Nanoindentation-Induced phase transformations in ......i Nanoindentation-Induced phase...
Transcript of Nanoindentation-Induced phase transformations in ......i Nanoindentation-Induced phase...
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Nanoindentation-Induced phase
transformations in amorphous Germanium
Sarita Deshmukh
A thesis submitted for the degree of
Masters of Philosophy
of
The Australian National University
May 2016
Canberra, ACT
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CERTIFICATE
This thesis, to the best of my knowledge and belief, does not contain any results
previously published by another person or submitted for a degree or diploma at any
university except where due reference is made in the text.
Sarita Deshmukh
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To my parents
for showing me the value of education and to my husband
for giving me the support when I needed it the most.
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Acknowledgements
I firstly wish to thank my supervisors, A/Prof Jodie Bradby and Prof Jim Williams, for
their expert guidance, patience, and assistance in all aspects of research and for providing
me with all the necessary facilities for the research. Their enthusiasm for doing and
communicating quality research has been inspirational. I am greatly thankful to Jodie for
her strong support, continuous encouragement, and understanding when I deeply needed
it. I am also deeply grateful to her for her sincere and valuable guidance throughout the
extended period.
I sincerely thank Dr Bianca Haberl of the Oak Ridge National Laboratory for sharing her
knowledge and expertise on indentation with me, for stimulating discussions on Raman
results and working on my samples during Raman and FIB trips, which greatly helped to
progress my experimental work and further analysis of the results presented here. I would
like to thank Dr Simon Ruffell for carrying out the ion implantation in this thesis, and for
helpful discussions of results in the beginning of my project. I acknowledge Prof Paul
Munroe at the University of New South Wales for access to the FIB system and comments
on papers published as a result of this work. I am thankful to Dr Brett Johnson for his
detailed analysis of Raman results. Without his work and support it was not possible to
fully understand my results. I am grateful to Dr Brad Malone from University of
California, Berkeley, for doing DFPT calculations on my results. I am thankful to Dr
Leonardus Bimo bayu Aji from Lawrence Livermore National Laboratory for assistance
with relaxation study. I acknowledge and thank A/Prof Bradby for performing the TEM
contained in this thesis. I am thankful to Sherman Wong and Larissa Huston from the
Australian National University for proof reading and commenting on my thesis.
I am deeply grateful to the people who have given support and encouragement over the
course of this project for years. These include my parents, my in-laws, and my brother
Sujit Barde and I am thankful to my lovely kids Jai Deshmukh and Ira Deshmukh for
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being so good when I was working on my thesis. I am also grateful to my fellow students
in the department of Electronic Materials Engineering,
Finally, my deepest acknowledgement goes to my husband and best friend Ketan
Deshmukh for his love, patience, companionship, and emotional support throughout my
MPhil.
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Abstract
Semiconductors were traditionally considered to be classic ‘brittle’ materials, which
under indentation load behave elastically until undergoing sudden and generally
catastrophic failure via cracking. However, under certain conditions it is clear that many
semiconductors also undergo considerable plastic deformation. Such plastic deformation
mechanisms in semiconductor materials include defect generation and propagation, and
under point loading, phase transformation. Germanium (Ge) is one of the most important
semiconductors and is used in many technological applications. Crystalline Ge (c-Ge) has
been reported to undergo a wide range of deformation mechanisms during point loading
including twinning, defect generation as well as pressure-induced phase transformation.
In this study amorphous Ge (a-Ge) is chosen as a starting material to explore the
mechanisms of deformation that are excluded by the lack of long range order/crystallinity.
In the literature there is some controversy as to what is the preferred indentation-induced
deformation mechanism of Ge at room temperature. Some studies report twinning and
defect generation while others report that a high-pressure phase transformation occurs.
This thesis studies nanoindentation induced phase transformations in a-Ge. Ion
implantation has been used to amorphize crystalline Ge in this study. This eliminates the
competing deformation mechanisms of slip and twinning previously observed in c-Ge
deformed via nanoindentation. Nanoindentation is now commonplace tool for the
measurement of mechanical properties and also for inducing high-pressures required for
phase transformation at small scales. In this study two different nanoindenter tips are
used, spherical and Berkovich. Most of the work carried out using a spherical geometry
to avoid cracking. A wide range of techniques are employed in this work to study the
response of the indented a-Ge samples. These include micro-Raman spectroscopy,
scanning electron microscopy, focussed ion beam milling and cross-sectional
transmission electron microscopy.
An interesting range of deformation responses is observed. Nanoindentation of the a-Ge
samples shows that phase-transformation is readily induced, unlike c-Ge where phase
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transformations are only observed on occasion. Analysis of the nanoindentation curves
from a-Ge shows that, above a threshold limit, a pop-in event occurs on loading. After
the pop-in event the loading curves fall into two distinct deformation pathways. These
have been named family ‘a’ and family ‘b’. In one case family ‘b’ the end-phase is
predominantly observed to be diamond cubic Ge (dc-Ge) and the other case, the end-
phase appears to be a rhombohedral phase with 8 atoms per unit cell (r8). The r8 phase is
found to be unstable and transforms to hexagonal diamond Ge (hd-Ge) at room
temperature within hours.
The reason for these two different deformation pathways are related to the soft metallic
(β-Sn)-Ge which forms on loading. It is proposed that if this metallic region is
unconstrained by the indenter tip, the material is then extruded suddenly and during this
process it transforms to dc-Ge. This behaviour is labelled as family ‘b’. Whereas, if the
material is totally constrained under the tip, it transforms instead to unstable r8 structure
which then further transform to hd-Ge. This pathway is referred to as family ‘a’.
This work also examines the structure of the ion-implanted a-Ge as a function of
annealing at temperatures below the recrystallization temperature. This so-called
‘structural relaxation’ is similar to that previously observed in amorphous silicon (a-Si).
Moreover, similar to a-Si, the relaxation of a-Ge is shown here to lower its threshold for
deformation via phase transformation. Finally, as previous studies on indentation-induced
phase transformation in Ge have suggested that rate of loading and/or unloading may
influence the deformation behaviour, this work also investigated this parameter. Slow
loading rates are shown to mildly inhibit the phase transformation process of a-Ge.
This work establishes a clear set of conditions under which phase transformations can be
induced in Ge. In particular, the study shows that hd-Ge can be readily formed in a range
of a-Ge film thicknesses. This finding enables these technologically-promising additional
phases of Ge to be further studied and potential applications explored for the first time.
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Contents
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1. Introduction 1
1.1 Germanium ……………………...…………………………………………… 2
1.2 Literature review …………………………………………………………..... 3
1.2.1 Diamond anvil cell studies of Ge………...……………………………... 3
1.2.2 Nanoindentation study on crystalline Ge ……………………………............... 5
1.2.3 Nanoindentation study on amorphous Ge …………………………….…. 8
1.2.4 Diamond Anvil Cell study on crystalline Si……………….……………. 10
1.2.5 Nanoindentation study on crystalline Si and amorphous Si ……………. 11
1.3 Outline of this thesis…………………………………………………………… 11
2. Experimental Techniques 17
2.1 Ion-implantation………………………………………………………………… 18
2.1.1 Ion implantation damage…………………………………………………… 19
2.2 Sample preparation…………………………………………………………… 20
2.3 Nanoindentation………………………………………………………………. 20
2.3.1 Ultra micro indentation system (UMIS) ................................................... 22
2.3.2 Details of nanoindentation testing for this work ………………………... 29
2.4 Raman micro-spectroscopy ……………………………………………………. 31
2.5 Focused ion beam system …………………………......…………….…………. 34
2.6 Transmission electron microscopy ………………………………………….…. 35
3. Pressure-induced phase transformations in a-Ge 41
3.1 Experimental details …………………………………………………………. 42
3.2 Thin a-Ge films ………………………………………………………………. 43
3.3 Phase assignment of Raman peaks: …………………………………………… 53
3.4 Thick a-Ge films ………………………………………………………………. 57
3.5 Phase stability in the family ‘a’ case …………………………………………. 61
3.6 Summary of thin and thick films of amorphous Ge ……………….………… 62
4. Further details of phase transformations in a-Ge: Exploring
indentation conditions 65
4.1 Effect of relaxation of a-Ge on nanoindentation-induced phase transformation.
………………………...………………………………………………………...... 66
Contents
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4.2 Effect of indenter geometry on phase transformation pathways ………….…. 75
4.3 Effect on Loading/unloading rates on phase transformation in a-Ge…………. 80
5. Discussion conclusions and future work 88
5.1 Phase transformation of a-Ge under indentation ……………………….……. 89
5.2 Consideration of explosive crystallization ……………………………………89
5.3 Evidence of st12 from indentation studies ……………………………………90
5.4 Transformation pathways in a-Ge under indentation …………………………94
5.5 Discussion of literature results in light of results of this thesis ……………….97
5.6 Conclusions………………………………………………….…..…………….99
5.7 Future studies………………………………………………….……………...100
Contents
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List of figures
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List of Figures
Chapter 1
1.1 Schematic showing the phase transitions observed for c-Ge under Diamond anvil cell
(DAC) loading and unloading
1.2 The above figure shows the study by Jang et al nanoindentation-induced phase
transformation in germanium using cube-corner and Berkovich indenter.
1.3 Schematic showing the phase transitions observed for c-Ge under nanoindentation
loading and unloading.
1.4 Schematic showing the phase transitions observed for a-Ge under nanoindentation
loading and unloading.
1.5 Schematic of phase transformations of diamond cubic silicon in diamond anvil cell
(DAC) compression and decompression.
Chapter 2
2.1 Schematic showing the key features of tandem accelerator.
2.2 Schematic of the ultra-micro indentation system (UMIS).
2.3 Schematics of (a) indentation contact geometry and (b) P-h curve, according to Oliver
and Pharr analysis.
2.4 Schematic of load-displacement data from Field and Swain analysis.
2.5 Schematic of load-unload curve with a formation of “pop-in” using spherical indenter.
2.6 Schematic of load-unload curve with a formation of “pop-out” using spherical
indenter.
2.7 Schematic of load-unload curve with a formation of “pop-in” on loading curve and
“elbow” on unloading curve using spherical indenter.
2.8 Typical load-unload curve to 100 mN in a-Ge sample.
2.9 Raman spectrum of typical a-Ge.
2.10 Raman spectrum of metastable phases produced by applying pressure to a-Ge.
2.11 Raman spectrum of dc-Ge.
2.12 Schematic diagram of the dual beam column layout of an FIB system used in this
study.
2.13 Schematic of transmission electron microscopy imaging mode, where the image is
projected on the viewing screen.
List of figures
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2.14 Cross-sectional TEM image from an indent performed on a-Ge and selected area
diffraction patterns obtained at various regions.
Chapter 3
3.1 (a) A set of 10 load-unload curves in a ~ 700 nm a-Ge film using ~4.3 µm radius
spherical tip. Two types of deformation behaviour (blue family ‘a’ and red family ‘b’) are
observed (as determined by slope of the loading curve after pop-in. The horizontal arrow
indicates the onset of pop-in events. (b) Load-unload curves for indentation tests made in
the ~ 700 nm film using ~4.3 µm radius spherical tip to highlight the differences in typical
family ‘a’ and family ‘b’ behaviour.
3.2 Representative load-unload curves for indentation tests made in the ~ 1000 nm film
using a ~4.3 µm radius spherical tip, indicating both family ‘a’ and family ‘b’ behaviour.
The applied load is 100 mN or 120 mN and an occasional ‘pop-out’ is observed when the
maximum load (~100 mN) is close to the pop-in load.
3.3 (a) Normalised Raman spectra taken from family ‘a’ and family ‘b’ indents loaded to
100 mN using a ~4.3 µm radius tip in an ~700 nm thick a-Ge film. A Raman spectrum
from unindented a-Ge is shown for comparison. (b)Raman spectra taken from family ‘a’
and family ‘b’ indents loaded to 120 mN using a ~4.3 µm radius tip in an ~1000 nm thick
a-Ge film. A Raman spectrum from unindented a-Ge is shown for comparison.
3.4 (a) Bright field XTEM images of family ‘a’ indent in an ~700 nm film indented to
100 mN. Selected Area Diffraction Patterns (SADP) taken from the respective phase-
transformed region. (b) Bright field XTEM images of family ‘a’ indent in an ~1000 nm
film indented to 125 mN. Selected Area Diffraction Patterns (SADP) taken from the
respective phase-transformed region.
3.5 (a) Bright field XTEM images of family ‘b’ indent in an ~700 nm film indented to
100mN. Selected Area Diffraction Pattern (SADP) taken from the respective phase-
transformed region. (b) Bright field XTEM images of family ‘b’ indents in an ~1000 nm
film indented to 125 mN. SADP taken from the respective phase-transformed region.
3.6 Experimental Raman spectra of the indented a-Ge immediately after indentation fit
with a series of Gaussian fits (solid lines). An a-Ge line shape was included in the fit
(dashed line). The inset shows the low frequency region from (i) the indented a-Ge and
(ii) pure a-Ge showing the broad transverse acoustic a-Ge Raman band.
3.7 Experimental Raman spectra (i) from Fig. 3.6 compared to (ii) that of an indent
formed under similar conditions in a-Si. The intensity has been scaled for comparison.
The inset shows the low frequency region from the indented (i) a-Ge and (ii) a-Si
List of figures
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3.8: (a) Raman-active mode frequencies decided by DFPT for various Ge phases. The
upper bars are the experimentally observed peak positions, the width of the bar being the
associated standard deviation of the six indents measured. (b) The calculated st12 Raman
spectra. The r8 and bc8 intensities could not be calculated since they are metallic within
the calculations
3.9 (a) Load-unload curve from an ~1800 nm thick a-Ge film indented with a ~20 µm
radius spherical tip to maximum loads of 450 mN and 700 mN. (b) Raman spectra of the
~1800 nm film for the 700 mN indent with a spectrum from unindented a-Ge shown for
comparison. The broad peak centered at 295 cm-1 is characteristics of the hd-Ge band
observed for thinner films for Raman spectra taken after several days.
3.10 Bright field XTEM image of an indent in an ~1800 nm thick a-Ge film made with a
~20 µm radius spherical tip to a maximum load 700 mN. Image shows a SADP taken
from the phase-transformed region where the most intense spots have been indexed
predominately to hd-Ge and the amorphous material right under the transformed region.
3.11 Raman spectra straight after the indent and after various times ta at room temperature
from an ~1800 nm thick a-Ge film indented with a ~20 µm radius spherical tip to a
maximum load of 700 mN. The assignments for r8 and hd-Ge phases from DFPT
calculations (section 3.3) are also shown.
Chapter 4
4.1 Typical Raman spectra from relaxed a-Ge, showing the transverse optic (TO) peak.
(Note that the location of the transverse acoustic (TA) is 80 cm-1 and hence not measured
in this study. The half width ΓTO/2 is indicated.
4.2 Raman spectrum of unrelaxed and relaxed a-Ge samples annealed at 250o
C, 300oC
and 350oC each for 30 mins.
4.3 Calculated bond angle distortion versus the different annealing temperatures of a-G.
(Calculated using the Beeman relaxation equation).
4.4 TO line width measured from Raman spectra of a-Ge versus annealing temperature
(annealing time was 30 min).
4.5 Load-displacement curves of indents made to 100 mN with a spherical tip of ~ 4.3
µm radius in (a) unrelaxed a-Ge and (b) relaxed Ge (annealed at 350° C for 30 mins
4.6 (a) Raman spectra of a nanoindent made with 100 mN load in unrelaxed Ge. (b)
Raman spectra of a nanoindent made with 100 mN load in relaxed Ge (annealed at 350°
C for 30 mins).
List of figures
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4.7 Load-unload curves of nanoindents made to 100 mN in a-Ge using (a) ~4.3 µm
spherical tip. (b) The inset to (b) shows a single load-unload curve to clearly show the
pop-in event using Berkovich tip.
4.8 (a) Raman spectra of a nanoindent made with 100 mN load to a-Ge using ~4.3 µm
spherical tip. (b) Raman spectra of a nanoindent made with 100 mN load using Berkovich
tip.
4.9 (a) SEM image of a family ‘a’ nanoindent made with 100 mN load to a-Ge using ~4.3
µm radius spherical tip. (b) SEM image of a family ‘b’ nanoindent made with 100 mN
load to a-Ge using ~4.3 µm radius spherical tip. (c) SEM image of a nanoindent made
with 100 mN load using Berkovich tip.
4.10 Schematic of constrained family ‘a’ indent and unconstrained family ‘b’ indent
image was made with a certain in a-Ge using spherical tip.
4.11 slow load (200 increments) and standard unload (50 increments) with loading rate
~0.5 mN/s curve from a ~700 nm thin a-Ge film indented with ~4.3 µm radius spherical
tip to a maximum load of 100 mN (80 % curve falls in family ‘b’ and 20 % falls in
family ‘a’).
4.12 Raman spectra from indents made with a spherical tip using UMIS, fast unloading
rate, family ‘b’ spectra shows amorphous shoulder and possibility HPP in the family ‘a’
spectra (This Raman spectrum was taken after several days of indentation as the HPP are
unstable at room temperature (see Chapter 3)).
4.13 (a) XTEM image of family ‘a’ spherical indent using slow loading and standard
unloading rate. (b) XTEM image of family ‘b’ spherical indent using a slow loading and
standard unloading rate introduces blocks of amorphous material in the transformed
region and underneath the indent.
4.14 Fast load (2, 5, and 15 increments) and standard unload (50 increments) with
loading rate ~6 mN/s curve from a ~700 nm thin a-Ge film indented with ~4.3 µm
radius spherical tip to a maximum load of 100 mN (80 % curve falls in family ‘b’ and
20 % falls in family ‘a’).
Chapter 5
5.1 Raman spectra from indents by Kailer et al showing extra Raman band assigned to
mainly st12-Ge but hd-Ge is present in the middle curve.
5.2 <110> zone axis XTEM micrograph of ultrarapid loading with a spherical indenter of
~ 4 µm radius to ~ 165 mN s-1. Inset shows SADP.
List of figures
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5.3 Schematic showing the deformation pathways associated with the indentation of a-
Ge found in this study. The dashed transformation pathways indicate that this pathway is
unclear, for example, whether there are intermediate phases associated with the family
‘b’ transformation from (β-Sn)-Ge to dc-Ge on unloading and also for the family ‘a’
transformation from r8-Ge to hd-Ge at room temperature.
5.4 Schematic showing the deformation pathway associated with the indentation of
relaxed a-Si found in the study by Haberl et al.
List of tables
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List of Tables
1.1 High pressure phases and structure of germanium and for more details the references
contained theirin.
4.1 Summary of the deformation behavior of thick a-Ge layer after various relaxation
anneals. (- pop-in, х – no pop-in.).
4.2 Summary of the deformation behaviour of slow and fast loading/unloading rate.
List of acronyms
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List of Acronyms
a-Ge amorphous Ge
a-Si amorphous Si
AFM atomic force microscopy
BSE back-scattered electron
BF bright field
BC8 body-centered cubic structure with 8 atoms per primitive cell
β-Sn-Ge beta tin germanium
c-Si crystalline Si
CSIRO commonwealth scientific and industrial research organization
DAC diamond anvil cell
DF dark field
DP diffraction pattern
DLTS deep-level transient spectroscopy
FCC face-centered cubic
FIB focussed ion beam
hda-Ge high-density amorphous germanium
hd-Ge hexagonal diamond germanium
LA longitudinal acoustic
LO longitudinal optic
LVDT linear variable differential transformer
r8 rhombohedral with 8 atoms per primitive cell
RBS rutherford backscattering spectrometry
st12 simple tetragonal with 12 atoms per primitive cell
SADP selected area diffraction pattern
List of acronyms
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SEM scanning electron microscopy
TA transverse acoustic
TO transverse optic
TEM transmission electron microscopy
UMIS ultra-micro indentation system
XTEM cross-sectional transmission electron microscopy
Publications
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Publications
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Publications resulting from this work
1. Sarita. Deshmukh, B. Haberl, S. Ruffell,1 P. Munroe,2 J. S. Williams,1 and J. E.
Bradby. “Phase transformation pathways in amorphous germanium under indentation
pressure”. Journal of Applied Physics 115, 153502 (2014).
2. James S. Williams, Bianca Haberl, Sarita Deshmukh, Brett C. Johnson, Brad D.
Malone, Marvin L. Cohen, and Jodie E. Bradby. “Hexagonal germanium formed via a
pressure-induced phase transformation of amorphous germanium under controlled
nanoindentation”. Rapid Research Letters, Phys. Status Solidi 7,355–359 (2013).
3. Brett C. Johnson, Bianca Haberl, Sarita Deshmukh, Brad D. Malone, Marvin L. Cohen,
Jeffrey C. McCallum, James S. Williams, and Jodie E. Bradby. “Evidence for the r8 phase
of germanium”. Physics Review letters 110, 085502 (2013).
Introduction
CHAPTER 1
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CHAPTER 1
Introduction
Introduction
CHAPTER 1
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1.1 Germanium
Germanium (Ge) is an interesting semiconductor material but it has not been studied
extensively as compared to silicon (Si). Today the semiconductor industry has a renewed
interest in Ge and Si-Ge alloys to make high speed processors, due to higher carrier
mobilities of Ge and its alloys, and compatibility with many existing Si processing
methods. [1] There are many techniques to study semiconductor materials including those
to study mechanical properties. In this thesis, I have studied the behaviour of Ge under
pressure using the nanoindentation technique, and compared results with more
conventional diamond anvil cell (DAC) studies where crystalline Ge shows an interesting
series of phase transitions under pressure. However, there is less information available
for amorphous Ge phase transitions which has been the subject of recent interest and is
the material particularly studied in this thesis and discussed in the following sections.
One way to study the deformation of the material at the small scale is depth-sensing
nanoindentation. This technique was developed in the 1980s to study the hardness of
small volumes of material. A hard tip, generally made up of diamond, whose properties
are already known is pressed into the material with a well-defined load. Nanoindentation
can be used to monitor or measure changes in the material such as elastic deformation,
plastic deformation, high pressure phase formation, dislocation (formation and
propagation), mechanical twinning, hardness and elastic modulus. Nanoindentation is
also an important tool for measuring residual stresses, time dependent creep and probing
the mechanical properties of very small material volumes. In this study nanoindentation
is used as the prime way of deforming the material, since it can study the accurate
transformation of the material at very small load and penetration depths. Studying the
deformation of the material at such a small scale requires techniques like scanning
electron microscopy (SEM), Raman microspectroscopy and Transmission Electron
microscopy (TEM) where such characterisation techniques provide very valuable
information about the deformation of the material at the nanoscale. The centre of interest
of this study is the deformation of amorphous Ge under nanoindentation. Ge in its
amorphous form is less studied. However, from the literature, we know that it can undergo
phase transition under a range of loading and unloading conditions.
Introduction
CHAPTER 1
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1.2 Literature review
Although this thesis focuses on Ge, the literature review will also briefly cover studies
reported on Si due to the important similarities between these materials. However, the
bulk of the review will focus on Ge. The following section will cover the deformation of
both crystalline diamond cubic Ge (dc-Ge) and amorphous Ge (a-Ge) under pressure.
Two techniques are reviewed, DAC and nanoindentation. Schematics of the
transformation pathways of this material under pressure are given in the following
sections. Previous studies using the DAC technique have mainly focused on phase
transformation of dc-Ge under compression and decompression, whereas the
nanoindentation technique has similarly been used to study the transformation of the
material under loading and unloading. However, very few studies have used a-Ge as
starting material. In the following sections phase changes under both DAC and
nanoindentation in both dc and a-Ge are reviewed with the behaviour in Si reported at the
end of this chapter.
1.2.1 Diamond anvil cell (DAC) study on Ge
c-Ge
The transitions of Ge under hydrostatic stress in a DAC were first reported by Minomura
and Drickamer. [2] On DAC loading dc-Ge transforms at around 10 GPa pressure to the
metallic β-Sn phase, which is also called Ge-II and this phase is about 20 % more dense
than dc-Ge. [2] On increasing the pressure, β-Sn phase transforms to the simple
hexagonal (sh) phase via the intermediate orthorhombic Imma phase at pressures of 75-
90 GPa. [3] The transition from the sh phase to a hexagonal-closed-packed (hcp) [4, 5]
[6] structure was studied in model-calculations reported by [7] and study by Mujica et
al. [8] who found the intermediate Cmca phase, the same as that reported in Si. On slow
decompression the β-Sn phase has been reported to transform to a simple tetragonal
structure with 12 atoms in its unit cell, known as the st12 phase. [9, 10] In addition on
rapid decompression the metallic β-Sn phase found to transform to a body centered cubic
structure with 8 atoms in its unit cell, known as the bc8 phase. [11] This phase appears to
be unstable: it does not last for long periods and transforms to the hexagonal diamond
(hd) phase. [12] The sequence of dc-Ge transitions under pressures using DAC technique
is shown in the Fig. 1.1.
Introduction
CHAPTER 1
4
The reported sequence of high pressure phases of Ge is mainly comparable to Si but the
transition pressures are different, as is illustrated later in this chapter. There is
considerable confusion in the literature over the nomenculature of Ge phases with both
Roman numerals and structural terms used, as indicated in Table 1.1. In this thesis, the
phases of Ge will be referred to by their structure instead of Roman numerals as the
Roman numerals of these structures are somewhat confusing.
Table 1.1: High pressure phases and structure of Ge. [8] and for more details, consult
the references contained theirin.
a-Ge
Pressure-induced phase transformation of a-Ge is less studied as comapared to c-Ge.
However there are a few X-ray diffraction (XRD) studies under DAC hydrostatic
pressure, where a phase transition in the a-Ge material has been observed. In one such
study, Ge is made amorphous using sputtering techniques, and an amorphous-to-
crystalline phase transition was observed at around 6 GPa under presuure. [13] Such
compression gave mostly a-Ge with some crystalline inclusions. [13] The study by Imai
et al. [14] observed that upon increasing pressure, a-Ge transforms to the β-Sn phase at
Phase Name Structure
Ge-I Diamond cubic (dc)
Ge-II Body centered tetragonal (β-Sn)
No name Body centered orthorhombic(Imma)
No name Simple hexagonal (sh)
Ge-III Simple tetragonal (st-12)
Ge-IV Body centered cubic(bc8)
Ge-V Hexagonal diamond (hd)
No name Orthorhombic phase with 16 atoms in the
conventional unit cell and space group (Cmca)
No name Hexagonal-closed packed (hcp)
Introduction
CHAPTER 1
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7.6 GPa. This transition pressure is lower by 3 GPa in comparison with the c-Ge to (β-
Sn)-Ge transition. Upon releasing the pressure the β-Sn metallic phase transforms to bc8
Ge. In a latter study a-Ge is prepared using sputtering and pressure was applied using a
DAC with the presuure measured using the NaCl equation of state. [14] There are some
more intersting studies where the pressure-induced phase transition in Ge is studied. [15]
[16]
Figure 1.1: Schematic showing the phase transitions observed for dc-Ge under (DAC)
loading and unloading.
1.2.2 Nanoindentation study on crystalline germanium (c-Ge)
Previous nanoindentation studies on dc-Ge have produced many interesting and
conflicting results with many unanswered questions. There are also some differences
between indentation and DAC studies on Ge as reviewed in the previous section. In one
case, loading a Vickers indenter onto dc-Ge was found to transform it to a metallic β-Sn
Introduction
CHAPTER 1
6
phase and on unloading to the st-12 phase. [17] In another case, Gogotsi et al. [18] found
(from weak Raman signatures) metastable crystalline end phases of Ge, presumably form
metallization during nanoindentation loading, but plastic deformation of dc-Ge (i.e.
twinning) also occurs. Raman analysis by this group showed some evidence of the hd
phase that they suggested formed by twinning of dc-Ge. [19] In addition, a TEM study
by Lloyd et al. [20] showed the transformed zone immediately under the indent was
composed of a-Ge and a mixture of fcc and bcc crystals, cracking and dislocations around
the transformed zone. [20] Yet another study by Clarke et al. also reported, using
indentation and TEM that amorphous material is formed after using Vickers and Knoop
indentation. [21] Another interesting and more recent study by Jang et al. showed that
nanoindentation-induced phase transformation occurs in Ge when using a cube-corner
indenter. [22] Clear evidence for phase transformation was observed by SEM and Raman
analysis, and they found that the indenter geometry (cube corner and Berkovich indenter)
can influence the deformation mechanisms as shown in Fig 1.2. [23] Bradby et al. [24]
and Oliver et al. [25] suggested that under moderate loading rates using blunt indenters,
dc-Ge deformed mainly via plastic deformation (slip and twinning) but phase
transformation could occur if very rapid loading or sharp indenters were used. Finally,
Pharr et al. showed that nanoindentation induced phase transformation in dc-Ge (when it
can be induced at all) is comparable to silicon to some extent. [26] Indeed, the
nanoindentation study by Bradby et al. observed that no evidence of phase transformation
was found with Raman and TEM analysis, instead they classified the deformation as
twinning or dislocation formation in the material. [24]
Thus, there is much disagreement in the literature about the ability to cause phase
transformations in dc-Ge. These differences were explained by the difficulty supressing
plastic deformation, load and unload rate dependent behaviour [25] and indenter shape
dependences. [22] Studies under the right conditions show clear non dc-Ge end phases in
the literature, but also no consensus as to the structure of these phases and the pathways
for their production. The summary of these possible pathways is shown schematically in
Fig. 1.3.
Introduction
CHAPTER 1
7
Introduction
CHAPTER 1
8
Figure 1.2: The above figure shows the study by Jang et al. [23] nanoindentation-induced
phase transformation in germanium using cube-corner and Berkovich indenter.
Figure 1.3: Schematic showing the phase transitions observed for dc-Ge under
nanoindentation loading and unloading.
1.2.3 Nanoindentation study on amorphous germanium (a-Ge)
The study of amorphous materials has been the subject of interest for over a century now.
For example, the a-Si material in its hydrogenated form is an important electronic material
for thin-film transistor and photovoltaics and many other applications. [27, 28]
Amorphous materials are differentiated from crystalline solids due to the lack of long-
range order. [29] From the nanoindentation point of view, a-Si has been more widely
studied as compared to a-Ge. So far only two nanoindentation studies have been done on
a starting material of a-Ge. Patriarche et al. [30] reported that indentation of a-Ge films
prepared by low-temperature electron-beam evaporation onto a GaAs substrate appears
to crystallize to dc-Ge phase and phase transition to st-12-Ge under pressure from
Berkovich and Vickers indenters. [30] This transformation was shown to take place right
under the indenter. Another study performed by Oliver et al. [31] showed that phase
transformation was the dominant deformation mechanism under spherical indentation. In
this case, a-Ge was prepared by self-ion implantation into a dc-Ge substrate. The sequence
of transformations in nanoindented a-Ge appears similar to that of DAC [31] Fig. 1.4
Introduction
CHAPTER 1
9
summarises the reported a-Ge results where it appears phase transformation is readily
induced but the nature of the end phases is unclear.
In this thesis, a-Ge is formed by self-ion implantation. Three thickness of a-Ge are
prepared on dc-Ge substrates. Pressure–induced transformation in these a-Ge samples is
discussed in Chapter 3.
Figure 1.4: Schematic showing the phase transitions reported for a-Ge under
nanoindentation loading and unloading.
Introduction
CHAPTER 1
10
1.2.4 Diamond Anvil Cell (DAC) study on c-Si
Figure 1.5: Schematic of phase transformations of dc-Si in diamond anvil cell (DAC)
compression and decompression.
In this section the high pressure phases of dc-Si are given for a comparison with high
pressure phases of c-Ge. The schematic in Fig. 1.5 shows the sequence of phase
transformation in dc-Si (Si-I). On compressing the crystalline material, it transforms from
dc-Si to the metallic β-Sn structure (Si-II). [2, 32] Further increase of pressure transforms
it to the distorted orthorhombic (Si-XI) Imma phase, [33] and then phase transforming
completely to the sh Si phase (Si-V). [33] With further increase in pressure, it transforms
to another orthorhombic Cmca (Si-VI) [8] structure, which converts to the hcp structure
(Si-VII). [8, 34] Finally, it transforms to a fcc structure (Si-X). [34] These transitions
Introduction
CHAPTER 1
11
happen at various pressures, as noted in the schematic, and the free structure stays stable
up to 248 GPa. [34]
Upon decompression, once the β-Sn metallic phase is reached, according to Crain et al.
the material transforms to first a rhombohedral structure (r8) at ~10 GPa. This is followed
by a subsequent transformation to a bc8 structure upon further decompression to below 3
GPa. The bc8 remains after total decompression. [35]
1.2.5 Nanoindentation study of c-Si and a-Si
On nanoindentation loading, dc-Si transforms to the metallic phase (β-Sn-Si) and then on
slow unloading it undergoes transformation to a mixture of bc8 and r8. The obvious sign
of formation of these phases is a “pop-out” discontinuity event on the unloading load
versus displacement (P-h) curve. [36] An elbow shape on an unloading curve indicates
the transformation to a-Si commonly observed during fast unloading. The presence of the
phase has been confirmed using Raman and transmission electron microscopy (TEM)
analysis. If turns out that fast unloading usually results in a-Si whereas slow unloading
gives an r8/bc8 mixture. A nanoindentation study by Ruffell et al. on a-Si showed that
crystallization to bc8/r8 (Si-III/XII) occurs on unloading. [37] Thus, both dc-Si and
relaxed a-Si are readily phase transformed under nanoindentation pressure.
1.3 Outline of this Thesis
In view of the apparent difficulty in inducing dc-Ge parameters under indentation and the
confusion in the literature on the end phases that occur follow transformation (if it is
induced at all), this thesis has focused on indentation in a-Ge where it appears that
transformation is readily induced. The main aim of the study is to carefully map the
transformation pathways under controlled spherical indentation to clarify the confusion
in the current literature. Although mostly spherical tips were used, few experiments were
performed using a Berkovich tip to clarify certain observed behaviours. As well as P-h
curves, analysis of residual indents via Raman micro spectroscopy, scanning electron
microscopy (SEM), and transmission electron microscopy (TEM) was used to help
understand end phase transformation pathways.
Chapter 2 outlines the techniques that were used in this thesis, particularly
nanoindentation and its analysis, ion-implantation as well as characterisation by Raman
micro spectroscopy, focused ion beam (FIB) system, SEM, and TEM. Chapter 3 outlines
Introduction
CHAPTER 1
12
the thickness dependent pressure-induced phase transformations in ion-implanted a-Ge.
Chapter 4 is about the effect of relaxation on a-Ge and it also includes the effect of
indenter geometry on phase transformation pathways. In this chapter results of slow and
fast loading/unloading rates are also included. Chapter 5 outlines the concluding remarks
and summary of the deformation behaviour of a-Ge.
Introduction
CHAPTER 1
13
[1] Y. S. and N. Usami, Silicon-Germanium (Si-Ge) Nanostructures. 2011.
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Rev. B, vol. 62, no. 16, pp. R10603–R10606, Oct. 2000.
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[9] S. B. Qadri, E. F. Skelton, and A. W. Webb, “High pressure studies of Ge using
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[10] “A New Dense Form of,” vol. 139.
[11] C. H. Bates, F. Dachille, and R. Roy, “High-Pressure Transitions of Germanium
and a New High-Pressure Form of Germanium.,” Science, vol. 147, no. 3660, pp.
860–862, 1965.
[12] R. J. Nelmes, M. I. McMahon, N. G. Wright, D. R. Allan, and J. S. Loveday,
“Stability and crystal structure of BC8 germanium,” Phys. Rev. B, vol. 48, no. 13,
pp. 9883–9886, Oct. 1993.
[13] K. Tanaka, “Amorphous Ge under pressure,” Phys. Rev. B, vol. 43, no. 5, pp.
4302–4307, Feb. 1991.
[14] M. Imai, T. Mitamura, K. Yaoita, and K. Tsuji, “Pressure-induced phase
transition of crystalline and amorphous silicon and germanium at low
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Introduction
CHAPTER 1
14
[15] O. Shimomura, S. Minomura, N. Sakai, K. Asaumi, K. Tamura, J. Fukushima,
and H. Endo, “Pressure-induced semiconductor-metal transitions in amorphous
Si and Ge,” Philos. Mag., Aug. 2006.
[16] F. Coppari, A. Di Cicco, A. Congeduti, J. C. Chervin, F. Baudelet, and A. Polian,
“Amorphous germanium under high-pressure conditions,” High Press. Res., vol.
29, no. 1, pp. 103–107, 2009.
[17] A. Kailer, K. G. Nickel, and Y. G. Gogotsi, “Raman microspectroscopy of
nanocrystalline and amorphous phases in hardness indentations,” J. Raman
Spectrosc., vol. 30, no. 10, pp. 939–946, 1999.
[18] Y. G. Gogotsi, V. Domnich, S. N. Dub, A. Kailer, and K. G. Nickel, “Cyclic
Nanoindentation and Raman Microspectroscopy Study of Phase Transformations
in Semiconductors,” J. Mater. Res., vol. 15, no. 04, pp. 871–879, Jan. 2011.
[19] Y. G. Gogotsi, V. Domnich, S. N. Dub, A. Kailer, and K. G. Nickel, “Cyclic
Nanoindentation and Raman Microspectroscopy Study of Phase Transformations
in Semiconductors,” J. Mater. Res., vol. 15, no. 04, pp. 871–879, 2000.
[20] S. J. Lloyd, J. M. Molina-Aldareguia, and W. J. Clegg, “Deformation under
nanoindents in Si, Ge, and GaAs examined through transmission electron
microscopy,” J. Mater. Res., vol. 16, no. 12, pp. 3347–3350, 2001.
[21] D. R. Clarke, M. C. Kroll, P. D. Kirchner, R. F. Cook, and B. J. Hockey,
“Amorphization and conductivity of silicon and germanium induced by
indentation,” Phys. Rev. Lett., vol. 60, no. 21, pp. 2156–2159, 1988.
[22] J.-I. Jang, M. J. Lance, S. Wen, J. J. Huening, R. J. Nemanich, and G. M. Pharr,
“Micro-Raman mapping and analysis of indentation-induced phase
transformations in germanium,” in Materials Research Society Symposium
Proceedings, 2005, vol. 841, pp. 291–296.
[23] J. Il Jang, M. J. Lance, S. Wen, and G. M. Pharr, “Evidence for nanoindentation-
induced phase transformations in germanium,” Appl. Phys. Lett., vol. 86, no. 13,
pp. 1–3, 2005.
[24] J. E. Bradby, J. S. Williams, J. Wong-Leung, M. V Swain, and P. Munroe,
“Nanoindentation-induced deformation of Ge,” vol. 80. p. 2651, 2002.
[25] D. J. Oliver, J. E. Bradby, J. S. Williams, M. V. Swain, and P. Munroe, “Rate-
dependent phase transformations in nanoindented germanium,” J. Appl. Phys.,
vol. 105, no. 12, 2009.
[26] G. M. Pharr, W. C. Oliver, R. F. Cook, P. D. Kirchner, M. C. Kroll, T. R. Dinger,
and D. R. Clarke, “Electrical resistance of metallic contacts on silicon and
Introduction
CHAPTER 1
15
germanium during indentation,” J. Mater. Res., vol. 7, no. 04, pp. 961–972, 1992.
[27] M. J. Powell, “The Physics of Amorphous-Silicon Thin-Film Transistors,” IEEE
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[28] D. E. Carlson and C. R. Wronski, “Amorphous silicon solar cell,” Appl. Phys.
Lett., vol. 28, no. 11, p. 671, 1976.
[29] W. H. Zachariasen, “The atomic arrangement in glass,” J. Am. Chem. Soc., vol.
54, no. 1, pp. 3841–3851, 1932.
[30] G. Patriarche, E. Le Bourhis, M. M. O. Khayyat, and M. M. Chaudhri,
“Indentation-induced crystallization and phase transformation of amorphous
germanium,” J. Appl. Phys., vol. 96, no. 3, pp. 1464–1468, 2004.
[31] D. J. Oliver, J. E. Bradby, S. Ruffell, J. S. Williams, and P. Munroe,
“Nanoindentation-induced phase transformation in relaxed and unrelaxed ion-
implanted amorphous germanium,” J. Appl. Phys., vol. 106, no. 9, 2009.
[32] J. Z. Hu, L. D. Merkle, C. S. Menoni, and I. L. Spain, “Crystal data for high-
pressure phases of silicon,” Phys. Rev. B, vol. 34, no. 7, pp. 4679–4684, Oct.
1986.
[33] M. I. McMahon and R. J. Nelmes, “New high-pressure phase of Si,” Phys. Rev.
B, vol. 47, no. 13, pp. 8337–8340, Apr. 1993.
[34] S. J. Duclos, Y. K. Vohra, and A. L. Ruoff, “Experimental study of the crystal
stability and equation of state of Si to 248 GPa,” Phys. Rev. B, vol. 41, no. 17, pp.
12021–12028, Jun. 1990.
[35] J. Crain, G. J. Ackland, J. R. Maclean, S. Pawley, and S. Bc, “Phases of Silicon,”
vol. 50, no. 17, 1994.
[36] V. Domnich, Y. Gogotsi, and S. Dub, “Effect of phase transformations on the
shape of the unloading curve in the nanoindentation of silicon,” Appl. Phys. Lett.,
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Phys. Lett., vol. 89, no. 9, p. 091919, 2006.
Introduction
CHAPTER 1
16
Experimental techniques
CHAPTER 2
17
CHAPTER 2
Experimental Techniques
Experimental techniques
CHAPTER 2
18
This chapter provides information about the sample preparation and the operation and
principles of the experimental techniques used in this study. High energy implantation,
nanoindentation, Raman micro-spectroscopy and cross-sectional transmission electron
microscopy (XTEM) have been extensively used to synthesize amorphous surfaces,
induce phase transformations and characterize the resultant structures. XTEM samples
were prepared using a focused ion beam (FIB) milling technique.
2.1 Ion-implantation
Ion-implantation is a material modification process, where ions are accelerated in an
electric field and implanted into a solid to change its properties or crystal structure. This
technique in semiconductor implantation has the ability to introduce any impurity to the
substrate in a highly controlled fashion. The doping profiles can also be controlled by
modulating the energy, current and the position of the ion beam. [1] In this work, the ion
implantation technique is used to amorphize c-Ge in order to investigate the high pressure
behaviour of this material. The amount of ions implanted in the material (dose) is the
integral over time of ion current. The ion penetration depth is based on the energy of the
ions and the composition of the implanted material.
The schematic of a tandem accelerator for ion-implantation is shown in Fig. 2.1. Cesium
gas is used to sputter negative ions from a cathode. A number of ion species can be
implanted by varying the cathode source material. The ions are accelerated away from
the source (qi × Vi) at ~100 keV. After leaving the source, the ions pass through an
analysing magnet, which selects for the desired ionic species. The ion beam then passes
through the high-energy accelerator. The central terminal of the accelerator is held at a
high voltage Vt. This voltage is attained with a Pelletron system, which uses a chain of
metal pellets linked by nylon connectors to transport charge. The negative ions are
accelerated towards the central terminal. At the terminal, a small quantity of gas is
introduced. The gas strips away electrons from some of the negative ions. The resulting
positive ions of charge qt are then accelerated away from the terminal. The ions thus gain
a total energy of qiVt + qtVt. Another analysing magnet is used to select for the desired
energy and charge species. Finally, the ion beam reaches the sample chamber, where it is
raster-scanned to achieve a uniform implantation in the specimen over a selected area.
Experimental techniques
CHAPTER 2
19
The energy of ions that are implanted into the specimen is qiVi + qiVt + qtVt. (qi × Vi +
2qtVt).
The most important factors in ion implantation process are the distribution of implanted
ions and the distribution of deposited energy, the latter leading to disorder. These
distributions are dependent on ion energy, type of ions and the composition of the target.
The software package for stopping and range of ions in matter (SRIM) by J.F. Ziegler,
www.srim.org can be used to obtain both range and disorder (produced vacancy)
distributions.
Figure 2.1: Schematic showing the key features of a tandem accelerator.
2.1.1 Ion implantation damage
In this work ion implantation injects Ge+ ions into the c-Ge sample to cause
amorphisation. During this process ions lose energy during collisions until they come to
rest. [2] This collision process can be divided into (1) nuclear processes and (2) electronic
processes. Nuclear processes involve hard collisions of ions and the atom nuclei in the
material. These result in collision cascades of moving atoms in the material, thus
disordering the material lattice. Electronic processes involve interaction of ions with
lattice electrons. This process leads to slowing down of ions but not directly to disorder
production. If the implantation temperature is low enough the displaced atoms and defects
within the collision cascade are stable and immobile. At higher temperatures, defects
such as vacancies and interstitials can be mobile and significant annealing or annihilation
Experimental
area
High energy analysis
+ + + +
+ +
+ + + - + - - - - - - - - -
- - -
- - - - - -
+ + +
Magnet Magnet
High energy accelerator
Ion source injection energy Vi
Low energy analysis HV terminal Vt
Stripper gas
Experimental techniques
CHAPTER 2
20
of damage can occur during ion implantation. [1, 3] In this work, implanting Ge + ions
to cause the amorphisation does not introduce any impurities into the Ge substrate.
2.2 Sample preparation
In this work, c-Ge and three different a-Ge samples (~700 nm, ~1000 nm and ~1800 nm
thick films) were indented to study the pressure induced phase transformation behaviour
of a-Ge samples. The a-Ge samples were prepared using the high energy implanter (ANU
1.7 MV Pelletron tandem accelerator) at the department of Electronic Materials
Engineering (EME) at ANU. N-doped Ge (100) wafers were obtained from Wafer World,
West Palm Beach and implantation was carried out at liquid nitrogen temperature. To
make a ~700 nm thick amorphous layer, a fluence of 3 х 1015 cm-2 Ge ions with an energy
of 800 keV was used. Similarly, 1.3 MeV energy Ge+ ions were used with a fluence of 1
х 1015 cm-2 to make the ~1000 nm film and 3 MeV energy Ge ions with a fluence of 1 х
1015 cm-2 were used to make the thickest ~1800 nm sample. After implantation, samples
were cleaved into 1×1 cm -2 areas and cleaned with acetone and isopropanol.
2.3 Nanoindentation
Nanoindentation is a technique for measuring the mechanical properties of materials.
Conventional indentation hardness tests involve measuring the size (area) of a residual
plastic impression in the specimen as a function of the indenter load. This provides a
measure of the hardness of a sample. In nanoindentation, the size of the residual
impression is often only a few microns making it very difficult to obtain a direct measure
using optical techniques. Nanoindentation testing is performed using a sharp indenter
made from a hard material (commonly diamond). This indenter is pressed into the
specimen to extract the hardness and the elastic modulus from load-displacement curves.
It has become one of the most widely used techniques for measuring the mechanical
properties of films and soft structures. Other advantages of nanoindentation stem from
the ease with which a wide variety of mechanical properties can be measured. Both bulk
specimens and thin films can be measured, as well as the ability to probe a surface at
specific points creating a spatial mechanical property map. [4]
In nanoindentation testing, the initial response of the material is elastic but plastic
deformation can occur at higher loads. Typically, the depth of penetration beneath the
specimen surface is measured as the load is applied to the indenter. The known geometry
Experimental techniques
CHAPTER 2
21
of the indenter allows the size of the area of contact to be determined. Different indenter
tip geometries (including spherical, Vickers, Berkovich and conical) can be responsible
for the change of mechanical properties of the material. [8] Nanoindentation hardness
tests are generally made with spherical or pyramidal indenters (Berkovich) using load
versus penetration depth curves. [8] Details of the plastic deformation regime can be
studied from the load-unload measurements via discontinuity events such as pop-in or
pop-outs or departure of the unloading curve from that of loading. The nature of the
plastic deformation obtained from the details of load versus penetration depth curves
reveal much information about the pathway of deformation as well as the stresses
involved in the residual impressions.
Indentation tests on materials can probe both the elastic and plastic deformation behaviour
of the material. In brittle materials, plastic deformation is the most easily probed with
sharp indenters (Vickers or Berkovich) since high loads are needed under conditions that
minimize brittle fracture. In ductile material plastic deformation more readily occurs
using blunt indenters (spherical) at low loads. Indentation testing is not only a very useful
technique to measure the hardness of the material but can be used to measure other
mechanical properties like material strength, fracture and residual stresses in the material,
and hence has been an important tool in the study of materials for many years. [5]
The indentation hardness is defined as:
H = Pmax ∕ A
Where H – Hardness, Pmax – maximum applied load and A - (projected) area of the
residual impression. [6] As previously stated, the conventional method to measure
hardness requires imaging of the residual impression by optical microscopy to obtain the
area of the plastic zone. However, this method is not accurate for the micron sized residual
impressions associated with nanoindentation. Thus other methods are necessary. In
nanoindentation testing, the projected area of the residual impression for an indentation
subjected to a maximum load can be calculated from the indenter geometry and the P-h
curves according to the methods of Oliver and Pharr [7] or Field and Swain [8] as
indicated later. The geometry of the indenter plays an important role in nanoindentation
testing and in this work spherical indenters with a radius of ~ 4.3 μm or ~ 20 μm are used.
Experimental techniques
CHAPTER 2
22
2.3.1 UMIS (ultra micro indentation system)
Figure 2.2: Schematic of the ultra-micro indentation system (UMIS).
Fig. 2.2 shows a schematic of the UMIS-2000. During nanoindentation, a piezoelectric
actuator applies load to the main carriage. Leaf springs transfer force from the carriage to
the indenter shaft. A linear variable differential transformer (LVDT) measures the
displacement of the indenter shaft relative to the carriage: from this, using the spring
constant of the leaf springs, the force on the indenter tip can be calculated. Another LVDT
attached to the frame of the indenter measures the depth.
The force and the depth measuring systems are basically the same, differing only in the
gain of the final amplifier. They are based on high linearity LVDTs. The upper unit
measures depth and the lower unit measures the displacement of the force generating
Experimental techniques
CHAPTER 2
23
springs. The associated electronics are complex in order to achieve the very high
sensitivity and stability required by the system. [5]
The depth LVDT continuously monitors spring deflection as the indenter approaches the
specimen; it is the role of the “depth offset” circuit to reference the moment of contact as
being the zero penetration voltage and subtracting that voltage from all subsequent
readings. This enables the full range of the amplifiers and the A/D converter to be utilised.
The “force offset” circuit is activated during the zeroing phase to cancel any voltage
resulting from the force LVDT prior to a measurement cycle. The depth signal is
monitored by the analog interface and the various depth readings are measured at that
point. [5]
UMIS is used to perform indents in the range of 50 mN to 1000 mN in this work. The
UMIS nanoindenter can be operated in two modes, closed loop and open loop. In this
study we have used the closed loop mode. In the closed loop mode, a feedback loop is
used to obtain a precise value of load (or depth) at each measured increment on the loading
cycle. In open loop mode, no feedback is used; the load signal is simply ramped up at a
fixed rate. The closed loop mode gives more control over the loading cycle; the open loop
mode allows a higher rate of data collection, and allows higher maximum loading rates.
[9]
In this study spherical indenters are especially useful because of their smooth transition
from elastic to elastic-plastic contact. Berkovich indenters are also used for to measure
the hardness and other mechanical properties of the material but have been used to a lesser
degree in this thesis since the onset of phase transformation is more difficult to determine.
A Berkovich is a three sided pyramid which is geometrically self-similar. It has a very
flat profile, with a total included angle of 142.3 degrees and a half angle of 65.31 degrees.
[2] The Berkovich tip has the same projected area to depth ratio as a Vickers indenter but,
because it is designed to be sharper than the Vickers geometry, it ensures the more precise
control over the indentation process. [9] Oliver et al. study has reported nanoindentation
on Ge using both spherical and Berkovich indenters. Observations have clearly shown
phase transformation can be induced in Ge using both indenter types.
Experimental techniques
CHAPTER 2
24
Oliver and Pharr method
Oliver and Pharr has developed a method to analyse the load-displacement curves during
nanoindentation testing. This method was introduced in 1992 to measure the hardness, H
and elastic modulus, E by instrumented indentation technique and has been widely used
to characterize the mechanical properties of materials at small scale. The advantage of
this method is that, without imaging the residual impression, the mechanical properties
can be studied from applied load and displacement measurements. [4] The Oliver and
Pharr method was originally developed for analysis using sharp indenters like Berkovich,
but is applicable equally for spherical and other geometries. The schematic shows a
Berkovich indenter in 2.4 (a) and a typical load-displacement curve in Fig. 2.4 (b).
The most important assumption made by Oliver and Pharr is that the deformation
(recovery) of the material during unloading is entirely elastic. The area of the residual
impression after unloading is equal to the contact area of the indenter at maximum applied
load, which can be calculated as indicated below.
The procedure used to measure H and E is based on the unloading process shown
schematically in Fig. 2.5 (b) The basic assumption therein is that the contact periphery
‘sinks in’ in a manner that can be explained by indentation of a flat elastic half space with
rigid punches of simple geometry. This does not account for ‘pile-up’, which is material
that flows out from under the tip during indentation loading. Assuming, however, that
pile-up is negligible, the elastic models show that the amount of sink-in, hs, is given by:
hs = є S
P max , є = )2(
2
(2.1)
where є is a constant that depends on the geometry of the indenter and S is the material
stiffness obtained from the slope of the unloading curve in Fig. 2.5 (b).
The value of є = 0.75 for a paraboloid of revolution which approximates to a sphere of
small depths, or even a Berkovich tip, or є = 0.72 for conical indenter or є = 1 for a flat
Experimental techniques
CHAPTER 2
25
punch. The contact depth, hc along which the contact is made between indenter and
specimen (Fig. 2.5 (a)) can be calculated by:
hc = hmax - hs, (2.2)
where hmax is the total depth and the value of hs depends on the deflection of the surface
at the contact perimeter which in turn depends on the indenter geometry according to the
equation (2.1).
Letting F(h) be an “area function” that describes the projected area of the indenter at a
distance d back from its tip, the contact area Ac can be calculated by:
Ac = F (hc),
Ac = F(hmax-hs),
Ac = F (hmax- ∈Pmax
𝑆 ) , (2.3)
where F(h) is known as the tip area function. For ideal tip geometry, the area function is
a simple analytical formula but any real tip will deviate from the ideal due to blunting and
imperfections. Normally, the tip area function is found by indenting a material such as
fused silica in which the hardness and modulus are well known. Once the exact contact
area is determined the hardness H can be calculated by:
H = cA
P max (2.4)
The elastic modulus can be calculated from the contact area Ac and the stiffness S on
unloading as follows:
S = ceffAE
2, (2.5)
where β is a constant best estimated as 1.05 for a Berkovich indenter tip and 1 for a
spherical tip. [4] Thus, both the hardness and elastic modulus can be found entirely from
the tip geometry tip area function and the load-unload curves using equations (2.3 to 2.5).
Note that Eeff is the effective elastic modulus defined by:
(2.6)
The quantities E, ν, Ei and νi are the Young’s modulus and the Poisson’s ratio of the
specimen and the indenter tip. This method has been used extensively for a number of
i
i
eff EEE
22 111
Experimental techniques
CHAPTER 2
26
materials, but the problem of “pile-up” can introduce significant error for soft ductile
materials.
Figure 2.3: Schematics of (a) indentation contact geometry and (b) P-h curve, according
to Oliver and Pharr analysis. (Taken from Ref. [4] )
Experimental techniques
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27
Field and Swain method
The Field and Swain method [8] of analysis features a single partial unload rather than a
series of unload data points from maximum load. The advantage of this is speed and
convenience, only one single measurement during unloading is required and the need for
curve-fitting multiple data points obtained during a full unload is avoided. However, the
degree of partial unload must be chosen so that the unloading is elastic and no reverse
plasticity is involved. The speed of data acquisition may be important where the
measurements are affected by thermal drift of the instrument.
The overall shape of the load-unload curve reflects the material properties: Young’s
modulus, Poisson’s ratio, initial flow stress and strain hardening and the elastic properties
of the indenter. [8] Hardness can be calculated at each step of unloading of a single indent
Strain continuously increases with depth in a spherical indentation test and this can be
used to extract an indentation stress-strain relationship. [8]
Field and Swain developed a method to obtain mechanical properties by stimulating
force-displacement curves (using known material parameter) and comparing with the
partial load-unload data from the UMIS-2000 It has been shown [10] that in an ideal
plastic solid undergoing spherical indentation, the onset of plastic flow is controlled by
the value Pm / Y, where Pm is the mean pressure over the contact area of the indenter and
Y is the yield stress in simple tension or compression. [8]
Experimental techniques
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28
Figure 2.4: Schematic of load-displacement data from Field and Swain analysis [8]
The critical load for the onset of full plastic flow Pc in the material can then be calculated
from equation 2.7 using the following equation:
The contact pressure is given by the following equation: [11]
Pm = 3/1
3/23/2)9/16(
PR
Eeff
(2.7)
Where P is the load, R is the radius of the indenter, and Eeff is the effective modulus.
Pc = 32 )3()/)(16/9( YER eff (2.8)
Hardness and modulus can be found from Fig. 2.4 by first finding hs, which may be
obtained by partially unloading the indentation from ht, using the formula:
hs = hu(Pmax/Pu)2/3 – hmax / (Pmax/Pu)
2/3 – 1 (2.9)
where Pu and hu are the load and depth after partial unloading. The
Experimental techniques
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29
‘plastic component’ of the penetration depth (hp) can be calculated using:
hp = (hmax +hs)/2 (2.10)
The radius a of the circle of contact can be calculated using the below given equation:
a = 22 pp hRh (2.11)
The hardness and modulus can then be obtained from:
H = P/ (πa2) (2.12)
and Eeff = 3P / 4a(hmax-hs) (2.13)
2.3.2 Details of Nanoindentation testing for this work
Nanoindentation load-unload curves, particularly discontinuities and shape can reveal
changes in the material such as plastic deformation or phase changes.
Figure 2.5: Schematic of load-unload curve with formation of “pop-in” using spherical
indenter.
Experimental techniques
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30
Figure 2.6: Schematic of load-unload curve with formation of “pop-out” using spherical
indenter.
Figure 2.7: Schematic of load-unload with a formation of “pop-in” on loading curve and
“elbow” on unloading curve using spherical indenter.
For example, the P-h curves in Fig.’s 2.5 to 2.7 shows typical discontinuities and shape
changes that can depending on the loading and unloading conditions The discontinuities
observed in the load-unload curves are generally called as pop-in (Fig. 2.5) and pop-out
(Fig. 2.6) during loading and unloading, respectively. While pop-ins at the initial part of
Experimental techniques
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31
the loading usually indicates an elastic to plastic transition, at higher load it could be due
to fracture. Recent literature shows that pop-ins can also occur due to phase
transformations. [12] Pop-ins can also result from sudden dislocation formation (and
propagation) at a critical stress, as in the studies of Bradby et al [13,14] for compound
semiconductors and Oliver et al [15] for c-Ge. If the loading curve is smooth, without any
discontinuity, this is called a homogeneous plastic deformation. In some cases, a
continuous change in shape (elbow in fig. 2.7) can indicate plastic recovery or a
continuous phase change. In indentation of a-Ge the discontinuities observed indicate two
deformation pathways as shown in Fig. 2.8, where the pop-ins have been attributed to
phase transformation, as shown later. Note that a pop-out during unloading is attributed
to structural changes that occur under the indenter during pressure release. Pop-outs are
rarely observed in the current study.
Figure 2.8: Typical load-unload curve to 100 mN in a-Ge sample.
2.4 Raman micro-spectroscopy
The Raman spectroscopy technique relies on inelastic photon scattering. In Raman
Spectroscopy a visible laser interacts with phonons or other excitations in the sample
material. Raman scattering causes a shift in the photon energy. That shift in energy gives
information about the samples vibrational modes. When light is scattered in a material
Experimental techniques
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32
most photons are elastically scattered, referred to as Rayleigh scattering but a very small
amount of photons are inelastically scattered.
Raman scattered photons may either lose energy to a vibrational mode known as stokes
scattering, or absorb energy from a vibrational mode known as an anti-stokes scattering
[21] The analysis of the sample is done by irradiating a laser beam over the region of
interest in the sample. The Raman Spectrometer is used to determine the intensity and
wavelength of the light which is scattered in-elastically from the molecules and atoms of
the sample.
The Raman micro-spectroscopy technique is utilized to obtain information about phonon-
modes, specifically crystal structure, bonding arrangements, and stress. The scattered
photons are collected using a CCD detector. The most important advantage of Raman
spectroscopy is it does not require sample preparation unlike other techniques such as
TEM.
Raman spectroscopy is a commonly used technique with nanoindentation to investigate
phase changes under high pressure in various materials. [13,16] The Raman spectroscopy
system is based on four major components, the excitation source (laser), the sample
illumination system and light collection optics, the wavelength selector (that is filter or
spectrometer) and the detector (in our case a CCD detector).
In this study, Raman micro-spectroscopy was carried out using a Renishaw 2000
instrument, with a helium-neon exciting laser (632.8 nm) focussed to a spot size of the
order of 1 µm. Pressure induced phases were found to be sensitive to laser-induced
annealing at higher intensities, so the laser power was kept below 100 μW. The spectra
were recorded in 30s (max. 60s). A number of measurements were performed on several
residual indent impressions to confirm the meta-stable phases of Ge. Raman spectroscopy
is also sensitive to the bonding arrangements in amorphous material and gives rise to
broadened peaks such as those in Fig. 2.9. Fig 2.10. shows typical peaks from metastable
phases arising from applying pressure to a-Ge. Finally, Fig. 2.11 shows a Raman spectrum
of diamond cubic crystalline Ge.
Experimental techniques
CHAPTER 2
33
Figure 2.9: Raman spectrum of typical a-Ge.
Figure 2.10: Raman spectrum of metastable phases produced by applying pressure to a-
Ge (briefly explained in chapter 3 section 3.2).
(b)
(a)
Experimental techniques
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34
Figure 2.11: Raman spectrum of dc-Ge.
2.5 Focused ion beam (FIB) system
A dual beam FIB instrument was used in this study to prepare the cross-sections of indents
for transmission electron microscopy (TEM) imaging. The FIB has an energetic gallium
(Ga) ion beam with a high beam current for sputtering or milling. The Ga ion beam hits
the sample and sputters a small amount of material. This system uses scanning electron
microscopy (SEM) for imaging during the milling process. The sample is tilted to 52o to
allow ion-beam milling normal to the surface as shown in Fig. 2.12. The secondary ions
generated in the processes can be used to form an image similar to Scanning Electron
Microscopy.
The sample of interest in this study consists of arrays of indents on the a-Ge surface. In
single beam FIB both the tasks of milling and imaging are performed using the ion beam.
In the dual beam system, the electron column is mounted in a vertical position on the
vacuum chamber, the angle between ion and electron column as mentioned above is 52o.
In this way both electron and ion beams can be coincident on the same region of the
sample, provided the area of interest lies in the eucentric plane. The FIB column on the
dual beam offers much higher imaging resolution from the electron column if a field
emission source is used. [17]
(c)
Experimental techniques
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35
Figure 2.12: Schematic diagram of the dual beam column layout of the FIB system used
in this study.
The sample is mounted onto an SEM sample holder. The area of cross-section is marked
for milling. To avoid any beam damage to the sample, a 100 nm gold layer is deposited
prior to depositing a 1 µm platinum film. After a cross-section is milled to a thickness of
~ 1 μm, a J cut is performed by placing the cross-section at about 7o. Successfully
prepared thin cross-sections have been manually plucked from the material using a sharp
glass needle and placed on a TEM grid for further analysis. The dual-beam FIB system
used in this study, a FEI xT Nova NanoLab 200 FIB, is located at the Electron Microscope
Unit of the University of New South Wales.
2.6 Transmission electron microscopy (TEM)
TEM is a major characterization technique used in materials science to mainly
characterize nano-sized structures. [18] In a conventional TEM, a thin electron
transparent specimen (~ 100 nm thick ) is irradiated with an electron beam of uniform
current density [19] to form an image.
52o
Electron-
beam
Ion- beam
Experimental techniques
CHAPTER 2
36
The basic principle of TEM (Fig 2.13) is very similar to a light microscope. TEM is
capable of imaging at a significantly higher resolution than a light microscope. The major
difference is that electrons are used instead of photons and electromagnetic lenses are
used instead of glass lenses to focus the electron beam onto the sample. This enables the
examination of details as small as a single column of atoms, thousands of times smaller
than the smallest resolvable object in a light microscope. Unlike light microscopy, TEM
via electron diffraction allows crystal structure and perturbations in crystal structure such
as dislocations, twins, slip, and transformed phases to be directly imaged. [18]
The disadvantages of TEM include the time consuming sample preparation required to
obtain electron transparent specimens for viewing and the potential for changes in the
material as a result of the thinning process.
Figure 2.13: Schematic of transmission electron microscopy imaging mode, where the
image is projected on the viewing screen.
Main screen
Projector Lens
First intermediate Lens
Second intermediate Lens
Selected area aperture
Objective Aperture
Objective Lens
Sample
Condenser
Aperture
Second condenser Lens
First condenser Lens Virtual source
Experimental techniques
CHAPTER 2
37
Figure 2.14: Cross-sectional TEM image from an indent performed on a-Ge with selected
area diffraction patterns obtained of various regions.
Fig. 2.14 shows a typical bright field (BF) image of indented a-Ge. The selected area
diffraction (SAD) patterns confirm the presence of crystalline phases. The left and middle
images show typical SADs where the diffraction spots can be indexed (as we indicate
later) to pressure-induced phases and the right SAD shows the Halo rings representing a-
Ge. In the BF mode, electrons move as particles through the imaging system, and the
electron intensity not the wave amplitude, determines the image. [19, 20] In this mode
the contrast formation is a result of diffraction and absorption of the electrons from
regions in the sample. Thus, this mode gives strong contrast to crystal defects and also
reveals the crystalline phase transform material.
The instrument used in this study was a Philips CM 300.
a-Ge
c-Ge
Pt
Phase transformed
region
Experimental techniques
CHAPTER 2
38
[1] J. F. Gibbons, “Ion Implantation in Semiconductors???Part I Range Distribution
Theory and Experiments,” Proc. IEEE, vol. 56, no. 3, pp. 295–319, 1968.
[2] J. S. Williams, “Materials modification with ion beams,” Reports Prog. Phys.,
vol. 49, no. 5, pp. 491–587, 1999.
[3] J. R. Dennis and E. B. Hale, “Crystalline to amorphous transformation in ion-
implanted silicon: a composite model,” J. Appl. Phys., vol. 49, no. 3, p. 1119,
1978.
[4] W. C. Oliver and G. M. Pharr, “Measurement of hardness and elastic modulus by
instrumented indentation: Advances in understanding and refinements to
methodology,” J. Mater. Res., vol. 19, no. 01, pp. 3–20, 2004.
[5] A. C. Fischer-Crippss, Nanoindentation (Mechanical Engineering Series).
Springer Verlag), 2002.
[6] D. Tabor, The hardness of metals. (Oxford University Press, USA), 2000.
[7] W. C. Oliver and G. M. Pharr, “An improved technique for determining hardness
and elastic modulus using load and displacement sensing indentation
experiments,” J. Mater. Res., vol. 7, no. 06, pp. 1564–1583, Jan. 2011.
[8] J. S. Field and M. V. Swain, “A simple predictive model for spherical
indentation,” J. Mater. Res., vol. 8, no. 02, pp. 297–306, Jan. 2011.
[9] D. J. Oliver, “Nanoindentation-induced Deformation Mechanisms in
Germaniumo Title,” The Australian National University, 2008.
[10] H. A. Francis, “Phenomenological Analysis of Plastic Spherical Indentation,” J.
Eng. Mater. Technol., vol. 98, no. 3, pp. 272–281, 1976.
[11] K. L. Johnson, “Contact Mechanics,” Journal of the American Chemical Society,
vol. 37. pp. 1–17, 1985.
[12] J. E. Bradby, J. S. Williams, J. Wong-Leung, M. V. Swain, and P. Munroe,
“Mechanical deformation in silicon by micro-indentation,” J. Mater. Res., vol.
16, no. 05, pp. 1500–1507, 2001.
[13] J. E. Bradby, J. S. Williams, J. Wong-Leung, M. V Swain, and P. Munroe,
“Nanoindentation-induced deformation of Ge,” vol. 80. p. 2651, 2002.
[14] J. E. Bradby, J. S. Williams, J. Wong-leung, S. O. Kucheyev, M. V. Swain, and
P. Munroe, “Spherical indentation of compound semiconductors,” Philos. Mag.
Experimental techniques
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39
A, vol. 82, no. 10, pp. 1931–1939, Jul. 2002.
[15] D. J. Oliver, J. E. Bradby, J. S. Williams, M. V Swain, and P. P. Munroe,
“Thickness-dependent phase transformation in nanoindented germanium thin
films.,” Nanotechnology, vol. 19, no. 47, p. 475709, 2008.
[16] B. Haberl, J. E. Bradby, M. V. Swain, J. S. Williams, and P. Munroe, “Phase
transformations induced in relaxed amorphous silicon by indentation at room
temperature,” Appl. Phys. Lett., vol. 85, no. 23, p. 5559, 2004.
[17] P. R. Munroe, “The application of focused ion beam microscopy in the material
sciences,” Mater. Charact., vol. 60, no. 1, pp. 2–13, Jan. 2009.
[18] D. B. Williams and C. B. Carter, Transmission Electron Microscopy. Springer,
2009.
[19] R. by P. D. Brown, “Transmission Electron Microscopy-A Textbook for
Materials Science, by David B. Williams and C. Barry Carter,” Microsc.
Microanal., vol. 5, no. 06, pp. 452–453, Jan. 2003.
[20] L. Reimer and H. Kohl, Transmission Electron Microscopy. Springer, 2008.
Experimental techniques
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Pressure-induced phase transformations in a-Ge
CHAPTER 3
41
CHAPTER 3
Pressure-induced phase transformations in amorphous germanium
Pressure-induced phase transformations in a-Ge
CHAPTER 3
42
As previously outlined in chapter 1 of this thesis, indentation can induce phase
transformations under certain loading conditions in dc-Ge. However, there is considerable
confusion in the literature as to the metastable end phases that result and the
transformation pathways. It would appear that it is easier to phase transform a-Ge than
dc-Ge where there are competing deformation processes of slip or twinning. The studies
outlined in this chapter build on the prior work with the aim of resolving the reasons for
some of the confusion in the literature and better understanding the transformation
pathways of a-Ge.
In employing a-Ge as starting material it was hoped that the competing plastic
deformation pathways of slip and twinning in dc-Ge might be avoided. This chapter
examines a-Ge films on underlying dc-Ge substrates and all spherical indentation is used
to induce phase transformations. Different film thicknesses are examined and ex-situ
Raman spectroscopy and XTEM are the main methods to characterise end phases. Phase
stability is also examined in some cases and, in the case of Raman, theoretical calculations
of Raman peak positions are compared with experimental spectra in order to correctly
assign Raman peaks to the end phases.
3.1 Experimental details
A surface layer of a-Ge in Czochralski-grown Ge (100) wafers (dc-Ge) was made by self-
ion-implantation using the ANU 1.7 MV NEC tandem accelerator. The thickness of the
surface amorphous layers was ~700 nm and ~1000 nm. To form these layers, Ge+ ions
were implanted into the dc-Ge (as described in detail in section 2.2) at liquid nitrogen
temperature with the wafer surface normal 7° to the incident beam, within energy of 800
keV to a fluence of 3×1015 cm-2 to form the ~700 nm thick layer and 1.3 MeV to a fluence
of 1×1015 cm-2 to form the ~1000 nm film. Measurement of layer thicknesses was
performed by Rutherford Backscattering Spectrometry (RBS) [1], with 2 MeV He+ ions
channelled axially along the <100> direction in the underlying dc-Ge, with XTEM
employed to confirm that the amorphous layers were voidless and continuous to the
surface.
Indentation was performed at room-temperature on all thin film samples using an UMIS-
2000 instrument with a diamond spherical indenter tip of ~4.3 µm radius. Maximum loads
of 100 mN and 120 mN were applied in both the ~700 nm and ~1000 nm samples. A
loading and unloading rate of ~6 mN/s was used (50 increments). Arrays of 50–100
Pressure-induced phase transformations in a-Ge
CHAPTER 3
43
indents were made at each load for each film thickness. The residual indents were then
characterized by Raman spectroscopy and XTEM. Raman spectra from selected indents
were recorded using a Renishaw 2000 Raman system with a 632.8 nm laser. For TEM
analysis, cross-sections of selected indents were made with a FIB, as outlined in chapter
2. The FIB-prepared cross-sections were imaged using a Philips CM 300 TEM operating
at 300 kV. TEM samples were prepared for each condition and it should be noted that the
TEM results exhibited excellent repeatability.
A thicker a-Ge layer was also prepared using self-ion-implantation. The thickness of the
surface amorphous layer was ~1800 nm. To form this layer, Ge+ ions were again
implanted into dc-Ge at liquid nitrogen temperature with the wafer surface normal 7o to
the incident beam but in this case at an energy of 3 MeV to a 1 х 1015 cm-2 fluence.
Indentation was again performed at room-temperature using the UMIS-2000 but with a
diamond spherical indenter tip of radius ~20 µm. A maximum load of 700 mN was
applied and arrays of 50–100 indents were made at each load. Residual indents were again
characterized by Raman spectroscopy and XTEM. In some cases, to study the stability of
end phases, samples were stored in dry ice immediately after indentation and examined
after warming to room temperature by Raman spectroscopy after various time periods.
3.2 Thin a-Ge films
Figure 3.1(a) shows 10 separate several load-unload curves for indentation tests made in
the ~700 nm a-Ge film using a ~4.3 µm radius spherical tip and loaded to a maximum
force of 100 mN. The curves overlap on loading until the onset of a pop-in event as shown
with the arrow in Fig. 3.1(a). Following the pop-in events, the tests are observed to fall
into two discrete deformation pathways (shown in blue and red). The loading curves of
each pathway are displayed after pop-in but within each pathway they overlap. In this
work, these two pathways are hereafter referred to family ‘a’ and family ‘b’. After pop-
in, the two pathways exhibit different mechanical responses. This difference is partly
characterised by differences in stiffness (mN/nm), as is discussed later. An analysis of the
pop-in depth shows that for all tests in the same film, irrespective of family ‘a’ and family
‘b’ behaviour, the depth at which pop-in occurs is remarkably consistent. This behaviour
suggests that pop-in, which is shown in Fig. 3.1 (b), is the signature for a transformation
to a (β-Sn)-Ge phase. This is triggered identically irrespective of family ‘a’ and family
‘b’ behaviour. Thus, the load at which the pop-in event occurs does not appear to be
correlated with the deformation mode (family ‘a’ or family ‘b’). Instead, the critical
Pressure-induced phase transformations in a-Ge
CHAPTER 3
44
parameters in the loading curve that define family ‘a’ and family ‘b’ behaviour as shown
in Fig. 3.1(b) appears to be the magnitude of the pop-in event, with the penetration depth
at pop-in consistently larger for the family ‘b’ type curves and the shape of loading curve
after pop-in. There is no intermediate behaviour in between family ‘a’ and family ‘b’.
Over sets of 50 indents, the load-unload curves always fell into either family ‘a’ or family
‘b’ behaviour. For family ‘a’ behaviour, the pop-in event (penetration at pop-in) is smaller
than the family ‘b’ case and the slope of the loading curve after pop-in is similar to the
slope before pop-in occurs. For family ‘b’ behaviour, the initial pop-in is larger than the
pop-in for family ‘a’ and the slope of family ‘b’ curve after pop-in is smaller than the
slope before pop-in. For the ~700 nm film, pop-in occurs at 56 ± 2 mN, resulting in a
depth at pop-in of ~350 nm. Upon unloading the load-unload curves are smooth and
featureless without any discontinuity or pop-out events observed for both family ‘a’ and
family ‘b’ cases. The residual depths for both sets of curves does not show any significant
difference. For a ~4.3 µm radius spherical tip, the relative occurrence was roughly 60–
80% of indents exhibiting family ‘a’ behaviour on a sample with 50 indents.
Pressure-induced phase transformations in a-Ge
CHAPTER 3
45
Figure 3.1: (a) A set of 10 load-unload curves in a ~ 700 nm a-Ge film using ~4.3 µm
radius spherical tip. Two types of deformation behaviour (blue family ‘a’ and red family
‘b’) are observed (as determined by slope of the loading curve after pop-in). The
horizontal arrow indicates the onset of pop-in events. (b) Load-unload curves for
indentation tests made in the ~ 700 nm film using ~4.3 µm radius spherical tip to highlight
the differences in typical family ‘a’ and family ‘b’ behaviour.
Pressure-induced phase transformations in a-Ge
CHAPTER 3
46
Figure 3.2 shows typical load-unload curves for indentation tests in the ~ 1000 nm a-Ge
film using a ~ 4.3 µm spherical tip. In the ~1000 nm film, pop-in occurs at a load of 91 ±
3 mN and at a depth of ~550 nm. Thus, in both of these cases the pop-in occurs when the
tip has penetrated ~50 % of the a-Ge film thickness, which is discussed later as being
related to the significant plastic deformation of the films prior to pop-in during loading.
In addition, the slope of the loading curve after pop-in for family ‘a’ cases are again
consistently greater than that of the family ‘b’ cases, similar to the 700 nm film. However,
in some indents (up to 40 % of indents) that are loaded to a maximum load just above
pop-in, a ‘kink’ or pop-out is observed in family ‘b’ upon unloading as shown in Fig. 3.2.
The presence of such a pop-out and its possible significance is discussed later. Overall,
the behaviour of the ~700 and ~1000 nm films in terms of exhibiting family ‘a’ and family
‘b’type transformations are essentially identical.
Pressure-induced phase transformations in a-Ge
CHAPTER 3
47
Figure 3.2: (a) and (b) Representative load-unload curves for indentation tests made in
the ~1000 nm film using a ~4.3 µm radius spherical tip, indicating both family ‘a’ and
family ‘b’ behaviour. The applied load is 100 mN or 120 mN and an occasional ‘pop-out’
is observed when the maximum load (~100 mN) is close to the pop-in load.
Figure 3.3 (a) shows a set of typical Raman spectra for the ~700 nm film and Fig 3.3(b)
a similar Raman set for the ~1000 nm film. A spectrum from an un-indented (background)
area of this a-Ge film is also shown, which exhibits a typical broad Raman band centered
at ~270 cm-1. For the family ‘a’ Raman spectra in Fig 3.3(a) and Fig 3.3(b), there is
evidence of extra Raman bands at 202 cm-1, 225 cm-1, 246 cm-1, and 280–295 cm-1
strongly suggestive of a phase transformation during loading resulting in metastable high
pressure phases on unloading. The assignment of these Raman peaks will be discussed
later in this chapter (section 3.2). We have observed that some of these peaks are unstable
with time and this is also discussed in sections 3.2 and 3.4. The Raman spectrum of family
‘b’ indents is also shown in Fig. 3.3(a) and 3.3(b). This spectrum is identical in both ~700
nm and ~1000 nm cases and contains a single sharp peak close to 301 cm-1. This is
confirmed to correspond to the Raman signature of dc-Ge by comparing the family ‘b’
spectrum in Fig. 3.3(a) with that for a pristine dc-Ge sample. However, this peak is
slightly shifted from the expected position at 301 cm-1 and broadened, presumably as a
result of residual stress in this thin transformed a-Ge film. This dc-Ge peak is readily
distinguished from the upper broad peak in the Raman band which we label as HPP-Ge
Pressure-induced phase transformations in a-Ge
CHAPTER 3
48
centered at a wave number (of ~285-295 cm-1) as shown in the insert of Fig. 3.3(a) for
the family ‘a’ case.
Pressure-induced phase transformations in a-Ge
CHAPTER 3
49
Figure 3.3: (a) Normalised Raman spectra taken from family ‘a’ and family ‘b’ indents
loaded to 100 mN using a ~4.3 µm radius tip in an ~700 nm thick a-Ge film. A Raman
spectrum from unindented a-Ge is shown for comparison. (b) Raman spectra taken from
family ‘a’ and family ‘b’ indents loaded to 120 mN using a ~4.3 µm radius tip in an ~1000
nm thick a-Ge film. A Raman spectrum from unindented a-Ge is shown for comparison.
XTEM samples were prepared from both family ‘a’ and family ‘b’ indents in the ~700
nm and ~1000 nm a-Ge films. Figure 3.4 (a) shows a bright-field (BF) XTEM image of
a family ‘a’ indent in the ~700 nm film indented to a load of 100 mN. The underlying dc-
Ge substrate can be observed to deform via the generation of defects (slip and twinning)
as previously described in chapter 1 [2]. In the a-Ge layer, a clear region of phase-
transformed material can be observed, extending through the entire thickness of the film.
The inset to Fig. 3.4 (a) shows a selected area diffraction pattern (SADP) from the
transformed region. In this case, a selected area aperture was carefully positioned to be
entirely contained in the indented region with no significant contribution from the dc-Ge
substrate or the surrounding a-Ge. Indeed, this diffraction pattern is dominated by discrete
reflections strongly indicating the presence of crystalline phases, along with a small
amount of a-Ge. Indexing this pattern (see selected arrowed spots) indicates that all
reflections correspond closely to hd-Ge lattice spacings suggesting that the broad Raman
Pressure-induced phase transformations in a-Ge
CHAPTER 3
50
band centered around 285-295 cm-1 may be a signature for hd-Ge (see assignment in
section 3.2). However, the Raman peaks at lower wave numbers in the family ‘a’ case in
Fig. 3 suggests additional high pressure phases (see section 3.2) but such other phases are
not observed in the SADP pattern in Fig. 3.4 (a). This difference between the Raman and
XTEM data is discussed in detail in sections 3.2 and 3.4, but note that the XTEM data in
Fig. 3.4 (a) was taken weeks after indentation. The fact that it shows almost entirely hd-
Ge suggests that phases giving rise to the other peaks in the Raman spectra of family ‘a’
cases in Fig. 3 may be unstable.
Figure 3.4 (b) shows a XTEM image and the corresponding SADP from a typical family
‘a’ indent in the ~1000 nm film. Again, hd-Ge is clearly observed in the SADP taken
directly under the residual indent impression, with the other features essentially similar
to the ~700 nm film case. However, it can be noticed that there is only a slight amount of
deformation in the underlying dc-Ge substrate in this thicker film case. In addition, the
weak circled spots in the insert SADP of Fig. 4(b) have a d-spacing of 4.4 A indicating
that trace amounts of either st12-Ge or bc8-Ge (not observed in Raman spectra) may also
be present. Based on the previous observation of bc8-Ge on pressure release in a DAC, it
is possible that these weak extra spots arise from an intermediate bc8-Ge phase, as
discussed later in chapter 5.
Pressure-induced phase transformations in a-Ge
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51
Figure 3.4: (a) Bright field XTEM images of family ‘a’ indent in an ~700 nm film
indented to 100 mN. SADP taken from the respective phase-transformed region. (b)
Bright field XTEM images of family ‘a’ indent in an ~1000 nm film indented to 125 mN.
SADP taken from the respective phase-transformed region.
Pressure-induced phase transformations in a-Ge
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52
Figure 3.5: (a) Bright field XTEM images of family ‘b’ indent in an ~700 nm film
indented to 100mN. SADP taken from the respective phase-transformed region. (b)
Bright field XTEM images of family ‘b’ indents in an ~1000 nm film indented to 125
mN. SADP taken from the respective phase-transformed region and circled spots do not
index to dc-Ge but rather to either st12 or bc8 phases.
XTEM images and corresponding SADPs for family ‘b’ indents are shown for both the
~700 nm and ~1000 nm films in Figs. 3.5 (a) and 3.5 (b), respectively. They show clear
crystallinity within the phase transformed volume as well as deformation in the
underlying dc-Ge in the case of the thinner ~700 nm film. The most intense spots in the
corresponding SADPs in Figs. 3.5 (a) and 3.5 (b) can be indexed to predominately dc-Ge,
as expected from the Raman data shown in Fig. 3.3. However, the SADPs also show
evidence for some additional but weak diffraction spots (circled) in Figs. 3.5 (a) and 3.5
(b) that do not index to dc- Ge, but rather to either st12 or bc8 phases. The fact that there
are no observable Raman signatures for these phases would suggest that there is only a
trace amount of such non-dc-Ge phases present in residual family ‘b’ indents, (which is
discussed in later chapter 5).
Pressure-induced phase transformations in a-Ge
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53
3.3 Phase assignment of Raman peaks:
This results are consistent with the very recent reports of unstable r8-Ge [3] and its
“annealing” to a more stable hd-Ge phase at room temperature [4]. Since there is
considerable disagreement in the literature on the assignment of Raman peaks from
indented Ge (as discussed in chapter 1), experimental Raman peak positions from family
‘a’ spectra with calculations from density functional perturbation theory (DFPT) was
undertaken by our collaborators Malone and Cohen [5]. As it was a concern that some of
the end phases in the family ‘a’ case may be unstable (see previous section) Raman
spectra was taken immediately after indentation. Figure 3.6 shows such an experimental
Raman spectrum from a typical family ‘a’ case. The path of the spectrum in the 100-400
cm-1 wave number range can be fitted with a series of seven Gaussian line-shapes. Given
the clear presence of the broad a-Ge Raman spectrum arising from the underlying a-Ge
substrate, the a-Ge line-shape is included in the fit. The metastable high pressure end
phases give rise to peaks with Raman frequencies of 85.4±0.5, 202.3±0.7, 224±1, 246.3
cm-1(errors are the standard deviation from six separate indents studied). The 202.3 cm-1
line has a small shoulder at 213 cm-1. A broad band is also observed centered at 150 cm-
1.
As indicated earlier (outline more fully in section 3.5), the end phases in the family ‘a’
case are unstable at room temperature and rapidly transform. Most of the Raman lines
observed initially in Fig 3.6 decrease significantly in intensity whilst being observed at
room temperature while the band at 287-295 cm-1 increases. This band arises presumably
from hd-Ge consistent with the XTEM SADP’s in the previous section.
In order to investigate the nature of the experimental Raman peaks, a comparison of the
Ge spectra may be made to the r8/bc8 Si Raman spectrum. This is shown in Fig. 3.7,
noting that the Si data has been appropriately scaled to match the Ge spectrum [6]. It can
be seen in Fig. 3.7 that the metastable phases of Si and Ge are similar. Both r8 and bc8
are expected to coexist in a Si indent [6] formed under condition similar to those used for
Ge family ‘a’. It is well known that the main line observed here at 349 cm-1 in the Si
spectrum arises from the r8 phase. The normalised Raman frequency of this line is 201.6
cm-1 in Fig 3.9, which is in excellent agreement with the 202.3 cm-1 line for Ge. For Si,
the transition pressure for the r8 to bc8 transition is 2 GPa. According to the DFPT
calculations, Ge makes this same transition on pressure release at the lower pressure of
0.65 GPa [5]. It might therefore be expected that the Ge indent, confined within the
Pressure-induced phase transformations in a-Ge
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54
substrate, may contain a greater volume of r8 than the equivalent Si indent, and thus it
may well be possible that r8 alone is present after final indentation pressure release.
To further aid the interpretation of the experimental results, DFPT calculations have been
performed to give Raman peak positions of dc, st12, bc8 and r8 phases of Ge. The Raman
frequencies determined by DFPT are shown in Fig. 3.8 and compared to the
experimentally determined line positions extracted from Fig. 3.6. The DFPT results are
not corrected for the 2.4 cm-1 difference between the experimental (300.6 cm-1) and
theoretical Raman mode (298.2 cm-1) in dc-Ge. The metastable phases crystals in the
transformed zone of the family ‘a’ case are expected to be 5-30 nm in diameter so that
confinement effects may shift the Raman frequencies down [6]. An upper limit is
calculated to be -2 cm-1 for dc-Ge with the phonon confinement model [7]. It can be seen
that the frequency of the dominant Raman peak at 202.3 cm-1 is in excellent agreement
with the r8 line at 202.8 cm-1. No other calculated Raman lines are observed in the
vicinity. We therefore suggest that r8, giving rise to the dominant 202.3 cm-1 line, is
present after pressure release in the family ‘a’ case. In addition, other observed lines at
85 cm-1, 95 cm-1, 213 cm-1, 224 cm-1, 246 cm-1 and 277 cm-1 are also very close to the
calculated peak positions for r8-Ge. Similar Raman line-shapes have also been observed
in DAC experiments by Coppari et al. at pressures in the range of 3-8 GPa [8], suggesting
that the phases observed are similar to those produced in the present study. However, in
this earlier work, the end phase was assigned to st12-Ge and not r8, based on DFT
calculations. The st12 Raman intensities were also calculated and are shown in Fig 5.8
(b) and compared to previous calculations. Note that similar theoretical intensities cannot
be obtained for r8 and bc8 phases since they are Raman active. The peak positions appear
to be underestimated in the earlier calculation, where the dominant calculated line is close
to our experimental r8 line at 202.3 cm-1 which presumably led to an incorrect assignment
in the earlier work. We also note that the observed Raman peaks at 224 cm-1 and 246 cm-
1 are not close to the calculated st12 lines from the Coppari calculation. The discrepancy
between the Coppari calculation and the DFPT calculations for st12-Ge is not known, but
note that the dc Raman peak in that work was calculated as 292 cm-1 compared to here at
298.2 cm. Furthermore, the two dominant lines at 249 cm-1 and 275 cm-1 in the calculated
st12 spectrum agree well with the experimentally determined Raman peak positions of
st12-Ge formed in a DAC by Kobliska et al. [9] at 246 cm-1 and 273 cm-1. It is therefore
clear from the above calculations and arguments that the family ‘a’ indents do not contain
any detectable trace of st12; rather it is observed a dominant r8 phase which is the only
Pressure-induced phase transformations in a-Ge
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55
phase that gives rise to the dominant line at 202 cm-1 in the Raman spectrum. The other
Raman lines also agree well with those calculated for the r8 phase shown in Fig 3.8 (a).
However, as might be expected for a phase with a similar structure, four of these peaks
also agree with those calculated for the bc8 phase so that the presence of bc8 cannot be
ruled out entirely. Finally, the r8-Ge phase is unstable and, as it decays, the Raman band
at 285-295 cm-1 grows which corresponds to the calculated band for hd-Ge, as shown in
later section 3.5.
Figure 3.6: (colour online). Experimental Raman spectra of the indented a-Ge
immediately after indentation fit with a series of Gaussian fits (solid lines). An a-Ge line
shape was included in the fit (dashed line). The inset shows the low frequency region
from (i) the indented a-Ge and (ii) pure a-Ge showing the broad transverse acoustic a-Ge
Raman band [3].
Pressure-induced phase transformations in a-Ge
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56
Figure 3.7: Experimental Raman spectra (i) from Fig. 3.6 compared to (ii) that of an
indent formed under similar conditions in a-Si. The Raman shift has been scaled for
comparison. The inset shows the low frequency region from the indented (i) a-Ge and (ii)
a-Si [3].
Figure 3.8: (colour online). (a) Raman-active mode frequencies decided by DFPT for
various Ge phases. The upper bars are the experimentally observed peak positions, the
width of the bar being the associated standard deviation of the six indents measured. (b)
The calculated st12 Raman spectra. The r8 and bc8 intensities could not be calculated
since they are metallic within the calculations [3].
Pressure-induced phase transformations in a-Ge
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57
3.4 Thick a-Ge films
Fig. 3.9 (a) shows representative load/unload curves and associated Raman spectra for
indentation of the thickest (~1800 nm) a-Ge film. Indentation was performed on this
thicker a-Ge film using a ~20 µm radius spherical tip primarily to achieve a pop-in (phase
transformation) event, without cracking. For all indents, the slope of the loading curve
after pop-in is consistent with family ‘a’ behaviour. Out of an array of 50 indents, only
family ‘a’ behaviour was observed with the ~20 µm radius spherical tip. Figure 3.9 (a)
shows that, at a low maximum load of 450 mN, the load-unload curve is featureless, with
no major pop-in event detected but considerable plastic deformation occurring as
indicated by the residual penetration depth of ~200 nm following complete unloading.
Pressure-induced phase transformations in a-Ge
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58
Figure 3.9: (a) Load-unload curve from an ~1800 nm thick a-Ge film indented with a
~20 µm radius spherical tip to maximum loads of 450 mN and 700 mN. (b) Raman spectra
of the ~1800 nm film for the 700 mN indent with a spectrum from unindented a-Ge shown
for comparison. The broad peak centered at 295 cm-1 is characteristics of the hd-Ge band
observed for thinner films for Raman spectra taken after several days.
When the maximum load is increased to 700 mN, a pop-in occurs at a load of ~520 mN
and at a penetration depth of 950 nm. This is again at a penetration depth of half the film
Pressure-induced phase transformations in a-Ge
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59
thickness, similar to the thin films. Raman data taken from indents produced at this higher
load are shown in Fig. 3.9 (b). A single broad Raman peak centered at about 295 cm-1 can
be observed. Based on our earlier family ‘a’ behaviour for the thinner films, we suggest
that the dominant (stable) end phase is hd-Ge. Furthermore, our previously measured hd-
Ge Raman peak position in Fig. 3.3 corresponds closely with the observed broad Raman
band characterizing the stable end phase. Indeed, the fact that the other Raman peaks
associated with the r8-Ge phase are not observed by Raman in the case of the thicker a-
Ge film is almost certainly a result of the fact that the analysis was taken many days after
indentation. This delay between indentation and analysis appears to have led to
transformation of any residual r8 peaks to hd-Ge, as we show more definitively in the
following section 3.5. As shown in this next section, clear r8 Raman signatures can be
obtained when the Raman analysis occurs immediately after indentation.
Figure 3.10: Bright field XTEM image of an indent in an ~1800 nm thick a-Ge film made
with a ~20 µm radius spherical tip to a maximum load 700 mN. Image shows a SADP
taken from the phase-transformed region where the most intense spots have been indexed
predominately to hd-Ge and the amorphous material right under the transformed region
Pressure-induced phase transformations in a-Ge
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60
XTEM image of an indent loaded to 700 mN in the thick (~1800 nm) a-Ge film is shown
in Fig. 3.10. Unlike the XTEM of the thinner films; a clear phase-transformed region is
observed which does not extend throughout the entire a-Ge layer. There is no evidence of
plastic deformation (i.e., twinning or dislocations) in the underlying dc-Ge substrate in
this case. The SADP taken from the phase-transformed volume directly under the residual
indent impression shows predominantly intense reflections with a d-spacing consistent
with hd-Ge. However, there are very weak a-Ge rings as well as some additional weak
spots that indicate trace amounts of an additional phase that may be st12-Ge. This will be
discussed briefly in Chapter 5. Clearly, the XTEM results are consistent with the Raman
data, indicating that the “stable” dominant end phase is hd-Ge. It is also important to note
that only one dominant deformation pathway (family ‘a’) is observed for the thick a-Ge
film. This may suggest that the large (~20 µm radius) tip used for the indentation may
have contributed to this behaviour, by confining, for example, a larger volume of
transformed a-Ge between the tip and substrate.
A significant result from the ~1800 nm a-Ge film is that it appears to initially deform
plastically prior to the pop-in load. However, the plastic deformation process is not
sufficient to prevent continuous pressure build up during further loading and a
catastrophic phase transformation at higher indentation pressures occurs. This
transformation process may be enhanced through densification of the a-Ge during
indentation loading. This data indicates that an a-Ge to (β-Sn)-Ge transformation occurs,
presumably at pop-in, which signifies that a significant volume of material transforms
under the indenter to the denser and softer (β-Sn)-Ge phase. It is likely that the proximity
of the underlying harder crystalline substrate contributes to accompanying densification
of the a-Ge film and assists in reaching the necessary transformation pressure. In this
regard, it is noted that the depth at pop-in increases with the thickness of the film from
350 nm for the ~700 nm film, through 550 nm for the ~1000 nm film to 950 nm for the
~1800 nm film. This effect may be related to the initial plastic deformation of the a-Ge
films prior to phase transformation at the pop-in load.
Pressure-induced phase transformations in a-Ge
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61
Figure 3.11: Raman spectra immediately after indentation and after various times at room
temperature ~1800 nm thick a-Ge film indented with a ~20 µm radius spherical tip to a
maximum load of 700 mN. The assignments for r8 and hd-Ge phases from DFPT
calculations (section 3.3) are also shown.
3.5 Phase stability in the family ‘a’ case
It is clear that the dominant r8 end phase in the family ‘a’ case is unstable and appears to
transform to hd-Ge at room pressure and temperature. This transformation is illustrated
in Fig. 3.11. After indentation, a series of family ‘a’ indents (identified from load-unload
curves) were immediately stored in dry ice and transported to the Raman instrument.
After warming to room temperature, Raman spectra were measured as a function of time
as shown in Fig. 3.11. In this figure, the calculated r8 and hd-Ge peak positions (section
3.3) are shown. It is clear that the r8 to hd-Ge transformation takes place in a time scale
of hours. About one week after indentation all of the r8 phase has transformed to hd-Ge.
Such a case is not shown in Fig. 3.11 but the Raman spectrum in Fig. 3.9(b) shows such
a case. Thus, the family ‘a’ behaviour is now clear. On unloading (β-Sn)-Ge transforms
into r8-Ge which is unstable at RT and transforms to hd-Ge. This instability explains the
apparent inconsistency between the Raman and XTEM data for the family a’ case in
section 3.2.
Pressure-induced phase transformations in a-Ge
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62
3.6 Summary of thin and thick films of a-Ge
A significant conclusion from the results in this chapter is, when ion implanted a-Ge films
on dc-Ge substrates are subjected to indentation with a spherical tip, despite significant
plastic deformation, it is possible to cause pressure-induced phase transformations under
the indenter. This event is sudden, it involves the phase transformation of a large volume
of a-Ge, and it is signified by a substantial pop-in excursion in the loading curve. Two
groups of behaviour are observed during indentation. In one case (family ‘a’), the volume
of metallic (β-Sn)-Ge phase that forms at pop-in phase transforms to the r8-Ge phase on
unloading. Comparisons with DFPT calculations confirm that the predominant end phase
is r8-Ge and this comparison highlights some incorrect assignments of Raman data in the
literature. However, the r8 phase is unstable at room temperature and pressure and further
transforms to the hd-Ge phase. In the other case (family ‘b’), it would appear that the (β-
Sn)-Ge phase can trigger a direct transformation to dc-Ge but that there appears to be
trace amounts of st12-Ge within some residual indents. The data collected in this chapter
is not sufficient to explain why the two pathways (families) occur, particularly the
explanation for family ‘b’ behaviour. Hence, the following chapter examines a range of
other indentation and sample preparation details such as pre-annealing of the starting a-
Ge material, changes in load and unload rates, as well as close examination of the effect
of tip geometry on family ‘a’ and family ‘b’ behaviour.
Pressure-induced phase transformations in a-Ge
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63
[1] W.-K. Chu, J. W. Mayer, and M.-A. Nicolet, Backscattering Spectrometry. 1978.
[2] J. E. Bradby, J. S. Williams, J. Wong-Leung, M. V Swain, and P. Munroe,
“Nanoindentation-induced deformation of Ge,” vol. 80. p. 2651, 2002.
[3] B. C. Johnson, B. Haberl, S. Deshmukh, B. D. Malone, M. L. Cohen, J. C.
McCallum, J. S. Williams, and J. E. Bradby, “Evidence for the R8 phase of
germanium.,” Phys. Rev. Lett., vol. 110, no. 8, p. 085502, Feb. 2013.
[4] J. S. Williams, B. Haber, S. Deshmukh, B. C. Johnson, B. D. Malone, M. L.
Cohen, and J. E. Bradby, “Hexagonal germanium formed via a pressure-induced
phase transformation of amorphous germanium under controlled
nanoindentation,” Phys. Status Solidi - Rapid Res. Lett., vol. 7, no. 5, pp. 355–
359, 2013.
[5] B. D. Malone and M. L. Cohen, “Electronic structure, equation of state, and
lattice dynamics of low-pressure Ge polymorphs,” Phys. Rev. B, vol. 86, no. 5, p.
054101, Aug. 2012.
[6] B. C. Johnson, B. Haberl, S. Deshmukh, B. D. Malone, M. L. Cohen, J. C.
McCallum, J. S. Williams, and J. E. Bradby, “Evidence for the R8 phase of
germanium,” Phys. Rev. Lett., vol. 110, no. 8, 2013.
[7] L. J. Bruner and R. W. Keyes, “Electronic Effect in the Elastic Constants of
Germanium,” Phys. Rev. Lett., vol. 7, no. 2, pp. 55–56, Jul. 1961.
[8] H. Schäfer, The Structures of the Elements. New York: John Wiley & Sons,
1974.
[9] R. J. Kobliska, S. A. Solin, M. Selders, R. K. Chang, R. Alben, M. F. Thorpe,
and D. Weaire, “Raman Scattering from Phonons in Polymorphs of Si and Ge,”
Phys. Rev. Lett., vol. 29, no. 11, pp. 725–728, Sep. 1972.
Pressure-induced phase transformations in a-Ge
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Exploring indentation conditions
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65
CHAPTER 4
Further details of phase transformations in a-Ge: Exploring indentation
conditions
Exploring indentation conditions
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66
This chapter discusses the influence of other parameters that have been known to effect
the indentation-induced deformation of materials. This is presented in three sections. The
first section discusses the relaxation of a-Ge, the second part focuses on the effect of
indenter geometry on the phase transformation pathways, and the final section describes
the effect of loading and unloading rates on phase transitions.
4.1 Effect of relaxation of a-Ge on nanoindentation-induced phase
transformation
Before outlining the work on annealing of a-Ge, some definitions will first be explained.
Samples that have undergone an annealing step will be referred to as ‘relaxed’, while as-
implanted (un-annealed) samples will be referred to as ‘unrelaxed.’ This follows the
convention in the literature that has been established for both a-Ge and a-Si. [1–3] In this
work, a-Ge samples are annealed at temperatures ranging from 250-350° C for 30 mins.
This is below the temperature required to re-crystallize a-Ge [4] (~ 500° C) and annealing
below this threshold is thought to remove defects in the amorphous network such as bond
angle distortion or dangling bond which may be caused by the ion-implantation process.
[5, 6] The motivation for this work on a-Ge samples arises from similar studies on a-Si.
For ion-implanted a-Si, thermal annealing at 450° C for 30 minutes is known to fully
structurally relax the amorphous layer. [1] The different ‘state’ of the ion-implanted a-Si
after such a thermal anneal, so called ‘relaxation’, can be easily seen in the mechanical
properties of the sample with the relaxed form displaying slightly higher indentation
hardness. [7] Furthermore, studies have shown that, after relaxation, the preferred
mechanical deformation pathways becomes very similar to that of c-Si with a series of
pressure-induced phase transformation observed during indentation [8], whereas
unrelaxed a-Si deforms via a simple plastic flow mechanism. [1] No such systematic
study currently exists for a-Ge.
Exploring indentation conditions
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67
Experimental details of relaxation of a-Ge
To study the changes that occur during relaxation of a-Ge, a thick layer of ~ 1800 nm a-
Ge formed by ion-implantation (see chapter 2) was annealed using a tube furnace at three
different temperatures, 250o
C, 300o
C, and 350o C each for 30 minutes in an argon flow.
The samples were annealed in a quartz-boat and mechanically pushed into the centre of
the furnace using a quartz rod. After cooling to room temperature, Raman was done on
a-Ge samples to probe short range order which is dependent on the state of relaxation.
Raman spectra were taken using the 632 nm HeNe laser. The laser power was low to
avoid annealing unstable phases in the relaxed/unrelaxed Ge sample. The difference in
the state of the amorphous structure after annealing can be seen by subsequent analysis
of the Raman peak and by calculation of the bond angle distortion (as detailed in the
following section).
Figure 4.1: Typical Raman spectra from relaxed a-Ge, showing the transverse optic (TO)
peak. (Note that the location of the transverse acoustic (TA) is 80 cm-1 and hence not
measured in this study. The half width ΓTO/2 is also indicated.
Exploring indentation conditions
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68
Figure 4.2: Raman spectra of unrelaxed and relaxed a-Ge samples annealed at 250o
C,
300oC, and 350
oC each for 30 mins.
Exploring indentation conditions
CHAPTER 4
69
Figure 4.3: Calculated bond angle distortion versus the different annealing temperatures
of a-G. (Calculated using the Beeman relaxation). [9]
Figure 4.4: TO line width measured from Raman spectra of a-Ge versus annealing
temperature (annealing time was 30 min).
Nanoindentation was then carried out using the UMIS and a ~4.3 µm radius spherical tip
to loads of up to 100 mN. Raman was done on the residual indent impressions for further
analysis.
Exploring indentation conditions
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70
Results and discussion - relaxation of a-Ge
Previously in this thesis it has been seen that Raman microspectroscopy is useful in
identifying the different crystalline structures of Ge. However, it is also sensitive to the
short-range order in amorphous materials. Although phonon-confinement yields the sharp
Raman bands for crystalline structures, it does not apply to amorphous materials and so
inelastic scattering on all the phonon-modes are then observed. [9] Hence, the sensitivity
to the local bonding environment. Figure 4.1 shows a typical Raman spectra taken from
amorphous Ge (in this case a-Ge that has undergone a relaxation anneal at 350°C for 30
mins). The position of the peak associated with the transverse optic (TO) vibration mode
is shown at ~275 cm-1. The position and characteristics of the TO band is known to be
related to the bond-angle distortion of an amorphous network and is given by the Beeman
equation (equ.4.1). [9]
ΓTO = 15 + 6 Δθ (4.1)
In this equation Δθ is the bond-angle distortion (in degrees) and ΓTO is the full width of
the TO peak at half maximum height. In practice, to determine θ from experimental
Raman data, Γ/2 is measured on the high frequency side of the TO band as shown in Fig.
4.1. This avoids any contribution from other vibrational modes.
Figure 4.2 shows the Raman spectra taken from unrelaxed a-Ge and a-Ge annealed at
250°C, 300°C, and 350°C, respectively. A clear difference in the intensity and shape of
the unrelaxed a-Ge TO peak can be seen compared to the spectra taken after annealing.
To characterize changes to the amorphous structures of these four different samples, the
width of the TO peak, (ΓTO) was measured and the resultant bond angle distortion
calculated using on the Beeman relation given above. The bond angle distortion versus
the relaxation temperature is shown in Fig. 4.3. This figure shows there is a clear
difference in the magnitude of the bond angle distortion as a result of the annealing
process. Studies in a-Si show a similar drop in the bond angle distortion; from 10.8° for
unrelaxed (as-implanted) a-Si to 8.5° for samples at 450° C for 30 mins (fully relaxed).
[10] Figure 4.3 shows the bond angle distortion for a-Ge dropping from ~9.6° for
unrelaxed a-Ge to ~8.7° for a-Ge annealed at 350°C for 30 mins.
Another parameter that may suggest changes to the amorphous structure on annealing is
the position of the TO peak ω(TO). This is given in Fig. 4.4. This figure shows that the
Exploring indentation conditions
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71
position of the TO peak for a-Ge increases slightly with annealing. This is again consistent
with previous observations in a-Si, suggesting increasing order with relaxation anneals.
[11]
However, it should be noted that the position of the TO peak can also be effected by
interval stress and hence is not a strong indicator for relaxation by itself. [11] To probe
the effect on relaxation of a-Ge on the phase transformation pathway, a comparison
between the nanoindentation behavior of relaxed (350° C at 30 mins) and unrelaxed (as-
implanted) was conducted. Figure 4.5 shows the load-displacement curves made on
unrelaxed and relaxed a-Ge loaded to 100 mN using a spherical tip of radius ~4.3 µm. A
clear difference between the two nanoindentation curves is seen. In the unrelaxed case,
no pop-in is observed whilst a clear pop-in can be seen for the relaxed material. The pop-
in event was observed to occur at lower loads in the relaxed a-Ge, compared to the
unrelaxed samples.
Exploring indentation conditions
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72
Figure 4.5: Load-displacement curves of indents made to 100 mN with a spherical tip of
~ 4.3 µm radius in (a) unrelaxed a-Ge and (b) relaxed Ge (annealed at 350° C for 30 mins).
Raman spectroscopy was also conducted on selected residual indents made in the relaxed
a-Ge samples, indications of phase transformation were observed in the indents
displaying the pop-in behaviour, strongly suggesting that the occurrence of pop-in is
linked with the material undergoing a phase transformation. Raman spectra of the indents
made in unrelaxed and relaxed a-Ge is shown in Fig. 4.6. This figure shows a clear shift
in the main Raman peak from ~270 cm-1 to ~286 cm-1. This is consistent with the
transformation to hex-Ge (as detailed in section 3.3).
Exploring indentation conditions
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73
A summary of the indentation behavior of the a-Ge material with relaxation is shown in
table 4.1. This table shows the percentage of curves that contain a pop-in event for the Ge
sample with relaxation at different temperatures. Arrays of 5×5 indents were done to
collect these statistics. It is clear that unrelaxed a-Ge does not show a pop-in event when
indented under these conditions. However, after annealing this behaviour changes. After
annealing at 250°C for 30 mins some pop-in events are observed after indenting to 100
mN. A similar result is seen after annealing at 300°C for 30 mins. However, after
annealing at 350°C for 30 mins, pop-in events can be also observed at the lower load of
60 mN.
Table 4.1: Summary of the deformation behavior of thick a-Ge layer after various
relaxation anneals. (- pop-in, х – no pop-in.)
Thick sample
(~1800 nm a-Ge)
Load applied
60 mN
(pop-in)
Load applied
100 mN
(pop-in)
Unrelaxed Ge
х
х
relaxed at 250oC
for 30 mins
х
75 %
25 % х
relaxed at 300oC
for 30 mins
х
75 %
25 % х
relaxed at 350oC
for 30 mins
50 %
50 % х
75 %
25 % х
Exploring indentation conditions
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74
This preliminary study on the effect of relaxation annealing on a-Ge suggests that, like a-
Si, a-Ge undergoes structural changes during annealing. From the analysis of the bond-
angle distortion and TO peak position changes, it is clear that the structure of a-Ge is
affected by relaxation anneals. Furthermore, like a-Si, it appears that relaxed a-Ge is more
likely to deform via phase transformation. This is clearly a topic that could be explored
in more depth and will be mentioned in the ‘future studies’ section in Chapter 5.
Exploring indentation conditions
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75
Figure 4.6: (a) Raman spectra of a nanoindent made with 100 mN load in unrelaxed Ge.
(b) Raman spectra of a nanoindent made with 100 mN load in relaxed Ge (annealed at
350° C for 30 mins).
4.2 Effect of indenter geometry on phase transformation pathways
As detailed in the introductory chapter of this thesis, the previous reports of indentation-
induced deformation in Ge were done using a variety of indenter geometries. In this study,
to examine the influence of indenter geometry on the deformation of a-Ge, two different
shapes were utilised; (spherical and Berkovich).
Experimental details of effect of tip geometry
A series of indents was made in ~700 nm thin film of a-Ge with both a Berkovich and
spherical indenter of ~ 4.3 µm radius to a maximum load of 100 mN as shown in Fig 4.7.
As has been previously shown, load-unload curves using a spherical tip shows two
deformation pathways, so called family ‘a’ and family ‘b’. This is shown again in Fig.
4.7 (a). However, applying the same load using Berkovich tip shows only one type of
load-unload curve [as shown in Fig. 4.7 (b)]. This figure shows 20 individual indents to
show that only one type of ‘family’ is seen. The inset to Fig. 4.7 (b) shows a single load-
unload curve. A pop-in event can be clearly seen when the curves are lotted separately.
Looking at the slope of the loading curve after the pop-in event for indents made with the
Berkovich tip, it is more like that these indents are family ‘b’ type indents.
To understand the indentation-induced deformation induced by these two different tips,
Raman spectra was taken from the residual indent impressions made with the spherical
and Berkovich tips (on the same a-Ge sample). Spectra from indents made using 100 mN
were compared with pristine area of a-Ge sample. Figure 4.8 shows the Raman bands
observed from these samples, with a clear difference observed between the pristine and
deformed (indented) region.
The Raman taken from the spherical indents shows the clear difference between the two
‘families’ of indents (This is discussed in more detail in section 3.3.) Comparing these
spectra to the Raman spectrum recorded from an indent formed with the Berkovich tip, it
is clear that the Berkovich indent is showing family ‘b’ like behaviour, with a strong
Exploring indentation conditions
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76
Raman peak at 300 cm-1. A shoulder at 270 cm-1 can also be observed but this is likely
from the surrounding (background) a-Ge.
SEM was also done to understand these differences. This is shown in Fig. 4.9. This figure
shows a three residual indents from family ‘a’ (spherical), family ‘b’ (spherical), and
indents made using a Berkovich tip. A clear difference is observed.
Figure 4.7: Load-unload curves of nanoindents made to 100 mN in a-Ge using (a) ~4.3
µm spherical tip and (b) The inset to (b) shows a single load-unload curve to clearly show
the pop-in event using Berkovich tip.
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77
Figure 4.8: (a) Raman spectra of a nanoindent made with 100 mN load to a-Ge using
~4.3 µm spherical tip. (b) Raman spectra of a nanoindent made with 100 mN load using
Berkovich tip.
The SEM images shown of family ‘a’ are given in Fig 4.9 (a). The residual indent
impressions are ~ 4.0 µm in diameter and the edges are largely featureless. The SEM
images of the family ‘b’ indents are shown in Fig. 4.9 (b) and show that these indents are
Exploring indentation conditions
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78
a similar size but display features to the left of each indent impression in the form of
bright circular bands. Such bands are much more pronounced in the SEM images taken
from the indents made using a Berkovich tip shown in Fig. 4.8 (c). These bright bands
are likely due to the transformed material flowing out from beneath the tip as the tip is
unable to fully constrain the transformed zone. This is shown in the schematic in Fig.4.10.
Thus, the end phases observed under the Berkovich and family ‘b’ indents appear to be
formed under similar conditions.
Figure 4.9: (a) SEM image of a family ‘a’ nanoindent made with 100 mN load in a-Ge
using a ~4.3 µm radius spherical tip. (b) SEM image of a family ‘b’ nanoindent made
with 100 mN load in a-Ge using a ~4.3 µm radius spherical tip (c) SEM image of a
nanoindent made with 100 mN load in a-Ge using a Berkovich tip.
Exploring indentation conditions
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79
Figure 4.10: Schematic showing a constrained family ‘a’ indent and an unconstrained
family ‘b’ indent.
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80
4.3 Effect on Loading/unloading rates on phase transformation in a-Ge
Previous studies of indentation-induced phase transformations in Ge have suggested that
the rate of loading and/or unloading may influence the deformation behaviour. [12,13]
Indeed, Oliver et al. reported that dc-Ge shows a phase transformation could be induced
using both spherical and Berkovich tips if the loading rate exceeded 100 mN/s. Work by
Jang et al. reported a trend towards phase transformation with fast loading rates of 5 mN/s
but this was only reproducible using a sharp corner-cube indenter. No such work has been
done on the influence of loading/unloading rates on the deformation of a-Ge.
Experimental details of slow and fast loading/unloading on a-Ge
A series of indents was made in ~700 nm thin film of a-Ge with a spherical indenter of ~
4.3 µm radius and a maximum load of 100 mN. Indents made with a loading rate of 0.5
mN/s to 2 mN/s and unloading rate 1.3 mN/s to 0.6 mN/s. The tests were conducted using
the UMIS and the loading rates were determined from load verses time plots. A summary
of the range of loading and unloading rates on a-Ge is shown in Table 4.2.
Exploring indentation conditions
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81
Table 4.2: Loading/unloading rates used in this work.
Results and discussion of slow and fast loading/unloading on a-Ge
A preliminary study on the effect of loading and unloading rates on the phase
transformation of a-Ge was undertaken.
Firstly, the effect of the fast loading was investigated. Figure 4.11 shows load unload
curves of three sets of indents made using a standard unload rate of ~2 mN/s and loading
of ~6, 15, 50 mN/s, respectively. All three sets of indentation curves showed behaviour
previously observed for indents loaded at the standard loading rate of ~ 6mN/s (as shown
in Fig. 3.1) with both family ‘a’ and family ‘b’ indents displayed. This suggests that fast
loading, at least under the conditions investigated here, does not influence the phase
transformation pathways.
Maximum load
(100 mN)
Rate (mN/s)
Increments
(instrument
specific parameter)
standard
~2 mN/s
50
‘slow’
~0.5 mN/s
200
‘fast’
~100, 50, 20, 6 mN/s
1, 2, 5, 15
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82
The effect of faster unloading was then explored. A series of indents were made using
the standard loading rate (~6 mN/s) and fast unload of ~100 mN/s. Due to the fact that
loading/unloading rate can only be controlled by increasing or decreasing the number of
increments hence data points of the load unload curves recorded from rapid unload (1
increment) contained little information. Hence Raman of the residual indent impression
is presented instead. Figure 4.12 shows Raman taken from indents made using standard
loading rates but rapid (~20 mN/s) unload. Again both sets of families can be observed.
However, it appears that family ‘b’ has a higher shoulder compared to that observed in
the indents loaded and unloaded at standard rates. The shoulder could indicate a higher
amount of background a-Ge.
Given the previous work (Jang et al. [12] and Oliver et al. [13]) showed that phase
transformation is promoted by faster loading rates, it was decided to investigate the effect
on slower loading rates on the a-Ge samples studied here.
Figure 4.13 shows the load-unload curves of indents made using slow (~0.5 mN/s)
loading and standard unloading. The TEM of these indents is shown in Fig. 4.14. This
figure shows that the family ‘b’ indent contains regions of amorphous material which had
not been previously observed with the standard loading rate work. Thus it seems that the
slower rate may impact the transformation of the amorphous material during loading.
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83
Figure 4.11: Fast load (50, 20 and 6 mN/s) and standard unload (50 increments) with
loading rate ~6 mN/s curve from a ~700 nm thin a-Ge film indented with ~4.3 µm radius
spherical tip to a maximum load of 100 mN.
Figure 4.12: Raman spectra from indents made using a regular loading rate (mN/s) and
unloading rate (mN/s).
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84
Figure 4.13: Slow load (200 increments) and standard unload (50 increments) with a
slow loading rate (~0.5 mN/s) curve from ~700 nm thin a-Ge film indented with ~4.3 µm
radius spherical tip to a maximum load of 100 mN.
Exploring indentation conditions
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85
Figure 4.14: (a) XTEM image of family ‘a’ spherical indent using slow loading and
standard unloading rate. (b) XTEM image of family ‘b’ spherical indent using a slow
loading and standard unloading rate with clear blocks of amorphous material in the
transformed region.
[1] B. Haberl, J. E. Bradby, M. V. Swain, J. S. Williams, and P. Munroe, “Phase
transformations induced in relaxed amorphous silicon by indentation at room
temperature,” Appl. Phys. Lett., vol. 85, no. 23, p. 5559, 2004.
[2] D. J. Oliver, J. E. Bradby, S. Ruffell, J. S. Williams, and P. Munroe,
“Nanoindentation-induced phase transformation in relaxed and unrelaxed ion-
implanted amorphous germanium,” J. Appl. Phys., vol. 106, no. 9, 2009.
[3] L. B. Bayu Aji, S. Ruffell, B. Haberl, J. E. Bradby, and J. S. Williams,
“Correlation of indentation-induced phase transformations with the degree of
relaxation of ion-implanted amorphous silicon,” J. Mater. Res., vol. 28, no. 08,
pp. 1056–1060, Mar. 2013.
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[4] B. C. Johnson and J. C. McCallum, “Dopant-enhanced solid-phase epitaxy in
buried amorphous silicon layers,” Phys. Rev. B, vol. 76, no. 4, p. 045216, Jul.
2007.
[5] J. Fortner and J. S. Lannin, “Structural relaxation and order in ion-implanted Si
and Ge,” Phys. Rev. B, vol. 37, no. 17, pp. 10154–10158, 1988.
[6] I. D. Desnica-Frankovic, K. Furic, U. V Desnica, M. C. Ridgway, and C. J.
Glover, “Structural modifications in amorphous \ce{Ge} produced by ion
implantation,” Nucl. Instruments Methods Phys. Res. Sect. B, vol. 178, pp. 192–
195, 2001.
[7] J. S. Williams, J. S. Field, and M. V. Swain, “Mechanical Property
Characterisation of Crystalline, Ion Implantation Amorphised and Annealed
Relaxed Silicon with Spherical Indenters,” MRS Proc., vol. 308, p. 571, Feb.
2011.
[8] S. Ruffell, B. Haberl, S. Koenig, J. E. Bradby, and J. S. Williams, “Annealing of
nanoindentation-induced high pressure crystalline phases created in crystalline
and amorphous silicon,” J. Appl. Phys., vol. 105, no. 9, pp. 1–8, 2009.
[9] D. Beeman, R. Tsu, and M. F. Thorpe, “Structural information from the Raman
spectrum of amorphous silicon,” Phys. Rev. B, vol. 32, no. 2, pp. 874–878, Jul.
1985.
[10] B. Haberl, A. C. Y. Liu, J. E. Bradby, S. Ruffell, J. S. Williams, and P. Munroe,
“Structural characterization of pressure-induced amorphous silicon,” Phys. Rev.
B, vol. 79, no. 15, p. 155209, Apr. 2009.
[11] Leonardus Bimo Bayu Aji, “Structural relaxation process in pure amorphous
silicon,” The Australian National University, 2014.
[12] J. Il Jang, M. J. Lance, S. Wen, and G. M. Pharr, “Evidence for nanoindentation-
induced phase transformations in germanium,” Appl. Phys. Lett., vol. 86, no. 13,
pp. 1–3, 2005.
[13] D. J. Oliver, J. E. Bradby, J. S. Williams, M. V. Swain, and P. Munroe, “Rate-
dependent phase transformations in nanoindented germanium,” J. Appl. Phys.,
vol. 105, no. 12, 2009.
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Discussion conclusions and future work
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88
CHAPTER 5
Discussion, conclusions and future work
Discussion conclusions and future work
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89
5.1 Phase transformation of a-Ge under indentation
The nanoindentation response of a-Ge was investigated in this work and pressure-induced
phase transformation was identified as the primary mode of deformation. As shown in
chapter 3, when ion implanted a-Ge films on dc-Ge substrates are subjected to indentation
with a spherical tip, it is possible to cause pressure-induce phase transformations under
the indenter. This transformation event is sudden and most likely involves the
transformation of a large volume of a-Ge to the β-Sn phase. It is detected by a substantial
pop-in in the loading curve. Two groups of behaviour are observed during indentation. In
one case (family a), the volume of metallic (β-Sn)-Ge phase that forms at pop-in is totally
confined under the indenter tip. During unloading it is proposed that this metallic phase
progressively transforms to the r8-Ge phase. The identification of the r8 phase was
obtained by comparing experimental Raman peaks with those calculated using DFT
calculations. However, the r8 phase is unstable at room temperature and pressure and
further transforms to the hd-Ge phase as was also illustrated in chapter 3. In the other case
(family b), as was shown in chapter 4, the soft metallic (β-Sn)-Ge phase is not confined
under the indenter at pop-in and is extruded out from under the indenter tip. This is shown
in the SEM data of extrusion given in Chapter 4. In this case, the extruded (β-Sn)-Ge
phase appears to trigger a direct transformation to dc-Ge. Both Raman and TEM data in
chapter 3 indicates that dc-Ge is the main end phase. However, a trace amount of st12 Ge
was also observed in TEM diffraction patterns.
In the following section a possible process that could result in a β-Sn-Ge to dc-Ge
transformation (explosive crystallization) is explored. Then (section 5.3) the previous
evidence for st12 Ge is given and an explanation offered that involves high shear stress
during unloading.
In section 5.4, the results of this thesis are brought together into a summary of the
transformation pathways that cover family ‘a’ and family ‘b’ cases. This behaviour is
compared with the behaviour of relaxed a-Si under indentation. Finally, in section 5.5
some unanswered questions and possible future studies are discussed.
5.2 Consideration of explosive crystallization
Self-sustaining crystallization or explosive crystallization of amorphous material has
been the subject of interest from many years. [1–3] Explosive crystallization is a thermal
Discussion conclusions and future work
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90
process whereby heat released during crystallization drives the crystallization reaction
further. The process of explosive crystallization of a-Ge is one in which the
recrystallization of a small volume of a-Ge can trigger a runaway exothermic reaction
that crystallizes a large volume of a-Ge, hence driving the transition from a-Ge to dc-Ge.
[4] Mainly laser induced explosive crystallisation of a-Ge has been studied in the
literature, where the initial crystallization process is triggered by laser heating: explosive
crystallisation then transforms the whole film to dc-Ge. [5] The original study on
explosive crystallization in a-Ge reported that this heat release reaction could be triggered
by different methods such as “pricking with a sharp point” [3], whereby strain energy can
trigger the initial crystallisation, and this method can be related to the indentation process.
Oliver et al. has previously suggested that explosive crystallisation may have contributed
to an a-Ge to dc-Ge transformation under indentation but did not further explore
conditions under which this could occur. [6]
It is suggested here that in the explosive crystallization process, a pressure-induced phase
transformation to metallic (β-Sn)-Ge may be a possible intermediate step that “triggers”
a transformation to dc-Ge when it becomes unstable under very sudden pressure release.
In our indentation case, the very small volume of (β-Sn)-Ge that transforms to dc-Ge may
be insufficient to generate enough heat (noting our relatively thin film cases) to sustain
an explosive event into surrounding a-Ge. However, once the dc-Ge phase forms within
the extruded material, we suggest that there is a driving force (related to the heat of
crystallization [3, 4] for this phase to propagate upon pressure release in a continuous
fashion (into the remaining constrained (β-Sn)-Ge phase under the indenter) when the
metallic phase becomes unstable. To confirm this proposal, it may be worth exploring in
a future study the synergies between the two processes (indentation-induced
crystallization and explosive crystallization) in thick a-Ge films subject to ultra-fast, high
load indentation conditions. In terms of the trace amount of st12 Ge found in TEM
diffraction patterns of family ‘b’ transformations, evidence for this phase from the
literature is further reviewed now in the next section.
5.3 Evidence of st12 Ge from indentation studies
An examination of the indentation literature for dc-Ge shows that under severe loading
conditions it is possible to induce phase transformations and, in some cases, st12 Ge
appears to be the dominant end phase. Two examples are shown of a st12 Ge end phase
Discussion conclusions and future work
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91
from the literature, where it appears that high strain rates and high shear during unloading
are requirements for producing st12 Ge. [7, 8]
The first example in Fig. 5.1 is taken from the work of Kailer et al. who demonstrated
indentation-induced phase transformation in dc-Ge using Vickers indentation. [7] The
Raman data shown in Fig 5.1 show clear evidence for st12 Ge when the Raman peaks are
compared with the st12 assignments given in section 3.2
Figure 5.1: Raman spectra from selected indents in dc-Ge by Kailer et al [7] showing
extra Raman bands assigned to mainly st12-Ge but hd-Ge is present in the middle curve.
This study was carried out under high strain rates and high shear and the authors argued
that high shear stresses can fundamentally influence the phase transformation pathways
or even activate such transformations. Whereas the upper Raman curve shows mainly
st12 Ge, the middle curve indicates also some hd-Ge. The results of the current study
would suggest that this middle trace indicates mixed family ‘a’ and family ‘b’ behaviour.
Indeed, Gogotsi et al. [9] have suggested that hydrostatic compression and high shear can
lead to different deformation mechanisms and presumably both pressure components are
playing a role in the middle Raman case in Fig 5.1.
Discussion conclusions and future work
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92
In a second example, Oliver et al. [8] found that, when the loading rate is extremely fast
for spherical indentation of dc-Ge, it would appear that defect formation and propagation
cannot occur fast enough to prevent the pressure under the indenter exceeding the
transformation pressure. In such cases, phase transformations can occur and it would
appear that the rapidly changing stress gradients can lead not only to phase transformation
but to severe cracking as well as shown by Jang et al. [10] and Oliver et al. [8] In Fig.
5.2 we show an example of a typical deformation zone following ultra-fast loading
(Oliver et al. [8]) where evidence for st12 Ge is found.
Figure 5.2: BF <110> zone axis XTEM micrograph of ultrarapid loading with a spherical
indenter of ~ 4 µm radius to ~ 165 mN s-1. Inset shows SADP. (Taken from Oliver et al.
[8])
The BF XTEM in Fig. 5.2 was obtained from a residual indent (~4.3 μm radius spherical
indenter tip) in dc-Ge following loading to 80 mN at a loading rate of 165 mN/s. Several
features are evident in this micrograph: a small transformed zone under the indenter, a
much larger region surrounding the transformed zone that contains a dense array of
crystalline defects including twins, and severe cracking. The insert shows a SADP taken
from the transformed zone which contains several diffraction spots corresponding to the
st12-Ge phase and also some diffuse amorphous rings suggesting the presence of a
smaller amount of a-Ge, although ion beam thinning for sample preparation can also give
rise to a-Ge. Oliver et al. [8] suggest that phase transformations occur during indentation
Discussion conclusions and future work
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93
above a critical loading rate since the critical stress required for shear-induced defect
propagation rises with loading rate, whereas the critical stress for phase transformation is
load-rate independent in the case of Ge. This observation helps explain the difficulties
reported by many authors in detecting phase transformations under indentation.
Furthermore, the work of Oliver et al. [8, 11] indicates that, if the loading conditions are
such as to induce a transformation in dc-Ge under indentation, the tip geometry and details
of loading and unloading rate can dictate the phase evolution and the end phase observed.
Finally, it is clear that under high strain rates and high shear during unloading, st12 Ge
can be the dominant end phase following phase transformation. This conclusion is very
consistent with a recent DAC study by Williams et al. [12] who found that decompression
of (β-Sn)-Ge under high shear can lead to predominantly st12 Ge whereas under near
hydrostatic conditions (β-Sn)-Ge transforms to r8 then bc8 and finally hd-Ge. This latter
case is quite consistent with the family ‘a’ behaviour in the current indentation study.
Discussion conclusions and future work
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5.4 Transformation Pathways in a-Ge under indentation
Figure 5.3: Schematic showing the deformation pathways associated with the indentation
of a-Ge found in this study. The dashed transformation pathways indicate that this
pathway is unclear, for example, whether there are intermediate phases associated with
the “family b” transformation from (β-Sn)-Ge to dc-Ge on unloading and also for the
“family a” transformation from r8-Ge to hd-Ge at room temperature.
Having reviewed the likely micro-structural transformations occurring during indentation
based on our SEM, Raman, and TEM observations, we now summarize our proposed
transformation pathways for family ‘a’ and family ‘b’ behaviour in Fig. 5.3. Initially,
plastic deformation occurs on loading but the local pressure under the indenter continues
to build with increasing load until a catastrophic transformation of a large volume of a-
Ge to metallic (β-Sn)-Ge occurs under the indenter at pop-in when the tip penetration
depth is around half the film thickness. Two separate types of behaviour are seen. In the
case of family ‘a’, there is a smaller pop-in and the metallic phase is totally constrained
under the indenter. In this case, the slope of the loading curve remains the same as before
pop-in since it is dominated by the mechanical behaviour of the a-Ge matrix. On
unloading, (β-Sn)-Ge progressively transforms to the r8 phase which is unstable and
a-Ge a-Ge
(β-Sn)-Ge
(unconstrained)
(β-Sn)-Ge
(constrained)
dc-Ge
(trace st12)
r8-Ge
(unstable)
hd-Ge
plastic
deformation
Larger pop-in
(family b)
Smaller pop-in
(family a)
Loading
Unloading
extruded (β-Sn)-Ge
(unstable)
a-Gea-Ge a-Gea-Ge
(β-Sn)-Ge
(unconstrained)
(β-Sn)-Ge
(constrained)
dc-Ge
(trace st12)
r8-Ge
(unstable)
hd-Ge
plastic
deformation
Larger pop-in
(family b)
Smaller pop-in
(family a)
Loading
Unloading
extruded (β-Sn)-Ge
(unstable)
Discussion conclusions and future work
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95
further transforms at room pressure and temperature to the more stable hd-Ge phase. We
are not able to establish whether bc8-Ge is an intermediate phase in this rapid
transformation, although there may be some evidence from weak additional spots in TEM
SADPs that this is indeed the case. We have shown a dotted line in Fig. 5.3 for the r8 to
hd-Ge transformation pathway to leave open the possibility of such an intermediate phase.
In the case of family ‘b’, a large pop-in signifies that the soft (β-Sn)-Ge phase is extruded
from under the indenter and we suggest that this unconstrained material undergoes a
transformation directly to dc-Ge (with possibly of some a-Ge) within the extruded
material near the edge of the indenter contact area. On further loading, the slope of the
loading curve now departs from that before pop-in as a result of the softer extruded β-Sn
phase. We suggest that the sudden transformation to dc-Ge seeds nucleation of further
dc-Ge, first within the partly constrained (β-Sn)-Ge near the edge of the indenter contact,
then upon progressive pressure release through the remaining (β-Sn)-Ge phase from the
interface of (β-Sn)-Ge in contact with surrounding dc-Ge. We suggest that this process
may be somewhat akin to the previously observed explosive crystallization phenomenon
in a-Ge.
However, the family ‘b’ behaviour may be more complicated than Fig. 5.3 suggests and
we have used a dotted line to denote the transformation from (β-Sn)-Ge to dc-Ge on
unloading to leave open other possibilities. For example, we are not able to determine
whether there are any intermediate phases between (β-Sn)-Ge and the final dc-Ge phase.
In this context, the observation of likely trace amounts of the st12- Ge phase in residual
family ‘b’ indents warrants some comment. Interestingly, it is our rapid depressurization
family ‘b’ cases that appear to exhibit trace amounts of st12. Indeed, previous indentation
studies of dc-Ge have also clearly identified the st12-Ge end phase under conditions of
substantial extrusion, rapid depressurization and considerable shear [7, 8], as outlined in
the previous section. Thus, high pressure gradients and shear stress during unloading
appears to favour st12 Ge. In our studies, little st12 is obtained since the stress gradients
with spherical indenters are small.
Amorphous Si (a-Si) has been studied more extensively as compared to a-Ge in terms of
indentation. A study by Haberl et al. [13] shows that a-Si in its relaxed and unrelaxed
forms behave differently under nanoindentation . Unrelaxed a-Si is simply self-implanted
a-Si, whereas relaxed a-Si refers to implanted (amorphous) Si annealed at about 450o C
to repair broken bonds in the amorphous phase. [14] Under nanoindentation, relaxed a-Si
Discussion conclusions and future work
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96
undergoes phase transformation to a mixture of r8 and bc8 phases on slow pressure
release whereas unrelaxed a-Si does not undergo phase transformation. Rather, it deforms
via plastic flow in the amorphous phase. This is not the same as a-Ge behaviour where
both relaxed and unrelaxed a-Ge can undergo phase transformation after an initial plastic
deformation regime at lower indentation loads. However, the preliminary data shown in
section 4.1 does suggest a relaxation anneal also does promotes phase transformations in
a-Ge.
Figure 5.4: Schematic showing the deformation pathway associated with the indentation
of relaxed a-Si found in the study by Haberl et al. [13]
For completeness Fig 5.4 shows the phase transformation pathways for relaxed a-Si under
indentation. Following (β-Sn)-Si formation on loading to about 11-12 GPa, on unloading
slowly the end phase is a mixture of r8 and bc8 Si whereas fast unloading leads to a (β-
Sn)-Si to a-Si transformation. In terms of load-unload curves, slow unloading usually
shows a pop-out on unloading indicating a rapid transformation from (β-Sn)-Si to the
mixed r8/bc8 phase, whereas fast unloading gives an elbow in the unloading curve
indicative of an a-Si end phase. With indentation of a-Ge, pop-outs are rarely observed
under the conditions studied here, consistent with the gradual transformation of (β-Sn)-
Ge to r8 Ge for family ‘a’ cases. Although it should be noted that pop-outs were observed
in specific cases where unloading commenced shortly after a pop-in event was detected.
This is an experiment for future studies.
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5.5 Discussion of literature results in light of results of this thesis
Finally, it is appropriate, in light of the results in this thesis, to further comment on and
clarify some of the apparent inconsistencies in the previous literature for indentation
studies of Ge. Such inconsistencies are suggested to be a result of three issues: first, that
the majority of previous studies used dc-Ge as the starting material, where extreme
indentation conditions are needed to induce phase transformations; second, that wrong
assignment of Raman peaks has occurred in some cases; and third, that there has been a
lack of appreciation of separate transformation pathways, as shown in the current study.
For dc-Ge as starting material, appropriate choice of indenter shape, maximum load and
loading rate is crucial to obtaining a phase transformation rather than simply inducing
deformation via plastic flow of dc-Ge through slip and twinning. Indeed, sharp indenters,
high loads and/or fast loading rates were observed to favour deformation by phase
transformation. [7, 10, 11, 15, 16] When using sharp indenter tips, Jang et al. [10] noted
that extensive extrusion of material outside of the contact area always accompanied a
phase transformation and they suggested that this observation in itself can be used to infer
that a phase transformation had occurred. Using Raman mapping they showed that the
extruded material [10] contained a-Ge, but there was also strong evidence for
transformation of some of this phase to nanocrystalline dc-Ge. [17] Gogotsi and co-
workers [7, 9, 18] and Oliver et al. [8] also observed a-Ge around the residual indent area
(extruded material) when phase transformation of dc-Ge took place under indentation.
However, since the starting material was dc-Ge in all of these studies, it was extremely
difficult to distinguish the presence of (nanocrystalline) dc-Ge in the end phase from the
starting dc-Ge phase using Raman spectroscopy. Despite this limitation of detecting dc-
Ge as an end phase, we suggest that these observations of extruded material are consistent
with the family ‘b’ behaviour observed in the current study
Another limitation of using dc-Ge as the starting material is that extreme indentation
conditions are needed to force a phase transformation to occur in light of the preference
for the material to plastically deform via slip/twinning. As indicated above, sharp indenter
Discussion conclusions and future work
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98
tips and fast loading rate conditions will favour extrusion of the softer β-Sn phase from
under the indenter tip (family ‘b’ behaviour). In this thesis, the indentation conditions
needed to induce phase transformation in a-Ge resulted in a clear delineation between
family ‘a’ and family ‘b’ behaviour. In contrast, the extreme indentation conditions
involved in the previous dc-Ge studies appear to result (in many cases) to both family ‘a’
and family ‘b’ behaviour during a single indent, thus complicating interpretation of the
data. Indeed, the studies of Jang et al. support this proposal since, from Raman mapping,
they found crystalline Raman peaks corresponding to high pressure Ge phases in the
center of the indented zone. [19, 17] They tentatively interpreted one of the phases as bc8-
Ge although they noted that the Raman peaks were not well assigned in the literature.
They showed that this phase was unstable and appeared to transform to heavily strained
dc-Ge since the residual Raman peak was significantly shifted to lower wave number
compared to the starting dc-Ge peak at 301 cm-1. The results in this thesis, where the
Raman signatures of the various Ge phases (and XTEM data) are compared with DFPT
calculations (section 3.2), shows that the initial unstable Ge phase is not bc8 but r8 and
the stable end phase is hd-Ge and not strained dc-Ge. Gogotsi and co-workers [7, 9, 18]
also occasionally observed similar Raman signatures to those obtained by Jang et al. using
sharp indenters under high load conditions. They suggested a range of possibilities for
such phase identification, such as st12 and bc8, but also left open the possibility of
unstable r8-Ge and a stable hd-Ge end phase. Examination of their Raman signatures
would suggest that unstable r8-Ge and stable hd-Ge were indeed the most likely phases
under the indenter tip, along with the previously mentioned st12 phase that could arise
from fast unloading in cases where extrusion occurred (family ‘b’ behaviour) under high
shear conditions. In terms of previous indentation work in a-Ge by Patriarche et al. [20]
and Oliver et al. [6], both studies clearly observed phase transformations, but the authors
did not appreciate the possibility of different transformation pathways. The TEM data in
the former study, which used pointed Berkovich and Vickers indenters, showed both dc-
Ge and st12-Ge end phases, with the latter observed under the highest load conditions.
However, careful analysis of the Raman peak assignments from this study suggests that
there is almost certainly hd-Ge and bc8-Ge present. In the case of Oliver et al. [6] the
TEM data again clearly showed a dc-Ge end phase for loading to maximum loads just
above the pop-in load with a ~4 µm radius spherical indenter. It would seem clear that
the data from both of these previous studies indicate family ‘b’ behaviour under
conditions that favour extrusion of (β-Sn)-Ge and transformation to either dc-Ge or st12-
Ge, depending on the maximum load and indenter shape used. However, under the
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indentation conditions used in both of these studies it might be expected that family ‘a’
behaviour would also be probable in the confined region under the indenter tip, as in the
current study. Indeed, the possible misinterpretation of Raman assignments in the
Patriache et al. [20] case and careful examination of the loading curves and the Raman
spectra in the Oliver et al. study [6] strongly suggests some family ‘a’ behaviour similar
to the current study. Indeed, in the Oliver et al. [6] case, a similar slope of the loading
curve before and after pop-in and a Raman peak that was broad and shifted to the low
wave number side of the 301 cm-1 dc-Ge peak, is evidence for family ‘a’ behaviour, with
the latter observation strongly suggesting a hd-Ge end phase. Thus, these two previous a-
Ge studies appear to be entirely consistent with the current work. In addition, in the
previous literature there was no clear understanding that different transformation
pathways may occur depending on the indentation conditions since most previous
indentation studies of dc-Ge used extreme indentation conditions that favoured both
transformation pathways in Fig. 5.3. Finally, noting the common misinterpretation of
Raman signatures for the r8 and hd-Ge phases as bc8 and dc-Ge, respectively, there is
now reasonable consistency between previous works and the results of the current study.
5.6 Conclusions This thesis showed an interesting range of deformation responses is observed when
indenting different film thicknesses of a-Ge. Unlike c-Ge, phase transformations in a-Ge
are readily induced. On loading it was shown that, above a threshold limit, a pop-in event occurs after which
the loading curves fall into two distinct deformation pathways. These have been named
family ‘a’ and family ‘b’. In the case of family ‘b’ the end-phase is predominantly
observed to be dc-Ge. For family ‘a’, the end- phase is r8-Ge. This r8 phase is unstable
and transformed to hd-Ge at room temperature within hours. The mechanisms for these
two different deformation pathways are related to the characteristics of the soft metallic
phase which forms on loading. This work also examined several other processes related to a-Ge. The structure of a-Ge
as a function of annealing at temperatures was investigated. Similar to a-Si, a-Ge was
found to undergo ‘structural relaxation’. This relaxation of a-Ge was shown here to lower
its threshold for deformation via phase transformation. Finally, the effect of the loading
and unloading rate was also investigated. Slow loading rates are shown to mildly inhibit
the phase transformation process of a-Ge. Thus, in conclusion, this thesis has shown that phase transformations can be easily
induced in a-Ge and that hd-Ge can be readily formed in a range of a-Ge film
thicknesses.
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5.7 Future studies
There are several issues arising from this thesis that could form the basis of future studies.
Firstly, in this work it has been shown that nanoindentation-induced phase
transformations in a-Ge occurs but a-Ge appears to transform differently varying
film thickness. Tip geometry may play an important role as has been found for dc-
Ge. The deformation of thin a-Ge films clearly and consistently shows two
pathways and it would be interesting to examine such behaviour (in a-Ge) under
different tip geometries and size of spherical indenters.
It is also important to follow up on the suggestion that the transformation from (β-
Sn) to dc-Ge in the extruded region triggers explosive crystallization. This could
be done using different thicknesses of a-Ge (since there is expected to be a
thickness dependence). Also different tip geometries and loading/unloading rates
could assist in probing this phenomenon.
The occurrence or absence of a pop-out event requires further study.
Indenting dc-Ge at low temperature may lead to phase transformations favoured
over deformation by slip and twinning. In such cases it would be interesting to
compare dc-Ge and a-Ge behaviour.
Investigating the temperature dependence of deformation in Ge (amorphous and
crystalline forms) would be illuminating, similar to the studies carried out for Si
[21].
Finally, it would also be of interest to study III-V covalent and other
semiconductors in both crystalline and amorphous forms to see if their
deformation behaviour is similar to that of dc-Ge and a-Ge in the current study.
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