Characterisation of scandium-based III-

nitride thin films

Hei Chit Leo Tsui

Department of Materials

Imperial College London

This thesis is submitted in part fulfilment of the requirements for the degree of

Doctor of Philosophy

March 2016

I

Abstract

Wurtzite III-nitrides are widely used in optoelectronic applications. However, the external

quantum efficiency of III-nitride-based light emitting diodes in the deep-UV region is

extremely low compared to those emitting in the visible region. This problem has motivated

the search for better materials that can help. Theoretical calculations predict that alloying ScN

and GaN can produce wurtzite-structure semiconducting ScxGa1-xN films with direct band

gaps in the UV region and a lattice parameter – band gap relationship that differs significantly

from that of the AlxGa1-xN alloys used conventionally. Therefore, this thesis investigates the

growth, composition, microstructure and optical properties of ScxGa1-xN thin films.

Epitaxial ScxGa1-xN (0 ≤ x ≤ 0.5) thin films were grown using molecular beam epitaxy under

metal-rich conditions. The alloy composition was determined by four different techniques. A

linear relationship was established between the Sc flux measured in the growth chamber and

the Sc content measured by Rutherford backscattering, whereas the compositions measured

by X-ray photoelectron spectroscopy were 5–8% lower than that by Rutherford backscattering

and information obtained from X-ray and electron diffraction (i.e. the a and c lattice

parameters and the c/a ratio) cannot provide a reliable estimation of the Sc content. Structural

analysis confirmed that ScxGa1-xN can be stabilised in the wurtzite structure up to x = 0.26

using metal-rich growth conditions, which is in line with theoretical predictions and is

significantly greater than the value of x = 0.17 for the ScxGa1-xN films grown under N-rich

conditions reported previously.

II

UV-Vis absorption measurements showed that the direct optical band gap of ScxGa1-xN

increases from 3.33 eV to 3.89 eV as Sc content increases from x = 0 to x = 0.26. This trend is

consistent with theoretical predictions but contradicts the observations reported by other

groups. Instead, nanoscale cubic inclusions, revealed by aberration-corrected scanning

transmission electron microscopy, are responsible for the observed decrease in band gap as

the Sc content increases.

Finally, valence band offset measurements indicated that type I and type II heterojunctions

can be formed by depositing ScxGa1-xN on AlN and on GaN respectively.

III

Declaration of originality

I declare that the work contained in this thesis is my own work and any references to other

work are appropriately cited. Some of the work in this thesis has been published in the

following journal articles.

H. C. L. Tsui, L. E. Goff, S. K. Rhode, S. Pereira, H. E. Beere, I. Farrer, C. A. Nicoll, D. A.

Ritchie and M. A. Moram, Band gaps of wurtzite ScxGa1-xN, Appl. Phys. Lett. 106, 132103

(2015)

H. C. L. Tsui, L. E. Goff, N. P. Barradas, E. Alves, S. Pereira, H. E. Beere, I. Farrer, C. A.

Nicoll, D. A. Ritchie and M. A. Moram, The effect of metal-rich growth conditions on the

microstructures of ScxGa1-xN films grown using molecular beam epitaxy, phys. stat. solidi (a)

212, 2837 (2015)

H. C. L. Tsui, L.E. Goff, R. G. Palgrave, H. E. Beere, I. Farrer, D. A. Ritchie and M. A.

Moram, Valence band offset of ScxGa1-xN/AlN and ScxGa1-xN/GaN heterojunctions, J. Phys.

D: Appl. Phys. 49, 265110 (2016)

H. C. L. Tsui, L. E. Goff, N. P. Barradas, E. Alves, S. Pereira, R. G. Palgrave, R. J. Davies, H.

E. Beere, I. Farrer, D. A. Ritchie and M. A. Moram, Composition measurement of epitaxial

ScxGa1-xN films, Semicond. Sci. Technol. 31, 064002 (2016)

Copyright declaration

The copyright of this thesis rests with the author and is made available under a Creative

Commons Attribution Non-Commercial No Derivatives licence. Researchers are free to copy,

distribute or transmit the thesis on the condition that they attribute it, that they do not use it

for commercial purposes and that they do not alter, transform or build upon it. For any reuse

or redistribution, researchers must make clear to others the licence terms of this work.

IV

Table of Contents

Acknowledgements VII

List of Figures IX

List of Tables XIV

List of Acronyms XV

1. Introduction 1

1.1 Gallium nitride (GaN) 5

1.2 Scandium nitride (ScN) 8

1.3 Scandium gallium nitride (ScxGa1-xN) 11

1.3.1 Theoretical predictions 11

1.3.2 Experimental reports 14

1.4 Related alloy systems 18

1.4.1 Scandium aluminium nitride (ScxAl1-xN) 18

1.4.1.1Theoretical predictions 18

1.4.1.2 Experimental reports 20

1.4.2 Scandium indium nitride (ScxIn1-xN) 24

1.4.3 Other transition metal (TM) III-nitrides alloys 24

1.5 Conclusions and motivation for the work presented in this thesis 25

1.6 Reference 27

2. Characterisation techniques 35

2.1 Atomic force microscopy (AFM) 35

2.2 X-ray diffraction (XRD) 39

2.3 Transmission electron microscopy (TEM) 44

2.3.1 Sample preparation 44

2.3.2 Components in a TEM 45

2.3.3 Electron diffraction 46

2.3.4 Imaging modes 50

2.3.5 Mass-thickness contrast, diffraction contrast and phase contrast 52

V

2.3.6 Scanning transmission electron microscopy (STEM) 53

2.4 Rutherford backscattering spectrometry (RBS) 55

2.5 X-ray photoelectron spectroscopy (XPS) 60

2.6 Raman spectroscopy 64

2.7 Ultraviolet-visible (UV-vis) absorption and reflectance spectrophotoscopy 68

2.8 Reference 72

3. Compositional analysis of ScxGa1-xN thin films 75

3.1 Rutherford backscattering spectrometry (RBS) 75

3.2 X-ray photoelectron spectroscopy (XPS) 79

3.3 Composition determination from lattice parameters and c/a ratio measurements 85

3.4 Scanning transmission electron microscopy (STEM) 89

3.5 Conclusions 91

3.6 Reference 92

4. Growth and microstructure of ScxGa1-xN thin films 95

4.1 Metal-rich growth conditions for GaN 95

4.2 Growth rate 97

4.3 Surface morphology 99

4.4 Structural determination 102

4.5 Microstructural analysis 108

4.6 Conclusions 113

4.7 Reference 115

5. Optical properties and band offsets of wurtzite ScxGa1-xN thin films 117

5.1 Optical band gaps 117

5.2 Refractive indices 122

5.3 Valence band offsets of ScxGa1-xN/AlN and ScxGa1-xN/GaN heterojunctions 126

5.4 Conclusions 132

5.5 Reference 133

6. Conclusions and future work 137

6.1 Conclusions 137

VI

6.2 Future work 140

6.3 Reference 142

Appendix A 145

VII

Acknowledgements

It is my pleasure to take this opportunity to thank many people who helped and supported me

during this PhD project.

I owe my deepest gratitude to my supervisor Dr. Michelle Moram for giving me opportunity

to join the Functional Nitrides group and undertake this project. I am grateful for her patient

during the training of TEM specimen preparation and operation, guidance of the project,

helpful discussions and feedback and valuable advice. I would also like to thank Prof. Norbert

Klein for his kind support and discussions.

I would like to thank Dr. Lucy Goff, Dr. Harvey Beere, Dr. Ian Farrer, Dr. Christine Nicoll

and Prof. David Ritchie at University of Cambridge for growing all the samples I needed in

this project, without them I would not be able to carry out the characterisations presented in

this thesis.

I would like to show my appreciation to Dr. Mahmoud Ardakani, Mrs Ecaterina Ware and Dr.

Catriona McGilvery for their training on the TEM instruments and daily support at Imperial

College and Dr. Sneha Rhode for her help on aberration-corrected STEM at University of

Cambridge. In addition, I would like to thank Dr. Victoria Bemmer and Mr Richard Sweeney

for their support on AFM and XRD facilities at Imperial College.

Furthermore, I would like to express my gratitude to Dr. Robert Pagrave at University College

London for his generous support on XPS analysis and Dr. Nuno Barradas, Dr. Eduardo Alves

VIII

and Dr. Sergio Pereira at the C2TN - Centro de Ciências e Tecnologias Nucleares,

Universidade de Lisboa, Portugal for the RBS analysis.

I am grateful to everyone in Functional Nitride group and Imperial College London, in

particular, Ben, Kevin, Sneha, Jason, Chris and Izzati for all the fun, sharing and support. In

addition, thanks to all the brothers and sisters in the fellowship at St Martin-in-the-Fields

Chinese congregation for their support and encouragement.

I would like to thank my parents, who have sacrificed hugely for my education and

development, and my sister for their unreserved love since my birth.

Finally, I give thank and praise to Lord God of all creation for His guidance, blessing and

grace.

IX

List of Figures

Figure 1.1 Band gap vs a lattice parameter plot from experiment (for AlN, GaN and

InN) and from theoretical predictions, corrected with respect to existing

experimental data (for unstrained ScxGa1-xN and ScxAl1-xN). 2

Figure 1.2 Schematic diagram of a blue-emitting LED (multiple quantum wells

made from low In content InxGa1-xN). 2

Figure 1.3 EQE vs. emission wavelength for UV-LEDs. 3

Figure 1.4 (a) Hexagonal wurtzite structure (yellow plane: (0001) ; red plane:

(112̅0); blue plane: (101̅0) note that this figure shows a non-primitive

unit cell and (b) cubic zinc blende structure. 6

Figure 1.5 Crystallographic orientation relationship between GaN and sapphire. 7

Figure 1.6 One unit cell of the cubic rock-salt structure of ScN, where the red

spheres represent Sc and the green spheres represent N. 9

Figure 1.7 Calculated band structure of ScN along high symmetry directions of the

Brillouin zone. 10

Figure 1.8 Calculated band structure for wurtzite GaN, wurtzite ScxGa1-xN (x =

0.125 and 0.25) and wurtzite ScN. 13

Figure 1.9 HRTEM and FFT images of ScxGa1-xN with x = 0.05 and 0.17. 15

Figure 1.10 Cross-sectional weak-beam dark field TEM images of the overgrown

GaN layer and ScxGa1-xN (x = 0.08) on GaN template. 16

Figure 1.11 Cross-sectional weak-beam dark field TEM images of ScxGa1-xN films (x

= 0.012, 0.035 and 0.059). 17

Figure 1.12 Calculated band structure for wurtzite AlN, wurtzite ScxAl1-xN (x = 0.125

and x = 0.25) and wurtzite ScN. 19

Figure 1.13 Variation of the piezoelectric response as a function of Sc concentration

for ScxAl1-xN films grown at a substrate temperature of (a) 580 ˚C and (b)

400 ˚C. 21

Figure 1.14 Cross-sectional HRTEM and corresponding FFT images of ScxAl1-xN (x

= 0.1, 0.2 and 0.3) grown at 400 ˚C and 800 ˚C. 22

X

Figure 2.1 Schematic diagram of AFM. 36

Figure 2.2 (a) A diagram showing Bragg scattering in real space and (b) the Ewald

sphere construction in reciprocal space. 42

Figure 2.3 Rotational axes of an X-ray diffractormeter. 43

Figure 2.4 Schematic diagram of a basic TEM. 46

Figure 2.5 (a) Relrod in reciprocal space created from diffraction from a crystalline

specimen and (b) The relrod at 𝐠ℎ𝑘𝑙 when the beam is away from the

exact Bragg condition. The Ewald sphere intercepts the relrod at a

negative value of 𝐬 which defines the vector 𝐊 = 𝐠 + 𝐬. The intensity of

the diffracted beam as a function of where the Ewald sphere cuts the

relrod is shown on the right of the diagram. In this case the intensity has

fallen to almost zero. 49

Figure 2.6 The Kossel cones intercept the Ewald sphere, creating parabolas which

approximate to straight lines in the DPs becauseθB is small. 50

Figure 2.7 Standard indexed diffraction pattern at (a) < 112̅0 > and (b) < 101̅0 >

zone axis for a hexagonal material; (c) two beam condition and (d) g-3g

condition. 51

Figure 2.8 Schematic of the HAADF detector setup for Z-contrast imaging in a

STEM The conventional ADF and BF detectors are also shown along

with the range of electron scattering angles gathered by each detector. 54

Figure 2.9 A diagram illustrating the scattering process in RBS. 56

Figure 2.10 Schematic diagram of a RBS spectrometer with a tandem accelerator. 59

Figure 2.11 (a) X-ray induced photoelectron emission (b) Auger electron emission

through atomic relaxation. 61

Figure 2.12 Schematic diagram of XPS. 62

Figure 2.13 Changes of energy level of scattering processes. 65

Figure 2.14 (a) Phonon modes of wurtzite GaN (b) Raman spectrum of GaN at

different scanning directions. 67

Figure 2.15 Schematic diagram of Raman spectroscopy. 68

Figure 3.1 RBS spectra for ScxGa1-xN grown on a MOVPE AlN buffer layer (a) x =

0; (b) x = 0.08; (c) x = 0.15; (d) x = 0.26. 76

Figure 3.2 The relationship between Sc content measured by RBS and Sc flux

measured in the MBE chamber before growth. 78

XI

Figure 3.3 XPS spectrum for ScxGa1-xN (x = 0.26) grown on MOVPE AlN. 80

Figure 3.4 Depth profiling of (a) MOCVD Si-doped GaN; (b) GaN on MOCVD Si-

doped GaN and (c) ScxGa1-xN (x = 0.18) grown on MOCVD Si-doped

GaN. 81

Figure 3.5 XPS (a) Ga 3d and (b) Sc 2p spectra for ScxGa1-xN grown on MOVPE

AlN. 82

Figure 3.6 XPS peak position for (a) Ga 3d; (b) Sc 2p3/2 and (c) N 1s peaks; (d) Sc

content (from XPS and RBS) variations with Sc flux for ScxGa1-xN grown

on different GaN and AlN buffer layers. 83

Figure 3.7 XRD diffractograms of the 0004 reflection for (a) ScxGa1-xN on MBE

GaN; (b) ScxGa1-xN on MOVPE GaN; (c) ScxGa1-xN on MOVPE AlN. 86

Figure 3.8 (a) Lattice parameter c (red square) and a (blue circle) of ScxGa1-xN

grown on MOVPE AlN. 86

Figure 3.9 (a) c/a ratio of ScxGa1-xN measured by experiment and predicted by

theory; (b) Sc content (obtained by matching the measured c/a ratio to the

trend obtained from theory [46]) variations with Sc flux. 88

Figure 3.10 (a) Cross-section TEM image of ScxGa1-xN (x = 0.26) on AlN (insert:

selected area diffraction pattern at < 112̅0 > zone axis) and (b)

corresponding STEM HAADF image. 90

Figure 3.11 The relationship between the Sc flux and Sc content in ScxGa1-xN films

grown on MOVPE AlN as measured by RBS (red squares and the dotted

line indicates a linear relationship), XPS (blue circles), c/a ratio measured

from electron diffraction patterns and fit to theoretical simulation from

Ref. [46] (green diamonds). 91

Figure 4.1 (a) Growth rate of GaN films and 1 x 1 m AFM images of GaN films

grown under (b) N-rich and (c) metal-rich conditions. 97

Figure 4.2 (a) Growth rate of ScxGa1-xN films (red square: on MBE GaN; blue circle:

on MOVPE GaN; green diamond: on MOVPE AlN) and (b) growth rate

of ScN films. 99

Figure 4.3 (a) Root-mean-square (RMS) roughness and (b) feature size of ScxGa1-xN

on different buffer layers (red square: on MBE GaN; blue circle: on

MOVPE GaN; green diamond: on MOVPE AlN). 100

Figure 4.4 1 x 1 m AFM images of ScxGa1-xN films on different buffer layers. 101

XII

Figure 4.5 1 x 1 m AFM images of ScxGa1-xN films on MBE GaN (a) x = 0.38 (Z-

scale = 27 nm) (b) x = 0.50 (Z-scale = 132 nm). 101

Figure 4.6 Selected area diffraction patterns for (a) pure wurtzite phase and (b)

mixed cubic and hexagonal phase. 102

Figure 4.7 Typical XRD diffractogram for MBE-grown GaN grown on MOVPE-

grown AlN. 103

Figure 4.8 Rocking curves for (a) MBE GaN, (b) MOVPE GaN and (c) MOVPE

AlN on sapphire substrate. 103

Figure 4.9 Cross-section dark field TEM images of the buffer layers (a) MBE GaN;

(b) MOVPE GaN; (c) MOVPE AlN (All images were obtained from the

< 2̅110 > zone axis). 104

Figure 4.10 Plan-view dark field TEM images of (a) GaN and (b) ScxGa1-xN (x =

0.26) (insert: the corresponding electron diffraction pattern of the

< 0001 > zone axis where the images were obtained). 106

Figure 4.11 Raman spectra for ScxGa1-xN on MBE GaN. 108

Figure 4.12 Cross-section bright field TEM images of ScxGa1-xN (a) x = 0.08, (b) x =

0.15 and (c) x = 0.26, with their corresponding selected area diffraction

patterns (d), (e) and (f) obtained from the < 2̅110 > zone axis. 109

Figure 4.13 Cross-section dark field TEM images of ScxGa1-xN (x = 0.15) films on

different buffer layers (a) on MBE GaN; (b) on MOVPE GaN; (c) on

MOVPE AlN (insert: the corresponding electron diffraction pattern of the

< 2̅110 > zone axis where the images were obtained). 109

Figure 4.14 (a) Cross-section dark field TEM images of ScxGa1-xN (x = 0.15) films on

MOVPE AlN buffer layer showing high stacking faults density and (b)

the corresponding diffraction pattern showing streaky pattern. 110

Figure 4.15 (a) Mixed hexagonal and cubic diffraction pattern and (b) the

corresponding indexed pattern. 111

Figure 4.16 (a) Cross-sectional dark field TEM images of a ScxGa1-xN film with x =

0.50 (white circles indicate the locations from which the diffraction

patterns in the insets (1) and (2) were taken); (b) cross-setional bright

field TEM image showing twinned ScxGa1-xN grains with the rock-salt

structure embedded in a matrix of hexagonal ScxGa1-xN. 112

Figure 4.17 STEM HAADF image of a ScxGa1-xN film with x = 0.5. 113

XIII

Figure 5.1 Transmittance curves with Tauc plots inserted for ScxGa1-xN films with

various x grown on (a) MBE GaN and (b) MOVPE GaN buffer layer. 118

Figure 5.2 (a) Transmission curves with Tauc plot inserted for ScxGa1-xN films with

various x grown on MOVPE AlN buffer layer and (b) Band gaps of

ScxGa1-xN with different buffer layers. 119

Figure 5.3 Dark-field TEM images taken along the < 112̅0 > zone axis of ScxGa1-

xN films grown on (a) MBE GaN, (b) MOVPE GaN and (c) MOVPE

AlN. 121

Figure 5.4 Aberration-corrected STEM-HAADF images taken along the < 112̅0 >

zone axis of ScxGa1-xN films, showing (a) a region of cubic stacking, (b)

an I1 stacking fault and (c) an I2 stacking fault. 122

Figure 5.5 Reflectance curves for ScxGa1-xN films grown on MOVPE AlN. 123

Figure 5.6 Refractive index at 632.8 nm for ScxGa1-xN films grown on MOVPE AlN

buffer layer. 125

Figure 5.7 XPS valence band spectra for (a) AlN and (b) ScxGa1-xN (0 ≤ x ≤ 0.15). 127

Figure 5.8 Variations of valence band offset of ScxGa1-xN/AlN heterojunctions as a

function of Sc content. 130

Figure 5.9 Band alignments of ScxGa1-xN/AlN heterojunctions. 131

XIV

List of Tables

Table 2.1 Relative intensity of split XPS peaks. 63

Table 3.1 RBS measurement of Sc content and film thickness for ScxGa1-xN. 77

Table 4.1 FWHM values of the rocking curve for ScxGa1-xN (0002) peak. 105

Table 4.2 Sc content (x) measured using energy-dispersive X-ray spectroscopy

(EDX) for a ScxGa1-xN film with a nominal overall composition of x =

0.50 at the points indicated in Figure 4.17. 113

Table 5.1 Binding energy of the core level and valence band maxima (VBM) of ScxGa1-xN

and AlN. 128

Table 6.1 Summary of piezoelectric coefficients of III-nitride alloys. 140

XV

List of Acronyms

ADF Annual dark field

AFM Atomic force microscopy

BF Bright field

CBM Conduction band minimum

CDF Centred dark field

CL Cathodoluminescence

CVD Chemical vapour deposition

DC Direct current

DF Dark field

DFT Density functional theory

EDX Energy dispersive X-ray spectroscopy

EIE Electron injection efficiency

EQE External quantum efficiency

ERDA Elastic recoil detection analysis

FWHM Full width at half maximum

HAADF High angle annular dark field

HEMT High electron mobility transitor

HRTEM High resolution transmission electron microscopy

HSA Hemispherical sector analyser

HVPE Hydride vapour phase epitaxy

IQE Internal quantum efficiency

IR Infrared

LA/LO Longitudinal acoustic/ longitudinal optical

LED Light emitting diode

LEE Light extraction efficiency

MBE Molecular beam epitaxy

MOCVD Metal-organic chemical vapour deposition

MOVPE Metal-organic vapour phase epitaxy

XVI

MQW Multiple quantum well

PFM Piezoelectric force microscopy

PIPS Precision ion polishing system

PL Photoluminescence

PLD Pulsed laser deposition

RBS Rutherford backscattering

RF Radio frequency

RMS Root-mean-square

SAW Surface acoustic wave

SIMS Secondary ion mass spectroscopy

STEM Scanning transmission electron microscopy

SPM Scanning probe microscopy

STM Scanning tunnelling microscopy

TA/TO Transverse acoustic/ transverse optical

TDD Threading dislocation density

TEM Transmission electron microscopy

UV-vis Ultraviolet-visible

VBM Valence band maximum

WBDF Weak-beam dark field

XRD X-ray diffraction

XPS X-ray photoelectron spectroscopy

1

Chapter 1

Introduction

Wurtzite-structure group III nitrides (AlN, GaN and InN) have a wide range of applications

including light emitting diodes (LEDs), lasers and high electron mobility transistors (HEMTs).

These nitride semiconductors and their alloys have direct band gaps between 6.2 eV (AlN)

and 0.7 eV (InN) [1–3], which enables the tuning of the emission wavelength from ultraviolet

(UV) to infra-red when used in optoelectronic devices (Figure 1.1). UV–A LEDs (320–400

nm) are of interest for polymer curing and as an optical pump for the phosphors used in white

LEDs, while the UV–B (290–320nm) and UV–C (200–290 nm) emitters are suitable for water

purification and germicidal applications [1, 4–6]

The performance of an optoelectronic device is quantified by the external quantum efficiency

(EQE), which is the ratio of the number of photons emitted to the number of electrons

injected, in the case of an LED (typical structure shown in Figure 1.2). The EQE is

determined by three separate contributions: internal quantum efficiency (IQE), which is the

proportion of radiative recombination out of the total recombination of electron-hole pairs;

electron injection efficiency (EIE), which is the proportion of carriers that can produce

recombination out of the total number of carrier injected; and light extraction efficiency

(LEE), which is the proportion of photons that are release from the device out of the total

number of photon generated [4, 5, 8].

Introduction

2

Figure 1.1 Band gap vs a lattice parameter plot from experiment (for AlN, GaN and InN) and

from theoretical predictions, corrected with respect to existing experimental data (for

unstrained ScxGa1-xN and ScxAl1-xN). Reproduced from Ref. [7] with permission of The Royal

Society of Chemistry.

Figure 1.2 Schematic diagram of a blue-emitting LED (multiple quantum wells made from

low In content InxGa1-xN).

Introduction

3

A high EQE of 70% has been achieved for LEDs emitting in the visible region, however the

EQE for UV LEDs is typically less than 5% and the EQE tends to decrease as the emission

wavelength becomes shorter (Figure 1.3) [5, 6]. There are at least eight reasons [4] why the

EQE of AlxGa1-xN-based UV-LEDs tends to decrease as the emission wavelength decreases.

Figure 1.3 EQE vs. emission wavelength for UV-LEDs [5]. © IOP Publishing. Reproduced

with permission. All rights reserved.

Of these, the threading dislocation density (TDD) is known to be a major factor. An

extremely high TDD of 1010

cm-2

is typically observed in the epitaxy of AlN and AlxGa1-xN

films, which is two orders of magnitude higher than that of GaN and InxGa1-xN films. This

may be related to the three dimensional growth mode that typically occurs during AlxGa1-xN

Introduction

4

film growth [4]. These dislocations are thought to introduce non-radiative recombination

centres into the films, thereby reducing the IQE [9]. The IQE of AlxGa1-xN can be increased

from 1% to 60% if the TDD is reduced from 1010

to 108 cm

-2 [8, 10, 11].

In addition, the IQE can also be reduced significantly by the quantum-confined Stark effect,

where the probability of radiative recombination is reduced due to the spatial separation of

electrons and holes by the internal electric fields that arise across the quantum well due to the

spontaneous and piezoelectric polarisation. This effect is more pronounced as the Al

concentration increases in the AlxGa1-xN alloy since the piezoelectric coefficient of AlN is the

highest among the III-nitrides [4, 12–14]. The low carrier confinement (electron leakage) and

low hole injection (due to poor p-type doping in these materials), which effectively reduce the

EIE, and, the lack of UV transparent templates and substrates, which reduce the light

extraction efficiency, are the challenges for producing UV LEDs with an EQE over 10% [4,

5].

Therefore, it is of interest to explore alternative wurtzite-structure nitride semiconductors with

different lattice parameter – band gap relationships, especially for applications in the deep-UV

region. Sc appears to be a promising candidate to alloy with III nitrides in this regard. Since

Sc has unoccupied 3d orbitals, sp3 hybridisation is maintained around atoms as it is

introduced into the tetrahedrally bonded III nitrides, which contributes to the high phase

stability of Sc-III nitides alloys in the wurtzite structure (up to 27% of Sc in ScxGa1-xN with

consideration of spinodal decomposition) [15] compared to other transition-metal III nitride

alloys (e.g. 4% of Mn in MnxGa1-xN) [16]. Moreover, an increase in band gap was predicted

with increasing lattice parameter for ScxGa1-xN, following a trend which is different from

other conventional III nitride alloys (Figure 1) and which could lead to new heterostructure

Introduction

5

designs and strain engineering for electronic devices. Therefore, this thesis focuses on the

characterisation of this new semiconducting material.

1.1 Gallium nitride (GaN)

GaN is a tetrahedrally–bonded semiconductor which is stable in the hexagonal wurtzite

structure (space group: P63mc). This is a polar structure with piezoelectric and pyroelectric

properties. The cubic zinc blende phase (space group: F4̅3m) is also metastable and can be

produced under certain growth conditions (Figure 1.4). The difference between the hexagonal

and cubic phase is the stacking pattern, where the hexagonal phase has AaBbAaBbAaBb

stacking and the cubic phase has AaBbCcAaBbCc stacking, where upper-case letters refer to

the stacking of the metal sub-lattice and lower-case letters refer to the stacking of the nitrogen

sub-lattice. The stacking difference leads to differences in the properties. For example, the

band gap of wurtzite GaN is 0.2 eV higher than that of its cubic counterpart. Apart from the

direct wide band gap (3.4 eV [1]), GaN is also well known for its high thermal decomposition

temperature of 800–1000 ˚C [17–19] and high chemical resistivity [20, 21] along with high

elastic modulus (C11 = 377–390 GPa) and bulk modulus (B = 117–160 GPa) [22–24]

Introduction

6

Figure 1.4 (a) Hexagonal wurtzite structure (yellow plane: (0001); red plane: (112̅0); blue

plane: (101̅0)), note that this figure shows a non-primitive unit cell and (b) cubic zinc blende

structure.

Epitaxial GaN and other III-nitride thin films can be produced by several techniques,

including metalorganic chemical vapour deposition (MOCVD), metalorganic vapour phase

epitaxy (MOVPE), molecular beam epitaxy (MBE), pulsed laser deposition (PLD) and

reactive sputtering. Sapphire, silicon and silicon carbide (SiC) are the most widely used

substrates for III-nitrides [1, 25–30], however, dislocations and defects are inevitably

generated during the growth due to the lattice mismatch and thermal expansion coefficient

mismatch between the nitride layer and the substrates (Figure 1.5). The dislocation density of

a high quality (MOCVD-grown) GaN film is usually in order of 108 cm

-2, which can be

suppressed down to the order of 107 cm

-2 by optimising the growth conditions and buffer

layers [31–36].

(a) (b)

Introduction

7

Figure 1.5 Crystallographic orientation relationship between GaN and sapphire.

Typically, the as-grown GaN films suffer from unintentional n-type doping with an electron

concentration n of 1017

cm-3

or greater, leading to a high electrical conductivity. Possible

sources of this unintentional n-type doping include N vacancies [37–39], as well as impurities

such as oxygen and carbon incorporated during the growth [40–44]: however, in films grown

by MOCVD on sapphire, the highly conductive layer is localised primarily at the interface

and is due to oxygen incorporation during the early stage of film growth [38]. Silicon is the

most widely used n-type dopant because its chemical precursor (SiH4) is highly volatile and

easily delivered to a MOVPE growth chamber without creating any ‘memory’ effects. Si is

also incorporated easily into the growing GaN film without greatly degrading its crystal

quality and an n-type carrier concentration as high as 1019

cm-3

can be achieved. However, it

Introduction

8

was reported that the electron mobility decreases as the electron concentration increases and

this was attributed to the increase in the scattering probability of the ionised dopants [45, 46].

Though it is known that p-type GaN is much more difficult to produce than n-type GaN due

to the unintentional n-doped nature of GaN films and higher bonding energies for the dopants

[47], p-type GaN has been achieved by using Mg, Be, Zn and C [48–57].

1.2 Scandium nitride (ScN)

Like other transition metal nitrides, scandium nitride (ScN) is stable in the cubic rock-salt

structure (space group: Fm3m) (Figure 1.6) with high value of hardness (21 GPa) and Young

modulus (356 GPa) [58] and a high melting point calculated to be 2600 ˚C [59, 60], which

make it favourable for wear-resistant coatings [59, 61]. ScN has a lattice parameter a of

4.51 Å [62] and the in-plane lattice mismatch between [111]-oriented ScN and [0001]-

oriented GaN is only 0.4%. Therefore, ScN interlayers have been used as dislocation-blocking

layers for GaN heterostructures, in which the dislocation density can be reduced from

10-9

cm2 to 10

-7 cm

2 [31, 63]. The electronic structure of ScN has been investigated by both

simulations and experiments (Figure 1.7). The measured direct band gap of pure ScN varies

between 2.1 eV and 2.4 eV and an indirect band gap of 0.9–1.6 eV is predicted from

theoretical calculations [58, 61, 64–67]. In addition, ScN has also been of interest for solar

energy conversion [68] and thermoelectric applications due to its high thermal stability and

high electrical conductivity [62, 69, 70].

Introduction

9

Figure 1.6 One unit cell of the cubic rock-salt structure of ScN, where the red spheres

represent Sc and the green spheres represent N.

ScN thin films have been grown on sapphire, MgO and Si substrates by a range of growth

techniques, including chemical vapour deposition (CVD), reactive magnetron sputter

deposition and molecular beam epitaxy (MBE) [59, 61, 65, 71–74]. Under N-rich growth

conditions, square-shaped and pyramid-shaped grains are observed while spiral growth is seen

under Sc-rich conditions, which is probably due to the increase in surface diffusion associated

with excess Sc. However, the oxygen affinity of Sc is higher than that of other nitride-forming

transition metals, for example Ti and Zr [75]. As a result, oxygen incorporation is also of

concern in the growth of ScxGa1-xN, as oxidation is expected to produce either n-type doping

and hence an increase in the measured band gap through the Moss-Burstein effect (at

concentrations up to approximately 1020

cm-3

) or an increase in the band gap through alloying

effects (at higher concentrations above approximately 1020

cm-3

). However, although oxygen

impurities shift the Fermi level towards the conduction band, the overall electronic structure

of ScN is not affected [69]. The effect of oxygen incorporation into ScxGa1-xN is as yet

unknown.

Introduction

10

Figure 1.7 Calculated band structure of ScN along high symmetry directions of the Brillouin

zone [76]. Reprinted from J. Appl. Phys. 107, 033715 (2010). Copyright 2010, AIP

Publishing LLC.

The stabilities of different possible crystal structures of ScN were firstly investigated by

Takeuchi et al. with a view to understanding the likely thermodynamic stability of ScxGa1-xN

alloys. The lattice parameters and formation energies of ScN in its rocksalt, CsCl, NiAs, zinc

blende and wurtzite phases were calculated and it was concluded that wurtzite ScN is

metastable and would be difficult to stabilise experimentally [77]. In contrast, Farrer and

Bellaiche predicted that ScN should be unstable in the wurtzite structure but metastable in a

hexagonal BN-like fivefold-coordinated structure [78]. Furthermore, the behaviour of

hexagonal ScN under compressive strain was calculated by Ranjan et al. [79]. For a

theoretical compressive strain of 0% to 3.4% in the basal plane, ScN changes from a non-

polar to a polar structure, while the band gap remains unchanged. As the theoretical

compressive strain increases from 3.4% to 6.4%, the band gap of ScN increases accordingly

and a wurtzite-like structure becomes favourable when the compressive strain exceeds 6.4%.

Introduction

11

1.3 Scandium gallium nitride (ScxGa1-xN)

1.3.1 Theoretical predictions

The crystal structure, phase stability and electronic structure of ScxGa1-xN, along with some

basic properties including piezoelectric coefficient, have been calculated.

As the ground state of GaN (wurtzite) and ScN (rocksalt) are different, the crystal structure of

ScxGa1-xN changes as a function of Sc content. Dismukes and Moustakas suggested that GaN

and ScN should be highly soluble in the Sc-rich rock-salt structure ScxGa1-xN phase, based on

the predicted lattice parameters [80], whereas Farrer and Bellaiche predicted that ScxGa1-xN

should have the hexagonal wurtzite-like structure up to intermediate Sc concentrations and the

rock-salt phase at high Sc concentrations [78]. A precise phase transition point of x = 0.66 at

which ScxGa1-xN should turn from the wurtzite to the rock-salt structure was calculated by

Zhang et al. [15]. However, this is unlikely to be relevant experimentally because unstrained

ScxGa1-xN is calculated to become unstable at x = 0.11 if spinodal decomposition is taken into

consideration. The alloy can be stabilised up to x = 0.27 by straining parallel to the (0001)

plane so that the in-plane a lattice parameter matches that of GaN. ScxGa1-xN in cubic

structures (zinc blende, rocksalt and CsCl) were investigated by Zerroug et al.. It was

calculated that out of all the cubic phases investigated, the zinc blende structure is preferred

for Sc contents up to x = 0.5 while the rocksalt structure is preferred from x = 0.75 [81].

It has been predicted that ScN is unstable in the wurtzite structure but metastable in a layered

hexagonal structure (h-ScN). Farrer and Bellaiche calculated that the primitive cell volume of

Introduction

12

h-ScN is 15% larger than that of GaN, with a 16% increase in lattice parameter a and a 26%

decrease in the axial c/a ratio [78]. Calculations by Constantin et al. and Zhang et al. also

gave similar results. Constantin et al. predicted that the change in lattice parameter a is

greater than that of the lattice parameter c, leading to anisotropic distortions in the lattice.

Besides, both the bond lengths of Ga-N and Sc-N increase as the Sc concentration increases,

along with an increase in the in-plane bond angle and a decrease in the out-of-plane bond

angle, suggesting an evolution towards the hexagonal layered structure as the Sc

concentration increases [82].The calculations of Zhang et al. predicted that an abrupt change

in c/a ratio and u parameter should occur between x = 0.5625 and 0.6875, where the c/a ratio

decreases from 1.48 to 1.24 and the u parameter increases from 0.404 to 0.498 [15]. The

structural properties of cubic ScxGa1-xN were also calculated by Zerroug et al. and Yurdasan

et al., where the change of lattice parameter of zinc blende ScxGa1-xN is expected to follow

Vegard’s law.

Farrer and Bellaiche predicted that h-ScN is an indirect band gap material, therefore the

nature of the ScxGa1-xN band gap would change from direct to indirect as the Sc concentration

increases [78]. The calculation by Zhang et al. suggested that ScxGa1-xN is a direct band gap

material up to x = 0.5 and the band gap of ScxGa1-xN increases with increasing Sc

concentration. It was also predicted that the increase of Sc concentration should lower the

onset energy of Sc-3d state, however, the Ga-4s, 4p and N-2s, 2p states remain dominant at

the conduction band minima, so the electronic structure of ScxGa1-xN is very similar to that of

GaN at point (Figure 1.8) [15]. This is favourable for semiconductor device applications.

Introduction

13

Figure 1.8 Calculated band structure for wurtzite GaN, wurtzite ScxGa1-xN (x = 0.125 and

0.25) and wurtzite ScN [15]. Reprinted from J. Appl. Phys. 114, 133510 (2013). Copyright

2013, AIP Publishing LLC.

The elastic constants of ScxGa1-xN have also been calculated. It is predicted that both C33 and

the bulk modulus decrease 41% and 15%, respectively, while the Poisson ratio increases 70%

as Sc concentration increases to x = 0.375. These changes are much greater than in the related

alloy system InxGa1-xN. The softening effect of the addition of Sc to the GaN can be attributed

to the increase in bond length and in-plane lattice parameter, which lead to a lower bulk

modulus, in addition to the increase in bond ionicity, which lowers the shear moduli [83]. As

the magnitude of effective charges is high in ScxGa1-xN, which arises from the hybridisation

between the d orbitals of Sc and p orbitals of N, a high piezoelectric response is also expected

[78]. A ferroelectric behaviour is also predicted for ScxGa1-xN with x = 0.625, where its

polarity can be switched along the c axis by a small electric field of 2.1×106 Vcm

-1, which is

at the same level as other commonly known ferroelectric materials, PbTiO3 and BaTiO3 [15].

Introduction

14

The calculations for the phase stability, structural and electronic properties of ScxGa1-xN by

Zhang et al. [15] will be considered as the theoretical reference in this thesis. This is because,

in Zhang’s calculations, a special quasi-random structure was considered, which models the

short range order of the random alloy and minimises the periodicity errors [144], whereas the

atomic stacking was assumed to be along the [0001] direction in the wurtzite structure in

previous calculations [145]. Moreover, the c/a ratio was fixed in previous calculations [145],

while the relaxation of the supercell structure (both the lattice parameter and internal

coordinates) was considered in Zhang’s calculations.

1.3.2 Experimental reports

The first ScxGa1-xN films were prepared by Little and Kordesch in 2001 by reactive co-

sputtering, where direct current (DC) sputtering was used for ScN and radio-frequency (RF)

sputtering for GaN. The films were deposited on quartz substrates with growth temperatures

between 300 and 675 K and the Sc concentration x was between 0.2 and 0.7. The XRD data

indicated that the films were either amorphous or microcrystalline and the measured optical

band gaps of these ScxGa1-xN films decreased linearly from 3.5 eV to 2.0 eV with increasing

Sc concentration [84].

Constantin et al. deposited ScxGa1-xN films on sapphire (0001) substrates using molecular

beam epitaxy (MBE) with an RF plasma nitrogen source under nitrogen-rich (N-rich)

conditions. 3 growth regimes were determined, resulting in different preferred crystal phases:

wurtzite-like (x ≤ 0.17), transitional (0.17 ≤ x ≤ 0.54) and rock-salt (x ≥ 0.54). In the wurtzite

regime, AFM data indicated a 3D growth mode. The surface became smoother as the Sc

Introduction

15

concentration increased. While ScxGa1-xN films with x = 0.05 showed relatively high crystal

quality, a high density of stacking faults was observed in films with higher Sc contents, at and

above x = 0.17 (Figure 1.9). The lattice parameter a and c increased by 0.08 Å and 0.006 Å

respectively, indicating a lattice distortion, where the bond angle became smaller as the Sc

concentration increased. The high-resolution TEM data and the high amount of backscattering

in the RBS data also confirmed the existence of lattice distortions and stacking faults. The

optical band gap of ScxGa1-xN decreased from 3.37 eV to 2.15 eV with increasing Sc

concentration, similar to the report by Little et al. [82, 85].

Figure 1.9 HRTEM and FFT images of ScxGa1-xN with x = 0.05 and 0.17 [82]. Reprinted

from J. Appl. Phys. 98, 123501 (2005). Copyright 2005, AIP Publishing LLC.

Introduction

16

As ScN is easily contaminated by oxygen, other studies have used NH3 as the reactive N

source for MBE growth of ScxGa1-xN films. The growth rate of ScxGa1-xN is lower than that of

GaN because the introduced Sc atoms appear to reduce the sticking coefficient of Ga. Both

the c and a lattice parameters increased as Sc concentration increased, however, the c/a ratio

indicated the films were strained. Although there was no evidence for compositional

segregation in the films, a higher a-type dislocation density was observed in films with

increasing Sc concentration (Figure 1.10) [86].

Figure 1.10 Cross-sectional weak-beam dark field TEM images of the overgrown GaN layer

and ScxGa1-xN (x = 0.08) on GaN template [86]. Reprinted from J. Appl. Phys. 106, 113533

(2009). Copyright 2009, AIP Publishing LLC.

Knoll et al. also deposited ScxGa1-xN films with up to x = 0.08 on sapphire under N-rich

conditions using NH3-MBE. The growth rate of the ScxGa1-xN films was found to be

independent of the substrate temperature. High densities of a-type threading dislocations were

observed, with some bent at the interface, which can relax the misfit strains. All films were

found to be unintentionally n-doped and photoluminescence (PL) spectra showed that all

films emitted at 362 nm while the relative intensity of the broad peak at 580 nm increased

with increasing Sc concentration [87]. While the dislocation density of ScxGa1-xN films with x

= 0.012 is comparable to the GaN template, a significantly higher density of I1-type basal

Introduction

17

stacking faults and planar faults were observed in the films with x = 0.059 (Figure 1.11) [88].

The local Sc coordination environment and electronic properties were also studied by Knoll et

al.. An increase in structural disorder was observed with increasing Sc concentration,

associated with increasing local deformation in the Sc-N bonding environment [89].

Although all the reported MBE-grown ScxGa1-xN films were grown under N-rich condition,

there was no clear explanation for this available in literature. However, consideration of the

growth mechanism of ScN provides a motivation for the use of N-rich conditions. According

to Smith et al., the Sc-rich conditions lead to non-stoichiometric growth and therefore a

higher density of dislocations and N-vacancies in the ScN films [59]. Therefore, it seems that

stoichiometric growth of ScxGa1-xN films may be achieved more easily using N-rich

conditions.

Although MOVPE is the major manufacturing technique for producing high quality

semiconductor films [90], ScxGa1-xN films have been grown either by sputtering or by MBE

as a suitable Sc precursor for MOVPE growth has not been developed. Saidi et al.

demonstrated MOVPE-grown Sc-doped GaN using Cp3Sc as a precursor. However, although

the Sc was distributed uniformly in the film and no secondary phase was detected, the amount

of Sc incorporated was too low to form a true ScxGa1-xN alloy. It seemed that the Cp3Sc

precursor was unable to reach the substrate due to parasitic reactions. Therefore a Sc

precursor with a higher vapour pressure must be developed to enable the MOVPE growth of

ScxGa1-xN [91].

Introduction

18

Figure 1.11 Cross-sectional weak-beam dark field TEM images of ScxGa1-xN films (x =

0.012, 0.035 and 0.059) [88]. Reprinted from Appl. Phys.Lett. 104, 101906 (2014). Copyright

2014, AIP Publishing LLC.

There are no reports of the growth of ScxGa1-xN using pulsed laser ablation (PLD). This is

because it is not possible to make a suitable ScxGa1-xN ablation target with an oxygen

impurity level below 1% using standard target preparation procedures.

1.4 Related alloy systems

1.4.1 Scandium aluminium nitride (ScxAl1-xN)

1.4.1.1 Theoretical predictions

The c/a ratio of wurtzite ScxAl1-xN was predicted to decrease and the a lattice parameter was

predicted to increase with increasing Sc concentration [15]. The DFT calculation performed

by Mayrhofer et al. suggested that the Al-N and Sc-N bond lengths increase by 0.027 Å and

0.038 Å respectively as the Sc concentration increases from x = 0.0625 to x = 0.5 [92].

Introduction

19

Zhang et al. investigated the phase stability of ScxAl1-xN using density functional theory

(DFT), finding that ScxAl1-xN prefers the wurtzite structure up to x = 0.56, however, it is

stable only up to x = 0.06 if spinodal decomposition is taken into consideration. By straining

to AlN or GaN, ScxAl1-xN should be stabilised up to x = 0.4 [15]. Hoglund et al. studied the

mixing enthalpies of different structures of ScxAl1-xN, finding that ScxAl1-xN should remain in

the wurtzite structure up to x ≤ 0.45 [93].

Consistent with Zhang et al., the calculation by Zukauskaite et al. indicated that increasing

the lattice parameter a leads to a decrease in the phase stability, therefore in-plane

compressive strain can help stabilise the wurtzite phase of ScxAl1-xN [94].

The optical band gap of ScxAl1-xN was predicted to become indirect as the Sc concentration

increased above 0.25 because the conduction band minimum (CBM) and valence band

maximum (VBM) move towards M from , due to the influence of the Sc 3d states in the

ScxAl1-xN CBM, which flatten the electron dispersion as the Sc concentration increases

(Figure 1.12) [15].

Both the calculations by Zhang et al. and Deng et al. indicated an increase in bond length and

iconicity and a decrease in bond angle and covalency with increasing Sc concentration [83,

95]. The local distortion and softening effect in ScxAl1-xN produced by the addition of Sc

appear to be responsible for the relatively large increase in piezoelectric response [96]. Caro

et al. performed a thorough study on the piezoelectric coefficients and moduli along with

elastic constants of ScxAl1-xN and the results indicated a greater increase in 𝑒33 than 𝑒15 and

𝑒31 with increasing Sc concentration [97].

Introduction

20

Figure 1.12 Calculated band structure for wurtzite AlN, wurtzite ScxAl1-xN (x = 0.125 and x =

0.25) and wurtzite ScN [15]. Reprinted from J. Appl. Phys. 114, 133510 (2013). Copyright

2013, AIP Publishing LLC.

1.4.1.2 Experimental reports

Akiyama et al. showed a significant increase in the out-of-plane piezoelectric coefficient d33

in (0001)-oriented ScxAl1-xN films compared to (0001)-oriented AlN films grown under

similar conditions. Using dual RF frequency magnetron reactive sputtering, ScxAl1-xN films

were deposited on n-type Si (100) with growth temperatures of 400 ˚C and 580 ˚C. TEM

images revealed that a phase transition occurred between x = 0.41 and x = 0.45 [98]. A 𝑑33 of

27.6 pCN-1

at x = 0.36 was obtained from a film grown at 400 ˚C, where the maximum d33 of

24.6 pCN-1

was measured from a film with x = 0.43 grown at 580 ˚C, indicating a growth

temperature dependence of the piezoelectric response (Figure 1.13) [98, 99]. The piezoelectric

response also showed a dependence on the N2 concentration and substrate temperature, as

Introduction

21

both affect the crystal orientation, whereas no influence from film thickness was observed if

the film was thicker than 0.4 m [100]. Most importantly, the electromechanical figure of

merit for ScxAl1-xN is 5 times higher than that of AlN, which is comparable to other

commonly known piezoelectric materials, for example PZT and PMN-PT [101].

Figure 1.13 Variation of the piezoelectric response as a function of Sc concentration for

ScxAl1-xN films grown at a substrate temperature of (a) 580 ˚C and (b) 400 ˚C [99]. Reprinted

from Appl. Phys. Lett. 95, 162107 (2009). Copyright 2009, AIP Publishing LLC.

Instead of wurtzite ScxAl1-xN, Hoglund et al. investigated the structural properties of cubic

ScxAl1-xN. Magnetron sputtering was used to deposit ScxAl1-xN films with x between 0 and 1

on MgO (111) and Al2O3 (0001) substrates with either ScN (111) or AlN as seed layers. The

composition analysis results suggested that the incorporation of Al leads to a higher film

density and helps to suppress the incorporation of oxygen in the ScxAl1-xN films. Epitaxial

growth was observed up to x = 0.22, followed by a decrease in the crystal quality as the Sc

concentration increased up to x = 0.40, at which point complete phase separation occurred.

The cubic rock–salt phase was observed as the Sc concentration increased beyond x = 0.49

[93, 102]. A thermal stability investigation performed on cubic ScxAl1-xN films with x = 0.57

Introduction

22

showed phase separation, leading to wurtzite AlN and cubic ScN, after an 1.5 hr annealing at

1100 ˚C [103].

Figure 1.14 Cross-sectional HRTEM and corresponding FFT images of ScxAl1-xN (x = 0.1,

0.2 and 0.3) grown at 400 ˚C and 800 ˚C [104]. Reprinted from J. Appl. Phys. 111, 093527

(2012). Copyright 2012, AIP Publishing LLC.

Zukauskaite et al. also deposited ScxAl1-xN films on sapphire with a TiN (111) seed layer

using DC magnetron sputtering. The growth temperatures were between 400 ˚C and 800 ˚C

and the Sc concentration varied from x = 0 to x = 0.3. The crystal quality was found to

Introduction

23

decrease with increasing Sc concentration and phase separation was observed in films grown

at higher temperatures (Figure 1.14) [104]. Compared to AlN, an increase in the dielectric

constant and electromechanical coupling factor was measured from ScxAl1-xN with x = 0.2,

while both bulk modulus and elastic modulus decreased with increasing Sc concentration. A

15% increase in voltage generation was also measured from ScxAl1-xN compared to AlN [105,

106].

Closely lattice-matched ScxAl1-xN/InyAl1-yN superlattices were also grown using sputtering.

The increase in In concentration improved the crystal quality for both Sc0.3Al0.7N/In0.37Al0.63N

and Sc0.3Al0.7N/In0.52Al0.48N and there was no sign of composition mixing in the layers [94].

Deng et al. investigated the optical and electronic properties of both wurtzite and cubic

ScxAl1-xN, where films were deposited by magnetron co-sputtering on sapphire (0001)

substrate for x = 0 – 0.45 [96, 107] and on MgO (001) substrate for x = 0.8 – 1. The crystal

quality decreased as the Sc concentration increased up to x = 0.34, while the film was in the

rock-salt structure at x = 0.45 [108]. A decreasing trend in the optical band gap of ScxAl1-xN

with increasing Sc concentration was measured [107] and both Raman and IR reflectance

results showed redshifts in phonon modes with increasing Sc content, indicating bond

softening [95].

Mayrhofer et al. prepared ScxAl1-xN films with x between 0 and 0.15 by reactive magnetron

sputtering on Si (100) substrate and found a similar redshift in phonon frequencies [109]. The

addition of Ar in the sputtering gas during the growth of ScxAl1-xN was found to improve the

crystal quality and orientation of the films [92]. A surface acoustic wave (SAW) device made

Introduction

24

with ScxAl1-xN x = 0.27 showed a lower wavelength and acoustic velocity and a higher

resonance frequency compared to a similar AlN SAW device [110, 111].

Bohnen et al. also deposited ScxAl1-xN on 6H-SiC (0001) with a ScN seed layer using hydride

vapour phase epitaxy (HVPE), producing nanowires with a length of 1 m and a diameter

between 50 and 150 nm for x = 0.05, although the Al concentration was higher on the

nanowire surface [112]. Features at 4.4 eV and 3.5 eV were observed in cathodoluminescence

(CL) and attributed to carbon and oxygen impurities, while a peak at 2.4 eV was attributed to

the d-d transition between Sc atoms in the alloy [113].

1.4.2 Scandium indium nitride (ScxIn1-xN)

Calculations by Takeuchi et al. suggest that ScxIn1-xN is stable in the wurtzite structure due to

the small difference in lattice parameters between wurtzite ScN and wurtzite InN. However,

the band structure calculation is not trustworthy as the relaxation of the c/a ratio and the u

parameter were not taken into consideration [78]. Currently, there are no experimental reports

available on ScxIn1-xN.

1.4.3 Other transition metals (TM) III-nitrides alloys

Other transition metal nitrides have also been explored for forming alloys with III nitrides.

Wurtzite-structure TM-GaN and TM-AlN have been interested for their ferromagnetic

behaviour, which is of interest for spintronic devices [16, 114–132], while TM-AlN alloys in

Introduction

25

the cubic rock-salt phase have been used for hard coating applications [134–142]. In general,

the phase stability of these TM-III-nitride alloys is determined by the difference in atom size

and electronic structure between the transition metal and the group III element [143]. Most

research focuses on incorporating the first row of the d block elements in III nitrides, as their

atomic sizes are relatively close to those of Al and Ga. The existence of partially occupied 3d

orbitals, which favour sp3d hybridisation instead of sp

3 hybridisation, leads to the low

solubility of transition metals in wurtzite-structure III nitrides. For example, only 0.4% of Fe

can be incorporated stably in wurtzite FexGa1-xN [7, 16, 140]. However, Sc has empty 3d

orbitals, which facilitates sp3 hybridisation, and therefore ScxGa1-xN and ScxAl1-xN can be

stabilised in the wurtzite structure up to much higher Sc concentrations compared to other

TMs [15]. Moreover, the electronic structure of TM-III nitrides is highly affected by the local

lattice distortion (towards sp3d hybridisation) around the TM atoms, whereas the influence of

the distortion is not significant for ScxGa1-xN [15, 140].

1.5 Conclusion and motivation for the work presented in this

thesis

As presented in section 1.3, both theoretical calculations and experimental results suggest that

ScxGa1-xN is a promising candidate for optoelectronic applications with III nitrides. The

understanding of the relationship between the thin film growth conditions, the microstructure

and the materials properties, in particular optical and electronic properties, are crucial for

designing and producing devices with desirable functions. Although the GaN films grown

under metal-rich conditions show higher quality than those grown under N-rich conditions, all

the reported MBE-grown ScxGa1-xN thin films were prepared under N-rich conditions.

Introduction

26

Therefore, this work aims to investigate the influence of the metal-rich conditions on the

growth and microstructure of ScxGa1-xN thin films. Moreover, as the physical properties of

ScxGa1-xN are highly composition dependent, a precise composition measurement of the alloy

is required. Different composition measurement methods (both direct and indirect) will be

studied and their accuracies will be evaluated so as to provide guidelines for future growth of

this alloy. On the other hand, the optical band gap and refractive index of ScxGa1-xN will be

investigated for its potential application of UV emission. Previous experimental results

showed that the optical band gap of ScxGa1-xN decreases with increasing Sc concentration,

which is in contrast to the results of the recent high quality theoretical calculations. One

motivation of this work is to explain the difference between the theoretical studies and

experiments results. In addition, the band alignment and offset of the heterostructures

composed of ScxGa1-xN and other III nitrides will be studied, as heterostructures and multiple

quantum wells (MQWs) are commonly used in LEDs and laser diodes.

The physical properties of GaN and ScN and the recent of ScxGa1-xN are summarised in this

chapter and the characterisation techniques used in this study will be explained in Chapter 2.

The composition and microstructural analysis for ScxGa1-xN thin films grown under metal-rich

conditions will be discussed in Chapter 3 and Chapter 4 respectively. In addition, the optical

properties, in particular the band gaps and refractive indices of ScxGa1-xN and the band offsets

of ScxGa1-xN/AlN heterostructures, will be presented in Chapter 5. Finally, Chapter 6 will

summarise all the results and discuss the possible future work.

Introduction

27

1.6 Reference

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[2] H. Angerer, D. Brunner, F. Freudenberg, O. Ambacher, M. Stutzmann, R. Hopler, T.

Metzger, E. Born, G. Dollinger, A. Bergmaier, S. Karsch and H. –J. Korner, Appl. Phys.

Lett. 71, 1504 (1997)

[3] V. Yu. Davydov, A. A. Klochikhin, R. P. Seisyan, V. V. Emtsev, S. V. Ivanov, F.

Bechstedt, J. Furthmuller, H. Harima, A. V. Mudryi, J. Aderhold, O. Semchinova and J.

Graul, phys. stat. sol. (b) 229, R1 (2002)

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35

Chapter 2

Characterisation techniques

2.1 Atomic force microscopy (AFM)

Atomic force microscopy (AFM) was invented by Bining, Quate and Gerber in 1986 based on

previous invention of scanning tunnelling microscopy (STM) by Bining et al. in 1982 [1,2].

Both AFM and STM are catergorised as scanning probe microscopy techniques (SPM)

because in both cases the measurement relies on scanning a very tiny and sharp tip across a

surface. Since its invention, AFM has become the standard technique for surface morphology

analysis. AFM allows nanoscale 3-dimensional surface measurement on almost any sample in

almost any environment, with minimal or no sample preparation.

An AFM includes an optical microscope placed at the top for locating the sample and the area

of interest [3]. The force and the distance between the tip and the sample surface are

monitored and maintained by a force transducer and a feedback loop control. An optical

sensor is commonly used as a force transducer, in which a laser shines onto the tip and the

reflection of the laser is monitored by a photodetector. A schematic diagram of AFM is shown

in Figure 2.1.

Characterisation techniques

36

Figure 2.1 Schematic diagram of AFM (based on Innova AFM Manual) [4].

An AFM can be operated in contact mode, tapping mode (oscillation mode) and non-contact

mode. Among these modes, tapping mode is most commonly used for inorganic thin films,

which have relatively hard surfaces and relatively low surface roughnesses. In tapping mode,

the tip vibrates at its resonant frequency. When the tip interacts with the sample surface,

damping occurs and leads to a change of the oscillation. The change of the tip oscillation is

measured by the photodetector (force transducer) and a feedback signal is used to adjust the

voltage applied to the piezo stage in order to change the height of the stage to maintain the set

force [3].

Several parameters can be controlled in order to acquire good quality AFM images, including

image size, number of lines in the image, scan speed, image rotation angle (useful for

identifying artifacts), set-point voltage (acts as a force reference point for comparing the

voltage output from the force sensor) and PID control [3]. The lateral resolution of an AFM

Characterisation techniques

37

image is determined by the radius of curvature of the tip and is typically between 10–40 nm

depending on the type of tip and on the morphology of the surface. The vertical resolution is

much better than the lateral resolution and it is limited primarily by the stability of the

instrument with respect to mechanical vibrations and the performance of the feedback loop.

Vertical height measurements made using AFM can reach sub-atomic precision. The set-point

voltage represents the force between the tip and the sample surface and this interaction force

is used as the reference for the feedback loop to adjust the height of the stage. In the case of

tapping mode, a lower set-point voltage means a greater interaction force, i.e. the tip is closer

to the surface. If the tip is set too close to the surface, the lifetime of the tip would be

shortened as the tip is easily damaged. The PID control refers to the proportional gain (P),

integral gain (I) and derivative gain (D). These gain parameters tell the feedback loop,

according to Equation 2.1 [3], how sensitive it is to response to the difference between the

measured force (from the photodetector) and the set-point value.

𝑍𝑣 = 𝑃 × 𝑍𝑒𝑟𝑟 + 𝐼 × ∫𝑍𝑒𝑟𝑟𝑑𝑡 + 𝐷 × 𝑑𝑍𝑒𝑟𝑟𝑑𝑡

(2.1)

Three types of data can be obtained during an AFM scan: height, amplitude and phase. The

height provides information about the surface morphology and roughness. The amplitude

signal can be used to identify features and shapes and provides useful feedback while

optimising image acquisition, while the phase signal gives information about the mechanical

homogeneity of the sample as it can be influenced by the hardness and the adhesion of the

surface. Data processing is normally required before presenting AFM results, typically

including image “levelling” and “flattening” [3].

Characterisation techniques

38

Data levelling, which is usually the first step of the data processing, adds a constant to each

line of the scan in order to move the minimum height of the image to zero. Data flattening,

also called background subtraction, is used to correct for systematic artefacts in the scan. This

is done by fitting each line of the scan to a polynomial equation and then subtracting the

polynomial shape. Parabola flattening means a 2nd

order equation is applied and this is

commonly used as it can remove the effect of scanner bow and ensure a flat background of

the image [3, 5, 6]

Although the AFM image acquisition and processing are relatively straightforward, artifacts

in the images could lead to misinterpretation of the results. Artifacts can be generated by a

blunt, contaminated or broken probe, a miscalibrated piezoelectric scanner, mishandling of

data and ambient vibrations. Typical artifacts include repeated features, streaks and sheared

images and can be resolved by adjusting the scan parameters, reducing the scan speed and/or

changing the tip. Examples of images with different kinds of artefacts can be found in Ref. [3].

All AFM images in this thesis were taken using a Bruker Innova AFM. The tip (model name:

NCHV) with a resonant frequency of 320 kHz and a force constant of 42 N/m was used for

measurements and all measurements were done at room temperature. All images were

scanned at 1 Hz with 512 lines and processed using WSxM 4.0 Beta 7.0 [5] with parabola

flattening.

Characterisation techniques

39

2.2 X-ray diffraction (XRD)

X-ray diffraction (XRD) is the standard technique for crystallographic analysis for thin films,

powders and bulk samples in which a parallel or slightly divergent beam of monochromatic

X-rays is directed at a specimen with known angle(s) of incidence and the directions of the

elastically scattered beams are then recorded for a range of scattering angles. A diffractogram

shows the distribution of scattering angles of the incident X-rays, which (for crystalline

materials) relate to the Bravais lattice group and the size of the crystal unit cell. In order to

obtain a useful diffractogram, the wavelength of the radiation needs to be of the order of the

lattice spacing (around 1 Å).

Reciprocal space is a fundamental concept useful for understanding diffraction from a crystal.

The Bravais lattice of a crystal can be represented by a reciprocal lattice through a Fourier

transformation. A lattice vector in real space (r) and reciprocal space (r*) can be represented

by Equation 2.2a and b, where the relationship between the length of these vectors are

described in Equation 2.2c and the reciprocal lattice vector is always perpendicular to the

other two axes in real space, for instance a* is perpendicular to b and c. By convention, the

incident beam and the reflected beam are represented by wave vectors 𝐤0 and 𝐤 in reciprocal

space [7].

𝑟 = 𝑛1𝑎 + 𝑛2𝑏 + 𝑛3𝑐

(2.2a)

𝑟∗ = 𝑚1𝑎∗ +𝑚2𝑏

∗ +𝑚3𝑐∗

(2.2b)

𝑎∗ = 1

𝑎, 𝑏∗ =

1

𝑏, 𝑐∗ =

1

𝑐 (2.2c)

Characterisation techniques

40

The Laue equations (Equation 2.3a–c) describe the path difference generated due to the

scattering of the wave and the crystal lattice spacing. In the case of elastic scattering, the

magnitude of the incident beam and the scattered beam are the same (|𝐤0| = |𝐤|). Bragg’s

Law describes a specific condition of scattering that the angle of the incident beam is equal to

that of the reflected. When the Bragg condition is satisfied, the reflected beams experience a

constructive interference and a reflection from a particular set of crystal planes results,

forming a diffraction spot. The path difference between the reflected beams is 2𝑑 sin 𝜃

(Figure 2.2a and Equation 2.4a). In Equation 2.3a–c and 2.4a, Δ is the path difference; a, b, c

are the lattice parameters of a crystal structure relating to the x, y, z axes respectively; α and α0

are the incident and scattering angles in Laue equations; h, k, l are the indices of a particular

crystal plane; d is the interplanar spacing; n is the order of reflection of a particular crystal

plane and λ is the wavelength of the radiation. A wave vector g is used to denote the change

of the wave vector during the scattering. An Ewald sphere (the reflecting sphere in Figure

2.2b) with a radius of 1/λ can be constructed to show the scattering of the waves in reciprocal

space. If a reciprocal lattice point intersects with the edge of the Ewald sphere, this point

satisfies the Bragg condition and gives rise to a diffraction spot. Considering an elastic

scattering and the magnitude of the wave vector 𝐤0 and 𝐤 equal to the radius of the Ewald

sphere 1/λ, the wave vector g would then equal to 2 sin 𝜃 𝜆⁄ . From the Bragg’s law, the

magnitude of 𝒈ℎ𝑘𝑙, a wave vector corresponding to a crystal plane (hkl), equals to 1 𝑑ℎ𝑘𝑙⁄ and

it is always perpendicular to the crystal plane (hkl) (Equation 2.4b) [7]. By rotating the crystal

about its origin, different crystal planes can be included in the Ewald sphere, thus showing

how the Bragg condition is satisfied for these different planes.

X-rays are generated by hitting a metal target with a high energy electron beam in a vacuum

tube. The ground state electrons of the metal are excited by the incident electron beam and

Characterisation techniques

41

leave holes in the electron orbital. X-rays are emitted when electrons at the higher energy

state fall back to the ground state. If the hole created in the K-shell is filled by an electron

from the L-shell, the energy change during this refilling process gives rise to the characteristic

Kα X-ray with a fixed wavelength. However, other transitions also occur which may produce

emission peaks of similar wavelengths (e.g. Kβ) and a continuous background of

‘Bremmstrahlung’ X-rays are also produced. Therefore, a monochromator is required so that

only the X-ray with the desired wavelength is used. If the wavelength of the incident beam is

not monochromatic or the incident beam is not nearly parallel, a range of reciprocal lattice

points would be covered by the Ewald sphere, and this affects the resulting diffractogram.

∆ = 𝑎(cos 𝛼 cos 𝛼0) = ℎ𝜆

∆ = 𝑏(cos 𝛼 cos 𝛼0) = 𝑘𝜆

∆ = 𝑐(cos 𝛼 cos 𝛼0) = 𝑙𝜆

(2.3a)

(2.3b)

(2.3c)

𝑛𝜆 = 2𝑑 sin 𝜃

(2.4a)

2 sin 𝜃

𝜆=𝑛

𝑑= 𝑔

(2.4b)

The goniometer is the component which can tilt or rotate about different axes, allowing the

sample to be scanned across different angles and allowing different reciprocal lattice points to

fulfil the Bragg condition (Figure 2.3). The angle of rotation of the goniometer can be finely

adjusted to within 0.0001º, which leads to an error of ±10-5

Å for the lattice parameter

measurement. The crystal interplanar spacings can be obtained through the Bragg equation

from the measured angles, and therefore the lattice parameters of the crystal can be calculated

Characterisation techniques

42

using Equation 2.5 for a hexagonal crystal. A detail discussion of X-ray diffraction of III-

nitrides can be found in Ref. [8].

Figure 2.2 (a) A diagram showing Bragg scattering in real space and (b) the Ewald sphere

construction in reciprocal space.

1

𝑑2= 4

3 (ℎ2 + ℎ𝑘 + 𝑘2

𝑎2) +

𝑙2

𝑐2 (2.5)

(a)

(b)

Characterisation techniques

43

Figure 2.3 Rotational axes of an X-ray diffractormeter.

All the XRD diffractograms presented in this thesis were obtained using a PANalytical MRD

with a Cu Kα source.

2.3 Transmission electron microscopy (TEM)

Transmission electron microscopy (TEM) in bright field or dark field imaging mode allows

the microstructures of a thin film to be imaged on a nanometer scale. In diffraction mode,

crystallographic information about the film can be obtained. Compositional information and

atomic scale resolution images can also be obtained from a specimen using high-resolution

scanning transmission electron microscopy (STEM) in high-angle annular dark field imaging

(HAADF) mode.

Characterisation techniques

44

2.3.1 Sample preparation

TEM specimens need to be electron transparent, which means that electrons can pass through

the sample and produce a sufficient signal-to-noise ratio at the detector without undergoing

excessive inelastic scattering. The thickness required to achieve electron transparency

depends on the mean free path of the electrons, which is affected by the energy of electrons

and the atomic mass of the material. A thinner specimen is required if the electron energy is

low or the atomic number of the material is high. The usual thickness of a specimen is

between a few tens to a few hundreds of nanometers.

To make a cross sectional sample, a strip 2 mm in width, is cleaved from the wafer. It is then

cut into 2 mm x 2 mm squares. Every second square is rotated 90° horizontally and the two

squares are stuck together face to face by epoxy glue, which is then cured on a hotplate at

125°C for 2 hours. One side of the sample is then polished using SiC grinding papers to

obtain a relatively flat surface followed by a tripod polishing with a series of diamond

grinding papers, from 30 μm to 0.1 μm. The polished side is then mounted on a copper grid

using epoxy and the glue is cured on hotplate at 125° for 1 hour. The sample is then thinned

by grinding until its thickness becomes 200 μm. A disc grinder is then used for further

grinding until 80 μm is reached. A dimple grinder is then used to thin the central part of the

sample. 6 μm diamond paste is used in the initial stage, changing to 1 μm paste when

thickness is nearly 25 μm. Dimpling is stopped when the thickness at the centre is about 20

μm. The central part of the sample is then further polished by a precision ion polishing system

(PIPS). The ion gun energy is set to 5 keV and the guns are tilted at ±7°. The sample is ion

milled in the PIPS until a small hole occurs and interference fringes can be seen under an

optical microscope.

Characterisation techniques

45

TEM specimen can also be prepared using focused-ion beam (FIB) technique [9], however,

the use of Ga ion beam to cut and thin the specimen is not suitable for the materials under

investigation in this thesis, as Ga ions can easily implant in the ScxGa1-xN thin films and

influence both the structural and composition analysis results.

2.3.2 Components in a TEM

The electron beam is formed by extracting electrons from the gun. There are two types of

electron gun commonly used: a themionic gun (based on tungsten filaments or LaB6 crystals)

and a field emission gun [10]. The beam is then focused by condenser lens C1 through the

condenser aperture and projected onto the sample by condenser lens C2. The beam is then

converged by the objective lens, passing through the objective aperture and an intermediate

image is formed. This image is then magnified by the intermediate image lens. The image is

then further magnified and projected onto the screen by the projector lenses. In diffraction

mode, the diffraction is formed by a parallel electron beam on the back focal plane, which is

at the same plane as the objective aperture. The diffraction pattern is then magnified by the

intermediate lens and the projector lens (Figure 2.4) [11].

Under a magnetic field (from the lenses), electrons move in a spiral path from the gun

towards the specimen. However, the existence of the non-uniform magnetic field, caused by

the non-perfect cylindrical symmetry of the soft iron and the imperfect microstructure of the

soft iron, leads to astigmatism. This can be corrected by stigmators, which generate a field to

compensate the distortion of the magnetic field [12, 13]. In order to achieve a fine spot size

for sub-angstrom imaging (HR-(S)TEM), it is essential to perform spherical aberration

correction. Spherical aberration arises from the off optic axis electrons which are bent by the

Characterisation techniques

46

lenses towards the axis but which become focused before the intended focal point of the near-

optic axis rays (positive spherical aberration). Quadrupole/Octupole and hexapole correctors

[12, 14] have been developed in order to produce negative spherical aberration to balance the

positive spherical aberration. The value of adjustment that is required for the correctors is

calculated using the Zemlin tableau method, which measures the changes in the

diffractograms obtained from the incident beam at a range of angles around the optic axis

[12–16].

Figure 2.4 Schematic diagram of a basic TEM.

2.3.3 Electron diffraction

A high energy electron beam is the requirement for TEM and 200 kV is normally used. By

knowing the accelerating voltage, the wavelength of the electron can be calculated by the de

Broglie relationship (Equation 2.6a–c), where p, m, v and λ are the momentum, mass (9.11 ×

10−31 kg), velocity and wavelength of the electron, h is the Planck’s constant (6.626 × 10−34

Characterisation techniques

47

Js) and e is the charge of electron (1.602 × 10−19 C). However, the relativistic mass needs to

be taken into consideration as the electrons at very high energy travel nearly at the speed of

light c (Equation 2.6d). Consequently, the wavelength of electrons at 200kV and 300 kV are

2.51 pm and 1.97 pm respectively [18]. Despite the difference in wavelength, the Laue

equation and Bragg’s Law also apply to the scattering of electrons.

𝑝 = 𝑚𝑣 = ℎ

𝜆

(2.6a)

𝑒𝑉 = 1

2𝑚𝑣2

(2.6b)

𝜆 = ℎ

√2𝑚𝑒𝑉

(2.6c)

𝜆 = ℎ

√2𝑚𝑒𝑉(1 +𝑒𝑉2𝑚𝑐2

)

(2.6d)

Due to the limited thickness of a crystalline TEM specimen, the reciprocal lattice points

appear as elongated rods, which are referred as relrods [17]. The existence of relrods relaxes

the conditions required for the Bragg condition to be met: a diffraction spot is formed when

the edge of Ewald sphere cuts through any part of the relrod. The intensity variation of the

diffraction spot is shown in Figure 2.5, where the Bragg condition is perfectly fulfilled when

the Ewald sphere intersects the centre of the relrod. An excitation error 𝒔 (or effective

excitation error 𝒔𝑒𝑓𝑓) is used to denote the distance from the g, the ideal Bragg condition, and

a deviation parameter (ϕg) can be obtained by taking the characteristic length (ξg) for the

diffracted vector into consideration (Equation 2.7a and b, where t is the specimen thickness).

The intensity of a diffracted beam is directly related to the deviation parameter and a weak

Characterisation techniques

48

beam can be formed by achieving a large value of s [19]. Moreover, as the wavelength of high

energy electron is much shorter than that of X-rays, the radius of the Ewald sphere is much

larger, thus the edge of the Ewald sphere intersects more reciprocal lattice points. Therefore,

unlike XRD, electron diffraction does not require sample rotation to acquire a diffractogram

and multiple diffraction spots can be seen within the same diffraction pattern. However,

because the length of the relrods depends on the thickness of the specimen, the intensities of

the diffraction spots will be affected by specimen thickness, as well as by the electron

wavelength (and hence the radius of the Ewald sphere). Due to the short wavelength of the

electrons and hence the low scattering angles, lattice parameters can only be obtained with

low precision from electron diffraction patterns, typically within 1–2% Also, electron beams

can be re-diffracted due to the much higher inelastic scattering cross-section of electrons

compared to X-rays, resulting in ‘double diffraction’ and hence intensities which deviate from

theoretical predictions for that crystal. Therefore, no qualitative information can be obtained

from the intensity of the diffraction spots.

Kikuchi lines are formed when incoherent scattering occurs in a thick specimen. As the

electrons are scattered in all direction, Kossel cones which consist of a range of incident k are

formed and only some of these electrons achieve the Bragg condition. These Kossel cones are

projected onto the screen and appear as two parallel lines, one corresponds to (hkl) plane

while the other corresponds to (ℎ̅�̅�𝑙 )̅ plane, and these are Kikuchi lines (Figure 2.6). The

relative position of the Kikuchi line can indicate whether the excitation error is positive or

negative, which is helpful for setting up the two-beam condition. Moreover, as Kikuchi lines

are directly related to the crystal structure, they can be traced to a particular plane or the zone

axis and a Kikuchi map can be constructed to show the relative orientational relationship of

different crystal planes in reciprocal space [18].

Characterisation techniques

49

Figure 2.5 (a) Relrod in reciprocal space created from diffraction from a crystalline specimen

and (b) The relrod at 𝐠ℎ𝑘𝑙 when the beam is away from the exact Bragg condition. The Ewald

sphere intercepts the relrod at a negative value of 𝐬 which defines the vector 𝐊 = 𝐠 + 𝐬. The

intensity of the diffracted beam as a function of where the Ewald sphere cuts the relrod is

shown on the right of the diagram. In this case the intensity has fallen to almost zero.

Reproduced from Transmission Electron Microscopy A Textbook for Materials Science, Ch.

17, 2009, p.274, D. B. Williams and C. B. Carter. With permission of Springer.

𝑠𝑒𝑓𝑓 = √𝑠2 +

1

ξg2

(2.7a)

|ϕg|2= (

𝜋𝑡

ξg)

2𝑠𝑖𝑛2(𝜋𝑡𝑠𝑒𝑓𝑓)

(𝜋𝑡𝑠𝑒𝑓𝑓)2 (2.7b)

(a)

(b)

This material is unavailable due to copyright

restrictions.

Characterisation techniques

50

Figure 2.6 The Kossel cones intercept the Ewald sphere, creating parabolas which

approximate to straight lines in the DPs becauseθB is small. Reproduced from Transmission

Electron Microscopy A Textbook for Materials Science, Ch. 19, 2009, p.312, D. B. Williams

and C. B. Carter. With permission of Springer.

2.3.4 Imaging modes

Bright field (BF) images are formed by inserting the objective aperture to select the direct

(undiffracted or straight through) beam which lies parallel to the optic axis. The brightest spot

in the electron diffraction pattern is formed by the direct beam. Dark field (DF) images are

formed by using the objective aperture to select the diffracted beam whereas centred dark

field (CDF) images require a tilting of the electron beam so that the diffracted beam is on the

optic axis in order to reduce the spherical aberration.

This material is unavailable due to

copyright restrictions.

Characterisation techniques

51

Figure 2.7 Standard indexed diffraction pattern at (a) < 112̅0 > and (b) < 101̅0 > zone axis

for a hexagonal material; (c) two beam condition and (d) g-3g condition.

In order to acquire high quality images for defects, stacking faults and dislocations, weak-

beam dark field (WBDF) imaging can be performed, which gives strong contrast as well as

crystallographic orientation information. Prior to setting the weak beam condition, the

orientation of the specimen has to be known, which can be done by tilting the sample to a

zone axis: for example, < 101̅0 > and < 112̅0 > can typically be located from a cross-

sectional sample of a hexagonal III-nitride film grown in the [0001] orientation (Figure 2.7a

and b). In order to form a WBDF image, the two beam condition is required, where the Ewald

sphere intercepts only the 0 and g relrods, resulting in two strong diffraction spots (Figure

2.7c). The two beam condition is achieved by tilting the sample until it is close to the Bragg

condition while keeping the excitation error s small and positive. Kikuchi lines can be used as

an indicator for setting up two beam condition as one will pass through the g spot if the g is at

Bragg condition and s = 0. To achieve the g-3g condition, the sample is further tilted from the

(a) (b)

(c) (d)

Characterisation techniques

52

two beam condition until the 3g diffraction spot is strong, meaning that the Ewald sphere is

intercepting the 0 and 3g relrods (Figure 2.7d). By tilting the electron beam, the g spot,

instead of the 0 spot, is on the optic axis and a WBDF image can be formed by using the

objective aperture is to select the g spot. Setting up different diffraction conditions can help

determining the directions of dislocations and thus identifying their types [19].

2.3.5 Mass-thickness contrast, diffraction contrast and phase contrast

The contrast in TEM images arises from the relative intensity difference between two adjacent

areas, which depends on the signal generated by the electrons that reach the screen or the

detector compared to the signal generated by the detector noise. There are two types of

contrast: amplitude contrast, which includes mass-thickness contrast and diffraction contrast,

and phase contrast.

Mass-thickness contrast, as its name suggests, is sensitive to the atomic number and thickness

of the specimen. As the mean free path of electrons is constant when the electrons pass

through the specimen, more incoherent elastic scattering occur at the regions with heavier

mass or greater thickness, and thus a higher number of electrons are scattered off optic axis.

Therefore, in a BF TEM image, the regions associated with higher atomic mass or greater

thickness appears to be darker.

Diffraction contrast arises from coherent elastic scattering, where the Bragg condition is

satisfied. The Bragg condition can be reached by tilting the specimen, so that the two-beam

condition is achieved, where only the direct beam and one strong diffracted beam are seen.

The diffraction contrast is sensitive to the crystal orientation and defects as both of them

Characterisation techniques

53

would change the diffraction condition, thus the intensity of the coherent scattered electron

beam contributed to the image. WBDF is the image mode that benefits from the diffraction

contrast [18].

Phase contrasts effects appear as the periodic fringes in the image, which are produced by the

interference of more than one diffracted electron beam. The intensities of electron beams

change periodically depend on the excitation error s and the thickness t of the specimen,

which is expressed in mathematical form in Equation 2.8 [18]. Three forms of phase contrast

can typically be seen in TEM images: lattice fringe, which occur when multiple diffracted

beams interact to produce an image (high resolution TEM), Moiré patterns (including

rotational and translational patterns) which occur when the incident electron beam passes

through two superimposed regions of different crystal structure and/or orientation, and

Fresnel contrast. A more detailed physical and mathematical explanation for phase contrast

can be found in Ref [18].

𝐼 = 𝐴2 + 𝐵2 − 2𝐴𝐵 sin(2𝜋𝑔′𝑥 − 𝜋𝑠𝑡) (2.8)

2.3.6 Scanning transmission electron microscopy (STEM)

In contrast to conventional TEM, where the objective aperture is used to select the

direct/diffracted beam to form a BF/DF image on the phosphor screen and/or camera, a

scanning TEM (STEM) uses concentric detectors to scan across the sample for imaging,

allowing BF and annular DF (ADF) images to be produced. The BF detector is placed at the

on-axis position and it collects the signal from the direct beam. The BF images in STEM

show better resolution and contrast than conventional TEM as chromatic aberration affects the

image formation in conventional TEM but not in STEM. However, the STEM BF is noisier

Characterisation techniques

54

than conventional TEM due to the low collection efficiency of electrons. This can be

improved by using a larger detector [20]. An ADF image is formed by collecting all the

scattered electrons at the conjugated back focal plane, thus producing better contrast and

minimising aberrations. An image showing almost exclusively mass-thickness contrast can be

obtained through a high angle ADF (HAADF) detector, which collects the scattered electrons

with an angle > 50 mrad (Figure 2.8) [18].

Figure 2.8 Schematic of the HAADF detector setup for Z-contrast imaging in a STEM The

conventional ADF and BF detectors are also shown along with the range of electron scattering

angles gathered by each detector. Reproduced from Transmission Electron Microscopy A

Textbook for Materials Science, Ch. 22, 2009, p.380, D. B. Williams and C. B. Carter. With

permission of Springer.

This material is unavailable due to copyright restrictions.

Characterisation techniques

55

The TEM and STEM images presented in this thesis were taken using a JEOL 2000Fx and a

JEOL 2100 with a HAADF detector at 200 kV. With the assistance of Sneha Rhode at

Department of Material Science and Metallurgy, University of Cambridge, UK, aberration-

corrected HAADF images were taken using a Titan3 80–300 at 300 kV with a probe

convergence semi-angle of 15 mrad and spherical aberrations up to the third order in the

electron beam “probe” were corrected by recording Zemlin tableau diffractograms.

2.4 Rutherford backscattering spectrometry (RBS)

Rutherford backscattering spectrometry is a technique that uses ion scattering by Coulomb

repulsion for compositional analysis. A high energy ion beam, usually 4He with 2 MeV, is

directed onto the sample surface, and the energy of the backscattered ions is then measured.

The ion scattering is caused by the interaction between the ions and the nuclei of the atoms,

where energy is transferred from the incident ion to the target atom (Figure 2.9). Assuming an

elastic collision in which energy and momentum are conserved, the energy of the scattered

ion can be determined and a kinematic factor (K) can be defined as the ratio of the energy of

the scattered ion and the incident ion (Equation 2.9). If the ion is backscattered directly (θ =

180˚), the ratio of the scattered ion energy to the incident energy would be at its lowest value

while the ratio of the recoil atom energy to the incident energy would be at its highest values

(Equation 2.10a and b). It is seen that the kinematic factor is highly dependent on the masses

of the incident ion (M1) and target atom (M2) and a small change in M2 leads to a large

change of K, therefore a high mass resolution can be obtained from RBS spectra, especially

for light elements [21].

Characterisation techniques

56

Figure 2.9 A diagram illustrating the scattering process in RBS.

𝐾 = 𝐸1𝐸0=

(

√(𝑀2

2 −𝑀12sin2𝜃) + 𝑀1 cos 𝜃

𝑀2 + 𝑀1)

2

(2.9)

𝐸1𝐸0= (

𝑀2 −𝑀1𝑀2 +𝑀1

)2

(2.10a)

𝐸2𝐸0=

4𝑀1𝑀2(𝑀1 + 𝑀2)2

cos2𝜙 (2.10b)

The incident ions can lose their energies through inelastic collisions with the target atom

nuclei and the electronic excitations with the electrons surrounding the nucleus, therefore

some energy will be lost when the ions travel through one layer of atoms (Equation 2.11a).

The energy loss can also be described by a stopping cross section (ε), which is calculated by

dividing the energy loss by the number of atoms in a given area (Equation 2.11b). If the

sample consists of several layers of compounds, the energy loss (∆𝐸) in each layer can be

Characterisation techniques

57

calculated using the thickness and the backscattering energy loss factor (S) which is derived

using surface energy approximation (Equation 2.12) [22].

−𝑑𝐸

𝑑𝑥= 2𝜋𝑍1

2𝑒4

𝐸∙ 𝑁 ∙ 𝑍2 ∙ (

𝑀1𝑚) ln

2𝑚𝑣2

𝐼

(2.11a)

𝜀 = (1

𝑁)𝑑𝐸

𝑑𝑥

(2.11b)

∆𝐸 = ∆𝑡 ∙ [𝑆] = ∆𝑡 ∙ [𝐾𝑑𝐸

𝑑𝑥|in +

1

|cos 𝜃|

𝑑𝐸

𝑑𝑥|out] (2.12)

If the scattering is only caused by the repulsive force between the incident ion and the target

atom nucleus, a scattering cross section (σ) can be calculated using Equation 2.13. The yield

of the scattered ion (Y) detected depends on the masses of the ions and the target atoms as

well as the thickness of the layer (Equation 2.14a and b). Therefore, the detection limit of

RBS varies from 1015

atoms/cm2 for light elements (e.g. C, N and O) to 10

10 atoms/cm

2 for

heavy elements (e.g. Au and Pb) [23, 24]. A RBS spectrum is formed by plotting the yield of

the ions against their energy. By measuring the heights of the ion yield, the ratio of the

elements can be calculated (Equation 2.15 and 2.16).

A RBS consists of three main parts: an ion source, a particle accelerator and a detector. The

choice of the ion source depends on the type of accelerator, where a positive ion source is

used for a single stage accelerator while a negative ion source is used for a tandem accelerator.

The positive ions are generated through a plasma discharge process, in which duoplasmation

and radio frequency (RF) plasma sources are the most commonly used. By adding a charge

exchange system to a positive ion source, negative ions can be obtained. The details of the ion

Characterisation techniques

58

producing mechanism and different types of ion generation technique can be found in Ref.

[25].

𝜎(𝜃) = 𝑑𝜎

𝑑Ω= (

4𝑍1𝑍2𝑒2

4𝐸0)

2

(sin−4𝜃

2− 2 (

𝑀1𝑀2)2

+ ⋯)

(2.13)

𝑌 = 𝜎(𝜃) ∙ 𝛺 ∙ 𝑄 ∙ 𝑁∆𝑡

(2.14a)

𝑌(𝑡) = (𝑍1𝑍2𝑒

2

4𝐸(𝑡))

2

∙ 𝑁 ∙ 𝑄 ∙ 𝛺 ∙ ∆𝑡

(2.14b)

𝐻 = 𝑌𝜀

[𝑆]

(2.15)

𝑁𝐴𝑁𝐵= 𝐻𝐴∆𝐸𝐴𝜎𝐵𝐻𝐵∆𝐸𝐵𝜎𝐴

(2.16)

The Van de Graaf accelerator accelerates ions to the high energies required for the experiment.

Positive charges are continuously supplied to a belt which transports the positive charges to

the high voltage terminal so that the terminal is highly positive and thus the positive ions

leaving the terminal are accelerated towards the ground through the tube. In a single stage

accelerator, positive ions go through the high voltage terminal directly from the ion source,

the ions are then accelerated down the tube and directed to the analysing chamber. In a

tandem accelerator (Figure 2.10), the negative ions from the source are accelerated firstly by

the attraction of the positive high voltage terminal. After going through the electron stripper,

the ions become positive and experience the same accelerating process as in the single stage

Characterisation techniques

59

accelerator. Since there are two accelerating steps in the tandem accelerator, higher ion

energies can be achieved.

Figure 2.10 Schematic diagram of a RBS spectrometer with a tandem accelerator [26].

With the assistance of Dr. Nuno Pessoa Barradas, Dr. Eduardo Alves and Dr. Sergio Pereira

at the C2TN - Centro de Ciências e Tecnologias Nucleares, Universidade de Lisboa, Portugal,

RBS measurements were carried out using a beam of 4He at 2 MeV with an incidence angle

of 0˚ and a standard detector was placed at 140˚ and two pin-diode detectors located

symmetrically to each other at 165˚. IBA DataFurnace NDF v9.6d [27] was used to analyse

RBS data and the accuracy of the composition measurement is about 1% [28].

Characterisation techniques

60

2.5 X-ray photoelectron spectroscopy (XPS)

X-ray photoelectron spectroscopy (XPS) is used to determine elemental compositions and

chemical bonding states. When combined with an ion gun for sample ablation, it also allows

depth composition profiling, which is helpful for analysing multi layered structures, for

instance quantum wells. However, limitations of XPS include its lack of imaging capacity and

its insensitivity to hydrogen and helium.

XPS detects the energies of photoelectrons, which can be used to determine the chemical

bonding states of elements within a compound sample. Monochromatic X-rays are used to

induce the emission of photoelectrons from the core energy level of an atom. As the electrons

in different orbitals experience different binding force from the atomic nuclei, the binding

energy (𝐸𝐵) for each electron is unique. When a core-level electron absorbs the energy (hv)

from the incident X-rays, the binding energy is overcome and a photoelectron leaves the atom

with a particular kinetic energy (𝐸𝑘) which is then analysed by the electron spectrometer

(Figure 2.11). The photoelectron emission process and energy relationship can be calculated

using Equation 2.17, where W is the work function of the analyser. The kinetic energy is

measured but the binding energy derived from this is used for data [29].

𝐵𝑖𝑛𝑑𝑖𝑛𝑔 𝑒𝑛𝑒𝑟𝑔𝑦 (𝐸𝐵) = ℎ𝜈 − 𝑘𝑖𝑛𝑒𝑡𝑖𝑐 𝑒𝑛𝑒𝑟𝑔𝑦 (𝐸𝑘) −𝑊 (2.17)

Characterisation techniques

61

Figure 2.11 (a) X-ray induced photoelectron emission (b) Auger electron emission through

atomic relaxation.

Auger electron emission occurs when an ionised atom relaxes, i.e. when an electron drops

from a higher energy level to a lower energy level. The generation of photoelectrons in XPS

leaves behind ionised atoms. Therefore, characteristic Auger peaks also appear in the XPS

spectra and some of them may overlap with the XPS peaks and lead to problems with

quantitative analysis. For example, in the XPS spectrum of GaN, the Ga Auger peaks overlap

with the N 1s peak if the Al Kα source is used; in order to quantify concentration of N,

complex curve fitting model is required or a different X-ray source is needed to shift the Ga

Auger peaks away [30].

The X-ray generation mechanism is the same as described in the XRD section. However,

instead of Cu, Mg Kα (1253.6 eV) and Al Kα (1486.6 eV) are the most commonly used

source for XPS as their natural line widths are 0.36 eV and 0.43 eV respectively, which are

smaller than that of Cu (2.11 eV) [31]. A monochromator, usually a quartz crystal, is used to

obtain a narrow line width and eliminate satellite peaks. A X-ray line width of 0.25 eV can be

achieved by applying a monochromator to an Al Kα source. A hemispherical sector analyser

(a) (b)

Characterisation techniques

62

(HSA) is the most commonly used electron spectrometer for XPS (Figure 2.12). A voltage is

applied to the two sides of the hemispheres in order to separate photoelectrons according to

their kinetic energy. An ultra-high vacuum environment is required for performing XPS as a

long mean free path is needed to avoid scattering of the emitted photoelectrons before they

reach the detector [29].

Figure 2.12 Schematic diagram of XPS (the dotted line indicates the path of the emitted

photoelectron).

A survey scan is first performed to obtain the featured peaks across a wide range of binding

energies, from 0 to 1350 eV (depending on the source), then a high resolution scan is

performed within a small range of energies to investigate the binding energies of the

photoelectrons from a particular orbital. Apart from the s orbital, peaks from p, d and f

orbitals split into two due to the electron spin interactions. The ratio of the intensity of the

Characterisation techniques

63

split peaks are listed in Table 2.1. Satellite peaks may occur occasionally if the emitted

photoelectron excites a valence electron to a higher level [29].

𝑝12⁄∶ 𝑝3

2⁄ 1:2 𝑑3

2⁄∶ 𝑑5

2⁄ 2:3 𝑓5

2⁄∶ 𝑓7

2⁄ 3:4

Table 2.1 Relative intensity of split XPS peaks

The relative concentration of a constituent (𝐶𝑥) in a sample can be calculated from Equation

2.18, where 𝐴𝑥 is the corresponding peak area and 𝑆𝑥 is the relative sensitivity factor of a

particular element while 𝐴𝑖 and 𝑆𝑖 are the total peak area and relative sensitivity factor of all

elements in the sample respectively [30]. The relative sensitivity factor depends on the X-ray

flux, the photoelectric cross-section for the atomic orbital, the angular efficiency factor, the

efficiency of formation of photoelectrons, the mean free path of the photoelectron, the area of

the sample measured and the detection efficiency. These factors are dependent on the

instrument and/or the X-ray wavelength and the relative sensitivity factor for each element is

unique.

𝐶𝑥 = 𝐴𝑥 𝑆𝑥⁄

∑ 𝐴𝑖 𝑆𝑖⁄𝑖 (2.18)

XPS has been used for studying the native oxide of Ga and Al in GaN and AlN as the oxygen

incorporation affect the performance of electronic devices [32–35]. XPS has also been use in

composition measurements of nitride alloys such as AlGaN and InGaN [36–39].

With the assistance of Dr. Robert Palgrave at University College London, UK, XPS

measurements were performed using a Thermo Scientific Kα instrument with a

monochromated Al Kα X-ray source. Survey scans were performed by focusing X-rays at a

Characterisation techniques

64

spot size of 400 µm with 200 eV while 50 eV was used for high resolution region scans.

Sample charging was corrected by a dual beam charge compensation system and the binding

energy scale was calibrated using Cu, Ag and Au. The detection limit of the instrument is

about 1% and the accuracy for the composition analysis is about 3% [40].

2.6 Raman spectroscopy

Inelastic scattering of light was first observed by Raman and Krishnan in 1928, however,

Raman spectroscopy was not widely used for scientific research until the invention of laser.

Raman spectrometers detect the change in polarizability of a molecule during the vibration

induced by the incident laser and have become a standard tool for chemical structure

determination. Infra-red (IR) absorption is another technique which relies on the vibrations of

the molecules but requires a change in dipole moment, therefore, Raman spectroscopy and IR

absorption have been considered as a complimentary techniques to each other as the Raman-

active vibrations are IR-inactive and vice versa [41].

When light interacts with material, the energy of photons can either be absorbed, where

electrons are excited to higher energy level, or scattered, where energy is transferred to

molecular vibrations. In the elastic scattering, also called Rayleigh scattering, only the

electron clouds of the molecule interact with the incident photons. As the energy transfer

between the electron cloud and incident photon is very small, there is no detectable change in

frequency of the photon before and after the scattering. On the other hand, in the inelastic

scattering, a large energy transfer involved in the interactions between the molecules and the

Characterisation techniques

65

incident photons, therefore, there is a notable change in frequency of the photons, which is

called the Raman shift [41–43].

The electron cloud around the nucleus or molecules are polarised (due to the electric field of

the incident laser) and electrons are promoted to an unstable virtual energy state when the

laser excites the molecule. The energy level of this virtual state is determined by the extent of

the electron polarisation, which depends on the frequency of the laser, and the lifetime of this

energy state is very short as no nuclear movement is involved [41, 42].

Figure 2.13 Changes of energy level of scattering processes.

Raman scattering can be divided into two types: Stokes and anti-Stokes scattering (Figure

2.13). Stokes scattering refers to the one when electrons are excited from a ground state to a

virtual state and then fall back to their first excited vibrational state while in anti-Stokes

scattering the electrons are excited from their first excited vibrational state and then fall back

to their ground state. The intensity of anti-Stokes scattering is generally a few orders of

Characterisation techniques

66

magnitude less than that of Stokes scattering, therefore the Raman shift normally refers to

Stokes scattering unless it is specified as anti-Stokes scattering. The Raman shift, which is the

frequency change, is determined by the energy difference between the ground state and the

vibrational states, while the energy difference is related to the mass of the atoms in the

material and the force constant of the bonds between the atoms. Raman shift are usually

presented as a wavenumber (�̅�) with a unit of cm-1

. As Raman scattering originates from the

electronic transitions, the Raman shift is temperature dependent. The intensity of Raman shift

can be calculated using Equation 2.19, where K is constant, l is the power of laser, α is the

polarisability of the electric dipole and ω is the frequency of the incident laser [42].

𝐼 = 𝐾𝑙𝛼2𝜔4 (2.19)

Different from the vibrations in molecules, the collective oscillations occurring within the

lattice are referred to as phonons in a crystal. The phonon modes can be categorised using the

direction, longitudinal (L) and transverse (T), and the frequency, acoustic (A) and optical (O).

Therefore, there are LA, TA, LO and TO modes can be induced in a crystal by the laser

excitation. As atoms are interconnected via a 3-dimensional network in a crystal, the lattice

vibrations are different in various space groups. A, B, E and T are used to denote the

relationship between the vibrations and symmetries, where A and B represent singly

degenerate vibrations along the c-axis while E represents doubly degenerate vibrations

perpendicular to the c-axis and T represents triply degenerate vibrations. Due to the

anisotropic property of phonons, the Raman peaks are dependent on the directions of the

incident and scattered light (Figure 2.14) [42, 43].

Characterisation techniques

67

Figure 2.14 (a) Phonon modes of wurtzite GaN (b) Raman spectrum of GaN at different

scanning directions [44]. © IOP Publishing. Reproduced with permission. All rights reserved.

Figure 2.15 shows the components in a Raman spectrometer. A visible laser with a particular

wavelength (532 nm or 785 nm) with a spot size of approximatedly 1 µm is directed to the

sample surface. The scattered photons are directed to a diffraction grating (600 gr/mm or

1800 gr/mm) before reaching the detector. The spectral resolution of the Raman is determined

by the distance between the grating and the detector (focal length), the groove density of the

diffraction grating and the wavelength of the laser. A high spectral resolution can be achieved

using a long focal length, a high groove density grating and a short wavelength laser.

Raman spectroscopy is easy to use as no sample preparation is required. However, some

unwanted effects may occur during the scanning. Interference could occur if there is a

fluorescence effect induced by the excited electrons; ambient temperature changes and

background radiation could affect the frequency shift; exposing the sample to the laser could

(a) (b)

Characterisation techniques

68

also lead to damage. Calibration of Raman spectroscopy is recommended to perform on daily

basis as the ambient temperature change could affect the Raman shift. The calibration can be

done by using a material with a known Raman shift, for instance Si [42, 43].

Figure 2.15 Schematic diagram of Raman spectroscopy (green line: the pathway of the laser).

2.7 Ultraviolet-visible (UV-vis) absorption and reflectance

spectrophotometry

Ultraviolet-visible (UV-vis) absorption and reflectance spectrophotometry are commonly

used to investigate the optical properties of semiconductors including the band gap and

refractive index. The absorption and reflectance measurements are complementary to each

Characterisation techniques

69

other as they correspond to the two aspects of light-matter interactions. The light source for

both the absorption and reflectance measurements can generate light with a range of

wavelengths from 190 nm to 1200 nm. The energy of an electromagnetic wave can be

calculated using Equation 2.20, where E is the energy in eV (1 eV = 1.602 × 10−19 J), h is

the Planck’s constant (6.626 × 10−34 Js), c is the speed of light (3 × 108 ms-1

) and λ is the

wavelength of the light in nm. Therefore, the energy range that UV-vis spectrophotometry can

measure is between 6.53 eV to 1.55 eV [45].

𝐸 = ℎ𝑐

𝜆 (2.20)

For absorption spectrophotometry, the detector measures the transmittance (T) which is

plotted against the wavelength of the light or the photon energy. Transmittance can be

converted directly to absorbance by Equation 2.21. By taking the thickness of the film into

account, the absorption coefficient (α, eVcm-1

) as a function of energy can be obtained and

the optical band gap can be extracted from the Tauc plot [46–48]. Equation 2.22 shows the

relationship between the absorption coefficient and band gap (Eg), where n = ½ and 2 for

direct and indirect optical transitions respectively. By extrapolating the linear region in the

Tauc plot, the x-intercept can be found which gives the band gap of the materials.

𝐴𝑏𝑠 = log (1

𝑇)

(2.21)

𝛼ℎ𝑣 = 𝐴(ℎ𝑣 − 𝐸𝑔)𝑛

(2.22)

For the reflectance measurement, the light shines perpendicularly onto the sample surface,

while the detectors are located surrounding the light source, measuring the reflected light near

Characterisation techniques

70

the surface normal. Similar to the transmittance curve, the reflectance is plotted against the

wavelength of light. The instrument software used the Cauchy equation (Equation 2.23, where

n is refractive index, λ is the wavelength of light, A, B and C are material constants) and

Kramers-Kronig relationship (Equation 2.24a and b, where 𝜀𝑟′ and 𝜀𝑟

′′ are the real and

imaginary parts of the relative permittivity of the material respectively, ω is the frequency, ω’

is the integration variable and P is the Cauchy principle value) [49] to simulate the reflectance

curve by varying the refractive index, extinction coefficient, thickness and surface roughness

and the set of parameters that yield the best match with the experimental curve by least square

fitting is considered to be the result [50]. Although, UV-vis reflectance measurements are

commonly used for measuring thin film thicknesses (using the theoretical materials optical

constants), it was used to measure the refractive index of the films in this project. One

advantage that UV-vis reflectance measurements have over absorption measurements is that

they can be used for measuring films grown on any substrate whereas the absorption

measurement requires a transparent substrate, which limits its application to those films with

Si substrates.

𝑛 = 𝐴 + 𝐵

𝜆2+ 𝐶

𝜆4

(2.23)

𝜀𝑟′(𝜔) = 1 +

2

𝜋 𝑃 ∫

𝜔′𝜀𝑟′′(𝜔′)

𝜔′2 − 𝜔2𝑑𝜔′

∞

0

(2.24a)

𝜀𝑟′′(𝜔) = −

2𝜔

𝜋 𝑃 ∫

𝜀𝑟′(𝜔′)

𝜔′2 − 𝜔2𝑑𝜔′

∞

0

(2.24b)

In this project, an Agilent Technologies Cary 5000 Uv-Vis-NIR spectrophotometer was used

for the UV-vis absorption measurement and a Filmetrics F20-UV was used for reflectance

measurement. Both the absorption and reflectance measurements were carried out at room

Characterisation techniques

71

temperature and the photon wavelength range varied from 200 nm to 800 nm. For the UV-vis

absorption, the baseline correction was done by setting the transmittance of the bare sapphire

substrate to be 100% while a black plate was used to block the beam for the zero correction.

The background calibration for UV-vis reflectance was done by allowing the light to shine

onto the black specimen stage, while a Si substrate was used for reference measurements.

Characterisation techniques

72

2.8 Reference

[1] G. Binning, C. F. Quate and Ch. Gerber, Phys. Rev. Lett. 56, 930 (1986)

[2] G. Binning, H. Rohrer, Ch. Gerber and E. Weibel, Phys. Rev. Lett. 49, 57 (1982)

[3] P. Eaton and P. West, Atomic Force Microscopy (Oxford University Press, United States,

2010) p.9 – 48

[4] Innova AFM Manual, Veeco Metrology, Inc., 112 Robin Hill Rd., Santa Barbara, CA

93117

[5] I. Horcas, R. Fernandez, J. M. Gomez-Rodriguez, J. Colchero, J. Gomez-Herrero and A.

M. Baro, Rev. Sci. Instrum. 78, 013705 (2007)

[6] P. Klapetek, D. Necas and C. Anderson, Gwyddion user guide (2016), http://gwyddion.net

[7] D. Brandon and W. D. Kaplan, Microstructural Characterisation of Materials, 2nd

edition

(John Wiley & Sons Ltd., England, 2011) p.55-90

[8] M. A. Moram and M. E. Vickers, Rep. Prog. Phys. 72, 036502 (2009)

[9] D. B. Williams and C. B. Carter, Transmission Electron Microscopy A Textbook for

Materials Science (Springer, USA, 2009) Ch. 10

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Materials Science (Springer, USA, 2009) Ch. 5

[11] D. B. Williams and C. B. Carter, Transmission Electron Microscopy A Textbook for

Materials Science (Springer, USA, 2009) Ch. 9

[12] D. B. Williams and C. B. Carter, Transmission Electron Microscopy A Textbook for

Materials Science (Springer, USA, 2009) Ch. 6 and Ch. 9

[13] S. J. Pennycook, A. R. Lupini, M. Varela, A. Y. Borisevich, Y. Peng, M. P. Oxley, K. van

Benthem and M. F. Chisholm, Scanning Microscopy for Nanotechnology Techniques and

Applications (Springer, United States, 2006) Ch. 6

[14] A. Bleloch and A. Lupini, Mater. Today 7, 42 (2004)

[15] C. Hetherington, Mater. Today 7, 50 (2004)

[16] F. Zemlin, Ultramicroscopy 4, 21 (1979)

[17] D. B. Williams and C. B. Carter, Transmission Electron Microscopy A Textbook for

Materials Science (Springer, USA, 2009) Ch. 12

[18] D. B. Williams and C. B. Carter, Transmission Electron Microscopy A Textbook for

Materials Science (Springer, USA, 2009) Ch. 1

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73

[19] D. B. Williams and C. B. Carter, Transmission Electron Microscopy A Textbook for

Materials Science (Springer, USA, 2009) Ch. 13 and Ch. 27

[20] P. Ansell and M. Dixon, Why STEM Not TEM?,

http://www.spectral.se/spectral.nsf/f164f3e9b82f0febc1256dcc004611c1/d4a98a973f4e02

90c12571e300376e06/$FILE/208%20Why%20STEM%20Not%20TEM.pdf

[21] L. C. Feldman and J. W. Mayer, Fundamentals of Surface and Thin Film Analysis (North-

Holland, United States, 1986) Ch.2

[22] L. C. Feldman and J. W. Mayer, Fundamentals of Surface and Thin Film Analysis (North-

Holland, United States, 1986) Ch.3

[23] Rutherford Backscattering Spectrometry, Philips Innovation Services, Technical note 6,

October 2013, http://www.innovationservices.philips.com/sites/default/files/materials-

analysis-rbs_0.pdf

[24] V. Havranek, V. Hnatowicz, J. Kvitek and V. Perina, Nucl. Instrum. Meth. Phys. Res. B

72, 224 (1992)

[25] G. D. Alton, Nucl. Instr. Meth. Phys. Res. B 73 221 (1993)

[26] M. Jaksic, F. Paszti, A. Kotai and S. Fazinic, Instrumentation for PIXE and RBS IAEA-

TECDOC-1190 (International Atomic Enegy Agency, Austria, 2000)

[27] N. P. Barradas, E. Alves, C. Jeynes and M. Tosaki, Nucl. Instrum. Methods Phys. Res. B

247, 381 (2006)

[28] N. P. Barradas, E. Alves, S. Pereira and I. M. Watson, Nucl. Instrum. Meth. Phys. Res. B

266, 1402 (2008)

[29] J. F. Watts and J. Wolstenholme, An introduction to surface analysis by XPS and AES

(John Wiley & Sons Ltd., England, 2003)

[30] C.D. Wagner, W. M. Riggs, L. E. Davis. J. F. Moulder and G. E. Muilenberg, Handbook

of X-ray photoelectron spectroscopy (Perkin-Elmer Corporation, USA, 1979)

[31] M. O. Krause and J. H. Oliver, J. Phys. Chem. Ref. Data 8, 329 (1979)

[32] W. Wei, Z. Qin, S. Fan, Z. Li, K. Shi, Q. Zhu and G. Zhang, Nanoscale Res. Lett. 7, 562

(2012)

[33] K. Prabhakaran, T. G. Andersson and K. Nozawa, Appl. Phys. Lett. 69, 3212 (1996)

[34] N. Shiozaki, T. Sato and T. Hashizume, Jpn. J. Appl. Phys. 46 1471 (2007)

[35] D. Li, M. Sumiya, S. Fuke, D. Yang, D. Que, Y. Suzuki and Y. Fukuda, J. Appl. Phys. 90,

4219 (2001)

[36] T. Hashizume, S. Ootomo, S. Oyama, M. Konishi and H. Hasegawa, J. Vac. Sci. Techol. B

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19, 1675 (2001)

[37] J. Kotani, M. Kaneko, H. Hasegawa and T. Hashizume, J. Vac. Sci. Techol. B 24, 2148

(2006)

[38] R. A. Oliver, M. J. Kappers, C. J. Humphreys and G. A. D. Briggs. J. Appl. Phys. 97,

013707 (2005)

[39] T. D. Veal, P. H. Jeffereson, L. F. J. Piper, C. F. McConville, T. B. Joyce, P. R. Chalker,

L. Considine, H. Liu and W. J. Schaff, Appl. Phys. Lett. 89, 202110 (2006)

[40] R. Palgrave (private communication, 2015)

[41] J. R. Ferraro, K. Nakamoto and C. W. Brown, Introductory Raman Spectroscopy, 2nd

Edition (Elsevier, USA, 2003) Ch. 1

[42] P. Vandenabeele, Practical Raman spectroscopy: an introduction (John Wiley & Sons,

Ltd., United Kingdom, 2013)

[43] E. Smith and G. Dent, Modern Raman spectroscopy: a practical approach (John Wiley &

Sons, Ltd., United Kingdom, 2005)

[44] H. Harima, J. Phys: Condens. Matter 14, R967 (2002)

[45] T. Owen, Fundamentals of modern UV-Visible spectroscopy (Agilent Technologies,

Germany, 2000)

[46] J. Tauc, R. Grigorovici and A. Vancu, phys. stat. sol. 15, 627 (1966)

[47] J. Tauc, Mat. Res. Bull. 3, 37 (1968)

[48] E. A. Davis and N. F. Mott, Philos. Mag. 22, 903 (1970)

[49] S. Kasap, C. Koughia, J. Singh, H. Ruda and S. O’Leary, Springer Handbook of

Electronic and Photonic Materials (Springer, USA, 2006) Ch. 3

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75

Chapter 3

Composition analysis of ScxGa1-xN thin films

Composition measurement of ternary alloys is crucial, as the physical properties, for instance

optical band gap and piezoelectric coefficient, usually vary as a function of the composition

[1–5]. However, no exact composition determination can be carried out during the growth in

the MBE chamber, where it is only possible to make indirect measurements indicating the

approximate metal fluxes. Therefore, ex-situ composition measurement after growth is

required. In this chapter, four different composition measurement approaches are evaluated

and compared so as to determine a suitable method for ScxGa1-xN films.

3.1 Rutherford backscattering spectrometry (RBS)*

RBS is established as a measurement technique for bulk materials which can provide the

average composition up to a depth of about 2 µm and can also provide depth-dependent

composition measurements when combined with modelling approaches [6, 7]. RBS is well

established as a thin film composition measurement technique, especially for III-V materials,

for which it can provide highly accurate measurements with only around 1% error [6, 8–11]

* RBS measurements and analysis were carried out with the assistance of Dr. Nuno Pessoa Barradas, Dr.

Eduardo Alves and Dr. Sergio Pereira at the C2TN - Centro de Ciências e Tecnologias Nucleares, Universidade

de Lisboa, Portugal.

Composition analysis of ScxGa1-xN thin films

76

and detection limits ranging from 1015

atoms/cm2 for light elements such as carbon, nitrogen

and oxygen to 1010

atoms/cm2 for heavy elements such as gold and lead [12, 13]. Moreover, it

does not require standard references and only the ratio between the elements is used for

calculating the composition of the sample, thus the measurement error can be cancelled out:

RBS data is considered as the composition reference in this study [12, 13]. However, as RBS

is not sensitive to light elements, it cannot detect light impurities or anion vacancies in III-

nitrides effectively, therefore other techniques, for instance XPS, SIMS, ERDA or

photoluminescence are required for such analysis.

Figure 3.1 RBS spectra for ScxGa1-xN grown on a MOVPE AlN buffer layer (a) x = 0; (b) x =

0.08; (c) x = 0.15; (d) x = 0.26.

Typical RBS spectra are shown in Figure 3.1. The yield of the backscattering ion is

determined by the scattering cross section and it is proportional to the square of the atomic

number (Z) of target elements, thus RBS is most sensitive to heavy elements. The scattering

(a) (b)

(c) (d)

Composition analysis of ScxGa1-xN thin films

77

cross section of Ga is about 2.2 times larger than that of Sc, this means that Ga is more likely

to scatter the incoming beam of He ions, therefore the peak at the higher energy end (higher

channel numbers) comes from Ga and the peak at the lower energy end comes from Sc [14].

Sc flux (nA) x (Sc content) Film thickness (nm) TEM measured film thickness (nm) Thickness difference (%)

0 0 536 ± 11 582 ± 3 7.90

1 0.078 206 ± 4 207 ± 2 0.48

2 0.146 210 ± 4 214 ± 1 1.87

3 0.178 215 ± 4 213 ± 1 0.94

4 0.258 235 ± 5 228 ± 1 3.07

Table 3.1 RBS measurement of Sc content and film thickness for ScxGa1-xN

By considering the stopping cross section of each constituent and measuring the height and

the width of the peaks, the composition and the thickness of layers can be calculated. The

stopping cross section is the energy loss of the incident He ion in each atomic layer of the film,

therefore the thickness of the films can also be calculated from the width of the peak. A

simulation is also generally performed to improve the accuracy of the obtained composition

values and thicknesses. The calculated stopping power of GaN and ScN are 45.32 eV Å-1

and

18.58 eV Å-1

respectively for 2 MeV 4He ions [15, 16]. (Note that the density input for

calculation for GaN and ScN are 8.85 × 1022

atoms cm-3

and 3.748 × 1022

atoms cm-3

respectively). For instance, the Ga peak in the Figure 3.1a is wider than those in Figure 3.1b–

d suggesting that the He ions lose more energy within the layer, and therefore indicating a

thicker film. The film thicknesses calculated from the RBS spectra for ScxGa1-xN are in good

agreement with the values measured from TEM (within 4%), and only in slightly poorer

agreement for GaN (within 8%). The values are consistent within experimental uncertainty,

which arises mostly from uncertainty in measuring thicknesses accurately from TEM images

(this depends on the calibration of the instrument and the tilt angle of the TEM specimen with

respect to the electron beam) [17] (Table 3.1). Moreover, uncertainty may also arise in the

Composition analysis of ScxGa1-xN thin films

78

RBS measurements if the sample is slightly misaligned in the RBS analysis chamber and that

small angle is not taken into account when carrying out the calculation.

Under the growth conditions used to produce these samples, the Sc flux measured in the

growth chamber appears to have a linear relationship with the composition of ScxGa1-xN

(Figure 3.2). This suggests that the flux value provides a reliable indicator of the resulting

film composition with Equation 3.1. Though this relationship may not be applicable for other

growth instruments, a standard can be easily established with some calibrations.

𝑥 (Sc content) = 0.0645 × Sc flux (3.1)

Figure 3.2 The relationship between Sc content measured by RBS and Sc flux measured in

the MBE chamber before growth.

Composition analysis of ScxGa1-xN thin films

79

3.2 X-ray photoelectron spectroscopy (XPS)†

XPS is another direct composition measurement technique; it is highly surface sensitive and

almost all the signal comes from the top 10 nm of the sample surface. In addition, it is

sensitive to light elements and provides the information on the chemical bonding state of each

element, therefore XPS can be used to assess the impurity concentration in the films (if these

are present at concentrations above the detection limit, which is between 1 at% and 0.1 at%

[18, 19]) as well as for composition determination. Since XPS is very surface sensitive,

impurities, such as oils, carbon dioxide and water vapour adsorb on the sample surface when

the specimen is exposed in air and could potentially affect the composition measurement.

Therefore, the scan area was sputtered using an ion gun for 30 s in order to clean the sample

surface and ensure the acquired spectra come only from the sample instead of from the sample

plus the surface impurities.

A typical XPS survey spectrum for ScxGa1-xN is shown in Figure 3.3. The survey scan (with 1

eV energy resolution) gives an overall indication of the elements present in the sample being

analysed, however, it is not sufficient for composition calculations as some of peaks cannot be

resolved, for example the boxed area in Figure 3.3, where the Sc 2p, N 1s and Ga Auger

peaks appear within a range of just 10 eV, therefore higher resolution scans (with 0.1 eV

energy resolution) are required. It is known that Auger peaks of some elements appear in XPS

spectra, and some of them interfere with the XPS peaks and make the analysis more difficult.

In the case of ScxGa1-xN, the Ga Auger peaks overlap with the N 1s XPS peak.

† XPS measurements were carried out with the assistance of Dr. Robert Palgrave at the Department of Chemistry,

University College London, UK.

Composition analysis of ScxGa1-xN thin films

80

Figure 3.3 XPS spectrum for ScxGa1-xN (x = 0.26) grown on MOVPE AlN (upper right inset:

enlarged from the boxed area; dotted vertical lines: theoretical Auger peak positions; solid

vertical lines: theoretical XPS peak positions).

Concerns have been raised in the literature that impurities such as fluorine (frequently present

in the Sc metal used for evaporation due to the metal refining process) may be incorporated in

the ScxGa1-xN films at levels up to several %, affecting its physical properties [20–22].

However, no F 1s peak was observed from the XPS spectra and there is no detectable fluorine

in the Sc metal according to the supplier. Oxygen (O) is also a possible impurity as it is

known that ScN often suffers from oxygen contamination which arises during film deposition

due to the high reactivity of Sc with background water vapour in the deposition chamber [22,

23]. In order to investigate the oxygen concentration, a MOCVD Si-doped GaN film was used

as a reference sample for XPS analysis. No oxygen incorporation was found using the

secondary ion mass spectroscopy (SIMS) analysis performed on a sample grown in the same

chamber and under the same conditions [24, 25], where the detection limits of SIMS is about

ppm [26]. As shown in Figure 3.4, the O 1s peak from the reference sample disappeared from

the spectrum after 60 s of ion etching, indicating that the O 1s peak in the spectra taken at 30 s

Composition analysis of ScxGa1-xN thin films

81

and 60 s of etching most likely originated from the re-adsorption of the etched surface

impurities or the residual water vapour in the analysis chamber. The same depth profiling

analysis was performed on the both GaN and ScxGa1-xN samples with MOCVD Si-doped GaN

buffer layer and similar spectra were observed for all as-received, 30 s etched and 60 s etched

steps. The O 1s peak intensities from the spectra are similar to that of the reference MOCVD

Si-doped GaN, therefore, it can be concluded that there is no detectable oxygen is

incorporated in the ScxGa1-xN films during film growth under these conditions. Moreover,

there is no observable peak at the theoretical position for the Auger peaks of C, O and F

(dotted vertical lines in Figure 3.3), this confirms that the levels of these impurities in the

films are below the detection limits for XPS under these analysis conditions.

Figure 3.4 Depth profiling of (a) MOCVD Si-doped GaN; (b) GaN on MOCVD Si-doped

GaN and (c) ScxGa1-xN (x = 0.18) grown on MOCVD Si-doped GaN.

To assess the oxygen incorporation level further, the positions of the Ga 3d and Sc 2p peaks

were investigated (Figure 3.5). The Ga 3d peak is at 19.4 eV, which is close to the literature

value of Ga–N 19.8 eV [27] whereas binding energy of Ga–O is about 20.5 eV [27, 28]. On

the other hand, the Sc 2p3/2 position is at 400 eV, which is close to the literature value of Sc–

(a) (b) (c)

Composition analysis of ScxGa1-xN thin films

82

N 400.4 eV [29] whereas binding energy of Sc–O is about 401.71 eV [30]. (Note that the XPS

values in the literatures were calibrated using the Cu, Ag and Au, which are as same as we did

in our experiment.) This is consistent with the previous finding that oxygen incorporation in

the ScxGa1-xN films is below the detection limit for XPS.

Figure 3.5 XPS (a) Ga 3d and (b) Sc 2p spectra for ScxGa1-xN grown on MOVPE AlN.

Furthermore, there is no significant shift for Ga 3d and Sc 2p3/2 peak positions whereas the N

1s peak position shows a trend of about 2 eV towards decreasing energy as the Sc content

increases (Figure 3.6a–c). The slight shift to lower binding energy for the Ga 3d and Sc 2p

peaks consistent with the nitridation of Ga and Sc [31, 32] as is the shift in N 1s peak position

given that the lower binding energy in N 1s peak is expected given the lower binding energies

of the metal-N bond [33]. By integrating the area of each constituent peak, the ratio of Sc and

Ga can be determined and the results are shown in Figure 3.6d. Nearly all the Sc

concentrations measured by XPS are below the RBS values. When comparing the XPS and

RBS measurement data for samples of ScxGa1-xN on MOVPE AlN, it can be seen that XPS

(a) (b)

Composition analysis of ScxGa1-xN thin films

83

consistently underestimates the Sc content by 5–8%. This can be attributed to the high surface

sensitivity of XPS, with sample depth < 10 nm, combined with the fact that the ion sputtering

is expected to remove the Sc and N faster than Ga from the surface (bond energy of ScN 6.72

eV/atom [34] is lower than that of GaN 8.92 eV/atom [35, 36]). The lower Sc content may

indicate a more Ga-rich surface compared to the bulk RBS measurement [37]. Moreover, the

Ga LMM auger peaks interfere with the N 1s photoelectron spectrum (Figure 3.5) [38, 39],

which leads to overestimation of N concentration and therefore apparent lower Sc content

[37].

Figure 3.6 XPS peak position for (a) Ga 3d; (b) Sc 2p3/2 and (c) N 1s peaks; (d) Sc content

variations with Sc flux for ScxGa1-xN grown on different GaN and AlN buffer layers (dotted

line in (d) indicates the linear relationship between RBS values and Sc flux).

(a) (b)

(c)

(d)

Composition analysis of ScxGa1-xN thin films

84

However, the Sc content measured by XPS varied slightly at the same Sc flux for the samples

with different buffer layers. For instance, at a fixed Sc flux of 1 nA, the Sc contents x are 0.06,

0.04 and 0.02 for samples with buffer layers of MBE GaN, MOVPE GaN and MOVPE AlN

respectively. This effect became more pronounced as Sc flux was increased to 4 nA where the

Sc content measured by XPS are 0.31, 0.27 and 0.21 respectively. This effect may be

explained as follows. MOVPE-grown GaN and AlN are typically Ga-polar, whereas MBE-

grown GaN is typically N-polar [40]. If the ScxGa1-xN films inherit the polarity of the buffer

layers, then this is likely to affect the degree of Sc incorporation during the growth, as

differences in surface energetics are already known to affect the relative incorporation rates of

impurities into GaN [41–43]. Unfortunately it is not possible to determine the polarity of the

ScxGa1-xN films directly using conventional etching techniques, due to the high etching rates

associated with the presence of Sc. Additionally, the strain state of III-nitride alloy films is

known to affect the relative incorporation rates of the different metals during growth.

Generally, compressive film stress tends to reduce the relative incorporation rates of the larger

metal atoms [44]. This effect may explain the difference in Sc content between ScxGa1-xN

films grown on MOVPE GaN and MOVPE AlN buffer layers, in which lower Sc

incorporation is found for ScxGa1-xN films grown on MOVPE AlN buffer layers, which have a

smaller in-plane lattice parameter compared to GaN and which would therefore be expected to

produce greater tensile stress in these films (although it is not possible to determine the degree

of strain relaxation in these films a priori). This effect may be further enhanced for ScxGa1-xN

than for InxGa1-xN, as a much greater expansion of the in-plane a lattice parameter is expected

as a function of increasing Sc content in ScxGa1-xN compared to that found for increasing In

content in InxGa1-xN, due to the ‘flattening’ of the wurtzite unit cell with increasing Sc content

in ScxGa1-xN.

Composition analysis of ScxGa1-xN thin films

85

3.3 Composition determination from lattice parameters and c/a

ratio measurements

X-ray diffraction is a standard technique for crystal quality and lattice parameter

measurements for thin films. The measured a and c lattice parameters of III-nitrides are highly

affected by residual stain, concentration and size of impurities along with the calibration of

the diffractometer and measurement conditions, therefore a wide range of value lattice

parameters have been reported for III-nitrides. Nevertheless, a small measurement error of

0.0002% can be achieved by following a method summarised in Ref. [45]. As lattice

parameters measurements are commonly used as an indicator of the composition of ternary

III-nitride alloys [46–48], for reference, we also assess its use for ScxGa1-xN alloys.

Since the c lattice parameters of ScxGa1-xN across the composition range used here are very

close to that of GaN, the 0004 peaks of ScxGa1-xN for the samples with MBE GaN and

MOVPE GaN buffer layers cannot be distinguished from the 0004 peaks of the GaN buffer

layers (Figure 3.7). The 0004 peaks of ScxGa1-xN can be observed more easily for the films

grown on an AlN buffer layer, where the ScxGa1-xN peak shifts slightly to the higher angle,

indicating a decrease in c lattice parameter as Sc content increases to x = 0.26 (Figure 3.8, red

lines). However, this is in contrast to the theoretical prediction that the c lattice parameter

increases as the Sc content increases up to x = 0.3, suggesting either that Sc introduces a

greater distortion away from the standard wurtzite crystal structure than predicted, or that

defects are introduced which reduce the c/a lattice parameter ratio. On the other hand, the

measured a lattice parameter increases as the Sc content increases, which matches with the

predicted trend. However, the measured a values are generally lower than the theoretical

calculations. This is most likely due to the influence of in-plane compressive strain induced in

Composition analysis of ScxGa1-xN thin films

86

the ScxGa1-xN by the underlying GaN, which has a smaller a lattice parameter (Figure 3.8,

blue lines). The degree of relaxation of this in-plance strain cannot be determined, but is

likely to be greater at higher Sc contents where a lattice parameter mismatch is greater. The

change in the a lattice parameter is greater than that of the c lattice parameter, due to the bond

angle distortion in the wurtzite structure induced by the incorporation of Sc into GaN [49].

Figure 3.7 XRD diffractograms of the 0004 reflection for (a) ScxGa1-xN on MBE GaN; (b)

ScxGa1-xN on MOVPE GaN; (c) ScxGa1-xN on MOVPE AlN.

Figure 3.8 (a) Lattice parameter c and a of ScxGa1-xN grown on MOVPE AlN.

(a) (b) (c)

Composition analysis of ScxGa1-xN thin films

87

Vegard’s law (previously used for composition determination in III-nitride alloys [50, 51])

does not apply for ScxGa1-xN in which the c/a ratio changes as a function of composition [47].

Furthermore, since there is no bulk ‘standard’ reference lattice parameters for ScxGa1-xN, the

experimental data must be compared to theoretical predictions in order to estimate the Sc

content using the c lattice parameter. However, although the theoretical calculations

considered a quasi-random structure [47], the microstructure and defect density of the film

were not taken into account and this may lead to the difference between the predicted and

measured trends. Therefore, it is not possible to use the measured ScxGa1-xN c lattice

parameter to determine film compositions.

However, the c/a lattice parameter ratio can also be determined using the selected area

diffraction patterns from both the < 011̅0 > and < 2̅110 > ScxGa1-xN zone axis (Figure

3.9a). Since only the ratio is measured (not the absolute lattice parameter values) then the

measurements are free from any errors in the calibration of the magnification in the TEM and

are affected only by the measurement errors inherent in determining the centre of the

diffraction spots in the diffraction pattern. The average c/a ratio for buffer layers MBE GaN,

MOVPE GaN and MOVPE AlN are 1.632 ± 0.006, 1.634 ± 0.004 and 1.602 ± 0.002

respectively. The ratios for GaN are slightly higher than the literature values while the ratio

for AlN is comparable to the literature values [45].

It is clear that the c/a ratio decreases as Sc content increases, which is consistent with the

XRD measurement and the simulation data [47], where the variation in the a lattice parameter

is greater than that for the c lattice parameter. However, the c/a ratio of ScxGa1-xN grown on

MBE GaN and MOVPE GaN are lower than that of ScxGa1-xN grown on MOVPE AlN

(Figure 3.9b, green diamonds). This is consistent with a greater degree of relaxation of the

Composition analysis of ScxGa1-xN thin films

88

residual compressive strains in the ScxGa1-xN grown on MOVPE AlN compared to the other

two series of films and therefore also with the fact that the Sc content estimated from the c/a

ratio for this series of films are closest to those determined from the RBS measurement.

Figure 3.9 (a) c/a ratio of ScxGa1-xN measured by experiment and predicted by theory; (b) Sc

content variations with Sc flux (obtained by matching the measured c/a ratio to the trend

obtained from theory [47]).

Moreover, the measured c/a ratio deviates more from the predicted trend when x > 0.15,

resulting in an overestimation of the Sc content when that is calculated by fitting the

measured c/a ratio to the theoretical predictions (Figure 3.9b). This again may be due to the

lattice mismatch strain and/or the differences in thermal contraction between the different

layers that arise after the cooling from the growth temperature. The thicknesses of all ScxGa1-

xN films are about 200 nm, which is larger than the predicted critical thickness for strain

relaxation [52], therefore the lattice mismatch strain should in theory be relaxed: the increase

in a lattice parameter as Sc content increases does indicate some strain relaxation. However, it

is not possible to tell whether the strain has relaxed completely due to uncertainty in the cause

of the deviation in the c/a ratio compared to predictions. Therefore it is not possible to

perform corrections to improve the accuracy of this estimation.

(a) (b)

Composition analysis of ScxGa1-xN thin films

89

3.4 Scanning transmission electron microscopy (STEM)

The RBS and XPS spectra are obtained from relatively large measurement areas of 4 mm2 and

0.16 mm2 respectively, therefore, they are not sensitive to any nanoscale phase separation that

might be present. On the other hand, transmission electron microscopy (TEM) allows the

defect microstructure of the film to be imaged and by operating the scanning TEM (STEM)

mode with a high angle annular dark field (HAADF) detector, images with Z contrast can be

obtained. Although the contrast in STEM-HAADF images is affected by the strain fields

around crystallographic defects and by variations in the total thickness of the specimen,

contrast due to these effects can be identified by comparing the STEM-HAADF images with

the corresponding dark field images (revealing the defect microstructure) and by assessing the

specimen thickness effects on the diffraction patterns obtained from difference areas of the

film. Any remaining contrast can then be assigned to compositional differences. Following

this approach, the contrast in Figure 3.10 can be assigned to strain contrast and specimen

thickness variations. Therefore we conclude that the ScxGa1-xN films are compositionally

homogeneous without evidence for any phase separation at length scales exceeding about 10

nm (the approximate detection limit from these images).

N. B. An energy dispersive X-ray (EDX) detector is commonly attached to a TEM, providing

a convenient option for the analysis of the chemical composition of the TEM specimen.

However, as all the specimens in this study were prepared using mechanical grinding and ion

milling, the X-ray signals from carbon and copper (contaminations from the ion milling

process) often dominate the spectrum and reduce the already limited accuracy of

compositions determined from EDX spectra. Futhermore, accurate EDX analysis would

requires standard TEM speciments of known composition and thickness, which are not

Composition analysis of ScxGa1-xN thin films

90

available for this material system. Nevertheless, EDX in the TEM does offer site specific

composition analysis of the specimen, which is helpful for indicating large compositional

differences between two phases (as shown in Section 4.5). Electron energy loss spectroscopy

(EELS) is another option for elemental analysis in TEM. However, the energy of the K edge

of N (401 eV) and L2 and L3 edges of Sc (407 eV and 402 eV respectively) are very close [53],

it is not possible to distinguish them from each other experimentally. Therefore, although

EDX and EELS were available in JEOL 2100 TEM, they were not used to measure the film

compositions in this study. Secondary ion mass spectroscopy (SIMS) is known for the very

high accuracy with which it can achieve elemental analysis. However, a series of reference

samples of known concentration is required for calculating the composition, as matrix effects

may affect the analysis significantly [54]. Therefore, SIMS was also not chosen as one of the

techniques in this study.

Figure 3.10 (a) Cross-section TEM image of ScxGa1-xN (x = 0.26) on AlN (insert: selected

area diffraction pattern at < 112̅0 > zone axis) and (b) corresponding STEM HAADF image.

(a) (b)

Composition analysis of ScxGa1-xN thin films

91

3.5 Conclusions

Figure 3.11 summarises the composition measurement results using different techniques. A

linear relationship is found between the Sc flux and Sc content determined by RBS

(considered as the reference technique due to its high accuracy). Therefore, the Sc flux

provides a reasonable estimation of the amount Sc incorporated during the growth of ScxGa1-

xN films. XPS analysis is found to produce x composition values which are 5–8% lower than

values from RBS. On the other hand, though a rough trend in the correct direction is observed

from both the lattice parameters and c/a ratio as a function of Sc content, the film composition

cannot be estimated from them accurately due to the uncertainty in the strain state of the

ScxGa1-xN films, the uncertainty in the effect that the defect microstructure may have on the

c/a ratio of the ScxGa1-xN films and the lack of accurate experimentally determined reference

lattice parameters for ScxGa1-xN combined with uncertainty in the accuracy of the reference

values obtained from calculations of Ref. [47].

Figure 3.11 The relationship between the Sc flux and Sc content in ScxGa1-xN films grown on

MOVPE AlN as measured by different techniques.

Composition analysis of ScxGa1-xN thin films

92

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95

Chapter 4

Growth and microstructure of ScxGa1-xN thin

films

ScxGa1-xN has been produced using sputtering and molecular beam epitaxy (MBE) with

plasma–assisted N2 or NH3 as a nitrogen source [1–3]. The growth regimes have been

investigated by Constantin et al. [2], and it was determined that the wurtzite phase of ScxGa1-

xN can be maintained up to x = 0.17. However, in theory, the Sc content could go up to 0.27

for the wurtzite phase according to the calculations by S. Zhang et al. [4]. Moreover, despite

the fact that a smooth surface can best be achieved for GaN using metal-rich growth

conditions, all the reported ScxGa1-xN films were grown under N-rich conditions. Therefore,

the effects of metal-rich growth conditions for ScxGa1-xN were investigated and the results are

presented and discussed in this chapter.

4.1 Metal-rich growth conditions for GaN

Prior to the growth of ScxGa1-xN, the parameters required to provide metal-rich growth

conditions have to be determined for GaN, which can be done by measuring the film growth

rate and correlating this with the surface morphology. Given a fixed supply rate of active

nitrogen to the growth surface, the growth rate will increase as the metal flux increases, and

Growth and microstructure of ScxGa1-xN thin films

96

then saturate once metal-rich conditions are reached. In contrast, under N-rich conditions, the

growth rate will continue to increase as the metal flux increases (Figure 4.1a). In addition, the

surface morphology of a GaN film is highly affected by the growth conditions, where a flat

surface can be obtained under the metal-rich conditions whereas the N-rich conditions

produce a rough surface. There is some evidence to suggest that N-rich conditions provide a

higher diffusion barrier for the Ga adatoms at the surface of an (0001)-oriented film, leading

to an energetically unstable (0001) surface which then leads to roughening (i.e. reducing the

total surface energy by exposing different crystallographic planes with lower surface energies

per unit area) [5, 6]. Figure 4.1 shows AFM images of GaN films grown under metal-rich and

N-rich conditions and it is clear that a relatively smooth surface is produced under metal-rich

conditions while N-rich conditions lead to higher roughnesses. These experiments helped to

establish the growth parameters for metal-rich and N-rich conditions in our MBE equipment.

Starting with the known growth parameters (growth temperature, Ga flux, chamber pressure

and N2 plasma power) for metal-rich conditions for GaN growth, the ScxGa1-xN films were

then grown by adding the Sc flux to the metal-rich condition for GaN.

Growth and microstructure of ScxGa1-xN thin films

97

Figure 4.1 (a) Growth rate of GaN films and 1 x 1 m AFM images of GaN films grown

under (b) N-rich and (c) metal-rich conditions. All images were processed using parabolic

flattening.

4.2 Growth rate

The growth rate is expected to be limited by the supply of active N under metal-rich

conditions, which means the growth rate should be constant, remaining independent of the

total metal flux (Ga and Sc). However, the ScxGa1-xN film growth rate increased as the Sc flux

increased and was 15%–30% higher than that of GaN grown under metal-rich conditions

(Figure 4.2a). This increased growth rate can be attributed to the catalytic decomposition of

N2 by Sc, which has been reported previously for the case of ScN growth. ScN films can be

(b) (c)

(a)

Growth and microstructure of ScxGa1-xN thin films

98

grown directly from N2, without using a N2 plasma source [7], whereas a plasma source is

necessary for GaN growth, due to the insufficient reactivity of N2 with Ga [8]. This catalytic

effect has been confirmed in our reactor by growing pure ScN under the comparable

conditions that used for ScxGa1-xN growth, without switching on the N2 plasma source (Figure

4.2b). As a result, this catalytic effect leads to uncertainty regarding the true metal-to-nitrogen

ratio at the growth surface, as it suggests that additional active nitrogen has become available,

alongside the increased total metal flux. Therefore additional evidence is needed to determine

whether the films were grown in the metal-rich or nitrogen-rich growth regime.

On the other hand, the growth rate of GaN on both MBE GaN and MOVPE AlN buffer layers

are close with a difference of 20 nm hr-1

, however, as Sc content increases, the growth of

ScxGa1-xN on MBE GaN is constantly 100 nm hr-1

faster than that grown on MOVPE AlN.

This discrepancy in growth rate indicates that there is a slightly influence of the buffer layers

materials on the growth rate of ScxGa1-xN. The growth rates for N-polar GaN (typical for

MBE-grown GaN) are higher than for Ga-polar GaN (MOVPE-grown GaN and AlN) [9].

Furthermore, although the growth conditions including the N plasma power, N2 chamber

pressure, effusion cell temperatures are kept constant for all sample growth, the substrate

temperature for the ScxGa1-xN grown on MOVPE AlN are about 50 ºC lower than the other

samples. Literature reports indicate that the deposition rate of GaN is highly temperature

dependent, where a 0.3 µm hr-1

increase was observed as the temperature increased from 700

ºC to 780 ºC [10, 11]. Therefore, the growth rate differences can most likely be explained by

differences in growth temperature and the polarity of the buffer layer.

Growth and microstructure of ScxGa1-xN thin films

99

Figure 4.2 (a) Growth rate of ScxGa1-xN films and (b) growth rate of ScN films.

4.3 Surface morphology

The surface roughnesses of the ScxGa1-xN films decreased as the Sc content increased, until a

phase transition to the rock salt structure (confirmed by Raman spectra presented in section

4.4) occurred. This decrease occurred mainly due to a decrease in the average lateral feature

size (Figure 4.3). A similar trend has been reported for MBE-grown films of MnGaN [12] and

ScGaN [13], where the decrease of lateral feature size was attributed to the decrease in

average surface adatom mobility, which is a result of an increase in the average diffusion

barrier height related to the increased surface concentration of the transition metal elements,

as well as the lower mobility of the transition metal atoms on these surfaces compared to Ga.

In addition, the morphologies of ScxGa1-xN films for 0 ≤ x ≤ 0.26 are comparable to those of

MnGaN grown under the Ga-poor metal-rich regime in Ref. [12]. Moreover, as shown in

Figure 4.4, it is certain that the GaN was grown under metal-rich conditions. Therefore, we

conclude that these films were grown under metal-rich conditions, as expected.

(a) (b)

Growth and microstructure of ScxGa1-xN thin films

100

Figure 4.3 (a) Root-mean-square (RMS) roughness and (b) feature size of ScxGa1-xN on

different buffer layers. (N. B. The error for (a) RMS roughness is ± 0.2 nm and for (b) feature

size is ± 2 nm. Both are too small to be seen in the plots).

The higher roughness found for the high Sc content ScxGa1-xN film (x = 0.38 and 0.5) are

probably due to the presence of relatively large inclusions having the rock-salt crystal

structure (Figure 4.5). The electron diffraction patterns (Figure 4.6) confirm that ScxGa1-xN

transforms from pure wurtzite structure to a mixed cubic and hexagonal phase and the surface

roughness of ScxGa1-xN increases significantly as it undergoes the transition, as observed from

the cross-sectional TEM data. Although it is not possible to determine whether the cubic

diffraction pattern comes from the zinc blende structure or rock-salt structure, the peaks in the

Raman spectra (shown in Figure 4.11 in section 4.4) of both the x = 0.38 and 0.5 ScxGa1-xN

films are close to the rock-salt ScN reported in the literature whereas the peaks belonging to

zinc blende GaN are not observed. Therefore, it is highly possible that the ScxGa1-xN

transforms to the rock-salt structure at high Sc content.

(a) (b)

Growth and microstructure of ScxGa1-xN thin films

101

x (Sc content) on MBE GaN on MOVPE GaN on MOVPE AlN

0

0.08

0.26

Figure 4.4 1 x 1 m AFM images of ScxGa1-xN films on different buffer layers. All images

were processed using parabolic flattening.

Figure 4.5 1 x 1 m AFM images of ScxGa1-xN films on MBE GaN (a) x = 0.38 and (b) x =

0.50. All images were processed using parabolic flattening.

(a) (b)

Growth and microstructure of ScxGa1-xN thin films

102

Figure 4.6 Selected area diffraction patterns for (a) pure wurtzite phase (x = 0.26) and (b)

mixed cubic and hexagonal phase (x = 0.38).

4.4 Structural determination

X-ray diffraction is used to determine the crystal structure and evaluate the crystal quality. A

typical XRD diffractogram for GaN grown on AlN is shown in Figure 4.7, where the lattice

parameters can be calculated from the peak positions. Only the (000x) peaks can be observed

in this symmetric scan as both ScxGa1-xN and GaN were grown along the c-axis. However, the

c lattice parameter of ScxGa1-xN is very close to GaN, therefore, the (000x) peaks cannot be

distinguished if ScxGa1-xN is grown on GaN and thus the only way to reveal the c lattice

parameter of ScxGa1-xN is using an AlN buffer, although of course the differences in lattice

parameter, total film thickness and film growth temperature between the two sets of samples

will mean that the strain state of ScxGa1-xN will be different in both and therefore the c lattice

parameters will be different for the same compositions. A detailed discussion regarding the

variation of lattice parameter with composition for ScxGa1-xN is included in the composition

measurement chapter.

(a) (b)

Growth and microstructure of ScxGa1-xN thin films

103

Figure 4.7 Typical XRD diffractogram for MBE-grown GaN grown on MOVPE-grown AlN.

Figure 4.8 Rocking curves for (a) MBE GaN, (b) MOVPE GaN and (c) MOVPE AlN on

sapphire substrate.

The full width half maximum (FWHM) value of an omega scan (also called a rocking curve)

is typically used as a measure of single crystal quality, as it is an approximate indicator of the

density of defects in the film (depending on the crystallographic displacement introduced by

each type of defect and on the reflection used). The rocking curves for films of MBE GaN,

MOVPE GaN and MOVPE AlN are shown in Figure 4.8. The FWHM for MBE GaN is

slightly higher than that of MOVPE grown GaN and AlN, as expected given that MOVPE

typically produces films with better crystal quality than MBE. The TEM micrographs also

(a) (b) (c)

Growth and microstructure of ScxGa1-xN thin films

104

confirmed that high densities of planar defects, parallel to the basal plane of GaN, and grain

boundaries are seen in MBE GaN (indicated by yellow arrows in Figure 4.9a). On the other

hand, only dislocation lines, propagate along the c direction, are seen in the MOVPE-grown

buffer layers (indicated by yellow arrows in Figure 4.9b and c). However, the identifications

of dislocation type were not performed as this is not the focus of this thesis.

Figure 4.9 Cross-section dark field TEM images of the buffer layers (a) MBE GaN; (b)

MOVPE GaN; (c) MOVPE AlN (All images were obtained from the < 2̅110 > zone axis).

The FWHM values of the rocking curve for ScxGa1-xN grown on different buffer layers are

listed in Table 4.1. The FWHM for ScxGa1-xN on MBE GaN is close to 1º, indicating that the

film is not single crystal. This appears to be due to the in-plane rotation between different

grains that developed in the ScxGa1-xN film. Consideration of the electron diffraction patterns

of the plan-view TEM images, where one <0001> pattern is observed in the MBE GaN

(Figure 4.10a) while two <0001> patterns with about 20º rotation from each other are

observed in the ScxGa1-xN (Figure 4.10b), confirmed the in-plane rotation. Comparing the

rocking curve FWHM values for ScxGa1-xN on MBE GaN and on MOVPE AlN, the crystal

quality of the buffer layer is most likely one factor affecting the ScxGa1-xN growth. However,

for the samples of ScxGa1-xN grown on MOVPE GaN, it is not possible to confirm what

(a) (b) (c) <0001> <0001> <0001>

Growth and microstructure of ScxGa1-xN thin films

105

proportion of the FWHM value can be attributed to the ScxGa1-xN films compared to the

MOVPE GaN buffer layer (N. B. the FWHM value is very close to the bare MOVPE GaN).

Firstly, the c lattice parameters between ScxGa1-xN and GaN are very close, and therefore an

omega scan will show a signal from both films combined. Secondly, the intensity of the XRD

signal is thickness dependent: the highest proportion comes from the surface of the sample,

but a significant proportion also comes from greater depths, typically extending beyond 1 µm

from the sample surface. The film thicknesses of ScxGa1-xN grown on MOVPE GaN are about

only 230 nm, which means the signal from the higher quality 500-nm thick GaN buffer layer

underneath dominate the peak intensity. In contrast, the thicknesses of ScxGa1-xN films grown

on MBE GaN exceed 800 nm, so most of the signal from these films will come from the

ScxGa1-xN film. After all, there was no indication from the XRD spectrum for all ScxGa1-xN

films that a secondary phase is included in the alloy although a phase transition was expected

at x > 0.26.

Rocking curve FWHM (º)

x (Sc content) on MBE GaN on MOVPE GaN on MOVPE AlN

0.08 1.05 0.19 0.55

0.15 1.37 0.20 0.84

0.18 - 0.20 0.78

0.26 1.28 0.18 1.16

0.38 1.09 - -

0.50 1.55 - -

Table 4.1 FWHM values of the rocking curve for ScxGa1-xN (0002) peak

In order to further study the structural properties, Raman spectroscopy was performed before

moving on to the TEM analysis, which provides conclusive information for both crystal

Growth and microstructure of ScxGa1-xN thin films

106

structure and microstructure. Wurtzite ScxGa1-xN has polar structure (giving rise to

characteristic Raman peaks in which the position changes as a function of film strain and

alloy composition) whereas NaCl-structure ScxGa1-xN has non-polar structure (should not give

rise to any first-order Raman peaks). Therefore structural and compositional changes in the

ScxGa1-xN films can be tracked by observing changes in the position and intensity of the peaks

as a function of increasing Sc concentration.

Figure 4.10 Plan-view dark field TEM images of (a) MBE GaN and (b) ScxGa1-xN (x = 0.26)

grown on MBE GaN (insert: the corresponding electron diffraction pattern of the < 0001 >

zone axis where the images were obtained).

Raman spectra obtained from ScxGa1-xN with various Sc concentrations are shown in Figure

4.11. The Raman spectra presented were all taken from the z(x,x)z scattering configuration,

which means the direction of the incident laser is parallel to the c-axis. Therefore, for the

wurtzite structure, the E2L, E2

H and A1(LO) modes should appear in the spectrum taken in this

direction. However, the intensity of the E2L and A1(LO) phonon modes were not sufficiently

strong to be seen, and only the E2H mode (at 568 cm

-1) can be identified. On the other hand,

peaks appear at 418 cm-1

, 432 cm-1

, 451 cm-1

, 578 cm-1

and 751 cm-1

due to the sapphire

substrate [14].

(a) (b)

Growth and microstructure of ScxGa1-xN thin films

107

As the Sc concentration increased from 0 to 0.26, it can be seen that the shape of the spectrum

remained the same, with the only change observed being in the peak position of the E2H

phonon mode of the wurtzite structure. The increased Sc content is believed to be the cause of

the redshift of the E2H phonon mode from 568 cm

-1to 559 cm

-1. A similar trend has been

reported in ScxAl1-xN [15]. Though the redshift of E2H phonon peaks can be caused by the in-

plane stress induced by the film-substrate lattice mismatch or thermal expansion coefficient

mismatch, the ScxGa1-xN films are most likely free from strain induced by the lattice

mismatch because the film thicknesses are significantly greater than the critical thickness

suggested by Zhang et al. [16]. The magnitude of this shift is also much greater than that

typically induced by strain (1–2 cm-1

), indicating that it is due to compositional changes.

Moreover, the E2H peak become asymmetric and reduces in intensity as the Sc concentration

increases, consistent with a decrease in crystal quality [17], for example due to increasing

concentrations of basal-plane stacking faults.

As Sc content increased beyond x = 0.26, the Raman spectrum changes significantly and this

is attributed to the phase change from wurtzite to cubic. The broad peaks centred at 424 cm-1

and 676 cm-1

are believed to be the LA/TA and LO/TO phonon modes from the cubic ScN

(visible due to the local relaxation of selection rules due to disruption of crystallographic

symmetry introduced by high densities of defects), while the E2H phonon peak of the wurtzite

structure disappears. It is possible that the cubic structure arises from the zinc blende phase of

GaN, however, the peaks from cubic GaN (TO: 553 cm-1

, LO: 740 cm-1

) were not observed

[22–24] and it is clear that the peak from rock-salt ScN dominate the spectra. Later results

confirm that a mixture of hexagonal and cubic phases existed in the ScxGa1-xN films with x =

0.38 and x = 0.5. Most likely, the Raman signal from the remaining hexagonal regions

dropped below the detection limit due to increased densities of defects in the hexagonal

Growth and microstructure of ScxGa1-xN thin films

108

regions and due to misorientation of the hexagonal regions away from the [0001] axis, which

would be expected to produce a spreading of intensity across the peaks.

Figure 4.11 (a) Raman spectra for ScxGa1-xN on MBE GaN and (b) enlarged boxed area in

(a).

4.5 Microstructural analysis

The microstructures of the ScxGa1-xN (0 < x < 0.26) grown on MBE GaN are shown in Figure

4.12. All ScxGa1-xN films have a columnar structure, which is common only found in MBE-

grown GaN and ScN [18–20]. Considering the corresponding selected area diffraction

patterns for the cross-section of the film with the lowest Sc content (x = 0.08), different

diffraction patterns were clearly superimposed on each other, suggesting relative in-plane

rotational misorientations. However, individual grains each show hexagonal diffraction

(a) (b)

Growth and microstructure of ScxGa1-xN thin films

109

patterns and this agrees with the XRD results indicating that they were all [0001]-oriented

with respect to the surface normal (Figure 4.12a and d).

Figure 4.12 Cross-section bright field TEM images of ScxGa1-xN grown on MBE GaN (a) x =

0.08, (b) x = 0.15 and (c) x = 0.26, with their corresponding selected area diffraction patterns

(d), (e) and (f) obtained from the < 2̅110 > zone axis.

Figure 4.13 Cross-section dark field TEM images of ScxGa1-xN (x = 0.15) films on different

buffer layers (a) on MBE GaN; (b) on MOVPE GaN; (c) on MOVPE AlN (insert: the

corresponding electron diffraction pattern of the < 2̅110 > zone axis where the images were

obtained).

(a) (b) (c)

(a) (b) (c)

(d) (e) (f)

Growth and microstructure of ScxGa1-xN thin films

110

A plan-view TEM image taken for ScxGa1-xN (x = 0.26) showed that there were two major in-

plane orientation of the grains occurring in ScxGa1-xN but not in the GaN buffer layer (Figure

4.10 in section 4.4). On the other hand, there was no such in-plane misorientation found in the

ScxGa1-xN films grown on MOVPE GaN and AlN buffer layers. As suggested by the rocking

curve of the MOVPE GaN and AlN buffer layers that show higher crystal quality than the

MBE grown GaN buffer layer, the TEM micrographs confirmed the difference between them.

Figure 4.9 (in section 4.4) shows only dislocation lines in the MOVPE GaN and AlN, whereas

stacking faults and grain boundaries were found in the MBE grown GaN buffer layer.

Figure 4.14 (a) Cross-section dark field TEM images of ScxGa1-xN (x = 0.15) films on

MOVPE AlN buffer layer showing high stacking faults density and (b) the corresponding

diffraction pattern showing streaky pattern.

Stacking faults were also found in all ScxGa1-xN films, where the films grown on MOVPE

AlN buffer layer showed higher stacking fault densities than those grown on GaN (Figure

4.13). A part of the ScxGa1-xN film (x = 0.15) is shown in Figure 4.14a, where the horizontal

bright lines are the stacking faults and there were streaks along the perpendicular direction

found in its corresponding selected area diffraction pattern (Figure 4.14b). An increase in

stacking fault density with increasing Sc content was observed previously. for ScxGa1-xN

(a) (b)

Growth and microstructure of ScxGa1-xN thin films

111

grown under N-rich conditions by Constantin et al. [13]. However, no such trend was found

in our films.

Figure 4.15 (a) Mixed hexagonal and cubic diffraction pattern and (b) the corresponding

indexed pattern.

According to the theoretical calculations, the alloy becomes unstable with respect to spinodal

decomposition when Sc content is higher than x = 0.27 [4], as confirmed by Raman

spectroscopy, a structural change occurred when Sc content is beyond 0.26. A selected area

diffraction pattern taken from the film with mixed hexagonal and cubic phases is shown in

Figure 4.15 and as it is indexed, it includes one hexagonal pattern and two cubic patterns. As

seen in the diffraction pattern the hexagonal < 2̅110 > zone axis and the cubic < 011 >

zone axis are parallel. The two cubic orientations suggest the presence of twin grains, which

can be observed in Figure 4.16b. The inclined lamellar twin structure (indicated by white

(a) (b)

Growth and microstructure of ScxGa1-xN thin films

112

arrows) is commonly found in cubic materials and is believed to be a result of stress [25 – 28].

However, the formation of the cubic twin grains in ScxGa1-xN was not further investigated as

this is out of the scope of this thesis.

Figure 4.16 (a) Cross-sectional dark field TEM images of a ScxGa1-xN film grown on MBE

GaN with x = 0.50 (white dotted ellipse emphasises the round grain; white circles indicate the

locations from which the diffraction patterns in the insets (1) and (2) were taken); (b) cross-

sectional bright field TEM image showing twinned ScxGa1-xN grains with the rock-salt

structure embedded in a matrix of hexagonal ScxGa1-xN.

As indicated by the selected area diffraction patterns taken from two different regions in the

film (Figure 4.16a, insert 1 and 2), the columnar structure regions are similar to those found in

the pure wurtzite films (x ≤ 0.26), whereas the large round grains (Figure 4.16a, white dotted

ellipse) show clear cubic symmetry. Moreover, STEM HAADF images (Figure 4.17), indicate

higher Sc content in the cubic regions compared to the hexagonal regions. Therefore, energy

dispersive X-ray spectroscopy (EDX) was performed in order to determine the compositional

homogeneity of the ScxGa1-xN films. These data indicate that the Sc concentration in the cubic

region is higher than that of the hexagonal regions (Table 4.2). This may either have occurred

due to phase decomposition during growth, or to the preferential incorporation of Sc with

(a) (b)

Growth and microstructure of ScxGa1-xN thin films

113

respect to Ga in the growing cubic phase grains compared to the growing hexagonal phase

grains.

Point x (Sc content) ± 0.05

1 (hexagonal) 0.56

2 (hexagonal) 0.55

3 (cubic) 0.69

4 (cubic) 0.62

5 (cubic) 0.90

6 (cubic) 0.95

7(hexagonal) 0.55

Figure 4.17 STEM HAADF image of a

ScxGa1-xN film with x = 0.5 (black squares

indicate the points where EDX measurements

were carried out)

Table 4.2 Sc content (x) measured using

energy-dispersive X-ray spectroscopy (EDX)

for a ScxGa1-xN film with a nominal overall

composition of x = 0.50 at the points

indicated in Figure 4.17.

4.6 Conclusions

The growth of ScxGa1-xN films under metal-rich conditions by MBE has demonstrated. The

catalytic effect of Sc on the decomposition of N2 may cause uncertainty regarding the growth

N-rich or metal-rich nature of the growth conditions, nevertheless, metal-rich conditions are

confirmed using the surface morphology analysis. Stacking faults are found in the ScxGa1-xN

films, as observed previously for ScxGa1-xN films grown by MBE [13]. Single-phase wurtzite

phase structure films are confirmed for ScxGa1-xN films with x ≤ 0.26, which agrees with the

Growth and microstructure of ScxGa1-xN thin films

114

theoretical calculation by Zhang et al., and this is 9% higher than that reported by Constantin

et al.[2, 21] Therefore, it is concluded the metal-rich MBE growth conditions can help to

stabilise the wurtzite phase of ScxGa1-xN. However, ScxGa1-xN films with higher Sc contents

show mixed wurtzite and cubic NaCl-structure phases, where the cubic phase regions have

much higher Sc content compared to the hexagonal phase regions.

Growth and microstructure of ScxGa1-xN thin films

115

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Growth and microstructure of ScxGa1-xN thin films

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117

Chapter 5

Optical properties of wurtzite ScxGa1-xN thin

films

It is essential to investigate the optical behaviour of ScxGa1-xN to assess its potential for use in

optoelectronic applications. The optical band gap, refractive index and heterojunction band

alignment are the three important parameters required for designing optoelectronic devices [1].

In this chapter, the optical behaviours of ScxGa1-xN are investigated; however, the discussion

focuses on the wurtzite phase ScxGa1-xN (x ≤ 0.26), as the wurtzite structure is the

thermodynamically stable polymorph of GaN used in current devices.

5.1 Optical band gaps

Ultraviolet-visible (UV-vis) spectrophotometry was used to study the optical properties of

ScxGa1-xN. Both the transmittance and reflectance spectra include interference fringes in the

energy transparent region (the energy range below the band gap of the semiconductor). The

fringes originate from the interference between the beams of light reflected internally from

different interfaces within the sample. The fringes can be used to obtain information regarding

layer thicknesses, refractive indices and extinction coefficients [2–5].

Optical properties of wurtzite ScxGa1-xN thin films

118

Figure 5.1 Transmittance curves with Tauc plots inserted for ScxGa1-xN films with various x

grown on (a) MBE GaN and (b) MOVPE GaN buffer layer.

Generally, a transmittance curve appears at high transmission (low absorbance) with

interference fringes at the energy range below the optical band gap of the semiconductor (3.4

eV or 364 nm in the case of GaN), and the curve becomes a straight line when the energy of

the incident light approaches the band gap of the material, leading to zero transmission (100%

absorbed). However, in the case of multilayer films, only the lowest band gap can be revealed

from the transmittance curve as it absorbs all the lights before the other layers do. For

instance, if a GaN film is grown on an AlN buffer layer, only the band gap of GaN will be

shown in the spectrum as GaN has a lower band gap (3.4 eV) than AlN (6.2 eV). In general, a

Tauc plot (Equation 2.22) [6, 7] is needed to extract the band gap from the transmittance

curve (Section 2.7). As the (𝛼ℎ𝑣)2 decreases drastically as a straight line above the energy

transparent region, it indicates that the nature of the primary optical transition of GaN or

ScxGa1-xN is direct. By extrapolating this straight line to the x-axis, the band gap can be

determined.

(a)

(b)

Optical properties of wurtzite ScxGa1-xN thin films

119

Figure 5.2 (a) Transmission curves with Tauc plot inserted for ScxGa1-xN films with various x

grown on MOVPE AlN buffer layer and (b) Band gaps of ScxGa1-xN with different buffer

layers.

The transmittance curves for ScxGa1-xN films grown on three different buffer layers (MBE

GaN, MOVPE GaN and MOVPE AlN) are shown in Figure 5.1 and 5.2a. As the Sc

concentration increases, the linear region of the transmittance curves shifts to a lower energy

range for ScxGa1-xN on MBE GaN buffer layer, whereas all the transmittance curves for

ScxGa1-xN films grown MOVPE GaN overlap each other. The band gaps of ScxGa1-xN were

extracted from the Tauc plots and are plotted as a function of Sc content in Figure 5.2b.

Considering the case of ScxGa1-xN grown on MBE GaN, the band gaps obtained from the

spectra clearly come from the ScxGa1-xN films, not from the GaN buffer layer, because the

band gaps decrease with increasing Sc content, starting from the band gap of GaN at around

3.4 eV. This trend was found previously by Little et al. and Constantin et al. [9, 10]. The

possibility of the contribution to the measured band gap from the zinc blende phase in the

MBE GaN buffer layer can be ruled out as no cubic diffraction pattern was observed from the

MBE GaN buffer layer and there was no cubic phase indication from the Raman spectra.

Moreover, the buffer layers were grown in the same chamber and under the same condition. If

there was zinc blende GaN absorbing light during the measurements, the measured band gaps

(a) (b)

Optical properties of wurtzite ScxGa1-xN thin films

120

should remain the same value as the Sc content increases (as in the MOVPE GaN case

discussed below). On the other hand, the band gaps obtained from the ScxGa1-xN grown on

MOVPE GaN remain at around 3.4 eV independent of Sc content (Figure 5.2b), in which case

it is not possible to tell conclusively whether. The data show the band gaps of the ScxGa1-xN

films or tare limited by absorption due to the MOVPE GaN buffer layer. Only the lowest band

gap within a heterostructure can be obtained from the transmission measurement, therefore

AlN (band gap of 6.2 eV) was used as a buffer layer in order to reveal the band gaps of the

ScxGa1-xN films. The linear region of the transmittance curves for the ScxGa1-xN films grown

on MOVPE AlN shift to higher energies, in contrast to the ScxGa1-xN films on MBE GaN,

indicating that the band gaps increase with increasing Sc content (Figure 5.2a) and this

perfectly agrees with the theoretical calculations by Zhang et al. once the latter is corrected

for the effects of temperature and of the choice of functional on the band gap, using GaN as a

reference (theoretical calculations assume a temperature of 0 K, whereas the experimental

band gap measurements are made at room temperature and are therefore approximately 0.1

eV lower) [8]. ScN is easily contaminated by oxygen incorporation and such impurities and

vacancies affect the band gap of ScN [11, 12]. However, our reference ScN and GaN films

prepared in the same reactor under comparable growth conditions had band gaps consistent

with the oxygen-free reference values of 2.1 eV [12–14] and 3.4 eV respectively, indicating

that any oxygen incorporation occurred at levels too low to affect the band gap measurements.

Optical properties of wurtzite ScxGa1-xN thin films

121

Figure 5.3 Dark-field TEM images taken along the < 112̅0 > zone axis of ScxGa1-xN films

grown on (a) MBE GaN, (b) MOVPE GaN and (c) MOVPE AlN.

The choice of buffer layer therefore influences the band gaps of ScxGa1-xN films. Moreover,

the ScxGa1-xN films that showed decreasing band gap with increasing Sc content produced by

Little et al. and Constantin et al. were reported to have poor crystal quality and/or high

stacking faults densities [9, 10]. Our microstructural analysis revealed that planar formed in

ScxGa1-xN films grown on all different buffer layers from the TEM images (Figure 5.3). This

suggests that stacking faults are not responsible for the discrepancy in the band gap trends.

The aberration-corrected STEM-HAADF images show that I1 and I2 basal stacking faults

were found in the ScxGa1-xN on all buffer layers, whereas only the ScxGa1-xN grown on MBE

GaN includes regions with cubic zinc blende stacking (Figure 5.4). This cubic stacking has

also been reported for ScxGa1-xN films grown using NH3-MBE on MOVPE GaN buffer layers,

in which nitrogen-rich conditions are present [15] (N. B. the samples of Constantin et al. were

also grown under nitrogen-rich conditions [10, 16]). The band gap of zinc blende GaN is 0.2

eV lower than that of wurtzite GaN [17, 18]; therefore, the nanoscale inclusions with cubic

stacking are believed to be responsible for the reduction in band gaps in the ScxGa1-xN. This is

consistent with the HRTEM data from the ScxGa1-xN prepared by Constantin et al., showing a

high density of planar defects, which could include inclusions of the cubic structure (although

the HRTEM data is difficult to interpret conclusively) [10].

(a) (b) (c)

Optical properties of wurtzite ScxGa1-xN thin films

122

Figure 5.4 Aberration-corrected STEM-HAADF images taken along the < 112̅0 > zone axis

of ScxGa1-xN films, showing (a) a region of cubic stacking, (b) an I1 stacking fault and (c) an

I2 stacking fault. ‡

5.2 Refractive indices

In addition to the absorption, light-matter interactions also include refraction. The dielectric

constant describes the response of the material under an electric field and this property is

frequency dependent. The high frequency dielectric constant (𝜀∞ ) refers to the dielectric

response in the optical frequency range (~1015

Hz) whereas the relative permittivity, or static

dielectric constant, 𝜀𝑟, refers to the dielectric response in the low frequency range, which is

usually obtained from capacitance measurements. At low frequencies, all polarisation

mechanisms (including the ionic and electronic polarisations in ScxGa1-xN) can respond to the

external electric field, however, at optical frequencies, only electronic polarisation can

respond fast enough to match the frequency of the electric field component of the incoming

light. Therefore, the value of the static dielectric constant is usually higher than that of the

high frequency dielectric constant. The dielectric behaviour of the material determines its

‡Aberration-corrected STEM-HAADF images were taken with the assistance of Sneha Rhode at Department of

Materials Science and Metallurgy, University of Cambridge, UK

(a) (b) (c)

Optical properties of wurtzite ScxGa1-xN thin films

123

refractive behaviour: the optical refractive index of ScxGa1-xN for any given composition x is

related to the real part of the dielectric constant at optical frequencies by 𝜀∞ = 𝑛2

The band gap results and TEM images reported in previous sections show that the ScxGa1-xN

grown on MBE GaN contains nanoscale regions of cubic stacking, which leads to undesirable

sub-gap optical absorption. Therefore, refractive index measurements were performed using

UV-Vis spectrophotometry data only for the ScxGa1-xN films grown on MOVPE AlN. UV-Vis

spectrophotometry data are straightforward to analyse, providing measurements of the

refractive index n for films of thickness > 50 nm (as is useful, for example, when assessing

the suitability of materials for use in distributed Bragg reflectors within optoelectronic

devices).

Figure 5.5 Reflectance curves for ScxGa1-xN films grown on MOVPE AlN (red lines:

experimental curves; blue lines: fitting curves)

Optical properties of wurtzite ScxGa1-xN thin films

124

Simulated reflectance spectra must be modelled and fitted to the experimental data to obtain

values of n and of the extinction coefficient. The fitting is done by varying the parameters in

the Cauchy equation and the Kramers-Kronig relationship to yield the best fit with the

measured spectrum considering the root-mean-square error (which leads to a goodness of fit

value) between the calculation and measurement at every data point across the whole

wavelength. The goodness of fit value indicates how well the simulated data fit the measured

data, where a value of 1 indicates a perfect match (Figure 5.5) (full details of the fitting

procedure are given in Ref. [19, 20]). All goodness of fit values exceed 0.87 for ScxGa1-xN

films with x ≤ 0.18, while a lower value of 0.72 was obtained for x = 0.26, indicating less

reliable result.

In addition, the film thicknesses obtained from fitting simulated data to the experimental data

are consistent with those measured from the cross-sectional TEM images within the margin of

error. Furthermore, the refractive indices of the GaN films, the AlN buffer layer and sapphire

substrate determined using this method are measured by this approach is 2.3 ± 0.17, 2.04 ±

0.15 and 1.84 ± 0.14 respectively, which are consistent between all samples and consistent

with the literature values of 2.29 – 2.4 for GaN [21–26] 2.03 – 2.15 for AlN [23, 27–31] and

1.77 for sapphire [32, 33]. The refractive index of semiconductors is affected by many factors,

including the crystal quality and levels of unintentional doping, which are related to the

growth conditions, the buffer layer and/or substrate employed. As a result, a range of

refractive indices have been reported for GaN and AlN [24, 34] and the values obtained here

fall within that range.

Optical properties of wurtzite ScxGa1-xN thin films

125

An increase in the refractive index of ScxGa1-xN can be observed as the Sc content increases

(Figure 5.6). This is similar to the behaviour of InxGa1-xN where n increases with increasing In

content x, consistent with several calculations, although one experiment suggested that the

influence of In content on the refractive index is relatively weak [35–38]. As presented in

Section 4, the crystal quality and microstructure of ScxGa1-xN films are comparable as Sc

increases, therefore the variation in refractive index is due to the incorporation of Sc.

Considering a similar alloy, Gall et al. demonstrated that the high frequency dielectric

constant of ScxAl1-xN increases with increasing Sc content, which is attributed to the stronger

electronic polarisation due to the mixing of valence and conduction band states introduced by

the Sc [39]. If this is true for ScxGa1-xN, then, higher Sc contents should also lead to higher

refractive indices in ScxGa1-xN alloy compared to GaN. However, according to Zhang et al.’s

recent calculation [8], the conduction band minima of ScxAl1-xN primarily consist of the Sc 3d

states whereas the conduction band minima of ScxGa1-xN primarily consist of Ga 4s, 4p and N

2s, 2p states. Therefore, the refractive indices of ScxGa1-xN remain at the similar level with

that of GaN as Sc increases.

Figure 5.6 Refractive index at 632.8 nm for ScxGa1-xN films grown on MOVPE AlN buffer

layer.

Optical properties of wurtzite ScxGa1-xN thin films

126

5.3 Valence band offset of ScxGa1-xN/AlN and ScxGa1-xN/GaN

heterojunctions§

It is also important to understand the influence of the Sc incorporation on the band alignment

of the ScxGa1-xN/AlN heterostructure for electronic and optoelectronic applications. XPS was

used for measuring the valence band offset [40, 41] as the valence band maximum (VBM)

and the binding energy of the core level (𝐸𝐶𝐿) of the layers can be directly measured by this

technique whereas other techniques, such as optical spectroscopy and electrical measurements,

require simulation and fitting [42, 43]. In general, three samples are required to complete the

band offset measurement of a heterostructure: one film of each material alone, with a

thickness greater than the XPS sampling depth, plus one heterostructure in which the

heterojunction lies within the XPS sampling depth, i.e. the top layer is less than 10 nm thick.

In our case, the samples were a relatively thick (~ 100 nm) AlN film; a very thin (~ 5 nm)

ScxGa1-xN film grown on AlN and a relatively thick (~ 100 nm) ScxGa1-xN film grown on AlN.

The valence band offset (∆𝐸𝑣) is then calculated using Equation 5.1, where the energy terms

with ScGaN or AlN are taken from the XPS spectra of the relatively thick films whereas the

energy terms with ScGaN/AlN were taken from the XPS spectra of the very thin

heterostructure.

∆𝐸𝑣 = (𝐸𝐺𝑎 3𝑑𝑆𝑐𝐺𝑎𝑁 − 𝐸𝑉𝐵𝑀

𝑆𝑐𝐺𝑎𝑁) − (𝐸𝐴𝑙 2𝑝𝐴𝑙𝑁 − 𝐸𝑉𝐵𝑀

𝐴𝑙𝑁 ) + (𝐸𝐴𝑙 2𝑝𝑆𝑐𝐺𝑎𝑁/𝐴𝑙𝑁

− 𝐸𝐺𝑎 3𝑑𝑆𝑐𝐺𝑎𝑁/𝐴𝑙𝑁

) (5.1)

§ XPS valence band measurements were carried out with the assistance of Dr. Robert Palgrave at the Department

of Chemistry, University College London, UK.

Optical properties of wurtzite ScxGa1-xN thin films

127

The valence band spectra for AlN and ScxGa1-xN are shown in Figure 5.7. Due to instrument

availability, measurements for the GaN/AlN samples were carried out at Imperial College

London whereas measurements for the ScxGa1-xN/AlN samples (0.08 ≤ x ≤ 0.15) were carried

out at University College London (both locations had identical equipment models). The

valence spectrum for AlN was obtained from both instruments and the spectra appeared to be

extremely close to each other (Figure 5.7a) and the Al 2p peaks were at 73.11 eV and 73.10

respectively, this indicates the consistency of the results although two different instruments

were used. The valence band spectra for ScxGa1-xN were similar to that of GaN (Figure 5.7b),

where the peaks at about 5 eV and 9 eV correspond to the p states [44–46]. This is consistent

with Zhang’s calculation that the valence band maximum for ScxGa1-xN is governed by the N

2p state for x ≤ 0.25 [8]. The valence band maximum (VBM) was determined from the XPS

valence spectra using the linear extrapolation method [47] and the values of the VBM, Al 2p

and Ga 3d binding energies for ScxGa1-xN and AlN are listed in Table 5.1.

Figure 5.7 XPS valence band spectra for (a) AlN and (b) ScxGa1-xN (0 ≤ x ≤ 0.15).

(a) (b)

Optical properties of wurtzite ScxGa1-xN thin films

128

The energy difference between the core level and the valence band maximum of the bulk

layers (in this case they are (𝐸𝐺𝑎 3𝑑𝑆𝑐𝐺𝑎𝑁 − 𝐸𝑉𝐵𝑀

𝑆𝑐𝐺𝑎𝑁) and (𝐸𝐴𝑙 2𝑝𝐴𝑙𝑁 − 𝐸𝑉𝐵𝑀

𝐴𝑙𝑁 ) in Equation 5.1) would

not be affected by the band bending induced by the strains or the piezoelectric field [48] and it

is also true for ScxGa1-xN that the values of the term (𝐸𝐺𝑎 3𝑑𝑆𝑐𝐺𝑎𝑁 − 𝐸𝑉𝐵𝑀

𝑆𝑐𝐺𝑎𝑁) are consistent within

the margins of error at 17.80 ± 0.05 eV for x = 0, 0.08, 0.10 and 0.15 respectively, although

they are slightly higher than the literature values of 17.02 ± 0.09 eV – 17.76 ± 0.03 eV [49–

51]. Therefore, the variation of valence band offset (∆𝐸𝑣) with increasing Sc content solely

stems from the core energy difference measured at the ScxGa1-xN and AlN interface

(𝐸𝐴𝑙 2𝑝𝑆𝑐𝐺𝑎𝑁/𝐴𝑙𝑁

− 𝐸𝐺𝑎 3𝑑𝑆𝑐𝐺𝑎𝑁/𝐴𝑙𝑁

).

Sample Region Binding energy (eV) (± 0.05) FWHM

AlN Al 2p 73.11 1.16

VBM 2.42 –

ScxGa1-xN

x = 0

thin film Ga 3d 20.00 1.61

Al 2p 73.30 1.22

thick film Ga 3d 20.00 1.34

VBM 2.20 –

ScxGa1-xN

x = 0.08

thin film Ga 3d 19.87 1.67

Al 2p 73.57 1.21

thick film Ga 3d 19.82 1.68

VBM 2.07 –

ScxGa1-xN

x = 0.10

thin film Ga 3d 19.77 1.73

Al 2p 73.54 1.23

thick film Ga 3d 19.73 1.71

VBM 1.92 –

ScxGa1-xN

x = 0.15

thin film Ga 3d 19.52 1.77

Al 2p 73.33 1.25

thick film Ga 3d 19.66 1.69

VBM 1.83 –

Table 5.1 Binding energy of the core level and valence band maxima (VBM) of ScxGa1-xN and AlN.

Optical properties of wurtzite ScxGa1-xN thin films

129

The valence band offset for GaN/AlN heterojunction was determined as 0.42 ± 0.05 eV,

which is close to the experimental value 0.4 eV and the theoretical value 0.44 eV reported by

Rizzi et al. [52] and Nardelli et al. [53] respectively. However, a wide range of values have

also been reported as the valence band offset for GaN/AlN heterojunctions, from 0.4 – 1.36

eV [49–51, 54] as measured by XPS and from 0.85 – 1.15eV as obtained through calculations

[55–57]. King et al. suggested that the difference arises from the large distribution of the

measured energy difference between the core level and the valence band maximum(𝐸𝐺𝑎 3𝑑𝐺𝑎𝑁 −

𝐸𝑉𝐵𝑀𝐺𝑎𝑁), which stems from the sensitivity to surface stoichiometry and defects of the valence

band maximum [54]. Thus the difference in growth techniques, film polarity and defect

densities could lead to the different values of valence band maximum. In addition, the

determination of valence band maximum using different methods might also contribute to the

range in measured values of the valence band offset [47, 54].

The valence band offset for ScxGa1-xN /AlN heterojunction increased from 0.42 eV to 0.95 eV

as the Sc content increased from 0 to 0.15 (Figure 5.8). The strain-induced piezoelectric

polarisation was reported as the reason for the difference between the valence band offset for

InN/GaN (1.05 ± 0.25 eV) and GaN/AlN (0.70 ± 0.24 eV) [49], where the lattice mismatch

in InN/GaN (11%) is greater than than of GaN/AlN (2.5%). However, as all the ScxGa1-xN

films were thicker than the theoretical critical thickness [58] (relaxed), the strain-induced

piezoelectric field is not responsible for the increase in valence band offset of the ScxGa1-xN

/AlN heterostructure.

This increase in valence band offset with increasing Sc content can be attributed to the

internal distortions in bonding that result from the introduction of Sc into GaN. The internal

distortions in bonding increase linearly with increasing Sc content within the composition

Optical properties of wurtzite ScxGa1-xN thin films

130

range measured [62] and produce a similar effect to the epitaxial strain in conventional III-

nitrides but with larger magnitude. A large band offset of 0.65 eV in the GaN/AlN

heterojunction is caused by the lattice distortions associated with epitaxial strain [55] and

greater distortions are present in ScxGa1-xN alloys, where the decrease in the c/a ratio and the

increase in the u parameter (as presented in Section 3.3) are greater than those induced by

strain in the conventional III-nitrides [8]. These distortions are also expected to produce an

increase in spontaneous polarisation with increasing Sc content for ScxGa1-xN [56–58]. The

spontaneous polarisation of ScxAl1-xN was predicted to increase from -0.089 Cm-2

to -0.296

Cm-2

as Sc content increases from 0 to 0.5 [63]. Similar results can be expected for ScxGa1-xN

as the effects of Sc on structure and local bonding environment in wurtzite ScxGa1-xN are

similar to that of wurtzite ScxAl1-xN [8, 58, 61], even though no theoretical calculation was

performed.

Figure 5.8 Variations of valence band offset of ScxGa1-xN/AlN heterojunctions as a function

of Sc content.

∆𝐸𝑐 = (𝐸𝑔𝐴𝑙𝑁 − 𝐸𝑔

𝑆𝑐𝐺𝑎𝑁) − ∆𝐸𝑣 (2)

The conduction band offset (∆𝐸𝑐) can be found from Equation 2, where the band gap of AlN

is 6.2 eV [8, 64] and the corresponding band gaps of ScxGa1-xN with different Sc contents

Optical properties of wurtzite ScxGa1-xN thin films

131

were extracted from the Tauc plots presented in Section 5.1. Therefore, the band alignment of

ScxGa1-xN/AlN heterojunctions can be established as shown in Figure 5.9. Since the band gaps

of ScxGa1-xN (0 ≤ x ≤ 0.15) are smaller than that of AlN and both the conduction band

minimum (CBM) and valence band maximum (VBM) lie within the band gap of AlN, a type I

heterojunction is formed, similar to other III-nitrides heterostructures [49]. This type of

heterojunction is favourable for charge recombination as the electrons and holes can be

confined on the same side of the interface. Therefore, this is commonly used in LED and laser

diodes [43, 65].

On the other hand, Figure 5.9 also indicates that a type II staggered heterojunction could be

formed by ScxGa1-xN and GaN, as only the CBM or VBM lies within the band gap of the

materials on the other side of the interface [66–68]. This band alignment is beneficial to

charge separation, which is essential for solar cell [69–72], water splitting [73, 74], tunnelling

field effect transistors and double heterojunction bipolar transistors [75–77].

Figure 5.9 Band alignments of ScxGa1-xN/AlN heterojunctions.

Optical properties of wurtzite ScxGa1-xN thin films

132

5.4 Conclusions

The optical properties of wurtzite ScxGa1-xN thin films (0 ≤ x ≤ 0.26) have been investigated.

The band gaps of ScxGa1-xN films grown by MBE on MOVPE-grown GaN and MOVPE-

grown AlN templates increase with increasing Sc content, which matches theoretical

calculations. In contrast, the band gaps of ScxGa1-xN films grown by MBE on MBE-grown

GaN templates decrease with increasing Sc content, consistent with previous experimental

results. Electron microscopy revealed the presence of nanoscale cubic (zinc-blende)

inclusions in ScxGa1-xN films grown on MBE GaN, but not in any of the other ScxGa1-xN

films. Therefore, the observed decrease in band gap with increasing Sc content is attributed to

sub-gap optical absorption introduced by these inclusions. Furthermore, the refractive indices

of ScxGa1-xN films with Sc contents x ranging from (0 ≤ x ≤ 0.26) were found to be very close

to that of GaN. This is attributed to the fact that the electronic structure of ScxGa1-xN near the

valence band maximum and the conduction band minimum remains similar to that of GaN as

Sc content increases, according to theoretical calculations. Finally, the valence band offsets

for ScxGa1-xN/AlN heterojunction were found to increase slightly with increasing Sc content,

which is due to the increase in spontaneous polarisation associated with the internal distortion

in bonding. Similar to other III-nitrides, the ScxGa1-xN/AlN heterojunction is determined to be

type I, which is suitable for UV optoelectronic application, whereas a type II heterojunction

can be formed in ScxGa1-xN/GaN, which could expand the range of applications for III-

nitrides.

Optical properties of wurtzite ScxGa1-xN thin films

133

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Chapter 6

Conclusions and future work

6.1 Conclusions

The growth of ScxGa1-xN (0 ≤ x ≤ 0.5) thin films under metal-rich conditions using MBE has

been demonstrated for the first time and the growth, composition, structural and optical

properties of the resulting films were investigated in this thesis.

The composition of the ScxGa1-xN alloys was determined by both direct (RBS and XPS) and

indirect (c/a ratio and c lattice parameter data from both X-ray and electron diffraction

experiments) measurements. The Sc content measured by XPS was found to be 5–8 % lower

than that measured by RBS, the standard technique. Additionally, the c/a ratio and c lattice

parameters were found to be unreliable indication of the Sc content of the ScxGa1-xN films due

to the non-linear relationship influence of c and a lattice parameters with x and the difficulty

of determining separately the influence of in-plane strain and/or (possibly incomplete) film

relaxation on these parameters. However, the Sc effusion cell beam flux measurements have a

linear relationship with the Sc content x under metal-rich growth conditions, therefore the Sc

flux can be used as an indicator of the ScxGa1-xN film composition for growth in a calibrated

MBE reactor.

Conclusions and future work

138

Structural analysis using XRD and TEM indicated a phase transition from the hexagonal

wurtzite to a cubic NaCl structure occurred for x ≥ 0.26, which is consistent with theoretical

calculations and occurs at a value of x that is 0.09 higher than for the ScxGa1-xN films grown

under nitrogen-rich conditions reported previously [1, 2]. This suggests that metal-rich growth

conditions can be used to help stabilise Sc in its hexagonal wurtzite-like crystal structure,

which is preferable for integration with conventional III-nitrides in device applications. The

microstructures of ScxGa1-xN films were similar to those of GaN grown under comparable

conditions, all of which had columnar microstructures. However, both in-plane rotations

between columns and nanoscale planar defects were observed in the ScxGa1-xN films. In the

films displaying a mixed wurtzite and cubic phase, rounded grains (cubic phase) were

observed to form within the columnar structure (wurtzite), and compositional analysis using

EDX indicated that the Sc content at the cubic regions was higher than in the wurtzite regions,

indicating that a phase decomposition occurred, either during and/or after growth.

The optical band gaps of wurtzite ScxGa1-xN films were also investigated as a function of their

Sc content x and two trends were observed depending on what underlying layer the film was

grown on: (1) for films grown on top of MBE-grownn GaN layers, the direct optical band gap

decreases as the Sc content increases, agreements with experimental results reported

previously in the literatures [1, 3] whereas (2) for films grown on top of MOVPE-grown AlN

or GaN layers, the direct optical band gap increases as the Sc content increases, in contrast to

early predictions [4, 5] but in agreement with the predictions of recent high quality theoretical

calculations [6]. The band gap reduction in the ScxGa1-xNfilms grown on MBE-grown GaN

layers is attributed to the presence of nanoscale cubic inclusions, as revealed by aberration-

corrected STEM. Very little change was observed in the optical refractive indices of wurtzite

Conclusions and future work

139

ScxGa1-xN films as the Sc content x increased, which is probably due to the similar electronic

structure around the point both GaN and ScxGa1-xN. These data provide experimental

evidence supporting the recent theoretical predictions by Zhang et al. [6] regarding both the

phase stability and the optical band gaps of wurtzite ScxGa1-xN films.

In addition, XPS measurements reveal that the ScxGa1-xN/AlN heterostructures form Type I

heterojunctions, in which the valence band offsets increase with increasing x. This is due to

the addition of Sc generates internal distortion in bonding which leads to an increase in

spontaneous polarisation of the wurtzite structure. The relative valence and conduction band

alignments between ScxGa1-xN and GaN can also be obtained indirectly, using AlN as a

reference material, from which it can be determined that ScxGa1-xN/GaN heterostructures

should form Type II heterojunctions, in which the valence band offsets increase with

increasing x.

Overall, stable, epitaxial ScxGa1-xN films free from nanoscale inclusions and planar defects

and with wide direct band gaps were obtained on GaN for x ≥ 0.26, which is very promising

for future applications in Sc-based wide band gap optoelectronic devices and potentially also

in HEMTs.

Conclusions and future work

140

6.2 Future work

Similar to GaN, the grown ScxGa1-xN films were unintentionally doped and showed n-type

conductivity because of the presence of impurities. In order to obtain highly resistive ScxGa1-

xN films, C [7–10], Fe [11–14] and Cr [15–17] co-doping will be used to compensate the

excess charges from the impurities.

High electron mobility transistor (HEMT) is the main component for power electronics and

AlxGa1-xN has been the major material for such applications because of its large breakdown

field and capability to form 2D electron gas. However, the performance of HEMT using

AlxGa1-xN/GaN heterostructure as the active layer is limited by the surface traps, the resulting

drain current collapse and the electron scattering [18–21]. InxAl1-xN/GaN has been proven its

potential to replace AlxGa1-xN for improving the device performance of HEMTs, however, the

production of high quality InxAl1-xN film is still difficult [22–25]. On the other hand, as

indicated in Chapter 5 that the spontaneous polarisation in ScxGa1-xN is large and the

conduction band offset for ScxGa1-xN/AlN and ScxGa1-xN/GaN heterojunctions are

comparable to InxAl1-xN/GaN [26, 27]. Therefore, the performance of HEMT with ScxGa1-xN

will be investigated.

𝑒33 (Cm-2

)

x AlxGa1-xN [28] InxGa1-xN [29] ScxGa1-xN [5, 30] ScxAl1-xN [31]

0 0.73 0.29 0.57 1.46

0.25 0.91 0.30 1.02 2.03

0.5 1.10 0.315 1.82 3.34

Table 6.1 Summary of piezoelectric coefficients of III-nitride alloys

Conclusions and future work

141

As predicted, the incorporation of Sc in wurtzite III-nitrides can enhance the piezoelectric

coefficients and they are higher than the conventional III-nitride alloys (Table 6.1). Therefore,

the piezoelectric coefficient of wurtzite ScxGa1-xN will be measured by double beam

interferometry and piezoelectric force microscopy (PFM). Apart from the piezoelectric

coefficient, the dielectric constant is another important parameter that affects the energy

conversion efficiency in piezoelectric energy harvesting devices. It has been reported that the

dielectric constant of ScxAl1-xN increases slightly as Sc content increases [32]. However, as

predicted theoretically [6] and demonstrated experimentally [33, 34], the influence of Sc on

the band structures for ScxGa1-xN and ScxAl1-xN is different. The dielectric constant will be

measured using impedance spectroscopy across a range of frequencies. A piezoelectric energy

harvester using ScxGa1-xN as the active layer will be fabricated and its performance and

design will be evaluated and optimised.

It is also important to investigate the polarity of the ScxGa1-xN films as the direction of the

spontaneous and piezoelectric polarisations appear to influence the defect microstructure in

ScxGa1-xN strongly and are known to affect the formation of 2D electron gas in HEMT [28,

35]. Etching has historically been used to determine the polarity of III-nitride films, however,

the presence of Sc could lead to difficulties of interpreting the etching results as the behaviour

of ScN and GaN under KOH/NaOH etching are different [36, 37]. Therefore, it is essential to

explore the possibilities of other techniques to identify the polarity of ScxGa1-xN, in particular

convergent electron beam diffraction and electron backscattering [38–42].

Conclusions and future work

142

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Appendix A

Permission for third party copyright works

Here is the list of permissions obtained for reproducing figures in this thesis from third party

copyright works and the permission documents are attached.

Figure Source of work, copyright holder and year

Figure 1.1, page 2 Journal of Materials Chemistry A (2014), 2, 6042 (figure 4)

©2014 The Royal Society of Chemistry

Figure 1.3, page 3 Semiconductor Science and Technology (2011), 26, 014036 (figure 1)

© 2011 IOP Publishing Ltd

Figure 1.7, page 10 Journal of Applied Physics (2010), 107, 033715 (figure 1a)

© 2010 AIP Publishing LLC

Figure 1.8, page 13 Journal of Applied Physics (2013), 114, 133510 (figure 6b)

© 2013 AIP Publishing LLC

Figure 1.9, page 15 Journal of Applied Physics (2005), 98, 123501 (figure 3)

© 2005 AIP Publishing LLC

Figure 1.10, page 16 Journal of Applied Physics (2009), 106, 113533 (figure 7)

© 2009 AIP Publishing LLC

Figure 1.11, page 17 Applied Physics Letter (2014), 104 101906 (figure 2)

© 2014 AIP Publishing LLC

Figure 1.12, page 19 Journal of Applied Physics (2013), 114, 133510 (figure 6a)

© 2013 AIP Publishing LLC

Figure 1.13, page 21 Applied Physics Letter (2009), 95, 162107 (figure 1)

© 2009 AIP Publishing LLC

Figure 1.14, page 22 Journal of Applied Physics (2012), 111, 093527 (figure 6a)

© 2012 AIP Publishing LLC

Figure 2.5b, page 49 Transmission Electron Microscopy A Textbook for Materials Science

Ch. 17, 2009, p.274

© 2009 Springer

Figure 2.6, page 50 Transmission Electron Microscopy A Textbook for Materials Science

Ch. 19, 2009, p.312

© 2009 Springer

Figure 2.8, page 54 Transmission Electron Microscopy A Textbook for Materials Science

Ch. 22, 2009, p.380

© 2009 Springer

Figure 2.14, page 67 Journal of Physics: Condensed Matter (2002) 14, R967

© 2002 IOP Publishing Ltd