crystallization and martensitic transformation behavior of niti shape memory alloy ... ·...

Crystallization and Martensitic TransformationBehavior of NiTi Shape Memory Alloy Thin Films

A dissertation presented

by

Xi Wang

to

The School of Engineering and Applied Sciences

in partial fulfillment of the requirements

for the degree of

Doctor of Philosophy

in the subject of

Engineering Sciences

Harvard University

Cambridge, Massachusetts

May 2007

Thesis advisor Author

Joost J. Vlassak Xi Wang

Crystallization and Martensitic Transformation

Behavior of NiTi Shape Memory Alloy Thin Films

Abstract

The microstructure evolution and shape memory properties of near-equiatomic

Ni-Ti thin films were investigated. Ni-Ti thin films sputter-deposited at room tem-

perature are usually amorphous in their as-deposited state. This observation provides

an opportunity to control the microstructure by adjusting the crystallization condi-

tions. The temperature dependence of the crystallite nucleation and growth rates

is measured for amorphous Ni-Ti thin films sandwiched between two SiNx layers.

Crystallites are shown to nucleate homogeneously in the film and to grow with an

interface-controlled mechanism. The reaction between Ni-Ti and surrounding layers

results in a small composition shift at these interfaces and suppresses heterogeneous

nucleation at these interfaces. The crystal growth rate shows a film thickness de-

pendence and is much slower in thinner films. We propose that hydrogen present in

surrounding SiNx layers is responsible for this decrease of the crystal growth veloc-

ity. By manipulating nucleation and growth rates, unprecedented control over the

microstructure of the films is possible. Martensitic transformation behavior of Ni-Ti

thin films of submicron thicknesses was investigated using the substrate-curvature

technique. The appropriate annealing condition was chosen such that the grain size

iii

Abstract iv

is much larger than the film thickness. Consequently, the effect of film thickness is

independent of the grain size. The transformation temperature starts to decrease

when the film thickness is below 400 nm. This decrease is associated with an in-

creasing energy barrier to transformation in thinner films. A crystallization study in

which amorphous films are annealed by a scanning laser was performed experimen-

tally and numerically. The nucleation and growth mechanisms in the laser annealing

process were found to be the same as for furnace annealing. Uniform microstruc-

ture and shape memory properties were locally introduced in the films by the laser.

A 3-D thermal model was developed to simulate the crystallization behavior of the

laser annealing process of amorphous Ni-Ti thin films. The crystallization kinetics

parameters determined in the furnace annealing study were included in the model

to allow us predict the size of the crystallized region as a function of laser annealing

parameters.

Contents

Title Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

1 Introduction 11.1 Shape memory alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Physical metallurgy of Ni-Ti alloy . . . . . . . . . . . . . . . . . . . . 4

1.2.1 Phase diagram . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.2 Martensitic transformation in Ni-Ti alloys . . . . . . . . . . . 61.2.3 Crystal structure of martensite . . . . . . . . . . . . . . . . . 71.2.4 Precipitation and its effect . . . . . . . . . . . . . . . . . . . . 8

1.3 The objective and outline of the thesis . . . . . . . . . . . . . . . . . 12

2 Experimental techniques 142.1 Film deposition process . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.1.1 Sputter system . . . . . . . . . . . . . . . . . . . . . . . . . . 142.1.2 Thickness uniformity and composition control . . . . . . . . . 15

2.2 Stress measurement techniques . . . . . . . . . . . . . . . . . . . . . 182.3 Transmission electron microscopy (TEM) . . . . . . . . . . . . . . . . 21

3 Crystallization kinetics of amorphous Ni-Ti thin films 223.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.2 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3.1 Crystal morphology . . . . . . . . . . . . . . . . . . . . . . . . 263.3.2 Growth kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . 313.3.3 Nucleation kinetics . . . . . . . . . . . . . . . . . . . . . . . . 39

v

Contents vi

3.3.4 Tailoring the microstructure . . . . . . . . . . . . . . . . . . . 433.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4 Size effects in martensitic transformation behavior 474.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.2 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.3.1 Microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . 504.3.2 Stress-temperature curves . . . . . . . . . . . . . . . . . . . . 51

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.4.1 Transformation under substrate constraint . . . . . . . . . . . 614.4.2 Film thickness effect . . . . . . . . . . . . . . . . . . . . . . . 634.4.3 Micromechanics model . . . . . . . . . . . . . . . . . . . . . . 66

4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5 Laser annealing of amorphous Ni-Ti thin films 705.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705.2 Crystallization behavior of laser annealing process . . . . . . . . . . . 71

5.2.1 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.2.2 Processing window . . . . . . . . . . . . . . . . . . . . . . . . 735.2.3 Nucleation and growth kinetics . . . . . . . . . . . . . . . . . 735.2.4 Microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . 775.2.5 Shape memory behavior . . . . . . . . . . . . . . . . . . . . . 82

5.3 Thermal model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 865.3.1 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 865.3.2 Finite element modeling . . . . . . . . . . . . . . . . . . . . . 895.3.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 92

5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

6 Conclusions 1016.1 Summary and concluding remarks . . . . . . . . . . . . . . . . . . . . 1016.2 Suggestions for future work . . . . . . . . . . . . . . . . . . . . . . . 105

Bibliography 106

List of Figures

1.1 Schematic diagram of the region of shape memory effect and supere-lasticity effect. (from Otsuka and Wayman [1]) . . . . . . . . . . . . . 3

1.2 Phase diagram of Ni-Ti alloy system [2], to which the phase equilibriumbetween the B2 and Ni4Ti3 phases is added [3]. (from Otsuka andKakeshita [4]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Martensitic start temperature, Ms, as a function of Ni content forbinary Ni-Ti alloys. The solid line is from thermodynamic calculations.(from Tang [5]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4 Precipitation in Ti-rich Ni-Ti thin films heat-treated at various tem-perature for 1hr: (a) NiTi2 precipitates with random orientation; (b)NiTi2 precipitates with the same orientation as that of Ni-Ti matrix;(c) plate precipiates and oriented NiTi2 precipitates; (d) plate precipi-tates (high temperature form); (e) plate precipitates (low temperatureform); open circles indicate no precipitates and solid triangles indicatefilms are still amorphous after heat treatment. (after Kawamura et al[6]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1 A photograph of the inside of the sputter chamber. . . . . . . . . . . 152.2 (a) Thickness uniformity as a function of z-position of the substrate

holder and gun tilt angle. (b) Deposition rate of Cu film calculatedfrom mean thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3 RBS spectrum for the composition measurement (2 MeV He+ on a 60nm Ni-Ti film). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.4 The composition as a function of Ti gun power. . . . . . . . . . . . . 182.5 Scanning laser beam Radius of Curvature (ROC) system. Reprinted

from Ph.D. thesis of J. Mullin with permission. . . . . . . . . . . . . 192.6 Geometry of the curvature measurement for the ROC system. . . . . 20

3.1 Cross-sectional TEM images of partially crystallized Ni-Ti films: (a)Film thickness 200 nm; (b) Film thickness 800 nm. . . . . . . . . . . 27

vii

List of Figures viii

3.2 EDS line scans across amorphous layers at silicon nitride interfaces:(a) NiTi-LPCVD Si3N4 interface; (b) NiTi-PECVD SiNx interface. . . 29

3.3 (a) Cross-sectional TEM image of a partially crystallized 800 nm filmwithout PECVD SiNx capping layer; (b) EDS line scan across the filmsurface in (a). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.4 Cross-sectional TEM images of the Ni-Ti film with an artificial compo-sition inhomogeneity: (a) Nucleation occurs at film surface; (b) Twoheterogeneously nucleated grains impinged together upon growth. . . 31

3.5 Plan-view TEM image of a disk-shape Ni-Ti grain. . . . . . . . . . . 323.6 Optical micrographs of an 800 nm film subjected to multiple annealing

steps at 435 C: (a) 10 mins; (b) 13 mins; (c) 16 mins; (d) 19 mins.The times are total annealing time. Crystals have been demarcatedwith a white line to guide the eye. . . . . . . . . . . . . . . . . . . . . 34

3.7 AFM scans (dimension: 100x100 µm) of a 200 nm film subjected tomultiple annealing steps at 445 C: (a) 5 mins; (b) 7 mins; (c) 9 mins.The times are total annealing time. . . . . . . . . . . . . . . . . . . . 35

3.8 Crystal growth velocity in films with different thicknesses as a functionof temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.9 Apparent activation energy for crystal growth as a function of the Ni-Tifilm thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.10 Nucleation kinetics of the 800 nm Ni-Ti film at 435 C: (a) Number ofcrystals N obtained from size back-extrapolation. (b) Untransformedvolume fraction interpolated from the measurements after each anneal. 40

3.11 Arrhenius plots of the steady-state nucleation rate and the time lag in800 nm sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.12 Comparison between the activation energies determined in this workand those in the literature. . . . . . . . . . . . . . . . . . . . . . . . . 44

3.13 Average grain size for an 800nm Ni-Ti film as a function of isothermalannealing temperature. The solid line is calculated from Equation 3.8using the nucleation and growth rates in Table 3.4. . . . . . . . . . . 45

4.1 Microstructure of the 290 nm Ni-Ti thin film after 20 mins heat treat-ment at 450 C: (a) SEM image shows the average grain size is about15 µm; (b) Cross-sectional TEM image shows thin amorphous layersremain at both top and bottom interfaces. . . . . . . . . . . . . . . . 52

4.2 Residual stress in as-deposited amorphous Ni-Ti thin films. . . . . . . 534.3 Stress-temperature curves of Ni-Ti films on Si substrate: (a) With-

out subtracting contribution from SiNx film; (b) After subtracting thestress in SiNx layer, the residual stress of Ni-Ti film in martensitephase as a function of reciprocal film thickness; (c) After subtractingthe stress in amorphous Ni-Ti layers, the stress-temperature curve ofcrystalline Ni-Ti layer was obtained. . . . . . . . . . . . . . . . . . . . 56

List of Figures ix

4.4 (a) Film stress in the 910 nm film on different substrates as a functionof temperature; (b) Linear fits of stress drop curves upon cooling for allfilm thickness; The temperature values at the intersection with σ=400MPa in (b) are plotted in (c) for the demonstration of the size effect. 59

4.5 The low stress in the film on Corning glass substrate caused two-steptransformation. The inset is the thermal cycle history during the stressmeasurement. The open symbol in temperature profile corresponds tothe open symbol in stress data. . . . . . . . . . . . . . . . . . . . . . 60

4.6 Room temperature XRD of the 290 nm film shows the transformationis indeed complete at the end of the stress drop. . . . . . . . . . . . . 62

4.7 Stress-temperature curves of the 470 nm film treated with hydrogen.The behavior of the same film before the treatment is added for com-parison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.8 Energies associated with the transformation. . . . . . . . . . . . . . . 67

5.1 Optical micrograph of the film surface after laser annealing. . . . . . 745.2 Process window of Ni-Ti films as a function of laser power density and

scan speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745.3 Cross-section TEM image of a partially crystallized Ni-Ti film by laser

annealing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755.4 (a) Low magnification TEM image showing two sets of mutually per-

pendicular R-phase needle domains in a grain; (b) The electron diffrac-tion pattern taken from both the matrix and needle domains shows a[001]B2 type zone with two sets of 1/3 superlattice reflections along〈110〉∗B2; (c) HRTEM image taken from the crystal-amorphous inter-face, the trace of the interface marked by solid lines reveals a steppedgrowth interface along 100B2 and 110B2 planes. . . . . . . . . . . 76

5.5 Microstructure at the center of the laser trace. Scan speed is 4 mm/s,and laser power is (a)7.6 W (b) 8.2 W (c) 8.8 W respectively. The insetdiffraction pattern from dark grain in (a) shows [111]B2 type zone ofR-phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.6 Microstructure at various locations of the crystallized region (width ∼400 µm): (a) at the center; (b) approximately 100 µm away from thecenter; (c) approximately 200 µm away from the center. . . . . . . . . 78

5.7 Plan-view TEM images show the microstructure within the crystalline-amorphous boundary in Ni-Ti film after laser annealing. . . . . . . . 79

5.8 Room temperature XRD for a sample with multiple-line scan. . . . . 805.9 (a) TEM image of 〈011〉 type II twin as main microstructure of marten-

site in the laser annealed Ni-Ti films; (b) Electron diffraction patterntaken from the region in (a), incident electron beam //[110]M//[101]T . 80

5.10 110 pole figure of the laser annealed Ni-Ti film. . . . . . . . . . . . 82

List of Figures x

5.11 (a) Schematic illustration of parallel arrays of crystalline band pro-duced by multiple line scans; (b) Determine the stress in crystallineregion using Equation 5.1. . . . . . . . . . . . . . . . . . . . . . . . . 84

5.12 The stress-temperature curves along the RD (a,b) and TD (c,d) direc-tions for different crystallization fraction. (a) and (c) show the averagestress in the specimens; (b) and (d) show the stress in the crystallineregions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.13 Schematics of laser annealing experiment set-up. . . . . . . . . . . . . 885.14 Typical PSI measurement of the NiTi film surface after laser annealing. 935.15 (a) A typical dynamic measurement of the reflected laser power; (b)

Apparent reflectivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . 945.16 PSI measurement for high power laser beam. Vertical lines observed

in the crystallized region are measurement artifacts resulting from thepresence of the oxide layer that perturbs the interference pattern usedto measure the height profile. . . . . . . . . . . . . . . . . . . . . . . 96

5.17 Temperature contour in Ni-Ti film calculated from FEM (Parameters:P=3 W, v=4 mm/s, R=42%.). The laser moves from the right to theleft. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

5.18 (a) Temperature profile in Ni-Ti film at various locations away fromthe laser center; (b) Peak temperature and transformation fraction asa function of distance away from the laser center. . . . . . . . . . . . 98

5.19 Comparison between the predicted size of crystallized zone and exper-imental results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

List of Tables

3.1 Deposition conditions of PECVD SiNx film (Recipe: SiNINDX). . . . 243.2 Hydrogen plasma treatment conditons. . . . . . . . . . . . . . . . . . 383.3 The Arrhenius parameters for the nucleation of 400 nm and 800 nm

Ni-Ti films. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.4 The Arrhenius parameters for the crystallization of amorphous Ni-Ti

in the temperature range from 410 C to 445 C (taken from the 800nm film). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.1 Deposition conditions of PECVD SiNx film (Recipe: SiNLST). . . . . 504.2 Stresses in different layers of Ni-Ti thin films. . . . . . . . . . . . . . 57

5.1 Thermal properties of fused quartz substrate [7]. . . . . . . . . . . . . 915.2 Thermal properties of Ni-Ti at room temperature [8]. . . . . . . . . . 91

xi

Acknowledgments

Graduate life would not have been the same without the people who have gener-

ously helped me over the past six years. On this very page, I would like to express

my deep gratitude to them.

My first and foremost thanks go to my advisor, Prof. Joost Vlassak for his guid-

ance and encouragement these years. I am very fortunate to have been his advisee.

His continuous support and motivation bring this work to its fruition. He is generous

with his time and always available when I have questions about the research. A lot

of breakthrough in this thesis was inspired from our discussions. I have learned more

than knowledge from him. He told me doing research is not just collecting and inter-

preting the data, but finding the truth and presenting them logically to the academic

community. From his own experience as a non-native English speaker, he encouraged

me to speak English as much as possible. His dedication to perfection on polishing

paper helped me learn how to precisely and concisely write academic papers. So,

Joost, it has been a truly rewarding experience to work with you, and thanks for

everything.

I would also like to thank Prof. Frans Spaepen for being on my research committee

and for his invaluable suggestions and comments on my research. I first met him at

his AP282 course. I am from a mechanics background. This course opened the door of

materials science field to me. Not only the knowledge I learned from his lectures, but

also his way of thinking about materials science problems inspired me in particular.

Now the course is still one of the most favorite topics in the afternoon tea time.

I would like to thank Prof. John Hutchinson and Prof. Zhigang Suo for serv-

ing in my research committee and their invaluable suggestions and comments during

xii

Acknowledgments xiii

various stages of this work. I really enjoyed discussions with Prof. Mike Aziz about

crystallization kinetics and laser annealing process. I am also grateful to Prof. Shri-

ram Ramanathan for being in my defence committee, especially I asked him only two

weeks before the defence. His comments on my thesis is also appreciated.

I would like to express my gratitude to Prof. Yves Bellouard at Eindhoven Univer-

sity of Technology in the Netherlands and Dr. Zhenyu Xue for their contributions on

laser annealing study. I benefited immensely from Yves, who continually sent me lat-

est experimental results and exchanged thoughtful ideas with me. The collaboration

with him has been a truly fruitful experience.

I sincerely thank Warren MoberlyChan, who brought me to the TEM world. I still

keep the TEM lab report he graded. His comments are always valuable for improving

my TEM skills. I also appreciate the generous help from Cheng-Yen Wen, Vidya

Ramaswamy, David Bell and Anthony Garratt-Reed for TEM experiments.

I am also grateful for the help of many CIMS staffs: Frank Molea, John Chervin-

sky, Jiangdong Deng, Ling Xie, John Tsakirgis, Dave Lange, Richard Schalek, and

Yuan Lu.

Many thanks to the members in thin film mechanics group: Yong Xiang, Youbo

Lin, and Patrick McCluskey; and the members in materials science group: Hongtao

Wang, Anita Bowles, Alex Donohue, Bola George, Byungha Shin, Taeseok Kim,

Roxanne Su, Ingo Ramsteiner, Johannes Kalb, and many others.

The last but not the least, I want to thank my family. Especially, to my parents.

Their love has always been the impetus that motivates me to go this far. I wish my

father had lived to see me finish my Ph.D. as he always cared about my education.

Acknowledgments xiv

Also thanks to my sister and twin-brother. They have been taking care of my mom

since I left for USA. In particular, I want to say thanks to my wife, Jing Cao, and

my beloved son, Eric. I am very lucky to have met Jing and married her at Harvard.

She has been my constant support through graduate school. Eric is a gift. He brings

me a lot of happiness in the late stage of the graduate life. My family, I love you all

and dedicate this thesis to you.

Dedicated to my beloved family.

xv

Chapter 1

Introduction

The success of materials science and engineering is driven by the simultaneous

development of fundamentals and applications. Thin film technology is a good ex-

ample. Thin film technology has been through an explosive development due to its

wide applications in many engineering fields across a range of industries. More impor-

tantly, it also provides a unique opportunity to extend our understanding of material

physics at multiple length scales. This research is part of the project to develop

a basic understanding of the mechanisms that control the mechanical properties of

metal and alloy thin film systems. It is focused on Ni-Ti shape memory alloy thin

films and its martensitic transformation behavior. In the next section, the basics of

shape memory alloy will be discussed. Then the physical metallurgy of Ni-Ti alloys

is briefly reviewed. The objective and the organization of this work are given at the

end of this chapter.

1

Chapter 1: Introduction 2

1.1 Shape memory alloys

Shape memory alloys (SMAs) are a unique class of metallic materials that can ex-

hibit shape memory effect (SME) and superelasticity effect (SE). Shape memory effect

is a property where the material is initially deformed at low temperature and then

recovers its original shape upon heating. Superelasticity represents elastic recovery

of strains up to 10% during the loading-unloading cycle at appropriate temperatures.

Those phenomena have been well understood as the results of thermoelastic phase

transformation between a high temperature austenite phase and a low temperature

martensite phase [1].

The mechanism of the shape memory effect is described as follows. Upon cool-

ing, the austenite phase starts to transform to martensite at Ms (martensite start

temperature). Since the martensite phase has lower symmetry than the austenite

phase, martensites with the same structure but in different crystallographic orien-

tations (called variants of martensite) can be formed. For example, in B2 (cubic)

to B19’ (monoclinic) transformation of Ni-Ti alloy, as many as 12 correspondence

variants can be formed. Formation of martensite in the parent phase will cause a

large strain due to the fact that the martensitic transformation is associated with a

shape change. A combination of two or four variants may form in tandem to reduce

this strain and this particular morphology is called self-accommodation. Variants in

this morphology are twin-related to each other. Twins introduced upon martensitic

transformation can act as a deformation mode if a stress is applied, since the twin

boundary in Ni-Ti is mobile. This process is called detwinning as a favorably oriented

variant grows at the expense of other less favorable ones. The deformation remains


when the stress is released. Upon heating, the martensite variants revert to their

original orientations in the austenite phase so that the original shape is restored. Or-

dinarily the shape memory effect is one-way as only the shape of the austenite phase

is memorized.

Superelasticity at high temperatures is essentially due to a stress-induced marten-

sitic transformation. Once the stress is released, the martensite is unstable at high

temperature, thus the reverse transformation happens and the strain is recovered.

Figure 1.1 schematically show the conditions when those two phenomena occur. It

is important to avoid slip deformation in order to realize superelasticity. For this

purpose, the precipitation hardening in Ni-Ti alloys is of importance and will be

discussed further later.

M

Cri

tica

l Str

ess

to Ind

uce

Mar

tens

ite

Critical Stress for Slip

Shape Memory Effect

Superelasticity

M A A

Str

ess

Temperature

sf fs

Figure 1.1: Schematic diagram of the region of shape memory effect and superelas-ticity effect. (from Otsuka and Wayman [1])


Some physical properties, like electrical resistivity, change upon martensitic trans-

formation and their quantity as a function of temperature can be used to determine

the characteristic temperatures of martensitic transformation: Upon cooling, the

austenite phase starts to transform to martensite at Ms (martensite start temper-

ature) and it becomes fully martensite at Mf (martensite finish temperature); In

reverse, upon heating, the martensite start to transform to austenite at As (austenite

start temperature) and becomes fully austenite at Af (austenite finish temperature).

Transformation hysteresis exists between forward transformation and reverse trans-

formation.

1.2 Physical metallurgy of Ni-Ti alloy

Research on shape memory alloys became much more extensive after the effect

was found in Ni-Ti alloys. Since then Ni-Ti based alloys became the most important

practical SMAs thanks to their excellent mechanical properties, corrosion resistance

and biocapatibility.

1.2.1 Phase diagram

The phase diagram is important for heat-treatments of the alloys and improvement

of material properties. Figure 1.2 shows the phase diagram of Ni-Ti alloy system [2].

For shape memory properties, the research interests are focused on the central region

bounded by the NiTi2 and Ni3Ti phases. In the middle, there is the NiTi phase, which

is associated with the shape memory effect. Upon cooling from high temperature, the

NiTi phase has an disorder-order transition from BCC to B2 at 1090 C indicated by


a dotted line according to Honma et al. [9]. But a very recent work [10] suggested

that there is no such transition and the observations by Honma et al. are probably

due to a eutectic reaction in the oxidation-affected layer. The NiTi phase retains a B2

(CsCl) type ordered structure until low temperature where martensitic transformation

happens. The lattice constant of B2 phase is 0.3015 nm at room temperature [11].

The boundary of the NiTi phase region is almost vertical on the Ti-rich side, but

there is some solubility on Ni-rich side at high temperature. The NiTi phase region

becomes very narrow at temperatures below 650 C.

Figure 1.2: Phase diagram of Ni-Ti alloy system [2], to which the phase equilibriumbetween the B2 and Ni4Ti3 phases is added [3]. (from Otsuka and Kakeshita [4])


1.2.2 Martensitic transformation in Ni-Ti alloys

Quenching from high temperature may preserve the solid solution without precipi-

tation and quenched Ni-Ti alloys show a one stage B2-B19’ transformation [12, 13, 14,

15, 16, 17, 18, 19]. The composition dependence of the transformation temperature is

shown in Figure 1.3. The transformation temperature shows almost no dependence

on excess Ti content. This is probably due to the fact that vertical boundary of

the NiTi phase region makes it difficult to get supersaturated Ti in a Ni-Ti matrix.

Therefore Ti-rich alloys have a relatively consistent matrix as equiatomic alloy so the

similar transformation behavior is expected. Note that this is not necessarily true for

films. On the Ni-rich side, however, one percent of excess Ni atoms can change the

transformation temperature by more than 100 C. This composition dependence of

martensitic transformation temperature is related to the composition dependence of

the elastic constants of martensitic alloys [20].

Sometimes a second type of transformation called the R-phase transformation is

observed. It is characterized by a rapid increase of electrical resistivity upon cooling

with very small temperature hysteresis (e.g., 1∼2 C), and the appearance of 1/3

superlattice reflections along 〈110〉∗ and 〈111〉∗ directions of B2 phase in the reciprocal

lattice. There are usually three ways to introduce the R-phase transformation prior

to the transformation to B19’ phase [1] such that the Ni-Ti alloy transforms in two-

steps: i.e., B2 → R → B19’: (1) in Ni-rich Ni-Ti alloys aged at an appropriate

temperature to have the precipitate of Ni4Ti3; (2) in ternary Ni-Ti-Al and Ni-Ti-Fe

alloys where a few % of Ni is substituted by Al or Fe; (3) in near-equiatomic Ni-Ti

alloys treated thermo-mechanically. The two-step transformation also depends on the


Figure 1.3: Martensitic start temperature, Ms, as a function of Ni content for binaryNi-Ti alloys. The solid line is from thermodynamic calculations. (from Tang [5]).

applied external stress [21]. For lower stress, the R-phase transformation temperature

is higher than the B19’ transformation temperature but it exhibits a smaller stress

dependence. Therefore, with increasing stress the B19’ transformation temperature

eventually exceed the R-phase transformation temperature and this leads to one stage

transformation.

1.2.3 Crystal structure of martensite

Two kinds of martensite phases, B19’ martensite and R-phase, are observed in

martensitic transformation of Ni-Ti alloy. The crystal structure of B19’ marteniste has

been studied by several groups [22, 23, 24, 25, 26]. It is now generally accepted that


it has a monoclinic structure with a P21/m space group. Lattice parameters obtained

by single crystal X-ray diffraction for a Ti-49.2at.%Ni alloy are: a = 0.2898nm, b =

0.4108nm, c = 0.4646nm and β = 97.78 [26].

The term ”R-phase” originates from the rhombohedral distortion. Using a hexago-

nal lattice for convenience, the lattice parameters are: a = 0.738 nm and c = 0.532 nm

[27]. The space group of the R-phase has been controversial for many years. P31m,

P3 and P3 have been reported [27, 28, 29, 30]. A recent study in which a spheri-

cal sample was suspended on an air cushion during neutron diffraction suggested P3

symmetry [31].

1.2.4 Precipitation and its effect

Under appropriate heat treatment, precipitates can form from the excess atoms

in the solution and thus affect the transformation temperature and shape memory

properties of Ni-Ti alloys.

According to the phase diagram, Ni solubility changes from zero at 600 C to

about 6 at.% at 1000 C. So it is easy to obtain supersaturated Ni in the Ni-Ti

matrix by quenching and precipitate reaction can occur upon aging at relative low

temperature. Nashida et al. [18] clarified the precipitation process in the Ni-48at.%Ti

alloy using TTT diagram and revealed that there are other metastable precipitates

such as Ni4Ti3 and Ni3Ti2 besides the equilibrium Ni3Ti phase depending on aging

temperature and time. Among them, Ni4Ti3 is the most important precipitate to

improve shape memory characteristics of both bulk and thin film of Ni-rich alloy

[32, 33, 34, 35, 36]. For this purpose, a metastable phase equilibrium between the


NiTi phase and the Ni4Ti3 phase has been determined recently [3] and also included

in the phase diagram (Figure 1.2). As the precipitation reaction proceeds, formation

of Ni-rich precipitates is accompanied by a decrease of the Ni content of the Ni-Ti

matrix; therefore the transformation temperature tends to increase upon aging. The

size and coherency of precipitates affect the transformation and mechanical strength of

materials as well. The stress field around fine (i.e., high density) and coherent Ni4Ti3

precipitates facilitates R-phase transformation and suppresses B19’ martensite since

a large deformation is associated with B19’ transformation. The critical stress for

slip deformation increases due to precipitation hardening. The resistance on B19’

martensitic transformation becomes weak when the size of precipitates is larger (i.e.,

the density is lower) if the aging continues. But the mechanical strength decreases

accordingly. High temperature or low temperature late precipitation products, Ni3Ti2

and Ni3Ti, do not have interfacial coherency with the B2 matrix. But the incoherent

boundaries may be preferential nucleation sites for martensite.

In contrast, precipitation hardening cannot be used on the Ti-rich side in bulk

alloys due to the vertical solubility limit. However, it is a different story in thin films,

since sputter-deposited Ni-Ti films are amorphous if the substrate is not intentionally

heated and Ti can be supersaturated in amorphous Ni-Ti films. Ishida et al. [37]

studied microstructure of Ni-51.8at.%Ti films after annealing at temperatures from

500 to 700 C, and correlated to the shape memory behavior measured with ther-

momechanical tensile test. NiTi2 precipitates appear to be evenly distributed inside

the grains except that for prolonged annealing (e.g., 700 C for 100 hours) they form

at grain boundaries just like in the bulk. This means that the precipitate inside


the grain is not stable. Also in contrast to its bulk counterpart, two-stage transfor-

mation happens in annealed Ti-rich films except the prolonged annealed one. They

also found that martensitic transformation temperature increases with increasing an-

nealing temperature and time. Kawamura et al. [38, 39] studied the transformation

behavior of Ti-rich films (up to 53.2at.%Ti) using differential scanning calorimetry

(DSC) and found that the R-phase transformation temperature is constant for all Ti

compositions and insensitive to the annealing temperature while the B19’ transforma-

tion temperature decreases with increasing Ti content and increases with increasing

annealing temperature. A more recent study by Ishida et al. [40] using thermome-

chanical tensile test revealed similar results.

When a slightly Ti-rich thin films is annealed at relatively low temperature (e.g.

near the crystallization temperature), a thin plate precipitate, also called Guinier-

Preston (GP) zones, will form in the matrix at the early stage [41, 42, 43]. A more

complete investigation of microstructure evolution of Ti-rich films subjected to heat

treatment at various temperature was done by Kawamura et al. [6] and the results

are shown in Figure 1.4. Depending on the composition and annealing temperature,

precipitates of different orientation relationship with B2 matrix and different mor-

phology can be formed. As a result of the drastic change in microstructure, the

transformation temperature and transformation strain both show strong dependence

on composition and heat treatment as we discussed above.

It should be noticed that there is a composition range near equiatomic composi-

tion, where no precipitates appear. Ni-Ti films in our study fall into this composition

range since the goal of this project is to study the size effect and we do not want


Figure 1.4: Precipitation in Ti-rich Ni-Ti thin films heat-treated at various temper-ature for 1hr: (a) NiTi2 precipitates with random orientation; (b) NiTi2 precipitateswith the same orientation as that of Ni-Ti matrix; (c) plate precipiates and orientedNiTi2 precipitates; (d) plate precipitates (high temperature form); (e) plate precipi-tates (low temperature form); open circles indicate no precipitates and solid trianglesindicate films are still amorphous after heat treatment. (after Kawamura et al [6]).

to couple any effect from precipitates. We also want to stay at slightly Ti-rich side

to minimize the dependence of Ms on the composition. Therefore, it is critical to

precisely control the composition of the films and this will be discussed in Chapter 2.


1.3 The objective and outline of the thesis

The research on SMA thin films was initiated over the last decade when thin

film technology rapidly developed and started to be widely used in many engineer-

ing applications. SMA thin films are of technological interest as actuator materials

in microelectromechanical systems (MEMS) because they possess a large deforma-

tion and recovery force compared to other performance materials [1]. Several early

attempts were made to fabricate Ni-Ti thin films [44, 45, 46, 47, 48, 49] and build

Ni-Ti thin film based microactuator prototypes, such as micropumps and microvalves

[50, 51, 52, 53, 54], microgrippers [55, 56] and microsensors [57, 58].

To date, however, the number of microdevices using Ni-Ti thin films as actuators

is still limited. It is mainly due to the lack of understanding of the material physics

of this material at the micro- and nanoscales. The high degree of miniaturization of

current and future MEMS devices requires the application of very thin films. Hence,

it is important to understand how the transformation behavior changes with decreas-

ing film thickness. Moreover, it was reported that the shape memory properties of

the Ni-Ti alloys depend sensitively on their microstructure [59, 60, 61]. To control

the microstructure of the material, it is important to understand the crystallization

behavior of Ni-Ti films given the fact that the as-deposited films are usually amor-

phous. Researchers are also exploring new processing techniques for Ni-Ti films in

MEMS applications. The objective of the current work is to gain some insights on

those issues. The thesis is organized as follows. Chapter 2 briefly introduces the

experimental techniques used in this study. Chapter 3 discusses the crystallization

kinetics of Ni-Ti thin films. Chapter 4 focuses on size effect on the transformation


behavior of Ni-Ti films. Chapter 5 presents a novel laser annealing technique which

allows us to crystallize the specific region of the film. Finally we summarize the results

and explore the future research directions in Chapter 6.

Chapter 2

Experimental techniques

2.1 Film deposition process

2.1.1 Sputter system

Ni-Ti thin films were deposited by means of direct current (DC) magnetron sput-

tering. The depositions were performed in a model ATC 1800 sputter deposition

system from AJA international. A photograph of the inside of the main chamber is

shown in Figure 2.1. The substrate is facing down and the gun is sputtering up. The

chamber maintains a base pressure less than 5×10−8 Torr. The system is equipped

with three confocal sputter guns. Each gun can be controlled independently by a DC

power supply (Advanced Energy 500) with maximum power, current and voltage of

500 W, 1 A, and 1200 V, respectively. The deposition is regulated in power control

in this research. The angle between the substrate normal and the target normal can

be varied from 0 to 45 degree by tilting the gun. A radio frequency (RF) source for

14

Chapter 2: Experimental techniques 15

Figure 2.1: A photograph of the inside of the sputter chamber.

sputter-cleaning substrate prior to deposition is also installed in the system. The sub-

strate holder can hold the substrate up to 4 inch in diameter. The substrate holder is

connected with a vertical translator such that it can move up and down with a stroke

of approximately 2 inches. This movement is to change the substrate-target distance.

The substrate can also be rotated and heated during the deposition. The heating is

from the irradiation of two quartz lamps. The system has a load-lock chamber so that

it is not necessary to break the vacuum in the main chamber except when changing

targets.

2.1.2 Thickness uniformity and composition control

The deposition parameters are optimized in order to batch fabricate uniformly

thick and near-equiatomic Ni-Ti thin films over 4 inch wafer area in a reasonable

period of deposition time. The thickness uniformity is optimized by changing the


16 17 18 19 20 21 22 23 2401234567891011

Thic

knes

s un

iform

ity (%

)

Tilt angle of sputter gun (Degree)

z = 2" z = 2.625" z = 3.375"

(a)

16 17 18 19 20 21 22 23 2414

16

18

20

22

24

26

28

30

32

34

Dep

ositi

on ra

te (n

m/m

in)

Tilt angle of sputter gun (Degree)

z = 2" z = 2.625" z = 3.375"

(b)

Figure 2.2: (a) Thickness uniformity as a function of z-position of the substrate holderand gun tilt angle. (b) Deposition rate of Cu film calculated from mean thickness.

z-position of the substrate holder and the inclination of the sputter gun and carried

out with a copper target. During the deposition, the Ar gas pressure is 5 mTorr;

DC power is 200 W; and the substrate is rotated at a speed of 20 RPM. Thickness

uniformity is defined as the thickness variation across 4 inch wafer area divided by the

mean thickness. The results are shown in Figure 2.2(a). The deposition rate of Cu

film is calculated from the mean thickness and the results are shown in Figure 2.2(b).

Please note that the z-position of the substrate holder is the reading on a scale

outside the chamber. The z-position number increases when the substrate holder

moves down and the substrate-target distance decreases. A thickness uniformity of

2.3% is achieved for a gun tilt of 20 degree and a z-position of the substrate holder

at 3.375 inch. These two parameters were used for all the following Ni-Ti thin film

depositions. At this configuration, the nominal distance between the target and the

substrate is approximately 100 mm.


The Ni-Ti films were grown by co-sputtering from an equiatomic Ni-Ti alloy

(99.9% purity) and an elemental Ti target (99.995% purity). Both targets are ob-

tained from Kurt J. Lesker company. The composition of the films was controlled by

varying the power to individual guns. The composition is determined by Rutherford

Backscattering Spectroscopy (RBS) using 2 MeV He ions. The Ni-Ti film prepared

for composition calibration is approximately 60 nm thick. At this thickness, the

backscattering spectrum shows separate peaks for each elements (see Figure 2.3).

The ratio of Ni and Ti in the sample can be obtained with excellent resolution simply

by using the total number of counts under the peak corresponding to each element.

Figure 2.4 shows the composition as a function of the power for Ti gun when the Ar

pressure is 1.5 mTorr and the power for Ni-Ti gun is fixed at 200 W. The error bar

is from the measurements at different places across a 4 inch wafer area.

600 650 700 750 800 850 900

Channel

0

5

10

15

20

25

NormalizedYield

1.2 1.3 1.4 1.5 1.6 1.7

Energy (MeV)

NiTi

Figure 2.3: RBS spectrum for the composition measurement (2 MeV He+ on a 60 nmNi-Ti film).


50 60 70 80 9048.5

49.0

49.5

50.0

50.5

51.0

51.5

Com

posi

tion

(at.%

Ti)

Ti gun power (W)

Figure 2.4: The composition as a function of Ti gun power.

2.2 Stress measurement techniques

Stress in Ni-Ti films is a very important characteristic for the transformation

behavior. Stress in a thin film on substrate can be measured through the curvature

of the substrate. This technique relies on the work done originally by G.G. Stoney

in 1909 [62]. He first related the curvature of the substrate to the stress in a film

deposited on it and that relationship is called Stoney equation since then

κ =6σhf

YsH2s

(2.1)

where κ is the curvature of the substrate, σ is the stress in the film, Ys is the biaxial

modulus of the substrate, hf and Hs are the thickness of the film and the substrate

respectively.


Figure 2.5: Scanning laser beam Radius of Curvature (ROC) system. Reprinted fromPh.D. thesis of J. Mullin with permission.

Many tools have been developed and employed to measure the curvature of sub-

strates. For the transformation behavior of Ni-Ti films, the stress in films was mea-

sured as a function of temperature with a scanning laser beam technique. The radius

of curvature (ROC) system using this technique was built by A. Witvrouw [63] and

improved by J. Mullin [64]. The setup is illustrated in Figure 2.5. The sample sits

in a furnace and a laser scanning optical system measures the curvature. The prism

driven by stepper motor is used to scan the laser beam across the sample. The re-

flected beam is tracked by a position-sensitive detector. Figure 2.6 shows how the

translations of beam along the sample and on the detector are related to the sample

curvature. The sample has a radius of curvature R. The beam scans along the sample

(or the sample moves relative to the beam) with a distance x where sin α ≈ x/R.

The resulted displacement D of reflected beam on the detector at a distance L from


the sample is given by tan 2α = D/L. Under small angle approximation, combining

those two equations yielding

D/L ≈ 2α ≈ 2x/R (2.2)

So the curvature of the sample is

κ =1

R≈ D

2xL(2.3)

For this system, L is the focus length of the lens and is equal to 1 meter. Therefore,

the sample curvature is one half of the slope of detector vs. sample position curve.

R

xL

D

2α

α

sample

incident beam

reflected beam

R

L

sample

incident beam

reflected beam

Figure 2.6: Geometry of the curvature measurement for the ROC system.


2.3 Transmission electron microscopy (TEM)

Both plan-view and cross-sectional TEM samples were prepared and analyzed

to characterize the microstructure of Ni-Ti films. To prepare plan-view sample a

3 mm diameter disc was ultrasonically cut from thin film sample. The substrate

side of disc was ground away until the total thickness was about 150 µm. Then a

dimple grinder (Gatan model 656) was used to dimple the substrate side until the

thickness of the thinnest area was 10∼15 µm. The thin area was further thinned to

electron transparency by ion beam milling. To prepare the cross-sectional sample,

a thin film sample was glued between several bare Si substrate using epoxy. The

sandwich stacking was cut using a dicing saw into slices approximately 600 µm thick.

The slice was polished until the thickness is 10∼15 µm by tripod polishing (South

Bay Technology model 590). The thin cross-section foil was then transferred onto

a Cu-grid. Ion beam milling was conducted in a similar fashion as with the plan-

view sample. Samples were examined in a Philips 420 TEM operated at 100 kV and

JEOL 2010 FEG TEM operated at 200 kV. The quantitative composition analysis

was performed using a scanning transmission electron microscope (VG HB603 STEM)

equipped with an energy dispersive x-ray spectroscopy (EDS) detector.

Chapter 3

Crystallization kinetics of

amorphous Ni-Ti thin films

3.1 Introduction

The transformation behavior of a shape memory alloy depends sensitively on its

microstructure [59, 60, 61]. Ni-Ti thin films sputter-deposited at room temperature

are usually amorphous in their as-deposited state. This observation provides an

opportunity to control the microstructure and hence the transformation properties

by adjusting the crystallization conditions. Therefore, it is important to understand

the crystallization kinetics of this material. The crystallization of Ni-Ti has been

characterized as polymorphic with continuous nucleation and growth throughout the

crystallization process based on in-situ TEM studies [65, 66]. In this work, systematic

measurements of the crystal nucleation rate and growth velocity as a function of

temperature were performed for Ni-Ti films. From classic transformation theory, it

22

Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 23

is well known that those two quantities are essential to the definition of the final

microstructure, in that they determine the grain size of the material.

Ni-Ti thin films can be processed using conventional clean-room processes and

can be deposited on a variety of substrates making them attractive for MEMS ap-

plications. The high degree of miniaturization of current and future MEMS devices

requires the application of very thin films. Therefore, it is essential to understand the

crystallization kinetics and the resulted microstructure of this material when the film

thickness varies. More generally, size effect in crystallization of amorphous materials

is of practical and theoretical interest. It was demonstrated that in thin layers of

SbTe alloy used for optical recording, the crystallization speed can be thickness de-

pendent [67, 68]. Theoretical studies of phase transitions in confined two-dimensional

systems suggest that finite film thickness leads to important consequences in both

volume-induced crystallization and surface-induced crystallization [69, 70].

In the present study, we used a combined approach of annealing in a high-precision

furnace and microscopic tracking of individual crystallites to determine the temper-

ature dependence of the crystal nucleation rate and growth velocity in amorphous

Ni-Ti thin films. This approach was first developed by Kalb et al. [71] for the study

of thin films of amorphous Te alloys. Optical microscopy was used in this study pre-

dominantly because it provides much better statistics than atomic force microscopy

(AFM): AFM scan size is limited to 100×100 µm, while crystals can be as large as

80 µm under certain conditions.


Table 3.1: Deposition conditions of PECVD SiNx film (Recipe: SiNINDX).

Base pressure (Torr) 1×10−7

Working pressure (mTorr) 10Ar (sccm) 20N2 (sccm) 5.8

SiH4 (sccm) 55Microwave (W) 265

Deposition rate (A/s) 1.1

3.2 Experiments

The samples studied are stacks consisting of three thin film layers on Si substrates.

First an 80 nm thick Si3N4 layer was grown on Si (100) substrate using low-pressure

chemical vapor deposition (LPCVD). Next the Ni-Ti layer was deposited by means of

DC magnetron sputtering. The stack was finished with a 30 nm thick SiNx layer using

plasma-enhanced chemical vapor deposition (PECVD) to prevent excessive oxidation

of Ni-Ti films during heat treatments. During the Ni-Ti deposition, the Ar working

pressure was 1.5 mTorr. The thickness of Ni-Ti layer is varied from 200 to 1500 nm.

The composition of the films was measured to be 50.5±0.2 at.%Ti using RBS. X-ray

diffraction (XRD) and high-resolution TEM (HRTEM) confirmed that the structure

of the as-deposited films was entirely amorphous. The PECVD SiNx film was prepared

with a NEXX Cirrus-150 system. The deposition conditions are listed in Table 3.1.

The samples were annealed isothermally in a furnace of a Perkin-Elmer Pyris 1

differential scanning calorimeter (DSC) in a flowing argon atmosphere. The samples

were cut into small square pieces of 4×4 mm to fit into the DSC furnace (dimensions:

9 mm diameter × 4 mm height). The heating rate was 500 C/min and there was no

overshoot on approaching the final temperature. The temperature uncertainty during


annealing was less than 0.1 C. Samples were annealed isothermally at temperatures

ranging from 410 to 445 C. After annealing for a certain period of time, each sample

was investigated using optical microscopy (Nikon Eclipse ME600L) or AFM (Digital

Instruments 3100). The sample was then returned to the furnace and annealed at

the same temperature for an additional period of time, followed by observation under

the microscope at the exact same location. This annealing/observation process was

repeated until each sample was fully crystallized. The isothermal crystal growth

velocity was determined by measuring the increase in diameter of specific crystals

from subsequent micrographs. The nucleation parameters were determined based on

the back-extrapolation method developed by Koster and Blanke [72]. The time of

nucleation for each crystal was back-extrapolated by measuring its size at the end of

the heat treatment and using the growth kinetics determined.

The samples with a Ni-Ti thickness of 400 nm or above were examined using op-

tical microscopy, while the 200 nm samples were examined using AFM. Due to the

densification that takes place upon crystallization, the film thickness can be reduced

by as much as 5%, enabling direct observation of the crystallites using optical mi-

croscopy as light scatters from the crystallite boundaries. Moreover, the surface relief

caused by the martensitic phase transformation inside crystalline particles makes it

straight forward to distinguish the crystallites from the amorphous matrix. When

the film thickness is small, however, the thickness reduction is relatively small and

the martensitic transformation is suppressed, thus it is difficult to make the obser-

vation under optical microscopy and AFM in tapping mode was used instead. The

temperature dependence of growth velocity were investigated for all film thicknesses


while the temperature dependence of nucleation rate were measured for 400 and 800

nm films.

3.3 Results and discussion

3.3.1 Crystal morphology

Figure 3.1 shows cross-sectional TEM images of partially crystallized films of

thickness 200 nm and 800 nm. The crystal is disk-shaped and is much longer later-

ally than in the through-thickness direction. A closer look at the image shows that

the crystal has not yet reached the substrate interface or the film surface and thin

amorphous layers remain at these locations. This indicates that the crystal nucle-

ates inside the film; heterogeneous nucleation at the film-substrate interface and the

film surface did not occur. The amorphous layer is approximately 15∼20 nm at the

NiTi-PECVD SiNx interface, and approximately 10 nm at the NiTi-LPCVD Si3N4

interface. The thickness of those amorphous layers is independent of the Ni-Ti film

thickness, which indicates that it is caused by the same mechanism. At higher mag-

nification, another layer which is approximately 5 nm thick can be observed at the

NiTi-PECVD SiNx interface. This layer is very likely titanium oxide according to the

composition analysis below. EDS line scans were performed on the amorphous layers

at the interface with the silicon nitride. Figure 3.2 show the EDS line scans across

NiTi-LPCVD Si3N4 interface and NiTi-PECVD SiNx interface respectively. At both

interfaces, the Ti signal rises earlier than the Ni signal when the STEM probe goes

into the NiTi layer, indicating there is a Ti-rich layer at the interface. From the line


(a) (b)

Figure 3.1: Cross-sectional TEM images of partially crystallized Ni-Ti films: (a) Filmthickness 200 nm; (b) Film thickness 800 nm.

scan profile, the thickness of this Ti-rich layer is estimated to be approximately 4

nm at the NiTi-PECVD SiNx interface and 1.5 nm at NiTi-LPCVD Si3N4 interface.

From Figure 3.2(b), there is also a significant amount of oxygen at the PECVD SiNx

interface, which suggests that the thin Ti-rich surface layer consists of titanium oxide.

The Ti-rich at the interface should be accompanied by a Ti-depletion region next to

it. The Ti depletion region is about 10∼15 nm at NiTi-PECVD SiNx interface which

is about 3 times of Ti-rich layer. The Ti depletion is not obvious at NiTi-LPCVD

Si3N4 interface most likely because the Ti-rich layer is much thinner there. We argue

here that the absence of heterogeneous nucleation in these films is a result of the

composition shift at those interfaces. The crystallization temperature of amorphous

Ni-Ti alloy increases with increasing Ni concentration around near-equiatomic com-


position [73, 74, 75]. Consequently, nucleation takes place homogenously inside the

film. To verify this mechanism, two experiments were conducted. In the first one, an

800 nm film without PECVD SiNx capping layer was annealed in a vacuum furnace.

Figure 3.3(a) shows cross-sectional TEM image of this film which is partially crystal-

lized. The oxidation was enhanced due to the lack of capping layer even though it

was annealed in the vacuum. EDS line scan across the film surface was performed on

this cross-sectional TEM sample and shown in Figure 3.3(b). The enhanced oxidation

caused a Ti depletion region of thickness approximately 50 nm. The resulted crystal

morphology is the same as shown in Figure 3.1(b) which suggests the composition

shift is the mechanism. In the second experiment, an 800 nm film with an artificial

composition inhomogeneity was prepared. During the deposition of the Ni-Ti layer,

the power of Ti gun was varied on purpose such that the first 100 nm Ni-Ti at LPCVD

Si3N4 interface and the last 100 nm at PECVD SiNx interface are 52.0 at.%Ti and

the 600 nm in the middle remains at 50.5 at.%Ti. Cross-sectional TEM on this film

(Figure 3.4) showed that crystals nucleate heterogeneously at the interface. The sig-

nificant change in nucleation and crystal morphology indicates that composition plays

an important role in the crystallization behavior of Ni-Ti thin films.

The morphology of the crystals indicates that the nuclei quickly consume most

of the film thickness, and then transition to a two-dimensional growth mode. This

results in the disk-shaped grains observed in plan-view TEM image (Figure 3.5).

Some crystals are nearly circular, while others show slight shape anisotropy. The

shape anisotropy is due to a slight orientation dependence of the growth velocity

and whether it can be observed depends on the orientation of the grain. EDS line


0 10 20 30 40 50 60

0

20

40

60

80

100

120

140

160

180

Cou

nts

(arb

.u.)

Distance (nm)

Nitrogen Oxygen Silicon Titanium Nickel

~1.5nm

LPCVDSi3N4

NiTi

(a)

0 10 20 30 40 50 60 70 80

0

20

40

60

80

100

120

140

160

180

200

PECVDSiNx

Cou

nts

(arb

.u.)

Distance (nm)

Nitrogen Oxygen Silicon Titanium Nickel

NiTi

~4nm

(b)

Figure 3.2: EDS line scans across amorphous layers at silicon nitride interfaces: (a)NiTi-LPCVD Si3N4 interface; (b) NiTi-PECVD SiNx interface.


(a)

0 10 20 30 40 50 60 70 80 90 100

0

50

100

150

200

250

300

350

400

Cou

nts

(arb

.u.)

Distance (nm)

Oxygen Titanium Nickel

Ti OxideTi-depletion region

(b)

Figure 3.3: (a) Cross-sectional TEM image of a partially crystallized 800 nm filmwithout PECVD SiNx capping layer; (b) EDS line scan across the film surface in (a).


(a) (b)

Figure 3.4: Cross-sectional TEM images of the Ni-Ti film with an artificial composi-tion inhomogeneity: (a) Nucleation occurs at film surface; (b) Two heterogeneouslynucleated grains impinged together upon growth.

scans were also performed across the growth front in cross-sectional TEM samples.

Within the resolution of the STEM (a few nanometers), no composition change across

the crystalline-amorphous interface could be observed, which indicates the growth is

interface-controlled.

3.3.2 Growth kinetics

Figure 3.6 shows a series of optical micrographs for an 800 nm film annealed at

435 C. Figure 3.7 shows a series of AFM scans for a 200 nm film annealed at 445

C. While existing crystals are growing, new nuclei appear at random locations in

the untransformed regions throughout the crystallization process. The isothermal

growth velocity was determined by measuring the diameter of grains in subsequent


Figure 3.5: Plan-view TEM image of a disk-shape Ni-Ti grain.


micrographs. Over the entire temperature range investigated, the isothermal growth

velocity was observed to be time-independent for all film thicknesses. The time-

independence implies that the growth was interface-controlled, in agreement with

the observation that there is no composition change across the growth front. The

isothermal growth velocity, however, strongly depends on film thickness at a given

temperature. It decreases when film thickness decreases in the temperature range

investigated. Figure 3.8 is an Arrhenius plot of the crystal growth velocities for all

film thicknesses studied. There is no measurable difference when the film thickness

changes from 1500 nm to 800 nm. The growth velocity starts to decreases when

the film thickness is below 600 nm. The deviation is not linear which results in an

increase in the apparent activation energy for crystal growth as shown in Figure 3.9.

This result is unexpected because the activation energy of an interface-controlled

growth process should not depend on the film thickness.

The composition shift can slow down the growth because it requires long range

diffusion to grow near-equiatomic NiTi phase out of composition shifted matrix. From

Figure 3.1 and Figure 3.2, the composition shift affected zones are only at the inter-

faces, while the bulk of the film has the same composition as the as-deposited film.

The film thickness dependence of crystal growth velocity in Figure 3.8 cannot be

attributed to the composition shift and must due to another cause.

Compare Figure 3.1(a) and Figure 3.1(b), the growth front is more curved in

thinner films. The curvature induced driving force is on the order of κγVm where κ

is the interface curvature, γ is the interface energy and Vm is the molar volume of Ni-

Ti. From Figure 3.1(a), the radius of curvature in the 200 nm film is approximately


(a) (b)

(c) (d)

Figure 3.6: Optical micrographs of an 800 nm film subjected to multiple annealingsteps at 435 C: (a) 10 mins; (b) 13 mins; (c) 16 mins; (d) 19 mins. The times aretotal annealing time. Crystals have been demarcated with a white line to guide theeye.


(a) (b)

(c)

Figure 3.7: AFM scans (dimension: 100x100 µm) of a 200 nm film subjected tomultiple annealing steps at 445 C: (a) 5 mins; (b) 7 mins; (c) 9 mins. The times aretotal annealing time.


16.0 16.2 16.4 16.6 16.8 17.0-8.0-7.5-7.0-6.5-6.0-5.5-5.0-4.5-4.0-3.5-3.0-2.5

Ln(u

) [gr

owth

vel

ocity

, u in

m

/s]

1/(KBT) (eV-1)

200 nm 400 nm 600 nm 800 nm 1500 nm

Figure 3.8: Crystal growth velocity in films with different thicknesses as a functionof temperature.

0 200 400 600 800 1000 1200 1400 16002.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

App

aren

t act

ivat

ion

ener

gyfo

r cry

stal

gro

wth

, Eg (e

V)

Film thickness (nm)

Figure 3.9: Apparent activation energy for crystal growth as a function of the Ni-Tifilm thickness.


50 nm. Take γ = 1 J/m2 and Vm = NAΩ = 1.6×10−5 m3/mol for Ni-Ti, κγVm =

0.32 kJ/mol, which is too small to explain the change in activation energy with film

thickness. The other effect is from the stress. The stress due to the densification

of crystalline phase can be very large locally. The energy associated with stress is

σεθVm where εθ is the volume strain upon crystallization. This energy is 1.6 kJ/mol

for σ = 1 GPa and εθ = 10%, which is very small too. Consequently neither curvature

nor stress can explain the thickness dependence of the crystal growth velocity. One

possibility remained is the hydrogen present in silicon nitride films. It is well known

that PECVD SiNx thin film contains a non-neglected amount of hydrogen coming

from its reactant and LPCVD Si3N4 has less [76]. And hydrogen is known to diffuse

very quickly in Ni-Ti alloys [77]. It has also been reported that hydrogen affects the

crystallization process of amorphous Ni-Ti alloys [78]. To study the effect of hydrogen

on the crystallization behavior, one more step was added in the sample preparation

to introduce hydrogen into the Ni-Ti films. Film with a thickness of 400 nm was

used in this experiment. After the deposition of the Ni-Ti layer, the sample was

treated with a hydrogen plasma in a Unaxis Shuttleline Inductive Coupled Plasma

(ICP) reactor. The plasma treatment conditions are listed in Table 3.2. After the

treatment, a 30 nm PECVD SiNx was grown on top of the Ni-Ti as before. XRD

confirmed that the structure of hydrogen treated film was still amorphous. The

treated sample underwent multiple annealing at 445 C. It was found that the crystal

velocity is approximately 5×10−3±3×10−4 µm/s, which is approximately seven times

lower than the untreated sample (0.033±0.002 µm/s). The measurement was repeated

on several treated samples, with very consistent results. The untreated samples were


Table 3.2: Hydrogen plasma treatment conditons.


H2 working pressure (mTorr) 5ICP power (W) 800RF power (W) 100DC Voltage (V) 125

Stage temperature(C) 25Time (s) 30

cut from the area right next to the treated samples on the same substrate so that the

composition variation from sample to sample would be too small to cause a significant

change in growth velocity. This experiment suggests that the hydrogen may be the

cause of the film thickness dependence of the crystal growth velocity. The hydrogen

in the silicon nitride film may diffuse into the Ni-Ti film upon high temperature

annealing. Because in this scenario, hydrogen diffuses into the Ni-Ti film from the

interfaces, it is evident that the effect of hydrogen increases with decreasing Ni-Ti

film thickness. Consequently, the growth velocity decreases when the film thickness

decreases. The 1500 nm and 800 nm films show no measurable difference which

indicates that the hydrogen content is too low to affect the growth in those films.

Therefore, it implies that the growth velocities in 1500 nm and 800 nm films are

close to the ”real” value. The fitting parameters obtained from the Arrhenius fit in

Figure 3.8 for the 800 nm film are listed in Table 3.4. The precise mechanism how

hydrogen affects the growth is not clear at this point and needs further investigation.


3.3.3 Nucleation kinetics

Figure 3.10(a) shows the number of crystals in a 800 nm film as a function of

time for crystallization at 435 C. The results were obtained using the crystal size

back-extrapolation, the validity of which is justified by the TEM observations (see

section 3.3.1). Each particle arises from one nucleation center, no multi-grain clusters

are observed as in Ti50Ni25Cu25 melt-spun ribbon [79]. The number of crystals is

normalized per unit volume because crystals nucleate homogenously in the film. The

error bar on the last data point is the same for all other points and is from the

measurement uncertainty of crystal diameters, i.e., it denotes the uncertainty in the

time when a specific crystal is nucleated. The number of crystals is initially extremely

small, but increases almost linearly after an incubation period. It implies that the

nucleation rate quickly reaches the steady-state. New crystals only nucleate in the

untransformed fraction of the film. Therefore the nucleation rate I(t) was obtained

from

I(t) =1

1− χ(t)

dN(t)

dt(3.1)

where N(t) is the crystal number per unit volume in Figure 3.10(a) and the crystalliza-

tion fraction χ(t) at time t was obtained by interpolating the measured crystallization

fractions after each anneal and is shown in Figure 3.10(b). The time lag τ is defined

as the initial transient period before the steady-state nucleation rate Iss is reached.

The Arrhenius graphs of the steady-state nucleation rate and the time lag for the

800 nm film are shown in Figure 3.11. Similar procedure was done on the 400 nm

film. The corresponding Arrhenius parameters for both 400 nm and 800 nm films are

listed in Table 3.3. The nucleation kinetics parameters are the same for 400 nm and


0 100 200 300 400 500 600 700 800 900 10000

1

2

3

4

5

6

7

8

N (

m-3)

Time (s)

(x10-4)

Incubation time

(a)

0 100 200 300 400 500 600 700 800 900 10000.0

0.2

0.4

0.6

0.8

1.0

1 -

Time (s)

(b)

Figure 3.10: Nucleation kinetics of the 800 nm Ni-Ti film at 435 C: (a) Number ofcrystals N obtained from size back-extrapolation. (b) Untransformed volume fractioninterpolated from the measurements after each anneal.


16.0 16.2 16.4 16.6 16.8 17.0 17.2-18

-17

-16

-15

-14

-13

-12

-11

ln(I ss

) [N

ucle

atio

n ra

te, I

ss in

m

-3s-1

]

1/(KBT) (eV-1)

En=5.72+/-0.14 eV

E =3.03+/-0.31 eV

4

5

6

7

8

ln() [Tim

e lag, in seconds]

Figure 3.11: Arrhenius plots of the steady-state nucleation rate and the time lag in800 nm sample.

Table 3.3: The Arrhenius parameters for the nucleation of 400 nm and 800 nm Ni-Tifilms.

400 nm 800 nmNucleation rate Iss ln(I0) = 81.66± 7.28 ln(I0) = 80.29± 1.09

(I0 in µm−3s−1) En = 5.83± 0.44 eV En = 5.72± 0.14 eVTime-lag τ ln(τ0) = −48.37± 9.86 ln(τ0) = −44.06± 5.12(τ0 in s) Eτ = 3.32± 0.59 eV Eτ = 3.03± 0.31 eV

800 nm films within measurement uncertainty, i.e., unlike the growth kinetics, they

do not show any thickness dependence. Therefore, the nucleation kinetics parameters

from both 400 nm and 800 nm films are close to the ”real” value. The fitting param-

eters obtained from the Arrhenius fit in Figure 3.11 for the 800 nm film are listed in

Table 3.4.

According to classical nucleation theory, the activation energy En for the steady-


Table 3.4: The Arrhenius parameters for the crystallization of amorphous Ni-Ti inthe temperature range from 410 C to 445 C (taken from the 800 nm film).

Growth velocity u ln(u0) = 47.25± 0.89 (u0 in µm/s) Eg = 3.12± 0.05 eVNucleation rate Iss ln(I0) = 80.29± 1.09 (I0 in µm−3s−1) En = 5.72± 0.14 eV

Time-lag τ ln(τ0) = −44.06± 5.12 (τ0 in s) Eτ = 3.03± 0.31 eV

sate nucleation process is given by

En = ∆Gc + Eg (3.2)

where ∆Gc is the energy barrier for the formation of a critical nucleus and Eg is the

activation energy for growth. Since TEM observations indicate that nucleation occurs

homogeneously, the nucleation barrier for homogenous nucleation in near-equiatomic

Ni-Ti is estimated as En-Eg=2.60±0.19 eV.

The activation energies obtained in this study are compared to literature data

for both bulk Ni-Ti [73, 80, 81] and thin films [82] in Figure 3.12. Most activation

energies in the literature are measured using DSC and represent for the overall crys-

tallization process, i.e., they do not distinguish between nucleation and growth. The

activation energy of the overall process in bulk materials can be estimated from the

present activation energies for nucleation and growth in two dimensions in the follow-

ing manner. The transformed fraction in an isothermal phase transformation can be

conveniently represented by the Johnson-Mehl-Avrami (JMA) model [83] using the

following equation:

χ(t) = 1− exp(−kctn

) (3.3)

where kc is the rate constant and n is the Avrami exponent. In the Avrami method,

the crystallization activation energy is determined from an Arrhenius relationship of


the form

t0.5 = t0 exp(

Ea

kBT

)(3.4)

where t0.5 is the time for 50% crystallization and Ea is the apparent activation energy.

From Equation 3.3, it follows that

t0.5 =(

0.7

kc

)1/n

(3.5)

If the crystals nucleate continuously at a constant rate I throughout the transforma-

tion and grow as spheres at a constant rate u, the rate constant kc = πIu3/3 and the

Avrami exponent n = 4. Equation 3.5 can then be written as

t0.5 =0.9

I1/4u3/4(3.6)

According to this equation, the activation energy for the overall crystallization process

in bulk materials is related to the present activation energies for nucleation and growth

by

Ea =1

4En +

3

4Eg (3.7)

As shown in Figure 3.12, this value (Ea = 3.77±0.07 eV) is indeed in very good

agreement with the literature data.

3.3.4 Tailoring the microstructure

The results of the kinetics study suggest that the microstructure of the films

should be well represented by the Johnson-Mehl model for thin film growth [84, 85].

This model applies to two-dimensional microstructures that are formed when the

nucleation and growth rates are constant. According to this model, the average


40 45 50 55 60 65 70 75 802

3

4

5

6

7

Ti content (at.%)

Act

ivat

ion

ener

gy (e

V)

Buschow (1983) Seeger (1994) Buchwitz (1993) Chen (2001) This work The fitting curve

of Buschow results

En

Ea

Eg

Figure 3.12: Comparison between the activation energies determined in this work andthose in the literature.

grain diameter at impingement can be written as a function of the two-dimensional

nucleation and growth rates

d = 1.203(

u

I2d

)1/3

(3.8)

assuming grain boundaries are immobile after impingement. Figure 3.13 compares

experimental grain sizes and the values calculated from Equation 3.8 using the nu-

cleation and growth rates in Table 3.4. Very good agreement is achieved between

experiments and the model with only a slight deviation at low crystallization tem-

peratures. This deviation can be attributed to the long incubation times observed

at low temperatures. Any grains that nucleate during the incubation time can grow

significantly before other grain nucleate, resulting in a larger average grain size. It is

evident from the results in Figure 3.13, that the microstructure of near-equiatomic


400 420 440 460 480 5000

10

20

30

40

50

60

70

Ave

rage

gra

in s

ize

(m

)

Temperature (oC)

Film thickness 800nm Experimental measurement Johnson-Mehl model

Figure 3.13: Average grain size for an 800nm Ni-Ti film as a function of isothermalannealing temperature. The solid line is calculated from Equation 3.8 using thenucleation and growth rates in Table 3.4.

Ni-Ti films is readily tailored by manipulating the nucleation and growth rates: the

average grain size of an 800 nm Ni-Ti film can be varied from less than 5 µm to

as large as 60 µm depending on the precise crystallization temperature. Given an

appropriate heat treatment and in-plane film layout, it may even be possible to grow

single crystal films.

3.4 Conclusions

In conclusion, we have used an approach based on precise furnace annealing and

optical microscopy or AFM to measure for the first time the temperature dependence

of the nucleation and the growth processes for the crystallization of amorphous near-


equiatomic Ni-Ti thin films sandwiched between two SiNx layers. Crystallites are

shown to nucleate homogeneously in the film and to grow with an interface-controlled

mechanism. We propose that the reaction between Ni-Ti and surrounding layers

results in a small composition shift at these interfaces and suppresses heterogeneous

nucleation at these interfaces. As a result, the nucleation and crystal morphology can

be controlled by introducing composition inhomogeneity into the film. The crystal

growth velocity shows a film thickness dependence and is much slower in thinner

films. We propose that hydrogen present in the SiNx layer diffuses into Ni-Ti films

upon annealing to cause a significant decrease of crystal growth velocity. The effect of

hydrogen on the growth velocity was demonstrated with a hydrogen plasma treated

sample. Unlike the growth kinetics, the nucleation in the 400 nm film is not affected

by hydrogen present in the SiNx layer. By manipulating nucleation and growth rates,

unprecedented control over the microstructure of the films is possible. The nucleation

and growth kinetics parameters determined in this work are useful for modeling the

crystallization behavior of Ni-Ti thin films (see an example in Chapter 5).

Chapter 4

Size effects in martensitic

transformation behavior

4.1 Introduction

Effective design of MEMS structures requires knowledge of the constitutive be-

havior of the shape memory alloy films used in the device. In polycrystalline films,

transforming grains are constrained by the surrounding grains and the substrate, if

present. Any constitutive model has to account for this effect if it is to describe the

behavior of polycrystalline shape memory alloy films quantitatively. Unfortunately,

there is not much experimental data available on the behavior of shape memory alloy

thin films in the submicron region. This chapter will focus on the effect of film thick-

ness on the martensitic transformation in Ni-Ti thin films supported by a substrate.

The shape memory behavior of a Ni-Ti film is usually studied by applying a load

to the film and thermally cycling it [37, 40, 86, 87, 88]. This technique was used

47

Chapter 4: Size effects in martensitic transformation behavior 48

to study the effect of film thickness by Ishida and Sato [88]. Unfortunately, this

approach requires testing of freestanding films, which becomes increasingly difficult

with decreasing film thickness. Substrate curvature and electrical resistance measure-

ments can overcome this limitation and the film thickness can be in the nanometer

range [48, 89, 90, 91]. These techniques only work for films on substrates, however,

and the effect on the martensitic transformation of the residual stress in the film

must be considered. Furthermore, sputter-deposited Ni-Ti films are often amorphous

as-deposited and need to be crystallized at high temperature either during deposi-

tion or in a post-deposition anneal [47]. If the films are very thin, surface oxidation

and interfacial reactions between film and substrate that may occur during the heat

treatment, cannot be neglected. Thus, studying the shape memory behavior of very

thin films using these techniques is a real challenge. In this investigation, we have

tried to overcome some of the issues associated with the substrate curvature tech-

nique and used the technique to evaluate the effect of film thickness and stress in

near-equiatomic Ni-Ti films.

4.2 Experiments

Amorphous Ni-Ti thin films with thicknesses from 200 to 900 nm were deposited

at room temperature by means of DC magnetron sputtering. The Ar working pres-

sure was 1.5 mTorr. The composition of the films was measured to be 50.5± 0.2at.%

Ti using RBS. In order to control the residual stress in the Ni-Ti films, the films

were deposited on four different types of substrates: fused quartz and Si (100) sin-

gle crystal, Pyrex 7740 glass and Corning 0211 glass. Each of these materials has a


different thermal expansion coefficient and results in a different residual stress in the

Ni-Ti films after thermal treatment. Prior to the Ni-Ti deposition, all substrates were

coated with a 50 nm PECVD SiNx to ensure that the substrate surfaces presented to

the Ni-Ti were identical for the different types of substrates. Immediately after the

Ni-Ti deposition, a second layer of SiNx (∼30 nm) was coated onto the Ni-Ti film

surface to prevent oxidation of the films. The SiNx films were deposited with a NEXX

Cirrus-150 PECVD system. The deposition conditions are listed in Table 4.1. The

as-deposited NiTi films were crystallized by annealing at 450 C for 20 minutes in a

vacuum furnace with a base pressure of less than 5x10−7 Torr. During these anneals,

the SiNx coatings prevented reaction between the Ni-Ti and the underlying substrate

and the oxidation of the film. It is well recognized that the interfacial reaction in the

NiTi/SiNx system is significantly reduced compared to the reaction in the NiTi/Si

system under the same annealing conditions [92]. On cooling, the thermal mismatch

between the Ni-Ti films and the substrates resulted in different stress levels in Ni-Ti

films deposited on different substrates. The martensitic transformation behavior of

the thin films was investigated by measuring the film stress as a function of tem-

perature using the substrate curvature technique. Specimens were dipped in liquid

nitrogen for 5 minutes and allowed to come back to room temperature prior to the

stress measurements to insure that the Ni-Ti films were in the low-temperature phase.

The specimens were then cycled between 15 and 120 C in a He atmosphere, while

the curvature of the substrates was measured using a scanning laser beam. Stoney’s

equation [93] was used to calculate the film stress from the change in curvature. The

biaxial moduli of the substrates used in Stoney’s equation were 90.5, 180.8, 80.0 and


Table 4.1: Deposition conditions of PECVD SiNx film (Recipe: SiNLST).


Working pressure (mTorr) 10Ar (sccm) 20N2 (sccm) 5.8

SiH4 (sccm) 40Microwave (W) 265

Deposition rate (A/s) 1.1

97.3 GPa for fused quartz, silicon, Pyrex glass and Corning glass respectively. The

stress levels in the PECVD SiNx layers in both the as-deposited state and after heat

treatment were determined from separate samples without Ni-Ti. The microstruc-

ture of the annealed films was determined using scanning electron microscopy (SEM)

and transmission electron microscopy (TEM). The phase composition of the films at

room temperature was determined using X-ray diffraction with Cu Kα radiation on

a Bruker AXS diffractometer.

4.3 Results

4.3.1 Microstructure

Based on the results on the crystallization kinetics of amorphous Ni-Ti films in

Chapter 3 and through a judicious choice of the annealing conditions, it is possible

to precisely tailor the microstructure of the Ni-Ti films after the anneal. A heat

treatment of 20 minutes at 450 C was chosen for two reasons: First, it is possible to

crystallize the films over the entire range of thicknesses under this condition. This is

an important consideration because the crystallization kinetics is thickness dependent


and slows down significantly for very thin films. Second, this annealing condition

ensures a large grain size for all film thicknesses because it suppresses crystallite

nucleation, while allowing a reasonable crystallite growth rate. Figure 4.1(a) shows

a SEM image of the 290 nm Ni-Ti film after the heat treatment. The surface relief

caused by the martensite twins is quite evident in the image. The average grain size

of the film is approximately 15 µm, i.e., the grain aspect ratio is about 50:1. Similar

aspect ratios were achieved for other film thicknesses. The large aspect ratio of the

grains limits the interaction between adjacent grains and makes it possible to evaluate

the effect of film thickness independent of the grain size. For all practical purposes,

the films can be regarded as single-crystal films of random orientation. Figure 4.1(b)

presents a cross-sectional TEM image of the 290 nm Ni-Ti film. The image shows

that there remains an amorphous Ni-Ti layer of approximately 15 nm at both the top

and bottom interfaces after the heat treatment. Cross-sectional TEM examination of

the other films showed that these amorphous layers are present in all films and that

their thickness is independent of the Ni-Ti film thickness. This observation is similar

to that in Chapter 3. The heat treatment of 20 minutes at 450 C is not sufficient

to crystallize this layer, but the layer may be crystallized by annealing at a higher

temperature.

4.3.2 Stress-temperature curves

Figure 4.2 shows the residual stress in the as-deposited amorphous films. The

stress is tensile and it increases slightly with increasing film thickness. There is

no statistically significant difference in residual stress for films of a given thickness


(a)

(b)

Figure 4.1: Microstructure of the 290 nm Ni-Ti thin film after 20 mins heat treatmentat 450 C: (a) SEM image shows the average grain size is about 15 µm; (b) Cross-sectional TEM image shows thin amorphous layers remain at both top and bottominterfaces.


0 200 400 600 800 1000 12000

50

100

150

200

250

300

350

400

R

esid

ual s

tress

(MP

a)

Film thickness (nm)

Fused quartz Si (100) Pyrex Corning

Figure 4.2: Residual stress in as-deposited amorphous Ni-Ti thin films.

on different substrates. This observation is a strong indication that thanks to the

presence of the SiNx layer the structure of the films is indeed independent of the

substrate material.

When calculating the stress in Ni-Ti films from the substrate curvature measure-

ments, care should be taken since the complete film stack includes five layers: two thin

layers of PECVD SiNx, two thin layers of amorphous Ni-Ti and one layer of crystalline

Ni-Ti. To get the stress in just the crystalline Ni-Ti layer, the contributions from the

other layers need to be accounted for. This is especially important for the thinner

films where the thickness of the other layers is comparable to that of the crystalline

Ni-Ti. Figure 4.3 illustrates how this correction was performed for the films on the

silicon substrate. Figure 4.3(a) shows the stress-temperature curves for Ni-Ti films


of different thicknesses as measured without subtracting the contribution of the SiNx

films. All curves have the typical S-shape associated with the martensitic transforma-

tion: Upon cooling from elevated temperature, the films initially consist of austenite

and any variation in stress is due to the thermal mismatch between the austenite and

the substrate. On continued cooling, the martensitic transformation takes place and

the stress relaxes abruptly to a lower level because of the self-accommodating nature

of the martensite twin structure. On subsequent heating, the reverse transformation

to austenite leads to a complete recovery of the residual stress in the austenite. If the

SiNx and the Ni-Ti film are denoted as layers 1 and 2 with thicknesses h1 and h2, re-

spectively, the average stress in the films stack, σf , is given by the thickness-weighted

average of the stresses in these layers

σf = σ1h1

h1 + h2

+ σ2h2

h1 + h2

(4.1)

where σ1 and σ2 are the stresses in the respective layers. The stress in the SiNx films

was determined from separate samples without Ni-Ti. Before annealing, the residual

stress in the SiNx coatings on the Si substrate was almost zero. After annealing, the

stress was 348±25 MPa at room temperature and it did not change appreciably over

the temperature range of the curvature measurements. After subtracting the contri-

bution of the SiNx films, the stress in the martensite Ni-Ti after the transformation is

still slightly thickness dependent and it slightly increases with decreasing film thick-

ness, which is somewhat surprising given the large recoverable strain associated with

the martensitic transformation. The stress in the martensite is plotted against the

reciprocal Ni-Ti film thickness in Figure 4.3(b) for all films with the exception of the

190 nm film because it did not completely transform to martensite. The martensite


stress increases linearly with decreasing film thickness at a rate of 8.72 MPa·µm. We

attribute this increase to the presence of the amorphous layers at the top and bot-

tom interfaces of the Ni-Ti films. If the amorphous and crystalline Ni-Ti layers are

denoted as layers a and c with thicknesses ha and hc, respectively, the stress σ2 in

equation 4.1, is given by

σ2 = σaha

h2

+ σchc

h2

(4.2)

where σa and σc are the stresses in the respective layers. Rearranging Equation 4.2

results in

σ2 = σc + (σa − σc)ha

h2

(4.3)

i.e., the intercept on the stress axis in Figure 4.3(b) represents the stress in the crys-

talline layer, while the stress in the amorphous layers can be calculated from the

slope. Considering that ha = 30 nm, we find that the stress in the amorphous Ni-Ti

is equal to 320±42 MPa and the stress in the martensitic Ni-Ti is 28±2 MPa. Fig-

ure 4.3(c) shows the stress in the crystalline Ni-Ti layer as a function of temperature

after correcting for both the SiNx and the amorphous Ni-Ti layers.

Similar analyses were conducted for the films on the pyrex and fused quartz sub-

strates and the results are summarized in Table 4.2. As expected the stress in the

martensite is independent of the substrate material, while the stress in the amorphous

layer increases with increasing thermal mismatch between film and substrate.

From Figure 4.3(c), it is evident that the hysteresis loops that form as a result

of the martensitic transformation shift to lower temperatures as the film thickness

decreases. A direct comparison of the martensite transformation temperatures is

misleading, however, because films of different thickness are at different stress lev-


0 20 40 60 80 100 120 140 160

100

200

300

400

500

600

470 nm370 nm

290 nm190 nm

910 nm

Stre

ss (M

Pa)

Temperature (oC)

Ni-Ti on Si

(a)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.010

20

30

40

50

60

70

80

Stre

ss,

2 (M

Pa)

1/h2 ( m-1)

28 MPa

8.72 MPa. m

(b)

0 20 40 60 80 100 120 140 1600

100

200

300

400

500

600

700

800

470 nm370 nm

290 nm

190 nm

Temperature (oC)

Stre

ss (M

Pa)

Ni-Ti on Si

910 nm

(c)

Figure 4.3: Stress-temperature curves of Ni-Ti films on Si substrate: (a) Withoutsubtracting contribution from SiNx film; (b) After subtracting the stress in SiNx

layer, the residual stress of Ni-Ti film in martensite phase as a function of reciprocalfilm thickness; (c) After subtracting the stress in amorphous Ni-Ti layers, the stress-temperature curve of crystalline Ni-Ti layer was obtained.


Table 4.2: Stresses in different layers of Ni-Ti thin films.

Substrate SiNx (MPa) Uncrystallized NiTi (MPa) Martensite NiTi (MPa)Fused quartz 530±47 501±140 22±8Silicon (100) 348±25 320±42 28±2

Pyrex 285±31 263±43 32±3

els when the transformation starts. It is well known that this causes shifts in the

martensite transformation temperature [1]. The effect of the stress on the transfor-

mation temperature can be evaluated in the following manner. Figure 4.4(a) shows

the stress-temperature curves for 910 nm films deposited on three different substrates.

The results obtained for the Corning glass substrate are not included here for reasons

that will be discussed later. Because of the different thermal mismatch between film

and substrate, the stress in the austenite is different for each type of substrate. It

is evident from the figure, however, that the stress-temperature behavior during the

martensitic transformation is identical for the three different substrates, i.e., the three

curves overlap perfectly and the stress level after the transformation is the same, in-

dependent of the stress in the austenite prior to transformation. This observation

implies that the stress-temperature relationship during transformation is characteris-

tic for a given film thickness and that it reflects how the temperature at the onset of

the martensitic transformation, Ms, changes with the austenite stress. Indeed, the Ms

temperature can be defined by the intersection of linear fits to the stress-temperature

curve during transformation and the stress-temperature curve for the austenite as

depicted in Figure 4.4(a). Linear fits to the stress-temperature curves during trans-

formation are plotted in Figure 4.4(b) for all film thicknesses. The data points are

from stress-temperature curves during the transformation on different substrates.


Since the transformation in the 190 nm film was not complete in the temperature

range accessible to the substrate curvature system, the stress-temperature curve was

obtained from a fit of the stress recovery curve on heating (dash line in the figure),

translated to coincide with the cooling data. The slopes of the lines range from

20 to 38 MPa/K. The figure clearly demonstrates that the onset of the martensitic

transformation shifts to lower temperatures as the film thickness decreases. The Ms

temperature at a reference stress of 400 MPa is plotted as a function of film thickness

in Figure 4.4(c). The transformation temperature slightly decreases as the film thick-

ness decreases from 910 nm to 470 nm, but drops off quickly when the film thickness

is below 400 nm.

The results shown in Figure 4.4(a) have another important implication concerning

the maximum transformation strain associated with the martensitic transformation.

Because the stress level is not fully relaxed after transformation to martensite, one

might be tempted to assume that the stress drop associated with the martensitic

transformation is a measure for the maximum transformation strain for films of dif-

ferent thicknesses. Figure 4.4(a) clearly demonstrates that this is not correct: As the

stress in the austenite increases, so does the stress drop; the stress after transforma-

tion is always the same. The transformation strain has not been exhausted and it is

plausible that even much higher stress levels would be relaxed after transformation.

Figure 4.5 shows the stress in a 910 nm Ni-Ti film on Corning glass substrate.

The thermal mismatch between Ni-Ti and Corning glass is small and as a result

the residual stress in the Ni-Ti film is quite low after annealing. It is immediately

obvious that the stress-temperature behavior of this film is qualitatively different from


0 20 40 60 80 100 120 140

0

100

200

300

400

500

910 nm Ni-Ti film

Stre

ss (M

Pa)

Temperature (oC)

Fused quartz

Si

Pyrex

- Ms curve

(a)

0 20 40 60 80 1000

100

200

300

400

500

600

700

Stre

ss (M

Pa)

Temperature (oC)

190 nm

290 nm

370 nm

470 nm

910 nm

(b)

0 200 400 600 800 10000

10

20

30

40

50

60

70

80

= 400MPa

Tran

sfom

ratio

n te

mpe

ratu

re, M

s (o C)

Film thickness (nm)

Austenite

Martensite

(c)

Figure 4.4: (a) Film stress in the 910 nm film on different substrates as a function oftemperature; (b) Linear fits of stress drop curves upon cooling for all film thickness;The temperature values at the intersection with σ=400 MPa in (b) are plotted in (c)for the demonstration of the size effect.


0 20 40 60 80 100 1200

50

100

150

200

250

300

350

0 1 2 3 40

20

40

60

80

100

120

Time (hours)

Tem

pera

ture

(o C)

Stre

ss (M

Pa)

Temeprature (oC)

Rs

Ms

Figure 4.5: The low stress in the film on Corning glass substrate caused two-steptransformation. The inset is the thermal cycle history during the stress measurement.The open symbol in temperature profile corresponds to the open symbol in stress data.

the behavior for the other substrates: rather than one stress relaxation step, there

are two distinct stress drops on cooling. The first stress drop is due to the formation

of the R-phase, while the second drop is caused by the formation of B19’ martensite.

The presence of the R-phase is further confirmed by the small temperature hysteresis

between the forward and reverse transformations that occurs if the film is reheated

before the B19’ phase forms (open symbols in the figure) and B19’ is confirmed by

room temperature XRD. This observation is a clear indication that the residual stress

affects the transformation sequence and product. It has indeed been reported in the

literature that Ni-Ti undergoes a two-step transformation, B2 → R-phase → B19’,

if the applied stress is low [21, 94]. The reverse transformation, however, is clearly a

one-step transformation to austenite.


4.4 Discussion

4.4.1 Transformation under substrate constraint

The stress-temperature behavior during the martensitic transformation of a film

constrained by a substrate has been discussed at length by Roytburd et al. [95].

In particular, they proposed a model for the behavior of a single-crystal film on a

substrate based on the thermodynamics of constrained transformations. While the

Ni-Ti films considered in this study are polycrystalline, they have grain aspect ratios

of as large as 50:1. Consequently the interaction between the grains is very small and

the films can be regarded as very nearly single-crystalline, but with a macroscopic

behavior that is the average of the many grain orientations present in the films. The

overall shape of the stress-temperature curves reported here is indeed quite similar

to the curves predicted by Roytburd et al. There are, however, also a few notable

differences in transformation behavior: First, the results shown in Figure 4.4(a) clearly

indicate that the transformation strain is not exhausted by the stress drop because

the stress in the martensite is independent of the stress in the austenite right before

the transformation. According to the Roytburd model [95], there should then exist

a temperature range below the stress drop where austenite continues to transform

to martensite albeit with a different set of martensite variants that does not result

in any stress change. XRD measurements on Ni-Ti films indicate, however, that the

transformation is complete at the end of the stress drop. Figure 4.6, for instance,

shows a XRD spectrum for the 290 nm Ni-Ti film taken at a temperature right below

the stress drop after cooling from 120 C. Also shown is the spectrum for a film after


32 34 36 38 40 42 44 46 48 50 52 54 560

200

400

600

800

1000

1200

1400

1600

1800

M021A

110 M111

M002

M111

M110

Inte

nsity

(a.u

.)

2 Theta (degree)

M101

290 nm Ni-Ti film

cool to R.T. from 120 oC

heat to R.T. from LN2

Figure 4.6: Room temperature XRD of the 290 nm film shows the transformation isindeed complete at the end of the stress drop.

first cooling it down to liquid nitrogen temperature and then being allowed to heat

back to room temperature. Both spectra show strong martensite peaks alongside a

small austenite peak, indicating that most of the austenite has indeed transformed

to martensite at the end of the stress drop. The austenite peak is caused by a

small amount of residual austenite in the film that apparently does not transform

to martensite even at liquid nitrogen temperatures. If the transformation is indeed

complete at the end of the stress drop, it follows that the martensite variants that

form during the transformation are those that relax the stress in the austenite and not

just the variants that result in the largest in-plane expansion of the film as assumed

by Roytburd et al. [95].

The Roytburd model further predicts that the slope of the stress during transfor-


mation from austenite to martensite should be approximately 7 MPa/K for a single

crystal film with a (110) orientation. The films in this study have a random texture,

but it was shown by Shu and Bhattacharya [96] that the recoverable strain for a thin

film with (110) texture is the same as that for a film with random texture. Con-

sequently, one would not expect there to be a significant difference in slope. Even

so, the slopes measured in this study are significantly larger and vary from 20 to 38

MPa/K. Similar stress rates have been measured previously for films on substrates

[97, 98]. It has been suggested that the slope is the result of a stress gradient through

the film thickness [98]. This stress gradient causes a layer-by-layer transformation

sequence, in which the front of the transformed phase is parallel to the plane of

the film. According to this argument, the low stress in the martensite layer causes

a decrease in the average stress in the film, but it has no effect on the stress in

the untransformed austenite layer. As the temperature is lowered, the stress in the

austenite increases and the transformation proceeds further. The temperature range

over which the transformation occurs is then a measure for the stress gradient in the

film. The stress-gradient model does not explain, however, why the slopes in this

study are significantly larger than the slope predicted by the Roytburd model. If

anything, a stress gradient whould result in an even shallower slope. It seems that a

more sophisticated model is required to describe the observed behavior.

4.4.2 Film thickness effect

The effect of the film thickness on the martensite transformation temperature is

illustrated in Figure 4.4(c). It is evident that the onset of the martensitic trans-


formation shifts to lower temperatures as the film thickness decreases. The effect

is small for thick films, but becomes quite pronounced for films thinner than 400

nm. Ishida and Sato [88] have investigated the film thickness effect in freestanding

Ni-Ti thin films with thicknesses from 0.5 µm to 7 µm using the tensile test. They

observed a decrease in transformation temperature for films that were thinner than

1 µm and attributed this decrease to a shift in composition of the films as a result

of surface oxidation. There was a small composition shift in the amorphous layers

at the NiTi/SiNx interfaces discussed in Chapter 3. The crystalline layer, however,

has the same near-equiatomic composition as the as-deposited amorphous film. It is

clear that in this case the depression of the transformation temperature cannot be

attributed to a shift in composition caused by a reaction with the SiNx layers. Fur-

thermore, the transformation temperature of the 190 nm film is approximately 64 C

lower than that of the 910 nm film. If this change were due to a shift in composition,

the entire film would have to be about 1% richer in Ni based on the composition

dependence of the transformation temperature of bulk Ni-Ti as shown in Figure 1.3.

This is impossible for the annealing condition in this study given the slow diffusion

in amorphous Ni-Ti [99]. In Chapter 3, we showed that the hydrogen content in

PECVD SiNx may diffuse into Ni-Ti films upon heat treatment. It was reported

that hydrogen can affect the martensitic transformation [100, 101]. Therefore it is

possible that the size effect in Figure 4.4(c) is caused at least partially by hydrogen

present in SiNx film. To find it out, a simple experiment was conducted. The hydro-

gen plasma treatment we used in Chapter 3 apparently introduced more hydrogen

than that from PECVD SiNx. So we treated a 470 nm film with hydrogen plasma


0 20 40 60 80 100 120 1400

100

200

300

400

500

Stre

ss (M

Pa)

Temperature (oC)

Before H treatment Atfer H treatment

Figure 4.7: Stress-temperature curves of the 470 nm film treated with hydrogen. Thebehavior of the same film before the treatment is added for comparison.

and compared its stress-temperature curve before and after the hydrogen treatment.

After the hydrogen plasma treatment, the film was capped with PECVD SiNx and

annealed at 150 C for 10 mins to let hydrogen drive into the entire thickness. The

stress-temperature results are shown in Figure 4.7. The hydrogen slightly changed

the stress level and the stress drop curve has a shallower slope. The film even started

to transform at a little higher temperature. Based on this experiment, it is fair to say

that the hydrogen in SiNx film should not cause the pronounced shift for the onset of

the martensitic transformation when the Ni-Ti film thickness decreases. We conclude

that the observed decrease in transformation temperature with film thickness is an

intrinsic size effect.


4.4.3 Micromechanics model

Size effects related to the martensitic phase transformation in Ni-Ti have been

investigated for nano-sized poly-crystals [102], for isolated nano-crystals embedded in

a solid amorphous matrix [103], and for thin films [88, 90, 91]. In some cases, the size

effect is clearly due to oxidation [88, 90], but in other cases it can be explained using

a free energy argument [104, 105]. The condition for the onset of the martensitic

transformation can be written as [105, 106]

4gchem = UB (4.4)

where 4gchem denotes the difference of the free energy per unit volume of the un-

stressed austenite parent phase and the martensite product phase; UB represents the

energy barrier to transformation, which comprises the energy per unit volume asso-

ciated with the various interfaces, the elastic energy of the internal stresses, and a

friction term:

UB = ΓPB + ΓPA + ΓS + WPS −WAu + Fc (4.5)

The components of UB are illustrated schematically in Figure 4.8, which shows

twinned martensite plates. ΓPB is the interfacial energy of the martensite plate

boundaries; ΓPA is the interfacial energy difference with the austenite matrix upon

transformation from austeniste to martensite; ΓS is the change in interfacial energy

between film and substrate or capping layer as a result of the transformation. WPS is

the strain energy caused by the interaction between the plate ends and the substrate

or the capping layer, and WAu is the strain energy as a result of the residual stresses

in the austenite. Fc is the work of friction per unit volume of martensite. Because


Capping layer

Substrate

Martensite

plate I

AusteniteAustenite

h

d

Martensite

plate II

ΓPA

ΓS, WPS

ΓPB

Figure 4.8: Energies associated with the transformation.

of its self-accommodating nature, formation of the martensite phase results in a local

reduction of the residual stresses in the coating and hence in a reduction of the strain

energy. Consequently, the presence of residual stresses in the austenite lowers the

transformation barrier.

The various energy terms in Equation 4.5 scale differently with film thickness and

martensite plate width. Writing these dependencies explicitly we obtain

UB =γPB + γPA

d+

γS

h+ wPS

d

h−WAu + Fc (4.6)

where d represents the martensite plate width, h the film thickness, and where γPB,

γPA,γS, and wPS are defined through a term-by-term comparison of Equation 4.5 and

Equation 4.6. Minimizing the energy barrier with respect to d shows that the plate

width scales with the square root of the film thickness. This square root dependence

is consistent with measurements of the measured martensite plate widths over the

relatively narrow range of film thicknesses considered in this study. Equation 4.6 can


then be rewritten as

UB = 2

√(γPB + γPA)wPS

h+

γS

h−WAu + Fc (4.7)

According to this expression, the barrier to transformation increases with decreasing

film thickness. Taking reasonable values for γPB, γPA, γS, and wPS [105] shows that

the first term on the right hand side of Equation 4.7 dominates for films thicker than

40-50 nm, while the second term is important for very thin films. A comparison

of Equation 4.4 and Equation 4.7 shows that thinner films require a larger driving

force 4gchem for transformation. To a first approximation, the driving force can be

written as 4gchem=4s(T0 − T ) where T0 is the temperature of chemical equilibrium

between the austenite and the martensite and 4s is the difference of the entropy

per unit volume between the respective phases. It follows then that thinner films

require a larger under-cooling for transformation. This is indeed borne out by the

data in Figure 4.4(c), although the under-cooling seems to rise somewhat faster than

the simple square root dependence suggested by Equation 4.7.

It was reported in a TEM study by Waitz et al. [103] that a two-step trans-

formation, B2 → R-phase → B19’, occurs in isolated NiTi nano-crystals embedded

in an amorphous matrix when the crystallite size decreases below a critical value.

This transformation path leads to the formation of (001)B19’ compound twins in the

martensite. We have not seen any evidence for a two-step transformation with de-

creasing film thickness, although a two-step transformation does occur for films with

low values of residual stress. We also have not observed any (001)B19’ compound

twins in our films. It is possible that much smaller film thicknesses are required for

the two-step transformation to occur and compound twins to form.


4.5 Conclusions

The influence of the film thickness and film stress on martensitic transforma-

tion behavior of Ni-Ti thin films within submicron region was investigated using the

substrate-curvature technique. PECVD SiNx layers minimize interfacial reaction and

surface oxidation of Ni-Ti films and make the investigation of intrinsic size effect in

submicron region possible. Large grain size achieved by the appropriate annealing

condition makes it possible to evaluate the effect of film thickness independent of the

grain size. The microstructural details of the film helps the analysis and interpretation

of stress-temperature results measured by substrate curvature technique.

The following conclusions can be drawn based on our experimental observations:

(1) The stress-temperature curve upon transformation characterizes the stress depen-

dence of the transformation temperature for a given film thickness. (2) The maxi-

mum transformation strain in a Ni-Ti film under substrate constraint has not been

exhausted during the transformation. The stress in martensite Ni-Ti is independent

of the stress in austenite. (3) The level of film stress can change the transformation

sequence and product. If the stress in austenite is low, a two-step transformation of

B2 → R-phase → B19’ occurs instead of the direct B2 → B19’ transformation. (4)

The crystallized Ni-Ti layers have the same chemical composition independent of film

thickness and therefore the same driving force for transformation. Consequently, the

observed size effect is not due to a shift in composition, but to a geometric constraint.

(5) The energy barrier for the martensitic transformation increases with decreasing

film thickness causing a commensurate decrease in the transformation temperature.

Chapter 5

Laser annealing of amorphous

Ni-Ti thin films

5.1 Introduction

The ordinary shape memory effect (SME) used in SMA actuators is a one-way

process: a shape memory material that is deformed in its martensitic state (the

low-temperature phase) recovers its original shape when it transforms back to the

austenitic state (the high-temperature phase) upon heating; it does not however go

back to the deformed shape upon subsequent cooling. For actuators, the absence of

a spontaneous shape change upon heating and cooling introduces numerous design

challenges. A common solution consists of using a biasing mechanism to induce a

deformation on subsequent cooling. This biasing mechanism can be either an ad-

ditional mechanical element like a spring or it can result from a thermo-mechanical

process that introduces oriented precipitates or defects that promote the growth of

70

Chapter 5: Laser annealing of amorphous Ni-Ti thin films 71

martensitic variants with preferential orientations [32, 33, 107, 108, 109, 110, 111]. For

microsystems, introducing a biasing mechanism is a challenge because of the size of

the components (typically below a millimeter). As a result, SMA actuators in MEMS

have been limited mainly to bimorph-like mechanisms which only generate out-of-

plane motion. Recently, laser annealing of shape memory alloys (LASMA) emerged

as a promising approach for the fabrication of planar mechanisms [112]. This tech-

nique has the advantage that shape memory properties can be spatially distributed:

material locally crystallized by laser irradiation has shape memory properties and

can be used as an actuator, while untransformed material is passive and provides a

restoring force mimicking the behavior of a bias spring. In this chapter, we present

the results of experiments and thermal modeling of the laser annealing process for

amorphous Ni-Ti films.

5.2 Crystallization behavior of laser annealing pro-

cess

5.2.1 Experiments

Amorphous Ni-Ti thin films used in laser annealing experiments are 1.5 µm thick.

The substrate is 1 mm thick fused quartz slide. During the deposition, the Ar working

pressure was 1.5 mTorr. The composition of the films was measured to be 50.5 ±

0.2at.% Ti using Electron Microprobe Analysis (EMPA) or RBS.

In order to crystallize the Ni-Ti films, samples were annealed by scanning a laser

beam over the surface of the films along a straight line. This was done at Center for


Automation Technologies and Center for Integrated Electronics at Rensselaer Poly-

technic Institute. The laser source is a fiber-injected continuous wave (CW) high

power near-IR laser diode. The wavelength of the laser is 925 nm. The laser beam

had a Gaussian power distribution and a diameter of approximately 0.9 mm (i.e.,

the diameter at 1/e intensity) as determined using the knife-edge method [113]. The

specimen was mounted on a platform (Yaskawa, Robotworld) with three degrees of

freedom, capable of planar translational and rotational motions with micron resolu-

tion. In the experiments, the laser power was varied from 5.0 to 9.4 W; the scan

speed was varied from 1 to 8 mm/s. All scans were performed in air. During laser

annealing a thin oxide coating was formed on the Ni-Ti films. The oxide thickness

was determined from the reflectivity spectrum measured using a spectrophotometer

(Jasco V-570 NUV/VIS/NIR) and was typically in the range of 50∼100 nm for the

laser annealing parameters used in this study [114]. As expected the oxide thickness

increased with increasing laser power and decreasing scan speed. Oxide formation

could of course be reduced by performing the experiments in an inert atmosphere or

in vacuum environment.

Multiple line scans were performed to create large crystalline areas. In multiple

line scans, a short dwell time was introduced at the end of each line scan to allow

the sample to cool down between adjacent scans. Samples for texture analysis and

stress measurement were cut from these areas. X-ray diffractometry (Bruker AXS

diffractometer with Cu-Kα radiation) was used to investigate the texture of the films

after laser annealing. During the texture measurements, the samples were heated to

ensure that only the austenite phase was present. Pole figures were obtained for the


110, 200 and 211 reflections and analyzed using popLA.

5.2.2 Processing window

The laser beam was scanned across the film surface along a straight line. The

annealed section of the film was firstly investigated using optical microscopy. As

shown in Figure 5.1, the crystallized area is rough and shows surface relief in contrast

to the shiny uncrystallized area. The crystallized region was confirmed by TEM.

The width of the crystallized region is a few hundred microns. The annealing results

were investigated systematically as a function of laser power density (laser power

divided by beam area) and scan speed, and summarized in Figure 5.2. At a given

scan speed, the film transitions from amorphous to partially crystalline and eventually

fully crystalline with increasing laser power. If the laser power is too large, film and

substrate crack due to thermal shock. A similar transition occurs when the scan

speed is varied at constant laser power.

5.2.3 Nucleation and growth kinetics

Figure 5.3 shows a cross-sectional TEM image of a partially crystallized film.

Nucleation of the crystalline phase occurred homogenously in the film. Heterogeneous

nucleation at the film surface and the film-substrate interface were not observed. This

is consistent with the results in Chapter 3. It is likely due to a small composition

shift that occurs at these interfaces due to oxidation or reaction with the substrate.

Figure 5.4(a) is a low magnification TEM image of an individual grain showing

two sets of mutually perpendicular needle domains. Figure 5.4(b) is the electron


100um

annealed region

scan

dir

ecti

on

Figure 5.1: Optical micrograph of the film surface after laser annealing.

7 8 9 10 11 12 13 14 150

1

2

3

4

5

6

7

8

9

Sca

n sp

eed,

V (m

m/s

ec)

Laser power density, P (W/mm2)

Amorphous Partially crystalline Crystalline Cracking

Amorphous

Crystalline

Cracking

Figure 5.2: Process window of Ni-Ti films as a function of laser power density andscan speed.


Figure 5.3: Cross-section TEM image of a partially crystallized Ni-Ti film by laserannealing.

diffraction pattern taken from both the matrix and needle domains. The diffraction

pattern shows a typical [001]B2 type diffraction pattern of the R-phase with two sets

of 1/3 superlattice reflections along 〈110〉∗ direction. The transformation to R-phase

not to B19’ phase is probably due to the stress relief in thin foil geometry of TEM

sample. Since the rhombohedral distortion is very small, the pattern is indexed in

terms of the B2 system for convenience. Because a diffraction pattern taken from

only the matrix shows 1/3 superlattice reflections in only the [110]∗ reciprocal lattice

direction, the pattern indicates that the needle domains are twin-related to the matrix

with 100B2 type twinning planes. The twinning planes also correspond to the traces

of the domains. The growth interface between the crystal and amorphous matrix was

investigated on an atomic scale by HRTEM. Although the growth interface between

the crystal and amorphous matrix looks smooth at low magnification, HRTEM image

(Figure 5.4(c)) indicates that it actually consists of 100B2 and 110B2 planes.

Similar growth morphologies have been found in partially crystallized Ti50Ni25Cu25

melt-spun ribbon [79]. Quantitative EDS measurements were performed across the


(a) (b)

(c)

Figure 5.4: (a) Low magnification TEM image showing two sets of mutually per-pendicular R-phase needle domains in a grain; (b) The electron diffraction patterntaken from both the matrix and needle domains shows a [001]B2 type zone with twosets of 1/3 superlattice reflections along 〈110〉∗B2; (c) HRTEM image taken from thecrystal-amorphous interface, the trace of the interface marked by solid lines reveals astepped growth interface along 100B2 and 110B2 planes.


growth interface. The amorphous and crystalline phases share the same composition,

indicating that the crystallization reaction is partitionless.

The almost perfect circular shape of the crystals both in cross-sectional TEM (Fig-

ure 5.3) and in plan-view (Figure 5.4(a)) indicates that their general three-dimensional

shape is spherical. Evidently, grains grow isotropically until they impinge on each

other or until they touch the film surface or the substrate.

5.2.4 Microstructure

The TEM images in Figure 5.5 show the microstructure close to the center of the

laser trace for different laser power at a given scan speed. At low laser power, only a

few isolated grains are formed in an amorphous matrix. Once the laser power is large

enough to fully crystallize the film, the microstructure at the center is approximately

independent of laser power.

(a) (b) (c)

Figure 5.5: Microstructure at the center of the laser trace. Scan speed is 4 mm/s,and laser power is (a)7.6 W (b) 8.2 W (c) 8.8 W respectively. The inset diffractionpattern from dark grain in (a) shows [111]B2 type zone of R-phase.

As a result of the Gaussian intensity profile of the laser, a temperature gradient


is introduced in the film in the direction perpendicular to the laser trace. Figure 5.6

shows the microstructure at different places of the crystallized region (width ∼ 400

µm) in the direction perpendicular to the scan. Grain size and distribution are similar

across the entire crystalline region. Most grains are 1 to 1.5 µm in diameter although

there are a few grains as small as 0.3 µm. Combined with Figure 5.5, Figure 5.6

confirms that a uniform microstructure is formed in the crystallized region for the

annealing parameters used in this study. Thus, the shape memory properties are

expected to be uniform across the annealed areas also. This is certainly desirable

when using these materials in applications.

(a) (b) (c)

Figure 5.6: Microstructure at various locations of the crystallized region (width ∼400 µm): (a) at the center; (b) approximately 100 µm away from the center; (c)approximately 200 µm away from the center.

Figure 5.7 shows a series of plan-view TEM images mapping out the crystalline-

amorphous boundary. Due to the temperature gradient, the transition region from

fully crystalline to amorphous is approximately 30 µm in width.

Figure 5.8 shows a typical room temperature XRD spectrum of a sample that

underwent multiple-line scans and that is fully crystallized. After laser annealing,


2 m

crystalline-amorphous boundary (partially crystalline) crystallineamorphous

Figure 5.7: Plan-view TEM images show the microstructure within the crystalline-amorphous boundary in Ni-Ti film after laser annealing.

the material in the crystalline regions has transformed to martensite demonstrating

that shape memory properties can be introduced using laser annealing. Some R-phase

and untransformed parent phase are also present in the film at room temperature. No

precipitates are observed in the laser-annealed films because of the short annealing

times. The presence of the untransformed B2 phase may be related to the Ni-rich

layer that forms immediately below the surface oxide or to the presence of small grains

in the films that do not transform because of the size effect we discussed in Chapter 4.

Figure 5.9 is a TEM image of the martensite morphology most frequently observed

in the films. Electron diffraction pattern shows that 〈011〉 type II twins are prevalent

in the microstructure. This type of twin is also the most frequently observed twin in

bulk materials [115] and furnace annealed Ni-Ti thin films [116].

It is important to evaluate the crystallographic texture of laser annealed Ni-Ti

films because the recoverable strain depends on the texture of the films [96] and

because strong textures may lead to anisotropic shape memory behavior [117, 118],


37 38 39 40 41 42 43 44 45 46 4750

100

150

200

250

300

M111

M002

R300

R112

M111

M020

M110

M101

Inte

nsity

(arb

. uni

ts)

2 Theta (degree)

B2110

Figure 5.8: Room temperature XRD for a sample with multiple-line scan.

(a) (b)

Figure 5.9: (a) TEM image of 〈011〉 type II twin as main microstructure of martensitein the laser annealed Ni-Ti films; (b) Electron diffraction pattern taken from the regionin (a), incident electron beam //[110]M//[101]T .


making the design and fabrication of actuators more challenging. A typical 110

pole figure measured by XRD is shown in Figure 5.10. The laser scan direction is

labeled as the rolling direction (RD) in the figure. The pole figure shows that the

film is polycrystalline with a mostly random crystallographic texture. The random

texture is consistent with the homogenous nucleation mechanism described above.

If nucleation occurs homogenously inside an amorphous matrix, one would indeed

expect no preferential orientation of the nuclei. For an elastically anisotropic material

such as the Ni-Ti, the residual stress in the amorphous coatings could possibly induce

a texture in which grain orientations that are most compliant in the plane of the film

dominate. Based on the single-crystal elastic constants of Ni-Ti [119], this mechanism

would result in a 〈100〉 fiber texture for the B2 phase. Such a texture component

is not observed in these films, however, indicating that the strain energy associated

with the residual stress is not significant in defining the texture. This is consistent

with a number of studies on the stress evolution during crystallization of amorphous

Ni-Ti films [49, 120], indicating a relatively low residual stress in the range of -200 to

200 MPa. The isotropic texture observed in this study is in good agreement with a

study by Miyazaki et al. [118] in which it was demonstrated that ex-situ annealing of

amorphous Ni-Ti films leads to a uniform orientation distribution of the grains. We

argue here that this random texture is a consequence of the homogeneous nucleation

mechanism by which the crystalline phase forms. The random texture should be

contrasted with the strong 〈110〉 fiber texture commonly observed in Ni-Ti films

sputtered at elevated temperatures where the films are crystalline as deposited [118].

Under these deposition conditions, the crystalline phase nucleates on the surface of


RD

TD

Figure 5.10: 110 pole figure of the laser annealed Ni-Ti film.

the substrate naturally assuming an orientation that minimizes surface and interface

energies.

5.2.5 Shape memory behavior

The martensitic transformation behavior of laser annealed films was investigated

by measuring the film stress as a function of temperature using the substrate curvature

technique. In order to investigate the evolution of the residual stress in the crystallized

region as a function of temperature, multiple line scans were performed to create

arrays of parallel lines where the film was crystalline as shown in Figure 5.11(a).

Films with various volume fractions of crystalline material were produced by varying

the laser annealing parameters and the line spacing. For each volume fraction, two


sets of rectangular specimens (6×25 mm) were cut from these large arrays, i.e., one

set with the long edge of the specimen parallel to the laser scan direction (labeled as

RD in the figures) and one set perpendicular to the scan direction (labeled as TD).

The stress in the long direction of the specimens was measured using the substrate

curvature technique. Using this approach, the residual stresses both parallel and

perpendicular to scan direction could be measured. Stresses were calculated assuming

a biaxial modulus of 90.5GPa for the fused quartz substrate.

As illustrated in Figure 5.11, the average stress in the multiple-line specimens,

σav, depends on the stress in the crystalline and amorphous areas according to

σav = fσc + (1− f)σa (5.1)

where f = wc/(wa + wc) is the volume fraction of crystalline material. The stress in

the amorphous regions, σa, can be measured directly from the as-deposited samples;

the stress in the crystalline regions is denoted by σc and can be calculated using

Equation 5.1.

The stress-temperature curves in the RD and TD directions are shown in Fig-

ure 5.12. The stresses in both directions are the same over the range of annealing

parameters used in this study indicating that an equi-biaxial stress state exists in the

films. This is consistent with the random crystallographic texture and the uniform

microstructure. As a result of the uniform orientation distribution of the grains, the

shape memory behavior is expected to be isotropic with similar behavior in both RD

and TD directions. The stress-temperature curves show a closed hysteresis loop as a

result of the reversible martensitic transformation that occurs in these films. The re-

covery stress (∼350 MPa) is independent of the annealing parameters and represents


TD

averageσ

TD

averageσ

RD

averageσ

RD

averageσ

Amorphous

Crystalline

Amorphous

Crystalline

cw

aw

cw

aw

(a)

0 10 20 30 40 50 60 70 80 90 100 110050100150200250300350400450500

c (calculated)

av (measured)

a (measured)

Stre

ss (M

Pa)

Temperature (oC)

(b)

Figure 5.11: (a) Schematic illustration of parallel arrays of crystalline band producedby multiple line scans; (b) Determine the stress in crystalline region using Equa-tion 5.1.


0 10 20 30 40 50 60 70 80 90 100 110100

150

200

250

300

350

400

450

500

550

Stre

ss (M

Pa)

Temperature (oC)

along RD f = 50% f = 80% f = 90% f = 100%

(a)

0 10 20 30 40 50 60 70 80 90 100 110100

150

200

250

300

350

400

450

500

550

Stre

ss (M

Pa)

along RD f = 50% f = 80% f = 90% f = 100%

Temperature (oC)

(b)

0 10 20 30 40 50 60 70 80 90 100 110100

150

200

250

300

350

400

450

500

550

Stre

ss (M

Pa)

Temperature (oC)

along TD f = 50% f = 80% f = 90% f = 100%

(c)

0 10 20 30 40 50 60 70 80 90 100 110100

150

200

250

300

350

400

450

500

550

Stre

ss (M

Pa)

along TD f = 50% f = 80% f = 90% f = 100%

Temperature (oC)

(d)

Figure 5.12: The stress-temperature curves along the RD (a,b) and TD (c,d) direc-tions for different crystallization fraction. (a) and (c) show the average stress in thespecimens; (b) and (d) show the stress in the crystalline regions.


the actuating capability of the crystallized film. The temperature hysteresis is quite

small at approximately 20 C. This is beneficial for a fast actuation response in prac-

tical applications. Slight variation of the transformation temperatures from sample

to sample may be attributed to small differences in composition between the films.

It is evident that laser annealing indeed offers a technique for selectively crystallizing

Ni-Ti coatings and that the recovery stress can be used to actuate structures in a

MEMS device.

5.3 Thermal model

As shown above, laser annealing is a powerful technique to selectively crystallize

the material and introduce the functional properties. In this section, we present the

results of a thermal model of the laser annealing process for Ni-Ti thin films with the

goal of predicting the size of annealed zone as a function of laser annealing parameters.

Thermal modeling can not only be used to understand the physics of the annealing

process but also to predict the effects of varying experimental conditions.

5.3.1 Experiments

The specimens were 1.5 µm thick amorphous Ni-Ti thin films deposited on 1 mm

thick fused quartz slide (25 mm wide × 75 mm long). The composition of the films

was measured to be 50.5± 0.2at.%Ti. If the laser irradiation is on the film side, the

surface oxide layer that grows during the annealing changes the reflectivity of the

surface and hence varies the laser power absorbed by the specimen [114], making it

much more difficult to model the process. Alternatively, the laser can be scanned on


the substrate side so that the laser beam passed through the fused quartz substrate

before hitting the thin film. Irradiating on the substrate side does not avoid the

formation of oxide on Ni-Ti film surface, but the oxide does not interact with the

incident laser beam. Instead a rather stable interface between Ni-Ti film and fused

quartz substrate is presented to the laser beam. The laser scans were performed

in this fashion because with our experimental set-up it was impossible to perform

the laser annealing experiment in an inert atmosphere or in vacuum. This set of

experiments was done at Eindhoven University of Technology in The Netherlands.

The laser annealing experiment set-up is schematically illustrated in Figure 5.13.

It consists of a laser source, a power meter to monitor reflected beam power, two

other sensors for scattered power and transmitted power measurements, and a mov-

able sample stage. The laser source is a fiber-injected continuous wave (CW) high

power near-IR laser diode (Unique-Mode AG, Germany). The wavelength of the laser

is 805 nm. The laser beam had a Gaussian power distribution and a diameter of ap-

proximately 0.45 mm (i.e., the diameter at 1/e intensity) as determined using the

knife-edge method [113]. In the experiment set-up, the laser source is stationary, but

the sample is moved on a translation stage. The incidence of the laser is slightly off

the normal (approximately 6 degree off) to make space for other sensors and optics,

but it is as small as possible to keep the eccentricity of the laser beam close to unity.

The sample stage has one motorized degree of freedom with micron resolution. The

stage is fully programmable and its acceleration, speed, and position can be accu-

rately controlled. On the sample stage, the specimen (25×75 mm fused quartz slide)

is held at the short edge by two point clips. The contact points holding the specimens


High Brigthness laser

module

(λ = 805 nm, Unique-

mode AG) + Focusing optics

Powermeter (Coherent)

Si - Fast photodiode (DT 210 – Thorlabs)

+ Viewing optics

AsGa sensor + Viewing optics (DT

410 – Thorlabs)

Moving stage

(Physik Instrument)

NiTi thin film

Fused quartz slide

Figure 5.13: Schematics of laser annealing experiment set-up.

have limited surface (spanning over a 1.5 mm length) and were kept far away from

the irradiated area. Heat dissipation through the contact can therefore be neglected.

The sample stage moves relative to the stationary laser source to perform a laser

annealing scan.

The objective of the laser annealing experiments was to investigate the size of the

crystalline zone resulting from laser annealing as a function of the laser irradiance and

scan speed. For that purpose, a series of line scans were performed by scanning the

laser beam across the short axis of the fused quartz slide (i.e., 25 mm scan distance).

Each line was separated by at least 3 mm from its neighbor. For each line scan, the

laser was turned on first, then the sample is moved into and then out of the beam

path. The laser is approximately 6 degree of normal incidence. The laser power


was varied from 0.5 to 5.5 W and the scan speed was varied from 2 to 5 mm/sec.

All scans were performed in air in a thermally stabilized environment. The laser

was fired on the substrate side so that the light beam goes through the fused quartz

substrate before hitting the thin film. Doing so, as no oxide can form at the glass/film

interface, we expect to reduce the effect of surface oxide during the annealing process

on the laser absorption of the film. To estimate how much power is absorbed by the

specimen for a given incident beam energy, a dynamic reflected power measurement

was performed. A power meter monitors the reflected laser power when the scan

proceeds. The apparent reflectivity is defined as the ratio of the reflected laser power

and the incident one.

After the laser annealing experiments, to identify the size of the laser annealed

zone, the film surface was examined using a phase-shift interferometer (PSI) to obtain

the surface profile and to measure the width of crystallized region.

5.3.2 Finite element modeling

The temperature distribution induced by a moving laser beam was calculated

through a three-dimensional finite element model using ABAQUS, a commercial finite

element solver. The temperature profile depends on the incident energy absorbed by

the film. If the laser beam of a Gaussian profile moves at a velocity v in the x-

direction, the energy absorbed by the film is given by

F =P (1−R)

πr2exp[−(

x− vt

r)2 − (

y

r)2] (5.2)

where P is the total incident power, R is apparent reflectivity, and r is the Gaussian

(1/e) radius of the intensity.


Because of the mirror symmetry along the scan axis, only one half of the system

was modeled. The dimension of the model was 1.25 mm wide and 2.5 mm long,

and the laser is scanned along the long axis. The thin film was simulated using 4-

node quadrilateral shell heat transfer elements with five Simpson integration points

through the shell thickness; the substrate was modeled using 8-node linear brick

heat transfer elements. There were totally 105000 elements (5000 film elements and

100000 substrate elements). It was assumed that fused quartz substrate does not

absorb any energy when the laser travels within it. At the wavelength considered,

this is a reasonable assumption as the material transparency is close to 100%. The

heat loss to the ambient through the top and bottom surface was also assumed to

be negligible, as was the enthalpy of crystallization of Ni-Ti. The film elements were

subjected to a time-dependent heat flux as described by Equation 5.2. The density

of fused quartz and Ni-Ti is 2.203 g/cm3 and 6.45 g/cm3 respectively. The thermal

properties of fused quartz substarte and NiTi film used in the simulation are listed in

Table 5.1 and Table 5.2. The thermal conductivity and specific heat of fused quartz

substrates are temperature-dependent and were taken from reference [7]. The thermal

properties of the Ni-Ti film were assumed to be temperature-independent and their

room temperature values were used [8]. This assumption had only a small effect on

the temperature distribution because the temperature of the film is dictated mainly

by the temperature and thermal properties of the underlying substrate.

Once the temperature distribution in the Ni-Ti film is known, a criterion is needed

to determine where the film has crystallized. This criterion is based on classical

crystallization kinetics which consists of nucleation and growth process [83]. Without


Table 5.1: Thermal properties of fused quartz substrate [7].

Temperature (K) Thermal conductivity (W/cm/K) Specific heat (J/g/K)300 0.0138 0.741400 0.0151 0.904500 0.0162 0.987600 0.0175 1.038700 0.0192 1.075800 0.0217 1.105900 0.0248 1.1341000 0.0287 1.1551100 0.0336 1.1761200 0.0400 1.1921300 0.0482 1.2131400 0.0620 1.230

Table 5.2: Thermal properties of Ni-Ti at room temperature [8].

Thermal conductivity (W/cm/K) 0.18Specific heat (J/g/K) 0.837


considering incubation time for nucleation, the fraction of Ni-Ti that has transformed

from amorphous to crystalline at a given location after a time t is equal to

χ(t) = 1− exp−4

3π

∫ t

0I(T (τ))[

∫ t

τu(T (ξ))dξ]3dτ (5.3)

in this expression, I and u are the temperature-dependent steady-state homogenous

nucleation rate and crystal growth velocity, and T (t) is the temperature history of

the location under consideration. The nucleation and growth kinetics parameters

were taken from Table 3.4 in Chapter 3 since the nucleation and growth mechanism

in laser annealing are essentially the same as those in furnace annealing as shown

in section 5.2.3. Using Equation 5.3 and the temperature profile obtained from the

simulation, the transformed fraction can be determined as a function of location. The

boundary between the crystalline region and amorphous region is set at the location

where the transformation fraction is 50%. The width of the crystallized region is then

determined from the coordinates of this critical location.

5.3.3 Results and discussion

A typical measurement of the film surface after laser annealing using PSI is shown

in Figure 5.14. The X-Y plane is the film plane and the laser scan is along Y direction.

Since the oxide layer is present on the film surface and it is transparent to PSI signal,

Figure 5.14 is not the real surface topography profile as the oxide layer perturbs the

measurement. However, the crystallized zone in the center is easily distinguished from

the rest due to the roughness caused by martensitic transformation of crystalline area.

The densification of the material upon crystallization also makes a ”step” feature at

the boundary between crystallized zone and the rest amorphous region. With this


Figure 5.14: Typical PSI measurement of the NiTi film surface after laser annealing.

technique, the size of crystallized zone can be precisely measured with a resolution as

small as 0.5 µm. An estimate of the measurement accuracy is 5 µm which depends

on the user appreciation of the position of crystalline-amorphous boundary and the

instrument calibration.

A typical result of dynamic reflectivity measurement is shown in Figure 5.15(a).

The reflected signal reached steady-state a few seconds after the sample was moved

into the beam path. This is due to the transient response time of the power meter

used to monitor the reflected power. The steady-state implies that the laser power

absorption in the film is stable during the scan. The apparent reflectivity for each

line scan is determined by dividing the steady-state value with the incident laser

power. The results are shown in Figure 5.15(b). As the laser power increases, the

apparent reflectivity first decreases slightly. This may be attributed to change of

the absorption of the film with temperature. If the laser power is too high, the


0 2 4 6 8 10 12 14 16-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

sample moved out

App

aren

t ref

lect

ed p

ower

, Pre

flect (W

)

Time (s)

sample moved in

Steady-stateTransient region

Parameters:v=3 mm/sPlaser=3.17 W

(a)

2.0 2.5 3.0 3.5 4.0 4.515

20

25

30

35

40

45

50

App

aren

t ref

lect

ivity

(%)

Incident laser power (W)

v=2mm/s v=3mm/s v=4mm/s v=5mm/s

(b)

Figure 5.15: (a) A typical dynamic measurement of the reflected laser power; (b)Apparent reflectivity.


apparent reflectivity decreases significantly to 20∼30%. Figure 5.16 shows the surface

morphology observed after laser exposure at high energy. At this level of energy, all

the possible energy-dependant surface morphologies are found. In Figure 5.16, four

different regions are present. On the edges of exposed area, where the laser power

is the lowest, an oxide layer is visible but no evidence of crystallization is found.

Moving toward the center of the laser beam, a crystallized zone is observed. This

is clearly visible due to a change of roughness in presence of martensite similar to

Figure 5.14. Moving closer to the center, a wrinkled zone is typically observed and

is attributed to heat-induced delamination of the film. Finally, in the center of the

beam, a damaged region is found where the film is completely turned into oxide.

Each of these regimes: oxidized, crystalline, wrinkled and ”damaged” yield different

optical absorption properties. In particular the damaged region is believed to cause

the most significant decrease of the apparent reflectivity as part of the laser beam is

now able to go through the specimen. This is supported by the sudden increase in

the transmitted signal monitored by the photodetector.

In the finite element modeling, R is fixed at 42% while P is varied. Figure 5.17

shows a typical temperature distribution in Ni-Ti film calculated from finite element

modeling (in this case, the laser power is 3 W and scan speed is 4 mm/s). The laser

beam moves from the right to the left. This temperature contour moves at the speed

of the laser scan in steady-state. The temperature of the film reaches 1070 K at

the center of laser trace. Away from the center, the temperature decreases dramat-

ically. The film far from the laser is still at room temperature which indicates the

dimensions of the FEM model are big enough to exclude any edge effects. The pro-


Figure 5.16: PSI measurement for high power laser beam. Vertical lines observed inthe crystallized region are measurement artifacts resulting from the presence of theoxide layer that perturbs the interference pattern used to measure the height profile.


Temperature(K)

+3.043e+02+3.681e+02+4.319e+02+4.958e+02+5.596e+02+6.234e+02+6.872e+02+7.511e+02+8.149e+02+8.787e+02+9.426e+02+1.006e+03+1.070e+03

Laser scan direction

Figure 5.17: Temperature contour in Ni-Ti film calculated from FEM (Parameters:P=3 W, v=4 mm/s, R=42%.). The laser moves from the right to the left.

cedure of determining the size of crystalline zone is demonstrated in Figure 5.18 for

the case shown in Figure 5.17. Figure 5.18(a) shows the temperature history profiles

at several locations away from the laser center. Figure 5.18(b) shows the maximum

temperature the film experienced as a function of distance away from the laser cen-

ter. Using nucleation and growth kinetics parameters, the transformation fraction

was calculated using Equation 5.3 and also plotted in Figure 5.18(b). The transfor-

mation fraction drops quickly from 100% to zero over a distance of approximately

20 µm due to the rapid decrease of peak temperature. This suggested the width of

crystalline-amorphous boundary in laser annealing is in the order of a few tens µm.

This is consistent with the observation in Figure 5.7. We chose 50% as the cut-off

point of crystallized zone. The predicted size of crystallized region is simply 2 times

the distance of the location where the transformation is equal to 50%. Figure 5.19

shows the comparison between the predicted size of crystallized zone and experimen-

tal results. The horizontal axis in Figure 5.19 is the apparent laser power absorbed by


0.0 0.1 0.2 0.3 0.4 0.5 0.6200

300

400

500

600

700

800

900

1000

1100

1200

Tem

pera

ture

(K)

Time (second)

y=0 m y=100 m y=148 m y=206 m y=294 m

(a)

0 50 100 150 200 250 300 350 400400

500

600

700

800

900

1000

1100

1200

Distance from the center ( m)

Pea

k te

mpe

ratu

re (K

)

wC/2

50% crystallization

Temperature

0

20

40

60

80

100 Fraction Transform

ation fraction (%)

(b)

Figure 5.18: (a) Temperature profile in Ni-Ti film at various locations away fromthe laser center; (b) Peak temperature and transformation fraction as a function ofdistance away from the laser center.


1.0 1.5 2.0 2.5

200

300

400

500

600

700

800

V = 4 mm/s

V = 5 mm/s

V = 3 mm/s

Wid

th (

m)

Absorbed laser power, P(1-R) (W)

V = 2 mm/s

Solid symbol: ExperimentOpen symbol: Simulation

Figure 5.19: Comparison between the predicted size of crystallized zone and experi-mental results.

the film, i.e., P (1-R). For the ”damaged” cases when the laser power is high as shown

in Figure 5.16, a value of 40% for the apparent reflectivity was used. The simulation

results have been shifted by a factor of 0.82±0.02 for all scan speeds on laser power

axis to get good agreement with experimental results. This shift indicates that the

simulation systematically overestimates the laser power needed to create a given crys-

tallization size. This kind of deviation could be due to the systematical uncertainty

of measured laser power or thermal properties of the material. The overall agreement

between the simulation and experiment by adjusting a single factor indicates that the

thermal model catches the key mechanism of laser annealing process.


5.4 Conclusions

In conclusion, we have investigated a laser annealing technique that allows us to

selectively crystallize an amorphous Ti-Ni film in specific areas where shape memory

properties are desired. The film undergoes homogenous nucleation and has a random

crystallographic texture after crystallization. The crystallized films have a uniform

microstructure across the annealed area for the range of laser annealing parameters

used in this study. The material in the crystallized regions transforms to martensite

at room temperature demonstrating that shape memory properties can be selectively

introduced. Stress measurements show that a significant recovery stress is achieved

in the laser annealed films making them useful materials for actuator devices. We

have developed a method to simulate the crystallization results of laser annealing

process of amorphous Ni-Ti thin films using a 3-D thermal model. The temperature

profile induced by the laser beam was calculated using finite element method. The

experimentally determined crystallization kinetics parameters were included in the

model to allow us predict the size of the crystallized region as a function of laser

annealing parameters. The simulation results match well with the experiments by a

shift of single factor which is related to systematic uncertainty in the process. The

model can also be used in the crystallization study of other material systems by laser

annealing such as phase change materials in data storage industry.

Chapter 6

Conclusions

6.1 Summary and concluding remarks

The solid-state phase transformations in the Ni-Ti alloy system are the excellent

case study for the processing-microstructure-property relationship in materials sci-

ence and engineering. They include not only martensitic transformations, from which

shape memory and superelastic effects arise, but also crystallization upon which the

microstructure evolves and which can change the shape memory characteristics. Ni-

Ti thin films are of technological interest as actuator materials in advanced MEMS

devices which attracted extensive research attentions on the fabrication, characteri-

zation, and modeling of these materials. Of particular importance is to understand

how the solid-state phase transformations behave and scale in Ni-Ti films. We have

designed a series of experiments to quantitatively investigate the crystallization ki-

netics and size effects in the martensitic transformation in Ni-Ti films of submicron

thicknesses. We also explored the laser annealing process as a novel local crystalliza-

101

Chapter 6: Conclusions 102

tion technique. We conclude by summarizing the main findings and implications of

the current research.

The fact that Ni-Ti films are usually amorphous in their as-deposited state pro-

vides an opportunity to control the microstructure by adjusting the crystallization

conditions, and consequently control their shape memory properties. Crystalliza-

tion of amorphous Ni-Ti films includes continuous nucleation and growth processes.

Quantitative measurement of the crystallite nucleation and growth rates and their

temperature dependence were performed for amorphous Ni-Ti thin films sandwiched

between two SiNx layers. We found that the nucleation is very sensitive to chem-

ical composition. The reaction between Ni-Ti films and surrounding layers results

in a small composition shift of these interfaces and suppresses nucleation at those

locations. As a result, crystallites nucleate homogeneously inside the film. By com-

pensating the composition shift, nucleation can occur at the interface resulting in dif-

ferent microstructure. In near-equiatomic Ni-Ti films, the crystal growth is interface-

controlled. But the growth rate is strongly affected by hydrogen content in Ni-Ti

films. Hydrogen present in the surrounding SiNx layers diffuses into Ni-Ti films upon

annealing and slows down the growth process in thinner films. This findings implies a

new approach to control the crystallization process by introducing various amount of

hydrogen in the Ni-Ti matrix. A preliminary study showed that overexposuring Ni-Ti

films to hydrogen plasma results in metal hydride films, but a nanocrystalline Ni-Ti

film can be formed after decomposing hydride at 500 C [121]. By understanding the

crystallization process and manipulating nucleation and growth rates, an unprece-

dented control over the microstructure of the films is possible. The average grain


size of an 800 nm Ni-Ti film can be varied from less than 5 µm to as large as 60

µm depending on the precise crystallization temperature. Given an appropriate heat

treatment and in-plane film layout, it may even be possible to grow single crystal

films.

The size effect in martensitic transformation is not a new topic but there are rather

few reports on Ni-Ti films in the literature. This is so because decoupling composition

shift and the intrinsic size effect in Ni-Ti thin films is difficult. Using the conven-

tional substrate curvature technique, we have designed sample preparation procedure

to overcome those issues and have studied shape memory behavior of Ni-Ti thin films

of submicron thicknesses. SiNx layers minimize the interfacial reaction and surface

oxidation of Ni-Ti films and made the investigation of intrinsic size effect possible.

Large grain size achieved by appropriate annealing makes it possible to evaluate the

effect of film thickness independent of the grain size. We found the transformation

temperature starts to decrease when film thickness is below 400 nm. This decrease

is associated with an increasing energy barrier to transformation in thinner films. A

simple micromechanics model predicts the square root dependence of transformation

temperature on film thickness while our data show a steeper dependence. It seems

that a more sophisticated model is required to describe the observed behavior. The

results also give some insights on transformation under substrate constraint. The

results show that the transformation strain is not exhausted upon transformation.

The stress drop curve upon transformation represents the stress-dependence of the

transformation in films on substrates but it is much higher compared to the depen-

dence predicted by the existing model. Lower austenite stress results in two-stage


transformation as in bulk material.

As a novel technique of local crystallization, laser annealing process of Ni-Ti thin

films were studied both experimentally and numerically. The nucleation and growth

mechanisms in the laser annealing process were found to be the same as in furnace

annealing, which established the ground for using experimentally determined crystal-

lization kinetics parameters to predict the crystallization results of laser annealing.

Based on that, a 3-D thermal model has been developed to simulate the crystalliza-

tion behavior of the laser annealing process and allowed us to predict the size of the

crystallized region as a function of laser annealing parameters. Uniform microstruc-

ture and shape memory properties were locally introduced in the films by the laser.

The results indicate that the crystallization behavior is strongly affected by the laser

power, scan speed, and the laser profile. Apparently, the crystallized region of a few

hundred microns and a transition region of tens of microns in a Ni-Ti film of thickness

a few microns would not generate the actuation of planar mechanism. In order to

achieve the planar mechanism, a much smaller crystallized region and a much nar-

rower transition are required. This will need a more sophisticated control of the laser

beam. But with the current set-up, a complicated pattern can be easily transferred

onto a thin sheet of functional material. By using different properties in crystallized

region and amorphous region, it is possible to achieve a designed morphology change

in this thin structure. This would be particularly attractive to optical and biomedical

applications.


6.2 Suggestions for future work

The subjects of this work are of technologic and scientific interest in many aspects.

Although extensive efforts have been made, it is far from complete and needs more

exploration.

Hydrogen plasma treatment was found to dramatically affect the crystallization

kinetics of Ni-Ti thin films. But its precise mechanism is not clear and needs further

investigation. A lot of coatings and processing techniques in semiconductor industry

consists of hydrogen and it makes the integration of Ni-Ti film into advanced de-

vices more challenging. Understanding of the microstructure evolution under various

conditions is of particular value for the applications.

Electrical resistance measurement is a promising technique to study the shape

memory properties of thin film on substrate down to nanometer range. It is also

easy to incorporate with the cooling system so that the temperature studied can be

easily extended to liquid nitrogen temperature. Our sample preparation experiences

should come in handy in this measurement. In-situ TEM is a powerful tool to si-

multaneously observe the microstructure change upon transformation. Advances in

nanotechnology make it possible to fabricate nanoparticles or nanocrystals of shape

memory alloys. The in-situ investigation on nanosize materials will further extend the

experimental work on size effect. Inclusion into the constitutive behavior model of

various microstructural features will lead to more precise and predictive constitutive

laws for shape memory alloy films.

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