Department of Electrical and Electronic Engineering

Chittagong University of Engineering and

Technology

THEORETICAL STUDY OF INTERMEDIATE BAND

QUANTUM DOT SOLAR CELL

MOHAMMAD KAWSER ALAM BIBEKANANDA NATH

ID: 1502009 ID: 1502013

APRIL, 2021
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A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE

REQUIREMENTS FOR THE DEGREE OF

BACHELOR OF SCIENCE

IN

ELECTRICAL AND ELECTRONIC ENGINEERING

SUPERVISED BY:

PROF. DR. MAHMUD ABDUL MATIN BHUIYAN

PROFESSOR

DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING

CUET
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Declaration
This thesis is a presentation of our original research work. Whenever contributions of
others are involved, every effort has been made to indicate this clearly, with due
reference to the literature and acknowledgment of collaborative research and
discussions. This work was done under the guidance of Professor Dr. Mahmud Abdul
Matin Bhuiyan, at Chittagong University of Engineering and Technology, Chittagong-
4349, Bangladesh.

MOHAMMAD KAWSER ALAM BIBEKANANDA NATH

ID: 1502009 ID: 1502013
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Abstract
For the fulfilment of the demand of increasingly growing energy crisis alternative
sources of electrical energy is required and, in this case, renewable energy plays an
important role. Among dissimilar types of sources of renewable energy solar
photovoltaic can be the most potential source of energy. Though a vast amount of
research is conducted on improving the cell efficiency using 1st and 2nd generation
solar cells but they can not provide desired efficiency. Actually, in single junction solar
cells those photons having energy lower than band gap energy aren’t engrossd at all
rather transmit through the substantial which means they can not utilize full sun
spectrum. Moreover, in single junction cells power conversion efficiency is mainly
curtailed by heat and transmission loss. However, introduction of intermediate band
can upsurge the efficiency of the cell by a large margin as in that case even the sub
band gap photons can be engrossd and radiative transition occurs between bands that’s
why effect of thermalization is very low. We propose a model of intermediate band
solar cell using quantum dot where InAsN is chosen as a dot substantial and AlPSb is
chosen as a barrier substantial. The proposed cell has been designed using MATLAB
Software. We investigate the effect of dot size and inter dot distance on intermediate
bands position and efficiency of the cell by changing dot size from 2nm-6nm and by
changing inter dot distance to some certain value by keeping dot size 4.5 nm at which
certain quantity of bands can be included. Moreover, we examine the impact of
phosphorus content on the efficiency of the proposed cell by changing content from
10%-96%. Our designed model of single IB produces efficiency of 38.88% and for
double bands provides an efficiency of 51.91% for InAs.98N.02/AlP.3Sb.7 for
phosphorus content 30% and for triple band we obtain an efficiency of 63.12% for
InAs.98N.02/AlP.92Sb.08 for dot size 4.5nm for phosphorus content 92%.
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Acknowledgement
Motivation is the best weapon to grow interest in any field and the person who
motivated us towards the field of growing demand ‘Renewable Energy’ is our
supervisor Prof. Dr. Mahmud Abdul Matin Bhuiyan. First of all, we want to
acknowledge our supervisor sir for giving space to his research group and without his
constant support, guidance and encouragement it would be impossible to continue our
research over this extremely complex section of emerging photovoltaics. During
research our main barrier was the calculation for bands position which is the base of
the QDIBSC performance analysis. It would be sin if we don’t acknowledge two
person Abou El-Maaty Aly and Ashraf Nasr regarding this calculation. Last of all,
we want show our heartiest thanks to all teachers of department of EEE, CUET for
raising their helping hand while we need any support.
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TABLE OF CONTENTS
Declaration .................................................................................................................. ii
Abstract ...................................................................................................................... iii
Acknowledgement ..................................................................................................... iv
LIST OF FIGURES .................................................................................................. xi
LIST OF TABLES .................................................................................................. xiv

CHAPTER I ............................................................................................................... 1
INTRODUCTION...................................................................................................... 1
1.1 Introduction ............................................................................................................ 1
1.2 Motivation .............................................................................................................. 1
1.3 Thesis Objectives ................................................................................................... 3
1.4 Thesis organization ................................................................................................ 4

CHAPTER II .............................................................................................................. 5
LITERATURE REVIEW ......................................................................................... 5
2.1 Introduction ............................................................................................................ 5
2.2 Solar Energy ........................................................................................................... 5
2.4.2 Second Generation Solar Cell ...................................................................... 8
2.4.3 Third Generation Solar Cell....................................................................... 10
2.4.3 Fourth Generation Solar Cell ..................................................................... 11
2.5 Requirement of Solar Cell Substantial ................................................................. 12
2.6 Quantum Dot (QD) Intermediate Band Solar Cells ............................................. 12
2.7 Scope of this work ............................................................................................... 14
2.8 Related Published Works on Quantum Dot Solar Cells (QDSC) ........................ 15
2.9 Chapter Summary ................................................................................................ 18

CHAPTER III .......................................................................................................... 19

SOLAR CELL PHYSICS........................................................................................ 19
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3.1 Introduction .......................................................................................................... 19

3.2 Bandgap ............................................................................................................... 19
3.3 Intrinsic Carrier Concentration ............................................................................ 20
3.4 Symmetry Carrier Concentration ......................................................................... 20
3.5 Fermi Level .......................................................................................................... 21
3.5.1 n-Type and p-Type Conductivity............................................................... 21
3.6 P-N Junctions ....................................................................................................... 22
3.7 Built In Voltage.................................................................................................... 23
3.8 Heterojunction ...................................................................................................... 24
3.9 Bias of PN Junctions ............................................................................................ 25
3.10 Solar Cell Operation .......................................................................................... 26
3.11 Equivalent Circuit of Solar Cell ......................................................................... 27
3.12 Solar Cell Design Principles .............................................................................. 28
3.13 Requirements for a Solar Cell Substantial ......................................................... 29
3.14 Solar Cell Performance Parameters ................................................................... 29
3.14.1 Short-Circuit Current Density.................................................................. 30
3.14.2 Open-Circuit Voltage............................................................................... 30
3.14.3 Maximum Power Point ............................................................................ 30
3.14.4 Fill Factor................................................................................................. 31
3.14.5 Efficiency ................................................................................................. 31
3.14.6 Series Resistance ..................................................................................... 31
3.14.7 Parasitic Resistance ................................................................................. 32
3.14.8 Shunt Resistance ...................................................................................... 32
3.14.9 Non-Ideal Diode Behavior ....................................................................... 32
3.14.10 Captivation of Light............................................................................... 33
3.14.11 Captivation Coefficient .......................................................................... 33
3.14.12 Captivation Depth .................................................................................. 34
3.14.13 Generation Rate ..................................................................................... 34
3.14.14 Lifetime.................................................................................................. 35
3.14.15 Exterior Recombination ......................................................................... 36
3.14.16 Diffusion Length .................................................................................... 36
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3.14.17 Quantum efficiency ............................................................................... 37

3.14.18 Spectral Response .................................................................................. 38
3.14.19 Loss Mechanisms .................................................................................. 39
3.14.20 Shockley-Queisser limit ........................................................................ 40
3.15 Chapter Summary .............................................................................................. 40

CHAPTER IV........................................................................................................... 41
QUANTUM DOT INTERMEDIATE BAND SOLAR CELL ............................. 41
4.1 Introduction .......................................................................................................... 41
4.2 Quantum Dot ........................................................................................................ 41
4.3 Physics of QDs ..................................................................................................... 42
4.4 Applications of QDs ............................................................................................ 43
4.5 Quantum confinement .......................................................................................... 43
4.6 Introduction of Intermediate Band using quantum dot ........................................ 44
4.7 Design Considerations of Intermediate Band Solar Cell ..................................... 45
4.7.1 Dot Size ..................................................................................................... 45
4.7.2 Dot Spacing (Dot Density) ........................................................................ 45
4.7.3 Dot Regularity ........................................................................................... 46
4.7.4 Substantials ................................................................................................ 46
4.7.5 Doping ....................................................................................................... 46
4.7.6 Electron Mobility and Hole Mobility ........................................................ 47
4.7.8 n+ layer doping .......................................................................................... 47
4.7.9 p+ layer doping .......................................................................................... 47
4.7.10 n+ and p+ layer thickness ........................................................................ 48
4.7.11 Quantity of IBs ........................................................................................ 48
4.8 Formation of IB within the band gap ................................................................... 50
4.9 Working principle for the intermediate band solar cell ....................................... 51
4.10 Effect of Bands on Efficiency ............................................................................ 52
4.11 Implementation of QDIBSC .............................................................................. 52
4.12 Potential of QDIBSC ......................................................................................... 53
4.12 Our Proposed Model .......................................................................................... 54
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4.13 Chapter Summary .............................................................................................. 54

CHAPTER V ............................................................................................................ 55
METHODOLOGY .................................................................................................. 55
5.1 Introduction .......................................................................................................... 55
5.2 Investigation Of Dissimilar Generations Of Solar Cell ....................................... 56
5.2.1 First Generation Solar Cell ........................................................................ 56
5.2.2 Second Generation solar cells .................................................................... 57
5.2.3 Third Generation Solar cell ....................................................................... 57
5.3 Selection of Appropriate Substantials .................................................................. 58
5.4 Design Consideration of QDIBSC ....................................................................... 59
5.5 Design Constraints of QDIBSC ........................................................................... 60
5.6 MATLAB ............................................................................................................. 60
5.7 Simulation of QD Intermediate Band Solar Cell ................................................. 61
5.8 Chapter Summary ................................................................................................ 62

CHAPTER VI........................................................................................................... 63
MODELING AND SIMULATION ........................................................................ 63
6.1 Introduction .......................................................................................................... 63
6.2 Numerical Modeling ............................................................................................ 63
6.3 Equations Related To Simulation ........................................................................ 63
6.3.1 Mathematical Formulation ........................................................................ 64
6.3.2 Design Considerations ............................................................................... 64
6.3.3 Determination of Intermediate Bands Position.......................................... 65
6.3.4 Determination of Short Circuit Current ..................................................... 69
6.3.5 Determination of Open Circuit Voltage .................................................... 71
6.3.6 Determination of Efficiency ...................................................................... 72
6.4 Simulation and Results of AlPxSb(1-x)/ InAs0.98N0.02 IBQDSC ........................... 72
6.5 Comparison of Dissimilar Output Parameters for Single IB, Double IB and Triple
IB Solar Cells ............................................................................................................. 88
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CHAPTER VII ......................................................................................................... 91

CONCLUSION ........................................................................................................ 91
7.1 Summary of Work Done ...................................................................................... 91
7.2 Future Work ......................................................................................................... 92
7.3 Final Conclusion .................................................................................................. 93

REFERENCES ......................................................................................................... 94

APPENDIX ............................................................................................................. 103

APPENDIX-A ......................................................................................................... 103
A1: MATLAB CODE FOR DETERMINING THE CHANGE IN BARRIER BAND
GAPS WITH PHOSPHORUS CONTENT. ............................................................ 103
A2 : MATLAB CODE FOR DETERMINING POSITION OF INTERMEDIATE
BANDS 104
A3: MATLAB CODE FOR DETERMINING REVERSE SATURATON CURRENT
108
A4 : MATLAB CODE FOR DETERMINING EFFICIENCY ............................... 110
A5 : MATLAB CODE FOR OBTAINING DISSIMILAR CURVES FROM DATA
TABLE. 113
A5.1 : MATLAB CODE FOR OBTAINING THE EFFECT OF DOT SIZE ON
BANDS POSITION. ........................................................................................ 113
A5.2 : MATLAB CODE FOR OBTAINING THE EFFECT OF DOT SIZE ON
EFFICIENCY. .................................................................................................. 114
A5.3: MATLAB CODE FOR OBTAINING THE EFFECT OF PHOSPHORUS
CONTENT ON EFFICIENCY. ........................................................................ 114
A6 : MATLAB APP CODE .................................................................................... 115
A6.1 : MATLAB APP CODE TO DESIGN THE APP TO CALAULATE
DISSIMILAR PARAMETERS. ....................................................................... 115
A6.2 : MATLAB APP CODE TO DRAW PV AND IV CURVE. .................. 118

APPENDIX-B ......................................................................................................... 122

B1: Design view of “App Designer” for QDIBSC_Simulator.mlapp ..................... 122
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B2: Code view of “App Designer” for QDIBSC_Simulator.mlapp ........................ 122

B3: Design view of “App Designer” for IV_Curve.mlapp ...................................... 123
B4: Design view of “App Designer” for IV_Curve.mlapp ...................................... 123
B5: Design view of solar cell model in MATLAB Simulink .................................. 124
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LIST OF FIGURES

Figure 2.1: A typical household solar PV system ........................................................ 5

Figure 2.2: Benefits of solar PV.................................................................................. 6

Figure 2.3: 1st generation wafer-based silicon solar cell ............................................ 7

Figure 2.4: 2nd generation thin film solar cells .......................................................... 8

Figure 2.5: 3rd Generation Solar Cell ........................................................................ 9

Figure 2.6: 4th Generation Solar Cell ........................................................................ 10

Figure 2.7: Working mechanism of quantum dot ...................................................... 11

Figure 2.8: Working mechanism of intermediate band solar cell .............................. 12

Figure 3.1: Bandgap in metals, semiconductor and insulator .................................... 18

Figure 3.2: Space Charge ........................................................................................... 22

Figure 3.3: Band bending in Heterojunction .............................................................. 23

Figure 3.4: Energy-band diagram for two isolated semiconductors in which space
charge neutrality is assumed to exist in each region ................................................. 24

Figure 3.5: Energy Band Diagram of Heterojunction ................................................ 24

Figure 3.6: Energy-Band Diagram of a CuTex/CdS/CdTe Heterojunction Solar Cell

.................................................................................................................................... 25

Figure 3.7: Ideal Solar Cell J-V curve ...................................................................... 26

Figure 3.8: Generation of EHP in a solar cell under illumination ............................. 26

Figure 3.9: Equivalent Circuit of Solar Cell ............................................................. 27

Figure 3.10: Effect of increasing series resistance. .................................................... 30

Figure 3.11: Effect of reducing parallel resistances ................................................... 31

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Figure 3.12: Quantum Efficiency............................................................................... 37

Figure 3.13: Spectral Response……………………………………………………...38

Figure 4.1: The schematic core shell configuration of the quantum dot core. ........... 40

Figure 4.2: Transition of electrons in a multi intermediate bands (3 IBs). ................ 43

Figure 4.3: N-band IBSC showing band quantitys and transition energies ............... 48

Figure 4.4: Band diagram of a substantial containing an intermediate band ............. 50

Figure 4.5: Proposed Solar Cell model ...................................................................... 53

Figure 5.1: Code User Interface ................................................................................. 60

Figure 6.1: Minibands formation in superlattice structure Kronig-Penney Model…64

Figure 6.2: Plot of Left Hand Side of Equation (6.9) f(ɛ) vs ɛ curve………………..66

Figure 6.3: Reduced zone representation of E-k relationship .................................... 67

Figure 6.4: Extended zone representation of E-k relationship ................................... 68

Figure 6.5: Some parts of MATLAB code and command window output for reverse
saturation calculation for 3IBs and for content value 0.92……………………….....73

Figure 6.6: Some parts of MATLAB code and command window output for
efficiency for 3IBs and for content value 0.92........................................................... 74

Figure 6.7: Effect of Phosphorus Content on Barrier Substantial

Bandgap…………...78

Figure 6.8: Effect of Phosphorus Content on effective mass of electron in Barrier

Substantial .................................................................................................................. 79

Figure 6.9: Effect of QD size on Intermediate Bands Position.................................. 82

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Figure 6.10: Effect of QD size on Efficiency ............................................................ 83

Figure 6.11: Effect of Phosphorus on Efficiency ....................................................... 85

Figure 6.12: PV and IV curve for proposed cell for theree IB ……………………….85

Figure 6.13: Effect of Inter Dot Distance on Proposed Cell’s Efficiency…………..87

Figure 6.14: IV and PV Curve for 3 IBQDSC with dot size 4.5 nm and inter dot
distance 2.6 nm……………………………………………………………………...88
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LIST OF TABLES

Table 2.1: Cell Structure and Performance from literature review………………….16

Table 3.1: Basic solar cell parameter………………………………………………..28
Table 4.1: Excitation Bohr radius and bandgap of some common semiconductors...41
Table 5.1: Appropriate substantials for barrier and
dot………………………………..58
Table 6.1: Parameters Required For The Determination of Effect of Phosphorus
Content on Barrier Bandgap and Effective Mass of Electron in Barrier Region……72
Table 6.2: Effect of Dot Size on IBs Width and Position in QDIBSC for inter dot
distance 2.6 nm……………………………………………………………………...74
Table 6.3: Effect of Inter Dot Distance on IBs Width and Position in QDIBSC for
quantum dot size 4.5 nm…………………………………………………………….78
Table 6.4.: Parameters of the AlPxSb(1-x)/ InAs0.98N0.02 for IBQDSC to Calculate
Reverse Saturation Current ( Jo)…………………………………………………….80
Table 6.5: Parameters of the AlPxSb(1-x)/ InAs0.98N0.02 for IBQDSC Efficiency
Calculation (Only for phosphorus content 0.92)……………….................................81
Table 6.6: Performance Analysis Table for multi intermediate band
InAs.98N0.02/AlPxSb(1-x) QDIBSC (Showing Effect Of Dot Size and Phosphorus
Content on Cell’s Efficiency)……………………………………………………….83
Table 6.7: Effect of Inter Dot distance On Proposed Cell’s Efficiency……………..87
Table 6.8: Obtained Efficiency, FF, Voc and Jsc for one, two and three intermediate
bands quantum dot solar cell for dot size 4.5 nm and inter dot distance 2.6 nm……89
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CHAPTER I

INTRODUCTION

1.1 Introduction

For the fulfilment of the demand of increasingly growing energy crisis alternative
sources of electrical energy is required and, in this case, renewable energy plays an
important role. The current asymmetries in the distribution of nonrenewable sources
of energy is unsustainable, meaning we can assume with complete assurance that with
the status quo of energy production, exploitation of nonrenewable resources will
consist in the progressive enervation of an primarily fixed supply in which there will
be no significant additions. Renewable energy is the possible way to compete with the
present energy crisis because it is absolutely replenished and never run out. Solar
energy is a huge source of renewable energy and only possible way to convert sunlight
into electricity is solar cell. So solar cell research is very important for efficient
collection of solar energy for mankind. The thesis work overviews the new trends of
multi-band quantum dot solar cell research and development.

1.2 Motivation

The PV industry has grown into a multi-billion-dollar business and the production of
PV modules, large area conglomerates of solar cells, surpassed the 1 GW for the
primary time in 2004 and is expected to reach 10GW by 2022 [1,85]. The market has
been growing at double-digit rates over recent years (20–40% annually) and prices,
typically referred to in dollars per peak watt ($/Wp), are continuously falling, roughly
with a “learning curve” of 80% [1,2,85]. A further upsurge of the cumulative
production by an element of 100 will cause cost equality with fossil fuels. This can be
expected to occur in roughly 15 years if the technology continues to follow the 80%
learning curve. Unfortunately, learning curves tend to experience a “change in slope”
once a technology is sufficiently matured and costs stabilize because it was seen for
gas and wind turbines in the early 1960’s and 1990’s respectively [3]. Photovoltaic
 2

today’s economic success of PV is important as it fosters future developments, but it

crucially hinge on political incentives such as “feed-in tariffs,” as they have been
established in several European countries [4,85], installation subsidies, or high
electricity costs in general. However, taking the incentives as granted or into account,
the high electricity costs in parts of the planet, e.g., Japan, photovoltaic energy may be
a highly competitive and lucrative market today. This demand has caused a major
shortage in the solar module market and a great rush toward increasing the production
capacity in 2004. Returning to the green aspect of photovoltaic energy conversion, PV
is an inherently clean sort of energy once it's installed within the field. Solar modules
convert the incident radiation directly into electricity, require no fuel, and produce no
exhausts or other bi-products [85]. However, to be a sustainable clean form of energy,
one also needs to consider what is necessary to produce a solar module. Other frequent
objections to solar energy are that they require huge land areas which we might not
have enough rare substantials to supply substantial quantities of solar cells. The
question of sustainability requires that solar modules “generate” substantially more
energy during their estimated 30-year lifespan than what's necessary within the
manufacturing process of the solar module. Recently several design schemes are
proposed to extend the facility conversion efficiency of photovoltaic devices. By using
two or more p – n solar cell junctions, tandem cells made of dissimilar semiconductors,
a multi heterojunction design yields a better match to the solar spectrum than a single-
junction cell and may provide the efficiency of conversion greater than 50%.1 In fact,
two-junction solar cells [5] have been fabricated using GaAs and InP semiconductor
alloys, providing the very best power conversion efficiency of 30.2% for AM 1.5
spectra [86]. Such high efficiency, which is very close to the theoretical limit has been
achieved in the structure with optimized band gaps and with good current and lattice
matching [3]. There are only a few ways that provide the direction to upsurge the
efficiency above the Shockley-Queisser limit. These include manufacturing cells that
introduce more than two light-formed carrier populations and providing cells that
reshape the incoming spectrum so that more of the energy contained in the broadband
incident light may be utilized by the cell in carrier generation. These ways include hot
carrier generation, impact ionization solar cells, multiband solar cells, impurity level
solar cells, quantum well solar cells, thermophotovoltaic, and Thermo photonic solar
cells. The quantum-dot intermediate band solar cell (QD-IBSC) has been proposed as
a practical procedure to implement the intermediate band solar cell (IBSC) [8–9]. The
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limiting efficiency for this structure is 63.2% under maximum concentration (the sun
being assumed as a blackbody at 6000 K). Briefly, the performance of the IBSC relies
on obtaining a cloth that exhibits an intermediate band (IB), half-filled with electrons,
within what ordinary semiconductors constitute the bandgap [87].

To summarize the current situation, the solar cell market is highly lucrative at the
moment due to guaranteed feed-in tariffs and high electricity prices in parts of the
world. The learning curves predict further substantial price reductions because the
market grows at rates of 20–40%. Other than economic considerations, there are not
any constraints in view which will limit the success of solar power [85].

1.3 Thesis Objectives

Solar cells are the most vital part of a solar PV system. The main problem of the solar
cell is that its efficiency is very poor for generation of cost-effective electricity. The
supreme theoretical efficiency of single junction solar cells is about 31%. It is called
Shockley Quisser limit. To rise the efficiency of the solar cell beyond this limit we
have chosen the Intermediate Band Solar Cell (IBSC). Another problem of the solar
cell is higher cost than the conventional source of electricity. Curtailing the cost of the
solar cell will diminish the cost of solar electricity. So, the main objective of our work
is to propose highly efficient solar cell for cost-effective solar electricity. Therefore,
we chose QDIBSC. To design and simulate solar cell, proper tool is the primary need.
But as QDIBSC is an emerging solar cell there is no suitable software to simulate
QDIB solar cells. Thus we have chosen well established MATLAB code to simulate
the proposed cells. The main objectives of this thesis is to design the mathematical
model of the intermediate band quantum dot solar cell (IBQDSC) are given below:

1. To investigate third generation solar cell.

2. To design and model of Intermediate Band Quantum Dot Solar cells.
3. To simulate the designed cell using MATLAB software.
4. Numerical analysis with dissimilar substantial for higher conversion efficiency
of the proposed cells.
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1.4 Thesis organization

This dissertation shows how a solar cell can be modeled and simulated for exploring
higher conversion efficiencies for the application of photovoltaic. The organization of
this thesis is as follows.

The first chapter of this thesis includes background motivation, energy crisis and
alternative energy. The motivation behind the solar energy is considered as the best
clean alternative energy and the solar cell is the only solution to harness electricity
from the sun is discussed. The reasons for choosing quantum dot solar cell are also
discussed. Scopes and objectives of this thesis are discussed in this chapter. Chapter
two provides a brief description of the development of solar cell research.

Classification of solar cells according to generation is discussed. The base line

structure and modeling parameters of solar cells are discussed and recent world records
in solar cell research are overviewed.

Chapter three explains the basic solar cell physics behind the working principle of a
solar cell. Basic physical phenomena like p-n junction formation, junction types,
carrier generation and recombination are discussed.

Chapter four explains the working of Quantum Dot Intermediate Band Solar Cell. How
it can overcome the phonon loss in first and second-generation solar cell in discussed
in this chapter.

Chapter five highlights the modeling parameters and characterization of a solar cell.
Simulation strategies, solar cell simulation software, and their features are introduced
here.

Chapter six highlights the simulation, results and analysis of the performance
parameters of a solar cell.

Finally, Chapter seven, conclusion highlights the summary of the results of the whole
work and possible feature extensions and scopes of this topic and what we can do in
future.
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CHAPTER II

LITERATURE REVIEW

2.1 Introduction

An ever-growing inhabitant means an ever-growing condition for energy. Nowadays,

scarcity of energy cannot be deprived of. It is essential in every walk of life. Energy
sources can be largely categorized as renewable and non-renewable. Knowing the
horrible fact that nonrenewable sources will eventually diminish, the importance of
renewable sources cannot be undervalued. The most important characteristic while
utilizing them is their impact on the environment. This paper momentarily presents the
importance of renewable sources of energy owing to the background of fossil fuel
predicament. Major importance is placed on the use of substitute energy technologies.
Some tenders of renewable sources and future of energy is also discussed.

2.2 Solar Energy

The sun is a major source of renewable free energy (i.e., solar energy) for the planet
Earth. Currently, new technologies are being applied to generate electricity from
harvested solar energy. These actions have already been proven and are widely
practiced throughout the world as renewable alternatives to conventional non hydro
technologies. Theoretically, solar energy possesses the potential to adequately fulfill
the energy demands of the whole world if technologies for its harvesting and supplying
were readily available [10]. Nearly four million exa joules (1 EJ = 1018J) of solar
energy reaches the earth annually, ca. 5 × 104 EJ of which is claimed to be easily
harvestable [11]. Despite this huge potential and upsurge in awareness, the
contribution of solar energy to the global energy supply is still negligible [12].

2.3 Solar Photovoltaic

Photovoltaic systems use to utilize sunlight into electricity. A system is made up of

one or more solar photovoltaic panels, AC to DC power converter (also known as an
 6

Figure 2.1: A typical household solar PV system [17].

inverter), a tracking system. A small PV system may supply energy to a single

customer, or to an isolated device like a lamp or a weather tracker. Large grid-
connected PV systems can supply the energy needed by many customers [14]. PV
systems assortments from small, rooftop or building-integrated systems with
capacities from a few to several tens of kilowatts, to large utility-scale power stations
of hundreds of megawatts. Nowadays, most PV systems are grid-connected in most of
the countries, while off-grid or stand-alone systems account for a small portion of the
market.

Operating quietly and without any moving parts or environmental emissions, PV

systems have developed from being genuine market applications into a mature
technology used for mainstream electricity generation. A rooftop system make up the
invested energy for its manufacturing and installation within 0.7 to 2 years and
produces about 95 percent of net clean renewable energy over a 30-year service life.

2.4 Solar Cell

Solar Cell converts light energy into the electricity. A photovoltaic cell is essentially a
contact diode. It utilizes photovoltaic effect to convert light energy into electricity.
Although this is often basically a junction diode, but constructional it's bit dissimilar
form conventional contact diode [88]. A very thin layer of semiconductor device is
grown on a comparatively thicker semiconductor device. When light reaches the
contact, the sunshine photons can easily enter within the junction, through very thin p-
type layer. The light energy, within the sort of photons, supplies sufficient energy to
 7

produce the symmetry condition of the junction [88]. The unrestricted electrons in the
exhaustion region can quickly come to the n-type side of the junction. Similarly, the
holes within the depletion can quickly come to the p-type side of the junction. Once,
the afresh formed free electrons come to the n-type side, cannot further cross the

Figure 2.2: Benefits of solar PV [27].

junction due to barrier potential of the junction. Similarly, the afresh formed holes
once come to the p-type side cannot further cross the junction became of same barrier
potential of the junction. As the attentiveness of electrons becomes higher in one side,
i.e. n-type side of the connection and attentiveness of holes becomes more in another
side, i.e. the p-type side of the junction, the contact will behave sort of a small battery
cell. A voltage is about up which is understood as photo voltage. If we connect a little
load across the junction, there'll be a small current flowing through it [88].

2.4.1 First Generation Solar Cell

The cell consists of a large-area, single-crystal, single layer p-n junction diode, capable
of generating usable electrical energy from light sources with the wavelengths of
sunlight [89]. The cells are characteristically made using a dissemination process with
silicon wafers. These silicon wafer-based solar cells are the dominant technology in
the commercial production of solar cells, accounting for more than 86% of the
terrestrial solar cell market [17]. Typical solar panels are shown in Figure 2.3.

Advantages:
1) Spectral captivation range is high.
 8

Disadvantages:
1) Expensive manufacturing technology.
2) Growing of ingots is a high energy intensive process.
3) Most of the energy is wasted as heat.

Figure 2.3: First generation wafer-based silicon solar cell [17].

2.4.2 Second Generation Solar Cell

These cells are based on the use of thin epitaxial deposits of semiconductors on lattice-
matched wafers. There are two classes of epitaxial photovoltaics - space and terrestrial.
Space cells typically have higher AM0 efficiencies (28-30%) in production, but have
a higher cost per watt. Their thin-film cousins have been developed using lower-cost
processes, but have lower AM0 efficiencies (7-9%) in production [89]. There are
currently production. Examples include amorphous silicon, polycrystalline silicon,
micro- of thin-film technology theoretically results in reduced mass so it allows fitting
panels on a quantity of technologies/semiconductor substantial under investigation or
in mass light or flexible substantial, even textiles. Second generation solar cells now
comprise a small segment of the terrestrial photovoltaic market, and approximately
90% of the space market. A 2nd generation thin film solar cell is shown in Figure 2.4
[17,89].

Examples of 2nd Generation Solar Cell are given below-

 9

1. Amorphous silicon (a-Si)

2. Polycrystalline silicon (poly-Si)
3. Cadmium telluride (CdTe)
4. Copper indium gallium selenide (CIGS) alloy
1. Amorphous silicon cells deposited on stainless-steel ribbon [90].
a. Can be deposited over large areas by plasma-enhanced chemical vapor
deposition.
b. Can be doped in a fashion similar to c-Si, to form p- or n-type layers.
c. Used to produce large-area photovoltaic solar cells.
d. Bandgap ~ 1.7eV

Figure 2.4: Second generation thin film solar cells [17].

2. Polycrystalline silicon [90]

a. Consists solely of crystal silicon grains (1mm), separated by grain boundaries.
b. Main advantage over amorphous Si: mobility of the charge carriers can be
magnitudes of order higher.
c. Bandgap ~ 1.1eV]
3. Cadmium Telluride (CdTe) cells deposited on glass [90].
a. Crystalline compound formed from cadmium and tellurium with a zinc blende
(cubic) crystal structure.
b. Typically sandwiched with cadmium sulfide (CdS) to form a pn junction
photovoltaic solar cell.
c. Cheaper than Silicon, especially in thin-film solar technology – not as efficient.
d. Bandgap ~ 1.58eV.
4. Copper gallium indium diselenide (CIGS) solar cells [90]
a. Deposited on either glass or stainless-steel substrates.
b. More complex 9 heterojunction model.
 10

c. Bandgap ~ 1.38eV.

Advantages
1. Lower manufacturing costs reduced mass.
2. Lower cost per watt can be achieved.
3. Less support is needed when placing panels on rooftops.
4. Allow fitting panels on light or flexible substantial, even textiles [90].

Disadvantages
1. Typically, the efficiency of thin-film solar cells is lower compared with silicon
(wafer-based) solar cells.
2. Amorphous silicon is not stable.
3. Augmented toxicity [90].

2.4.3 Third Generation Solar Cell

They are proposed to be very dissimilar from the previous semiconductor devices as
they do not rely on a traditional p-n junction to separate photo formed charge carriers.
For space applications quantum well devices (quantum dots, quantum ropes) [89].
1. Nanocrystal Solar Cells.
2. Photo electrochemical cells
3. Quantum Dot Solar cell.
4. Dye-sensitized hybrid solar cells.
5. Polymer solar cells [90].

Figure 2.5: Third Generation Solar Cell [27].

Advantages

1. Low Energy, High throughput processing technologies.

 11

2. Polymer cells- chemically synthesized.

3. Polymer cells- Low substantial cost.
4. Graetzel cells- attractive replacement for existing technologies in “low
density” applications like rooftop solar collectors.
5. Graetzel cells- Works even in low-light conditions.
6. DSSC- Potentially rechargeable [90].

Disadvantages:
1. Practically efficiency is lower compared to silicon (wafer-based) solar cells.
2. Polymer solar cells
3. Degradation effects: efficiency is decreased over time due to environmental
effects.
4. High Bandgap.
5. PEC cells undergo degradation of the electrodes from the electrolyte [90].

2.4.3 Fourth Generation Solar Cell

This hypothetical generation of solar cells may consist of composite photovoltaic

technology, in which polymers with nano particles can be mixed together to make a
single multi spectrum layer [90]. Then the thin multi spectrum layers can be stacked
to make multi spectrum solar cells more efficient and cheaper based on polymer solar
cell and multi junction technology used by NASA on Mars missions (Figure 2.6). The
coating that adapts dissimilar types of light is first, then another layer for the light that
passes and last is an infra-red spectrum layer for the cell—thus converting some of the
heat for an overall solar cell composite [90]. This is on research based work. This
might come in near future and will sponsor to upsurge the efficiency and may be used
in every aspect of energy sources.

Figure 2.6: Fourth Generation Solar Cell [27].

 12

2.5 Requirement of Solar Cell Substantial

1 A straight band gap with nearly finest values for either homojunction or
heterojunction devices.
2 A high ocular captivation constant, which lessens the requirement for high
minority carrier lengths.
3 The possibility of producing n-type and p-type substantial, so that the formation of
homo junction as well as heterojunction devices is feasible.
4 A good framework and electron attraction match with large band gap window layer
ingredients such as CdS and ZnO so that heterojunctions with low interface state
densities can be formed and deleterious band spikes can be avoided [84].
These requirements are satisfied by a quantity of II-IV compounds and a wide range
of multilayer semiconductors mainly based on copper ternary compounds with the
chalcopyrite structure. Foremost among those substantials, that have emerged as
leading candidates are the chalcopyrite-type Copper ternaries, primarily CuInSe2
[19,84].

2.6 Quantum Dot (QD) Intermediate Band Solar Cells

The chief boundaries of the photovoltaic translation device are that low energy photons
cannot excite charge carriers to the conduction band, therefore do not sponsor to the

Figure 2.7: Working mechanism of quantum dot.

devices current and high umph photons are not proficiently used due to a poor match
to the energy gap. However, if intermediate levels are declared into the energy gap of
a predictable solar cell, then low energy photons can be used to encourage charge
carriers in a stepwise manner to the conduction band. In totaling, the photons would
be better harmonized with energy shifts between bands. Quantum Dot Solar cell has
 13

an efficiency of maximum 11.91%. But it can be augmented to a higher value by using

intermediate band between conduction band and the valance band. With a single
intermediate band, it’s efficiency is obtained about 63.72% and with double
intermediate band it’s efficiency is obtained about 70%. In conventional solar cells
when a photon incident on p-n junction only an electron is thrilled and it is reached to
the conduction band if the photon energy E> Eg. Normally this electron will again
drop to the lower lumo of the conduction band by releasing energy but as the whole
conduction band is divided into many energies bands amount of released energy is
very small and thus it is mainly released as heat. On the other hand, in case of quantum
dots electron is confined in to a small energy bandgap and when a photon incident with
sufficient energy an electron will thrilled towards the conduction band and when it
drops towards the lower lumo of the conduction band it will release such amount of
energy which is almost equal to the energy of photon. This released photon then again
strikes an electron in the valance band and generates EHP as shown in Figure 2.7.
Thus, where in a conventional solar cell only a single electron hole pair is formed by
photon. In case of, quantum dot solar cell two electron hole pair is formed by a single
photon incident. As the quantity thrilled electron upsurges for short circuit current also
upsurges and it will produce greater efficiency. Quantum dot solar cell is designed by
using quantum dots which acts as an absorbing photovoltaic substantial. It attempts to
replace bulk substantial which is used in the first- and second-generation solar cells

Figure 2.8: Working mechanism of intermediate band solar cell [16].

such as silicon, copper indium gallium selenide (CIGS) or cadmium telluride (CdTe).
Energy bandgap of a quantum dot can be tuned across a wide range of energy levels
by changing their size. This property makes quantum dots as an exciting substantial
for multi-junction solar cells. Quantum dot solar cells follows relaxed optical selection
rules thus they are capable of absorbing wide range of incident radiation. Generally,
 14

low energy electrons cannot reach to the conduction band from the valance band. Thus,
solar cells cannot use a wide range of wavelength of the light energy to release electron
from valence band and it cannot convert a large amount of sun energy to the electrical
energy which causes a decrease in the conversion efficiency. To bring the low energy
electrons due to incident of lower energy photon to the conduction band intermediate
bands are used. The intermediate band works by two step captivation of the valance
band photons which provides the extra generation of electron-hole pairs. In Quantum
dot solar cells with intermediate band Solar Cell (QDIBSC) at first the low energy
electron is thrilled to the intermediate band. Further absorbing some energy this
electron will jump towards the conduction band from the intermediate band as shown
in Figure 2.8. As the lower energy electrons now thrilled to the conduction band more
current will flow and a large amount of open circuit voltage will be maintained and
conversion efficiency will be greatly augmented.

2.7 Scope of this work

Quantum dot solar cells are an emergent field in solar cell explore that uses quantum
dots as the photovoltaic substantial. Quantum dots have band gaps that are tunable
transversely a wide series of energy levels by changing the quantum dot size. This stuff
makes quantum dots striking for multi-junction solar cells, where a variety of
dissimilar energy levels are used to extract more energy from the solar range. The
dynamic presentation of the quantum dot tactic has led to extensive research in the
field. Their efficiency of 5.4% is midst the highest observed for QDSCs and even
though quite low linked to that of commercial bulk silicon cells (about 22%), it has a
potential for upgrading outside silicon cells [28].

Third-generation solar cells goal towards translation proficiencies yonder the

Shockley–Queisser limit through cutting-edge PV concepts such as multi junction
cells, ocular up- and down converters, multiple carrier generation by impact ionization,
adulteration band cells and so on. Over the last few years, quantum dots (QDs) have
attracted wide-ranging attention due to their outstanding opto-electronic properties.
Their captivation spectrum can be tailored to changing their size which makes them
attractive for PV applications. Nano composite solar cells can be easily formed in
dissimilar shapes and geometries, which allow self-light tracking and waveguide
integration. All these devices are characterized by a single band gap and belong to the
 15

group of second-generation PVs. QD-based devices were also proposed to realize

third-generation PVs and to achieve conversion efficiencies beyond the Shockley–
Queisser limit. Single junction PV cells based on QDs engrossrs are dynamic
candidates as building blocks in third-generation multi junction device due to the
tenability of the captivation spectrum. QD based solar cells can be used to design low
cost solar panel. As it is cost effective, it can be used for designing power system for
spacecraft. This form of solar cell exhibits 50-60% internal quantum efficiencies.
Many kinds of solar chargers like laptop battery charger, solar mobile charger, power
cell for calculators can be designed by this QD based solar cells. The efficiency can be
augmented by introducing multi-intermediate band within the valence band and
conduction band. We are moving toward this.

2.8 Related Published Works on Quantum Dot Solar Cells (QDSC)

As the efficiency of the conventional solar cell is poor so research is being done on 3rd
generation solar cells, quantum dot solar cell is one of them. A good quantity of
researchs on quantum dot solar cells have been published in recent years. Among
dissimilar types of third generation solar cells quantum dot solar cell has a higher value
of efficiency. By the introduction of intermediate band efficiency further upsurges.
This method of fabricating intermediate band solar cell is proposed by Luque and
Marti in 1997 [19]. The time-inhinge onent Schrödinger equation is employed to
determine the optimum width and location of the intermediate band [20]. Quantum dot
solar cell efficiency can be augmented by using 15ifferent sizes of dots along with
various distance between the dot sizes. By using InAs0.9N0.1/GaAs0.98Sb0.02 as an
intermediate band substantial and taking the dot size and spacing between dots 3.5nm
and 2nm respectively efficiency is obtained about 36.7% [21]. Higher spacing between
dots reduces the efficiency. If the dots are closely associated then then electron can
tunnel through one dot to another. The design constraints of QDIBSC are dot size,
doping, spacing, regularity and intermediate band quasi-fermi level clamping.
Substantial lifetime is determined by the injection level and recombination between
conduction band and valence band electron hole pair. The reduction in the value of PR
causes a drop in efficiency from 63.2% to 58.2%. Reduction in fill factor from 1 to .52
drops the efficiency further to 46% [22]. For focused light effectiveness is initiate to
be higher than the unconcentrated light. The standards of Voc in the full captivation
case are advanced than that in the unconcentrated case. From a solar cell point of view,
 16

this performance generally ensues because the acceptable large width of quantum dots
will acquire high photons and it then excites a large quantity of electrons: high induced
current density [20]. This is because the light energy is much larger than the bandgap
energy. Reduction in light concentration reduces the value of efficiency to 39.5% [22].
Intermediate band of the QDIBSC can be made from dissimilar types of substantials.
Such as, GaAs/InAs, InGaAs/AlGaAs, GaAs(1-x)Sbx, InGa(1-x)Nx/GaN. Among them
InAs/GaAs has lower efficiency because this lattice types are mismatched. To
overcome this problem PbTe/Cd0.7Mg0.3Te intermediate band solar cell is used [23].
Semiconductor bandgap can be divided into two contributions. First one is that thermal
expansion causes other one is electron phonon insertion [20]. By using multi-
intermediate band efficiency of the quantum DOT can be highly augmented. It is
initiate that maximum efficiency obtained from the single intermediate band is about
63.2% [24]. Efficiency is upsurge to about 73% while 5 layers of intermediate band is
used. Width of IB can be governed by tuning the inter dot distance. PCE (power
conversion efficiency) can also be governed by tuning the position of fermi energy
bands as well as changing the doping concentration [25]. Though theoretical value of
efficiency is higher but this type of design cannot be implemented because upsurge in
the quantity of band effects the conductivity of the other bands. Until now many
mismatched alloys such as GaNAs or ZnTeO, short-period superlattices (SLs), or
InAs/GaAs quantum dots (QDs) are used as intermediate mayerials. IB solar cells have
one IB energy level and just cover a small part of the solar spectrum due to the narrow
bandgaps of the host substantials. Instead of the using In-rich InGaN, Ibs are
introduced into the low-In content InGaN p-n junctions, the captivation can be easily
extended to the lower photon energies through the IB transitions and thus quantity
available electrons in conduction band is greatly augmented. InxGa(1−x)N system for
IB solar cell has a unique property of widely tunable bandgap energy, with which the
captivation region can be tailored to match the full solar spectrum by introducing
multi-level intermediate bands (MIB) from changing In compositions inside one p-n
junction. This work opens up an interesting opportunity for high-efficiency QDIB solar
cells in the photovoltaics field. Moreover, difficulties in In-rich InxGa(1−x)N, such as
the high-quality thick film growth and p -type doping can be removed in InGaN solar
cells [26].
 17

From the published work we initiate that for the single junction solar cell the efficiency
is not more than 33%. To upsurge the efficiency, we initiate that researcher worked on
intermediate band. From dissimilar paper we initiate that the efficiency upsurges as
the intermediate bands are used. The efficiency varied with substantial. For 1 band the
efficiency is between 30% to 50% and for 2 bands the efficiency is between 50% to
60%.

The literature review of our thesis work is summarized in a table for clear concept of
the efficiency of dissimilar generation and dissimilar the solar cells.

Table 2.1: Cell Structure and Performance from literature review

Cell structure Performance Ref. & year

CIGS η =17.5% (single-junction [66] & 2011
cell)

CdTe η =11.4% (single-junction [66] & 2011

cell)

InAs0.9N0.1/GaAs0.98Sb0.02 η =36.7% , Jsc=67.8, Voc= [68] & 2012

dot system (dotsize=3.5nm) 1.02, FF(%)=84.1

lead salt QDs(PbTe, PbSe or higher than 60% [69] & 2013
PbS)

Quantum Dot Sensitized Solar efficiency of [70] & 2012

Cells 11.9%.(fabricated)

Amodified polysulfide redox A very high fill factor of [71] & 2013
couple, [(CH3)4 0.89 was observed
N]2S/[(CH3)4N]2Sn

CIS/ZnS (CIS-Z) QDs efficiency of 6.66% [72] & 2015

(fabricated) Voc=.58V,
Jsc=19.73, FF=0.58

CdSe/CdS co-sensitized ZnO efficiency of [73] & 2013

nanowire 3.60%(fabricated)
 18

Voc=.685V, Jsc=12.6,
FF=0.42

Single Junction, GaAs η = 31% [80] & 2018

1Band QDSC (InAs/GaAs) efficiency of 31.83% [74] & 2013
(simulated)

1Band QDSC (PbSe/GaAs) efficiency of 40% [75] & 2017

(simulated)

2 Band QDSC (Al0.4Ga0.6 η = 62.81% [76] & 2014

As/In0.42Ga0.58As) (simulated)
1Band QDSC (InAs0.9 η = 42.39% [77] & 2016
N0.1/GaAs0.98Sb 0.02 ) (simulated)
2 Band QDSC (InxGa1- η = 55.26% [78] & 2018
xN/GaN) (simulated)
1Band QDSC (GaAs/InAs) η = 56% [79] & 2012
(simulated)
1Band QDSC(PbSe/GaAs) η = 37.52% [81] & 2017
2 IB QDSC η = 51.6% [82] & 2014
(IAs.9N.1/GaAs.98Sb.02)
2 IB QDSC η = 49.27% [83] & 2018
(In.75Ga.25N/GaN)

2.9 Chapter Summary

In this chapter, we had studied many articles related to the solar cell. From these
articles, one can get an idea about the classification of solar cells. By the way, we have
explained solar energy, solar cell etc. We have discussed especially the quantum dot,
quantum dot solar cells and QDIB solar cells. In the next chapter, we will discuss the
physics of solar cells and explain them properly.
 19

CHAPTER III

SOLAR CELL PHYSICS

3.1 Introduction

In this chapter, we will discuss various parameters related to the solar cell such as
semiconductor device physics etc.

3.2 Bandgap

In physics, a band gap, also called an energy gap or bandgap, is an energy home in a
compacted where no electron states can exist. In graphs of the electronic band
construction of objects, the band gap typically refers to the energy change (in electron
volts) amid the highest of the valence band and the bottom of the conduction band in
paddings and semiconductors [82]. A semiconductor may be a substantial with a little
but non-zero band gap that performs as an insulator at temperature but permits thermal
irritation of electrons into its conduction band at temperatures that are underneath its
freezing point. In difference, a stuff with an outsized band gap is an insulator. In
conductors, the valence and conduction bands may overlay, in order that they might
not have a band gap [82]. The Figure 3.1 shows bandgap in semiconductor [41].

Figure 3.1: Bandgap in metals, semiconductor and insulator [41].

 20

3.3 Intrinsic Carrier Concentration

The updraft excitation of a carrier from the valence band to the conduction band
generates permitted transporters in both bands. The concentration of those carriers is
named the intrinsic carrier concentration, denoted by ni. Semiconductor substantial
which has not had impurities added thereto so as to vary the carrier concentrations is
named intrinsic substantial [83]. The intrinsic carrier concentration is that the quantity
of electrons within the conduction band or the quantity of holes within the valence band
in intrinsic substantial. This quantity of carriers hinge ons on the band gap of the fabric
and on the temperature of the fabric. A large band gap will make it harder for a carrier
to be thermally stimulated across the band gap, and thus the intrinsic carrier
concentration is lower in higher band gap substantials. Alternatively, growing the
temperature makes it more likely that an electron is going to be thrilled into the
conduction band, which can upsurge the intrinsic carrier concentration. This renders
directly to solar cell efficiency [83]. Intrinsic carriers are the electrons and holes that
sponsor in conduction. The concentration of those carriers is reliant upon the
temperature and band gap of the fabric, thus affecting a stuff's conductivity. Knowledge
of intrinsic carrier concentration is linked to our indulgent of photovoltaic cell
efficiency, and the way to maximize it. The exact value of the intrinsic carrier
concentration in silicon has been extensively studied thanks to its importance in
modeling. At 300 K the widely accepted value for the intrinsic carrier concentration of
silicon, ni, is 9.65 x 109 cm-3 as measured by Alternate, which is an update to the
beforehand recognized value given by Sproul. A method for the intrinsic carrier
concentration in silicon as a role of temperature is given by Missiakos [83].

3.4 Symmetry Carrier Concentration

Semiconductors encompass majority and minority carriers. The more plentiful charge
carriers are the bulk carriers; the less plentiful are the minority carriers. The symmetry
carrier concentration are often augmented through doping. The total quantity of carriers
in the conduction and valence band is called the symmetry carrier concentration. The
product of minority and majority charge carriers may be a persistent [83]. The quantity
of carriers inside the conduction and valence band with no superficially applied bias is
named the symmetry carrier concentration. For majority carriers, the symmetry carrier
concentration is satisfactory to the intrinsic carrier concentration plus the quantity of
free carriers supplementary by doping the semiconductor [83]. Under most conditions,
 21

the doping of the semiconductor is numerous orders of extent greater than the intrinsic
carrier concentration, such the amount of majority carriers is roughly equal to the doping
[83].

3.5 Fermi Level

At low temperatures, electrons in a quartz occupy the lowermost possible energy states.
According to Pauli’s exclusion principle, each permissible energy state can be engaged
by, at most, two electrons, each of reverse spin. Hence, at low temperatures, all
accessible states during a quartz up to a specific energy state are going to be engaged
by two electrons. This energy level is called the Fermi level (EF) [42,84].

3.5.1 n-Type and p-Type Conductivity

A substantial with conductivity in between highly conductive alloys and highly resistive
insulators is called a semiconductor. Semiconductors can be catalogued as direct and
indirect. In a semiconductor at room temperature, the communal outer electron lattice
has a small likelihood of ahead enough energy to break permitted from valence band to
conduction band. But at high temperature electron has a higher likelihood of ahead extra
vibration energy. The semiconductors can be doped with contamination atoms to
change the degree of conductivity. Semiconductors having additional electrons are
called n-type because it is conquered by free negative charges, electrons. The
contamination atoms that are introduced to add the additional electrons are called
donors because they donate a free electron to the conduction band. A massive majority
of these donors will be ionized. The total quantity of electrons in the conduction band
can be similar to by the quantity of donor impurity atoms ND. The Fermi level (EF) is in
the central of the bandgap in an intrinsic semiconductor [84]. In n-type doped
semiconductors, the Fermi level is loosened in the direction of the conduction band EC
and in p-type doped semiconductors, the Fermi level moves towards the valence band
EV. Figure 3.2 shows the energy band diagrams of isolated n and p-type substantials
[39]. The position of the Fermi levels can be determined from the equations given
below.

For n-type, Efn – Ec = kT/q ln (ND/NC) (3.1)

For p-type, Ev – Efp = kT/q ln (NA/NV) (3.2)

 22

where k is the Boltzmann constant, T is the absolute temperature, Efn and Efp are the
Fermi levels for n and p type region, EC is the energy level at the bottom of the
conduction band, Ev is the energy level at the top of the valence band, NC and NV are
the actual concentration of states in the conduction and valence band correspondingly,
ND and NA are the donor and acceptor concentrations correspondingly.

3.6 P-N Junctions

When two out-of-the-way p-type and n-type substantial are electrically connected they
form a p-n junction. The p-n junctions can be classified as
a. Homojunctions and
b. Heterojunctions.
A homojunction is a semiconductor boundary that occurs between layers of alike
semiconductor substantial; these ingredients have equivalent band gaps but typically
have dissimilar doping [82]. In most applied cases a homojunction happens at the
boundary between an n-type (donor doped) and p-type (acceptor doped) semiconductor
like silicon, this is often called a contact. A hetero-structure is made by sporadic
semiconductors of various types with dissimilar band gaps and dissimilar electron
affinities so as to make an alternating variation of the potential seen by electrons in the
conduction band and holes in the valence band. The simplest example of hetero-
structure is that the simple hetero-junction between two dissimilar semiconductors with
energy band offsets. These semiconducting ingredients have inadequate band gaps as
against a homojunction. There is an preliminary movement of free electrons from the
n-type region to the p-type region and free holes from the p-type to n-type. These origins
the establishment of a depletion region which opposes the further movement of charge
carriers [91]. This depletion region has permanent charges gives rise to the space charge
which is shown in Figure 3.2 [39].

Figure 3.2: Space Charge [39].

 23

Under thermal symmetry, the electron and hole current densities are given by

𝛿𝐸𝑓
Jn = µn. n. (3.3)
𝛿𝑥
𝛿𝐸𝑓
Jp = µp.n. (3.4)
𝛿𝑥

Where μn and μp is electron and hole mobility correspondingly, EF is the Fermi energy,
n and p is the electron and hole concentration correspondingly.

3.7 Built In Voltage

The built-in voltage during a semiconductor contemporary the potential across the
depletion region in symmetry. Since symmetry suggests that the Fermi energy is
constant through the p-n diode, the interior potential must alike the variance between
the Fermi energies of every region. For zero net electron and hole current concentrations
we necessitate that the Fermi level should be constant throughout the sample. This
causes a twisting of the bands of the semiconductor foremost to the potential being
established. Figure 3.3 shows the band twisting of the semiconductor. This potential is
given by [91],

Vbi = kTln (NAND/ni2) (3.5)

Where k is the Boltzman’s constant, T is the absolute temperature, NA and ND is the

acceptor and donor concentration correspondingly, ni is the intrinsic concentration.

Figure 3.3: Band bending in Heterojunction [42].

 24

3.8 Heterojunction

A heterojunction is a connection designed between two unlike semiconductor things.

Figure 3.4: Energy-band diagram for two isolated semiconductors in which space
charge neutrality is assumed to exist in each region [43]

Heterojunctions are two categories, isotype, and an isotype heterojunction. Isotype

heterojunctions are the one designed with ingredients of same conductivity and an
isotype are designed with ingredients of dissimilar conductivities [91]. The band
twisting of heterojunctions is not as flat as the homojunction because of variance in
electron affinities, work functions, etc. These cause boundary states or band
disjointedness which form the recombination centers. The energy band diagram of two
semiconductor ingredients prior to creating a junction is shown in Figure 3.4 [43].
Where Eg1 and Eg2 are the bandgap of two dissimilar semiconductors Φm1 and Φm2 are
work functions. χ1 and χ2 are electron affinities. Ε1 and Ε2 are permittivity. The energy
band diagram of a heterojunction is shown in Figure 3.5. The band discontinuities are
given by

ΔEC= χ1- χ2 (3.6)

ΔEF=Eg1-Eg2- ΔEC (3.7)

Figure 3.5: Energy Band Diagram of Heterojunction [43]

 25

The total inbuilt potential, Vd, is adequate to the wholety of incompletely inbuilt
voltages Vd1 and Vd2, where Vd1 and Vd2 are the electrostatic potentials of the
semiconductors. Most of the thin film solar cells are heterojunction based. The
Cu(InGa)Se2 / CdS solar cell, which is the subject of study here, is an isotype
heterojunction. The energy band diagram of a CuInSe2 / CdS / ZnO heterojunction solar
cell is shown in Figure 3.5 [43]. ZnO is the front see-through contact. As of its high
band gap, almost all the light permits through to the underlying layers. Most of the
occurrence light permits through the wider band-gap window layer CdS and is engrossd
in the lower band-gap CuInSe2 layer [92]. Energy-Band Diagram of a
CuInSe2/CdS/ZnO Heterojunction Solar Cell is shown in Figure 3.6 [44].

Figure 3.6: Energy-Band Diagram of a CuTex/CdS/CdTe Heterojunction

Solar Cell [44].

3.9 Bias of PN Junctions

1. Forward bias happens when a voltage is practical across the photovoltaic cell
such that the electric field designed by the P-N junction is diminished. It
simplicities carrier dispersion across the depletion region, and primes to
augmented dispersion current.
2. In the attendance of an exterior circuit that repeatedly delivers majority
carriers, recombination upsurges which continually reduces the incursion of
carriers into the solar cell. This upsurges dispersion and eventually
intensifications current across the exhaustion region [83].
3. Reverse bias happens when a voltage is pragmatic crossways the photovoltaic
cell such that the electric field designed by the P-N junction is augmented.
Dispersion current reductions.
 26

Semiconductor devices have three modes of operation [83]:

1. Thermal Symmetry: At thermal symmetry there are no exterior efforts such as light
or pragmatic voltage. The currents symmetry each other out so there is
no remaining current within the device.
2. Steady State: Below steady state there are exterior efforts such as light or pragmatic
voltage, but the conditions do not alteration with time. Devices characteristically
activate in stable state and are either in forward or reverse bias.
3. Temporary: If the pragmatic voltage vicissitudes speedily, there will be a petite
interruption before the photovoltaic cell retorts. As solar cells are not secondhand for
high-speed procedure there are few additional fleeting belongings that need to be
occupied into account [83].

3.10 Solar Cell Operation

The procedure of the photovoltaic cell is based on subsequent three steps. In step one,
Photons in daylight triumph the solar array and are engrossed by semiconducting
substantials. In step two, the occurrence photon produces electron hole pair by
redeeming electron from the atoms. The electron hole pairs stream concluded the
substantial to harvest electricity. Due to the special configuration of solar cells, the
electrons are only allowable to move in a solitary direction. In step three, Solar cell is
proficient of altering daylight unswervingly into DC electricity [42]. When a solar cell
is unprotected to a solar spectrum, the photons with energy superior than Eg are
engrossed and the substantial conveys those with energy fewer than Eg. Hence if we

Figure 3.7: Ideal Solar Cell J-V curve [43]

know the energy bandgap of the semiconductor then we can see the wavelength range
of light that will be engrossed by the semiconductor by means of the equation.
1 .24
λ= (3.8)
Eg
 27

here Eg is in eV and λ is in microns. These engrossed photons consequence in the

cohort of electron-hole pairs (EHP); these charge carriers verbose to the space charge
district and are then brushed crossways the connection if not recombined. These subtle
carriers give upsurge to the photocurrent [91]. The ideal J-V curves of a solar cell
under dark and irradiated conditions are shown in Figure 3.7 [43]. In the dark, the
solar cell is a simple p-n junction and can be given by the diode equation [42,91]
𝑞𝑉
I= I0[ 𝑒 𝐾𝑇 -1] (3.9)
I0 is the diode inundation current, V is the applied bias, k is the Boltzmann’s constant,
T is the out-and-out temperature. Under irradiated conditions there is an added current
due to the photo caused current; therefore, the above equation vagaries to equation 3.10.

Figure 3.8: Generation of EHP in a solar cell under illumination [42].

𝑞𝑉
I = I0[ 𝑒 𝐾𝑇 -1]- IL (3.10)

Where IL is the photo formed current.

Under radiance the built-in potential of the solar cell deviations due to additional
carriers being formed which result in remaining charges on the n and p side.

3.11 Equivalent Circuit of Solar Cell

The corresponding circuit of an ideal photovoltaic cell as cell under radiance is shown
in the Figure 3.10 [43]. Here the current source is equivalent to IL which is the photo
created current. The series resistance, RS, is the amalgamation of the bulk resistance of
the semiconductor, the bulk resistance of the metal contacts and the contact resistance
amid the contacts and the probe [91]. The shunt resistance, Rsh, decreases the seepage
current in the p-n junction. The series resistance is given by the reciprocal cross of the
slope of the I-V curve when the solar cell is forward biased. The shunt resistance is
 28

originate out by taking the reciprocal cross of the slope of the I-V curve when the solar
cell is converse biased [91].

Figure 3.9: Equivalent Circuit of Solar Cell [43].

3.12 Solar Cell Design Principles

Solar cell design includes stipulating the strictures of a photovoltaic cell construction
so as to exploit efficacy, given a particular set of restraints [83]. These restraints are
going to be distinct by the working situation during which solar cells are shaped. for
instance, during a profitable situation where the goal is to stock a competitively valued
photovoltaic cell, the value of manufacturing a precise photovoltaic cell construction
must be taken into deliberation. However, during a investigate situation where the goal
is to supply a extremely well-organized laboratory-type cell, exploiting efficiency
instead of cost, is that the main deliberation. The alteration between the high
hypothetical efficacies and therefore the efficacies restrained from telluric solar cells is
due mainly to two factors [83]. the prime is that the hypothetical supreme efficacy
estimates accept that energy from each photon is optimally castoff, that there are not
any unengrossd photons which each photon is engrossed during a substantial which
structures a band gap adequate to the photon energy. this is often attained in theory by
molding an immeasurable pile of solar cells of numerous band gap constituents, each
engrossing only the photons which resemble precisely to its band gap. The second factor
is that the high hypothetical efficacy forecasts assume a high concentration ratio [83].
Presumptuous that temperature and resistive belongings don't govern during a
concentrator photovoltaic cell , cumulative the sunshine concentration correspondingly
upsurges the short-circuit current. Since the open-circuit voltage (Voc) also hinge ons
on the short-circuit current, Voc upsurges logarithmically with light level. Furthermore,
since the utmost fill factor (FF) upsurges with Voc, the utmost possible FF also upsurges
 29

with concentration. the extra Voc and FF upsurges with captivation which permits
concentrators to realize higher efficacies [83].
In designing such single junction solar cells, the ethics for exploiting cell efficacy are:
cumulative the quantity of light collected by the cell that is bowed into carriers, growing
the collection of light-formed carriers by the p-n junction, curtailing the forward bias
dark current, mining the current from the cell deprived of resistive fatalities [83].

3.13 Requirements for a Solar Cell Substantial

The quantity of ingredients which revelation the photovoltaic consequence and can be
used for solar cell construction is large. To be valuable for real-world PV applications,
however, the device desires to please plentiful necessities. The first obligation is to
proficiently adapt solar energy into electricity. Second, the substantial used needs to be
cheap, available in large quantities and nontoxic. Third, the device making method
should be cheap, fast, simple and ecologically benign. Fourth, the device recital should
be steady for prolonged periods of time [85]. To make solar cells, the underdone
supplies—silicon dioxide of either quartzite gravel or crushed quartz—are first placed
into an electric arc incinerator, where a carbon arc lamp is practical to release the
oxygen. The goods are carbon dioxide and molten silicon.

3.14 Solar Cell Performance Parameters

There are numerous solar panel productivity constraints that can be restrained and
initiate throughout flash test, serving to judge on the recital quality of a solar panel. The
basic solar cell demonstration parameters are listed in the Table 3.1 [43].

Table 3.1: Basic solar cell parameter [43]

Parameter Symbol Unit Determined by

Open Circuit Voltage VOC V J=0
Short circuit current density JSC mA/cm2 V=0
Maximum power voltage Vmax V V at (JV)max
Maximum power current Jmax mA/cm2 J at (JV)max
Fill Factor FF - (JV)max/(VOCJSC)
Efficiency Η % (JV)max/Pincident
 30

Alteration efficiency is normally the constraint of most interest for solar cell
applications. It is frequently wrecked down into three dissimilar parameters:
1) Short circuit current density (JSC)
2) Open circuit voltage (VOC)
3) Fill factor (FF).

3.14.1 Short-Circuit Current Density

The short-circuit current, i.e., the current at V = 0, hinge on on the quantity of photo-
formed carriers and the gathering efficacy. The quantity of formed carriers can be
exploited by diminishing the area taken by contact grids and by adequately bushy
engrossrs, which permit all of the photons with satisfactory energy to be engrossed.
Assortment efficacy be contingent on the recombination apparatuses [85]. The losses in
short-circuit current can be analyzed from the quantum efficiency curves. The short-
circuit current density Jse that can be obtained from the standard 100 mW/cm2 solar
spectrum The incoming light, i.e., that part of the solar spectrum with photon energy hv
larger than the band-gap energy Eg=1.155 eV of the specific engrossr would resemble
to a (maximum possible) Jsc of 41.7 mA/cm2.

3.14.2 Open-Circuit Voltage

Open-circuit voltage is the voltage at nil current when the onward current symmetrys
the photo formed current. The open-circuit voltage is equivalent to the alteration in
quasi-Fermi levels for electrons and holes between the two sides of the device and its
supreme is resolute by the engrossr band-gap Eg. From the diode equation, Voc is equal
to [85]: VOC = kT/q ln [(JL / J0) + 1] (3.11)

The saturation current J0 hinge ons on the substantial belongings and the cell structure
and is imperfect by recombination coming from several dissimilar recombination
instruments: recombination in the bulk CIGS, in the space-charge region and at the
CdS/CIGS interface.

3.14.3 Maximum Power Point

The power mined from the cell is a product of current and voltage. At some point on
the current-voltage curve (i.e., for a specific load) this product has a supreme value.
That point is extreme-power point and the conforming current and voltage are referred
to as the maximum-power current Jmp and the maximum-power voltage Vmp [85].
 31

3.14.4 Fill Factor

In addition to Voc and Jsc, the maximum power hinge ons on how “square” the curve is.
The “squareness” is well-defined by fill factor (FF):

FF = VmpImp / VocIsc (3.12)

3.14.5 Efficiency

Conversion Efficiency involves all these three parameters and can be computed as [85]:

η = VpIp / Pin = FF . Voc .Isc/ Pin (3.13)

Pin is the happening light power on the cell. It is commonly taken to be 100 mW/cm2
for standard solar radiance. This radiance is referred to as AM 1.5 radiance and it is
correspondent to sunlight temporary through 1.5 times the air mass of vertical radiance
[85].

3.14.6 Series Resistance

The series resistance ascends from the resistance of the cell substantial to current flow,
mostly through the front peripheral to the contacts and from resistive contacts. Series

Figure 3.10: Effect of increasing series resistance [43].

resistance is a specific tricky at high current concentrations, for case under concentrated
light. Effect of Series Resistance on I-V curve is shown in Figure 3.10. Series resistance
in a solar cell has three causes: firstly, the undertaking of current through the emitter
and base of the solar cell; secondly, the contact resistance between the metal contact
and the silicon; and finally, the resistance of the top and rear metal contacts. The main
influence of series resistance is to lessen the fill factor, although unduly high values
 32

may also lessen the short-circuit current. chief influence of series resistance is to lessen
the fill factor, although unduly high values may also lessen the short-circuit current.

3.14.7 Parasitic Resistance

In real cells, power is dissolute through the resistance of the contacts and through escape
currents around the sides of the device. These effects are equivalent electrically to two
scrounging resistances in series (Rs) and in parallel (Rsh) with the cell concentrated light.
Effect of Series Resistance on I-V curve is shown in Figure 3.10.

3.14.8 Shunt Resistance

The parallel or shunt resistance ascends from seepage of current through the cell, around
the ends of the device and between contacts of dissimilar division. It is a problem in
ailing rectifying devices. Parallel resistances also lessen the fill factor as shown in
Figure 3.11 [43]. For an efficient cell, we want Rs to be as small and Rsh to be as large
as possible. When parasitic resistances are included, the diode equation becomes

J = Jsc - J0[eq(V+JARs)/kT-1] - [(V+JARs)/Rsh] (3.14)

Figure 3.11: Effect of reducing parallel resistances [43].

3.14.9 Non-Ideal Diode Behavior

The ideal diode behavior of Eq. 3.15 is seldom seen. It is common for the dark current
to hinge on weaker on the bias. The real necessity on V is quantized by an ideality
issue and the current voltage characteristic given by the non-ideal diode equation,
J =Jsc - Jo (eqV/mkT - 1) (3.15)
 33

m naturally deceits between 1 and 2. In record-efficiency CIGS cells [45], rs and rsh
belongings are insignificant and the best diode quality factors achieved are around 1.3.
More typical values for these parameters are RS ~1 cm2, rsh> 500 cm2 and A ~1.5.

3.14.10 Captivation of Light

Photons occurrence on the peripheral of a semiconductor are going to be either

replicated from the highest exterior, are going to be engrossed inside the substantial or,
failing either of the above two processes, are going to be diffused through the fabric.
For photovoltaic devices, reflection and transmission are typically measured loss
instruments as photons which aren't engrossed don't generate power. If the photon is
enchanted it's the likelihood of exhilarating an electron from the valence band to the
conduction band. A key think about significant if a photon is engrossed or taken is that
the energy of the photon. Therefore, as long as the photon has sufficient energy will the
electron be thrilled into the conduction band from the valence band. Photons dropping
onto a semiconductor substantial are often divided into three groups supported their
energy compared thereto of the semiconductor band gap:

1. Eph < EG Photons with energy Eph less than the band gap energy EG cooperate
only feebly with the semiconductor, short-lived through it as if it were see-
through.
2. Eph = EG have just enough energy to generate an electron hole pair and are
proficiently engrossed.
3. Eph > EG Photons with energy much superior than the band gap are mightily
engrossed. However, for photovoltaic tenders, the photon energy superior than
the band gap is distorted as electrons rapidly thermalize back down to the
conduction band ends.

3.14.11 Captivation Coefficient

1. Dissimilar semiconductor ingredients have dissimilar captivation constants.

2. Ingredients with higher captivation constants more voluntarily engross photons,
which stimulate electrons into the conduction band.
3. Knowing the captivation constants of ingredients aids engineers in defining
which solid to use in their solar cell designs [83].
The constant of captivation governs how far into a cloth light of a specific wavelength
can infiltrate before it's engrossed. In a substantial with a coffee coefficient of
 34

captivation, light is merely poorly engrossed, and if the fabric is thin enough, it'll appear
see-through there to wavelength [83]. The coefficient of captivation hinge ons on the
fabric and also on the wavelength of sunshine which is being engrossed. Semiconductor
substantials have a pointy edge up their coefficient of captivation, since light which has
energy below the band gap doesn't have sufficient energy to excite an electron into the
conduction band from the valence band. Consequently, this light is not engrossed [83].

3.14.12 Captivation Depth

The association between constant of captivation and wavelength makes it in order that
dissimilar wavelengths infiltrate dissimilar distances into a semiconductor before most
of the sunshine is engrossed. The captivation depth is given by the inverse of the
coefficient of captivation, or α-1 [83]. The captivation depth may be a useful parameter
which provides the space into the fabric at which the sunshine drops to about 36% of
its unique strength, or alternately has dropped by a factor of 1/e. Since high energy light
(short wavelength), like blue light, topographies a large coefficient of captivation, it's
engrossed during a short distance (for silicon solar cells within a couple of microns) of
the exterior, while red light (lower energy, longer wavelength) is engrossed less
strongly. Even after a couple of hundred microns, not all red light is engrossed in silicon
[83].

1. The captivation depth is given by the inverse of the captivation coefficient, and
describes how deeply light penetrates into a semiconductor before being
engrossed.
2. Higher energy light is of a shorter wavelength and has a shorter captivation
depth than lower energy light, which is not as readily engrossed, and has a
greater captivation depth.

3. Captivation depth affects aspects of photovoltaic cell design, such as the depth
of the semiconductor substantial [83].

3.14.13 Generation Rate

The generation rate stretches the quantity of electrons made at each point in the device
due to the captivation of photons. Generation is an important parameter in solar cell
operation [83].
 35

1. The generation of an electron-hole pair can be computed at any location within

the photovoltaic cell, at any wavelength of light, or for the whole standard
solar spectrum.
2. Generation is the extreme at the exterior of the substantial, where the majority
of the light is engrossed.
3. Because the light used in PV tenders comprises many dissimilar wavelengths,
many dissimilar generation rates must be taken into account when designing a
solar cell [83].

3.14.14 Lifetime

If the quantity of minority carriers is augmented above that at symmetry by some

temporary peripheral excitation (such as incident sun), the excess minority carriers will
decay back to that symmetry carrier concentration due to and through the process of
recombination. A perilous parameter in a solar cell is the rate at which recombination
occurs. Such a process, known as the "recombination rate" hinge ons on the quantity of
surplus minority carriers [83]. If for example, there are no surplus minority carriers,
then the recombination rate must be zero. Two parameters that are fundamental to
recombination rate are the minority carrier lifetime and the minority carrier diffusion
length. The first will be discussed here. The minority carrier lifetime of a substantial,
denoted by τn or τp, is the average time which a carrier can spend in an thrilled state
after electron-hole generation before it recombines [83]. It is often just mentioned to as
the "lifetime" and has nothing to do with the stability of the substantial. Stating that "a
silicon wafer has a long lifetime" typically means minority carriers formed in the bulk
of the wafer by light or other means will persist for a long time before recombining.
Hinge oning on the structure, solar cells made from wafers with long minority carrier
lifetimes will typically be more effective than cells made from wafers with short
minority carrier lifetimes. The terms "long lifetime" and "high lifetime" are used
interchangeably [83].
1. The lifetime of a semiconductor is reliant upon the recombination rate, which is
reliant on the concentration of minority carriers.
2. The lifetime of the substantial takes into account the dissimilar categories of
recombination.
3. Lifetime is a pointer of the effectiveness of a solar cell, and thus is a key
deliberation in selecting substantial for solar cells [83].
 36

3.14.15 Exterior Recombination

1. Areas of flaw, such as at the exterior of solar cells where the lattice is disturbed,
recombination is very high.
2. Exterior recombination is high in solar cells, but can be imperfect.
3. Understanding the impacts and the ways to limit exterior recombination primes
to better and more full-bodied solar cell designs [83].
Any imperfections or scums within or at the external of the semiconductor promote
recombination. Since the exterior of the solar cell signifies an unadorned disturbance of
the crystal lattice, the exteriors of the solar cell are a site of particularly high
recombination. The high recombination rate in the vicinity of a exterior depletes this
region of minority carriers [83]. A contained region of low carrier concentration causes
carriers to flow into this region from the surrounding, higher concentration regions.
Therefore, the exterior recombination rate is restricted by the rate at which minority
carriers move towards the exterior. A parameter called the "exterior recombination
velocity", in units of cm/sec, is used to specify the recombination at a exterior. In a
exterior with no recombination, the movement of carriers towards the exterior is zero,
and hence the exterior recombination velocity is zero. In an exterior with infinitely fast
recombination, the movement of carriers towards this exterior is restricted by the
maximum velocity they can attain, and for most semiconductors is on the order of 1 x
107 cm/sec [83]..

3.14.16 Diffusion Length

The second associated parameter to recombination rate, the "minority carrier diffusion
length," is the average reserve a carrier can move from point of generation until it
recombines. As we shall see in the next chapter, the diffusion length is closely related
to the collection likelihood. The minority carrier lifetime and the diffusion length hinge
on strongly on the type and extent of recombination processes in the semiconductor
[83]. For many types of silicon solar cells, SRH recombination is the leading
recombination mechanism. The recombination rate will hinge on the quantity of faults
present in the substantial so that as doping the semiconductor upsurges the defects in
the solar cell. Doping will also upsurge the rate of SRH recombination. In addition,
since Auger recombination is more possible in heavily doped and thrilled substantial,
the recombination process is itself enhanced as the doping upsurges. The method used
 37

to fabricate the semiconductor wafer and the processing also have a major impact on
the diffusion length [83].
1. Diffusion length is the average length a carrier moves between generation and
recombination.
2. Semiconductor substantial that are heavily doped have greater recombination
rates and consequently, have shorter diffusion lengths.
3. Higher diffusion lengths are indicative of substantial with longer lifetimes and
are, therefore, an important quality to consider with semiconductor substantial
[83].

3.14.17 Quantum efficiency

Quantum efficiency (QE) is well-defined as a ratio of collected carriers to photons

incident on a tool at each wavelength. within the ideal case, every photon generates an
electron-hole pair which sponsors one carrier to the photocurrent and therefore the
quantum efficiency is 100% for photon energies above the band gap and 0 below. In
real cells, that's never the case no matter efforts to attenuate reflection loss, some light
is reflected from the front exterior of the photovoltaic cell. The primary step in QE loss
analysis is to correct for reflection loss [85]. The corrected QE curve are often
mentioned because the internal QE. Photons with energies less than the band-gap don't
sponsor to the current; therefore, the long wavelength cut-off of the quantum efficiency
curve are often wont to estimate the engross band gap. As shown in Figure 3.12 short
wavelength losses are the results of the captivation within the CdS (λ< 520 nm) layer
and therefore the TCO (λ< 375 nm) layer, because the photons formed in these layers
generally don't get collected to the terminals [85]. While quantum efficiency ideally has
the square shape shown above, the quantum efficiency for many solar cells is reduced
thanks to recombination effects. an equivalent mechanism which affects the gathering
probability also affect the quantum efficiency [83]. for instance, front exterior
passivation affects carriers formed near the exterior, and since blue light is captivated
very on the brink of the exterior, high front exterior recombination will affect the "blue"
portion of the quantum efficiency. Similarly, green light is captivated within the bulk
of a photovoltaic cell and a coffee diffusion length will affect the gathering probability
from the photovoltaic cell bulk and reduce the quantum efficiency within the green
portion of the spectrum [83]. The quantum efficiency is often viewed because the
assortment probability due the generation profile of one wavelength, integrated over the
 38

device thickness and normalized to the incident quantity of photons [83]. The photons
with energies slightly higher than the band gap will penetrate deepest energies of TCO
(3.3 eV) and CdS (2.4 eV) yields the current loss due to captivation in CdS.
𝐽𝐿 = 𝑞 ∫ 𝐴𝑀1.5 (𝜆)𝑄𝐸(𝜆)𝑑𝜆 (3.16)

Incorporation within a sure wavelength range can control the segment of photocurrent
lost due to a specific loss mechanism. For example, integration between band gap [85].

Figure 3.12: Quantum Efficiency [46].

3.14.18 Spectral Response

The spectral response is theoretically nearly like the quantum efficiency. The quantum
efficiency gives the amount of electrons output by the photovoltaic cell compared to the
amount of photons incident on the device, while the spectral response is that the ratio
of the present formed by the photovoltaic cell to the facility occurrence on the
photovoltaic cell [92]. A spectral response curve is shown below. The ideal spectral
response is limited at long wavelengths by the absence of the semiconductor to step up
photons with energies below the band gap. This limit is that the same as that encountered
in quantum efficiency curves. The ideal spectral response is limited at long wavelengths
by the lack of the semiconductor to soak up photons with energies below the band gap.
This limit is that the same as that met in quantum efficiency curves. However, unlike
the square shape of QE curves, the spectral response decreases at small photon
wavelengths. At these wavelengths, each photon features a large energy, and hence the
ratio of photons to power is condensed. Any energy above the band gap energy isn't
utilized by the photovoltaic cell and instead goes to heating the photovoltaic cell. The
inability to completely utilize the incident energy at high energies,
 39

and therefore, the incapability to step up low energies of sunshine represents a big power
loss in solar cells consisting of a single p-n junction [83].

Figure 3.13: Spectral Response [46].

3.14.19 Loss Mechanisms

1. Reflection” losses are familiarized by partial attention of the front exterior by

nontransparent contacts (i.e., metal contact fingers) or by reflection at substantial
interfaces. By experimentation, these losses are diminished by the application of
anti-reflective coatings.
2. “Window” captivation in the short-wavelength region is negligible due to the high
band-gap energy of this substantial. Free electron captivation in the ZnO layer can
lower the quantum efficiency in the high wavelength region, but this effect is
typically small and neglected in the numerical simulations [85].
3. “Buffer” captivation represents one of the major losses in today’s CIGS thin-film
solar cells. Thinning of the CdS or replacing it with a higher band-gap substantial
is possible alternatives.
4. “Recombination” losses are familiarized by less-than-ideal collection efficiencies
of photo formed carriers. The longer the wavelength, the deeper the generation of
carriers and the higher the likelihood of recombination.
5. “Deep penetration” of carriers. These losses are inherent to every semiconductor
as light with photon energy of hv < Eg is not engrossed [85].
 40

3.14.20 Shockley-Queisser limit

In physics, the Shockley–Queisser limit or thorough balance limit denotes to the greatest
hypothetical efficiency of a photovoltaic cell paying a contact to pucker power from the
cell. It was first computed by William Shockley and Hans Queisser-Shockley in 1961
[43]. The black height is energy that can be mined as useful electrical power (the
Shockley Queisser efficiency limit) the pink height is energy of below-bandgap
photons; the green height is energy lost when hot photo formed electrons and holes relax
to the band edges; the blue height is energy lost in the tradeoff between low radiative
recombination versus high operating voltage [46]. Designs that exceed the Shockley-
Queisser limit work by overwhelming one or more of those three loss processes [82].

3.15 Chapter Summary

In this chapter, we have discussed various parameters related to the solar cell operation.
Here we have discussed dissimilar terms related to a p-n junction which give a clear
concept about the solar cell. In Figure 3.10 equivalent circuit of solar cells has been
shown which gives a good idea of how solar cells work. The article on quantum
efficiency will help to understand how photo current generates in solar cells. We also
have focused on loss mechanism of solar cell which will help one while designing a
solar cell. In the next chapter, we will use this knowledge to model and simulate the
solar cell. In the next chapter, we will discuss device structure and simulation process
of the modeled solar cell.
 41

CHAPTER IV

QUANTUM DOT INTERMEDIATE BAND SOLAR CELL

4.1 Introduction

In this chapter, we will discuss various parameters related to the quantum dot and
quantum dot intermediate band solar cell (QDIBSC) basics etc.

4.2 Quantum Dot

Quantum dots (QDs) are man-made nano scale crystals that can conveyance electrons.
When UV light hits these semiconducting nanoparticles, they will emit light of varied
colors. These artificial semiconductor nanoparticles that have initiate applications in
composites, solar cells and fluorescent biological labels. Small quantum dots, such as
colloidal semiconductor nano crystals, can be as small as 2 to 10 nanometers,
conforming to 10 to 50 atoms in diameter and a total of 100 to 100,000 atoms within
the quantum dot volume as in Figure 4.1. Semiconductor quantum dots (QDs) have a
latent to upsurge the power conversion efficiency in photovoltaic operation because of
the augmentation of photo excitation. Quantum dots (QDs) are semiconductor elements
a twosome of nanometers in size, having optical and electronic belongings that fluctuate
from larger particles thanks to quantum physics. They are a central topic in
nanotechnology.

Figure 4.1: The schematic core shell configuration of the quantum

dot core [27].
 42

For intermediate band solar cells using self-assembled technique. QDs, destruction of
a reduction of open circuit voltage presents challenges for further efficiency
enhancement. Semiconductor quantum dots (QDs) have pinched considerable interest
for more than 20 years because of the optoelectronic advantages based on a zero-
dimensional system [93]. The photovoltaic applications using self-assembled quantum
dots (SAQDs) and colloidal quantum dots (CQDs) have the potential to enhance the
photo generation of carriers through the QD energy level or band [27].

Table 4.1: Excitation Bohr radius and bandgap energy of some common
semiconductors [39].

Semiconductor Excitation Bohr Radius Bandgap Energy (eV)

Structure (nm)
PbS 40.0 0.41
GaAs 28.0 1.43
CdTe 15.0 1.50
CdSe 10.6 1.74
ZnSe 8.4 2.58
CdS 5.6 2.53

4.3 Physics of QDs

In a wholesale semiconductor, electrons and holes are abundant to move and there's no
confinement and hence they need continuous energy values, where energy levels are
so on the brink of each other and packed. Thus, in bulk substantial when an electron
lessening occurs from the upper lumo of conduction band they will move from one
distinct energy level to other and as those discrete energy levels are very close to each
other those electrons relaxation release a little amount of energy as a form of heat. But
in case of QD the physics is totally unlike. Here conduction band has no thickly packed
energy states rather as their size is too small conduction bands has only few energy
states typically two detached from each other by a large distance. As energy alteration
is higher in this case when an electron lessening occurs from upper lumo of conduction
band to lower lumo they will release great amount of energy as a form of photon not
as phonon. This will provide additional advantage as this photon will be further
captivated by another electron in the valence band and causes excitation. So basically,
 43

here captivation of one photon from sun produces the generation of multiple electrons.
The parting of between the electron-hole is named Bohr’s radius. This table presents
some examples of excitation Bohr radius in some common semiconductors [39].

4.4 Applications of QDs

1. Quantum dot solar cells are an evolving field of solar cell study.
2. Actual due to quantum dots’ ability to specially engross and emit radiation that
results in the ideal generation of electric current and voltage.
3. QD based solar cells can be used to design low cost solar panel.
4. As it is cost effective it can be used for designing power system for spacecraft.
5. Many kinds of solar chargers like laptop battery charger, solar mobile charger,
power cell for calculators can be designed by this QD based solar cells.
6. Neuro-quantum structures
7. Single-electron devices, for instance, transistors
8. Tunable Lasers
9. Photodetectors, Sensors, TV.

4.5 Quantum confinement

Quantum dot is a zero-dimensional substantial not like quantum wire or quantum

wells. In quantum dot the motion of a single carrier is restricted in all three dimensions
and thus it is confined to zero density of states. Quantum confinement define electrons
in terms of energy levels, potential wells, valence bands, conduction bands, and
electron energy band gaps. The quantum confinement consequence is detected when
the size of the particle is too small to be electron and hole in nanocrystals meaningfully
hinge on on the substantial properties, namely, on the Bohr radius. These belongings
take place in bigger nanocrystals and hinge on the substantial properties, namely, on
the Bohr radius = 2.34 nm and of about 10 nm, which would have Cd-related
compounds such as CdTe, CdZnTe, and CdTeSe. Quantum confinement effects in one,
two, or three dimensions in solids lead to augmented electronic bandgaps. This electron
confinements heavily affect the substantial’s physical, optical and electrical properties.
The quantum confinement effect is detected when the size of the particle is too small
to be comparable to the wavelength of the electron. To comprehend this effect we
break the words like quantum and confinement, the word confinement means to limit
the motion of randomly moving electron to restrict its motion in specific energy levels
 44

and quantum replicates the atomic realm of particles. So as the size of a particle
diminution till we a reach a nano scale the decrease in confining dimension makes the
energy levels discrete and these upsurges or widens up the band gap and eventually the
band gap energy also upsurges.

4.6 Introduction of Intermediate Band using quantum dot

Main disadvantage of a photovoltaic alteration device is that it cannot use the energy
of sub band gap photons. In order to upsurge the efficiency of the cell by using the
energy of the sub band gap photons the concept of introduction of intermediate band
solar cell is at first familiarized by Luque & Marti on 1997.Till now several practical
approaches have been taken to introduce intermediate bands. Three methods among
them are most commonly used for research purpose. Intermediate bands can be formed
by using quantum dot in a periodic way, by using highly mismatched alloys and by
using hyper doped silicon. In this work we will analyze the performance of a multi-
intermediate band solar cell on the basis of periodic quantum dot arrays. In this
approach an intermediate band may be formed by positioning uniformly shaped
quantum dots adjacent adequate and periodically sufficient so that their wave function
couple together. Quantum dots must be of unchanging shape for proper working
otherwise highly mismatch will occur in device performance which can lead to the
thermalization loss rather improving cell performance [64]. In the case of quantum dot
is surrounded by a barrier substantial, the mini bands form within the forbidden band
gap of barrier substantial. Eigen energies of the bound stationary states within a
confining potential are the location of mini bands formed by periodic array of uniform
confining potentials [64]. It will be investigated in this work that introduction of one,

Figure 4.2: Transition of electrons in a multi-intermediate band (3 IBs) [37].

 45

two and three intermediate bands inside the band gap of the barrier substantial has a
higher efficiency compared to the single band gap conventional devices.
Transition of electrons between dissimilar bands due to photon incident is illustrated
in Figure 4.2 for three intermediate band quantum dot solar cell. There are total ten
transition for three intermediate bands QD solar cell structure. An electron from
valence band can excite directly to the conduction band or to the first, second or third
intermediate band. Upward transitions from valence band are denoted by EVI1, EVI2,
EVI3, Ecv for valence band to first IB, valence band to first IB, valence band to first IB
and from valence band to conduction band energy bandgap, respectively. Similarly,
upward transitions from first IB is denoted by EI1I2, EI1I3 and ECI1 for first IB to second
IB, first IB to third IB and first IB to conduction band energy bandgap, respectively.
Upward transition, upward transitions from second IB is denoted by EI2I3, ECI2 and ECI1
for second IB to third IB and second IB to conduction band energy bandgap,
respectively. Finally, only upward transition for third IB is denoted by ECI3. In a
conventional solar cell with an upsurge in carrier population the Fermi level split to
two chemical potential but in case of the intermediate band solar cell the fermi level
split into several chemical potential which are designated by µVI1 , µVI2 , µVI3 , µI1I2 , µI2I3
, µCI1 , µCI2 , µCI3. They are used to determine the probability existence of electron in the
conduction band or holes in the valence band [65].

4.7 Design Considerations of Intermediate Band Solar Cell

Performance of the intermediate band solar cell hinge ons on several design
parameters. Hinge onency of several parameters on the cell’s performance is given
below.

4.7.1 Dot Size

Position of the confined energy levels hinge ons on the size of the dot, its shape, and
substantials used. It is initiate that with an upsurge in dot size the efficiency of the cell
decreases for the same value of substantial content [62].

4.7.2 Dot Spacing (Dot Density)

In order to obtain high captivation coefficient quantum dots must be placed closely to
each other but very close to each other also lead to a decrease in widths of bands. That’s
why it’s better to use identical dots which are carefully slanted together at a distance
 46

of 100Å without the appearance of stimulated emission even at the maximum light
concentration. It is also initiate that the density of the dots can be kept below one order
of magnitude from the density of states at the conduction and valence band still
providing a compressing of the quasi-Fermi level of the electrons at the IB within kT
even when the cell is operated up to 1000 suns [31].

4.7.3 Dot Regularity

The alteration in the size and the regularity with which dots are manufactured affects
the performance of the cell at least in two ways. First, it upsurges the bandwidth of the
IB. A rough estimate predicts that dispersion in the size of the dots of 10% can be
tolerated without producing a bandwidth of the IB that causes stimulated emission
problem [31]. Second, because the regularity decreases, the electron wave function at
the IB becomes more localized affecting the radiative recombination rates through its
hinge on the matrix changeover elements [87].

4.7.4 Materials

According to Levy et al. such type of substantial combination (QD/Barrier) must be

chosen where the conduction band offset between dot and barrier substantial is large
compared to their valance band offset and conversion efficiency is initiate to be 60%
while assuming QDs are spherical. The reason behind low valence band offset
requirement is to reduce the possibility of undesired transitions and reducing the barrier
band gap [65]. Moreover, thinner solar cells are desired as it requires less substantial
and manufacturing cost will also reduce. It must be ensured that the intermediate bands
must not interact with others nor with the conduction or valence bands [94].

4.7.5 Doping

As a design consideration the intermediate bands are considered to be half filled which
is required for receipt of electrons from the opposite bands. this will be attained by n
doping at the barrier region with a degree that hinges on the space between the dots.
For dots of about 39Å in radius and a distance between dots of between 100 and 900Å,
the doping of the barrier region should be placed between 1016 and 4×1018 cm−3 [34].
In any case, this doping is like one impurity per QD. The doping process within the
engineering of solar cell is to form a contact by the injection of contamination
substantial into a silicon wafer. When the plasma jet is irradiated to the layer of dopant
 47

substantial, the dopant substantial is diffused to be doped into the doping layer of
wafer.

4.7.6 Electron Mobility and Hole Mobility

In physics, the electron mobility symbolizes how rapidly an electron can transfer
through a metal or semiconductor, when hauled by an electrical field. There is an alike
quantity for holes, called holes flexibility. The carrier mobility or flexibility refers to
both electron and hole mobility or flexibility. Electron mobility or flexibility is always
specified in units cm2/(V.s). Conductivity is proportional to the product of mobility of
carrier concentration [34,94].

4.7.8 n+ layer doping

As the junction depth upsurges, the reverse saturation current of the cell diminutions
and the open circuit voltage upsurges. On the other side, the dead region part of the n+
emitter near the cell exterior upsurges. The dead region is a region with very small
minority carrier lifetime leading to killing the photo formed eh pairs. Therefore, the
photovoltaic device response to the photons with short wave lengths becomes weaker
and the photocurrent Iph will be smaller by increasing the junction depth. Therefore,
there's an optimum junction depth which maximizes the photovoltaic cell efficiency
with the photovoltaic cell. This thickness is about 0.2 micrometer. Concerning the
effect of the doping concentration, as the doping concentration upsurges, the reverse
saturation current decreases and the open circuit voltage of the cell upsurges.
Increasing the doping concentration over certain optimum value leads to band gap
narrowing which results in the upsurge of the reverse saturation current and the
reduction of the open circuit voltage. Bandgap narrowing may be a consequence of
heavy doping effects. Therefore, there's an optimum doping concentration of the n+
emitter. Quantitative analysis and measurements showed that the optimum doping
concentration is about 10^19/ cm^3 [35].

4.7.9 p+ layer doping

The doping captivation affects mostly the conversion efficiency of the solar cells. As
the doping density growths, the opposite fullness current decreases resulting in a rise
within the circuit voltage and therefore the conversion efficiency. This upsurge is
sustained until the high doping effects begins to seem. The high doping effects are the
 48

lessening of the bandgap and the marginal carrier life time. Both causes the reverse
overload current to decrease again after reaching a peak with the doping captivation in
the substrate. The optimum substrate doping concentration amounts to about
10^17/cm^3 [35]. The back exterior field is achieved by producing a p+ layer under
the rear metallization. This layer reflects the minority carrier electrons and stop them
from reaching the highly recombining metal- silicon contact. Decreasing minority
carrier recombination basically enhances the conversion efficiency [35].

4.7.10 n+ and p+ layer thickness

The side toward the light must be of smaller thickness so that a large quantity of
photons quickly before recombination occurs. The minority carriers (holes within the
n-region or electrons within the p-region) must be ready to visit the junction. The key
is the size of depletion region and the diffusion length of minority carriers on each side.
Only the electron-hole pairs formed within the depletion region and within one
minority carrier diffusion length of the depletion region are going to be captured at the
contacts and produce current. All other electron-hole pairs are going to be lost to
recombination. When an electron-hole pair is formed within the n region, holes, the
minority carriers must make their way through the n-region into the depletion region
and on through the p-region. They are only in peril within the n-region, where there
are many electrons to recombine with them cancelling out the electron-hole generation
event. Similarly, electron-hole pairs in the p-region produces electrons, minority
carriers on the p-side, which must make it to the n-side. The side that the light strikes
first is critical, assume it is the n-side for purposes of illustration. Since the n-side is
that the side where the sunshine strikes first, it's particularly important for it to
effectively capture electron-hole pairs. If it's too long, it'll be too long on the exterior,
the farthest point from the junction, where captivation is strongest. This is deadly
because the copious quantity of electron-hole pairs created near the exterior would be
lost. Thus, the n-side, the exterior side of the junction must be relatively short. The p-
side can be as long as wanted because the alternative is that photons pass through
without creating an electron-hole pair [27].

4.7.11 Quantity of IBs

Figure 3.2 shows the umph band diagram of an IBSC with N bands. It can be seen that
as the quantity of bands in an IBSC upsurges, the quantity of inflammation paths
 49

upsurges and unfolding the device can become quite composite. We outline an
inflammation path as the energy path an electron takes when it is thrilled from one
band to another. Connected with each excitation path is a changeover energy which is
the photon energy mandatory to produce an excitation. For a device with a large
quantity of bands, an electron can be thrilled from the valence band to the conduction
band via many dissimilar inflammation paths. In this section, we present a method of
describing an IBSC with an arbitrary quantity of bands. From Figure 4.3, several things
of interest can be observed.
1. A N band IBSC, in general, will have N/2 intermediate bands and N(N-1)/2
dissimilar inflammation paths.
2. Each band is labeled with a quantity, starting with 1 for the valence band and
classification each intermediate band as 2,3,4 going up in energy until the conduction
band is reached and chosen with the quantity N. Adjacent bands are separated by a
single energy gap [37].

Figure 4.3: N-band IBSC showing band quantitys and transition energies [37]

3. There is a changeover energy connected with each inflammation path. This is the
energy mandatory for a photon to be thrilled from the starting band to the finishing
band. The extent will hinge on the excitation path under deliberation.
 50

4.8 Formation of IB within the band gap

The first technique is to familiarize small, homogenous QD structures into a single

junction device [21]. This produces an IB, which may be adjusted by altering the form
and size of the QDs. For an investigational device to show high-efficacy potential, it
must validate that it can produce current from the captivation of sub-bandgap photons
while conserving the device's output voltage. Using quantum dots, some
investigational devices, such as InAs/GaAs, have been made-up in laboratory. Another
technique of fabricating an IB device is to use highly unjust alloys. The use of those
unjust alloys familiarizes an IB thanks to the band anti-crossing (BAC) device [82].
this is often essentially the splitting of the valence or conduction band, counting on the
alloy type, into two bands [82]. These substantial’s are typically made from III-V
alloys; however, they need also been fabricated with II-VI alloys. The most studied
alloys are ZnTe doped with O and GaAs doped with N [82]. Both these devices have
experimentally shown the captivation of sub-bandgap photons, however, neither has
been able to demonstrate voltage preservation. Despite this, ZnTeO devices have
established a better photocurrent and efficacy than a analogous single bandgap ZnTe
device. Unfortunately, both structures exhibit an efficiency of but 1% . Moving
forward, more research is required to seek out substantial’s with natural partly
occupied IB bands to get higher efficiency to utilize more photons and extract more.
Finally, the last approach is to familiarize deep level impurities (DLI) into a
semiconductor bulk substantial [82]. This method is analogous to highly mismatched
alloys; however, the doping percentages are much less. The biggest question with these
devices is that the non-radiative recombination, predominantly Shockley-Read-Hall,
significantly upsurges. Noteworthy research during this field was aimed toward
achieving “lifetime recovery”, or the power to extend carrier lifetime by introducing
more DLIs. In particular, it had been believed that lifetime recovery might be achieved
by increasing the DLI concentrations to the insulator to metal transition. Krich
disproved this and in the process proposed a “figure of merit” to determine if
substantial would be suitable for high-efficiency IB’s. The idea was that if the non-
radiative recombination lifetime was meaningfully above the transit time for an
electron to movement from the conduction band to the IB, then the substantial could
upsurge efficiency [82]. Essentially, the electron could reach the IB before
recombining, resulting in a better induced photocurrent. This figure of merit has been
 51

wanting to elucidate why no usable device has been fabricated using highly doped
silicon. Chalcogen doped silicon, in particular, have low figures of merit due to their
small non-radiative recombination lifetimes. More research needs to be done to find a
bulk semiconductor substantial that exhibits higher non-radiative recombination
lifetimes to achieve IB devices.

4.9 Working principle for the intermediate band solar cell

The intermediate band solar cell uses a higher quantity of the incidence photons from
the sun over the application of the intermediate band. Within the conduction band (CB)
and the valence band (VB) the intermediate band solar cell encompasses a intermediate
band (IB) put in the band gap between the conduction and valence band. As seen in
Figure 4.4 the band gap of the semiconductor EG is remote into two sub-band gap EL
and EH. EH ≡ EI−EV is the difference between the balance Fermi energy of the
intermediate band and the highest point of the valence band. EL ≡ EC−EI is the energy
modification between the base of the conduction band and the balance Fermi energy
of the intermediate band, and we have that EG = EH +EL. The width of the intermediate
band hinges on QD size, dot distance and others factors. The transmission band,
valence band and intermediate band are shown along with the symmetry Quasi Fermi
energy of the intermediate bands. By absorbing photons three transitions are possible.
(1) An electron is moved from the conduction band to the intermediate band.
(2) An electron is moved from the intermediate band to the conduction band.
(3) An electron is moved from the valence band to the conduction band. The symbols
are explained in the text. The division of the whole band gap into two sub-band gaps

Figure 4.4: Band diagram of a substantial containing an intermediate band [38].

makes retention of photons with energies not exactly the aggregate band gap
 52

imaginable, encouragement a long-drawn-out photocurrent. To create an electron-hole

pair by consumption of photons with energies less than EG, two changeovers are
necessary. In one of the changeovers an electron is moved from the valence band to
the intermediate band leaving a hole behind in the valence band [38], envisaged as
transition (1) in Figure 4.4. In the second changeover the electron is transferred from
the intermediate band to the conduction band, visualized as transition (2) in Figure 4.4.
In addition, we have the “normal” creation of an electron-hole pair by captivation of a
photon and the direct transfer of an electron from the valence band to the conduction
band, visualized as transition (3) in Figure 4.4. The intermediate band has to be
partially filled with electrons to make both transition (1) and (2) possible. A partly
filled band comprises both void states to oblige electrons being exchanged from the
valence band to the transitional band and filled states to release electrons being driven
into the conduction band. The Fermi energy of the intermediate band has to be
positioned within the intermediate band to fulfill this condition [38].

4.10 Effect of Bands on Efficiency

Luque and Marti first derived a hypothetical limit for an IB device with one mid
gap energy state using thorough balance. They assumed no carriers were collected at
the IB which the device was under full concentration [82]. They initiate the
utmost efficacy to be 63.2%, for a bandgap of 1.95eV with the IB 0.71eV from either
the valence or conduction band. Under one sun radiance the restraining efficiency is
47%. Green and Brown long-drawn-out upon these results by deriving the theoretical
efficiency limit for a tool with infinite IBs. By familiarizing more IB’s, even more of
the incident spectrum are often utilized. After performing the detailed balance, they
initiate the utmost efficiency to be 77.2% [82]. This efficacy is a smaller amount than
that of a multijunction cell with infinite junctions. This is often because in multi
junction cells, electrons are captured exactly after being thrilled to a better energy
level, while in an IB device, the electrons still need another energy transition to
succeed in the conduction band and be placid.

4.11 Implementation of QDIBSC

Quantum dots are semiconducting elements that are abridged beneath the dimensions
of the Exciton Bohr radius and thanks to quantum physics considerations, the electron
energies which will exist within them become finite, much alike energies in an atom.
 53

Quantum dots are cited as "artificial atoms". These energy levels can be adjusted by
changing their size, width, interdot distance which consecutively describes the
bandgap. The dots can be full-grown over a range of sizes, permitting them to express
a variety of bandgaps without changing the original substantial or construction
techniques [94]. In typical wet chemistry preparations, the tuning is accomplished by
varying the synthesis duration or temperature. The ability to adjust the bandgap makes
quantum dots desirable for solar cells. For the sun's photon distribution spectrum, the
Shockley-Queisser limit indicates that the utmost solar conversion efficiency occurs
during a substantial with a band gap of 1.34 eV. However, substantial with lower band
gaps are going to be better suited to get electricity from lower-energy photons (and
vice versa) [94]. Single junction employments using lead sulfide (PbS) colloidal
quantum dots (CQD) have bandgaps which will be tuned into the far infrared,
frequencies that are classically difficult to realize with traditional solar cells. Half of
the solar power reaching the world is within the infrared, most within the near infrared
region. A quantum dot photovoltaic cell makes infrared energy as available as the other
[94]. Moreover, CQD offer easy synthesis and preparation. While postponed during a
colloidal liquid form they will be easily handled throughout production, with a fume
hood because the most complex equipment needed. CQD are typically manufactured
in small batches, but are often mass-formed. The dots are often disseminated on a
substratum by spin coating, either by hand or in an automatic process. Large-scale
production could use spray-on or roll-printing systems, dramatically reducing module
construction costs [95].

4.12 Potential of QDIBSC

Semiconductor quantum dots (QDs) have a potential to upsurge the power adaptation
efficacy in photovoltaic operation because of the augmentation of photoexcitation.
Recent developments in self-assembled QD solar cells (QDSCs) and colloidal QDSCs
are reviewed, with a focus on understanding carrier dynamics. For intermediate-band
solar cells using self-assembled QDs, defeat of a reduction of open circuit voltage
presents challenges for further efficacy improvement. This lessening mechanism is
deliberated constructed on recent reports. In QD sensitized cells and QD heterojunction
cells using colloidal QDs well-controlled heterointerface and exterior passivation are
key issues for enhancement of photovoltaic performances [96]. QD solar cells have the
potential for solar, or photovoltaic cells that reduce wasteful heat and capitalizes on
 54

the amount of the sun's energy that is converted to electricity. This is noteworthy in
the direction of making solar energy more cost-competitive with predictable power
sources [97].

4.12 Our Proposed Model

In our work we proposed the cell model as Figure 4.5 where InAs.98N.02 is taken as the
dot substantial and AlPxSb(1-x) is taken as the barrier substantial. Layer’s thickness are
taken as per the above Figure.

Figure 1: Proposed Model of 3IB QDIBSC

Figure 4.5: Proposed Solar Cell model

4.13 Chapter Summary

In this chapter, we have discussed various parameters related to the intermediate band
solar cell operation. In Figure. 3.2 working principle of inter mediate band solar cells
has been shown which gives a good idea of how inter mediate band solar cells work.
In the next chapter, we will use this knowledge to model and simulate the solar cell. In
the next chapter, we will discuss device structure and simulation process of the
modeled solar cell.
 55

CHAPTER V

METHODOLOGY

5.1 Introduction

In this chapter, we will discuss how we simulate the performance parameters of the QD
solar cells. There are many simulation software for simulating solar cells parameters
like AMPS 1D, wxAMPS, SCAPS, ASA, PC1Detc. These softwares are suitable for
thin film solar cells or any other solar cells. But immerging solar cells like QD solar
cells, it is difficult to find simulation software that is suitable to simulate it. So we have
used MATLAB to simulate the solar cells. This chapter deals with modeling, equation
related to dissimilar parameters of the solar cells and MATLAB codes which have been
used to solve these equations as well as to simulate the cells. Our followed Methodology
is given below
 56

5.2 Investigation Of Dissimilar Generations Of Solar Cell

Though a vast amount of research is conducted on improving the cell efficiency using
first- and second-generation solar cells but they cannot provide desired efficiency.
Actually, in single junction solar cells those photons having energy lower than band gap
energy aren’t engrossd at all rather transmit through the substantial which means they
cannot utilize full sun spectrum. Moreover, in single junction cells power conversion
efficiency is mainly curtailed by heat and transmission loss. One of the solutions to this
problem is Multi junction Solar Cell in which light transmits through wider band gap
substantial and is engrossd in a narrow band gap substantial which is placed at back.
Highest efficiency for multi junction solar cell is obtained about 44.4% using triple
junction consist of InGaP/GaAs/InGaAs [62]. But to achieve higher efficiency (above
50%) numerous third generation solar cells are proposed.

5.2.1 First Generation Solar Cell

The first-generation solar cells are mainly Silicon based and about 80% of total solar
panel around the world are first generation solar cells. Till now Si based cells are most
stable than other types of cells that’s why they are mostly used. But their main
disadvantage is that this type of cells has lower efficiency at high temperature thus at
sunny day. So, this type of cell cannot utilize the full energy of sun. Some commonly
used first generation solar cell’s explanation is given below:

5.2.1.1 Monocrystalline Silicon Solar Cell

This is the oldest solar cell technology and still the most popular solar cells made from
thin wafers of silicon. They are also called monocrystalline solar cells because the cells
are sliced from large single crystals. Till now maximum efficiency is obtained from
these types of cells is about 24.2% [42]. Besides, monocrystalline based solar panels to
lose their efficiency as the temperature upsurges about 25˚C, so they need to be installed
in such a way as to permit the air to circulate over and under the panels to improve their
efficiency.

5.2.1.2 Polycrystalline Silicon Solar Cell

Here silicon wafer is formed from multiple Si crystals rather than single crystal. For this
reason, they also cheaper compared to monocrystalline Si cells. Though this type of
 57

cells is cheap but panels made up from this type of cells has efficiency only up to 19.3%
[42].

5.2.1.3 Amorphous Silicon Solar Cell

In this type of cells silicon crystals are not developed through wafer rather thin layer of
silicon is deposited on to a substrate such as metal, glass and plastic. Sometimes several
layers of silicon are doped in slightly dissimilar ways to respond to dissimilar
wavelengths of light where they are laid on top of one another to improve the efficiency.
Though the production methods are complex but less energy intensive than crystalline
panels. But their efficiency is very low and only about 10% and they are not generally
good for roof installation.

5.2.2 Second Generation solar cells

They are typically called thin-film solar cells because they are made from few
micrometers’ thick layers of semiconductor substantials. The combination of using less
substantial and lower cost manufacturing processes allow the manufacturers of solar
panels made from this type of technology to produce and sell panels at a much lower
cost. There are basically three types of second-generation solar cells. amorphous silicon
and two that are made from non-silicon substantials namely cadmium telluride (CdTe),
and copper indium gallium di selenide (CIGS). Together they accounted for around
16.8% of the panels sold in 2009. This type of cells has a laboratory-based efficiency
of about 20% and module-based efficiency of 13.5% [42].

5.2.3 Third Generation Solar cell

In order to eliminate the losses associated with first- and second-generation solar cells
third generation solar cell is introduced. There are dissimilar types of third generation
solar cells. Some highly research based and emerging cells are given below.

5.2.3.1 Perovskite Solar cell

This type of cell has a perovskite structured compound most commonly it can be an
inorganic or organic Pb or Tin halide-based substantial. This layer is used as an active
layer for photon captivation. In 2020 power conversion efficiency obtained from this
type of cell is about 25.5% for single junction and for Si based tandem cells efficiency
is obtained about 29.15% [47]. So far, most types of perovskite solar cells have not
 58

reached sufficient operational stability to be commercially manufactured. Besides,

toxicity associated with Pb is a growing concern in this type of cell. That’s why these
types of cells aren’t much popular.

5.2.3.2 Dye-sensitized solar cell

This type of cell is a form of thin film solar cell where a semiconductor substantial is
created between photo sensitized anode and a photo electrochemical layer which is
called electrolyte. Here actually organic dyes are used as the active layer for photon
captivation. In this type of cell, a photosensitive dye produces electrons and charge
separation occurs at the exterior between dye and electrolyte. Highest efficiency
obtained from this type of cell is about 12% to 15% [47], which is very low. Besides,
this type of cell has instability problem.

5.2.3.3 Quantum Dot Solar Cell

In this type of cell QD (a nanometer range substantial generally ranges from 1-10nm)
is used as the light absorbing substantial. They are introduced to eliminate the
disadvantages associated with the bulk substantial soar cells such as CIGS, CdTe, Si
based cells etc. The most exciting property of QD is their bandgap tuning property
where the bandgap can be changed by changing the QD size. This property makes them
suitable in using multi-junction cells where dissimilar types of substantials are used for
absorbing dissimilar energies photons to improve the cell efficiency. Another approach
is used to improve the efficiency of the cell using QD by introducing intermediate bands
inside the bandgap of a substantial called barrier substantial. This introduction of IB
helps the cell to absorb even the low energy photons. Though using quantum dots the
experimental results obtained from InAs/GaAs device is obtained about 18.3% [47].
But it can be augmented to higher value by using IBs. Theoretical maximum efficiency
can be obtained about 63.12% for single band and about 72% for multi bands [1].

5.3 Selection of Appropriate Substantials

To select the appropriate substantials, we have gone through a lot of books and papers.
In the selection of appropriate substantials, we focused on dissimilar parameters like the
band gap, the content for dissimilar alloys, the conduction band offset between barrier
and dot substantials, the dot size, the combination of barrier and dot to get the flexibility
 59

for dissimilar dot size like spherical, orthorhombic, pyramidical and etc. The table
shows the appropriate combination of barrier and dot.

Table 5.1: Appropriate substantial for barrier and dot [82].

for the QD-IBSC containing intermediate band under unconcentrated light, the effective
band gap must be in the range of 2.06 eV ≤ Eg ≤ 2.71 eV and under fully concentrated
light band gap must be lower for better efficiency which is 1.63 eV ≤ Eg ≤ 2.31eV for
an efficiency ≥ 62%. For dot substantial the band gap should be small [82]. We have
used AlPSb as the barrier as it’s band gap ranges from 1.456eV-2.38eV for dissimilar
phosphorus content. We have used InAs0.98N.02 as the dot substantial. The reason behind
taking Nitrogen content as 2% is that in this value the dot band gap has a value of
0.25eV. The AlPSb/InAsN combination is most flexible in the sense
that its design is suitable for dissimilar dot structures [82].

5.4 Design Consideration of QDIBSC

1. All recombination is radiative in nature. Radiative recombination happens when

an electron within the conduction band recombines with a hole inside the
valence band and consequently the extra energy is released within the sort of a
photon. Radiative recombination is thus the radiative changeover of an electron
within the conduction band to an unfilled state (hole) inside the valence band.
2. Recombination lifetime between all bands is larger than carrier relaxation time
in each band. The carrier lifetime (recombination lifetime) is well-
defined because the usual time it takes an additional minority carrier to
recombine. As mentioned within the previous section, three recombination
mechanisms band-to-band, trap-assisted (or SRH) and Auger recombination
 60

regulates the recombination lifetime.

3. Carrier concentrations in each band labeled by its own quasi-Fermi level. A
quasi-Fermi level may be a tenancy employed in quantum physics and
predominantly in solid state physics for the Fermi level that designates the
population of electrons distinctly within the conduction band and valence
band, when their populations are displaced from symmetry.
4. The intermediate bands are measured to be half filled with electrons. It is
necessary to lodge electrons coming up from the VB and to supply electrons to
be propelled into the CB. Complete photon captivation selectivity.
5. Complete photon captivation selectivity. All the incident photons are considered
to be engrossed by the device.

5.5 Design Constraints of QDIBSC

1. The familiarized IB is often unfilled, demanding donor carriers to partially fill

it. It is quite impossible to get a substantial which could provide half-filled IB
within the barrier.
2. The devices are characteristically only operative at low temperatures as they
are disposed to to thermal escape. But working under the sun may upsurge the
temperature and device performance may get lowered.
3. The use of QDs upsurges non-radiative recombination, which decreases sub-
bandgap presentation. It is important to get radiative recombination for higher
efficacy but majority radiation is non-radiative in nature.
4. Cumulative the amount of QD layers can improve sub-bandgap performance,
but also upsurges the lattice strain on the device. It is seen in fabricated QDSC
that to get one intermediate band it required 40 layers of QD but this huge
quantity of layers upsurges the strain on the structure.

5.6 MATLAB

The popularity of MATLAB is partly due to its long history and thus it is well devolved
and well tested. MATLAB is programmable and has the same logical relation, condition
and loop structures as other programming languages, such as Fortran, C, BASIC and
Pascal. Thus, it can be used to teach programming principles. So, we have used
MATLAB (R2018a) to solve all given equations given in the next chapter for
determining intermediate bands position, open circuit voltage, short circuit current and
 61

to simulate power conversion efficiency of AlPxSb(1-x)/InAs0.98N0.02 for one, two and

three intermediate bands.

5.7 Simulation of QD Intermediate Band Solar Cell

To simulate QD intermediate band solar cell we have used “MATLAB Text Editor” and
“App Designer”. To solve the equations first we have to open MATLAB. Then we have
written the integral equations on the editor. After solving equations, we will find the
values of parameters. Then we have to run some MATLAB programs written in
MATLAB editor saved as.mfile. After that, we developed an app in MATLAB “App
Designer” which gives us values of JSC, FF, Voc, efficiency as shown in Figure 5.1.
Moreover, we develop MATLAB code for the determination of effect of dissimilar
parameters on cells performance. Full simulation result is given to the Chapter 06.

Figure 5.1: Code User Interface

Figure 5.1: Code User Interface.

.
 62

5.8 Chapter Summary

In this chapter, we have discussed the methodology of simulation of the QD solar

cell. As it QDIBSC is an emerging solar cell, no such software not yet been developed
to simulate its parameters. So, we have used MATLAB to simulate this solar cell. We
have used. “MATLAB Text Editor” and “App Designer” to solve basic equations of
this cell and developed MATLAB codes to evaluate dissimilar parameters of it. Details
MATLAB codes have been shown in the appendix. In next chapter, we will discuss
modeling and simulation of the cell. We will discuss effect of dissimilar parameters on
cells performance.
 63

CHAPTER VI

MODELING AND SIMULATION

6.1 Introduction

In this chapter, we will discuss how we simulate the performance parameters of the QD
solar cells. As there is no established software for immerging solar cells like QD solar
cells, it is difficult to measure performance of QDSC. So, we have used MATLAB to
simulate the solar cells. This chapter deals with modeling, equation related to dissimilar
parameters of the solar cells and MATLAB codes which have been used to solve these
equations as well as to simulate the cell parameters.

6.2 Numerical Modeling

In this article we have discussed numerical modeling of the cell that is evaluating photo
current, current extract from p-type substantial (Jp), n-type substantial (Jn), dot
substantial (JD), barrier substantial (JB), reverse saturation current (JO), VOC and JSC
using equations. In following articles, we have discussed the numerical equations
related with these parameters.

6.3 Equations Related To Simulation

Numerical equations related to simulation are given below. Important equations related
to photocurrent which is formed by solar irradiance and makes JSC flows through the
circuit then we have discussed equations related with calculating efficiency, VOC and
FF. From those equations we made up MATLAB codes to determine the parameters to
calculate the discussed factors. As there is no established software or website to simulate
the QDIBSC we rely upon MATLAB and we calibrate the codes with published work
and we initiate that our code is well suited to simulate the mathematical model.
 64

6.3.1 Mathematical Formulation

In our study, a heterostructure of one, two and three IBs InAs.98N.02/AlPxSb(1-x) QDIBSC
is considered. The reasons behind the selection of this substantial is given below.
1. For the QD-IBSC containing intermediate band under unconcentrated light, the
effective band gap must be within 2.06 eV ≤ Eg ≤ 2.71 eV and under fully
concentrated light band gap must be lower for better efficiency which is 1.63 eV
≤ Eg ≤ 2.31eV for an efficiency ≥ 62%. For dot substantial the band gap should
be small [65].

2. We have used AlPSb as the barrier as its band gap ranges from 1.456eV-2.38eV
for dissimilar phosphorus content (We have changes phosphorous content from
0.1 to 0.96).

3. We have used InAs0.98N.02 as the dot substantial. The reason behind taking
Nitrogen content as 2% is that in this value the dot band gap has a value 0f .25eV
[65].

4. The AlPSb/InAsN combination is suitable for dissimilar dot structure and

concentration factor [65].

We can define our work on several aspects. They are given chronologically as below

1. Determination of intermediate bands position and width by using Kronig-Penny

Model. This bands position changes with a change in QD size.
2. Determination of barrier band gap by changing phosphorus content.
3. Determination of short-circuit current (Jsc).
4. Determination of open-circuit voltage (Voc) from Jsc and reverse saturation
current (Jo).
5. Finally, determination of efficiency of proposed cell on basis of QD size,
phosphorus content and inter dot distance.

6.3.2 Design Considerations

Efficiency calculation is performed by considering the detailed balance calculations

performed by Shockley and Queisser. Assumptions taken for the efficiency calculation
for QDIBSC are given below [28].
 65

1. Radiation engrossd by the device at a temperature of Ts = 6,000K and ambient

Ta = 300K and emits radiation at ambient temperature Ta = 300K.
2. All transitions are radiative in nature between bands.
3. All photons are engrossd which indicates complete photons captivation.
4. Quasi-fermi levels are considered to be constant throughout the cell.
5. No carriers are extracted from the intermediate bands.
6. Total photon flux equals to total charge carrier pairs obtained at terminals.

6.3.3 Determination of Intermediate Bands Position

Conferring to the alteration in bandgap energies, there are energy partings between the
valence band (VB) and conduction bands (CB) of this substantial called the valence
band offset (VBO) and conduction band offset (CBO). The discontinuous
semiconductor substantial and offsets create one-dimensional potential wells [52].
These wells have extra energy levels in the band offsets related to the QD semiconductor
substantial. The QD semiconductor substantial is completely enclosed by a barrier
semiconductor substantial, thus the energy spectrum is discrete. If the quantity of QDs
is augmented and settled in a periodic lattice, the energy levels upsurge and split to
create the bands. These bands are called IBs and are located inside the bandgap of the
barrier or host semiconductor substantial. The bandwidth energies of the IBs hinge on
the spacing of the QDs within the lattice and wave vector overlap [53]. The barrier
semiconductor substantial, which is called the intrinsic substantial, is located between
the p–n emitters and comprises a periodic array of QDs for another semiconductor
substantial. Regularity is important for the size and spacing of the QDs to determine the
optimum position of the IBs. The discrete energy levels in the QDs are computed using
the time dependent Schrödinger equation is [63],

−ℏ2
( 2m ∇2 + V) K = EK (6.1)

Figure 6.1: Intermediate bands formation in lattice structure using Kronig-Penney Model [63].
 66

Where, ħ is the Plank’s constant, 𝑚 is the effective mass, second order dissimilarial
operator, potential energy, total energy of charge carrier and 𝑘 is the wave vector.

Here, assuming charge carrier is travelling in positive 𝑥 direction for one-dimensional.

Thus, boundary conditions are obtained as follows [63],

V0 , for x = LB
V(x) =   { (6.2)
0 , for x = LQD

Here, 𝑉o is CBO, 𝐿𝐵 is interdot distance, and 𝐿QD is the QD width. 𝑇 is the period of
considered potential indicate in Figure 6.1 and T = 𝐿𝐵 + 𝐿QD.

The solution of Schrödinger wave equation by using the above two boundary conditions
are obtained as below [63].

d2 k 2mE
+ k = 0 ,  for x = LQD (6.3.1)
dx2 ℏ2

d2 k 2m(E−V0 )
+ k = 0,  for x = LB (6.3.2)
dx2 ℏ2

Using Kronig-Penney model solution of (4.3.1) and (4.3.2) is [63],

σ2 −δ2
sinh(σLB )  sinh(σLQD )  −   cosh(σLB )  cosh(σLQD )  =
2σδ

cos(LB + LQD )k (6.4)

Dissimilar parameters of equation 6.4 can be assumed as follow,

2mB (V0 −E) 2mB V0

σ2 = = (1 − ε) ,
ℏ2 ℏ2

2mQ V0 E
δ2 = ε,       ε = v (6.5)
ℏ 0

where 𝑚𝐵, 𝑚𝑄 are electron effective mass in barrier and QDs region, respectively.
Therefore, from (6.4), the factors in the first term can be expressed as follows:

σ2 −δ2 mQ −(mQ +mB  )ϵ

                                           = 1/2 (6.6)
2σδ 2(mQ mB ϵ)  (ϵ−1)1/2

Moreover, other arguments of equation 6.4 for hyperbolic and sinusoidal functions can
be well-defined as:
1
                                             σLB = μAB (1 −  ϵ)1/2  ,   δLQD = AQ ϵ2 ,
 67

1
LB 2m V 2
μ=L , AB = LQD ( ℏB2 0)
QD

1
2m V 2
AQ = LQD ( ℏQ2 0) (6.7)

Substituting these definitions into equation 6.4, it will become as

mQ −(mQ +mB  )ϵ 1⁄

2
1/2 1/2
  sinh[ μAB (1 −  ϵ)1/2 ]sin(AQ ϵ) +cosh [ μAB (1 −  ϵ)1/2 ]
2(mQ mB ϵ)  (ϵ−1)

1⁄
2
cos(AQ ϵ) = cos[kLQD (1 + µ)]k for ϵ < 1, (6.8.1)

mQ −(mQ +mB  )ϵ 1⁄

2
1/2 1/2
  sinh[ μAB ( ϵ − 1)1/2 ]sin(AQ ϵ) +cosh[ μAB ( ϵ − 1)1/2 ]
2(mQ mB ϵ)  (ϵ−1)

1⁄
2
cos(AQ ϵ) = cos[kLQD (1 + µ)]k for ϵ > 1, (6.8.2)

μAB
cosAQ −   sinAQ   =   cos[kLQD (1 + µ)]k for ϵ = 1. (6.8.3)
2

The left-hand side of (6.8.1), (6.8.2) and (6.8.3) can be represented by (𝜖) where 𝜖 is the
ratio of total energy of electrons over conduction band offset [63]. Considering,

F(ϵ)  =  cos[kLQD (1 + µ)]k (6.9)

L E
Where, µ = L B and ϵ =  V
QD 0

The equation 6.9 is solved graphically using MATLAB.

Figure 6.2: Plot of Left-Hand Side of Equation (6.9) f(ɛ) vs ɛ curve.

 68

Right-hand side (RHS) of equation (6.9) is a function of k (wave vector) only and it is
constrained to the range -1 to +1. Two horizontal dotted lines of the Figure 6.2
represents two extreme points of the RHS of equation (6.9). Allowed energy ranges will
be such values for which F(ϵ)  lies between the horizontal lines. In Figure 6.2 those
allowable energy ranges are represented by rectangular area and the gaps between them
represents forbidden energy gaps through which electrons cannot propagate. For
rectangular regions cos[k𝐿𝑄𝐷 (1 + µ)]𝑘 varies within limit and k varies from 0 to
(±𝜋/𝑇). Thus, there will be some real values of k which will satisfy equation (6.9). On
the other hand, those gaps between rectangular areas there will be no real values for k
to satisfy equation 6.9. Figure 6.3 indicates allowed energy ranges along with

Figure 6.3: Reduced zone representation of E-k relationship.

wavevector states in proposed substantial one dimensional crystal by using same values
π
used for Figure 6.2. Here, wave vector (k) changes from 0 to (± 𝑇) on both sides of the

curve and those allowed energy bands from Figure 6.3 are introduced. From this curve
𝑑𝐸 π
it is initiate that (𝑑𝑘 ) is zero at boundary values of k which is 0 and (± 𝑇 ). It indicates

that electron velocity will tends to zero as it moves towards crystal boundary. So,
electron’s momentum is confined within the allowable ranges of k. Figure 6.4 shows
𝑛π
the allowed energy bands for k = ( 𝑇 ). From curve, IB’s positions within the CBO is
 69

Figure 6.4: Extended zone representation of E-k relationship.

obtained. From those curves by determining band position and band width we computed
the short circuit current and then using this current we computed the Voc, fill factor and
efficiency. To calculate solar cell parameters, we put values of band position and band
width in the MATLAB codes in MATLAB Text editor and initiate the results.

6.3.4 Determination of Short Circuit Current

Amount incident flux density on cell can be obtained using Roosbroeck Shockley
equation which is,

Ex
2μϵ E2 dE
N(Ea , Eb , T, μ) = h3 c2 ∫ E −µ (6.10)
Ey ekb T−1

In the above equation Ex and Ey indicates lower and upper limit of photon flux for any
transitions, respectively. T stands for temperature, μ represents chemical potential, h
and kb denotes Planck constant and Boltzmann constant, respectively and c indicates
light velocity. Solution of Schrodinger’s Equation which describes electron dispersion
of the proposed model. Bandgap energies are arranged as EI1I2>EI2I3>EvI1>EcI3. Total
flux is equal to the quantity of carriers collected to the contact [63]. There are two
conditions to obtain the balance analysis when the IBQDSC operates [63]. The current
density coming to the IBs should be equal to the current density leaving them [63], i.e,

JVI1+JVI2+JVI3 = JCI1 +JCI2+JCI3 (6.11)

 70

Where, (JVI1+JVI2+JVI3) represents total current densities entering the three IBs and (JCI1
+JCI2+JCI3) indicates total current densities leaving those IBs. Though this constraint
cannot take place easily but for this proposed model it will be true as intermediate bands
are assumed to be half filled. The chemical potential (μCV) should be equal to the sum
of the quasi-Fermi levels [63], i.e,

µCV = µVI1 + µI1I2 + µI2I3 + µCI3 (6.12)

Photo formed current density can be obtained from the multiplication of charge carrier
flux with the electron charge. Total current density can be obtained from quantity of
photons engrossd and emitted by the cell. Thus

JT = JCV+JCI1 , for 1 intermediate bands

JT = JCV+JCI1 + JCI2 , for 2 intermediate bands

JT = JCV+JCI1 + JCI2 + JCI3 , for 3 intermediate bands (6.13)

here, Jcv is the current density results from transition of electrons from VB to CB and
it’s value can be computed as follows [63].

JCV = q[ SC× 𝜖 × N(ECV,∞,TS,0)+(1-SCnS)× N(ECV,∞,TC,0) - N(ECV,∞,TC, µ𝑐𝑣 )] (6.14)

As incoming and outgoing current densities are considered to be equal [63]. Thus,

q[SC×𝜖×N(ECI1, ECV,TS,0)+(1-SC×𝜖)× N(ECI1, ECV,Ta,0) - N(ECI1,ECV,Ta, µCI1 )].

= q[SC×𝜖×N(EV1, ECI,TS,0)+(1-SC×𝜖)× N(EVI, ECI,Ta,0) - N(EVI,ECi,Ta, µIV )] (6.15.1)

Thus, values of JCI1, JCI2, JCI3 can be obtained as below.

JCI1 = q[SC×𝜖×N(ECI1, ECV,TS,0)+(1-SC×𝜖)× N(ECI1, ECV,TC,0) - N(ECI1, ECV,TC, µCI1

)]. (6.15.2)

Where, JCI1 is current density results from the transition of electrons from the first IB to
CB.

JCI2= q[ SC×𝜖×N(ECI2, EVI2,TS,0)+(1-SCnS)× N(ECI2, EVI2,TC,0) - N(ECI2, EVI2,TC, µCI2

)]. (6.15.3)

Where, JCI2 is current density results from the transition of electrons from second IB to
CB.
 71

JCI3= q[ SC×𝜖×N(ECI3, EVI3,TS,0)+(1-SCnS)× N(ECI3, EVI3,TC,0) - N(ECI3, EVI3,TC, µCI3

)] (6.15.4)

Where, JCI3 is current density results from the transition of electrons from the third IB
to CB.

Here, SC = Solar Constant , in which it is equal to 1 at the earth and 1/ɛ at the exterior
of the sun. As, we calculate for unconcentrated light it’s value is taken equals to 1.

𝜖 = Geometric factor whose value is 2.016x10-5 [63].

6.3.5 Determination of Open Circuit Voltage

Minority carrier generation due to thermal excitation in the intermediate region can be
obtained by the following expression:

E
Js1 = Aeff exp (− akT
eff
) (6.16)

Where, a is the ideality factor. Expression for Eopt is

Eeff = [ 1- nDVD].EgB + nD.VD.EgD (6.17)

Here, EgD represents the band gap of quantum dot substantial. nD, VD indicates volume
density and volume of QDs respectively. EgB, EgD are the barrier and QD substantial
bandgap respectively. And, Expression for Aopt is as follow

Aopt = e 4πn2kT/c2h3 Eeff , (6.18)

Here, n is the average refractive index in IB region. e indicates electron charge. Minority
carrier generation on the depletion region edge can be obtained by the following
expression:

EgB
Js2 = A exp (− vkT) (6.19)

DP Dn
Where, A = e NcNv(N +N ) (6.20)
D LP A Ln

Here, Nc and Nv is the effective density of states for barrier substantial. NA and NV are
the donor and acceptor in n-type and p-type regions, respectively and in equation (6.19)
v is the ideality factor. Total reverse saturation current is obtained as follows:

Jo = JS1+JS2 (6.21)
 72

Open circuit voltage ( Voc) is computed by using the value of Jsc and Jo in the following
equation:

kT JS
Voc = ln ( J C − 1) (6.22)
q 0

6.3.6 Determination of Efficiency

Finally, PCE is computed as belows:

VOC ×JSC ×FF

η= (6.23)
Pin

Here, Pin = σsT4, σs is Stefan’s constant and it’s equal to 5.67 x 10-8 W/m2 K4.

6.3.7 Determination of barrier substantial bandgap with change in phosphorus

content
We use AlPxSb(1-x) as the barrier substantial. In our work we change the phosphorus
content of the barrier substantial hinge oning on which AlPSb bandgap changes. AlPSb
is formed by the combination of AlP and AlSb. The value of bandgap with phosphorus
content is obtained from the following equation [62].

Eg,AlPSb(x) = x . Eg,AlP + (1-x) Eg,AlSb – b . x(1-x) (6.24)

In equation 6.25 Eg,AlPSb(x) indicates the value of barrier bandgap energy as a function
of phosphorus content. Eg,AlP and are bandgap of AlP and AlSb respectively. Here, b
indicates the bowing parameter.

6.3.8 Determination of effective mass of electron with change in phosphorus

content
The change in electron effective mass with the change in phosphorus content is obtained
by using the following equation [62].

m*AlPSb(x) = x . m*AlP + (1-x) m*AlSb (6.25)

6.4 Simulation and Results of AlPxSb(1-x)/ InAs0.98N0.02 IBQDSC

The simulations of proposed cell were done by MATLAB. We have used

MATLAB Text Editor” of MATLAB to solve integrations related with JSC, VOC. This
section comprises all results that is obtained after humongous quantity of calculations.
Obtained results can be formulated in a stepwise manner in the following form.
 73

Step 1: In first step intermediate bands position are computed by varying QD size,
Phosphorus content and inter dot distance.

According to Kronig Penny Model which is already discussed in section 6.4.3 band
position hinge ons on the CBO and carrier effective mass in barrier region. Band offset
and effective mass of electron in the barrier region again hinge ons on the value of
Phosphorus content. All required data are listed in Table 6.1. Value shown in table is
used in equation 6.24 and by using this equation the band gap for AlPSb is computed
as it is an alloy substantial. Then by using equation 6.25 we computed the effective
mass for AlPSb. All the values are taken from published work and published book
which are listed as references in the table. The most important parameter used in this
table is blowing parameter which is used to calculate the band gap. Position of the
confined energy levels hinge ons on the size of the dot, its shape, and substantials used.
It is initiate that with an upsurge in dot size the efficiency of the cell decreases for the
same value of substantial content [62]. In order to obtain high captivation coefficient
quantum dots must be placed closely to each other but very close to each other also lead
to a decrease in widths of bands. That’s why it’s better to use identical dots which are
safely stacked together at a distance of 100Å without the appearance of stimulated
emission even at the maximum light concentration.

Table 6.1: Parameters Required For The Determination of Effect of Phosphorus

Content on Barrier Bandgap and Effective Mass of Electron in Barrier Region

Parameters Value Units Reference

Bandgap of AlP, Eg,AlP 2.45 eV [52]
Bandgap of AlSb, Eg,AlSb 1.161 eV [52]
Bowing parameter of 2.7 eV [52]
AlPSb, b
Free electron resting 9.11e-31 kg [27]
mass, mo
Effective mass of 0.212mo kg [52]
electron in AlP, m*AlP
Effective mass of 0.14mo kg [52]
electron in AlSb, m*AlSb
 74

In order to determine the band offset (difference between the barrier and QD bandgap)
change in barrier band gap with a change in phosphorus content is obtained in Figure
6.5. From this figure it is clear that the relation between bandgap and phosphorus
content is not proportional but elliptical. The bandgap is lowest between 0.3 to 0.4
phosphorus content after those upsurges with content.

Figure 6.5: Effect of Phosphorus Content on Barrier Substantial Bandgap.

Obtained curve in Figure 6.5 is drawn by using equation 6.24. From Figure 6.5 it is
initiate that the effect of phosphorus content on the band gap of barrier substantial has
a parabolic or bowing shape relationship. This occurs due to the presence of blowing
parameter in equation 6.24. From Figure 6.5 it is initiate that minimum value of barrier
band gap is obtained for phosphorus content 0.34.

As, bands position is not only hinge oning on the value of barrier band gap it also hinge
ons on the carrier effective mass in the barrier region. Thus, in order to obtain the effect
of phosphorus content on the carrier effective mass in barrier region is obtained by using
equation 6.25. Then position of the bands are determined by changing the dot size. As
change in phosphorus content value has been changed the effective mass of electron
and band offset which provides an impact on the bands position along with the QD size
according to Kronig Penny model as discussed in section 6.3.3
 75

Figure 6.6: Effect of Phosphorus Content on Electron effective mass in Barrier Region.

Mathematical equations regarding this model is solved by generating MATLAB code

which is listed in Table 6.2. Here, Phosphorus content is changed from 0.1 – 0.96 and
QD size is changed from 2-6nm with 0.5nm interval. From this table we initiate the
band position and band width for dissimilar dot size and for dissimilar phosphorus
content. These values are used to calculate the Voc, Jsc and FF.

Table 6.2: Effect of Dot Size on IBs Width and Position in QDIBSC for inter dot
distance 2.6 nm

Phosphorous Dot Position Position Position width width of width Possible

content size of of of of II band of Maximum
I band II band III I band III Quantity
band band of IBs
0.96 2 0.3225 1.128 1.498 0.0014 0.052 0.179 2
2.5 0.2615 1.162 1.57 0.0035 0.105 0.424 2
3 0.2171 1.144 1.435 0.0064 0.271 0.451 2
3.5 0.1833 1.046 1.453 0.0098 0.178 0.364 2
4 0.1567 0.9102 1.53 0.0134 0.1268 0.322 3
4.5 0.1353 0.7812 1.572 0.0168 0.104 0.352 3
5 0.1179 0.6718 1.551 0.0196 0.0953 0.468 3
5.5 0.1036 0.5815 1.463 0.0222 0.0917 0.391 3
6 0.1 0.5073 1.338 0.0158 0.0887 0.289 2
0.94 2 0.3233 1.129 1.5 0.0015 0.052 0.182 2
2.5 0.2622 1.162 1.572 0.0035 0.107 0.429 2
3 0.2176 1.144 1.436 0.0066 0.219 0.454 2
3.5 0.1837 1.046 1.456 0.01 0.179 0.366 2
4 0.157 0.9102 1.533 0.0136 0.1278 0.325 2
 76

4.5 0.1356 0.7812 1.574 0.017 0.1061 0.363 3

5 0.1184 0.6721 1.552 0.0196 0.0959 0.472 2
5.5 0..1036 0.5817 1.464 0.0226 0.0913 0.391 3
6 0.1 0.5073 1.338 0.0161 0.0913 0.29 2
0.92 2 0.3241 1.129 1.503 0.0015 0.053 0.184 2
2.5 0.2628 1.163 1.574 0.0037 0.108 0.433 2
3 0.2182 1.144 1.437 0.0066 0.222 0.457 2
3.5 0.1841 1.046 1.459 0.0102 0.18 0.368 2
4 0.1574 0.9102 1.536 0.0138 0.1288 0.328 2
4.5 0.1359 0.7815 1.578 0.0172 0.106 0.354 3
5 0.1186 0.6723 1.554 0.02 0.0975 0.475 2
5.5 0.1039 0.5817 1.464 0.0226 0.0939 0.392 3
6 0.1 0.5077 1.338 0.0165 0.0916 0.291 2
0.9 2 0.325 1.13 1.506 0.0015 0.054 0.186 2
2.5 0.2635 1.164 1.576 0.0037 0.109 0.438 2
3 0.2187 1.145 1.438 0.0068 0.223 0.461 2
3.5 0.1845 1.046 1.461 0.0104 0.181 0.371 2
4 0.1577 0.9102 1.539 0.014 0.1298 0.330 2
4.5 0.1362 0.7816 1.578 0.0173 0.1069 0.371 2
5 0.1185 0.6721 1.555 0.0204 0.0983 0.481 2
5.5 0.104 0.5819 1.468 0.0231 0.0942 0.389 3
6 0.1 0.5077 1.338 0.017 0.0928 0.292 2
0.89 4 0.158 0.9109 1.541 0.0141 0.1301 0.333 2
4.5 0.1363 0.7823 1.58 0.0171 0.1088 0.374 2
5 0.1187 0.6727 1.556 0.0207 0.0996 0.484 2
5.5 0.1041 0.5825 1.466 0.0234 0.0954 0.374 3
6 0.1 0.6018 1.339 0.0174 0.0937 0.294 2
0.88 4 0.1581 0.9109 1.543 0.0141 0.1301 0.333 2
4.5 0.1365 0.7821 1.581 0.0177 0.1095 0.376 2
5 0.1188 0.7729 1.557 0.0209 0.1001 0.486 2
5.5 0.1042 0.5827 1.467 0.0235 0.0958 0.394 2
6 0.1 0.6023 1.339 0.0176 0.0941 0.295 2
0.87 4.5 0.1366 0.8921 1.583 0.0177 0.1097 0.377 2
5 0.1189 0.673 1.558 0.021 0.1004 0.488 2
5.5 0.1042 0.5827 1.467 0.0237 0.0964 0.395 2
0.86 4 0.1585 0.9109 1.545 0.0145 0.1321 0.337 2
4.5 0.1367 0.7823 1.584 0.0181 0.1105 0.379 2
5 0.119 0.673 1.559 0.0212 0.101 0.49 2
5.5 0.1043 0.5827 1.467 0.0238 0.0969 0.396 2
0.85 4 0.1586 0.9108 1.547 0.0147 0.1383 0.338 2
4.5 0.1369 0.7824 1.585 0.0182 0.1109 0.381 2
5 0.1104 0.673 1.559 0.0213 0.1016 0.493 2
5.5 0.1044 0.5828 1.467 0.0239 0.0973 0.396 2
0.84 4 0.1588 0.9109 1.548 0.0148 0.1311 0.34 2
4.5 0.137 0.7825 1.586 0.0183 0.1115 0.382 2
5 0.1192 0.6731 1.56 0.0215 0.1021 0.496 2
5.5 0.1045 0.5828 1.468 0.0241 0.0979 0.396 2
0.83 4 0.159 0.9108 1.55 0.0149 0.1342 0.341 2
 77

4.5 0.1372 0.7825 1.587 0.0184 0.112 0.385 2

5 0.1193 0.6732 1.56 0.0216 0.1024 0.498 2
5.5 0.1046 0.5829 1.468 0.0242 0.0983 0.397 2
0.82 4 0.1592 0.9109 1.551 0.015 0.1341` 0.343 2
4.5 0.1373 0.7824 1.589 0.0185 0.1126 0.386 2
5 0.1194 0.6732 1.561 0.0218 0.1031 0.501 2
5.5 0.1047 0.583 1.468 0.0243 0.0988 0.398 2
0.81 4 0.1594 0.9109 1.553 0.0151 0.1351` 0.344 2
4.5 0.1374 0.7827 1.59 0.0188 0.113 0.389 2
0.8 4.5 0.1375 0.782 1.59 0.0187 0.1132 0.389 2
5 0.1205 0.6729 1.562 0.0209 0.1037 0.504 2
5.5 0.1049 0.5829 1.469 0.0243 0.0981 0.396 2
6 0.1 0.5084 1.339 0.0191 0.0967 0.298 2
0.7 4.5 0.1392 0.7824 1.602 0.0198 0.119 0.41 2
5 0.1209 0.6736 1.569 0.023 0.108 0.53 2
5.5 0.1057 0.5835 1.471 0.026 0.104 0.402 2
6 0.1 0.5091 1.34 0.0213 0.1021 0.304 2
0.6 4.5 0.1403 0.7829 1.614 0.0215 0.1238 0.43 2
5 0.122 0.6741 1.576 0.0246 0.1143 0.643 2
5.5 0.1066 0.584 1.475 0.0274 0.1096 0.405 2
6 0.1 0.5099 1.34 0.0235 0.1066 0.312 2
0.5 4.5 0.1419 0.7838 1.629 0.0232 0.1309 0.454 2
5 0.1231 0.6755 1.583 0.0266 0.1203 0.584 2
5.5 0.1076 0.5849 1.477 0.0294 0.1159 0.413 2
6 0.1 0.5106 1.342 0.0262 0.1129 0.319 2
0.4 4.5 0.1435 0.7841 1.642 0.0251 0.1381 0.571 2
5 0.1245 0.6764 1.59 0.0284 0.1267 0.618 2
5.5 0.1085 0.5858 1.48 0.0314 0.1221 0.418 2
6 0.1 0.5116 1.342 0.288 0.1173 0.328 2
0.3 4.5 0.145 0.7848 1.653 0.0267 0.1441 0.507 2
5 0.1254 0.6776 1.598 0.0305 0.1327 0.584 2
5.5 0.1095 0.5865 1.482 0.0332 0.1281 0.426 2
6 0.1 0.5121 1.344 0.0313 0.125 0.335 2
0.2 4.5 0.1468 0.7859 1.669 0.0294 0.1543 0.542 2
5 0.1269 0.6797 1.606 0.0329 0.1411 0.59 2
5.5 0.1106 0.5873 1.485 0.0359 0.1369 0.437 2
6 0.1 0.5129 1.344 0.0349 0.1335 0.348 2
0.1 4.5 0.1487 0.7856 1.687 0.0322 0.1634 0.575 2
5 0.1284 0.6796 1.613 0.0359 0.1512 0.596 2
5.5 0.118 0.5882 1.489 0.0384 0.1461 0.445 2
6 0.1 0.5143 1.345 0.0379 0.1415 0.359 2

Several points are obtained from Table 6.2 which are given below:

1. Moreover, for phosphorus content 0.9 to 0.94, 3 IB is not possible for dot size
5nm and 6nm. For, content 0.96, 3IB is not possible for dot size 6nm and for
 78

0.9, 3IB is not possible for 4.5 nm. For content 0.89, 3IB is only possible for dot
size 5.5nm.
2. Band gap value upsurges with the upsurge of Phosphorus content.
3. Band position will get lower value with the upsurge of dot size.
4. Band width will get larger value with the upsurge of dot size.
5. Due to the change of band gap, the change in band position and band width is
negligible for same dot size.
6. Most important point is that though the value Jsc is high for dot size below 4nm
for any value of band gap. but it is seen from the obtained data that below 4 nm
the position of 2nd and 3rd band is very close (less than 0.5eV) which may cause
an interaction between bands. This will lead to thermalization loss. Thus, it is
better to use dot size over 4 nm.
7. From Table it is seen that with a decrease in phosphorus content the intermediate
bands positioned higher by a slight amount and band’s width is also upsurges
for a small amount for same dot size. The reason behind it is that with a decrease
in phosphorus content potential barrier height decreases which upsurge the
penetration depth of the carrier and the wave length of carrier wave function
decreases which upsurges the energy as indicated in equation 3.8 of Chapter 3.
Thus, electrons will occupy higher energy states and more electron
accumulation occurs which upsurge the efficiency with a decrease in
phosphorus content for the same dot size. But as the bands are taken higher
position quantity of bands that can be introduced will be decreased with a
decrease in phosphorus content.
Interdot distance’s effect on the position of intermediate bands are given in the Table
6.3 by keeping dot size 4.5 nm.

Table 6.3: Effect of Inter Dot Distance on IBs Width and Position in QDIBSC for
quantum dot size 4.5 nm

Phosphorous Inter Position Position Position width width width of

content Dot of I band of II of III of I of II III band
Distance (eV) band band band band (eV)
(nm) (eV) (eV) (eV) (eV)

0.92 2.6 0.1359 0.7815 1.578 0.0172 0.106 0.354

2.7 0.1378 0.7858 1.517 0.0133 0.0937 0.315

 79

2.8 0.1392 0.7893 1.463 0.0103 0.0816 0.272

3 0.1414 0.7956 1.372 0.0059 0.0614 0.205

0.3 1.7 0.1251 0.7603 0.0741 0.2697

1.8 0.1301 0.766 0.0616 0.238

2 0.139 0.7761 0.0411 0.1895

2.6 0.145 0.7848 0.0267 0.1441

2.8 0.1495 0.7929 0.0172 0.1137

3 0.1527 0.8001 0.0105 0.0878

Figure 6.7: Effect of Quantum Dot Size on Intermediate Bands Position for phosphorus
content 0.92.

Figure 6.7 indicates the effect of QD size on intermediate bands position for phosphorus
content 0.92 and inter dot distance 2.6 nm. Figure 6.7 indicates with an upsurge in the
size of QD intermediate bands are positioned lowered and the width of bands also get
decreased. Thus, more intermediate bands can be introduced between conduction and
valence bands by increasing dot size. Because as the lower band occupies the lower
position, it gives more space for higher bands. This mechanism happens as with an
upsurge in QD size the wavelength of the wave function upsurges. As wavelength is
inversely proportional to the energy according to the equation, upsurge in wavelength
will cause a decrease in the energy thus bands position. The reason behind the widening
of upper bands compared to lower ones is the satisfactory carrier accumulation in upper
 80

bands in quantized energy states than the lower bands. From Figure 6.7, it is also seen
that for one intermediate bands position decreases with an upsurge in QD size. This also
true for triple intermediate bands. But for double intermediate band quantum dot solar
cell at a particular dot size about 2.5 nm band position is augmented rather decreasing.
This is an important observation and it is particularly obtaining when the dot size and
inter dot distance are close compared to each other. In this case inter dot distance is 2.6
nm. From Figure 6.8, it is seen that effect of inter dot distance on the intermediate bands
position is inverse to that of dot size. Here, upsurge in inter dot distance upsurges the
position of the bands. The reason behind it is that, from Table 6.3, it is seen that with a
decrease in in the inter dot distance width of intermediate bands upsurges. This occurs
because with a decrease in inter dot distance coupling of carrier wave function upsurges
which cause discrete energy level of each QD to split into multiple quantized energy
states. According to Pauli’s exclusion principle, it is impossible for any two electrons
to occupy same energy states, so each electron will occupy dissimilar quantized states.
This will create several discrete quantized states within each band and as carrier

Figure 6.8: Effect of Inter Dot Distance on Intermediate Bands.

accumulation is higher at upper bands, upper bands will contain more quantized energy
states than lower ones and causes an upsurge in width of upper bands. As, the width of
upper bands upsurges band’s position will also get higher.

Step 2: Proposed Cell Efficiency Calculation For dissimilar Dot size and Inter dot
distance.
The Peak power (Pmax), Jsc, Voc, FF determines the performance of a solar cell. Jsc
of a photovoltaic cell hinge ons on the incident flux on the photovoltaic cell. Here,
 81

AM1.5 spectrum is taken in calculation as standard cell measurement. Voc

corresponds to the forward bias voltage, at which the dark current density
compensates the photocurrent density. The fill factor is the ratio between the
maximum power (P max = Jmpp .Vmpp) formed by a solar cell and the product of Jsc
and Voc. In this work value of FF is computed by designing a typical solar cell in
MATLAB Simulink by considering the effect of series parasitic resistance (Rs) and
parallel parasitic resistance (Rsh) which are already discussed in Chapter 3.
MATLAB Text Editor” of MATLAB to solve dissimilar types of integrations related
with JSC and for calculation of VOC. Table 6.4 shows the parameters for the calculation
of reverse saturation current which is required for the calculation of open circuit voltage.
By using these parameters, we computed the open circuit voltage by putting the values
of parameters into the MATLAB code as there is no software or website to calculate the
open circuit voltage of QDIBSC.

Table 6.4.: Parameters of the AlPxSb(1-x)/ InAs0.98N0.02 for IBQDSC to Calculate

Reverse Saturation Current ( Jo)

Parameters Value Units Reference

Temperature, T 27 ⁰C [62]
Bandgap of QD substantial, Egd 0.25 eV [65]

Bandgap of Barrier substantial, Egb 2.184 eV Figure 6.6

Value of donor concentration, ND 1e18 cm-3 [35]

Value of acceptor concentration, NA 1e17 cm-3 [35]
Effective Density of States in CB, NC 2.3719e19 cm-3 [35]

Effective Density of States in VB, NV 2.1593e19 cm-3 [35]

Value of refractive index of i region, n 3.9357 [35]
Value of ideality factor, v 1.2 [35]
Value of diffusion length of holes, LP 7.576e-5 cm Appendix A
Diffusion length of electrons, Ln 1.1961e-5 cm Appendix A
Diffusion constant of electrons, Dn 11.56661 cm2 s-1 Appendix A

Diffusion constant of holes, DP 1.7698 cm2 s-1 Appendix A

Volume of QDs, vD 1.77e-18 cm-3 From Dot size

Incident power density (for 1 sun,AM 1.5 1587.2 W/m2 [62]
condition), Pin
 82

Dissimilar parameters and values of intermediate bands position from Table 6.2 are
listed in Table 6.5 which will be used for the calculation of power conversion efficiency
for proposed cell having one, two and three intermediate bands. But in Table 6.5 values
of all required parameters are listed only for phosphorus content 0.92. To get all required
values all the parameters value can be put in the MATLAB code and we computed the
values for all phosphorus content which are listed in Table 6.5.

Table 6.5: Parameters of the AlPxSb(1-x)/ InAs0.98N0.02 for IBQDSC Efficiency

Calculation (Only for phosphorus content 0.92)

Parameters Value Units

Temperature 27 ⁰C
Barrier Band Gap 2.184 eV
First Band Position 0.1359 eV
Second Band Position 0.7815 eV
Third Band Position 1.578 eV
First Band Width 0.0172e-3 eV
Second Band Width 0.106e-3 eV
Third Band Width 0.354e-3 eV
Conduction Band Offset 1.934 eV
Reverse Saturation Current 1.1539e-14 mA/cm2

Value of JSC, efficiency is obtained by running EFFICIENCYFINAL.m and VOC is

computed from Open_ckt_Voc.m file of MATLAB by using data from Table 6.1 and

Figure 6.9: Some Portions of MATLAB Code and Command Window Output for Calculation of VOC .
 83

Table 6.2. Obtained results are listed in Table 6.6. Table 6.7 shows the simulation result
of JSC, VOC, FF and efficiency for AlPxSb(1-x)/ InAs0.98N0.02 for intermediate multiple
bands. From Table 6.2 it is already initiate that it is impossible to include more than
three intermediate bands within barrier substantial for the proposed substantial. In
Figure 6.9 some portions of MATLAB code and command window output for the
calculation of open circuit voltage is shown. Here, reverse saturation current is obtained
by using those values listed in Table 6.4. In this code various sign is used to express
various parameters like Nc is effective density of electrons, Nv is effective density of
holes, Dn is diffusion constant of electron, Dp is diffusion constant of hole, Ln is
diffusion length of electron, Lp is diffusion length of hole, Egb is band gap of barrier
substantials, Egd is band gap of dot substantials, a is ideality factor and n is refractive
index of intermediate region. In that table, diffusion length of electron, hole and
diffusivity of the carrier is obtained by formulating MATLAB code which is given in
APPENDIX A4.

Figure 6.10: Some Portions of MATLAB Code and Command Window Output
for Calculation of JSC and Efficiency.

In Figure 6.10 some portions of MATLAB code and command window output for the
calculation of short circuit current and efficiency are shown. The bandgap of the
selected substantial is tunable for dissimilar phosphorus content. Here, the efficiency is
measured for dissimilar phosphorus content and for dissimilar dot size from MATLAB
 84

coding as indicated in Figure 6.9 and 6.10. As, humongous quantity of calculations are
performed it is totally impossible to show each and every figure. That’s why in Table
6.6 only data for phosphorus content 0.92 and for dot size of 4.5nm are shown.

Table 6.6: Performance Analysis Table for multi intermediate band

InAs.98N0.02/AlPxSb(1-x) QDIBSC (Showing Effect Of Dot Size and Phosphorus
Content on Cell’s Efficiency)
Phosphorous Band Effective Dot Jsc Voc FF Efficiency
content gap mass of size
electron in
(eV) barrier (Kg) (nm) (mA/cm2) (V) (%)

0.96 2.313 0.20911*mo 4 115.6754 1.0285 0.7842 58.73

4.5 111.72 1.0276 0.7742 56
5 105.49 1.0261 0.7693 52.47
5.5 96.45 1.0238 0.7667 47.70
6 86.355 1.0209 0.7664 42.57
0.94 2.248 0.20768*mo 4 121.6857 0.9471 0.8447 61.34
4.5 117.347 0.9910 0.7901 57.89
5 110.827 0.9895 0.8015 55.38
5.5 101.602 0.9875 0.7964 50.34
6 91.239 0.9845 0.7955 45.02
0.92 2.184 0.20626*mo 4.5 122.97 0.9549 0.8532 63.12
5 116.113 0.9534 0.843 58.79
5.5 106.63 0.9511 0.8313 53.12
6 96.1232 0.9485 0.825 47.4
0.9 2.124 0.20483*mo 5 120.93 0.9105 0.8858 61.45
5.5 111.574 0.9174 0.8593 55.42
6 100.741 0.9148 0.8572 49.77
0.89 2.094 0.20406*mo 4 134.1012 0.8593 0.8241 72.17
4.5 127.5571 0.8580 0.8232 65.72
5 124.3952 0.8573 0.8297 63.82
5.5 114.9557 0.8553 0.8255 57.95
0.8 1.851 0.1976*mo 4.5 69.66 1.3802 0.7484 45.33
0.7 1.632 0.19034*mo 4.5 83.38 1.1913 0.8189 47.12
0.6 1.468 0.18375*mo 4.5 93.85 1.0589 0.8212 48.36
0.5 1.358 0.176*mo 4.5 100.64 0.9324 0.8354 49.39
0.4 1.301 0.168605*mo 4.5 104.09 0.9333 0.8473 51.86
0.3 1.298 0.1622*mo 4.5 104.36 0.9333 0.8459 51.91
0.2 1.35 0.1537*mo 4.5 101.6289 0.9419 0.8649 50.16
0.1 1.456 0.146*mo 4.5 95.2646 0.9402 0.8665 48.90
 85

Several observations are obtained from Table 6.6 which are given below:
1. Efficiency as well as Jsc decreases with an upsurge in dot size, phosphorous
content and barrier band gap.
2. Most important point is that though the value Jsc is high for dot size below 4 nm
for any value of band gap. But it is seen from the obtained data that below 4 nm
the position of second and third band is very close (less than 0.5eV) which may
cause an interaction between bands shown in Table 6.5. This will lead to
thermalization loss. Thus, it is better to use dot size over 4 nm.
In order to determine the quantity of bands two conditions need to be satisfied.
Minimum distance between each band must be 0.5 eV or 20 KT and bands must lie
within the band offset [62]. From calculation as mentioned in observation 1 of Table
6.5, three intermediate bands can only be possible for phosphorus content above 0.89.
Rest data in the Table 6.5 are listed for two intermediate bands. So, in Table 6.6 from
phosphorus content 0.8 to 0.1 all cell power conversion parameters are listed for two
intermediate band quantum dot solar cell.
Listed data in Table 6.6 are shown graphically in Figure 6.11 and 6.12.

Figure 6.11: Effect of Quantum Dot Size on the Proposed Cell’s Efficiency.
From Figure 6.11 it is seen that cell efficiency decreases with an upsurge in dot size.
The main reason behind it is that as the dot size upsurges intermediate bands are
positioned lower. As, bands are close to the conduction and valence band photon
emission due to recombination accelerate than generation rate which cause an decrease
in the cell’s efficiency.
 86

From Figure 6.12 it is seen that as the barrier substantial content upsurges, cell
efficiency decreases for single, double and triple band cell. It occurs because with an
upsurge in phosphorus content the band offset upsurges which cause an upsurge in the
height of potential well. Thus, carrier penetration depth decreases which decrease the
carrier accumulation in the subsequent bands. Thus, cell’s efficiency decreases. As,
performance of the cell also hinge ons on the distance between each dot. And as
mentioned earlier for higher efficiency inter dot distance must be equal for each dot. In
Table 6.7 effect of inter dot distance on the proposed cell’s efficiency is shown. Here,
phosphorus content is taken 0.92 where three intermediate bands can be included within
the barrier substantial. From calculations it is initiate that three intermediate bands can
be introduced in this particular phosphorus content only from the range of 2.6 nm to 3

Figure 6.12: Effect of Quantum Dot Size on the Proposed Cell’s Efficiency.
nm. Besides, as maximum efficiency is obtained for two intermediate bands for
phosphorus content 0.3, here the effect of inter dot distance on two intermediate bands
are observed for this particular content value. From calculation it is initiate that for
phosphorus content 0.3 it is impossible to include two intermediate bands for inter dot
distance range 1.7 nm to 3nm.

Table 6.7: Effect of Inter Dot distance On Proposed Cell’s Efficiency

Phosphorous Band Inter Quantit Jsc Voc FF Efficiency
Content gap dot y of IBs
distance
(eV) (nm) (mA/cm2) (V) (%)
0.92 2.184 2.6 3 122.97 0.9549 0.8532 63.12
 87

2.7 3 119.7575 0.9542 0.8335 60.00

2.8 3 116.8204 0.9536 0.8442 59.25
3 3 111.8240 0.9525 0.833 55.9
0.3 1.851 1.7 2 102.1025 0.9329 0.8319 49.9
1.8 2 102.6781 0.9329 0.8313 50.16
2 2 103.6990 0.9332 0.8301 50.61
2.5 2 104.4854 0.9334 0.8459 51.91
2.6 2 105.1567 0.9335 0.8279 51.20
3 2 105.7072 0.9337 0.8238 51.23

Figure 6.13: Effect of Inter Dot Distance on Proposed Cell’s Efficiency.

From Figure 6.13 it is seen that initially efficiency is low for lower inter dot distance.
This occurs as photon emission due to recombination occurs due to smaller inter dot
distance. As the distance upsurges recombination rate decreases and this will lead to an
upsurge in the cell’s efficiency. After a certain distance about 2.6 nm, as the inter dot
band cell, efficiency decreases with an upsurge in the inter dot distance. Distance
upsurges efficiency starts to decrease and after that change in efficiency with inter dot
distance becomes almost negligible because of lower band width which is already
discussed. This occurs for double intermediate band cell. For triple intermediate bands
effect of the inter dot distance on the cell’s efficiency can be observed from Table 6.7.
From which it is seen that as the inter dot distance upsurges efficiency decreases. The
main reason behind this phenomenon is that as the distance between dots decreases,
quantum coupling of the wave function of carrier wave upsurges which cause an
 88

upsurge in band width. Though in case of 2 IBQDSC efficiency decreases, but for 3
IBQDSC for lower inter dot distance due to larger wave function coupling carrier
generation rate s higher compared to the recombination rate. This effect cause an
upsurge in efficiency. But as the distance between dot upsurges quantum coupling
decreases which cause a decrease in band width and at the same time it decreases
efficiency.
Figure 6.14 shows the PV and IV curve for phosphorus content of 0.92 and dot size of
4.5nm with inter dot distance 2.6 nm. Here, short circuit current is 1.2297 A by
considering cell area 1cm2 and open circuit voltage of 0.9333 V. From this IV and PV
curve fill factor value is obtained about 0.8459 by using equation 3.12. This curve is

Figure 6.14: IV and PV Curve for 3 IBQDSC with dot size 4.5 nm and inter dot distance
2.6 nm.

obtained by designing Solar cell model in MATLAB Simulink considering parasitic

resistances effect. Simulink model is given to the Appendix.

6.5 Comparison of Dissimilar Output Parameters for Single IB, Double IB and
Triple IB Solar Cells

By performing MATLAB simulation according to Figure 6.9, 6.10 we obtain Jsc, Voc,
and efficiency for dissimilar dot size at dissimilar phosphorus content. As mentioned
earlier FF is computed via designing solar cell model in MATLAB Simulink
considering effect of Rs and Rsh. Table 6.6 comprises all data that we have obtained
using the code. In Table 6.3 the effect of dot size on the intermediate bands position are
shown and in Table 6.4 the effect of dot size on the Jsc, Voc, FF and efficiency are
shown. Here, phosphorus content is changed from 0.1 – 0.96 and the dot size is changed
 89

from 2 nm to 6 nm by keeping inter dot distance 2.6 nm. Moreover, inter dot distance
is changed to the certain values at which conditions for multi-intermediate bands is
satisfied by keeping dot size 4.5 nm.

Table 6.8: Obtained Efficiency, FF, Voc and Jsc for one, two and three
intermediate bands quantum dot solar cell for dot size 4.5 nm and inter dot
distance 2.6 nm.

Parameters 1 IB (InAs.98N.02/ 2 IB (InAs.98N.02/ 3 IB (InAs.98N.02/

AlP.3Sb.7) AlP.3Sb.7) AlP.92Sb.08)
Voc 1.284 V 0.9333 V 0.9549 V
Jsc 60.1704 mA/cm2 104.36 mA/cm2 122.97 mA/cm2
FF 0.7987 0.8459 0.8532
Efficiency 38.88% 51.91% 63.12%

Basically, listed efficiencies are the highest efficiency that we have obtained for this
these cells from our huge amount of calculation. Table 6.6 clearly shows that with an
upsurge in quantity of intermediate bands short circuit current density upsurges and
efficiency upsurges significantly. Moreover, it is seen that with the introduction of 3
IBs total current density is augmented by two times that of a single band cell. From
Figure 6.11 it is seen that as the dot size upsurges intermediate bands positioned lower
in case of first and second band. But third band doesn’t follow the rule. In case of third
band maximum band position is obtained periodically with a period 2.5nm. From Figure
6.12 it is seen that QDIBSC’s efficiency decreases with an upsurge in dot size. The
maximum efficiency is 63.12% for phosphorus content 0.92 with an upsurge in
phosphorus content for single intermediate band solar cell and for double intermediate
band solar cell the efficiency doesn’t fall sharply with an introduction of third band is
only possible when the phosphorus content is equal or above 90% and for triple band
solar cell the efficiency is also fall sharply with an upsurge in phosphorus content.

6.6 Chapter Summary

In this chapter, effect of dissimilar physical parameters such as QD size, interdot
distance, barrier substantial content on the performance of InAs0.98N0.02/ AlPxSb(1-x)
QDIBSC is observed. Where, InAs0.98N0.02 is the quantum dot and AlPxSb(1-x) is
the barrier substantial and x represent the phosphorus content of the barrier substantial.
Moreover, hinge oning on the effect of this parameters how many intermediate bands
 90

can be introduced within the barrier substantial is computed by using Kronig Penny
model with the help of MATLAB coding. For InAs0.98N0.02/ AlPxSb(1-x) we have tuned
the bandgap by varying the phosphorus content and the dot size to observe the variation
of cell parameter. We have initiate the maximum efficiency (η) for 3 IBQDSC around
63.12%, the current density, JSC is 123 mA/cm2 assuming FF is 0.8459 and VOC is
0.9333 V for phosphorus content 0.92. For 2 IBQDSC maximum efficiency is obtained
around 51.91% and for single IBQDSC maximum efficiency is obtained around 38.88%
for phosphorus content 0.3. For each cell maximum efficiency is obtained for dot size
4.5 nm with inter dot distance 2.6 nm.

.
 91

CHAPTER VII

CONCLUSION

7.1 Summary of Work Done

At the beginning of our work, we have studied about the current status of energy. We
initiate that day-by-day energy crisis is increasing at an alarming rate. Fossil fuel is
diminishing very quickly. Scientists are thinking to move to the alternative energy
sources. Renewable energy will be the major energy source of the next generation.
There are many kinds of renewable energy like wind, biogas, biomass, tidal, geothermal
etc. Among them, the most potential source of energy. In our country, we can produce
electricity from solar very easily. Generation wise there are three types of solar cells
like first-generation, second-generation and third-generation solar cell. First-generation
solar cell is silicon wafer based solar cells. Their efficiency is very poor. Second-
generation solar cell are thin film solar cells. They are thinner than first-generation solar
cell. Thin films are cheaper than first-generation silicon based solar cells. As the
efficiency of first-generation and second-generation, solar cells are very poor so we
think about third generation solar cells. We have discussed third-generation solar cells
in chapter four. Many types of research are going on to improve its efficiency and results
are very impressive. Quantum dot solar cell is one of the third-generation solar cells. In
chapter four we have discussed QD and QDIBSC. We have chosen QD Intermediate
band solar cell as our base model. In chapter four we have shown our proposed cell
structure.

In this thesis work effect of dissimilar physical parameter such as QD size, interdot
distance, barrier substantial content on the efficiency of the proposed QDIBSC is
investigated. Here, InAs0.98N0.02/AlPxSb(1-x) QDIBSC performance has been observed
hinge oning on all physical parameters. Here, AlPxSb(1-x) is the barrier and InAs0.98N0.02
is the quantum dot which is surrounded by the barrier. At first, it is investigated how
 92

many bands can be introduced within the barrier which is obtained from the position of
intermediate bands. To determine IB’s position theory of Kronig-Penney model is used
with the help of Schrodinger wave equation. From the obtained curves of Figure 6.3,
6.4, 6.5 width of intermediate bands and the position of the bands from the valence band
is determined for dissimilar values of QD size and interdot distance. All curves are
obtained from the MATLAB code that is developed manually as there is no established
software for the simulation of third generation solar cell. After obtaining the values of
band position and width short circuit current density is obtained by using equation 6.14,
6.15.1, 6.15.2, 6.15.3, 6.15.4. Voc is obtained from the reverse saturation current (Jo)
by using equation 6.22. Finally, FF is computed by designing a solar cell model in
MATLAB Simulink by considering the effect of series and shunt parasitic resistances.
Last of all, proposed cell’s efficiency for dissimilar phosphorus content, dot size, inter
dot distance is computed from Jsc, Voc and FF by using equation 6.23. After that,
mentiond physical parameters effect on performance of proposed cell is observed which
is obtained through humongous amount of calculations listed in the tables of Chapter 6.
In this thesis work, we try to investigate how many intermediate bands can be included
to the proposed substantial and from obtained result it is observed that it is impossible
to introduce more than three intermediate bands within the barrier substantial for the
proposed cell.

7.2 Future Work

In this thesis, we have proposed a novel QDIBSC substantial aimed at increasing the
efficiency beyond the limits of the conventional solar cells. Moreover, we analyze the
performance of InAs.98N.02/AlPxSb(x-1) cell for dissimilar phosphorus content, QD size
and inter dot distance. This type of analysis can be performed on other types of
substantials provided they must have the property of being a QDIBSC substantial. This
work includes the effect of almost all physical parameters effect on the performance of
the cell. Effect of other parameters such as optical parameters, property of front and
back contact, p and n layer thickness, property of carrier lifetime within the bands on
the performance of the cell can be investigated. From, this work it is initiate that it is
impossible to introduce more than three bands within the proposed cell due to lower
band offset. So, in order to introduce more than three bands higher bandgap substantial
must be used, one possible substantial for this purpose can be InxGa(1-x)N/GaN as GaN
has a bandgap of 3.4 eV higher than AlPSb having maximum 2.38 eV. So, in future
 93

work can be done on this substantial to determine its performance for multiple bands.
Last of all, practical implementation of the cell can be done in order to determine the
true performance of the cell.

7.3 Final Conclusion

QDIBSC is a third-generation solar cell which can be a good solution for large
production of electrical energy from renewable energy. As its efficiency is high so it
can be used for space application, normal household appliances like mobile charger,
laptop charger, solar cooker, solar thermal plant etc. can be designed by using this solar
cell. The performance of one, two or three IBSC models are better than the conventional
solar cell. It is evident that conversion efficiency has significantly improved.
Conventional solar cell and second-generation solar cell like CdTe, CIGS, a-Si have
efficiency 20%, 21%, 12% respectively. But in case of QDIBSC, we initiate highest
efficiency for one IB 38.88%, for two IB 51.91% and around for three IB 63.12% for
dot size 4.5 nm with inter dot distance 2.6nm. Due to introduce IB, JSC has augmented
significantly thus efficiency also augmented. So QDIBSC can be the solution to low
efficiency problem of solar cells. QDIBSC device aimed at increasing the efficiency
beyond the Shockley Quisser limits of the conventional solar cells. Cost of solar cells
upsurges due to low JSC. From our work, we initiate that due to introduce of IB the value
of short circuit current density upsurges greatly. Usage, time and energy reduced, which
in-turns produce cost effective solar cells.
 94

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 103

APPENDIX

APPENDIX-A

This appendix comprises the whole source code for the MATLAB program referred in
the text and related codes:

A1: MATLAB CODE FOR DETERMINING THE CHANGE IN BARRIER

BAND GAPS WITH PHOSPHORUS CONTENT.

clc

clear all

close all

syms Eg

b = 2.7; %% blowing parameter AlP(x)Sb(1-x)

EgAlP = 2.45; %% Bandgap Energy of AlP

EgAlSb = 1.615; %% Bandgap Energy of AlSb

x = 0 : .01 : 1;

Eg = x.*EgAlP + (1-x).*(EgAlSb) -b.*x.*(1-x) %% Bandgap Energt of AlP(x)Sb(1-

x)

plot(x,Eg)

xlabel ('Phosphorus Content');

ylabel('Bandgap Energy');
 104

A2 : MATLAB CODE FOR DETERMINING POSITION OF INTERMEDIATE

BANDS

clc;

clear all;

close all;

set(0,'defaultlinelinewidth',1.5)

%Constants

h = 6.626e-34;

c = 2.998e8;

h_cut = 1.055e-34; %% h_cut = h./(2.*pi)

m0 = 9.109e-31;

e_const = 1.6e-19;

%inputs

U_eV= 1;

mq = .0279.*m0; %% effective mass of electron in quantum dot region

mb = .21053.*m0; %% effective mass of electron in barrier region

Lq = 4e-9; %% Width of a single dot

Lb = 2.6e-9; %% Barrier width

mu = Lb./Lq;

L = Lq+Lb; %% Period

%Derived values

U=U_eV*e_const;

Aq = Lq.*sqrt(2*mq*U/(h_cut^2))

Ab = Lb.*sqrt(2*mb*U/(h_cut^2))
 105

f = @(g) ((mq-(mq+mb).*g)./(2.*sqrt(mq.*mb.*g).*sqrt(1-g)))...

.*sinh(mu.*Ab.*sqrt(1-g)).*sin(Aq.*sqrt(g))...

+ cosh(mu.*Ab.*sqrt(1-g)).*cos(Aq.*sqrt(g))

g=linspace(.1, 2.5, 1e5);

fg=f(g);

g(isnan(g))=1;

plot(g,fg,'lineWidth', 2 )

hold on

plot([g(1) g(end)], [1, 1], 'r--')

plot([g(1) g(end)], [-1, -1], 'g--') %%U=' num2str(U_eV), ' eV;

ylim([min(fg)-.5, 3])

xlabel('\epsilon (=E/V_o) \rightarrow');

ylabel('f(\epsilon) \rightarrow');

title(['Plot of the RHS of the equation f(\epsilon) vs. \epsilon; '...

'for L=' num2str(L*1e10) char(197)...

' and Lb=' num2str(Lb*1e10) char(197)])

grid on

flg=abs(fg)<=1;

Figure

h1=gca;

hold on

xlabel('Crystal momentum, k(radian/meter) \rightarrow');

ylabel('Energy, E (eV) \rightarrow');

title(['Reduced zone representation of the E-k relationship '...

 106

'for L=' num2str(L*1e10) char(197)...

' and Lb=' num2str(Lb*1e10) char(197)])

xticks([-pi -pi/2 0 pi/2 pi]/(L+Lb));

xticklabels({'-\pi/(Lq+Lb)','-\pi/(2(Lq+Lb))','0','\pi/(2(Lq+Lb))','\pi/(Lq+Lb)'})

grid on

Figure

h2=gca;

hold on

xlabel('Crystal momentum, k(radian/meter) \rightarrow');

ylabel('Energy, E (eV) \rightarrow');

title(['Extended zone representation of the E-k relationship '...

'for L=' num2str(L*1e10) char(197)...

' and Lb=' num2str(Lb*1e10) char(197)])

xticks([-6*pi -5*pi -4*pi -3*pi -2*pi -pi 0 pi 2*pi 3*pi 4*pi 5*pi 6*pi]/(L+Lb))

xticklabels({'-6\pi/(Lq+Lb)','-5\pi/(Lq+Lb)','-4\pi/(Lq+Lb)' ...

'-3\pi/(Lq+Lb)','-2\pi/(Lq+Lb)','-\pi/(Lq+Lb)','0','\pi/(Lq+Lb)',...

'2\pi/(Lq+Lb)','3\pi/(L+Lb)'...

'4\pi/(Lq+Lb)','5\pi/(Lq+Lb)','6\pi/(Lq+Lb)'})

xtickangle(45)

grid on

prd=pi/(L+Lb);

plst=1;

k=1;

while ~isempty(flg) && k<6

 107

pos=find(flg);

if isempty(pos)

break

end

pfst=plst+pos(1)-1;

flg=flg(pos(1):end);

pos=find(~flg);

if isempty(pos)

break

end

plst=pfst+pos(1)-1;

flg=flg(pos(1):end);

kv=acos(fg(pfst:plst-1))/(L+Lb);

ev=g(pfst:plst-1)*U_eV;

if mod(k,2)

plot(h1,[-fliplr(kv), kv], [fliplr(ev),ev], 'b');

if k==1

plot(h2,[-fliplr(kv), kv], [fliplr(ev),ev], 'b');

else

plot(h2,kv+prd*(k-1), ev, 'b');

plot(h2,-fliplr(kv)-prd*(k-1), fliplr(ev), 'b');

end

else

plot(h1, [kv, -fliplr(kv)], [ev,fliplr(ev)], 'b');

 108

plot(h2,kv-prd*k, ev, 'b');

plot(h2,-fliplr(kv)+prd*k, fliplr(ev), 'b')

end

k=k+1;

end

A3: MATLAB CODE FOR DETERMINING REVERSE SATURATON

CURRENT

clc

clear all

close all

syms mb

mo = 9.109e-31;

mupAlP = 450.*mo; %% hole mobility of AlP

mupAlSb = 400.*mo; %% hole mobility of AlSb

mupAlPSb = (0.94.*mupAlP + 0.06.*mupAlSb )./mo

munAlP = 60.*mo; %% electron mobility of AlP

munAlSb = 200.*mo; %% electron mobility of AlSb

munAlPSb = (0.94.*munAlP + 0.06.*munAlSb )./mo

e = 1.6e-19

mopAlPSb = 0.1950.*mo

monAlPSb = 0.2076.*mo

Kb = 1.38e-23;

T = 300;

h = 6.626e-34
 109

taop = (mupAlPSb.*mopAlPSb)./e

taon = (munAlPSb.*monAlPSb)./e

Dp = (mupAlPSb.*Kb.*T)./e

Dn = (munAlPSb.*Kb.*T)./e

Lp = sqrt(Dp.*taop)

Ln = sqrt(Dn.*taon)

Nc = (2.*(((2.*pi.*monAlPSb.*Kb.*T)./(h.^2))^(3./2))).*(10e-6) %% in per cm

Nv = (2.*(((2.*pi.*mopAlPSb.*Kb.*T)./(h.^2))^(3./2))).*(10e-6) %% in per cm

riInP = 3.96317; %% refractive index of AlP

riInN = 2.59; %% refractive index of AlSb

riAlPSb = 0.98.*riInP + 0.02.*riInN

T=input('Please enter value of the temperature, celcius T=');

E_gd=input('Please enter the value of bandgap of QD substantial, E_gd=');

ND=input('Please enter the value of donar concentration of the substantial,ND=');

nD = input('Please enter the value of volume density of quantum dots,nD=')

NA=input('Please enter the value of acceptor concentration of the substantial, NA=');

Nc=input('Please enter the value of Effective Density of States in the Conduction

Band, Nc (cm-3)=');

Nv=input('Please enter the value of Effective Density of States in the Valence Band,
Nv (cm-3)=');

vD= ('PLese enter the value of volume of QDs,vD=')

n=input('Please enter the value of refractive index of i region, n=');

Dn=input('Please enter the value of diffusion constant of electrons,Dn=')

Dp=input('Please enter the value of diffusion constant of holes,Dp=')

Lp=input('Please enter the value of diffusion length of holes, Lp=');

 110

Ln=input('Please enter the value of diffusion length of electrons, Ln=');

Po=116; % incident solar flux(for 1 sun,AM 1.5 condition).

e=1.6e-19; % charge of electron.

E_gb=2.248; % band gap of Barrier.

E_gd= 0.25; % band gap of QD.

v=1.2; % ideality factor.

k=1.38e-23;

n=3.9357;

c=3e10;

h=6.63e-34/1.6e-19;

E_eff=(1-nD*vD)*E_gb+(nD*vD*E_gd);

A=e*Nc*Nv*(Dp/(ND*Lp)+Dn/(NA*Ln));

A_eff=(e*4*pi*n^2*k*(T+273))/(c^2*h^3*(E_eff).^2);

Js1=A_eff.*exp(-(E_gb*e)/(v*(T+273)*k));

Js2=A.*exp(-(E_eff*e)/(v*(T+273)*k));

disp('Value of reverse saturation current')

Jo=Js1+Js2 % reverse seturation current

disp('Value of open circuit voltage')

Voc=p*log((Jsc/Jo)+1)

A4 : MATLAB CODE FOR DETERMINING EFFICIENCY

clc;
clear all;
close all;
clc;

eps=2.16e-5; % geometric Factor

Sc=1;
 111

h_bar= 6.5821e-16; %% in eVs unit

c=3e10; %%in cm/s
KB=8.617e-5; %boltzman Constant in 'evK^-1' unit

T = 300 ;
Ts=6000; %Temp of at the exterior of sun
Ta= 300;
Efc = 0.441 ;
Efv = 0.4522;

%% Calculation of width of bands

delta_1 =0.0163e-3; %%(width of first band)
delta_2 =0.104e-3; %%(width of second band)
delta_3 = .365e-3; %%(width of third band)

%% Calculation of band position

Ecv = 2.184;
EVI1 =0.1359; %%(position of first band)
EVI2 =0.7815; %%(position of 2nd band)
EVI3 = 1.578; %%(position of 3rd band)
ECI1 = Ecv - ( EVI1 + delta_1)
ECI2 = Ecv - ( EVI2 + delta_2)
ECI3 = Ecv - ( EVI3 + delta_3)

%% Calculation of chemical potential

ucv = Ecv-0.8932;
uci1 = ECI1 + (delta_1./2) - Efc
uci2 = ECI2 + (delta_2./2) - Efc
uci3 = ECI3 + (delta_3./2) - Efc

uv1 = Ecv - uci1;

uv2 = Ecv - uci2;
uv3 = Ecv - uci3;

k = 1.38e-23 ;
n = .6312;
q1 = 1.6e-16;
t_opt = 23.01;

%%Calculation for No IB
f=@(x) (Sc.*eps.*x.^2)./(exp(x./(KB.*Ts))-1);

Jcv_0 = integral(f,Ecv,inf)

f=@(x) ((1-Sc.*eps).*x.^2)./(exp(x./(KB.*Ta))-1);

Jcv_01 = integral(f,Ecv,inf)

f=@(x) (x.^2)./(exp((x-ucv)./(KB.*Ta))-1);
 112

Jcv_001 = integral(f,Ecv,inf)

%% Calculation for single IB

f=@(x) (Sc.*eps.*x.^2)./(exp(x./(KB.*Ts))-1);

Jcv_1 = integral(f,ECI1,Ecv)

f=@(x) ((1-Sc.*eps).*x.^2)./(exp(x./(KB.*Ta))-1);

Jcv_11 = integral(f,ECI1,Ecv)

f=@(x) (x.^2)./(exp((x-uci1)./(KB.*Ta))-1);

Jcv_111 = integral(f,ECI1,Ecv)

%% Calculation For double IB

f=@(x) (Sc.*eps.*x.^2)./(exp(x./(KB.*Ts))-1);

Jcv_2 = integral(f,ECI2,Ecv)

f=@(x) ((1-Sc.*eps).*x.^2)./(exp(x./(KB.*Ta))-1);

Jcv_22 = integral(f,ECI2,Ecv)

f=@(x) (x.^2)./(exp((x-uci2)./(KB.*Ta))-1);

Jcv_222 = integral(f,ECI2,Ecv)

%% Calculation For Tripple IB

f=@(x) (Sc.*eps.*x.^2)./(exp(x./(KB.*Ts))-1);

Jcv_3 = integral(f,ECI3,Ecv)

f=@(x) ((1-Sc.*eps).*x.^2)./(exp(x./(KB.*Ta))-1);

Jcv_33 = integral(f,ECI3,Ecv)

f=@(x) (x.^2)./(exp((x-uci3)./(KB.*Ta))-1);

Jcv_333 = integral(f,ECI3,Ecv)

disp('Short Circuit Current')

 113

Jsc=(q1./(4.*pi.^2.*h_bar.^3.*c.^2)).*(Jcv_0+Jcv_01-Jcv_001+Jcv_1+Jcv_11-
Jcv_111+Jcv_2+Jcv_22-Jcv_222+Jcv_3+Jcv_33-Jcv_333)

Voc = 0.9549
Pin = 1587.2
FF = 0.8532
Efficiency = ((Jsc.*Voc.*FF.*10)./1587.2).*100

A5 : MATLAB CODE FOR OBTAINING DISSIMILAR CURVES FROM

DATA TABLE.

A5.1 : MATLAB CODE FOR OBTAINING THE EFFECT OF DOT SIZE ON

BANDS POSITION.

clc
clear all;
close all;

x = [2 , 2.5 ,3,3.5,4,4.5,5,5.5,6]
x1 = [4.5,5,5.5,6]
y1 = [.3241,.2628,.2182,.1841,.1574,.1359,.1186,.1039,.1]
plot(x,y1,'-rs','lineWidth', 2,'MarkerFaceColor','b','MarkerSize',10)
hold on;
y2 = [1.129,1.163,1.144,1.046,.9102,.7815,.6723,.5817,.5077]
plot(x,y2,'-bs','lineWidth', 2,'MarkerFaceColor','r','MarkerSize',10)
hold on;
y3 = [1.578,1.554,1.464,1.338]
plot(x1,y3,'-ks','lineWidth', 2,'MarkerFaceColor','k','MarkerSize',10)
hold on;
y4 =[1.934,1.934,1.934,1.934,1.934,1.934,1.934,1.934,1.934]
plot(x,y4,'--g','LineWidth',3)
xlabel('Quantum Dot Size(nm) \rightarrow');
ylabel('Intermediate bands position(eV) \rightarrow')
title('Intermediate bands position Vs QD Size for Phosphorus content 0.92');
grid on
 114

A5.2 : MATLAB CODE FOR OBTAINING THE EFFECT OF DOT SIZE ON

EFFICIENCY.

clc
clear all;
close all;
x = [4.5,5,5.5,6]
y1 = [63.12,58.79,53.12,47.4]
plot(x,y1,'lineWidth', 2 )
xlabel('Quantum Dot Size(nm) \rightarrow');
ylabel('Efficiency \rightarrow')
title('Efficiency Vs QD Size for Phosphorus Content 0.92 ');

A5.3: MATLAB CODE FOR OBTAINING THE EFFECT OF PHOSPHORUS

CONTENT ON EFFICIENCY.

clc
clear all;
close all;
x = [.3 ,.4 ,.5,.6,.7,.8,.9]
x1 = [.9 ,.92 , .94 ,.96 ]
y1 = [38.88 , 38.69 ,36.56, 32.8 , 27.52 , 20.89 , 16.56]
plot(x,y1,'-rs','lineWidth', 2,'MarkerFaceColor','b','MarkerSize',10)
hold on;
y2 = [51.91 , 51.86 ,49.39,48.36,47.12,46.8,45.37]
plot(x,y2,'-bs','lineWidth', 2,'MarkerFaceColor','g','MarkerSize',10)
hold on;
y3 = [65.93,63.12,57.89,56]
plot(x1,y3,'-ks','lineWidth', 2,'MarkerFaceColor','k','MarkerSize',10)
hold on;
xlabel('Phosphorus Content \rightarrow');
ylabel('Efficiency \rightarrow')
title('Efficiency Vs Phosphorus Content for dot size 4.5 nm');
 115

A6 : MATLAB APP CODE

A6.1 : MATLAB APP CODE TO DESIGN THE APP TO CALAULATE

DISSIMILAR PARAMETERS.

% Button pushed function: ViewOutputsButton

function ViewOutputsButtonPushed(app, event)

eps=2.16e-5; % geometric Factor

Sc=1;

h_bar= 6.5821e-16; %% in eVs unit

c=3e10; %%in cm/s

KB=8.617e-5; %boltzman Constant in 'evK^-1' unit

T = app.input1.Value ;

Ts=6000; %Temp of at the exterior of sun

Ta= 300;

Efc = 0.441 ;

Efv = 0.4522

%% Calculation of width of bands

delta_1 = app.input2.Value; %%(width of first band)

delta_2 = app.input3.Value; %%(width of second band)

delta_3 = app.input4.Value; %%(width of third band)

%% Calculation of band position

Ecv = app.input5.Value;

EVI1 = app.input6.Value;

EVI2 = app.input7.Value;
 116

EVI3 = app.input8.Value;

ECI1 = Ecv - ( EVI1 + delta_1)

ECI2 = Ecv - ( EVI2 + delta_2)

ECI3 = Ecv - ( EVI3 + delta_3)

%% Calculation of chemical potential

ucv = app.input9.Value;

uci1 = ECI1 + (delta_1./2) - Efc

uci2 = ECI2 + (delta_2./2) - Efc

uci3 = ECI3 + (delta_3./2) - Efc

uv1 = Ecv - uci1;

uv2 = Ecv - uci2;

uv3 = Ecv - uci3;

Rsh = 200 ; %% in ohm

k = 1.38e-23 ;

q1 = 1.6e-16;

%%Calculation for No IB

f=@(x) (Sc.*eps.*x.^2)./(exp(x./(KB.*Ts))-1);

Jcv_0 = integral(f,Ecv,inf)

f=@(x) ((1-Sc.*eps).*x.^2)./(exp(x./(KB.*Ta))-1);

Jcv_01 = integral(f,Ecv,inf)

f=@(x) (x.^2)./(exp((x-ucv)./(KB.*Ta))-1);

Jcv_001 = integral(f,Ecv,inf)

%% Calculation for single IB

 117

f=@(x) (Sc.*eps.*x.^2)./(exp(x./(KB.*Ts))-1);

Jcv_1 = integral(f,ECI1,Ecv)

f=@(x) ((1-Sc.*eps).*x.^2)./(exp(x./(KB.*Ta))-1);

Jcv_11 = integral(f,ECI1,Ecv)

f=@(x) (x.^2)./(exp((x-uci1)./(KB.*Ta))-1);

Jcv_111 = integral(f,ECI1,Ecv)

%% Calculation For double IB

f=@(x) (Sc.*eps.*x.^2)./(exp(x./(KB.*Ts))-1);

Jcv_2 = integral(f,ECI2,Ecv)

f=@(x) ((1-Sc.*eps).*x.^2)./(exp(x./(KB.*Ta))-1);

Jcv_22 = integral(f,ECI2,Ecv)

f=@(x) (x.^2)./(exp((x-uci2)./(KB.*Ta))-1);

Jcv_222 = integral(f,ECI2,Ecv)

%% Calculation For Tripple IB

f=@(x) (Sc.*eps.*x.^2)./(exp(x./(KB.*Ts))-1);

Jcv_3 = integral(f,ECI3,Ecv)

f=@(x) ((1-Sc.*eps).*x.^2)./(exp(x./(KB.*Ta))-1);

Jcv_33 = integral(f,ECI3,Ecv)

f=@(x) (x.^2)./(exp((x-uci3)./(KB.*Ta))-1);

Jcv_333 = integral(f,ECI3,Ecv)

Jsc=(q1./(4.*pi.^2.*h_bar.^3.*c.^2)).*(Jcv_0+Jcv_01-
Jcv_001+Jcv_1+Jcv_11-Jcv_111+Jcv_2+Jcv_22-Jcv_222+Jcv_3+Jcv_33-Jcv_333)

t_opt=22.5;

Jo=app.input10.Value;

e=1.6e-19;
 118

p=(1.38e-23*(T+273))/e;

Po=116;

Efficiency=(p*t_opt*(Jsc-Jo*(exp(t_opt)-1))/Po)*100

Voc=p*log((Jsc/Jo)+1)

FF=(Efficiency.*(1587.2))/(Jsc*Voc.*10)

app.output1.Value=Efficiency;

app.output2.Value=Voc;

app.output3.Value=FF;

app.output4.Value=Jsc;

end

end

end

A6.2 : MATLAB APP CODE TO DRAW PV AND IV CURVE.

% Button pushed function: IVCurveButton

function IVCurveButtonPushed(app, event)

K = 1.38065e-23;

q = 1.6e-19;

Iscn = .113;

Vocn = 1;

Kv = -.123;

ki = .0032;

Ns = 1;

T = 35+273 ;
 119

Tn = 25+273 ;

Gn = 1000;

a = 1.3;

Eg = 1.12;

G = 1000;

Rs = 0.001;

Rp = 400 ;

Vtn = Ns *(K*Tn/q);

Ion = Iscn/((exp(Vocn/(a*Vtn)))-1)

Io = Ion * ((Tn/T)^3)*exp(((q*Eg/(a*K))*((1/Tn)-(1/T))));

Ipvn = Iscn ;

Ipv = (Ipvn+ki*(T-Tn))*(G/Gn)

Vt = Ns*(K*T/q);

I = zeros(2,1);

i = 1;

I(1,1) = 0;

for V = .94 : -.01 : 0

I_part = Io*(exp((V+(I(i,1)*Rs))/(Vt*a))-1)+((V+(Rs*I(i,1)))/Rp);

I(i+1) = Ipv - I_part;

V1(i)=V;

P(i)=V*I(i);

i=i+1;

end

V1(i) = V1(i-1);
 120

P(i) = P(i-1);

V1 = transpose(V1);

plot(app.UIAxes,V1,I);

end

% Button pushed function: PVCurveButton

function PVCurveButtonPushed(app, event)

K = 1.38065e-23;

q = 1.6e-19;

Iscn = .113;

Vocn = 1;

Kv = -.123;

ki = .0032;

Ns = 1;

T = 35+273 ;

Tn = 25+273 ;

Gn = 1000;

a = 1.3;

Eg = 1.12;

G = 1000;

Rs = 0.001;

Rp = 400 ;

Vtn = Ns *(K*Tn/q);

Ion = Iscn/((exp(Vocn/(a*Vtn)))-1)

Io = Ion * ((Tn/T)^3)*exp(((q*Eg/(a*K))*((1/Tn)-(1/T))));
 121

Ipvn = Iscn ;

Ipv = (Ipvn+ki*(T-Tn))*(G/Gn)

Vt = Ns*(K*T/q);

I = zeros(2,1);

i = 1;

I(1,1) = 0;

for V = .94 : -.01 : 0

I_part = Io*(exp((V+(I(i,1)*Rs))/(Vt*a))-1)+((V+(Rs*I(i,1)))/Rp);

I(i+1) = Ipv - I_part;

V1(i)=V;

P(i)=V*I(i);

i=i+1;

end

V1(i) = V1(i-1);

P(i) = P(i-1);

V1 = transpose(V1);

plot(app.UIAxes,V1,P);

end

end
 122

APPENDIX-B
This appendix comprises the “App Designer” window regarding to “App designer” of
MATLAB by which we have make an app for proposed IBQDSC. Besides, in section
B5 designed solar cell model in MATLAB Simulink is given.

B1: Design view of “App Designer” for QDIBSC_Simulator.mlapp

B2: Code view of “App Designer” for QDIBSC_Simulator.mlapp

 123

B3: Design view of “App Designer” for IV_Curve.mlapp

B4: Design view of “App Designer” for IV_Curve.mlapp

 124

B5: Design view of solar cell model in MATLAB Simulink