalline NiTi ﬁlms on Si deposited at 693

0
-200 '
.400 '
-300 ...........
-1000 E . . i . . . . n . . . . i . . . . ‘
50 100 150 200 250
Time (ks)

111

 

T T r I T T T T 1 T T T T I T T T r

 

l l l j L L L I I l l I

 

 

 

100 15

 

 

 

 

 

 

K during thermal treatments with time starting at the ﬁrst isothermal annealing.

 

Stress (MPa)

112

 

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A” i 693 K
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e : 673 K

i,

 

 

-1000Initiljrllllllilltllllnl

 

Annealing time (ks)

Figure 4-2(c) Stress relaxation in as-sputtered NiTi ﬁlms on Si deposited at 693
K during the ﬁrst 25 ks isothermal holding at different temperatures. Timing
started at each temperature.

 

Ln(K(6, T))

113

 

 

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Compressive Stress (MPa) ’

Figure 4-3 Plots of ln(k(o; T) ) vs. 0' from stress relaxation curves for the
crystalline ﬁlms deposited at 693 K and isothermally annealed at different
temperatures (to be continued).

-2.2

‘-3.0

 

Ln(K(6. T))

-3.4

-3.8

-1.0

-1.2

—l.4

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114

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Stress (MPa)

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lOOO/T (K-l)

Figure 4-4(a) Calculations of activation volume (upper) and activation energy
(lower) based on the intercepts and slopes in Figure 4-3 for the ﬁrst stage of stress
relaxation in fully crystalline ﬁlms.

 

116

 

 

 

 

 

 

 

 

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1000/T(K'1)

Figure 4-4(b) Calculation of activation volume (upper) and activation energy
(lower) calculations based on the intercepts and slopes in Fig. 4-3 for the second stage
of stress relaxation in fully crystalline ﬁlms.

J.“

‘ ﬁrm-(‘0

 

117

 

 

 

 

 

 

 

 

 

 

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r.

  

 

 

 

 

 

g .........
g I
m d
j
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n n l 1 A 1 l 1 1 A A l n n 1 n
150 200 250 300

 

Time (ks)

Figure 4-5(a) Stress variation of an initially partially crystalline NiTi on Si
deposited at 623 K during thermal treatment with time starting at the ﬁrst isothermal
annealing.

118

 

 

OIIII923KTriflttIII'IIIIIITVII—t
° 863K .

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Stress (MPa)

 

 

 

_2m 1 l l l l l L J 1 l l l l L l L l l l J 1 I l I l l l l l
O 3 6 9 12 15
Annealing Time (ks)

Figure 4-S(b) Stress relaxation curves of the NiTi ﬁlm on Si deposited at 623 K
during the ﬁrst 15 ks of isothermal holding at different temperatures after the ﬁlm
became fully crystalline. Timing started at each temperature.

119

 

 

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'125 130 1 so 100 120 140
Compressive Stress (MPa) >

 

3
i

l -
35

 

Figure 4-6 Plots of In( k( 0', T )) vs. 0' from the stress relaxation curves for the
initially partially crystalline ﬁlms deposited at 623 K and isothermally annealed at
different temperatures (to be continued).

 

Imﬁ... ..1 ..

 

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120

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Compressive Stress (MPa)

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Figure 4-7(a) Diffusion volume (upper) and activation energy (lower)
calculations based on the intercepts and slopes in Fig. 4-6 for the ﬁrst stage of
stress relaxation after crystallization of a partially crystalline ﬁlm.

 

122

 

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Figure 4-7 (b) Calculations of activation volume (upper) and activation energy
(lower) based on the intercepts and slopes in Fig. 4-6 for the second stage of stress
relaxation after crystallization of the initially partially crystalline ﬁlm.

123

 

O I 1 I I l I I T 1 TI 1 rrj 1 I I I l I I I I 1 I I I I I I
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Stress (MPa)
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Time (ks)

 

 

 

Figure 4-8(a) Stress relaxation of an amorphous NiTi ﬁlm on Si deposited at 473 K
during thermal treatment with time starting at the ﬁrst isothermal annealing.

Stress (MP3)
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124

 

 

 

 

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O 20 40 6O 80 100
Annealing Time (ks)

Figure 4-8(b) Stress relaxation curves of the amorphous NiTi on Si deposited
at 473 K and isothermally annealed at different temperatures with time starting
each isothermal annealing.

 

ln(k(0’, T))

125

 

 

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Compressive Stress )

 

Figure 4-9 Plots of ln(k(0', T) vs. ofor an as-sputtered amorphous NiTi on Si
deposited at 473 K during isothermal annealing at various temperatures.

126

 

 

    

 

 

 

 

 

 

 

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b" - .
t ' i ‘
2 '15 r “1
o _ ; .
*5. .
O 5 . , .
£3" _20 '- . . i . . L 1 1 . . . i . . m. i . . . . I . . . .
g 1.4 1.5 1.6 1.7 1.8 1.9 2.0
1000/T(K'1)

Figure 4-10 Calculations of Actiation volume (upper) and activation energy (lower)
calculations for stress relaxation in fully amorphous NiTi on Si based on the intercepts
and slopes in Fig. 4-9.

 

127

 

 

 

 

 

 

 

 

200 I I I I : I I I I l I I ‘I I I I I I I I I I—ﬁ I—FI I I I I I I I
150 - . O O . .. .._
r 00 i O O 0% O o
g - V . - 1
V1 50 _ ..................................... . ................. I Stress Relaxation in _
- O _ ‘ Amorphous Film;
. i V II Nucleation of B2 Crystal; -. .
' 8 Tensile Stress I
O _- cg) H 111 Evolution During 5'
O . Crystallization .
‘ Relaxation due to Diffusion in '
IV the Polycrystal '
-50 I I l l I I I I I I I I I I I I l I l 1 l I I I I I l l I I I l l I47

 

 

 

 

0 1 2 3 4 5 6 7
Annealing Time (ks)

Figure 4-ll(a) Stress evolution in a NiTi ﬁlm deposited at ambient temperature
during isothermal annealing at 723 K. TEM shows that the microstructure of the aged
ﬁlm is free of precipitates.

 

128

 

250 I l l l I 1 l I I I I l

 

 

 

 

 

   

 

 

 

 

 

 

r I I I I I I
_ | l I
1 II 1114 IV I V , -
_ r V V ‘——————————>‘ . O O _
" I O ' ; Z
: (9 0 GD 0 Q : _
’3 o 3
m L . ..
E 100 _ . O 1
E : I Amorphous Film Stress-Relax'n :
VJ 50 ,_ ..................... .1
: II Nucleation of 32 Crystal .:
: III Crystallization: Tensile Stress :
0 Evolution Durin Densiﬁcation ‘:
g g
- IV Nucleation of Coherent Ni4Ti3: 3
_50 '_ ___________________ Slight Stress Relax'n. :
I V Growth of Ni4Ti3: Rapid Stress :
— - Relaxation Due to Topotaxy -
-1m 1 I l I I I I I l I I I l l I l I l r
0 l 2 3 4

Annealing Time (ks)

Figure 4-ll(b) Stress evolution in a ﬁlm deposited at 573 K during isothermal
annealing at 713 K. TEM shows that the microstructure of the aged ﬁlm contains
numerous Ni4Ti3 precipitates.

129

,)
I v m a mu

 

 

Figure 4-12 TEM micrographs showing the microstructures of the annealed ﬁlms with
two kinds of stress evolution behaviors during annealing at crystallization temperature:

(a) Microstructure is free of precipitates, corresponding to the ﬁlm with a relatively
lower relaxation rate after crystallization (see Fig 4-11(a));

(b) Large number of precipitates, corresponding to the ﬁlm with a relatively faster
relaxation rate after crystallization (see Fig. 4-11(b)).

130

 

 

 

 

 

 

 

 

 

Under tension
:’ i_.:_--_ --__"'..-—- T-‘I" (b)
Tensile side —" Under compression
’III I 'I I]: I'll“'(c)
Under bending
5““
\ (6)
Transformation

 

 

 

 

 

Compressive side <—

‘” ‘°’

Figure 4-13. Constrained annealing effect on precipitation and intrinsic two-way
memory effect mechanism in Ni-rich NiTi alloys proposed by Nishida et al.
[Nishida et al., 1987].

 

(a) Precipitate variant was selectively formed during annealing at 673 K ~ 873
K under bending stress for polycrystalline Ni-rich TiN i;

(b) Precipitate variant whose habit plane is most parallel to stress axis is
formed if the sample is annealed under tensile stress;

(c) Precipitate variant whose habit plane is most perpendicular to stress axis
is formed if the sample is annealed under tensile stress;

(d) Precipitates with different habit planes at different side of the sample are
formed if the sample is annealed under bending stress. Curved shape is
formed due to the relaxation of elastic constraint stress;

(e) When martensitic transformation is completed, the shape of the sample
is inverted due to the biasing effect of the particularly oriented
precipitates.

131

200

 

150
100

 

Stress (MPa)

LII
O
IIIIIUIIIU'UVIVVIU'IIIUIIIUU

 

A AA A A AAAAA. A A A AA

0.01 . 1 "io
Annealing Tirne (ks)

L

 

 

 

 

UTIUTT‘III'I'I'UI'IUI'IUU'U'I'U‘
llIll]IllILJIIIIIIllllllllllllelL

 

 

 

‘3 " n 4 A 1 J . . l . . A l . , a l . . n l L a n
1.38 1.4 1.42 1.44 1.46 1.48 1.5
1000/T (K-l)

Figure 4-14 (3), Stress variation monitoring crystallization during annealing of
amorphous NiTi ﬁlms deposited at ambient temperature on Si.

(b), Calculation of activation energy for crystallization of amorphous N iTi ﬁlms by
linear ﬁtting.

132

 

'3“) I I I I I I I I I j I I I j I I I I I
_ -
#- § .
400 -~‘ - -

LLI

ll
::—0—«
3I—O—4

t—O—t

l

 

 

 

é
a -500 - ~-
g _ § _
m l—
.2
.3 ” "
. l _
.5 -600 _. , _
r- q
r-l l l l l l l I l l l l l l 1 l I I l-
'7003.5 4 4.5 5 5.5

Ar Pressure (mTorr)

Figure 4-15 Intrinsic stress vs. working gas pressure for NiTi ﬁlms on Si
deposited at ambient temperature (Td ~ 400 K) with ﬁlm thicknesses ~15 to 2.5
microns.

133

 

0TIIIIIIIIIIIIIIIIIIIIITI

 

 

 

 

P -
r- -l
I— d
P -
Q _400 _.. ., ......... _
E. - -
a I "
a -600 __.. we ......... _
Q r- _
'5
.5 P -
.5 - _
-800 _,. -— .-
p -
h d
_1000 I I I I L I 1 LI I I I I I I I I I I I I I I I

273 373 473 573 673 773
Deposition Temperature ( K)

Figure 4-16 Intrinsic stress vs. deposition temperatures for NiTi ﬁlms on Si
deposited at constant working gas pressure of ~ 5.1 mTorr with ﬁlm thickness 1.5 to
2.5 microns.

Intrinsic Stress (MPa)

Figure 4-17 Intrinsic stress for as- sputtered NiTi on Si vs. the ratio of working gas
pressure to deposition temperature, and ratio of working distance (W d) to mean free-

 

 

 

 

 

 

 

 

 

 

 

134
1.2 1.6 2.0 2.4
lllTllvllll[lgllllllEllllllgllllll
0.8 0.9 1.0 1.1 1.2%13 1.4 $1.5 1.6 1.7 1.8 1.9
llllllllIlllllilllllllllllllll‘illllllllllWllIlllllIlllllllIIIIIIIIIHIITIT
0.4 0.5 0.6: 0.7 0.8 0.9

OtTIlllllIlllllllllllllll'gITlllllllllWIélllllllIllllllIWllFlllI-l.
L ‘ ' -
-200 '-' ‘-4
- -l
400-... .3
-500- Z
- 1
: I] Varying working gas pressure wrth
-800 __,_ ambient deposition (Td~ ~400 K) . _
L .
a _ o _ Varying Td with constant working gas J
.. pressure (~ 5.1mTorr) _ . r

-1000—1 1 1 1 L 1 #1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0.006 0.008 0.01 0.012 0.014 0.016

PAr / T: mTorr/K

path of Ar (M), Ni (AM) and Ti (XTi) atoms. (combined Fig.4. 15 and 4.16).

'7

 

raﬁ

 

 

 
 

135
'200 _ I I I I I r F I I I I I I I I u I I r B
- a
.- —l
_.. ..._ :
I— .0 —I F
I— o' - i
I— 0' - I
A _ '0 - I
a _3m _ ......... ._..,'.,o. 1.. E
— .' -
g : ,0' : 15
In I— ; ' - u—w
g _ ......... ._-
— E. I'. d
U} I— I d
O |-' I-
." _ -
E 400 . .0, 1.-
- -
!— I-l
- d
I— d
-500 -.. ....
p- c-
h
I l l l I l I I I I I I I I I I l J I

 

 

 

_.
N
U.)
.b
M

Film Thickness (11m)

Figure 4-18 Intrinsic stress vs. ﬁlm thickness for NiTi on Si deposited at
ambient temperature (Td ~400 K) and constant Ar pressure (5.1 mTorr).

136

819'

 

 

   
    
 

 

 

 

8 W 7 F" a: I I I F r I I I r
as '1': .
co 2 '5.
b, ”x
a 5" ' 15MPa/K
F” g g - .
11111111111111111I11111111111111111‘ ‘:‘
40 50 (6)

 

600

 

 

NiTi: 1.3 pm;
Si: 300 um;
{-sz 533 K

   

Stress (MPa)
400
r

   

 

 

 

200
r

 

 

 

 

223 273 323 373 423
Temperature ( K)

Figure 4-19 Stress relief and recovery during a cooling/heating cycle of a Ni-rich
NiTi/Si composite after annealing for 2 hours at 723 K with X-ray diffraction
spectrum at room temperature (left-upper corner) and resistivity curve for free-
standing ﬁlm.

137

 

  
 
 

 

—o— After lst treatment;

—u— After 2nd treatment;
—-o-— After 3rd treatment;
-—o——dkﬁcr4ﬂ1UeaUBcnt

 
 

 

800

   

600

Stress (MPa)
400

 

 

  
   

 

 

 

 

8
N
"NiTi: 1:5 pm
0 ' SIOZI 0.2 run;
Si: 300 um; I
r - To: 473 K _ *
1 1 1 I 1 1 1 I 1 1 1 I 1 1 1 l 1 4 j ' ' ' " " '
273 293 313 333 353 373 393

Temperature (K)

Figure 4-20 Stress relief and recovery during cooling/heating cycles of a Ti-rich
NiTi/SiOz/Si composite after different heat treatments.

lst treatment: 723 K, 2 Hours (the ﬁrst cooling/heating cycle);

2nd treatment: 873 K, 1 Hour (the ﬁrst cooling/heating cycle);

3rd treatment: 873 K, 4 Hour (the ﬁrst cooling/heating cycle);

4th treatment: 873 K, 3.5 Hours (the second cooling/heating cycle).

The heat treatments were applied to the same sample so the effect was accumulative.

 

138

 

 

 

 

    

8733K, 2 Hours

Resistivity (Relative Unit)

     

 

 

 

 

 

I111I11111|11111
173 223 273 323 373
Temperature (K)

 

Figure 4-21 Resistivity vs. temperature curves of free-standing Ti-rich NiTi ﬁlms
that was annealed 2 hours at 723 K (upper) and additional 2 hours at 873 K (lower).

 

139

 

  
     

 

 

 

 

 

 

 

 

§ . I l U r I I I I I I I l I F I l I j I ‘ :
I J
g P ........... q i»
i 2 g
L _‘ :— 3.
§ . . to s.
. . Q
g : : E
1—1 N
v p' - :— c‘
a «3» - - a
P I C
.3. - - g.
8 - *- S
N ' .
. .l o
8 _ ............................... ............ .. ................ “c
.— _|_§. Resrstivity
L —o—;SU'CSS
2 00
O o’
293 313 333 353 373 393

Temperature (K)

Figure 4-22 Stress variation with temperature during the second cooling/heating cycle
of a Ti-rich NiTi/SiOz/Si composite that has been annealed at 723 K for 2.5 hours
followed by anneals at 873 K with accumulative time of 8.5 hours. In-situ resistivity
measurement was used to monitor phase transformation.

140

 

 

 

 

 

 

343
, 338 E
2'?”
G . 333 g
'8 1:.
D a
E 328 g
3 353g
5 E
.9 m
3% w 333 3

32’
313
293

 

 

 

 

 

     

 

 

   

173 223 273 323 373

Temperature (K) Annealing Hours

Figure 4-23 (a) Resistivity - temperature curves of Ti-rich NiTi ﬁlms annealed at
873 K for varying time during thermal cycles at stress-free states. (b), R-phase
transformation temperatures are stable; (c), martensitic transformation temperatures
increase with increased annealing time at 873 K.

141

 

Figure 4-24 Clacualtion of displacement of a cantilever deposited a NiTi layer resulting
from stress relaxation by phase transformations.

Considering only elastic deformation, the displacement at one end of the component
when the other end is secured can be determined by:

L
2R

D: *L

 

 

 

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