Crystallization and Martensitic Transformation Behavior of NiTi
Transcript of Crystallization and Martensitic Transformation Behavior of NiTi
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
c©2007 - Xi Wang
All rights reserved.
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
Chapter 1: Introduction 3
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])
Chapter 1: Introduction 4
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
Chapter 1: Introduction 5
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])
Chapter 1: Introduction 6
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
Chapter 1: Introduction 7
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
Chapter 1: Introduction 8
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
Chapter 1: Introduction 9
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
Chapter 1: Introduction 10
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
Chapter 1: Introduction 11
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.
Chapter 1: Introduction 12
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
Chapter 1: Introduction 13
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
Chapter 2: Experimental techniques 16
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.
Chapter 2: Experimental techniques 17
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).
Chapter 2: Experimental techniques 18
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.
Chapter 2: Experimental techniques 19
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
Chapter 2: Experimental techniques 20
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.
Chapter 2: Experimental techniques 21
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.
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 24
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
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 25
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
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 26
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
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 27
(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-
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 28
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
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 29
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.
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 30
(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).
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 31
(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
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 32
Figure 3.5: Plan-view TEM image of a disk-shape Ni-Ti grain.
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 33
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
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 34
(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.
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 35
(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.
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 36
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.
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 37
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
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 38
Table 3.2: Hydrogen plasma treatment conditons.
Base pressure (Torr) 2×10−6
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.
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 39
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
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 40
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.
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 41
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-
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 42
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
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 43
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
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 44
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
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 45
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-
Chapter 3: Crystallization kinetics of amorphous Ni-Ti thin films 46
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
Chapter 4: Size effects in martensitic transformation behavior 49
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
Chapter 4: Size effects in martensitic transformation behavior 50
Table 4.1: Deposition conditions of PECVD SiNx film (Recipe: SiNLST).
Base pressure (Torr) 1×10−7
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
Chapter 4: Size effects in martensitic transformation behavior 51
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
Chapter 4: Size effects in martensitic transformation behavior 52
(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.
Chapter 4: Size effects in martensitic transformation behavior 53
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
Chapter 4: Size effects in martensitic transformation behavior 54
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
Chapter 4: Size effects in martensitic transformation behavior 55
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-
Chapter 4: Size effects in martensitic transformation behavior 56
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.
Chapter 4: Size effects in martensitic transformation behavior 57
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.
Chapter 4: Size effects in martensitic transformation behavior 58
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
Chapter 4: Size effects in martensitic transformation behavior 59
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.
Chapter 4: Size effects in martensitic transformation behavior 60
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.
Chapter 4: Size effects in martensitic transformation behavior 61
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
Chapter 4: Size effects in martensitic transformation behavior 62
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-
Chapter 4: Size effects in martensitic transformation behavior 63
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-
Chapter 4: Size effects in martensitic transformation behavior 64
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
Chapter 4: Size effects in martensitic transformation behavior 65
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.
Chapter 4: Size effects in martensitic transformation behavior 66
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
Chapter 4: Size effects in martensitic transformation behavior 67
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
Chapter 4: Size effects in martensitic transformation behavior 68
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.
Chapter 4: Size effects in martensitic transformation behavior 69
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
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 72
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
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 73
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
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 74
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.
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 75
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
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 76
(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.
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 77
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
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 78
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,
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 79
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],
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 80
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 .
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 81
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
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 82
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
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 83
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
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 84
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.
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 85
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.
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 86
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
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 87
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
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 88
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
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 89
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.
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 90
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
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 91
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
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 92
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
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 93
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
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 94
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.
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 95
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-
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 96
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.
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 97
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
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 98
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.
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 99
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.
Chapter 5: Laser annealing of amorphous Ni-Ti thin films 100
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
Chapter 6: Conclusions 103
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
Chapter 6: Conclusions 104
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.
Chapter 6: Conclusions 105
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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