Design, Growth & Simulation of InGaN Solar Cells

“Design, Growth & Fabrication of InxGa1-xN
(0 ≤ x ≤ 0.25) Based Solar Cell”
A Dissertation submitted to Pt. Ravishankar Shukla University
for partial fulfillment of the requirements of degree
Master of Technology
(Optoelectronics & Laser Technology)
By
RAJKUMAR SAHU
School of Studies in Electronics & Photonics,
Pt. Ravishankar Shukla University, Raipur, C.G.- 492010, India
Under the Guidance of
Mr. Sonachand Adhikari
Scientist
Optoelectronic Devices Group
CSIR-Central Electronics Engineering Research Institute, Pilani
Rajasthan – 333031, India
July 2013- May 2014

Abstract
InGaN has a tunable direct band gap starting from 0.7 to 3.42 eV and also high radiation
hardness, which makes it one of the most useful material systems especially for photovoltaic
application. Since, the growth and fabrication techniques of InGaN has not reached maturity
level, there are still issues to be addressed in design of device, high quality wafer growth and
fabrication.
For a solar cell, there are four important parameters: Short Circuit Current (Jsc), Open
Circuit Voltage (Voc), Fill Factor (FF) and Efficiency (ŋ), which helps in determining its
characteristics. These parameters depend on various intrinsic and extrinsic material properties
and the major role in a solar cell depends on the minority carriers and the resistance offered in
path of current flow (series and shunt resistance).
Silvaco-Atlas was used to simulate and optimize p-i-n structure. Effects of various
physical parameter such as doping, layer thickness, grid spacing are investigated to get high
efficiency p-i -n double hetero-junction GaN/InGaN solar cell. Simulation result shows that an
efficiency of 9.42% with fill factor as high as 88.73% can be achieved with indium content of
15%. Schottky Diode & Multi Quantum Well (MQW) structure solar cell has also been
simulated however, those structure did not show expected high-efficiency results.
i

ACKNOWLEDGEMENTS
I would like to take this opportunity to acknowledge those who have provided the help
and guidance to complete my M.Tech. Their understanding and advice are an invaluable treasure
which I will never forget.
First, I would like to thank my supervisors, Mr. Sonachand Adhikari, CSIR-CEERI,
Pilani and Prof. Sanjay Tiwari, Pt. Ravishankar Shukla University, Raipur, for the support,
encouragement, constant guidance and constructive advices that they have given me throughout
all the stages of my research work. I also greatly appreciate the faith, they both have shown in
my abilities and capabilities.
I am grateful to Dr. Chandra Shekhar, Director, CSIR-CEERI, Pilani, for providing me
an opportunity to carry out most of the work reported in the thesis at CSIR-CEERI, Pilani.
I extend my sincere thanks to Dr. C. Dhanvantari, Group Leader, Optoelectronic
Devices Group, CSIR-CEERI, Pilani for giving me the opportunity to work in the field of
Optoelectronic devices.
I extend my sincere thanks to Dr. Suchandan Pal, Dr. Sumitra Singh, Shri S. Johri,
Mr. Kuldip Singh, & Mr. Ashok Chauhan, for their invaluable suggestion and support. I take
this unique opportunity to thank all the Scientific/Technical staff of Optoelectronics Devices
Group for making all the facilities available at time.
I extend my sincere thanks to Mr. Vinod Kumar Verma Technical Officer for his
constant support and help during the entire period of my project work.
I would like to extend my appreciation and thankfulness to my friends, and others who
are related directly or indirectly, for their tremendous co-operation and encouragement during
this work, without which the task would not have been possible.
I must also thank my parent Shri. Naba Kishore Sahu and Smt. Shanti Lata Sahu , my
younger sisters Miss. Rasmita, and Miss. Rajeshwari for their love, affection, and endless
support that has enabled me to reach this goal.
Finally, I would also like to express my deep sense of gratitude and respect towards all
those people who work for preserving nature and environment. Their works always inspire me to
work in this field. I also perceived that this is not the end of study in my life. I can understand
what kind of new life, and difficulties I have to face in near future. I also believe that I will
follow the same path but now with more curiosity and confidence.
Rajkumar Sahu
ii

TABLE OF CONTENTS
ABSTRACT i
ACKNOWLEDGEMENT ii
LIST OF FIGURES vii
LIST OF TABLES x
1 INTRODUCTION 1-16
1.1 HISTORY OF SOLAR ENERGY 1
1.2 SOLAR ENERGY AND HIGH EFFICIANCY EFFORTS 3
1.3 III-NITRIDE MATERIAL SYSTEM 6
1.4 III-NITRIDE MATERIALS PROPERTIES 7
1.5 CHALLENGES IN INGAN MATERIAL SYSTEM 12
1.5.1 SUBSTRATE 12
1.5.2 PHASE SSEPARATION 12
1.5.3 POLARIZATION AND PIEZOELECTRIC CONSTANT 13
1.5.4 P-TYPE DOPING 14
1.5.5 ABSORPTION DEPTH AND DIFFUSION LENGTH 14
1.6 SUMMARY 15
REFERENCES 16
2 SOLAR CELL BASICS 19-29
2.1 THE PHOTOVOLTAIC EFFECT 19
2.2 SEMICONDUCTOR CONCEPT 20
2.2.1 EQUILIBRIUM 20
2.2.2 NON EQUILIBRIUM 21
2.3 Characteristic of Photovoltaic Cell 22
iii

2.3.1 PHOTOCURRENT AND QUANTUM EFFICIENCY 22
2.3.2 DARK CURRENT AND OPEN CIRCUIT VOLTAGE 23
2.3.3 EFFICIENCY 25
2.3.4 PARASITIC RESISTANCES 27
2.4 SUMMARY 28
REFERENCES 29
3 INTRODUCTION TO SIMULATION SOFTWARE 30-44
3.1 SILVACO ATLAS 30
3.2 INPUT FILE STRUCTURE 31
3.3 STRUCTURE SPECIFICATION 33
3.3.1 MESH 33
3.3.2 REGION 34
3.3.3 ELECTRODE 34
3.3.4 DOPING 35
3.4 MATERIAL MODEL SPECIFICATION 35
3.4.1 MATERIALS 35
3.4.2 MODELS 36
3.4.3 CONTACT 36
3.4.4 INTERFACE 36
3.5 NUMERICAL METHOD SELECTION 37
3.6 SOLUTION SPECIFICATION 37
3.6.1 LOG 38
3.6.2 SOLVE 38
3.6.3 LOAD AND SAVE 38
3.7 RESULT ANALYSIS 38
3.8 BASIC EQUATIONS 39
3.9 FINITE ELEMENT ANALYSIS 40
3.10 ADDITIONAL MODELS 40
iv

3.10.1 SHOCKLEY-READ-HALL RECOMBINATION 41
3.10.2 RADIATIVE RECOMBINATION 42
3.10.3 AUGER RECOMBINATION 42
3.11 SUMMARY 43
REFERENCES 44
4 DESIGN OF InGaN SOLAR CELL 45-53
4.1 INTRODUCTION 45
4.2 EARLIER DEVELOPMENTS 45
4.3 SIMULATION OF INGAN SOLAR CELL 46
4.3.1 OPTIMIZATION OF P-I-N STRUCTURE 47
4.3.2 P-I-N STRUCTURE WITH VARYING INDIUM COMPOSITION 51
4.4 SUMMARY 52
REFERENCES 53
5 GROWTH OF GaN FILMS BY MOCVD 54-67
5.1 EPITAXY 54
5.2 GROWTH TECHNIQUES 54
5.2.1 MOLECULAR BEAM EPITAXY (MBE) 55
5.2.2 METAL ORGANIC CHEMICAL VAPOR DEPSITION 55
5.3 METAL ORGANIC CHEMICAL VAPOR DEPSITION(MOCVD)
GROWTH TECHNIQUE 55
5.3.1 CONFIGURATION 57
5.3.2 SOURCES 58
5.4 CHARACTERIZATION TECHNIQUES 59
5.4.1 IN-SITU-CHARACTERIZATION 59
5.4.2 Atomic Force Microscopy Measurement 64
5.4.3 Photoluminescence Measurement 65
5.5 SUMMARY 66
REFERENCES 67
v

6 FABRICATION OF GaN/InGaN SOLAR CELL 68-74
6.1 Device Processing Technology 68
6.2 MASK LAYOUT DESIGN 68
6.2.1 DIFFERENT DEVICE & TEST STRUCUURE 69
6.3 FABRICATION PROCESS OF GAN/INGAN SOLAR CELL 69
6.3.1 PHOTORESIST SPIN COAT 70
6.3.2 MESA ETCH 70
6.3.3 N-CONTACT METALLIZATION 71
6.3.4 CURRENT SPREADING LAYER 72
6.3.5 P-CONTACT METALLIZATION 73
6.4 SUMMARY 74
CONCLUSION & FUTURE WORK 75
APPENDIX A 76
APPENDIX B 78
vi

List of Figures
Chapter 1
Fig. 1.1 Best research cell efficiencies 4
Fig. 1.2 Light transfer through a three-junction solar cell 5
Fig. 1.3 Solar radiation and energy bandgap with Ga fraction in In1-xGaxN 7
Fig. 1.4 (a) Unit cell for the hexagonal wurtzite structure
(b) Wigner-Seitz unit cell for the III-nitrides. 8
Fig. 1.5 Bandgap energy versus chemical bond length for III-Nitrides and
other Semiconductors. 9
Fig. 1.6 Energy bandgap (eV) as a function of lattice parameter (Å) for
wurtzite III Nitride alloys 10
Fig. 1.7 Schematic comparison of band structures of (a) an ideal material,
and (b) a phase separated material. 13
Chapter 2
Fig. 2.1. Comparison of the photoelectric effect (left), where uv light
liberates electrons from the surface of a metal, with
the photovoltaic effect in a solar cell (right). 19
Fig. 2.2. Quantum effciency of GaAs cell compared to the solar spectrum.
The vertical scale is in arbitrary units, for comparison 23
Fig. 2.3. Current-Voltage characteristic of ideal diode in the light
and the dark. 23
Fig. 2.4. Equivalent circuit of ideal solar cell. 25
Fig. 2.5. The current voltage (black) and power{voltage (grey)
characteristics of an ideal cell. Power density reaches a maximum
at a bias Vm, close to Voc. The maximum power density Jm* Vm is
given by the area of the inner rectangle. The outer rectangle has
area Jsc*Voc. If the fill factor were equal to 1, the current voltage
curve would follow the outer rectangle. 26
Fig. 2.6 Equivalent circuit including series and shunt resistances. 27
Fig. 2.7 .Effect of (a) increasing series and (b) reducing parallel
vii

resistances. In each case the outer curve has Rs = 0 and
Rsh =. In each case the effect of the resistances is to reduce
the area of the maximum power rectangle compared to Jsc *Voc. 27
Chapter 3
Fig. 3.1 Atlas inputs and outputs 31
Fig. 3.2 Atlas command groups and primary statements 32
Fig. 3.3 Atlas mesh. 33
Fig. 3.4 Atlas region 34
Fig. 3.5 Atlas electrodes 35
Fig. 3.6 a) Indirect bandgap recombination
b) Direct bandgap recombination 41
Chapter 4
Fig. 4.1 p-i-n GaN/InGaN structure 47
Fig. 4.2 GaN/InGaN p-i-n structure 47
Fig. 4.3 Effect of changing p-GaN thickness with different p-doping
a.)Short Circuit Current Density b.) Efficiency
c.)Open Circuit Voltage d.) Fill Factor 48
Fig. 4.4 Effect of changing InGaN thickness on physical characteristic
of solar cell a.)Short Circuit Current Density
b.) Open Circuit Voltage 49
c.) Fill Factor d.) Efficiency 50
Fig. 4.5 Effect of changing n-GaN thickness on characteristic parameters
of solar cell a.)Short Circuit Current Density b.) Efficiency 50
Fig. 4.6 a.) Final Optimized structure of p-i-n GaN/InGaN double hetero
junction solar cell b.)I-V curve 51
Fig. 4.7 Effect of changing the In composition on various characteristic
parameter a.) Short Circuit Current density b.)Fill Factor 51
c.)Efficiency d.) Discontinuity in the valence band at the
hetero junction at high In content 52
viii

Chapter 5
Fig. 5.1 Schematic steps for MOCVD growth. 56
Fig. 5.2 Schematics diagram of a MOCVD system. 57
Fig. 5.3 Schematics diagram of MOCVD reactor 58
Fig. 5.4 Reflection from a 3-phase system. The shaded area shows multiple
internal reflections. 60
Fig. 5.5 Reflected intensity for a film with refractive index 2.4 on a
substrate with refractive index 1.7, and a probe wavelength of
635nm. An interference profile like this might be seen for GaN
growth on Sapphire, where the film has little absorption at
the probe wavelength. 61
Fig. 5.6 Theoretical reflected intensity for a film with refractive index 2.4
and k = 0.153, on a substrate with refractive index 1.7,
and a probe wavelength of 633nm. 62
Fig. 5.7 Schematic diagram of the in situ monitoring apparatus 63
Fig. 5.8 The typical trace of both reflectance intensity of the in situ monitor.64
Fig 5.9 AFM study of interrupted GaN growth runs 65
Fig. 5.10 A typical room temperature photoluminescence
scan for InGaN growth 66
Chapter 6
Fig. 6.1 Full Mask Layout design of InGaN Solar Cell 68
Fig. 6.2 Device with different dimension 69
Fig. 6.3 Process Flow chart of GaN/InGaN Solar Cell 69
Fig. 6.4 Sample after Mesa Etch 70
Fig. 6.5 Sample after n-contact lithography 71
Fig. 6.6 Resistance versus Contact separation from TLM 72
Fig. 6.7 Sample after current spreading lithography 72
Fig. 6.8 Sample after p-contact lithograph 73
ix

List of Tables
Table 1.1 Properties of group III-nitrides. 11
Table 1.2 Lattice mismatch and thermal expansion coefficient mismatch
of GaN with common substrates 12
Table 4.1 Test p-i-n output characteristics 47
Table 4.2 Characteristics parameters of p-i-n solar cell 51
Table 5.1 Sources of MOCVD system 58
x

INTRODUCTION
1.1 History of Solar Energy
The photovoltaic effect was first reported by Edmund Bequerel in 1839 when he
observed that the action of light on a silver coated platinum electrode immersed in electrolyte
produced an electric current. Forty years later the first solid state photovoltaic devices were
constructed by workers investigating the recently discovered photoconductivity of selenium.
In1876 William Adams and Richard Day found that a photocurrent could be produced in a
sample of selenium when contacted by two heated platinum contacts. The photovoltaic action of
the selenium differed from its photoconductive action in that a current was produced
spontaneously by the action of light. No external power supply was needed. In this early
photovoltaic device, a rectifying junction had been formed between the semiconductor and the
metal contact. In 1894, Charles Fritts prepared what was probably the first large area solar cell
by pressing a layer of selenium between gold and another metal. In the following years
photovoltaic effects were observed in copper-copper oxide thin film structures, in lead sulphide
and thallium sulphide. These early cells were thin film Schottky barrier devices, where a semi-
transparent layer of metal deposited on top of the semiconductor provided both the asymmetric
electronic junction, which is necessary for photovoltaic action, and access to the junction for the
incident light. The photovoltaic effect of structures like this was related to the existence of a
barrier to current flow at one of the semiconductor-metal interfaces (i.e., rectifying action) by
Goldman and Brodsky in 1914. Later, during the 1930s, the theory of metal-semiconductor
barrier layers was developed by Walter Schottky, Neville Mott and others.
However, it was not the photovoltaic properties of materials like selenium which excited
researchers, but the photoconductivity. The fact that the current produced was proportional to the
intensity of the incident light, and related to the wavelength in a definite way meant that
photoconductive materials were ideal for photographic light meters. The photovoltaic effect in
barrier structures was an added benefit, meaning that the light meter could operate without a
power supply. It was not until the 1950s, with the development of good quality silicon wafers for
Chapter 1
1

applications in the new solid-state electronics, that potentially useful quantities of power were
produced by photovoltaic devices in crystalline silicon.
In the 1950s, the development of silicon electronics followed the discovery of a way to
manufacture p-n junctions in silicon. Naturally n type silicon wafers developed a p type skin
when exposed to the gas boron trichloride. Part of the skin could be etched away to give access
to the n type layer beneath. These p-n junction structures produced much better rectifying action
than Schottky barriers, and better photovoltaic behaviour. The first silicon solar cell was reported
by Chapin, Fuller and Pearson in 1954 and converted sunlight with an efficiency of 6%, six times
higher than the best previous attempt. That figure was to rise significantly over the following
years and decades but, at an estimated production cost of some $200 per Watt, these cells were
not seriously considered for power generation for several decades. Nevertheless, the early silicon
solar cell did introduce the possibility of power generation in remote locations where fuel could
not easily be delivered. The obvious application was to satellites where the requirement of
reliability and low weight made the cost of the cells unimportant and during the 1950s and 60s,
silicon solar cells were widely developed for applications in space.
Also in 1954, a cadmium sulphide p-n junction was produced with an efficiency of 6%,
and in the following years studies of p-n junction photovoltaic devices in gallium arsenide,
indium phosphide and cadmium telluride were stimulated by theoretical work indicating that
these materials would offer a higher efficiency. However, silicon remained and remains the
foremost photovoltaic material, benefiting from the advances of silicon technology for the
microelectronics industry.
In the 1970s the crisis in energy supply experienced by the oil-dependent western world
led to a sudden growth of interest in alternative sources of energy, and funding for research and
development in those areas. Photovoltaic was a subject of intense interest during this period, and
a range of strategies for producing photovoltaic devices and materials more cheaply and for
improving device efficiency were explored. Routes to lower cost included photo-electrochemical
junctions, and alternative materials such as polycrystalline silicon, amorphous silicon, other `thin
film' materials and organic conductors. Strategies for higher efficiency included tandem and
other multiple band gap designs. Although none of these led to widespread commercial
development, our understanding of the science of photovoltaics is mainly rooted in this period.
2

During the 1990s, interest in photovoltaics expanded, along with growing awareness of
the need to secure sources of electricity alternative to fossil fuels. The trend coincides with the
widespread deregulation of the electricity markets and growing recognition of the viability of
decentralised power. During this period, the economics of photovoltaics improved primarily
through economies of scale. In the late 1990s the photovoltaic production expanded at a rate of
15-25% per annum, driving a reduction in cost. Photovoltaics first became competitive in
contexts where conventional electricity supply is most expensive, for instance, for remote low
power applications such as navigation, telecommunications, and rural electrification and for
enhancement of supply in grid-connected loads at peak use [Anderson, 2001]. As prices fall, new
markets are opened up. An important example is building integrated photovoltaic applications,
where the cost of the photovoltaic system is offset by the savings in building materials.
1.2 Solar Energy and High Efficiency Efforts
It is reported that 97.1% of world energy production is from fossil fuels and nuclear
power [1]. Oil, coal &natural gas are the major fossil energy sources from which high amount of
CO2 releases. CO2 is a greenhouse gas and considered to be the reason of the global warming.
On the other hand, nuclear power is not harmful for the atmosphere. But, the remnants of nuclear
reaction remain radioactive for many years and should be stored in particular chambers during
this time. Since world’s energy consumption increases rapidly, suffering from side effects of our
major energy sources is expected to increase unless renewable energy sources dominates the
area. It is reported that the potential of solar irradiation is at least 1000 times greater than that of
the summation of all other renewable energy sources which makes direct solar irradiation to be
the only global renewable energy source [2].
Solar cells or photovoltaic devices (PV) are designed to absorb sunlight and convert it
into usable electrical energy. The PV effect first discovered by A.E Becquerel and then Charles
Fritts produced first PV cell with only 1% efficiency in 1883. Bell Laboratories developed the
first modern PV cell using silicon p-n junction in 1954. Nowadays, the efficiency of crystalline
single junction silicon solar cells reaches up to 25% approaching to their theoretical limit of
33.7%. These efficiencies belong to sophisticated small scale laboratory production. Mass
produced and less expensive market modules produce lower efficiencies in between 15-20%.
3

In 2010, large commercial arrays cost down to $3.40/watt, which was from $8.00/watt
back in 2004 [3]. First generation silicon solar cells are dominating the market; however, they
still cost more than desired. Other alternatives are shown in the Figure 1.1 below may have the
potential of yielding higher efficiencies at lower cost.
Fig. 1.1 Best research cell efficiencies
There are different structures used for solar cell fabrications such as bulk materials, thin
films, organic polymers and organic dyes. Although, majority of the commercially available
solar cells are made from relatively low-cost Silicon (Si) bulk crystal, even lower cost thin film,
organic-inorganic PV systems have been investigated to compete with fossil fuels and nuclear
energy. On the other hand, the researches towards high efficiency multi-junction solar cells are
also focus of interest in concentrated PVs and extraterrestrial applications. It can be seen that
almost all of the solar cell studies has become mature with an exception of organic solar cell
studies which are towards the realization of low cost solar cells. To date, the top most PV
4

efficiency of 42.3% has been realized by three-junction InGaP/GaAs/Ge based devices under a
solar concentration of 406 suns. Higher efficiencies can be realized by using multiple band gaps
for solar cells. For a single junction solar cell, only the photon energies higher than the band gap
of the material is absorbed with an heat conversion of the excess energy of the photons above the
band gap energy and the rest of the photons with energy lower than the band gap can’t be
absorbed by the material. In the case of a multi-junction solar cell, introduction of additional
active regions with higher band gap materials to the top and lower ones to the bottom as
indicated in Figure 1.2. Higher energy photons are absorbed in high band gap window junction
and lower energy photos are transmitted to the next junction and this process is repeated for the
following junctions which
Fig. 1.2 Light transfer through a three-junction solar cell
decreases energy converted to heat and the number of the photons transmitted without absorbed
by a cell. Currently, the band gap of the InGaP window junction is ~1.8 eV however getting
higher efficiency solar cells requires using more than three junctions with the introduction of
higher band gap (>1.8eV) semiconductors for the top cell.
The most promising material system to obtain higher efficiencies is InGaN, whose band
gap energy can be tuned from 0.7 eV to 3.4 eV. Such an energy variation can cover most of the
solar spectrum. However, there are several drawbacks of InGaN alloys such as high lattice
mismatch between InN and GaN, high polarization charges at GaN/InGaN interface and low
carrier diffusion length [4]. First of all, due to the 11% lattice mismatch between InN and GaN,
the growth of high In content InGaN layers results in relaxed layers with high structural defects
which kills the minority carrier lifetime thus hinders light current generation. It is reported
5

regarding to InGaP/GaAs/Ge triple junction solar cells that even a lattice mismatch as low as
0.01% can significantly reduce the current generation [5]. Secondly, the presence of high
piezoelectric polarization field across the active region of conventional Ga-polar solar cells has
been simulated and shown to decrease the carrier collection dramatically [6]. Lastly, due to low
carrier diffusion length in InGaN alloys (~200 nm), it is required to design pin structures to have
drift assisted carrier collection.
1.3 III-Nitride Material System
Group III nitrides, consisting of Indium Nitride (InN), Gallium Nitride (GaN) and
Aluminium Nitride (AlN) their alloys (such as InGaN, AlGaN and InAlN) are direct band-gap
(0.7∼6.2eV) semiconductors with band gap energies spanning the range from ultraviolet to infra-
red, making them promising for various electronic and optoelectronic applications. Most of the
research work thus far has focused upon GaN and its alloys, InGaN and AlGaN, because of their
specific applications in blue/green light emitting diodes (LEDs), Laser Diodes (LDs), Solar Cell
& high frequency electronic devices. InN has received less attention since it has been difficult to
grow good crystalline quality material due to the low dissociation temperature of InN and lack of
a lattice and thermal expansion coefficient matched substrate.
The value of the band-gap energy of InN has not yet been conclusively established and it
has been a topic of debate as well as one of the reasons for the increased interest in the material.
Initial films deposited by reactive sputtering and electron beam plasma techniques produced
polycrystalline InN. Photoluminescence (PL) emission was not observed from these films.
Consequently the band-gap energy was determined using optical absorption or transmission
measurements to be 1.89 eV[7]. Recently, InN grown by metalorganic chemical vapour
deposition (MOCVD) [8] and molecular beam epitaxy (MBE) [9] showed PL emission near 0.7
eV suggesting that the band-gap energy of InN is much smaller than the previously reported
values. There is still controversy about the exact value of the band-gap energy but the newly
predicted low band-gap energy makes InN a suitable candidate, when alloyed with GaN, for
making high efficiency solar cells since the band gap range of InxGa1-xN provides a near-perfect
match to the solar energy spectrum (Figure 1.3) with conversion efficiency predicted to be as
6

high as 50% [10]. The 0.7 eV band-gap energy is also compatible with the wavelength range of
optical fibers providing another potential application for InN in high speed laser diodes and
photodiodes for optical communication. Also, the ability to grow good quality InN will
potentially help the growth of ternary nitrides such as InxGa1-xN with high In fraction (x > 0.20)
which are of interest for high brightness green LEDs and Laser diodes.
Fig. 1.3: Solar radiation and energy bandgap with Ga fraction in In1-xGaxN
1.4 III-Nitride Materials Properties
Like most semiconductors, the atom arrangement in the nitride semiconductors is
tetrahedrally co-ordinated; therefore each atomic site has the four nearest neighbours occupying
the vertices of a tetrahedron. The wurtzite crystal structure consists of two interpenetrating
hexagonal close packed sub-lattices. Each sub-lattice is shifted along the c-axis by 3/8 of the cell
height. GaN, AlN, or InN exhibits a stable hexagonal wurtzite crystal structure rather than a
meta-stable zinc-blende structure. In an ideal wurtzite structure, c/a ratio is 1.633. The deviation
7

from the ideal c/a ratio increases as the electro negativity difference between group III atoms and
group V atoms increases [11]. The c/a ratio can also be correlated with the differences in the
electro negativity. AlN has 1.601 of c/a and GaN exhibits 1.627 while InN shows 1.612. The
difference is attributed to the creation of the dipole, resulting in polarization. The space group for
the hexagonal wurtzite structure is P63mc (C4
6ν). The P63mc space group is created by the
combination of a 63 screw-axis along the c-axis, a mirror parallel to the c-axis and a-axis, and a
glide plane along the c-axis. The unit cell of the wurtzite crystal structure and the Wigner-Seitz
unit cell are shown in Figure 1.4 (a) and (b), respectively. A dashed line indicates a tetrahedral
bonding.
The Nitrogen atom has the strongest electro negativity among the group V elements. The
large difference in electro negativity between nitrogen and group III elements adds a strong ionic
bonding component to the covalent bonding between Ga, Al, or In, resulting in a tightly bonded
crystal structure. In addition, the charge carriers in the valence band of III-nitrides are well
localized due to the strong electron affinity of the nitrogen atoms. These characteristics make III-
nitride semiconductors leading materials for high-power/high-temperature applications.
8

Fig. 1.4: (a) Unit cell for the hexagonal wurtzite structure (b) Wigner-Seitz unit cell for the III-nitrides.
Nitrogen atoms create a large ionic bonding component in the III-nitride materials; thus,
these atoms play an important role in forming a tightly bonded crystal structure. The bonding
energy of AlN is 11.5 eV/atom while that of GaN is 8.9 eV/atom. In comparison, InN shows 7.7
eV/atom of bonding energy to 6.5 eV/atom from GaAs. The tightly bonded structure with a
larger bonding energy contributes to a chemical bond length that is shorter in comparison to
other semiconductors. Combined with the wide bandgap, this characteristic makes III-nitrides
perfect candidate materials for many optoelectronic applications operating in hostile
environments. Figure 1.5 shows the values of chemical bond lengths depicted for various
semiconductors [12].
Fig. 1.5: Bandgap energy versus chemical bond length for III-Nitrides and other Semiconductors.
All of the III-Nitrides crystallize in stable wurtzite (hexagonal Bravais lattice) and zinc-blende
(face-centered cubic Bravais lattice) polytypes. In a wurtzite form, the bandgaps are all direct.
One of the advantages of the III-Nitride material system is that the bandgap can be tunable from
9

6.2 eV (~ 200 nm) to 0.7 eV (~1771 nm) by alloying and forming hetero-structures with AlN and
InN, respectively. The fundamental bandgap energy of approximately 0.7 eV for wurtzite-
structure InN has been recently discovered [13-18] indicating InN is actually a narrow bandgap
compound semiconductor. It is quite different from the previously, widely accepted value of 1.9
eV (~ 653 nm). The recent discovery of wide bandgap energy for InN gives group III Nitride
semiconductors a big advantage for devices operated under various conditions. For example,
GaN alloyed with InN can be useful for devices for optical communications using long
wavelengths such as λ= 1.55 or 1.33 µm.
Fig. 1.6: Energy bandgap (eV) as a function of lattice parameter (Å) for wurtzite III Nitride alloys.
Figure 1.6 displays bandgap energy as a function of a lattice parameter for the wurtzite
III-Nitrides with Eg(AlN) = 6.2 eV, Eg(GaN) = 3.4 eV, and Eg(InN) = 0.7 eV. The zinc-blende
energy gaps are slightly lower and are directonly for GaN and InN. It is noted that the energy gap
of the InAlN ternary alloy covers a wide range of spectrum from the infrared for InN to the deep
ultraviolet for AlN. Hence, hetero-structures of wurtzite group III-Nitride alloys can be
incorporated into light emitters and detectors that operate in the entire range of the spectrum. The
10

composition dependence of the bandgap for InxGa1-xN shown in Figure 1.4 can be described by
the standard bowing equation 1.1.[19]
Eg
InGaN
(x) = Eg
InN
(x) + Eg
GaN
(1-x) – bx(1-x) (1)
For InGaN and AlGaN material systems, bowing parameters are found to be 1.43 eV and 1.0 eV,
respectively.Structural, electrical and thermal properties of III-Nitrides obtained from literature
are tabulated and provide in Table 1.1.[20-21]
Table 1.1. Properties of group III-nitrides
Properties GaN InN AlN
Crystal Structure Wurtzite Wurtzite Wurtzite
Melting Point (o
C)[20]
2791 2146 3481
Thermal Conductivity(W/cm/C)[21]
1.3 0.8 2
Band Gap (eV @ 300K)[20]
3.4 0.7 6.2
Electron Mobility (cm2
/V.s) [21]
900 4400 300
Hole Mobility (cm2
/V.s) [21]
30 39 14
Specific Gravity (g/cc) [21]
6.1 - 1.95
Specific Heat ( J/gmC) [21]
0.49 0.32 0.6
Thermal Diffusivity (cm2
/s) [21]
0.43 0.2 0.47
Lattice Constant ‘a’ (300K) [21]
0.3189 0.3533 0.3112
Lattice Constant ‘c’ (300K) [20]
0.5186 0.5760 0.4982
Dielectric Constant ‘ε0’[21]
9.5 8.4 8.5
11

1.5 Challenges in InGaN Material System
1.5.1 Substrate
The III-nitrides typically crystallize in a wurtzite crystal structure, unlike Si, Ge, and
GaAs which crystallize in a diamond or zinc-blend structure. Sapphire is the most commonly
used substrate for the growth of wurtzite GaN. However, due to the large lattice and thermal
mismatches between sapphire and III-Nitrides (16% for GaN on sapphire and 29% for InN to
sapphire) and thermal mismatch (-34% for GaN on sapphire and -100% for InN on sapphire)
between sapphire and III-Nitrides, epitaxial films on sapphire result in high dislocation densities,
typically in the 107
- 1010
cm-2
range. The dislocation densities and Thermal Expansion
Coefficient (TEC) mismatch is shown in Table 1.2. Other substrates are SiC and ZnO which
provide better lattice match. Figure 1.6 depicts band gap versus lattice constant values for
various semiconductor materials.
Table 1.2: Lattice mismatch and thermal expansion coefficient mismatch of GaN with common substrates
Substrate Lattice mismatch Thermal expansion
coefficient mismatch
Sapphire 16% -34%
SiC 3% +25%
ZnO 2% -14%
Si 17% +100%
1.5.2 Phase Separation
There exists of a solid phase miscibility gap in the InGaN alloy due to the large
difference in the lattice constants between GaN and InN, which is also the probable cause of
multiple phases and consequent multi-peak luminescence observed in the material [22-23]. The
equilibrium solubility of InN in the bulk GaN is approximately 6% at typical growth
temperatures used in MOCVD. However, the situation in thin InGaN films epitaxially deposited
on GaN virtual substrates is significantly different. Theoretical calculations [24] based on a
valence-force-field (VFF) model [25] predict that phase separation in InGaN
12

Fig. 1.7: Schematic comparison of band structures of (a) an ideal material, and (b) a phase separated material.
strongly depends not only on the temperature and In composition, but also on the strain state of
the InGaN films. Thus, one or more indium-rich phases come into existence in the InGaN alloy
layers during growth in an attempt to reach thermodynamic equilibrium during growth as shown
in Figure 1.7. Phase separation is usually identified as secondary peaks in addition to the primary
peak corresponding to the bulk material during photoluminescence and, while higher degrees of
phase separation are also identified via X-ray diffraction (XRD). In addition to acting as a
recombination channel, it can be correlated from quantum-well solar cells that the lower-band
gap phase separated material will also tend to pin down the Open-circuit voltage (VOC) of the
solar cell.
1.5.3 Polarization and Piezoelectric Constant
In addition to its band gap range, another unique feature of the III-nitrides is the strong
polarization or piezoelectric effects [26-27]. AlN, GaN and InN are all highly polar molecules,
such that at the interface between the materials, a large dipole may develop, which alters the
surface properties and induces an electric field in the bulk region between two surfaces. The
spontaneous polarization is particularly strong at AlN/GaN interfaces, and less so between GaN
and InN. In addition to electric fields induced by polarization, an electric field may also be
induced in the material by the piezoelectric fields, which are electric fields induced by strain in
the material. The piezoelectric coefficients are high in the III-nitrides, hence a substantial electric
field will develop in strained material.
13

1.5.4 P-type doping
Achieving p-type conductivity in InGaN alloys is difficult due to a high background
concentration of electrons. By improving the structural quality of GaN, p-type GaN can be
achieved but one still has a limit of less than ~low to mid 1018
cm-3
hole concentration due to the
deep activation energy of acceptors in GaN, which is approximately 160meV for Mg in GaN,
leading to approximately 1% of the incorporated Mg contributing to the hole concentration at
room temperature [28]. With InGaN, it is expected that higher hole concentrations can be
achieved due to a lower activation energy than for GaN. For example, the activation energies of
Mg were 141 and 80 meV for 4% and 14% In mole fraction, respectively [29]. The
corresponding electrical hole concentrations are 5.3×1018
and 1.6×1019
cm-3
[29].
1.5.5 Absorption Depth and Diffusion Length
The absorption depth (1/α) and the diffusion length (L)are critical parameters in making
high efficiency solar cells. The absorption coefficient is high in all of the InGaN range, and
importantly increases rapidly near the band edge. The high absorption is a critical factor in
achieving high collection since the absorption depth must be shorter than the diffusion length for
high collection.
While the recombination properties of InGaN films are critical in determining the
performance of photovoltaic devices. The recombination processes in the III-nitrides are
controlled by several possible processes: exitonic recombination, radiative recombination, non-
radiative, and recombination controlled by localization of carriers caused by phase separation in
In-rich InGaN alloys. The reported values of band-to-band radiative recombination coefficient,
vary from 1 x 10-8
to 2.4 x 10-11
cm³/s, but are typically on the order 7 x 10-10
[30]. However,
films in general have a high non-radiative recombination component, and measured lifetimes are
typically in the range of several hundred ps to 2 nano sec [31-33]. The diffusion length depends
on both the minority carrier lifetime and the diffusion coefficient. The majority carrier mobility
for n-type material is measured as high as 845 cm²/Vs for thick epilayers, but only 5 for minority
carrier in n-type and majority holes in p-type [34] and on the order of 500 for thinner layers. The
low mobilities for minority carriers mean that most extracted diffusion lengths are between 0.2 to
0.8 μm, but several reports give measured diffusion lengths of over 1 μm, [32-33].
14

1.6 Summary
Brief development history and great efforts to reach high efficiency solar cell is discussed
in chapter. Solar cell studies has become very mature with time and tending towards the low cost
solar cell but limiting efficiency motivates toward the study of new material which can be used
to make high efficiency solar cell. InGaN system fulfil all requirements to be considered as
promising material for photovoltaic application. Major growth related issues with InGaN
material is also highlighted.
15

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Bechstedt, J. Furthmuller, H. Harima, A.V. Mudryi, J. Aderhold, O. Semchinova, and J.
Graul, Phys. Stat. Sol. (b) 229, R1 (2002).
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17) J. Wu, W. Walukiewicz, W. Shan, K. M.Yu, J. W. Ager III, E. E. Haller, H. Lu, and W.
Schaff, Phys. Rev. B 66, 201403 (2002).
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Applied Physics Letters,vol.80,no.25,p.4741,(2002)
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(Retrieved May 2, 2011)
21) J.M. Olson et al, MOCVD Growth and Characterization of GaP on Si, Journal of Crystal
Growth, Vol.77, Issue 1-3, p.515-523, (1986).
22) I. Ho, and G. B. Stringfellow, “Solid phase Immiscibility in GaInN,” Appl. Phys. Lett.,
vol. 69, p. 2701, (1996).
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States in InGaN Epilayers,” Appl. Phys. Lett., vol. 70, p. 2822, (1997).
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25) I. H. Ho, G. B. String fellow, “Incomplete Solubility in Nitride Alloys,” Mater. Res. Soc.
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17

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51-54 (2000)
18

SOLAR CELL BASICS
2.1 The Photovoltaic Effect
Solar photovoltaic energy conversion is a one-step conversion process which generates
electrical energy from light energy. The explanation relies on ideas from quantum theory. Light
is made up of packets of energy, called photons, whose energy depends only upon the frequency,
or colour, of the light. The energy of visible photons is sufficient to excite electrons, bound into
solids, up to higher energy levels where they are free to move. An extreme example of this is the
photoelectric effect, the celebrated experiment which was explained by Einstein in 1905, where
blue or ultraviolet light provides enough energy for electrons to escape completely from the
surface of a metal. Normally, when light is absorbed by matter, photons are given up to excite
electrons to higher energy states within the material, but the excited electrons quickly relax back
to their ground state. In a photovoltaic device, however, there is some built-in asymmetry which
pulls the excited electrons away before they can relax, and feeds them to an external circuit. The
extra energy of the excited electrons generates a potential difference, or electro-motive force
(e.m.f.). This force drives the electrons through a load in the external circuit to do electrical
work. The effectiveness of a photovoltaic device depends upon the choice of light absorbing
materials and the way in which they are connected to the external circuit. The following chapter
will deal with the underlying physical ideas and the basic device physics of solar cells.
Fig. 2.1. Comparison of the photoelectric effect (left), where uv light liberates electrons from the surface of
a metal, with the photovoltaic effect in a solar cell (right).
Chapter 2
19

2.2 Semiconductor Concepts
Semiconductors are a family of solids in which there exists a moderate gap (up to a few
electron volts) in the distribution of allowed energy states. At T = 0 K in a pure material, this gap
separates one entirely filled band (valence band) from one that is entirely empty(conduction
band). For T > 0 K, a finite number of electronic states are occupied in the conduction band
(“free electrons”) and a finite number of states are unoccupied in the valence-band (“free holes”).
These free electrons and holes can gain kinetic energy since a quasi-continuum of higher or
lower states are available to them, respectively, and they are therefore able to respond to electric
fields and concentration gradients that allow for macroscopic current flow.
2.2.1 Equilibrium
The equilibrium concentrations of electrons and holes can be modified by extrinsic
dopants, but also by defect levels (additional states within the band gap) that are intrinsic to the
semiconductor. The occupation of conduction- and valence-band states is governed by Fermi-
Dirac statistics,





 


KT
EE
EF
f
exp1
1
)( (2.1)
where k is the Boltzmann constant and T the absolute temperature. Equation 2.1 describes the
probability of electron occupation in the conduction band and, similarly, 1-F(E) describes the
probability for holes in the valence band. If the Fermi-level Ef is not very close to either band
edge, EC − Ef>>kT and Ef – EV>>kT, F(E) and 1-F(E) can for many practical purposes be
replaced by the Boltzmann factors for electrons in the conduction band and holes in the





 

kT
EE f
exp and 




 

kT
EEf
exp (2.2)
valence band, respectively.
Semiconductors are classified as n- or p-type depending on whether electrons or holes
are the majority carriers. The Fermi level can be calculated by the following relations
20






 

kT
EE
Nn
fC
C exp. (2.3)
and





 

kT
EE
Np
Vf
V exp. (2.4)
where
2/3
2
*
2
.2 








h
kTm
N e
C

and
2/3
2
*
2
.2 








h
kTm
N h
V

(2.5)
are the effective densities of states in the conduction and valence band. For semiconductors
doped either with shallow donor or acceptor levels, n is similar to the donor density and p is
similar to the acceptor density. All parameters in Eq. 2.5 have their usual meaning, *
em and *
hm
are the electron and hole effective masses. In equilibrium, the product of n and p is constant and
depends only upon the temperature, effective masses, and band gap of the semiconductor,







kT
E
NNnnp
g
VCi exp..2
(2.6)
2.2.2 Non-equilibrium
In non-equilibrium conditions, such as under illumination or under carrier injection due
to externally applied electric bias, no uniform Fermi level exists. In steady-state, however, quasi-
Fermi levels, Efn and Efp, can be introduced, which are useful in the analysis and interpretation of
semiconductors. These quasi-Fermi levels are defined by





 

kT
EE
Nn
fnC
C exp. (2.7)
and





 

kT
EE
Np
Vfp
V exp. (2.8)
Assuming that Efn and Efp in the n- and p-type region of a p-n junction diode are in
equilibrium with the respective electrical contact, the difference between the quasi-Fermi levels
21

in the proximity of a diode’s space-charge region is given by the applied voltage V , and it
follows that the np product is voltage dependent







kT
qV
nnp i exp.2
(2.9)
2.3 Characteristic of Photovoltaic Cell
2.3.1 Photocurrent and Quantum Efficiency
The photocurrent generated by a solar cell under illumination at short circuit is dependent
on the incident light. To relate the photocurrent density, Jsc, to the incident spectrum we need the
cell's quantum efficiency (QE).QE (E) is the probability that an incident photon of energy E will
deliver one electron to the external circuit. Then
dEEQEEbqJ ssc  )()( (2.10)
Where bs(E) is the incident spectral photon flux density, the number of photons of energy
in the range E to E+dE which are incident on unit area in unit time and q is the electronic charge.
QE depends upon the absorption coefficient of the solar cell material, the efficiency of charge
separation and the efficiency of charge collection in the device but does not depend on the
incident spectrum. It is therefore a key quantity in describing solar cell performance under
different conditions. Figure 2.2 shows a typical QE spectrum in comparison with the spectrum of
solar photons. QE and spectrum can be given as functions of either photon energy or wavelength
 . Energy is a more convenient parameter for the physics of solar cells. The relationship
between E and  is defined by

hc
E  (2.11)
where h is Planck's constant and c the speed of light in vacuum.
22

Fig. 2.2. Quantum effciency of GaAs cell compared to the solar spectrum. The vertical scale is in arbitrary
units, for comparison.
2.3.2 Dark Current and Open Circuit Voltage
When a load is present, a potential difference develops between the terminals of the cell.
This potential difference generates a current which acts in the opposite direction to the
photocurrent, and the net current is reduced from its short circuit value. This reverse current is
usually called the dark current in analogy with the current Idark (V ) which flows across the
device under an applied voltage, or bias, V in the dark.
Fig. 2.3.Current-Voltage characteristic of ideal diode in the light and the dark.
Most solar cells behave like a diode in the dark, admitting a much larger current under
forward bias (V > 0) than under reverse bias (V < 0). This rectifying behaviour is a feature of
photovoltaic devices, since an asymmetric junction is needed to achieve charge separation. For
an ideal diode the dark current density Jdark (V) varies like
23

)1()( /
 Tkqv
odark
b
eJVJ (2.12)
where Jo is a constant, kb is Boltzmann's constant and T is temperature in degrees Kelvin.
The overall current voltage response of the cell, its current-voltage characteristic, can be
approximated as the sum of the short circuit photocurrent and the dark current (Fig. 2.3). This
step is known as the superposition approximation. Although the reverse current which flows in
reponse to voltage in an illuminated cell is not formally equal to the current which flows in the
dark, the approximation is reasonable for many photovoltaic materials. The sign convention for
current and voltage in photovoltaics is such that the photocurrent is positive. This is the opposite
to the usual convention for electronic devices. With this sign convention the net current density
in the cell is
)()( VJJVJ darksc  (2.13)
which becomes, for an ideal diode,
)1()( /
 Tkqv
osc
b
eJJVJ (2.14)
When the contacts are isolated, the potential difference has its maximum value, the open
circuit voltage Voc. This is equivalent to the condition when the dark current and short circuit
photocurrent exactly cancel out. For the ideal diode, from Eq. 2.14,






 1ln
o
sc
oc
J
J
q
kT
V (2.15)
Equation 2.15 shows that Voc increases logarithmically with light intensity. Note that
voltage is defined so that the photo-voltage occurs in forward bias, where V > 0. Figure 2.3
shows that the current-voltage product is positive, and the cell generates power, when the voltage
is between 0 and Voc. At V <0, the illuminated device acts as a photo-detector, consuming
power to generate a photocurrent which is light dependent but bias independent. At V >Voc, the
device again consumes power. This is the regime where light emitting diodes operate. We will
see later that in some materials the dark current is accompanied by the emission of light.
Electrically, the solar cell is equivalent to a current generator in parallel with an asymmetric, non
linear resistive element, i.e., a diode (Fig. 2.4). When illuminated,
24

Fig. 2.4.Equivalent circuit of ideal solar cell.
the ideal cell produces a photocurrent proportional to the light intensity. That photocurrent is
divided between the variable resistance of the diode and the load, in a ratio which depends on the
resistance of the load and the level of illumination. For higher resistances, more of the
photocurrent flows through the diode, resulting in a higher potential difference between the cell
terminals but a smaller current though the load. The diode thus provides the photo-voltage.
Without the diode, there is nothing to drive the photocurrent through the load.
2.3.3 Effciency
The operating regime of the solar cell is the range of bias, from 0 to Voc, in which the
cell delivers power. The cell power density is given by
P = JV (2.16)
P reaches a maximum at the cell's operating point or maximum power point. This occurs at some
voltage Vm with a corresponding current density Jm, shown in Fig. 2.5. The optimum load thus
has sheet resistance given by Vm/Jm. The fill factor is defined as the ratio
scsc
mm
VJ
VJ
FF  (2.17)
and describes the `squareness' of the J-V curve.
The efficiency  of the cell is the power density delivered at operating point as a fraction of the
incident light power density, Ps,
25

s
mm
P
VJ
 (2.18)
Efficiency is related to Jsc and Voc using FF,
s
ocsc
P
FFVJ
 (2.19)
Fig. 2.5. The current voltage (black) and power{voltage (grey) characteristics of an ideal cell. Power density
reaches a maximum at a bias Vm, close to Voc. The maximum power density Jm* Vm is given by the area of the inner
rectangle. The outer rectangle has area Jsc*Voc. If the fill factor were equal to 1, the current voltage curve would
follow the outer rectangle.
These four quantities: Jsc, Voc, FF and  are the key performance characteristics of a
solar cell. All of these should be defined for particular illumination conditions. The Standard
Test Condition (STC) for solar cells is the Air Mass 1.5 spectrum, an incident power density of
1000 W m-2
, and a temperature of 25o
C.
26

2.3.4 Parasitic resistances
In real cells power is dissipated through the resistance of the contacts and through
leakage currents around the sides of the device. These effects are equivalent electrically to two
parasitic resistances in series (Rs) and in parallel (Rsh) with the cell (Fig. 2.6).
Fig. 2.6.Equivalent circuit including series and shunt resistances.
Fig. 2.7 .Effect of (a) increasing series and (b) reducing parallel resistances. In each case the outer curve
has Rs = 0 and Rsh =. In each case the effect of the resistances is to reduce the area of the maximum
power rectangle compared to Jsc *Voc.
The series resistance arises from the resistance of the cell material to current flow,
particularly through the front surface to the contacts, and from resistive contacts. Series
resistance is a particular problem at high current densities, for instance under concentrated light.
The parallel or shunt resistance arises from leakage of current through the cell, around the edges
of the device and between contacts of different polarity. It is a problem in poorly rectifying
devices.
27

Series and parallel resistances reduce the fill factor as shown in Fig. 2.6. 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
sh
skTJARvq
osc
R
JARV
eJJJ s

 
)1( /)(
(2.20)
2.4 Summary
This chapter provide an introduction to photoelectric effect which leads to idea of solar
cell. A solar cell can be completely characterize by its four important parameters (Jsc, Voc, FF
and ). Basic equations are included which helps in determining these parameters and
dependence on other physical properties.
28

References
1) D. Anderson, Clean Electricity from Photovoltaics, eds. M.D. Archer and R.D. Hill,
London: Imperial College Press (2001).
2) M.A. Green, Photovoltaics: Coming of age", Conf. Record 21st IEEE Photo-voltaic
Specialists Conf. (1990).
3) E. Lorenzo, Solar Electricity: Engineering of Photovoltaic Systems (1994).
4) T. Markvart, Solar Electricity (2000).
5) J.N. Shive, Semiconductor Devices (1959).
6) C.A. Vincent, Modern Batteries (1997).
7) M. Wolf, Historical development of solar cells", Proc. 25th Power Sources Symposium,
1972. In Solar Cells, ed. C.E. Backus (1976).
29

INTRODUCTION TO SIMULATION SOFTWARE
3.1 Silvaco Atlas
Atlas is a software program used to simulate two and three-dimensional semiconductor devices.
Atlas includes following physical models
 DC, AC small-signal, and full time-dependency.
 Drift-diffusion transport models.
 Energy balance and Hydrodynamic transport models.
 Lattice heating and heat sinks.
 Graded and abrupt hetero-junctions.
 Optoelectronic interactions with general ray tracing.
 Amorphous and polycrystalline materials.
 General circuit environments.
 Stimulated emission and radiation
 Fermi-Dirac and Boltzmann statistics.
 Advanced mobility models.
 Heavy doping effects.
 Full acceptor and donor trap dynamics
 Ohmic, Schottky, and insulating contacts.
 SRH, Radiative, Auger, and surface recombination.
 Impact ionization (local and non-local).
 Floating gates.
 Band-to-band.
 Hot carrier injection.
 Quantum transport models
 Thermionic emission currents.
Chapter 3
30

Atlas can accept structure description files from Athena and DevEdit, but also from its
own command files (fig 3.1). The development of the desired structure in Atlas is done using a
declarative programming language. This is interpreted by the Atlas simulation engine to produce
results. A brief description of how a structure is built and simulated follows.
Fig 3.1. Atlas inputs and outputs
3.2 Input File Structure
Silvaco Atlas receives input files through DeckBuild. The code entered in the input file
calls Atlas to run with the following command:
go atlas
Following that command, the input file needs to follow a pattern. The command groups are listed
in Figure 3.2.
31

Fig. 3.2. Atlas command groups and primary statements
Atlas follows the following format for statements and parameters:
<STATEMENT><PARAMETER>=<VALUE>
The following line of code serves as an example.
DOPING UNIFORM N.TYPE CONCENTRATION=1.0e16 REGION=1
OUTFILE=my.dop
The statement is DOPING. The parameters are UNIFORM, N.TYPE, CONCENTRATION,
REGION, and OUTFILE. There are four different type of parameters: real, integer, character, and
logical. The back slash () serves the purpose of continuing the code in the next line. Parameters,
such as UNIFORM, are logical. Unless a TRUE or FALSE value is assigned, the parameter is
assigned the default value. This value can be either TRUE or FALSE. The Silvaco Atlas manual
needs to be referenced to identify the default value assigned to specific parameters.
32

3.3 Structure Specification
The structure specification is done by defining the mesh, the region, the electrodes and
the doping levels.
3.3.1 Mesh
The mesh used for this thesis is two-dimensional. Therefore, only x and y parameters are
defined. The mesh is a series of horizontal and vertical lines and spacing between them. From
Figure 3.3, the mesh statements are specified.
Fig. 3.3. Atlas Mesh.
general format to define the mesh is:
X.MESH LOCATION=<VALUE> SPACING=<VALUE>
Y.MESH LOCATION=<VALUE> SPACING=<VALUE>
For example, the x.mesh starting at -250 microns has spacing of 25 microns. That means it is
relatively coarse. The x.mesh becomes finer between -25 and 25 microns with a spacing of 2.5
microns. The y.mesh is similarly defined. For example, at y.mesh of -2.9 microns, the spacing is
0.01 microns. Then at location y.mesh of -2.8 microns, the spacing changes to 0.03 microns. The
mesh is coarser at y.mesh location of -1, when the spacing is 0.1. A coarse or fine mesh
determines the accuracy of the simulation. A coarse mesh produces a faster simulation, but less
accurate results. A fine mesh produces a slower simulation, but more accurate results. The areas
that have a finer mesh, therefore, are of greatest interest in the simulation.
33

3.3.2 Region
After defining the mesh, it is necessary to define the regions. The format to define the
regions is as follows:
REGION number=<integer><material_type> /
<position parameters>
From Figure 3.4, the code that defines the regions is identified. There are six regions defined.
The limits of each region are explicitly identified in the x- and y-axis. The regions must then be
given a material.
Fig. 3.4. Atlas region
3.3.3 Electrodes
The next structure specification corresponds to electrodes. Typically, in this simulation
the only electrodes defined are the anode and the cathode. However, Silvaco Atlas has a limit of
50 electrodes that can be defined. The format to define electrodes is as follows:
ELECTRODE NAME=<electrode name><position_parameters>
From Figure 3.5, the electrode statements are defined for the anode and the cathode. Note that
the cathode is defined with gold as the material. The x and y dimensions correspond to region 6
previously defined. Meanwhile, the anode is defined at the bottom of the cell for the entire x
range at y=0.
34

Fig. 3.5. Atlas electrodes
3.3.4 Doping
The last aspect of structure specification that needs to be defined is doping. The format of
the Atlas statement is as follows:
DOPING <distribution type><dopant_type> /
<position parameters>
3.4 Materials Model Specification
After the structure specification, the materials model specification is next. From Figure
28, the materials model specification is broken down into material, models, contact, and
interface.
3.4.1 Material
The format for the material statement is as follows:
MATERIAL <localization><material_definition>
Below are three examples of the material statement:
MATERIAL MATERIAL=Silicon EG300=1.1 MUN=1200
MATERIAL REGION=4 TAUN0=3e-7 TAUP0=2e-5
MATERIAL NAME=base NC300=4e18
35

In all examples, when MATERIAL appears first, it is considered the statement. When MATERIAL
appears a second time in the first example, it is considered a localization parameter. In the
second and third examples, the localization parameters are REGION and NAME, respectively.
Various other parameters can be defined with the material statement. Examples of these
parameters are the band gap at room temperature (EG300), electron mobility (MUN), electron
(TAUN0) and hole (TAUP0) recombination lifetimes, conduction band density at room
temperature (NC300), among others.
3.4.2 Models
The physical models fall into five categories: mobility, recombination, carrier statistics,
impact ionization, and tunnelling. The syntax of the model statement is as follows:
MODELS <model flag><general parameter> /
<model dependent parameters>
The choice of model depends on the materials chosen for simulation. The example below
activates several models.
MODELS CONMOB FLDMOB SRH
CONMOB is the concentration dependent model. FLDMOB is the parallel electric field
dependence model. SRH is the Shockley-Read-Hall model.
3.4.3 Contact
Contact determines the attributes of the electrode. The syntax for contact is as follows:
CONTACT NUMBER=<n> |NAME=<ename>ALL
The following is an example of the contact statement.
CONTACT NAME=anode current
3.4.4 Interface
The semiconductor or insulator boundaries are determined with the interface statement.
The syntax is as follows:
INTERFACE [<parameters>]
The following example shows the usage of the interface statement.
INTERFACE X.MIN=-4 X.MAX=4 Y.MIN=-0.5 Y.MAX=4
36

QF=1e10 S.N=1e4 S.P=1e4
The max and min values determine the boundaries. The QF value specifies the fixed oxide
charge density (cm-2
). The S.N value specifies the electron surface recombination velocity. S.P is
similar to S.N, but for holes.
3.5 Numerical Method Selection
After the materials model specification, the numerical method selection must be
specified. There are various numerical methods to calculate solutions to semiconductor device
problems. There are three types of solution techniques used in Silvaco Atlas:
• Decoupled (GUMMEL)
• Fully coupled (NEWTON)
• BLOCK
The GUMMEL method solves for each unknowns by keeping all other unknowns
constant. The process is repeated until there is a stable solution. The NEWTON method solves
all unknowns simultaneously. The BLOCK method solves some equations with the GUMMEL
method and some with the NEWTON method.
The GUMMEL method is used for a system of equations that are weakly coupled and
there is linear convergence. The NEWTON method is used when equations are strongly coupled
and there is quadratic convergence. The following example shows the use of the method
statement.
METHOD GUMMEL NEWTON
In this example, the equations are solved with the GUMMEL method. If convergence is not
achieved, then the equations are solved using the NEWTON method.
3.6 Solution Specification
After completing the numerical method selection, the solution specification is next.
Solution specification is broken down into log, solve, load, and save statements.
37

3.6.1 Log
LOG saves all terminal characteristics to a file. DC, transient, or AC data generated by a
SOLVE statement after a LOG statement is saved. The following shows an example of the LOG
statement.
LOG OUTFILE=myoutputfile.log
The example saves the current-voltage information into myoutputfile.log.
3.6.2 Solve
The SOLVE statement follows the LOG statement. SOLVE performs a solution for one or
more bias points. The following is an example of the SOLVE statement.
SOLVE B1=10 B3=5 BEAM=1 SS.PHOT SS.LIGHT=0.01
MULT.F FREQUENCY=1e3 FSTEP=10 NFSTEP=6
B1 and B3 specify the optical spot power associated with the optical beam numbers 1 and 3,
respectively. The beam number is an integer between 1 and 10. BEAM is the beam number of the
optical beam during AC photo-generation analysis. SS.PHOT is the small signal AC
analysis. SS.LIGHT is the intensity of the small signal part of the optical beam during signal AC
photo-generation analysis. MULT.F is the frequency to be multiplied by FSTEP. NFSTEPS is the
number of times that the frequency is incremented by FSTEP.
3.6.3 Load and Save
The LOAD statement enters previous solutions from files as initial guess to other bias
points. The SAVE statement enters all node point information into an output file. The following
are examples of LOAD and SAVE statements.
SAVE OUTF=SOL.STR
In this case, SOL.STR has information saved after a SOLVE statement. Then, in a different
simulation, SOL.STR can be loaded as follows:
LOAD INFILE=SOL.STR
3.7 Results Analysis
Once a solution has been found for a semiconductor device problem, the information can
be displayed graphically with TonyPlot. Additionally, device parameters can be extracted with
the EXTRACT statement. In the example below, the EXTRACT statement obtains the current and
38

voltage characteristics of a solar cell. This information is saved into the IVcurve.dat file. Then,
TonyPlot plots the information in the IVcurve.dat file.
EXTRACT NAME="iv" curve (V."anode", I."cathode")
OUTFILE="IVcurve.dat"
TONYPLOT IVcurve.dat
3.8 Basic Equations
Silvaco-Atlas is a physics-based simulator which has been explicitly designed for the
purpose of modelling semiconductor devices [1]. The simulation methodology is physics-based
in that the models invoked by the software tend to be derived from first principles or at least
empirically derived with careful attention placed to relating such models to the underlying
physics. Fundamentally, device operation is governed by and described in a set of two coupled,
partial differential equations: the Poisson equation and the equation of continuity. One may
consider two of the axioms to the theory of electrodynamics to be Gauss’ law
∇. = (3.1)
and the Ampère-Maxwell law
∇ × = +
1
(3.2)
these are two of the four Maxwell equations for linear, isotropic media. In the equation, E is the
electric field, ρ is the charge density, ε is the material permittivity, B is the magnetic field, μ is
the material permeability, J is the current density, and v is the speed of light in the medium.
Following (3.1), the relation of the electric field as the negative gradient of the electric potential
V yields the Poisson equation:
∇ = − (3.3)
Taking the divergence of (3.2) yields the equation of continuity:
∇. = − (3.4)
39

In semiconductor applications, it is customary to modify (3.4) to include the cumulative effects
of the generation G and recombination R of charge carriers [2]. Additionally, separate continuity
equations are written for the electron concentration n and the hole concentration p, respectively:
= − +
1
∇. (3.5)
= − −
1
∇. (3.6)
where q is the elementary charge. Equations (3.3), (3.5), and (3.6) are the governing laws of
semiconductor devices. These equations are solved iteratively by ATLAS to obtain a modelled
solution of device operation.
3.9 Finite Element Analysis
The simulation methodology used by ATLAS is a form of finite element analysis. A
device structure is defined throughout a rectangular mesh consisting of gridlines that vary in their
spatial separation. At each nodal point (i.e. at each intersection of two gridlines), (3.3), (3.5) and
(3.6) are iteratively solved until a self-consistent solution is obtained. Any other pertinent models
can also be included at each nodal point and supplement the fundamental equations.
The line spacing within the mesh must be fine enough to adequately resolve the device
structure; however, a greater number of nodal points lead to a greater amount of computation
time. Typically, the computation time is proportional to Nm
, where N is the number of nodes and
m ranges from 2 to 3 depending on the complexity of the problem [1]. The maximum number of
nodes allowed by ATLAS is 20,000. For more accurate results, the mesh spacing has to be made
finer in regions of large electric fields (i.e. near junctions) and made especially coarse in the
quasi-neutral region of the base. This scheme allows for the maximum compromise between
computational accuracy and speed.
3.10 Additional Models
Although the Poisson and continuity equations represent the fundamental laws governing
the operation of a semiconductor device, additional models are often necessary to properly
account for the dynamic nature of electrons and holes and to elaborate on the rich theory of
device physics. These models supplement the Poisson and continuity equations by determining
40

or modifying the variables contained in those laws. Other models usually dictate specific
values of carrier generation and recombination or place modifiers into the current densities of
(3.5) and (3.6), the continuity equations. The models that have been used for the solar cell
simulations described in this thesis are elaborated.
3.10.1 Shockley-Read-Hall Recombination
According to the Shockley-Read-Hall hall model [3-5], the recombination of charge
carriers can be treated as the separate capture of electrons and holes by trap center and their
subsequent annihilation at the trap center. This recombination mechanism, diagrammed in Fig.
3.5.a, is indirect in k-space and occurs due to the presence of a bulk trap density Nt energetically
located at a value Et within the semiconductor bandgap. Statistically, the net recombination rate
may be expressed as
=
−
+ + +
(3.7)
This form of the Shockley-Read-Hall model is utilized by ATLAS by calling SRH in the
MODELS statement; it acts as an input into the carrier continuity equations (3.5) and (3.6). The
carrier lifetimes may be regarded as empirical parameters and are set in the MATERIALS
statement by the TAUN0 and TAUP0 parameters for electrons and holes, respectively.
Fig. 3.6 a) Indirect bandgap recombination b) Direct bandgap recombination
41

3.10.2 Radiative Recombination
Another recombination process that tends to be very prevalent in semiconductor work is
that of radiative recombination. In this process, an electron in the conduction band directly
recombines with a hole in the valence band with no aiding agent nor variance in wave vector as
diagrammed in Fig. 3.5.b. This process releases a photon with energy equal to the bandgap and is
strongest in direct-gap semiconductors. Although a formal treatment of this process is best done
by considering Einstein’s theory of spontaneous emission, in practice it is often preferred to use
an empirically determined radiative recombination coefficient C [1, 6] such that the radiative
recombination rate is then
= ( − ) (3.8)
This process is invoked in ATLAS in the MODELS statement by calling OPTR and by defining
COPT in the MATERIALS statement.
3.10.3 Auger Recombination
Auger recombination occurs through a three particle transition whereby a mobile carrier
is either captured or emitted. In Auger recombination, an electron-hole pair recombines giving
up their energy to an electron in the conduction band, increasing its energy ,i.e., the energy
produced due to recombination of an electron and hole is given to a third carrier, which is excited
to a higher level without moving to another energy band. After the interaction, the third carrier
generally loses its excess energy to terminal vibrations. Since this process is a three-particle
interaction, it is normally only significant in non-equilibrium conditions when the carrier density
is very high.
The Auger recombination can be calculated from the equation
= ( − ) + ( − ) ( 3.9)
where An is the auger recombination coefficient for electrons and Ap is the auger recombination
coefficient for holes.
This recombination mechanism is invoked in ATLAS in the MODELS statement by calling
AUGER and by defining AUGN and AUGP in the MATERIALS statement.
42

3.11 Summary
This chapter presented an introduction to Silvaco Atlas, the structure of the input files,
and some of its statements. These statements are used in our simulation. Some basic equations
and models are also presented which are used by software in solving carrier transport and drift
diffusion problem associated with defined boundary conditions.
43

References
[1] ATLAS User’s Manual: Device Simulation Software, 06/11/08 Ed., Silvaco Data Systems,
Inc., Santa Clara, CA, (2008).
[2] S.M. Sze and K.K. Ng, Physics of Semiconductor Devices, 3rd Ed., John Wiley & Sons,
Hoboken, NJ, (2007).
[3] W. Shockley and W.T. Read, “Statistics of the Recombination of Holes and Electrons,”
Phys. Rev., vol. 87, pp. 835-842, (1952).
[4] R.N. Hall, “Electron-Hole Recombination in Germanium,” Phys. Rev., vol. 87, p. 387,
(1952).
[5] C.T. Sah, R.N. Noyce, and W. Shockley, “Carrier Generation and Recombination in p-n
Junctions and p-n Junction Characteristics,” Proc. IRE, vol. 45, pp. 1228-1243, (1957).
[6] J. Piprek, Semiconductor Optoelectronic Devices: Introduction to Physics and
Simulation, Elsevier Science, USA, (2003).
[7] J.S. Blakemore, “Approximations for Fermi-Dirac Integrals, Especially the Function F1/2
Used to Describe Electron Density in a Semiconductor,” Sol. State Elec., vol. 25, pp.
1067-1076, (1982).
[8] S.A. Wong, S.P. McAlister, and Z.M. Li, “A Comparison of Some Approximations for
the Fermi-Dirac Integral of Order 1/2,” Sol. State Elec., vol. 37, pp. 61-64, (1994).
44

DESIGN OF InGaN SOLAR CELL
4.1 Introduction
By having a tunable band gap from ~0.7 to 3.4 eV, InGaN alloys can cover the whole
visible spectrum and most part of the solar spectrum [1-2]. To date, it has been widely used in
ultra-violet, blue and green light emitting and laser diodes [3-5]. Although it was successful for
emitters, little research has been carried out for solar cell applications [6-8]. In addition to having
a perfect match with the solar spectrum, InGaN alloys have been shown to have great properties
for photovoltaic applications such as, high radiation damage resistant profile, direct band gap for
entire alloy range and high absorption coefficient near the band edge [9-10].
4.2 Earlier Developments
Many reports had been shown over InGaN photovoltaic (PV) devices. Janiet al [11] have
designed InGaN p–i–n and quantum-well solar cells, in which InGaN is treated as the active
layer. Hamzaoui et al [12] have investigated the theoretical possibilities of InGaN tandem PV
structures. And Yang et al [13] have studied the PV effects in InGaN p–n junctions. Brown et al
[14] investigated solar cell structure with p-GaN/n-InGaN hetero-junction and other structure
with graded InGaN layer at the p-GaN/n-InGaN interface on Si-substrate. Feng et al [15] also
studied the performance of p-i-n InGaN single homo-junction solar cell to determine the effect of
In content and the thickness of various layers on the characteristic parameters. These reports
shows various solar cell structures had been investigate by various researchers in the past decade
to get a high efficiency solar cell using InGaN with an appropriate structure.
Conversional solar cells have been designed with p-n junction configuration since,
minority carrier diffusion length is high enough (for Silicon; few hundreds of microns) so that
carrier collection probablity can be still high outside the depletion region whereas; GaN has been
reported to have much shorter diffusion lengths (~1μm) and InGaN has even lower diffusion
lengths (~0.2 μm) which is a strong function of recombination centers in the material. Because of
the high lattice mismatch between GaN and InN, material properties deteriodes for high Indium
Chapter 4
45

compositions which results in even shorter minority carrier diffusion lengths. Thus, it is
required to increase depletion region thickness for InGaN solar cells to collect more carriers. One
way to do this is simply lightly doping of donor and acceptor to n and p sides respectively.
However, this degrades open circuit voltage and minority carrier mobility of the solar cell. The
other solution is the design of InGaN solar cells with p-i-n configuration which is realized by
inserting an intrinsic region between p and n-regions. While keeping high doping concentrations
at p and n regions, by varying the thickness of the intrinsic region depletion thickness can be
controlled.
In this simulation, it is aimed to simulate GaN/InGaN p-i-n solar cell by varying intrinsic
layer thickness under standard AM 1.5 solar spectrum. Since the actual minority carrier lifetime
and mobility for InGaN is not well-known, the results will be addressed under a range of these
parameters. It is expected that the results will faster the understanding of InGaN p-i-n solar cell
operation towards the realization of high efficiency multi-junction solar cells.
4.3 Simulation of InGaN Solar Cell
We used Silvaco atlas which can solves the fully coupled nonlinear equations for 2-D and
3-D transport of electrons and holes in crystalline semiconductor devices. Silvaco is widely used
in simulation of devices such as LEDs, Solar Cells, FET, HEMTs, etc. Since, InGaN material
system is not too much studied so various parameters are unknown for this material system. It is
required to include appropriate material parameters. The material parameters which are included
in simulation are shown in appendix A. Some material parameters are extracted by interpolation
of material parameter of InN and GaN.
For the design of any device it is essential to validate the simulation so that a more
realistic design can be carried out. For validate our results we started simulation with a test
p-i-n structure with top bottom contact as shown in figure 4.1.The thickness of the p-GaN,
i-In0.15Ga0.85N and n-GaN regions are fixed at 100 nm, 100 nm, and 2.5µm, respectively.
Uniform doping values for the p- and n- regions are set to 5 x 1017
cm-3
and 6 x 1018
cm-3
,
respectively, while an n-type background impurity concentration in the i-region is set to
1 x 1016
cm-3.
46

Fig.4.1 p-i-n GaN/InGaN strucutre
p-i-nGaN /InGaN structure is simulated to determine the performance parameter of the solar cell.
The output of the device is shown in table 4.1
Table 4.1 Test p-i-n output characteristics
Jsc (mA/cm2
) Voc (Volts) Fill Factor Efficiency %
4.64 2.10 88.45 8.62
Simulation shows that the results obtained are comparable to the earlier reported results with
only difference is in substrate used. This simulation result provide a positive feedback to move
forward. Simulation code is included in Appendix B
4.3.1 Optimization of p-i-n Structure
Based on above test simulation result we moved forward for optimization of p-i-n
structure to get better efficiency. Fig 4.2 shows the p-i-n structure considered during the
simulation.
Fig. 4.2 GaN/InGaN p-i-n structure
47

In the simulation, First of all we optimised the p-GaN thickness and doping concentration by
keeping intrinsic layer thickness 100 nm with 1 X 1016
cm-3
donor concentration (because its
background doping is ~ 1X1016
cm-3
) and n-GaN thickness 2m with donor concentration of 6 x
1018
cm-3
. Spontaneous and piezoelectric polarization charges are also included in simulation. As
we started increasing the p-GaN thickness absorption of photons in the p-region increases as a
result carrier generation also increases which contributes in the increase of current density. It is
observed that current density (Jsc) increases till the thickness of 130nm after this Jsc starts falling
down as shown in Figure 4.3(a). It is found because as we further increase the p-GaN thickness,
generated charge carriers are not separated out instead they start recombining in P-region which
results in drop in the Jsc.
Fig. 4.3 Effect of changing p-GaN thickness with different p-doping a.)Short Circuit Current Density b.) Efficiency
c.)Open Circuit Voltage d.) Fill Factor
(b)(a)
(d)(c)
48

We also investigated the effect of doping by taking different doping concentration. Results shows
that Jsc first increases and then decreases with increase in doping concentration, shown in Figure
4.3(a). This decrease can be due to increase in recombination with high doping concentration.
Figure 4.3(c) Change in p-GaN thickness shows variation in open circuit voltages. Therefore,
Efficiency curve follow the Jsc curve as shown in Figure 4.3(b).
Figure 4.4 shows different characteristic parameter of solar cell with i-layer thickness. It
can be observed that Jsc increases with increasing i-layer thickness. Since i-layer is low bandgap
semiconductor compare to p-GaN, it can absorb the photons of some lesser energy than p-GaN.
Other hand we can say that photon absorption is supported in i-layer by high absorption
coefficient of InGaN material. As thickness of i-layer is increases it absorbs more photons and
generate charge carriers in i-layer as shown in Figure 4.4(a). Built in electric field of p-i-n
structure support separation of charge carriers and improve collection efficiency this results
increase Jsc with thickness. Increment in i-layer thickness from 100nm to 150nm shows slight
decrement in the Voc from 2.32 to 2.27 volts which may be due to the larger saturation current in
thicker cell. There is no significant change in the Fill Factor(FF). However, FF starts to decrease
as we increase the thickness because series resistance of the cell also increases with increasing
thickness of i-layer. If we now look for efficiency we observe that efficiency curve follows the
same trend of Jsc curve as shown in Figure 4.4(d) Since Voc and FF are almost constant.
Figure 4.4(d) shows that by varying the i-layer thickness efficiency goes upto 9.42%.
Material defects such as threading dislocation, traps etc. are not considered during simulation
(b)(a)
49

Fig. 4.4 Effect of changing InGaN thickness on physical characteristic of solar cell a.)Short Circuit Current
Density b.) Open Circuit Voltage c.) Fill Factor d.) Efficiency
After the p-GaN and i-layer thickness optimization when we varied the n-GaN thickness
Figure 4.5 shows no significant change in results. It may be because the maximum no of
available photons are already absorbed by the p-GaN and i-layer and very few carriers are
generated in n-GaN region. Also there is not much change by increase doping concentration of n-
GaN. So we kept the n-GaN thickness to 2 m at which Jsc and efficiency are higher.
Fig. 4.5 Effect of changing n-GaN thickness on characteristic parameters of solar cell a.)Short Circuit Current
Density b.) Efficiency
Figure 4.6 shows the final optimized structure with thickness of p-GaN, intrinsic layer (InGaN)
and n-GaN 100nm,150nm and 2µm respectively and p-type, n-type doping of 5x1017
cm-3
and
(d)(c)
(b)(a)
50

6x1018
cm-3
respectively, with calculated conversion efficiency, I-V curve. Calculated solar cell
parameters are shown in Table 4.2.
Table 4.2 Characteristics parameters of p-i-n solar cell
Jsc (mA/cm2
) Voc (Volts) Fill Factor Efficiency %
5.09 2.08 88.73 9.42
Fig. 4.6 a.)Final Optimized structure of p-i-n GaN/InGaN double hetero junction solar cell b.)I-V curve
4.3.2 p-i-n Structure With Varying Indium Composition
We optimized In composition in i-layer, varied the indium composition considering the same
structure as shown in Figure 4.6 (a). At first, with increase in In composition till 20% Jsc of the double
hetero-junction GaN/InGaN solar cell increases which contributes in rise in efficiency but beyond this
composition Jsc start falling down as shown in Figure 4.7(a).
(a) (b)
51

Fig. 4.7 Effect of changing the In composition on various characteristic parameter a.) Short Circuit Current density
b.)Fill Factor c.)Efficiency d.) Discontinuity in the valence band at the hetero junction at high In content
Reason of falling is found from the band diagram that shown in Figure 4.7(d), we
observed that with high In composition discontinuity of valence band at the hetero-junction is
increasing and prevents the generated minority holes in InGaN layer to crossing P-GaN region.
Which accounts for the recombination of photo generated holes in intrinsic layer. Therefore
absorption in only p-GaN region contribute in current. Fill factor also shows sharp dip due to
increase of series resistance with increasing valence band discontinuity and then it rises back to
its original value. Earlier reports had also shown such type of behaviour [14].
4.4 Summary
Simulations is conducted to design optimization of GaN/ InGaN p-i-n double hetero-
junction solar cell. Simulation shows that characteristic parameters of the solar cell strongly
depend on thickness of the layers, doping and Indium composition. 50% quantum efficiency is
achieved after optimization of structure. Simulation also shows that efficiency can be achieve up
to 9.42 % for indium content of 15%. Further efficiency can be increased by use of some
different structure which can remove the valence band gap discontinuity at the interface.
(d)(c)
52

Reference:
1) Wu J, Walukiewicz W, Yu K M, Ager J W III, Haller E E, Lu H, Schaff W J, Saito Y
and Nanishi Y Appl. Phys. Lett. 80 3967 (2002).
2) Xiao H L, Wang X L, Wang J X, Zhang N H, Liu H X, Zeng Y P, Li J M and Wang
Z G J. Cryst.Growth276 401.( 2005)
3) K. Tadatomo, H. Okagawa, Y. Ohuchi, T. Tsunekawa, Y. Imada, M. Kato and T.
Taguchi Jpn. J. Appl. Phy.40 L 583-L 585, (2001)
4) Y. Zhao, J. Sonoda, C. Pan, S. Brinkley, I. Koslow, K.Fujito, H. Ohta, S. P. Denbaars
and S. Nakamura. Appl. Phys. Express 3 (2010).
5) P. Stauss, A. Walter, J. Baur, and B. Hahn: presented at 7th Int. Conf. Nitride
Semiconductors (ICNS7) (2007).
6) C. Yang, X. Wang, H. Xiao, J. Ran, C. Wang, G. Hu, X. Wang, X. Zhang, J. Li and J.
Li Phy. Stat. Sol. (a) 204 No. 12, 4288-4291 (2007).
7) H. Hamzaoui, A. S. Bouazzi and B. Rezig Sol. Energy Mater. Sol. Cells 87,(2005)
8) O. Jani, I. Ferguson, C. Honsberg and S. Kurtz Appl. Phy.Lett.91 132117 (2007).
9) W. Walukiewicz, J. W. Ager, K. M. Yu, Z. Liliental-Weber, J. Wu, S. X. Li, R. E.
Jones, and J. D. Denlinger, J. Phys. D 39, R83 (2006).
10) J. Wu, W. Walukiewicz, K. M. Yu, W. Shan, J. W. Ager, E. E.Haller, H. Lu, W. J.
Schaff, W. K. Metzger, and S. Kurtz, J. Appl. Phys. 94, 6477 (2003).
11) Jani O, Honsberg C, Asghar A, Nicol D, Ferguson L,Doolittle A and Kurtz S 1st IEEE
Photovoltaic Specialists Conf.pp 37–42 (Lake Buena Vista, FL,(2005)
12) Hamzaoui H, Bouazzi A S and Rezig B Sol. EnergyMater. Sol. Cells 87 595(2005)
13) Yang C B et al Phys. Status Solidi a, at pressdoi:10.1002/pssa. 23202,(2007)
14) G.F. Brown, J.W.AgerIIIb, W.Walukiewiczb, J.Wua,bSolar Energy Materials & Solar
Cells 94 478–483 (2010)
53

GROWTH OF InGaN FILMS BY METAL ORGANIC CHEMICAL VAPOR
DEPOSITION (MOCVD)
5.1 Epitaxy
Epitaxy has Greek roots that consist of ‘epi’ which means upon and ‘taxis’ which means
‘arranged’. The term ‘epitaxial growth’ covers the film growth on a crystalline substrate in an
ordered manner where the atomic arrangement of the grown film accepts crystallographic
structure of the substrate. In other words, it could simply be the deposition of a monocrystalline
film on a monocrystalline substrate. Epitaxial growth is one of the most important techniques
that allows the production of various kinds of optoelectronic devices.
 Homo-epitaxy; crystalline film is grown on a substrate of the same material (i.e. Silicon thin
film on Silicon substrate).
 Hetero-epitaxy; crystalline film and substrate are different from each other (i.e. GaN thin
film on sapphire substrate).
5.2 Growth Techniques
The biggest problem is to find a suitable substrate for the epitaxial growth of III-Nitrides,
since the bulk growth of III-Nitrides has not been developed yet to produce substrates for home
epitaxy. Thus, III-Nitride epitaxial growth still needs to be performed on foreign substrates
(hetero-epitaxy) that have lattice and thermal mismatch between substrate and growing epitaxial
layers. Most common substrates for epitaxial growth of III-Nitrides are Sapphire and SiC.
Although SiC is a better match to III-Nitride films it is not widely available, due to its high cost
compared to that of sapphire.
Since foreign substrates have large mismatch with the growing III-Nitride films, one
should find unique solutions for high quality III-Nitride materials for device applications.
Molecular Beam Epitaxy (MBE) and MOCVD are some of the epitaxial methods for the
deposition of III-Nitrides [1].
Chapter 5
54

5.2.1 Molecular Beam Epitaxy (MBE)
In MBE growth, epitaxy takes places in ultra high vacuum (10-8
Pa) and the sources are
heated separately. It is possible to precisely control the temperature of the individual sources.
With the help of a MBE system, ultra pure materials can be grown. Ultra high vacuum levels
required for the deposition increases the cost of fabrication. Due to the low deposition rate and
high operation cost of the MBE systems is not suitable for mass production.
5.2.2 Metal Organic Chemical Vapor Deposition (MOCVD)
There are several different MOCVD systems (Nitride-based, As-based, Pbased and etc.)
for the deposition of materials. The material system that is desired to be deposited determines the
system configuration, primarily including sources and reactor design. There are metal-organic
sources such as Trimethylgallium (TMGa), Triethylgallium (TEGa), Trimethylaluminium
(TMAl), Trimethylindium (TMIn), Silane (SiH4), that are carried by carrier gasses like hydrogen
or nitrogen through a well organized piping system to a reactor and sent through the substrate,
following proper mixing and heating. MOCVD growth method is suitable for mass production
since it grows high purity materials and allows the use of multiple substrates at a time. Batch
production decreases the running costs of the system.
5.3 Metal Organic Chemical Vapor Deposition ( MOCVD ) Growth
Technique
Metal Organic Chemical Vapor Deposition growth technique have been in use for the
deposition of epitaxial thin films for more than thirty years. SiC based, GaN based, and As/P
based, materials can be deposited with MOCVD method. Growth temperature for As/P based
materials system is around 850o
C [2], where GaN based material systems need higher growth
temperatures around 1100 o
C [3]. Typically, nitrogen or hydrogen gas is used as a carrier gas.
MOCVD technique is the best method for the deposition of multilayer structures of III-Nitrides
and widely used for mass production. Depositions of InGaN/GaN and AlGaN/GaN structures for
various device applications have been widely investigated using MOCVD method [4].This
growth technique utilizes gas mixtures that contain the molecules to be deposited called
‘precursors’, to grow epitaxial thin films. The carrier gas, high purity hydrogen or nitrogen, has
to be chosen according to the growing material.
55

Figure 5.1 shows the sequence of steps during a typical MOCVD growth. There are four
regions as seen in the figure. The gas mixture, containing all the necessary molecules for the
material growth, is coming from the left side to the heated substrate. Sources that are in the gas
mixture diffuse down to the substrate. Diffused precursors react with each other and following
necessary chemical interactions, desired materials are grown on the substrate that is indicated in
the figure. Chemical reactions between precursors are
Figure 5.1.Schematic steps for MOCVD growth.
Ga (CH3)3 + NH3 GaN + organic by products
In (CH3)3 + NH3 InN + organic by products
Molecules that are absorbed by the surface of the substrate are not fixed on the surface; instead
they are mobile. Surface kinetics is not fully understood yet due to the lack of in-situ
measurement tools.
56

5.3.1 Configuration
Figure 5.2 shows a simple schematic diagram of a MOCVD system where only sources
and related pipelines are shown. The sources that are used during growth follows the necessary
lines to reach up to the reactor and others that are not used during growth falls into the ‘Vent-
Line’. MOCVD system also uses various kinds of electronic and pneumatic valves, mass flow
controllers, pressure controllers and switching systems for the atomic scale control of the
growing materials simply by precisely adjusting the amount of sources flowing towards the
reactor.
Figure 5.2.Schematics diagram of a MOCVD system.
Figure 5.3 shows a simple schematic diagram of a horizontal MOCVD reactor. The sources and
carrier gasses (H2 or N2) pass through the ‘Gas Inlet’ and reach the reactor. There is a ‘Rotating
Succeptor’ that carries the wafer holder. Rotation helps to improve the uniformity of growing
epitaxial layers. Heating of the reactor can be done by several methods. RF coil around the
reactor, as shown in the schematic, provides a uniform temperature gradient across the wafer.
This has prime importance for epi-growth.
57

Fig. 5.3.Schematics diagram of MOCVD reactor
5.3.2 Sources
Wide range of available source materials is one of the biggest advantages of MOCVD
system over those other thin film deposition methods. In MOCVD growth, generally alkyls of
the group II and III metals and hydrides of group V and VI elements are used. Diluted vapors of
these sources are transported to a reactor at high temperatures, where the parolysis reaction takes
place for epitaxial thin film growth.
In general, pyrolysis reaction can be generalized for III-V materials as follows
R3M + EH3 ME + 2RH
Where R, M and E are the alkyl radicals (C2H5or CH3), the group III metals (Ga, In, Al) and
the group V element (N, P, As, Sb), respectively.
Table 5.1.Sources of MOCVD system [5]
Name of Compound Acronomy Purpose
Trimethylgallium TMGa III element
Triethylgallium TEGa III element
Trimethylaluminium TMAl III element
Triethylaluminium TEAl III element
Trimethylindium TMIn III element
Triethylindium TEIn III element
Trimethylantimony TMSb V element
Triethylantimony TESb V element
Trimethylarsine TMAs V element
58

Dimethylasrinehydride DEAs V element
Arshine AsH3 V element
Phosphine PH3 V element
Silane SiH4 n-dopant
Disilane Si2H6 n-dopant
Dimethylzinc DMZn p-dopant
Diethylzinc DEZn p-dopant
Diethylberyllium DEBe p-dopant
Dimethylcadmium DMCd p-dopant
In MOCVD system, trimethyl sources are most often used due to their higher vapor
pressure and stability compared to others. It is also important to choose metal organic and
hydride sources that could easily decompose at the growth temperature of the desired material
systems.
5.4 Characterization Techniques
5.4.1 In-situ Characterization
Epitaxial growth is not only the first step for manufacturing optoelectronic devices but also a
determining factor for device performance. Therefore, precise control of the growth parameters
is crucial. Optical reflectance measurements could be used to investigate material properties like
growth rate, layer thickness, composition of ternary alloys and surface roughness [6].
The Interferometer uses Fabry-Perot interferometry to monitor and analyse the MOCVD
growth of thin-film materials. The easiest way to explain how the In-Situ Reflectance Monitor
works is to consider the simple three-phase system below, Figure 5.4, with an air/film and
film/substrate interface.
59

Fig. 5.4 Reflection from a 3-phase system. The shaded area shows multiple internal reflections [7].
Laser light is reflected at near-normal incidence from this 3-phase system. If the growing
layer is partially transparent to the probe wavelength and there is a difference in refractive index
of the substrate and growing layer, then an interference pattern will result from the two beams
reflected from the air/film and film/substrate interfaces. The reflected intensity of this interfering
light is given by:
=
+ + 2 ∆ ∝
1 + ∝ + 2 ∆ ∝
5.1
Where r1 and r2 are the Fresnel reflection coefficients for the air/film and film/substrate
interfaces, respectively, and are given by:
=
− 1
+ 1
5.2
=
−
+
5.3
Where nf and ns are the film and substrate refractive index, respectively. The periodicity (i.e.
peak-to-peak) in the interference pattern is governed by the probe wavelength and the film
refractive index, and is given in the above equation by the delta term:
60

2 = ∆=
4
5.4
Where λ is the probe wavelength and d the film thickness. If the film has low absorbance at the
probe wavelength, then the interference recorded during growth will have a profile similar to the
one shown in Figure 5.5
Fig. 5.5 Reflected intensity for a film with refractive index 2.4 on a substrate with refractive index 1.7, and a probe
wavelength of 635nm. An interference profile like this might be seen for GaN growth on Sapphire, where the film
has little absorption at the probe wavelength.
However, if the growing film has appreciable absorbance at the probe wavelength, then there
will be an overall attenuation of the reflected intensity, as shown in Figure 5.6. The effect of
absorbance of the probe wavelength by the growing film is given by the exponential term in the
equation for reflected intensity, where α is dependant on the film’s extinction coefficient at the
probe wavelength, i.e.
=
4
5.5
For the material GaN the film extinction coefficient is low (k < 0.01) for the red probe
wavelength (635nm) used in the Thomas Swan interferometer. Therefore attenuation of the
61

Design, Growth & Simulation of InGaN Solar Cells

Design, Growth & Simulation of InGaN Solar Cells

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