ABSTRACT
In diverse applications semiconductor materials need to be doped, sometimes to nearly degenerate levels.eg. In applications such as thermoelectric, transparent, electronics or power electronics. However many materials with finite band gaps are not dopable at all, while others exhibit strong preference toward allowing either p-type or n-type doping, but not both. In this work, we develop a model of strained band InGaAs/GaAsSb double quantum quantum well heterostructure on InP using transfer matrice and Model solid theory. This MATLAB program model was used to obtain the transmission coefficients, reflectance coefficients, transmission currents and electron/hole mobility. These were obtained theoretically by employing experimental binary band parameters obtained from literature.
TABLE
OF CONTENTS
Title Page i
Declaration ii
Certification iii
Dedication iv
Acknowledgements v
Table of Contents vi
List of Tables viii
List of Figures ix
Abstract xi
CHAPTER
1: INTRODUCTION
1.1 Background
of the Study 1
1.2 Lattice Matching 4
1.3 Aim/Objectives 5
1.4 Motivation
of Study 6
1.5 Significance
of the Study 8
1.6 Scope
of Study 8
CHAPTER 2: LITERATURE
REVIEW
2.1 Relevant
Research 9
2.2 Semiconductor
14
2.3 Crystal
Structure of Constituent Compounds 21
2.3.1 Zinc blende
composition 21
2.3.2
Binary compounds 22
2.3.2.1 Gallium arsenide (GaAs) 22
2.3.2.2 Indium
arsenide (InAs) 26
2.3.2.3 Gallium antimonide GaSb 29
2.4 Quantum
Well Heterostructure 32
2.4.1 Types of
heterostructures 34
2.4.2 Quantum
well 36
2.4.2.1 Infinte
well 37
2.4.2.3 Finite well 39
2.5 Density of States for Quantum Well 43
CHAPTER 3: MATERIALS
AND METHOD
3.1 Materials 46
3.1.1
Material
parameter 46
3.2 Methods 47
3.2.1 Band engineering 47
3.2.2 Semiconductor alloying 48
3.2.3
Lattice
constant 49
3.2.4
Band gaps 49
3.2.5
Band
offset 52
3.2.6 Transfer matrix 56
3.2.7 Carrier transport 60
3.2.8 Conductivity in a semiconductor 60
3.2.9 Carrier
density 62
3.2.10 Current
in a resonant tunneling diode 63
3.2.9 Carrier concentration in intrinsic
semiconductor 64
CHAPTER
4: RESULTS AND
DISCUSSIONS
CHAPTER
5: CONCLUSION AND
RECOMMENDATIONS
5.1 Conclusion 92
5.2 Recommendations 92
REFERENCES 93
APPENDICES 101
LIST OF TABLES
2.1: Periodic
table with semiconducting elements 15
2.2: Band parameter for GaAs
crystal lattice 24
2.3: Band parameter for InAs
crystal lattice 27
2.4: Band parameter for GaSb crystal
lattice 30
2.5: Summary
of the eigen energies for different well width for infinite well 39
2.6: Summary
of the eigen energies for different well width 43
3.1: Energy
band gaps of InAs, GaAs, GaSb and their respective empirical fitting parameters 51
3.2: Bowing parameters for some ternary alloys 51
3.3: Calculated
parameters used as computed by interpolation 55
3.4: Bowing
parameters for ternary alloy materials for
55
4.1: The summary of the Band gap of InGaAs for varying compositions
of
Indium 66
4.2: Summary
of the effective mass, effective density of state for conduction, valence band, and
intrinsic carrier concentration for
GaAs,
InAs, GaSb,
and
at 300K 75
4.3:
Band offset values at different
symmetric well masses 77
4.4: Well
width variation with energy eigenvalues 84
LIST OF FIGURES
1.1: Band line up of several ternary alloys that are lattice
matched to InP 4
1.2: Lattice match for different compounds and
alloys with their respective
band gap energy at 300 K 5
2.1: N-type
and P-type semiconductor 21
2.2: Gallium arsenide crystallizes in the zinc
blende crystal structure
2.3: Band energy dispersion for GaAs (001)
direction 25
2.4: Band energy dispersion for InAs (001)
direction 25
2.5: Band energy dispersion for GaSb (001)
direction 31
2.6: Variation
of band gap of materials with temperature 31
2.7: Type I straddling alignment heterostructure
35
2.8: Type II staggering alignment
heterostructure 35
2.9: Type III or broken –gap alignment
heterostructure 36
2.10: "Infinite" quantum well and
associated wave functions 38
2.11: Schematic diagram of a multiple quantum well
heterostructure 39
2.12: A graph of
against
for finite quantum well,
with superimposed plot of
against
for barrier
width of 100A, well width of 100A,
42
3.1: Conduction and valence band of a heterostructure 52
4.1: Band
gap as a function of temperature 67
4.2: Band
gap as a function of temperature 67
4.3: Band
gap as a function on the concentration of indium in InGaAs at a
temperature of 300 K 68
4.4: Band
gap as a function on the concentration
of indium in InGaAs at a
temperature of 300 K 68
4.5: Band
gap as a function on the concentration of indium in InGaAs at a
temperature of 300 K 69
4.6: Electron/Hole
Concentration as a function of Temperature for
In0.53Ga0.47 As 71
4.7: Electron/Hole
Concentration as a function of Temperature for
GaAs0.51S0.49 71
4.8: Electron/hole
concentration as a function of temperature for
In0.53Ga0.47As
at a temperature range of 0-300 K 72
4.9: Electron/hole
concentration as a function of temperature for
GaAs0.51Sb0.49
at a temperature range of 0-300 K 72
4.10: Electron/hole
concentration as a function of temperature for
In0.55Ga0.47As
at a temperature range of 0-300 K 73
4.11: The
calculated band offset of the conduction and valence for the
compressively
strained
type II
quantum
well 76
4.12: The
calculated band offset ratios of
for the compressively strained
type II quantum well 79
4.13: Variation of the composition of
indium in InGaAs with energy 80
4.14: Variation of the transmission
probability with energy at varying well
width
for strained InGaAs 83
4.15: Variation of the transmission
probability with energy at varying well
width
for unstrained InGaAs 83
4.16: Variation of the transmission
probability with energy at varying
thickness
of barrier 86
4.17: Variation of the transmission
probability with energy at variation of
conduction
band offset for strained InGaAs at 10 nm well width 86
4.18: Variation of the reflection
probability with energy at varying well
width
for strained InGaAs 87
4.19: Variation of the reflection
probability with energy at varying barrier
thickness
for strained InGaAs/GaAsSb
heterostructure 87
4.20: Variation
of the transmission probability as a function of energy at
varying
thickness of the barrier when passed through an electric field
of
0.1 eV 89
4.21: Variation
of the transmission probability as a function for varying
amount
of well depth 89
4.22: Variation
of the transmission probability as a function of conduction
band
offset 90
CHAPTER 1
INTRODUCTION
1.1 BACKGROUND OF THE STUDY
With
the advancement of crystal growth techniques, such as organic vapor phase
epitaxy (MOVPE) and molecular beam epitaxy (MBE), there came the desire to
produce faster and smaller semiconductor devices which are in layers at a time
having wide applications in different variety of fields at respective
wavelength. This has made it possible to obtain quantum wells and superlattices
with reproducible properties at the atomic scale. Reducing the dimensions of
the constituent materials, new properties of the semiconductors, were revealed (Cristian
and Cristian, 2007; Fissel et al.,,
2000; Rogalski, 2002). This helped in the tuning of the forbidden gaps so as to
enhance and widen the applications of such semiconductor device (Sadao, 2017).
The
smaller the well bandgap, the material becomes unstable and difficult to
process. This leads to non-uniformity when arrays of focal planes are made
(Levine, 1993). The electronic and optical properties can be altered by the
formation of heterostructures of these semiconductors which serves as quantum wells
(Meng, 2005). Changes can also be observed in the atomic structure which results
from direct influence of ultra-small length scale on the energy band structure
creating a quantum confinement effect (Toshihide and Kyozaburo, 1992).
The
confinement effect can in turn change the optical adsorption for bulk materials
to a series of steps (Meng, 2005). The most established quantum well
heterostructure laser structure ranging from 0.80-0.65
wave length
is lattice matched AlGaAs/GaAs quantum well which is in the near
infrared region. At longer wavelength, the materials of important are InP and
ternary and quaternary compound lattice matched to it. Smaller band-gap
semiconductor materials are useful when considering long wavelength range. This
is due to its power and efficiency, having its electrical and optical
properties stronger than other materials due to its energy band-gap closer to
light energy (Tasmeeh et al.,, 2015;
Kasap, 1999).
Most of these
quantum wells have attracted interest for laser applications due to their
potential for a reduction of the threshold current density, increase gain and
differential gain achievement obtained through confinement. Theoretical models
are developed to enable predictions of the physical properties of
heterostructures since quantum confinement of carriers in semiconductors
quantum wells leads to quantized subband energies (Samuel and Patil, 2008; Peng
et al.,, 2003).
Semiconductor
materials composed of the III-V periodic elements of different forms, binary,
ternary or even higher compositions are used to produce devices high electron
mobility, high speed, microwave amplification, low noise amplification,
wireless communication, low power voltage supply with low power dissipation e.t.c. Though, Semiconductor material produced
from the III-V composition possess some challenges when being processed. This
include difficulty to forming highly reliable ohmic rectifying contact, high
vapour pressure of the group V element compared to the group III elements, high
diffusivities of many acceptor dopants e.t.c (Shaikh, 2017; Rita et al.,, 2005; Willardson and Nalwa,
2001)
To model
the quantum well structure of a heterostructure, the relative band alignment of
the band edge between the quantum well and the barrier is very important, which
can be complicated when its strained effect is considered (Gonul et al.,, 2004). Similarly when
determining the electron tunneling for both biased and un-biased state, the
offsets of the materials are needed (Man et
al.,, 2016).
InGaAs
and GaAsSb are ternary alloys. While InGaAs alloy being the active component in
the active region of high speed electronic devices, infrared lasers, and long
wavelength quantum cascade lasers, GaAsSb results in large strain for quantum well
composition at long wavelength
(Vurgaffman et al.,, 2001; Klein et al.,, 2000).
GaInAs/GaAsSb possesses a type-II quantum well heterostructure line-up
with an effective gap of about 0.3 eV. This makes it suitable for infrared
generation and detection in 3-5 μm band. The combination of In0.53Ga0.47As
quantum wells and GaAs0.51Sb0.49 barriers, although commonly used for heterojunction-bipolar
transistors, (Willardson and Nalwa, 2001) was an unpublished area for quantum
devices.
Recently,
In0.53Ga0.47As/GaAs 0.51Sb0.49 heterostructures
were demonstrated to be a viable way to fabricate mid-infrared and THz quantum
cascade lasers (QCLs) (Gonul et al.,,
2004; Man Mohan el at, 2016). Interface roughness scattering was found to play an
important role in these devices (Vurgaffman et
al.,, 2001).
Transport
studies on symmetric THz QCL active regions identified asymmetrical scattering,
with an increased interface roughness for the inverted interfaces along the
growth direction, which resulted in parasitic current channels and, therefore,
higher threshold current densities. This alters the electronic bandstructure
and influences the emission wavelength of such devices (Klein et al.,, 2000). Figure 1.1 gives the
band lineup of several alloys which were lattice matched with InP substrate as
recorded by Zhao, (2014).
Figure 1.1: Band line up of several ternary alloys that
are lattice matched to InP. Data are taken from Yu (2014).
1.2 LATTICE
MATCHING
Matching of lattice
structures between two different semiconductors materials allows a region of
band gap change to be formed in a material without introducing a change in crystal
structure. (Wikipedia.org/). Perfect crystals are arrays of regularly spaced
atoms, but atomic spacing differs among compounds. Failure to match the atoms
in successive layers can produce defects in the crystal, which degrade its
optical, electronic, or mechanical properties.
Semiconductors can
accommodate small differences in atomic spacing, which produce some strain
within the crystal but not enough to cause damage. However, developers try to
minimize strain by limiting differences in lattice spacing. This is
particularly important in matching a deposited material to a substrate (Jeff, 2008).
Figure 1.2 shows the lattice matching of several compounds and alloys of IV,
III-V, II-VI, IV-VI elements of the periodic table.
Figure 1.2: Lattice match for different compounds
and alloys with their respective band gap energy at 300 K
1.3 AIM/OBJECTIVES
This
research work is aimed at giving the theoretical treatment of some of the
properties through arbitratrarily formed potential barriers of GaInAs/GaAsSb
heterostructure on InP substrate. This will be achieved with the following objectives.
i)
To develop a mathematical description to calculate the transmission
coefficient, reflectance coefficient, the absorbance and Resonant tunneling
current using transfer matrix, thereby building a theoretical basis for our
calculations.
ii) Use MATLAB program to compute the
transmission coefficient through the structure with an arbitrary number of
symmetry barriers and wells with or without bias (applied electric field)
iii) To study theoretically the effect of change
in the barrier thickness or width of the well to the quantum tunneling effect.
iv) Evaluate the Peak to Valley of an Ideal
Resonant Tunneling Diode using the current calculations.
v) Investigate the physical simulation of the
charge carrier distribution in GaInAs/GaAsSb heterostructure
vi) Calculate the current density and mobility (
with or without electric field)
1.4 MOTIVATION OF STUDY
The
choice of material semiconductors have direct band gap energy and are good choices
for Short Wavelength Infrared (SWIR) and Middle Wave Infrared (MWIR) optoelectronic
devices due to their bandgap range.
In
the past,
and
ternary
semiconductor materials were grown on lattice matched or mismatched binary
semiconductors such as GaAs or InP because of the closeness in their lattice
parameters. But today the ability to grow thick, high-quality epitaxial layers
of
and
on a
GaAs or InP, substrate is very limited due to lattice mismatch except for a
specific composition (Sadao and Kunishige, 1983; Guldner et al.,, 1986). For example, only
and
lattice matches to InP, and thus very good quality thick films of this
composition can be grown on InP. The strained critical thickness of
or
epitaxial layer depends on the extent of the lattice mismatch between
the ternary epitaxial layer and the binary substrates, normally < 1 m. Also,
the strained epitaxial layers grown on lattice mismatched substrates may have
strain-induced crystalline defects, which are known cause for dislocations,
rough surface morphologies, and interface cracking (Hashio et al.,, 2000). In order to overcome the limits imposed by lattice
mismatch, researchers have tried to pursue growing bulk ternary semiconductor
substrates (Dutta, 2010; Hayakawa et al.,,
2005; Nishijima et al.,, 2005). The
bulk III-V ternary
and
alloys provide many advantages over epitaxial
layers that are grown on binary III-V compound crystals. First, the bulk
ternary alloys can be used as new substrates to grow lattice matched, high
quality epitaxial layers with a large thickness for a wide range of
compositions and band gaps. This provides for extra freedom and more
opportunities for advancing novel optoelectronic device designs and band gap
engineering. Second, bulk growth is cost effective, and there is strong
potential for developing bulk
and
devices, thus avoiding the expensive and time-consuming
epitaxial deposition.
In
spite of the promising advantages of bulk
and
alloys,
the utilization of these materials for efficient optoelectronic devices has
been hampered by the challenges associated with their growth challenges. Bulk
ternary crystal growth requires stringent control over the synthesis conditions
in order to avoid crystal defects.
The
most serious problem encountered in melt-grown bulk ternary material is
cracking. Cracking is likely due to the combined results of a large
lattice/composition mismatch between the seed and the first-to-freeze crystal,
constantly changing composition along the length, and the induced stress due to
growth in a steep thermal gradient. Other crystal growth problems such as
precipitates, inclusions, residual impurities, high native defect concentrations,
and compositional variation across the substrate and from wafer to wafer are
also present. In the future, the quality of bulk ternary alloys must improve
greatly from its current state. Since prior research on
and
alloy
systems was limited to a narrow composition range (Kim et al.,, 2003), adequate knowledge of the optical and electrical properties
of this ternary system is lacking. Systematic studies of carrier concentration,
mobility, and resistivity for the
and
alloy systems as functions of composition have
not yet been reported although some work have been reported on InGaAs films
(Yeo et al.,, 2000; Fedoryshyn et al.,, 2010). Information on the
electrical properties of these materials is not only important to electronic
device applications, but can also be correlated to optical properties such as
carrier concentration dependent optical absorption (Bhat, 2008).
1.5 SIGNIFICANCE
OF THE STUDY
The
need and the desire to produce high quality quantum well alloy semiconductors
with improved band gap for specific areas of applications led to the choice of
the study on quantum well heterostucture of varying concentration of Indium in
InxGa1-xAs/GaAs0.51Sb0.49 on
InP substrate (001).
The
outcome of the study will provide a good theoretical background for the
development of the material, similar material of same class and materials with
similar characteristics.
1.6 SCOPE OF STUDY
This research work intends to explain and
explore theoretically the determination of the transmittance and reflectance of
a heterostructure of GaInAs/GaAsSb quantum well. This work intends to use the
theoretical bases for binary and ternary semiconductor compounds in relation to
quantum well to discuss the tunneling effect using transfer matrix method. The
band discontinuities (the valence and conduction band offset) were obtained
using the Model Solid theory. The intrinsic properties of the ternary compounds
and alloys were calculated theoretically and simulated using matlab programming
language.
Click “DOWNLOAD NOW” below to get the complete Projects
FOR QUICK HELP CHAT WITH US NOW!
+(234) 0814 780 1594
Login To Comment