Abstract
Group III-Nitride materials have ushered in scientific and technological breakthrough for lighting, mass data storage and high power electronic applications. Gallium Nitride (GaN) and related materials have found their suitability in blue light emitting diodes and blue laser diodes. Despite the current development, there are still technological problems that impede the performance of such devices. Quantum dots (QDs) are proposed to improve the optical and electronic properties of III-Nitride devices. Quantum confinement in spherical semiconductor quantum dot (QD) has been theoretically studied using the Brus Model based on the effective mass approximation and quantum confinement effects. The valence band degeneracy in Г point of the Brillouin zone and the effective mass anisotropy are also taken into account. It is found that the model used for the semiconductor nanocrystal exhibit quantum size dependence predicted by the particle-in-a-box model. The optical absorption and emission intensity spectra were also investigated in order to understand the effect of alloy composition(x) on the spectra. The results show that the ground state confinement energy is largely dependent on the radius of the dot and alloy composition(x). Thus, as dot radius decreases, the confinement energy increases. Hence, confinement energies could be fine tuned by changing the radius of QDs, which play a fundamental role in the optical and electronic properties of QDs. Also, the theoretically calculated absorption and emission intensity spectra shifted towards higher energies by increasing the alloy composition(x).
TABLE OF CONTENTS
Cover
Page
Title
Page i
Declaration ii
Dedication
iii
Certification iv
Acknowledgement v
Table
of Contents vi
List
of Tables ix
List
of Figures x
Abstract xiii
CHAPTER 1: INTRODUCTION
1.1
Background of the Study 1
1.2 Statement of Problem 3
1.3
Aim and Objectives of Study 4
1.4
Thesis Outline 4
CHAPTER 2: LITERATURE
REVIEW
2.1
Introduction to Semiconductor Quantum Dots 6
2.2
Size Quantization Effect 7
2.3
Applications of Quantum Dots 10
2.4
Physics of Wurzite Nitride 20
2.4.1
III-Nitride Wurzite Crystal Structure 26
2.5
Semiconductor Band Structure Engineering 27
2.6
Bloch’s Theorem 27
2.7
The K.P Perturbation Theory 31
2.8
Band Structure of Wurzite Semiconductor 36
2.9
Ternary Semiconductors: An Overview 39
2.10
Quantum dot Model 39
2.10.1
Particle in a Box 41
2.10.2
Mirror Boundary Condition 42
2.10.3
The Brus Model 46
CHAPTER 3: METHODOLOGY
3.1
Introduction 48
3.2
Method of Simulation 48
3.3 Numerical Calculation 49
3.5
Interpolation Scheme 51
CHAPTER 4: RESULTS AND
DISCUSSION
4.1
Effective Masses 54
4.2
Dielectric Constant 56
4.3
Binding Energy 64
4.4
Bandgap Energy 66
4.5
Confinement Energy 69
4.6
Quantum dot Absorption 84
4.7
Quantum dot Emission 87
CHAPTER 5: CONCLUSION
5.1
Conclusion 93
5.2
Recommendation 94
References 95
LIST OF TABLES
2.1: Comparison
between white LED, incandescent and compact fluorescent bulb 23
3.1: Electron and hole effective masses (in
unit of m0) of the binary materials 50
3.2: Dielectric constant of the binary alloys 51
3.3: Bowing parameter
(eV) for the WZ- Ternary material 53
3.4: Bandgap energy
(eV) and Varshni parameters α(meV/K)
and β(K) 53
4.1: Calculated
effective masses of electron and hole in unit of
for α-GaInN 54
4.2: Calculated
dielectric constant, Bohr radius(nm) and Bandgap energies(eV). 54
4.3: Calculated
reduced masses in unit of
and Binding energies(eV) . 54
LIST OF FIGURES
2.1: Density of states for particles. 7
2.2. Schematic Size
dependent Photoluminescence (PL) spectra. 8
2.3: A
schematic representation of excited states. 11
2.4: Energy-momentum diagram. 12
2.5: Schematic Bandgap Energy versus Lattice 16
2.6: Comparison between the
emission curves 19
2.7: Schematic diagram of Wurzite and zincblende
structure 21
2.8:Quantum
dot solar cell 22
2.9:QD
LED structure 23
2. 10: Fluorescence
spectra of quantum dots 24
2.11:Multicolor
quantum dot (QD) capability of QD imaging in live animals 25
2.12: Particle in a box 40
2.13: Mirror boundary Condition 42
2.14: Particle in a reflecting boundary 42
4.1: Electron effective mass parallel as a
function of alloy composition(x). 56
4.2: Electron effective mass perpendicular
as a function of alloy composition(x). 56
4.3: Electron effective mass parallel and
perpendicular as a function of x 57
4.4: Heavy hole effective mass parallel as
a function of alloy composition(x). 57
4.5: light hole effective mass parallel as
a function of alloy composition(x). 58
4.6: crystal field hole effective mass
parallel as a function of alloy composition(x). 58
4.7: Effective masses for hh,lh,ch
subbands parallel as a function of alloy (x) 59
4.8: Heavy hole effective mass
perpendicular as a function of alloy composition(x). 59
4.9: light hole effective mass
perpendicular as a function of alloy composition(x). 60
4.10: crystal field hole effective mass
perpendicular as a function of (x) 60
4.11: Heavy hole effective mass
perpendicular as a function of alloy composition(x). 61
4.12: Reduce mass of hh as a function of alloy
composition(x). 61
4.13: Reduce mass of lh as a function of alloy
composition(x). 62
4.14: Reduce mass of ch as a function of alloy
composition(x). 62
4.15: Reduce mass of hh,lh ch as a function of alloy
composition(x). 63
4.16: Dielectric constant parallel as a
function of alloy composition(x). 63
4.17: Dielectric constant perpendicular as
a function of alloy composition(x). 64
4.17: Dielectric constant parallel, perpendicular
as a function of alloy composition(x). 64
4.18: Binding energy as a function of
composition(x) for hh 65
4.19: Binding energy as a function of composition(x)
for lh 66
4.20: Binding energy as a function of
composition(x) for ch 67
4.21: Binding energy as a function of
composition(x) for hh,lh,ch 68
4.22: Bandgap energy as a function of
composition(x) for hh. 68
4.23: Bandgap energy as a function of
composition(x) for lh. 68
4.24: Bandgap energy as a function of
composition(x) for ch. 69
4.25: Bandgap energy as a function of
composition(x) for hh,lh,ch 69
4.26: confinement energy of hh at 0
composition(x) as the function of dot radius 70
4.27: confinement energy of hh at 0.25
composition(x) as the function of dot radius 70
4.28: confinement energy of hh at 0.5
composition(x) as the function of dot radius 71
4.29: confinement energy of hh at 0.75
composition(x) as the function of dot radius 71
4.30: confinement energy of hh at 1
composition(x) as the function of dot radius 72
4.31: confinement energy of lh at 0
composition(x) as the function of dot radius 73
4.32: confinement energy of lh at 0.25
composition(x) as the function of dot radius 73
4.33: confinement energy of lh at 0.5
composition(x) as the function of dot radius 74
4.34: confinement energy of lh at 0.75
composition(x) as the function of dot radius 75
4.35: confinement energy of lh at 1
composition(x) as the function of dot radius 76
4.36: confinement energy of ch at 0
composition(x) as the function of dot radius 76
4.37: confinement energy of ch at 0.25
composition(x) as the function of dot radius 77
4.38: confinement energy of ch at 0.5
composition(x) as the function of dot radius 77
4.39: confinement energy of ch at 0.75
composition(x) as the function of dot radius 78
4.40: confinement energy of ch at 1
composition(x) as the function of dot radius 79
4.41: confinement
energy of hh, lh, ch subbands at 0 = (x) as a function of dot 80
4.42: confinement
energy of hh, lh, ch subbands at 0.25 = (x) as a function of dot 81
4.43: confinement
energy of hh, lh, ch subbands at 0.5 = (x) as a function of dot 82
4.44: confinement
energy of hh, lh, ch subbands at 0.75 = (x) as a function of dot 83
4.45: confinement
energy of hh, lh, ch subbands at 1 = (x) as a function of dot 84
4.46: confinement energy for particle in
a box model and Brus model 84
4.47: Absorption at 0.25 composition(x)
as a function of energy 85
4.48: Absorption at 0.5 composition(x) as
a function of energy 86
4.49: Absorption at 0.75 composition(x)
as a function of energy 86
4.50: Emission intensity at 0.25
composition(x) as a function of energy 88
4.51: Emission intensity at 0.5 composition(x)
as a function of energy 89
4.52: Emission intensity at 0.75
composition(x) as a function of energy 90
CHAPTER 1
INTRODUCTION
1.1
BACKGROUND OF THE STUDY
Semiconductor quantum dots (SQDs) also known as artificial atoms
have attracted much attention for many potential applications due to their
unique physical and optical properties such as size-dependent band gap, size
dependent excitonic emission, enhanced nonlinear optical properties and
size-dependent electronic properties attributed to
quantum size-effect (QSE) (Ahmed,2010; Wei, 2014).Quantum dot materials bridges
the gap between bulk and nano, leading to a whole novel application in
electronics (Giannoccaro, 2016). Due to their size-based applications,
researchers have taken great attention in recent years to the optoelectronic
features of quantum dots(QDs). Varying particle size shows different optical
and electronic properties (Baer, 2005).
Many
theoretical researches have been embarked on to find the electronic as well as
optical characteristics of many semiconductor QDs. Past few decades has
witnessed the substantial expansion of Group III-nitride semiconductors (Xu,
2008). Most of the interest in nitride-based alloys and devices have been on
their unique benefit in short wavelength lights and high-power electrical
devices (Song, 2019). As a novel
material system, III-Nitride based resources are of specific interest as a
result of their wide band gap ranging from Infrared to ultraviolet frequencies
which are appropriate for electronic and optoelectronic device applications
(Steigerwald, 1997).
Several
devices such as green and blue light discharging diodes and laser diodes have
been realized in this material system (Puchtler, 2015). GaN and its alloys,
particularly InGaN have been proved to be most promising materials for optical
devices (Schubert, 2008). Although some dynamic improvement has been actualized
in the study of Nitride based devices, numerous fundamental characteristics are still uncertain or uninvestigated. For example,
information on the quantum confinements in wurzite Nitride QDs that take full
account of the existing anisotropy in the effective masses which is essential
for comprehending the conduct of the confined particles has not yet been researched.
Semiconductor
QDs restrain charges (electron, hole and excitons) with strong confined wave
function and distinct eigen energy values (Eric, 2019). Quantum confinement is
a distinguishing characteristics of QDs as it transforms the density of states
near the band edge (Bera,2010) with the transformation in density of electronic
states (Wei, 2014) size quantization of exciton states shifts the emission
spectrum as a function of sphere’s radius (Efros and Efros,1982). Energy of the
particles is increased in potential well with the reduction in size (Hassan,
2018). Quantum confinements occurs as a
result of changes in atomic structure taking place by decreasing the size of the
material. This sets the band gap and changes the energy levels from continuous
to discrete levels (Robinson, 2005). Alloying the QDs as well alters their
optoelectronic properties (Khan, 2018).
In
this work, Quantum confinement in spherical
semiconductor quantum dot is theoretically investigated in the Brus
Model. K.P Method is used to calculate physical properties of
QD taking full account of the existing
anisotropy in the effective masses and the valence band degeneracies.
1.2 STATEMENT OF PROBLEM
In
recent years, much focus have been drawn to the optoelectronic features of QDs
because of their size dependent applications. Variation in particle size displays
discrete disparity in optical and electronic properties. Among all
semiconductor nanoparticles, GaN and its alloys have been the focus of great
attention due to their importance in various applications such as optical
filters and sensors, optical recording resources, solar cells, laser materials,
biological labels and thermoelectric cooling materials. This is because
nanometer-scale semiconductor crystals comprised of groups III-Nitride are
described as particles smaller than the radius of the exciton Bohr (Nozik, 2002).
Although
some improvement has been actualized both theoretically and experimentally in
investigating the electronic and optical features of III-Nitride
semiconductors, many gaps are yet to be filled. For example, knowledge on the
quantum confinement in ternary wurzite type QD materials that take full account
of the existing anisotropy is yet to be reported. Hence, there is absolute need
for thorough study on these materials.
In
order to contribute to the understanding of the quantum properties of this
materials and the advancement of knowledge in the condensed matter, quantum
confinements in
spherical semiconductor QD is investigated.
1.3 AIM AND OBJECTIVES OF
STUDY
The
Aim of this study is to theoretically investigate quantum confinements in
spherical semiconductor quantum dots.
The
objectives of this study include:
1.
To investigate the effect
of alloy composition(x) on the physical and optical properties of
spherical semiconductor QD.
2.
To calculate the
confinement energy of
spherical semiconductor QD.
3.
To investigate the effect
of varying alloy composition(x) on dot radius and confinement energy of
spherical semiconductor QD.
4.
To investigate the effect
of alloy composition(x) on the absorption and emission intensity spectra of
spherical semiconductor QD.
1.4 THESIS OUTLINE
This thesis is focused on investigating the
influence of quantum confinement on the optical properties of semiconductor QDs
using
as a focus material and is organized as
follows: Chapter 1 comprises of Introduction, Statement of Problem, Research
objective. Chapter 2 discusses the physics of semiconductor QDs, The concept of
wurzite Nitride, followed by the discussion of three different quantum dot
models. In chapter 3 the methodology employed to investigate the objectives
stated in chapter 1 is revealed with relevant data for numerical calculation
and simulation. The results obtained and discussions are contained in Chapter 4
while Chapter 5 is the conclusion.
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