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.

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


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

3

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

5

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)


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.

[2] S. Minomura and H. G. Drickamer, “Pressure induced phase transitions in

silicon, germanium and some III–V compounds,” J. Phys. Chem. Solids, vol. 23,

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[3] Y. Vohra, K. Brister, S. Desgreniers, A. Ruoff, K. Chang, and M. Cohen, “Phase

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Allan, D. Häusermann, and M. Hanfland, “Imma phase of germanium at ∼80

GPa,” Phys. Rev. B, vol. 53, no. 6, pp. R2907–R2909, Feb. 1996.

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1994.

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Rev. B, vol. 62, no. 16, pp. R10603–R10606, Oct. 2000.

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912, 2003.

[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.

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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

temperatures,” High Press. Res., vol. 15, no. 3, pp. 167–189, Jan. 1996.

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.



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

Trans. Electron Devices, vol. 36, no. 12, pp. 2753–2763, 1989.

[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.,

vol. 76, no. 16, p. 2214, 2000.

[37] S. Ruffell, J. E. Bradby, and J. S. Williams, “High pressure crystalline phase

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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


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.


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

http://www.srim.org/


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


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.


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


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.


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


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


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] )


CHAPTER 2

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]


CHAPTER 2

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


CHAPTER 2

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.


CHAPTER 2

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


CHAPTER 2

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


CHAPTER 2

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.


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)


CHAPTER 2

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)


CHAPTER 2

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


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


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


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.



[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.


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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.


CHAPTER 2

40

Pressure-induced phase transformations in a-Ge

CHAPTER 3

41

CHAPTER 3

Pressure-induced phase transformations in amorphous germanium


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


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


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.


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.


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.


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


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.


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


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.


CHAPTER 3

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.


CHAPTER 3

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).


CHAPTER 3

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


CHAPTER 3

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


CHAPTER 3

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].


CHAPTER 3

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].


CHAPTER 3

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.


CHAPTER 3

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


CHAPTER 3

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


CHAPTER 3

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.


CHAPTER 3

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.


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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.


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63

[1] W.-K. Chu, J. W. Mayer, and M.-A. Nicolet, Backscattering Spectrometry. 1978.



[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.



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.


CHAPTER 3

64

Exploring indentation conditions

CHAPTER 4

65

CHAPTER 4

Further details of phase transformations in a-Ge: Exploring indentation

conditions


CHAPTER 4

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.


CHAPTER 4

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.


CHAPTER 4

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.


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.


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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


CHAPTER 4

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.


CHAPTER 4

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).


CHAPTER 4

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


CHAPTER 4

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.


CHAPTER 4

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


CHAPTER 4

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


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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.


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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.


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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.


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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.







[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.



pp. 1–3, 2005.



vol. 105, no. 12, 2009.


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87

Discussion conclusions and future work

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88

CHAPTER 5

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


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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


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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.


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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


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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.


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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)


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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


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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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97

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


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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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99

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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