Çukurova university institute of natural and ... - cu …library.cu.edu.tr/tezler/8116.pdf · this...

ÇUKUROVA UNIVERSITY INSTITUTE OF NATURAL AND APPLIED SCIENCES

MSc THESIS

Faruk KÜRKER

MICROFABRICATION BASED DESIGN AND SIMULATION OF HETEROJUNCTION SOLAR CELL

DEPARTMENT OF COMPUTER ENGINEERING

ADANA, 2010

ÇUKUROVA UNIVERSITY INSTITUTE OF NATURAL AND APPLIED SCIENCES

MICROFABRICATION BASED DESIGN AND SIMULATION OF

HETEROJUNCTION SOLAR CELL

Faruk KÜRKER

MSc THESIS

DEPARTMENT OF COMPUTER ENGINEERING We certify that the thesis titled above was reviewed and approved for the award of degree of the Master of Science by the board of jury on 21 / 09 / 2010. ……………….................... ………………………......... ……....................................... Asst.Prof.Dr. Mutlu AVCI Asst.Prof.Dr. Murat AKSOY Asst.Prof.Dr. Ramazan ÇOBAN SUPERVISOR MEMBER MEMBER This MSc Thesis is written at the Department of Institute of Natural And Applied Sciences of Çukurova University. Registration Number:

Prof. Dr. İlhami YEĞİNGİL Director Institute of Natural and Applied Sciences

Not:The usage of the presented specific declerations, tables, figures, and photographs either in this

thesis or in any other reference without citiation is subject to "The law of Arts and Intellectual Products" number of 5846 of Turkish Republic

I

ABSTRACT

MSc THESIS

MICROFABRICATION BASED DESIGN AND SIMULATION OF HETEROJUNCTION SOLAR CELL

Faruk KÜRKER

CUKUROVA UNIVERSITY INSTITUTE OF NATURAL AND APPLIED SCIENCES

DEPARTMENT OF COMPUTER ENGINEERING

Supervisor : Assist.Prof.Dr. Mutlu AVCI Year : 2010, Pages: 100

Jury : Asst.Prof.Dr. Mutlu AVCI : Asst.Prof.Dr. Murat AKSOY : Asst.Prof.Dr. Ramazan ÇOBAN

Solar cells outweigh all these energy sources due to their small weight and their relatively high power density. Advances in semiconductor design and fabrication are very rapid and everyday provide new ideas and means for improving cell performance.

In this thesis, investigates the potential use of InP/InGaAs/AlGaAs as photovoltaic material. Method for developing realistic simulation models of advanced solar cells is presented. Silvaco Atlas was used to simulate heterojunction solar cell. Electrical and optical properties of different materials are researched for such designs. The findings of this research show that InP/InGaAs/AlGaAs is a promising semiconductor for solar cell use. Key Words: Solar cell, photovoltaic device, heterojunction, Silvaco Atlas.

II

ÖZ

YÜKSEK LİSANS TEZİ

HETEROJONKSİYON GÜNEŞ PİLİNİN TASARIMI VE MİKROFABRİKASYON TABANLI BENZETİMİ

Faruk KÜRKER

ÇUKUROVA ÜNİVERSİTESİ FEN BİLİMLERİ ENSTİTÜSÜ

BİLGİSAYAR MÜHENDİSLİĞİ ANABİLİM DALI

Danışman : Yrd. Doç. Dr. Mutlu AVCI Yıl: 2010, Sayfa: 100 Jüri : Yrd. Doç. Dr. Mutlu AVCI : Yrd. Doç. Dr. Murat AKSOY : Yrd. Doç. Dr. Ramazan ÇOBAN

Güneş pilleri küçük ağırlıkları ve yüksek miktardaki güç yoğunluğundan dolayı diğer enerji kaynaklarından daha önemlidir. Yarı iletkenlerin dizaynı ve fabrikasyondaki gelişimi çok hızlıdır ve hemen hemen her gün yeni bir fikirle karşılaşabiliriz ve buda gittikçe gelişen hücre performansı anlamına gelebilir. Bu tezde, fotovoltaik malzeme olarak InP/InGaAs/AlGaAs potansiyel kullanımı araştırılmaktadır. Gelişmiş güneş hücreleri gerçekçi simülasyon modelleri geliştirmek için yöntem sunulmaktadır. Silvaco Atlas heterojunction güneş hücresini simüle etmek için kullanılmıştır. Farklı malzemelerin elektriksel ve optik özellikleri örnek dizaynlar için incelenmiştir. Bu araştırma bulguları InP/InGaAs/AlGaAs güneş pili kullanımı için umut verici bir yarı iletkendir.

Anahtar Kelimeler: Güneş pili, fotovoltaik aygıt, heterojonksiyon, Silvaco Atlas.

III

ACKNOWLEDGEMENTS

I would like to thank my supervisor Assist.Prof.Dr. Mutlu AVCI for his helps

and advices. Also, I would like to thank Electronics Engineer Mr. Bülent

BÜYÜKGÜZEL for his help and patience.

During all this work, my beloved wife and my family supported me with their

patience, helps and hearts. This thesis is dedicated to Efdal Zahid, Dilnur Gülsüm

and Emine with all my heart.

IV

CONTENTS PAGE

ABSTRACT ......................................................................................................... I

ÖZ ....................................................................................................................... II

ACKNOWLEDGEMENTS ............................................................................... III

CONTENTS ................................................................................................... IV

LIST OF TABLES........................................................................................... VIII

LIST OF FIGURES .............................................................................................X

LIST OF ABBREVIATONS .......................................................................... XIV

l. INTRODUCTION ............................................................................................ 1

1.1. Basic of Semiconductor Physics ................................................................ 2

1.1.1. Classification of Materials ............................................................ 2

1.1.2. Atomic Structure .......................................................................... 3

1.1.3. Electrons and holes ....................................................................... 8

1.1.4. Direct and Indirect Band Gaps ................................................... 10

1.1.5. Fermi Level ............................................................................... 11

1.2. Solar Cell Fundamentals ....................................................................... 13

1.2.1. The Photovoltaic Effect .............................................................. 14

1.2.1.1. The Electromagnetic Spectrum .............................................. 16

1.2.1.2. Band Gap ................................................................................ 17

1.2.1.3. Solar Cell Junctions .................................................................19

1.2.1.4. Lattice Matching ..................................................................... 20

1.2.1.5. AM0 Spectrum ........................................................................22

1.2.1.6. Current-Voltage Curves .......................................................... 24

1.2.1.7. Electrical Output ..................................................................... 25

1.3. Heterojunctions ......................................................................................26

2. PREVIOUS WORK ....................................................................................... 31

3. MATERIAL AND METHOD ........................................................................ 41

3.1. Materials ................................................................................................41

3.1.1. Ge (Germanium)..........................................................................42

3.1.1.1 Basic Information about Ge .....................................................42

V

3.1.2. InP (Indium Phosphorus) .............................................................46

3.1.2.1. Basic Information about Indium ................................................46

3.1.2.2. Basic Information about Phosphorus .........................................46

3.1.3. InGaAs (Indium Gallium Arsenic) ...............................................48

3.1.3.1. Basic Information about Gallium ...............................................48

3.1.3.2. Basic Information about Arsenic ..............................................48

3.1.4. AlGaAs (Aluminium Gallium Arsenic)........................................49

3.1.4.1. Basic Information about Aluminum ..........................................49

3.1.5. AlInGaP(=InAlAsP)(Aluminium Indium Gallium Phosphorus) ...51

3.2. TCAD Simulation Environment .............................................................. 52

3.2.1. Silvaco Atlas Simulation Software ............................................. 54

3.2.2. Silvaco Atlas ............................................................................. 55

3.2.3. Input File Structure ......................................................................55

3.3. Structure Specification ............................................................................ 57

3.3.1. Mesh .......................................................................................... 57

3.3.2. Region ........................................................................................ 58

3.3.3. Electrodes....................................................................................60

3.3.4. Doping ....................................................................................... 61

3.3.5. Materials Model Specification ................................................... 61

3.3.5.1. Material ....................................................................................62

3.3.6. Models ....................................................................................... 62

3.3.7. Light .......................................................................................... 63

3.3.8. Contact ....................................................................................... 63

3.3.9. Numerical Method Selection ...................................................... 63

3.3.10. Solution Specification .............................................................. 65

3.3.10.1. Log ........................................................................................ 65

3.3.10.2. Solve .................................................................................... 65

3.3.10.3. Load and Save ....................................................................... 66

3.3.11. Result Analysis ........................................................................ 66

3.4. Simple Simulation Source Code ............................................................. 68

3.4.1. Silvaco Library .......................................................................... 70

VI

4. RESEARCH AND DISCUSSION ................................................................. 71

4.1. The Simple InP Cell ................................................................................71

4.2. Heterojunction Cell .................................................................................76

5. CONCLUSION ............................................................................................. 81

6. REFERENCES .............................................................................................. 83

7. CURRICULUM VITAE ................................................................................ 87

8. APPENDIX ................................................................................................... 89

VIII

LIST OF TABLES PAGE

Table 1.1. Electron Configuration of IIIA, IVA, VA Group Elements ................... 5-6

Table 1.2. Definitions of n and p ........................................................................... 9

Table 1.3. Intrinsic carrier concentration at room temperature (300K) ................... 10

Table 1.4. Notable events in the history of photovoltaics ....................................... 15

Table 1.5. Approximate wavelength of various colors in vacuum .......................... 17

Table 1.6. Common semiconductor band gaps ...................................................... 17

Table 3.1. Material Defaults for semiconductors ................................................... 42

Table 3.2. Silvaco Atlas physical models .............................................................. 55

X

LIST OF FIGURE PAGE

Figure1.1. Materials classified by conductivity ........................................................ 2

Figure1.2. Partial periodic table ............................................................................... 3

Figure1.3. Order of electron shell filling .................................................................. 4

Figure1.4. Silicon Electron Shell Diagram............................................................... 5

Figure1.5. Covalent bonds of Si atom ...................................................................... 7

Figure1.6. Band gap diagrams ................................................................................. 8

Figure1.7. Structure of n-type and p-type doping .................................................... 9

Figure1.8. Direct and indirect band gaps ............................................................... 11

Figure1.9. Fermi distribution ................................................................................. 12

Figure1.10. Fermi level: intrinsic case ................................................................... 13

Figure1.11. Fermi level: n-type case ...................................................................... 13

Figure1.12. Fermi level: p-type case ...................................................................... 13

Figure1.13. The electromagnetic spectrum ............................................................. 16

Figure1.14. Effect of light energy on different band gaps ....................................... 19

Figure1.15. Simple cubic lattice structure .............................................................. 20

Figure1.16. Lattice constants ................................................................................. 21

Figure1.17. AM0 spectrum (Wavelength vs Irradiance) ......................................... 23

Figure1.18. AM0 spectrum (Energy vs Irradiance) ................................................. 23

Figure1.19. Sample IV curve used in efficiency calculations .................................. 24

Figure1.20. Solar cell IV characteristic .................................................................. 26

Figure1.21. Crystal dislocation in heterojunction ................................................... 27

Figure1.22. Band diagram of heterojunction formations ......................................... 28

Figure1.23.Band diagram of superlattice formation (a) undoped and (b) AlGaAs

doped ................................................................................................... 29

Figure 2.1. Optimized multi-junction solar cell (InGaP/GaAs) I-V curve ............... 32

Figure 2.2. Quad-junction InGaN solar cell IV curve ............................................. 33

Figure 2.3. I-V curve based on new bases discovered in smaller iteration test at

300 K ................................................................................................... 34

Figure 2.4. IV characteristic of the prototype triple MJ cell .................................... 35

XI

Figure 2.5. IV characteristic of Si solar cell............................................................ 36

Figure 2.6. I-V characteristics of InGaP/GaAs/InGaNAs/Ge cell. .......................... 37

Figure 2.7. I-V Curve of 36.28% 3J (0.82 µm InGaP/ 3.9 µm GaAs/ Ge) Cell

Model using Improved Genetic Algorithm Design Parameters,

AMO. ................................................................................................... 39

Figure 2.8. Current–voltage curve of a p-GaAs/i-n InGaAsN hetero-junction cell

with intrinsic layer width of 600 nm ..................................................... 40

Figure 3.1. n and k data base of Germanium .......................................................... 43

Figure 3.2. Direct Bandgap- Indirect Bandgap ....................................................... 44

Figure 3.3. The temperature dependence of the intrinsic carrier concentration ni. ... 45

Figure 3.4 Fermi level versus temperature for different concentrations of

shallow donors and acceptors. ............................................................. 45

Figure 3.5. n and k data base of Indium Phosphorus ............................................... 47


Figure 3.7. Fermi level versus temperature for different concentrations of

shallow donors and acceptors. ............................................................. 48

Figure 3.8. N and k data base of Aluminum Gallium Arsenic compounds. ............. 50


Figure 3.10. Silvaco’s TCAD suite of tools ............................................................ 53

Figure 3.11. Atlas inputs and outputs ..................................................................... 54

Figure 3.12. Atlas command groups and primary statements ................................. 56

Figure 3.13. Atlas mesh ......................................................................................... 57

Figure 3.14. Atlas region ....................................................................................... 59

Figure 3.15. Atlas regions with materials defined ................................................... 59

Figure 3.16. Atlas electrodes .................................................................................. 60

Figure 3.17. Atlas doping ....................................................................................... 61

Figure 3.18. Atlas material models specification .................................................... 62

Figure 3.19. Atlas numerical method selection ....................................................... 64

Figure 3.20. Atlas solution specification. ............................................................... 65

Figure 3.21. Atlas results analysis. ......................................................................... 66

Figure 3.22. Sample TonyPlot IV curve. ................................................................ 67

XII

Figure 4.1. Simple InP cell. .................................................................................... 71

Figure 4.2. The mesh ............................................................................................. 72

Figure 4.3. Mesh defined for the InP whole, top and bottom .................................. 72

Figure 4.4. Net Doping for the InP ......................................................................... 73

Figure 4.5. The layer structure of the InP ............................................................... 73

Figure 4.6 IV curve of InP .................................................................................... 75

Figure 4.7. Heterojunction prototype...................................................................... 76

Figure 4.8. Heterojunction cell ............................................................................... 77

Figure 4.9. The mesh ............................................................................................. 78

Figure 4.10. Mesh defined for the heterojunction cell whole, top and bottom ......... 78

Figure 4.11. Net Doping for the heterojunction cell................................................ 79

Figure 4.12. The layer structure of the heterojunction cell ...................................... 79

Figure 4.13. IV curve of heterojunction cell .......................................................... 80

XIV

LIST OF ABBREVIATONS

Symbol Description Unit

a Lattice constant Å

AUGN Electron Auger coefficients cm6/s

AUGP Hole Auger coefficients cm6/s

c Speed of light m/s

c Affinity eV

COPT Radiative recombination rate cm3/s

E Energy eV

e1, e2, n, k Optical constants –

eS Permittivity F/cm

EC Conduction band eV

EF Fermi energy level eV

Eg Energy bandgap eV

EV Valence band eV

f Frequency Hz

f(E) Fermi–Dirac distribution function –

h Plank’s constant J×s

I Current A

ISC Short circuit current A

k Boltzmann’s constant J/K

k Optical parameters (absorption index) –

kT Thermal energy eV

mn (MUN) Electron mobility cm2/V×s

mp (MUP) / hole mobility cm2/V×s

n Optical parameters (refractive index) –

P Power W

R Reflectivity –

r Resistivity W×m

s Conductivity S/m

XV

T Absolute temperature oK

TAUN / TAUP Electron / hole lifetimes s

V Voltage V

VOC Open circuit current V

1.INTRODUCTION Faruk KÜRKER

1

1. INTRODUCTION

It is expected by the authorities that the global energy demand will double

within the next 50 years. Fossil fuels are held responsible for the increased

concentration of carbon dioxide in the atmosphere of earth]. Hence, development of

renewable energy is one of the challenges to society in the 21st century. One of the

most popular renewable energy technologies is photovoltaics (PV). It is the

technology that directly converts daylight into electricity. PV is one of the fastest

growing of all the renewable energy technologies, in fact, it is one of the fastest

growing industries at present. Solar cell manufacturing technology of crystalline

silicon devices is growing by approximately 40% per year and this growth rate is

ever increasing (Janssen).

The purpose of solar cells is to change light energy into electrical energy with

the probable highest efficiency. Photo-electrons or photons make light. Photons carry

energy that is different according to the color, or wavelength of light. Electrical

energy is generated when photons incite electrons from the valence band into the

conduction band in semiconductor materials.

The aim of this study is to simulate a new heterojunction solar cell from

microfabrication steps to calculate its efficiency. Silvaco Atlas TCAD simulation

software is used for this simulation and efficiency investigation.


2

1.1. Basic of Semiconductor Physics

1.1.1. Classification of Materials

We categorize material according to their electrical properties as conductors,

insulators or semiconductors. The conductivity σ is a key parameter in identifying

the type of material. A sample of materials based on conductivity is presented in

Figure 1.1. The semiconductors fall between the insulators and the conductors

(Baldomero Garcia, 2007: 5).

Figure 1.1 Materials classified by conductivity (Sze, 2001: 8)

Semiconductors are found in elemental or compound form. Silicon (Si) and

Germanium (Ge) are examples of elemental semiconductors. Both of these

semiconductors are in group IV of the periodic table. An abbreviated periodic table is

shown in Figure 1.2. In addition to the group IV semiconductors, we can make

compounds with elements from groups III and V, respectively. Examples of III-V


3

semiconductors are Aluminum Phosphide (AlP), Gallium Nitride (GaN), Indium

Phosphide (InP), Gallium Arsenide (GaAs), among others. We can make

semiconductor compounds from groups II-VI, such as Zinc Oxide (ZnO), Cadmium

Telluride (CdTe), Mercury Sulfide (HgS), among others. Indium and Gallium form

group III elements, while Nitrogen is a group V element (Baldomero Garcia, 2007:

6).

Figure 1.2. Partial periodic table (http://www.nrc-cnrc.gc.ca/eng/education/elements/index.html)

1.1.2. Atomic Structure

At present, majority of solar cells are based on silicon (Si). This is because of

Si’s unique atomic structure and material properties. Si is a Group IV element with

atomic number 14 and the group IV designation denotes four electrons in its

outermost shell. This occurs because, as the atomic number increases, electron shells

are filled in the following order:(UTSLER, 2006: 3)

http://www.nrc


4

Figure 1.3. Order of electron shell filling (http://www.fordhamprep.org/gcurran/sho/sho/lessons/lesson36. html )

The arrangement of electrons in a Silicon atom is shown in Figure 1.4. The

first shell has two electrons, the second shell has eight electrons, outer shell has four

electrons. When Silicon atoms are together, the atoms from the outer shells are found

in covalent bonds. Therefore, a Silicon atom creates bonds with four other Silicon

atoms (Baldomero Garcia, 2007: 7)

http://www.fordhamprep.org/gcurran/sho/sh


5

Figure 1.4. Silicon Electron Shell Diagram

(http://commons.wikimedia.org/wiki/File:Electron_shell_014_ silicon. png)

As seen in table 1.1. electron configuration of IIIA, IVA, VA group of

elements.

Table 1.1. Electron Configuration of IIIA, IVA, VA Group Elements (http://en.wikipedia.org/wiki/Group_(periodic_table))

Atomic Number (Proton

Number)

Symbol Element

No. Of electrons/shell

5 B boron 2, 3

13 Al aluminium 2, 8, 3

31 Ga gallium 2, 8, 18, 3

49 In indium 2, 8, 18, 18, 3

81 Tl thallium 2, 8, 18, 32, 18, 3

http://commons.wikimedia.org/wiki/File:Electron_shell_014_

http://en.wikipedia.org/wiki/Group_(periodic_table))


6

Atomic Number (Proton

Number) Symbol Element

No. Of electrons/shell

6 C carbon 2, 4 14 Si silicon 2, 8, 4

32 Ge germanium 2, 8, 18, 4

50 Sn tin 2, 8, 18, 18, 4

82 Pb lead 2, 8, 18, 32, 18, 4

Atomic Number (Proton Number) Symbol Element No. Of electrons/shell

7 N nitrogen 2, 5

15 P phosphorus 2, 8, 5

33 As arsenic 2, 8, 18, 5

51 Sb antimony 2, 8, 18, 18, 5

83 Bi bismuth 2, 8, 18, 32, 18, 5

As seen in Figure 1.5, the elliptical dotted lines represent the covalent bonds

formed by the silicon atoms. When an electron is missing, the covalent bond stops

existing. A hole takes the place of the electron.


7

Figure 1.5. Covalent bonds of Si atom (Michalopoulous, 2002: 11)

Energy bands form one of the fundamental concepts of semiconductor

physics. These energy bands are the valence band, the conduction band, and the

forbidden gap or band gap (Pierret, 1996: 27). When an electron is in the valence

band, the covalent bond exists. In order for the electron to move from the valence

band into the conduction band, energy is required to excite the electron. The band

gap energy is the minimum energy necessary for the electron to move from the

valence band into the conduction band (Baldomero Garcia, 2007: 8)

We see in Figure 1.6 the band gap diagrams for conductors, insulators, and

semiconductors. This figure also shows the differences among the three types of

materials according to their electric properties. In the case of conductors, the band

gap is small or non-existent. But insulators have wide band gaps. Hence, much more

energy is required for the insulator to have electrons in the conduction band.


8

Figure 1.6. Band gap diagrams (Michalopoulous, 2002: 8)

Semiconductors have band gaps which are dependent on the material.

Because band gap is also dependent on temperature, it should be noted that all said

band gaps in this study are at room temperature (300 K.)

1.1.3. Electrons and Holes

A semiconductor at absolute zero temperature cannot conduct heat or

electricity (Nelson, 2003: 44). All of the semiconductor’s electrons are bonded. The

electrons get kinetic energy when the temperature is increased. Some of the electrons

are released and move into the conduction band. These electrons can conduct charge

or energy. We call the areas left by these electrons in the valence band as holes.

When the temperature of the semiconductor increases, the number of free electrons

and holes increases, too. So, the conductivity of the semiconductor is directly

proportional to temperature increases.

The conductivity of the semiconductor can be changed by exposing it to light

or by doping it. Photoconductivity consists of exposing the semiconductor with

photon energy larger than the semiconductor’s band gap. Doping consists of adding

impurities to the semiconductor material.


9

N-type and p-type doping are shown in Figure 1.7. The atom of the

semiconductor is represented by the blue circle and a +4. For example, a silicon atom

has four electrons in its outer shell. When silicon atoms are n-doped, atoms from

group V of the periodic table are added. Every added group V atom provides an

extra electron to donate. When silicon atoms are p-doped, the atoms from group III

of the periodic table are added. Each group III atom has one less electron than

silicon. Therefore, a hole is added. The number of carriers is increased by doping in

the semiconductor material.

Figure 1.7. Structure of n-type and p-type doping (Michalopoulous, 2002: 13)

An intrinsic semiconductor is a pure semiconductor with a insignificant

amount of impurity atoms (Pierret, 1996). By definition, the number of electrons and

holes in a semiconductor are shown by n and p. See Table 1.2.

Table 1.2. Definitions of n and p

n Number of Electron / cm3

p Number of Holes / cm3


10

In the case of an intrinsic semiconductor, the case shown below occurs:

inpn == (1.1)

For example reasons, ni is given for GaAs, Si and Ge and room temperature

(Pierret, 1996: 34). See Table 1.3 .

Table 1.3. Intrinsic carrier concentration at room temperature (300K) (http://www.ioffe.ru/SVA/NSM/Semicond/)

Carrier Concentration ( ni ) per cm3 Material

2×106 GaAs

2×1013 Ge

1×1010 Si

6.2×1022 InN

8.91022 GaN

1×107 InP

When solar cells use semiconductor materials from Table 1.3, the current level

is highest for Ge and lowest for GaAs. The current levels correspond in rank to the ni

levels provided in Table 1.3.

1.1.4. Direct and Indirect Band Gaps

Because the band gap is the minimum energy required to move an electron

from the valence band into the conduction band, it is necessary to differentiate

between direct and indirect band gaps.

Figure 1.8 shows the concept of direct and indirect band gaps. The blue part

shows the valence band. The tan part shows the conduction band.

http://www.ioffe.ru/SVA/NSM/Semicond/


11

Figure 1.8. Direct and indirect band gaps (Michalopoulous, 2002: 24)

When the valence band and the conduction band are together in wave vector k,

the semiconductor has a direct band gap. When the valence band and the conduction

band have different wave vector k, the semiconductor has an indirect band gap. The

k vector represents a difference in momentum. Photons have insignificant

momentum. In order to incite an electron from the valence band to the conduction

band in an indirect band gap semiconductor, in addition to a photon, a phonon is

necessary. The phonon is a lattice vibration. The phonon transfers its momentum to

the electron at the time the photon is absorbed. Consequently, a direct band gap

semiconductor is commonly better for optoelectronics. Silicon is an example of an

indirect band gap semiconductor. Gallium Arsenide and wurtzite Indium Gallium

Nitride form examples of direct band gap semiconductors.

1.1.5. Fermi Level

The Fermi function f(E) specifies the quantity of the existing states at energy E

are filled with an electron (Pierret, 1996). The Fermi function is a probability

distribution function defined as follows:


12

kTEE FeEf /)(1

1)( −+= (1.2)

Where E is the electron energy, EF is the Fermi level, k is Boltzmann’s

constant, and T is the temperature in Kelvin. A plot of f (E) is seen in Figure 1.9.

Figure 1.9. Fermi distribution (Michalopoulous, 2002: 15)

From the Fermi function, we can determine that when E=EF, then

f(E)=f(EF)=0.5.

Figure 1.10 shows the Fermi level for an intrinsic semiconductor. Figure 1.11

shows the Fermi level for n-type semiconductor. Figure 1.12 shows the Fermi level

for p-type semiconductor. From these Figures, we can deduce that the n-type

material has a larger electron carrier distribution whereas the p-type material has a

larger hole carrier distribution.


13

Figure 1.10. Fermi level: intrinsic case (Pierret, 1996: 42)

Figure 1.11. Fermi level: n-type case (Pierret, 1996: 42)

Figure 1.12. Fermi level: p-type case (Pierret, 1996: 42)

1.2. Solar Cell Fundamentals

After the basics of semiconductors, the logical step is to go on with solar cell

fundamentals.

Solar cell research started with Edmund Bequerel’s discovery of the

photovoltaic effect in 1839. He found that an electric current was produced when

light was applied to a silver covered platinum electrode immersed in electrolyte. The

next noteworthy step was was taken by William Adams and Richard Day in 1876.


14

They discovered that a photocurrent appeared when selenium was contacted by two

heated platinum contacts. Nevertheless, current was produced spontaneously by the

action of light. Continuing to build on these works, Charles Fritts developed the first

large area solar cell in 1894. He pressed a layer of selenium between gold and

another metal. Progress continued as the theory of metal semiconductor barrier layers

was established by Walter Schottky and other. In the 1950s, silicon was used for

solid state electronics. Silicon p-n junctions were used to improve on the

performance of the Schottky barrier. These silicon junctions had better rectifying

action and photovoltaic behavior. In 1954, Chapin, Fuller and Pearson developed the

first silicon solar cell, with a reported efficiency of 6%. Nevertheless, the cost per

Watt associated with these solar cells made them prohibitively expensive for

terrestrial use. However, where power generation was not practicable (i.e., space)

were suitable for solar cells. Satellites were the first clear application for silicon solar

cells. Since that time, solar cells have progressed gradually both in terms of

efficiency as well as materials used their production (Nelson, 2003: 2).

A brief list of events in the history of photovoltaics from 1939 until 2002 is

shown in Table 1.4.

1.2.1. Photovoltaic Effect

The photovoltaic effect is the process by which a solar cell changes the

energy from light into electrical energy. Photons make the light. The energy of these

photons changes according to the color (wavelength) of light. The material that

makes up the solar cell determines the photovoltaic properties when light is applied

(Nelson,2003: 1).

When light is absorbed by matter, such as metal, photons provide the energy

for electrons to move to higher energy states within the material. However, the

energized electrons return to their original energy state. In semiconductor materials,

there is a built-in asymmetry (band gap). This allows the electrons to be transferred

to an external circuit before they can return to their first energy state. The energy of

the excited electrons creates a potential difference. This electromotive force directs


15

the electrons through a load in the external circuit to perform electrical work

(Baldomero Garcia, 2007: 15-16).

Table 1.4. Notable events in the history of photovoltaics (Hegedus and Luque, 2003)


16

1.2.1.1. Electromagnetic Spectrum

Light is electromagnetic radiation. The frequency of light decides its color.

Figure 1.13. shows the visible part of the electromagnetic spectrum. Visible

wavelengths range from 390 nm (violet) to 780 nm (red). Table 1.4. shows the rough

wavelength range of visible colors (Baldomero Garcia, 2007: 15)

Figure 1.13. The electromagnetic spectrum (http://www.photobiology.info/Visser-Rolinski_files/Fig2.png)

http://www.photobiology.info/V


17

Table 1.5. Approximate wavelength of various colors in vacuum (http://physics.about.com/od/lightoptics/a/vislightspec.htm)

The Visible Light Spectrum

Color Wavelength (nm)

Red 625 - 740

Orange 590 - 625

Yellow 565 - 590

Green 520 - 565

Cyan 500 - 520

Blue 435 - 500

Violet 380 - 435

The sun releases light from ultraviolet, visible, and infrared wavelengths in

the electromagnetic spectrum. Solar irradiance has the largest magnitude at visible

wavelengths, highest in the blue-green (Nelson, 2003: 17).

1.2.1.2. Band Gap

The band gap of the semiconductor material determines how the solar cell

reacts to light. Table 1.5 shows a small sample of semiconductor band gaps.

Table 1.6. Common semiconductor band gaps

(http://www.ioffe.ru/SVA/NSM/Semicond/)

Material Band gap (eV) at 300 K

Si 1.12

Ge 0.66

GaAs 1.42

InP 1.34

http://physics.about.com/od/lightoptics/a/vislightspec.htm



18

The band gap of the semiconductor material decides the wavelength of light

that meet the requirements to generate electrical energy. The conversion formula

between band gap and wavelength is:

)()(

eVEghcm =µλ

(1.3)

)(24.1)(eVEg

m =µλ (1.4)

Where λ is the wavelength in micrometers, h is Planck’s constant, c is the

speed of light in vacuum, and Eg is the band gap in eV. One eV is approximately

equal to 1.6x10-19 J of energy. In the case of Indium phosphate, the wavelength that

corresponds to 1.34 eV is 0.9253 μm.

Figure 1.14. visualizes the concept of light absorption. When light has energy

greater than 1.1 eV, the silicon solar cell generates electricity. Light with less than

1.1 eV of energy is unused. Likewise, light with energy greater than 1.43 eV excites

the outer shell electrons of the gallium arsenide solar cell. And lastly, light with

energy greater than 1.7 eV is useful for aluminum gallium arsenide photovoltaic

material (Baldomero Garcia, 2007: 19)


19

Figure 1.14. Effect of light energy on different band gaps, (Baldomero

Garcia, 2007: 19)

1.2.1.3. Solar Cell Junctions

The discussion in the previous section discussed the effect of light energy on

different band gaps. When treated individually, each of the photovoltaic materials

from Figure 1.14. would act as a single junction solar cell.

Nevertheless, to increase the efficiency of the solar cell, multiple junctions

can be created. For example, in Figure 1.14., the top junction is made up of

Aluminum Gallium Arsenide. This junction will absorb light energy greater than 1.7

eV. Any unused photons will be filtered through to the next junction. The gallium

arsenide junction will, as aresult, absorb the photons with energy greater than 1.4 eV.

The remaining photons will be absorbed by the silicon junction. (Baldomero Garcia,

2007: 20)

Although the above paragraph described the basics of a multijunction solar

cell, such device may not produce the desired results due to lattice mismatch. The

next section covers the basics of lattice matching.


20

1.2.1.4. Lattice Matching

Semiconductors are three-dimensional in their cell structure. The simple

cubic structure serves to illustrate the concept of lattice and is shown in Figure 1.15.

Figure 1.15. Simple cubic lattice structure (http://en.wikipedia.org/wiki/File:Lattic_simple_cubic.svg)

Figure 1.15 shows that each side of the cube is represented by the letter “a”.

The separation “a” is the lattice constant. Each semiconductor material has a lattice

constant. Then, when creating multijunction solar cells, the lattices must be matched.

Figure 1.16 shows the lattice constants for several semiconductors. An

example given by P. Michalopoulos (Michalopoulous, 2002: 87) shows how to

lattice match Indium Gallium Phosphide to Gallium Arsenide.

http://en.wikipedia.org/wiki/File:Lattic_simple_cubic.svg


21

Figure 1.16. Lattice constants (Michalopoulous, 2002: 87)

The alloy Indium Gallium Phosphide consists of x parts of Gallium

phosphide and 1-x parts of Indium Phosphide. As a result, Indium Gallium

Phosphide is represented as In1-xGaxP.

GaAs has a lattice constant α=5.65Å, GaP has α=5.45Å and InP has α=5.87Å.

The goal is to create InGaP with a lattice constant that matches that of GaAs. The

formula to find x is given as:

InPGaP

InPGaAsInPGaPGaAs xxx

αααα

ααα−−

=⇔−+= )1.(. (1.5)

With x ≅ 0.52, In0.48Ga0.52P has α=5.65Å. A rough approximation of the

resulting band gap of In0.48Ga0.52P is given as follows:


22

InPG

GaPG

InGaPG ExxEE )1( −+= (1.6)

The equation gives a band gap of 1.9 eV for In0.48Ga0.52P. So, a dual-junction

solar cell of InGaP at 1.9 eV and GaAs at 1.4 eV can be built. (Baldomero Garcia,

2007: 21-22)

1.2.1.5. AM0 Spectrum

The place of the solar cell affects the input solar radiation spectrum. A solar

cell on Mars gets a different (smaller) spectrum than a solar cell on a satellite that

orbits Earth. The energy received outside Earth’s atmosphere is approximately 1365

W/m2. This spectrum is called Air Mass Zero or AM0. Terrestrial solar cells have to

deal with the reduction of the solar spectrum due to Earth’s atmosphere. This solar

spectrum is called AM1.5. For the purposes of this study, AM0 is used during

simulations.

Figures 1.17. and 1.18. show the AM0 spectrum with respect to wavelength

and energy, respectively. From Figure 1.18., we can see that semiconductor materials

with band gaps of less than 4 eV can extract most of the solar spectrum. (Baldomero

Garcia, 2007: 23)


23

Figure 1.17. AM0 spectrum (Wavelength vs Irradiance)

(http://rredc.nrel.gov/solar/spectra/am0)

Figure 1.18. AM0 spectrum (Energy vs Irradiance)

(http://rredc.nrel.gov/solar/spectra/am0)

http://rredc.nrel.gov/solar/spectra/am0

http://rredc.nrel.gov/solar/spectra/am0


24

1.2.1.6. Current-Voltage Curves

A typical solar cell current-voltage (IV) curve is presented in Figure 1.19.

Figure 1.19. Sample IV curve used in efficiency calculations (GRAY, 2003:

12).

From Figure 1.19., there are several points of interest. The short circuit

current (ISC) occurs when the voltage is zero. This is the peak value current. The

open circuit voltage (VOC) occurs when the current is zero. This is the highest

voltage. The dimensions of the larger rectangle in Figure 1.19. are determined by

VOC and ISC. Since power (P) is determined by the product of current times voltage,

the maximum power point occurs at (VMP,IMP).

The calculations for solar cell efficiency are as follows:

The point in the I-V curve where the product of the voltage and the current is

at its peak is called the maximum power point. It is Pmax = Vmax.Imax.


25

mpmpVIP =max (1.7)

Fill factor is the measure of the squareness of the I-V curve. It is defined as

follows,

ocsc

mpmp

ocsc VIVI

VIPFF == max (1.8)

Power conversion efficiency (PCE) is the proportion of the maximum power

obtained to the power input.

in

mpmp

in PVI

PP

== maxη (1.9)

Where Pmax is the maximum power point, FF is the fill factor, and η is the

efficiency. The fill factor measures the “squareness” of the IV curve.

1.2.1.7. Electrical Output

A solar cell is a p-n junction photodiode. In order to obtain the IV

characteristic of the solar cell, the dark current needs to be subtracted from the

photogenerated current.

DL III −= (1.10)

The dark current is the current through the solar cell when bias is applied in

the dark (Nelson, 2003: 30).

Graphically, the IV characteristic is obtained in Figure 1.20.


26

Figure 1.20. Solar cell IV characteristic (Baldomero Garcia, 2007: 26)

1.3. Heterojunctions

We call a junction created by the same semiconductive material

homojunction. As both sides of the junction have the same lattice constant, smooth

chemical bonds in the interface area is formed by the crystal atoms. Homojunctions

of materials with the same type of conductivity (p– or n–type) are called isotype

while those with a different one are called anisotype.

We call junctions created using different materials heterojunctions. Since

now the lattice constants do not match, the atoms create chemical bonds in the

heterointerface by adjusting their positions. This creates strain and causes crystal

dislocations and structure defects in depth. This will increase carrier scattering and

hence decrease their mobility. Additionally, atoms with dangling bonds will form

carrier traps acting as recombination centers, which will decrease carrier lifetime

(Figure 1.21).


27

Figure 1.21. Crystal dislocation in heterojunction (Michalopoulous, 2002: 45)

Then, materials with similar lattice constants are used, like GaAs with AlAs.

The use of ternary compounds, like GaP + InP, is also recommended, as their

proportion can adjust their lattice constant to the necessary levels. (GaP)0.51(InP)0.49

≡Ga0.51In0.49P is matched to GaAs (Michalopoulous, 2002: 45).

From an energy point of view, the formation of the heterointerface uses the

vacuum and Fermi energy levels is illustrated in Figure 1.22.


28

Figure 1.22.Band diagram of heterojunction formations (Michalopoulous, 2002: 46)

We have proposed the use of heterostructure films on porous Si. The

microscopic islands and grooves of the Si surface relieve the strains and reduce

dislocations. Finally, the use of alternative, very thin layers, of the two materials is

called superlattice and is known not only to reduce the formation of dislocations, but

increase the carrier mobility of the device. For instance, GaAs has a bandgap of

1.42eV and Al0.3Ga0.7As has 1.72eV. Their difference is 0.3eV. The process used to

produce such precisely thin layers is called molecular beam epitaxy (MOCVD). The

undoped structure will seem like in figure 1.23a. Si can be used to dope the AlGaAs

and make it n–type while the GaAs stays undoped. This will raise the Fermi level

and change the energy diagram like in figure 1.23b. Electrons from the donor (Si) in

AlGaAs will move into the GaAs layers for their lower energy conduction band.

Now the donor atoms that would cause carrier scattering are separated from the


29

carriers (Figure 1.23), hence the electron mobility in GaAs is increased. This increase

is far bigger than that of the bulk material and thus the carrier mobility is

significantly improved.

Figure 1.23.Band diagram of superlattice formation (a) undoped and b)

AlGaAs doped (SZE, 1981: 128)

Important heterojunction applications are photonic devices like

photodetectors, photodiodes, semiconductor lasers and solar cells.


30

2. PREVIOUS WORK Faruk KÜRKER

31

2. PREVIOUS WORK

This research is related to a Naval Postgraduate School thesis completed in

March 2002 by Panayiotis Michalopoulos titled “A Novel Approach for the

Development and Optimization of State-of-the-art Photovoltaic Devices Using

Silvaco“ and in June 2007 by Baldomero Garcia, Jr. titled “Indium Gallium Nitride

Multijunction Solar Cell Simulation Using Silvaco Atlas”.

Previous Silvaco Atlas solar cell simulations have been performed by Naval

Postgraduate School researchers. Michalopoulos investigated the feasibility of

designing solar cells using Silvaco Atlas. To demonstrate the use of Silvaco Atlas,

Michalopoulos simulated single-junction solar cells with Gallium Arsenide, dual-

junction solar cells with Indium Gallium Phosphide and Gallium Arsenide, and

triplejunction cells with Indium Gallium Phosphide, Gallium Arsenide, and

Germanium. The highest efficiency obtained with the triple-junction was 29,5%.

This result matched the 29,3% efficiency obtained with actual triple-junction solar

cells in production.

Green followed Michalopoulos’s work by simulating a quad-junction solar

cell. Realizing the complexity and the number of possible variables the make a multi-

junction solar cell, Bates developed an algorithm to further optimize Michalopoulos

and Green’s work. Bates also demonstrated that a solar cell can be optimized based

on environmental factors, specifically an optimal cell for the Martian light spectrum.

Bates provided excellent background on the use of Silvaco Atlas. Green,

Canfield and Baldomero Garcia continued to work on Silvaco Atlas solar cell design.

Jeffrey Lavery, Sheriff Michael's had done in 2008, "Quantum Tunnelling In

Model Of A PN Junction Silvaco" study named research is to accurately model the

tunnel junction interconnect within a multi-junction photovoltaic cell.

According to study results it is possible to model such effects as quantum

tunnelling in a photovoltaic solar cell. To this point, the tunnel junction in a multi-

junction cell was modelled as a vacuum to insulate the layers, then hardwired to pass

the current between cells. Although this is effective, the cell being modelled is not

fully optimized.


32

Agui and Takamoto experimental result were obtained, which data for an

InGaP/GaAs photovoltaic cell produced a VOC = 2.488V and an ISC = 23mA/cm2

(AGUI and TAKAMOTO, 1998).

Lavery’s’s thesis has reached the following ISC and VOC values. VOC = 2.5V

and an ISC = 22mA/cm2 with a FF = 84% and η = 29% (Figure 2.1).

Figure 2.1. Optimized multi-junction solar cell (InGaP/GaAs) I-V curve. (A/cm2 versus voltage)

Delfina Muñoz Cervantes and Cristóbal Voz Sánchez’s had done in 2008,

“Silicon heterojunction solar cells obtained by Hot-Wire CVD” study named

research the possibility to fabricate a-Si:H/c-Si heterojunction devices by Hot-Wire

Chemical Vapor Deposition (HWCVD) has been demonstrated. Finally, we have

also started the research of heterojunction solar cells on n-type c-Si substrates. The

best structure obtained on p-type substrates was symmetrically replicated on n-type

wafers. Then, preliminary heterojunction solar cells on n-type substrates reached

promising efficiencies up to 10.7%. The JV characteristics of bifacial solar cells on

p- and n-type wafers have also been measured for illumination from the rear side. A

slight response is obtained in both cases with Voc over 200 mV, moderated Jsc

around 10 mA×cm-2 and FF around 25%.


33

Baldomero Garcia and Sheriff Michael's had done in 2007, “Indium Gallium

Nitride Multijunction Solar Cell Simulation Using Silvaco Atlas” study named

research is investigates the potential use of wurtzite Indium Gallium Nitride as

photovoltaic material. Silvaco Atlas was used to simulate a quad-junction solar cell.

Each of the junctions was made up of Indium Gallium Nitride. The band gap of each

junction was dependent on the composition percentage of Indium Nitride and

Gallium Nitride within Indium Gallium Nitride. This research shows that Indium

Gallium Nitride is a promising semiconductor for solar cell use.

Baldomero Garcia’s thesis has reached the following ISC and VOC values. VOC

= 4.98 V and an ISC = 12.88 mA/cm2 with a FF = 88.06 % and η = 43.62 % ( Figure

2.2).

Figure 2.2. Quad-junction InGaN solar cell IV curve

Michael H. Sanders and Sheriff Michael's had done in 2007, “Modeling Of

Operating Temperature Performance Of Triple Junction Solar Cells Using Sılvaco’s

Atlas” study named research utilizes Silvaco’s ATLAS software as a tool to simulate

the performance of a typical InGaP/GaAs/Ge multi-junction solar cell at various

temperatures. Additional optimization is performed on the base thickness layers to

represent that enhancement for the proper operating environment can be achieved.


34

Results are shown for a multi-junction cell operating under Air Mass 0 at 300K,

325K, 350K, and 375K.

Michael H. Sanders’s thesis has reached the following Pmax value.

Pmax=41.7388 mW/cm2 ( Figure 2.3).

Figure 2.3. I-V curve based on new bases discovered in smaller iteration test at 300K.

William Alexander Gibson, Todd R. Weatherford’s had done in 2007,

“Comparison of Gallium Nitride High Electron Mobility Transistors Modeling In

Two and Three Dimensions” study named research looks at modeling Gallium

Nitride (GaN) High Electron Mobility Transistor (HEMT) Semiconductors. The GaN

device has potential future military use in the high power and high frequency

operation replacing costly millimeter wave tubes. This would affect military radar

systems, electronic surveillance systems, communications systems and high voltage

power systems by providing smaller and more reliable devices to drive operation.

The result of the HEMT device was modeled using Silvaco software package and

compared to an actual device on sapphire substrate. The HEMT modeling was done

in two and three dimension modeling software. Finally the software model showed

the improved thermal characteristics of the HEMT device on the diamond substrate

over that of the sapphire.


35

Panayiotis Michalopoulos and Sheriff Michael's had done in 2002, “A Novel

Approach For The Development And Optimization Of State-Of-The-Art Photovoltaic

Devices Using Silvaco” study named research a new method for developing realistic

simulation models of advanced solar cells is presented. Several electrical and optical

properties of exotic materials, used in such designs, are researched and calculated.

Additional software has been developed to facilitate and enhance the modeling

process. Furthermore, specific models of an InGaP/GaAs and of an InGaP/GaAs/Ge

multi-junction solar cells are prepared and are fully simulated. Finally, additional

optimization is performed on the last state–of–the–art cell, to further improve its

efficiency. The flexibility of the proposed methodology is demonstrated and example

results are shown throughout the whole process.

Panayiotis Michalopoulos’s thesis has reached the following ISC and VOC

values. VOC = 2.655V and ISC = 17.6mA/cm2 (Figure 2.4).

Figure 2.4. IV characteristic of the prototype triple MJ cell. (experimental data KING and FRIENDS, 2000)

Darin J. McCloy and Sheriff Michael's had done in 1999, “High Efficiency

Solar Cells: A Model in Silvaco” study named research develops a model in Silvaco

International's Virtual Wafer Fabrication (VWF) environment to assist advanced


36

solar celi developers in designing more efficient solar cells intended for use in space.

The complete model is intended to accurately predict the properties and

characteristics of an existing state-of-the art multiple junction solar celi. It was

concluded that Celi thickness was increased and decreased. The expected results in

the increased thickness case would be less current "collection" due to more electron

hole pair recombination. The total effect this would have on current at the cathode

would be determined by diffusion length and carrier lifetime.

Darin J. McCloy’s thesis has reached the following ISC and VOC values. (

Figure 2.5).

Figure 2.5. IV characteristic of Si solar cell.

Orlando Marvin Erickson's had done in 1989, “Analysis of Degradation

Mechanisms In Thin Film Cdte-Cds Heterojunction Solar Cells” study named

research a currently existing theory will be expanded and used to run simulations of

actual cells. The simulations will be compared to actual cells to determine the

validity of the theory and to propose methods for increasing cell lifetimes. This

modeled the cell first as metal / semiconductor then changed it to a metal / insulator /

semiconductor (MIS) contact. Simulations and the actual degraded cells it was seen


37

that the two correlated. Thus the MIS contact model appeared to be a correct theory for

our cell degradation.

The following articles were also written.

Sheriff Michael and Andrew Bates’s was written in 2004, “The Design And

Optimization of Advanced Multijunction Solar Cells Using The Silvaco ATLAS

Software Package” named in the article the design and optimization of advanced

multijunction photovoltaic devices, utilizing a newly introduced modelling technique

(J. Sol. Energy Mater. Sol. Cells, submitted for publication), is demonstrated. Also a

model of an InGaP/GaAs/InGaNAs/Ge four-junction solar cell is prepared and is

fully simulated. The major stages of the process are explained and the simulation

results are compared to published theoretical and experimental data. Below and as a

result of current-voltage characteristics were obtained.

Sheriff Michael and Andrew Bates article’s have reached the following ISC

and VOC values ( Figure 2.6).

Figure. 2.6. I-V characteristics of InGaP/GaAs/InGaNAs/Ge cell (MICHAEL and GREEN, 2003)


38

Michael H. Tsutagawa and Sherif Michael’s was written in 2009, “Trıple

Junctıon Ingap/Gaas/Ge Solar Cell Optımızatıon: the Desıgn Parameters for a

36.2% Effıcıent Space Cell Usıng Sılvaco Atlas Modelıng & Sımulatıon” named in

the article the design parameters for a triple junction InGaP/GaAs/Ge space solar cell

with a simulated maximum efficiency of 36.28% using Silvaco ATLAS Virtual

Wafer Fabrication tool. Design parameters include the layer material, doping

concentration, and thicknesses. An initial dual junction InGaP/GaAs model of a

known Japanese solar cell was constructed in Silvaco ATLAS to an accuracy of less

than 2% with known experimental Voe and Jse performance results, validating the

use of computer modeling to accurately predict solar cell performance. As a result of

Computer simulation and modeling of solar cell design appears to be a feasible way

to improve the speed and effectiveness of multi-junction solar cell design. The use of

genetic algorithm to find “the fittest” solution for doping concentrations and layer

thicknesses will aid in searching the vast solution space for the optimal design

parameters for high-efficiency solar cells. However, without the actual fabrication

and testing of these new cell designs, validation of these computer models and

simulations cannot be achieved nor trusted.

Michael H. Tsutagawa and Sherif Michael article’s have reached the

following ISC and VOC values. VOC = 2.76425 V and an ISC = 19.8531 mA/cm2 with a

FF = 89.453 % and η = 89.453 % ( Figure 2.7).


39

Figure. 2.7. I-V Curve of 36.28% 3J (0.82 µm InGaP/ 3.9 µm GaAs/ Ge) Cell Model using Improved Genetic Algorithm Design Parameters, AMO.

Masafumi Yamaguchi, Ken-Ichi Nishimura, Takuo Sasaki, Hidetoshi Suzuki,

Kouji Arafune, Nobuaki Kojima, Yoshio Ohsita, Yoshitaka Okada, Akio Yamamoto,

Tatsuya Takamoto and Kenji Araki’s was written in 2008, “Novel materials for high-

efficiency III–V multi-junction solar cells” named in the article developed high

efficiency (38.9% at 489-suns AM1.5G) InGaP/InGaP/Ge 3-junction solar cells and

large-area (5.445 cm2) 3-junction concentrator cell modules with an efficiency of

28.9%.

Masafumi Yamaguchi and Friends article’s have reached the following ISC

and VOC values. VOC = 0.73 V and an ISC = 22.57 mA/cm2 with a FF = 68 % and η =

11.27 % (Figure 2.8).


40

Figure. 2.8.Current–voltage curve of a p-GaAs/i-n InGaAsN hetero-junction cell with intrinsic layer width of 600 nm.

3.MATERIAL AND METHOD Faruk KÜRKER

41

3. MATERIAL AND METHOD

This section present an introduction to material properties and silvaco

atlas, the structure of the input files, and some of its statements.

3.1. Materials

Optical properties of materials used in this thesis are given below.

Symbol Unit Description

TAUN(τn) s Electron lifetimes

TAUP (τp) s Hole lifetimes

COPT cm3 s-1 Radiative recombination rate

AUGN(Cn ) cm6 s-1 Electron Auger coefficients

AUGP(Cp ) cm6 s-1 Hole Auger coefficients

EG300 eV Bandgap at 300K

PERMITTIVITY - Dielectric constant (static)

AFFINITY eV Electron affinity

MUN cm2V-1s-1 Electron motilities

MUP cm2V-1s-1 Hole motilities

NC300=2.77e19 cm-3 Electron density of states

(Effective conduction band

density of states )

NV300= 1.615e18 cm-3 Hole density of states

(Effective valence band density

of states)

Index.file=AlGaAs.opt Optical parameters n(refractive

index) and k(absorption index)


42

Table 3.1. Material Defaults for Semiconductors (http://www.ioffe.ru/ SVA/NSM/Semicond/)

Material Ge InP InGaAs AlGaAs x095

AlInGaP (=InAlAsP)

TAUN 1.0e-3 3e-6 1 1e-9 1e-7 s TAUP 1.0e-3 2e-9 1 1e-8 1e-7 s COPT 6.41e-14 1.2e-10 0 1.8e-10 1.5e-10 cm3 s-1 AUGN 1.0e-30 9.0e-31 0 5.0e-30 8.3e-32 cm6 s-1 AUGP 1.0e-30 9.0e-31 0 1e-31 1.8e-31 cm6 s-1 EG300 0.661 1.344 0.571 2.14 2.4 eV PERMITTIVITY 16.2 12.5 14.2 10.202 11.7

AFFINITY 4 4.38 4.13 3.507 4.2 eV MUN 3900 5400 256.15 2150 cm2V-1s-1 MUP 1900 200 116.35 141 cm2V-1s-1 NC300 1.0e19 5.7e17 1.15e17 2.77e19 1.2e20 cm-3 NV300 5.0e18 1.1e19 8.12e18 1.615e18 1.28e19 cm-3

3.1.1. Ge (Germanium)

3.1.1.1.Basic Information about Ge

Germanium is IVA group of element. Basic information and atomic

structure about Germanium are given below.

Germanium is a chemical element with the symbol Ge and atomic number

32, atomic mass 72.61 amu, number of protons/electrons 32 and number of

neutrons 41. Classification is metalloid, crystal structure cubic and color grayish.

Germanium has 4 valance electrons. (http://www.chemicalelements.com/elements

/ge.html)

The optical properties of germanium elements are given below.

# Vacuum

material material=Vacuum real.index=3.3 imag.index=0

# Ge material TAUN=1e-3 TAUP=1e-3 COPT=6.41e-14 AUGN=1.0e-31 AUGP=1.0e-31

material material=Ge EG300=0.661 PERMITTIVITY=16.2 AFFINITY=4

material material=Ge MUN=3900 MUP=1900

http://www.ioffe.ru/

http://www.chemicalelements.com/


43

material material=Ge NC300=1.0e19 NV300=5.0e18

material material=Ge index.file=Ge.opt (http://www.ioffe.ru/SVA/NSM/

Semicond/)

N and k data base of Germanium in figure 3.1.

Figure 3.1. N and k data base of Germanium

(http://www.ioffe.ru/SVA/ NSM/Semicond/)

Germanium is an indirect semiconductor. Thus to make transitions from

the valence band to the conduction band with the least amount of energy an

electron must absorb a photon and a phonon.

Indirect Bandgap- .70 eV at 77K

Direct Bandgap- .881eV at 77K (http://www.physics.purdue.edu/

research/ugrad_rsch/maccall/)

http://www.ioffe.ru/SVA/NSM/

http://www.ioffe.ru/SVA/

http://www.physics.purdue


44

Figure 3.2. Direct Bandgap- .881eV at 77K

Indirect Bandgap- .70 eV at 77K (http://www.physics.purdue.edu/research/ugrad_rsch/maccall)

http://www.physics.purd


45

Figure 3.3.The temperature dependence of the intrinsic carrier concentration ni. (http://www.ioffe.ru/SVA/NSM/Semicond/)

Dashed line shows Fermi level dependence versus temperature for intrinsic

Ge.

Figure 3.4. Fermi level versus temperature for different concentrations of

shallow donors and acceptors. (http://www.ioffe.ru/SVA/NSM /Semicond/)


http://www.ioffe.ru/SVA/NSM


46

3.1.2. InP (Indium Phosphorus)

3.1.2.1.Basic Information about Indium

Indium is IIIA group of element. Basic information and atomic structure

about Indium are given below.

Indium is a chemical element with chemical symbol In and atomic number

49, atomic mass 114.818 amu, number of protons/electrons 49 and number of

neutrons 66. Classification is other metals, crystal structure tetragonal and color

silveris. Indium has 3 valance electrons. (http://www.chemicalelements.com/

elements/in.html)

3.1.2.2.Basic Information about Phosphorus

Phosphorus is VA group of element. Basic information and atomic

structure about Phosphorus are given below.

Phosphorus is the chemical element that has the symbol P and atomic

number 15., atomic mass 30.97376 amu, number of protons/electrons 15 and

number of neutrons 16. Classification is non-metal, crystal structure monoclinic

and color white. Phosphorus has 5 valance electrons. (http://www.

chemicalelements .com/elements/p.html)

The optical properties of InP compounds are given below.

# Vacuum


# InP material TAUN=3e-6 TAUP=2e-9 COPT=1.2e-10 AUGN=9.0e-31 AUGP=9.0e-31

material material=InP EG300=1.344 PERMITTIVITY=12.5 AFFINITY=4

material material=InP MUN=5400 MUP=200

material material=InP NC300=5.7e17 NV300=1.1e19

http://www.chemical


47

material material=InP index.file=InP.opt (http://www.ioffe.ru/SVA/NSM

/Semicond/)

N and k data base of Indium Phosphorus in figure 3.5.

Figure 3.5. N and k data base of Indium Phosphorus

(http://www.ioffe.ru/SVA/NSM/Semicond/)

Figure 3.6. The temperature dependence of the intrinsic carrier concentration ni.(http://www.ioffe.ru/SVA/NSM/Semicond)

http://www.i


http://www.ioffe.ru/SVA/NSM/Semicond


48

Figure 3.7. Fermi level versus temperature for different concentrations of shallow donors and acceptors. (http://www.ioffe.ru/SVA/NSM /Semicond/)

3.1.3. InGaAs (Indium Gallium Arsenic)

3.1.3.1.Basic Information about Gallium

Gallium is IIIA group of element. Basic information and atomic structure

about Indium are given below.

Gallium is a chemical element that has the symbol Ga and atomic number

31., atomic mass 69.723 amu , number of protons/electrons 31 and number of

neutrons 39. Classification is other metals, crystal structure orthorhombic and

color white/silver. Gallium has 3 valance electrons. (http://www.

chemicalelements.com/elements/ga.html)

3.1.3.2.Basic Information about Arsenic

Arsenic is VA group of element. Basic information and atomic structure

about Arsenic are given below.

http://www.ioffe.ru/SVA/NSM


49

Arsenic is the chemical element that has the symbol As, atomic number

33., atomic mass 74.9216 amu , number of protons/electrons 33 and number of

neutrons 42. Classification is metaloid, crystal structure rhombohedral and color

gray. Arsenic has 5 valance electrons. (http://www.chemicalelements.com

/elements/as.html)

The optical properties of InGaAs compounds are given below.

# Vacuum


# InGaAs

material TAUN=1 TAUP=1 COPT=0 AUGN=0 AUGP=0

material material=InGaAs EG300=0.571 PERMITTIVITY=14.2 AFFINITY=4.13

material material=InGaAs MUN=5400 MUP=200

material material=InGaAs NC300=1.15e17 NV300=8.12e18

material material=InGaAs index.file=InGaAs.opt (Atlas User’s Manual, 2005: B-

24)

3.1.4.AlGaAs (Aluminum Gallium Arsenic)

3.1.4.1.Basic Information about Aluminum

Aluminum is IIIA group of element. Basic information and atomic

structure about Aluminum are given below.

Aluminium or aluminum is a silvery white member of the boron group of

chemical elements. It has the symbol Al and its atomic number is 13, atomic mass

26.981539 amu, number of protons/electrons 13 and number of neutrons 14.

Classification is other metals, crystal structure cubic and color silver. Aluminium

has 3 valance electrons. (http://www.chemicalelements.com/elements/al.html)

# Vacuum


#AlGaAs

material TAUN=1e-9 TAUP=1e-8 COPT=1.8e-10 AUGN=5.0e-30 AUGP=1e-31

material material=InP EG300=2.14 PERMITTIVITY=10.202 AFFINITY=3.507

http://www.chemicalelements.com

http://www.chemicalelements.com/elemen


50

material material=InP MUN=256.15 MUP=116.35


material material=InP index.file=AlGaAs9.opt (http://www.ioffe.ru/SVA/NSM/

Semicond/)

N and k data base of Aluminum Gallium Arsenic in figure 3.8.

Figure 3.8. N and k data base of Aluminum Gallium Arsenic compounds. (http://www.ioffe.ru/SVA/NSM/Semicond/)

http://www.ioffe.ru/SVA/NSM/



51

Figure 3.9. The temperature dependence of the intrinsic carrier concentration ni. 1. x=0, 2. x=0.3, 3. x=0.6, 4. x=1. (http://www.ioffe.ru /SVA/NSM/Semicond/)

3.1.5. AlInGaP (=InAlAsP) (Aluminium Indium Gallium Phosphorus)

The optical properties of AlInGaP compounds are given below. material TAUN=1e-7 TAUP=1e-7 COPT=1.5e-10 AUGN=8.3e-32 AUGP=1.8e-31

# Vacuum


# AlInGaP (=InAlAsP)

material TAUN=1e-7 TAUP=1e-7 COPT=1.5e-10 AUGN=8.3e-32 AUGP=1.8e-31

material material=InAlAsP EG300=2.4 PERMITTIVITY=11.7 AFFINITY=4.2

material material=InAlAsP MUN=2150 MUP=141

material material=InAlAsP NC300=1.2e20 NV300=1.28e19

Because of AlInGAP optical data are not available , AlGaAs0 optical data

is used.

material material=InAlAsP index.file= AlGaAs0.opt (Michalopoulous, 2002)

http://www.ioffe.ru


52

3.2. TCAD Simulation Environment

Silvaco is a company that specializes in the creation of simulation software

and targets almost every aspect of modern electronic design. The company

provides modeling and simulation capabilities from simple Spice–type circuits all

the way to detailed VLSI fabrication in their TCAD suite of tools (Figure 3.10).

They use user–friendly environments to facilitate design and a vast number of

different modeling options. The tools provide for creating complex models and

3D structural views.

The phenomena modeled range from simple electrical conductivity to

thermal analysis, radiation and laser effects with a wide variety of detailed layer-

growth processes and material properties (e.g. mobilities, recombination

parameters, ionization coefficients, optical parameters) add to the preciseness of

the simulation. However, there is no publicly available documentation of efforts

done by researchers or solar cell manufacturers to make use of this powerful tool

for the modeling of advanced solar cells, but only of simple structures so far.


53

Figure 3.10. Silvaco’s TCAD suite of tools (http://www.silvaco.com)

http://www.silvaco.com


54

To obtain this purpose, Atlas is a good combination of sophisticated in–

depth device analysis in 2D or 3D. In addition to that, it alters the focus on the

modeler of the actual design and exterminates all fabrication details. Like the rest

of TCAD applications, it is based on hundreds of widely accepted publications,

and numerious researches have verified their accuracy and correctness (Atlas

User’s Manual: 1-4)

3.2. 1. Silvaco Atlas Simulation Software

This thesis uses Silvaco Atlas to perform solar cell modeling.

In this thesis, Silvaco Atlas was extensively used. The DeckBuild run-time

environment received the input files. Within the input files, Silvaco Atlas was

called to execute the code. And finally, to view the output of the simulation

TonyPlot was used. Additionally, output log files were produced. The inputs and

outputs for Silvaco Atlas are depicted in Figure 3.11.

Figure 3.11. Atlas inputs and outputs (Atlas User’s Manual, 2005: 2-2)


55

3.2.2. Silvaco Atlas

Atlas is a software program that simulates two and three-dimensional

semiconductor devices. The physical models included in Atlas are presented in

Table 3.2.

Table 3.2. Silvaco Atlas physical models (Atlas User’s Manual, 2005: 1-2)

3.2.3. Input File Structure

Silvaco Atlas receives input files through DeckBuild. When we enter a

code in, Atlas is called by the input file to run with the following command:


56

go atlas

Following that command, the input file needs to follow a pattern. In Figure

3.12. the command groups are listed.

Figure 3.12. Atlas command groups and primary statements (Atlas User’s Manual, 2005: 2-8)

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 (\) continues the


57

code in the next line. Parameters, such as UNIFORM, are logical. Unless a TRUE

or FALSE value is assigned, the parameter is designated the default value. This

value can be either TRUE or FALSE. The Silvaco Atlas manual needs to be

admitted to identify the default value assigned to specific parameters.

3.3. Structure Specification

The structure specification is obtained by identifying 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 3.13., the mesh statements are indicated.

Figure 3.13. Atlas mesh (Bates, 2004: 18)

The general format to define the mesh is:

X.MESH LOCATION=<VALUE> SPACING=<VALUE>


58

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.

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 3.14, 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.


59

Figure 3.14. Atlas region (Bates, 2004: 19)

From Figure 3.15., the code defines the material for each region. Note that

the color coding identifies the material. The regions have vertical and horizontal

lines to mark their boundaries.

Figure 3.15. Atlas regions with materials defined (Bates, 2004: 19)


60

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 3.16., 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 xrange at y=0.

Figure 3.16. Atlas electrodes (Bates, 2004: 20)


61

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>

From Figure 3.17., the doping types and the doping levels are defined.

Doping can be n-type or p-type. The distribution type can be uniform or Gaussian.

Figure 3.17. Atlas doping (Bates, 2004: 21)

3.3.5. Materials Model Specification

After the structure specification, the materials model specification is next.

From Figure 3.18., the materials model specification is broken down into material,

models, contact, and interface.


62

Figure 3.18. Atlas material models specification (Atlas User’s Manual, 2005: 2-8)

3.3.5.1. 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

In all examples, when MATERIAL appears first, it is considered as the

statement. When MATERIAL appears a second time in the first example, it is

considered as a localization parameter. In the second and third examples, the

localization parameters are REGION and NAME, respectively. Various other

parameters can be defined as 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.

3.3.6. Models

The physical models fall into five categories: mobility, recombination,

carrier statistics, impact ionization, and tunneling. The syntax of the model

statement is as follows:


63

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.

3.3.7. Light

When the lighting is important for a device (like in solar cells), there is the

ability to use a number of light sources and adjust their location, orientation and

intensity. The spectrum of the light can be described in all the necessary detail.

Polarization, reflectivity and raytrace are also among the simulator’s features.

3.3.8. 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

3.3.9. Numerical Method Selection

After the materials model specification, the numerical method selection

must be specified. From Figure 3.19., the only statement that applies to numerical

method selection is the method.


64

Figure 3.19. Atlas numerical method selection (Atlas User’s Manual,

2005: 2-8)

There are several numerical methods to calculate solutions to

semiconductor device problems. Three types of solution techniques are 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 till 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 when there is linear convergence. The NEWTON method is used

when equations are strongly coupled with a 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 will not achieved, then the equations should not be solved using the

NEWTON method.


65

3.3.10. Solution Specification

After completing the numerical method selection, the next step is the

solution specification. Solution specification is broken down into log, solve, load,

and save statements, as shown in Figure 3.20.

Figure 3.20. Atlas solution specification (Atlas User’s Manual, 2005: 2-8)

3.3.10.1. 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.

3.3.10.2 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.


66

BEAM is the beam number of the optical beam during AC photogeneration

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 photogeneration

analysis. MULT.F is the frequency to be multiplied by FSTEP. NFSTEPS is the

number of times that the frequency is incremented by FSTEP.

3.3.10.3. 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

3.3.11. 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, as shown in Figure

3.21.

Figure 3.21. Atlas results analysis (Atlas User’s Manual, 2005: 2-8)


67

In the example below, the EXTRACT statement obtains the current and

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

Figure 3.22. shows the sample IV curve plotted by TonyPlot.

Figure 3.22. Sample TonyPlot IV curve


68

3.4. Simple Simulation Source Code

All source codes programming the simulations which will be mentioned in

the following chapters are indicated in Appendix F. In order to intensify the

understanding, to help further development by others and to prevent unnecessary

repetitions and confusion, the following scheme used to present the code. All the

files contain main sections structured in the same way:

go atlas # Definition of constants # Mesh # X-Mesh # Y-Mesh # Regions # Electrodes # Doping # Material properties # Models # Light beams # Solving

Each commented section is filled using code from its corresponding

subsections. For example for deriving the ISC and VOC of a simple InP cell, the

code becomes:

go atlas

# Definition of constants

# Mesh

mesh space.mult=1

# X-Mesh: surface=500 um2 = 1/200,000 cm2

x.mesh loc=-250 spac=50

x.mesh loc=0 spac=10


# Y-Mesh

# Vacuum


69

y.mesh loc=-0.1 spac=0.01

# Emitter (0.1 um)

y.mesh loc=0 spac=0.01

# Base (3 um)


# Regions

# Emitter

region num=1 material=InP x.min=-250 x.max=250 y.min=-0.1 y.max=0

# Base

region num=2 material=InP x.min=-250 x.max=250 y.min=0 y.max=3

# Electrodes

electrode name=cathode top

electrode name=anode bottom

# Doping

# Emitter

doping uniform region=1 n.type conc=2e18

# Base

doping uniform region=2 p.type conc=1e17

# Material properties


# InP

material material=InP EG300=1.344 PERMITTIVITY=12.5 AFFINITY=3.75



material material=InP index.file=InP.opt

# Models

models BBT.KL

# Light beams

beam num=1 x.origin=0 y.origin=-5 angle=90 \

power.file=AM0silv.spec wavel.start=0.21 wavel.end=4 wavel.num=50

# Solving

# Get Isc and Voc

solve init

solve b1=1


70

contact name=cathode current

solve icathode=0 b1=1

3.4.1. Silvaco Library

Silvaco maintains a property library of many materials common to

electronic devices. However, in order to push solar cell efficiency to higher levels,

researchers tend to use many exotic materials. For this purpose, Silvaco’s library

is uneffecieint since it isunder development and mostly incomplete.

The models used in this thesis are heavily dependent on the following

properties:

· Bandgap Eg (Eg-eV)

· Electron and hole density of states (Effective conduction band density of

states- Effective valence band density of states) NC (cm -3) and NV (cm-3)

· Electron and hole motilities MUN (cm2V-1s-1) and MUP (cm2V-1s-1)

· Lattice constant (a- Å)

· Permittivity (Dielectric constant (static))

· Electron and hole lifetimes TAUN (τn-s) and TAUP (τp-s)

· Electron affinity (c - eV)

· Radiative recombination rate COPT(cm3 s-1)

· Electron and hole Auger coefficients AUGN (Cn-cm6 s-1) and AUGP(Cp-

cm6 s-1)

· Optical parameters n (refractive index) and k (absorption index)

Values for most of these stated above have been provided by various

publications( burada alınan calısmaların belirtilmesi gerekebilir). As another part

of this thesis, a large number of such publications were analyzed. This collection

of information set has been identified, categorized and compared. Finally, the best

were selected and used in the simulations described in this thesis. Parameters, for

materials which were not found in publications, were mathematically

approximated. In addition, several wellstudied cells were also used as references

to provide calibration for these unknown values.

4.RESEARCH AND DISCUSSION Faruk KÜRKER

71

4. RESEARCH AND DISCUSSION

4.1. The Simple InP Cell

A material used in solar cells is InP. It produces quite high current (ISC ≅

9.04 mA/cm2) and a voltage of VOC ≅ 0.82 V. On this first attempt, the cell will

have the basic n–on–p structure shown in Figure 4.1:

Figure 4.1. Simple InP cell.

Isc = 4.52e-008*2.0e05 = 9.04e-3 µA/cm2 = 9.04 mA/cm2,

Voc=0.82 V.


72

Firstly, the mesh (Figure 4.2-4.3) is formed, taking special care to make it

denser near the junction and to have enough divisions per layer.

Figure 4.2. The mesh

Figure 4.3. Mesh defined for the InP whole, top and bottom.


73

Net Doping is shown in Figure 4.4 and the layer structure of the InP is

shown in Figure 4.5.

Figure 4.4. Net Doping for the InP

Figure 4.5. The layer structure of the InP.


74

The point in the I-V curve where the product of the voltage and the current

is at its peak is called the maximum power point. It is Pmax = Vmax.Imax. According

to IV curve of InP.

Imp ≅ 4.25e-8*2e5=9.5e-03 µA/cm2 = 9.5 mA/cm2,

Vmp ≅ 0.73 V

The point in the I-V curve where the product of the voltage and the current

is at its peak is called the maximum power point. It is Pmax = Vmax.Imax.

mpmpVIP =max

Pmax = 9.5*0.73 = 6.935 mW/cm2 = 6.935e-03 W/cm2 = 69.35 W/m2

Fill factor is is defined as follows,

ocsc

mpmp

ocsc VIVI

VIPFF == max

FF = 6.935 / (9.04*0.82) = 0.935

Power conversion efficiency (PCE) is the proportion of the maximum

power obtained to the power input.

in

mpmp

in PVI

PP

== maxη

Pin= 1365 W/m2 from AM0,

η = 69.35/1365= 5.08 %


75

Figure 4.6. IV curve of InP.


76

4.2. HETEROJUNCTION CELL

A material used in solar cells are Heterojunction cell. Heterojunction cell

will have the structure shown in Figure 4.7. and 4.8.,

Figure 4.7. Heterojunction prototype


77

Figure 4.8. Heterojunction cell


78

Firstly, the mesh (Figure 4.9-4.10) is formed, taking special care to make it

denser near the junction and to have enough divisions per layer.

Figure 4.9. The mesh

Figure 4.10. Mesh defined for the heterojunction cell whole, top and bottom.


79

Net Doping is shown in Figure 4.11 and the layer structure of the

heterojunction cell is shown in Figure 4.12.

Figure 4.11. Net Doping for the heterojunction cell.

Figure 4.12. The layer structure of the heterojunction cell.


80

Figure 4.13. IV curve of heterojunction cell.

According to the figure 4.5, we can find Imax and Vmax points.

Imax ≅ Imp ≅ 1e-7*2e5=0.02,

Vmax ≅ 0.9,

Pmax = Imax*Vmax = Imp*Vmp,

Pmax ≅ 0.02*0.9 ≅ 0.018 W/cm2

Pin= 1365 W/m2 from AM0,

η=Pmax/Pin =(0.018 W/cm2)/(1365W/m2)= 0,131868=13,19 %

5.CONCLUSION Faruk KÜRKER

81

5. CONCLUSION

This thesis focused on the development of a solar cell model that

emphasizes the use of optical constants (refraction and extinction coefficients n

and k). The model used default settings for other parameters, such as permittivity,

affinity, radiative recombination rate, electron and hole lifetimes, electron and

hole density of states, and lattice constants. One area of future research is to

obtain measured data for the above parameters.

In this thesis a new solar cell structure is proposed. Unlike popular InGaP

and GaAs solar cells, InGaAs and InP structure is built in silvaco environment.

The designed solar cell is proposed for satellites. Space spectrum AM0 test is

done with 900 degrees for the solar cell.

13-15% range efficieny is obtained from the simulations.

5.CONCLUSION Faruk KÜRKER

82

83

REFERENCES

AGUI T., TAKAMOTO T., 1998. E. Ikeda, and H. Kurita, “High-efficient dual-

junctionInGaP/GaAs solar cells with improved tunnel interconnectt,”

Indium Phosphide and Related Materials, 1998 International Conference

on, pp 203-206.

Atlas User’s Manual, Silvaco International, 2005.

BALDOMERO GARCIA, Jr., 2007. Indium Gallium Nitride Multijunction Solar

Cell Simulation Using Silvaco Atlas, Master Of Thesis, Naval

Postgraduate School Monterey, California, USA.

BATES A. D., 2004. Novel optimization techniques for multijunction solar cell

design using Silvaco Atlas, Master’s Thesis, Naval Postgraduate School,

Monterey, California.

CANFIELD B. J., 2005. Advanced modeling of high temperature performance of

Indium Gallium Arsenide thermophotovoltaic cells, Master’s Thesis,

Naval Postgraduate School, Monterey, California.

Color Wavelength Table, Cited on 26 August 2010,


Electron Configuration, Cited on 25 August 2010,

http://en.wikipedia.org/wiki/Group_(periodic_table)

GRAY J. L., 2003. “The physics of the solar cell”, in Handbook of Photovoltaic

Science and Engineering, A. Luque and S.S. Hegedus, eds, p. 12, John

Wiley & Sons.

GREEN M., 2003. The verification of Silvaco as a solar cell simulation tool and the

design and optimization of a four-junction solar cell, Master’s Thesis,

Naval Postgraduate School, Monterey, California.

HEGEDUS S. S. and LUQUE A., 2003. “Status, trends, challenges and the bright

future of solar electricity from photovoltaics”, in Handbook of

Photovoltaic Science and Engineering, Luque, A. and Hegedus S.S., eds,

p. 12, John Wiley & Sons,

http://www.chemicalelements.com/elements/p.html, Cited on 08 September 2010


http://en.wikipedia.org/wiki/Group_(periodic_table)

http://www.chemicalelements.com/elements/p.html

84

http://www.physics.purdue.edu/research/ugrad_rsch/maccall/, Cited on 08 September

2010

JANSSEN R.. Introduction to polymer solar cells, Departments of Chemical

Engineering & Chemistry and Applied Physics, Eindhoven University of

Technology, The Netherlands.

KING R.R., KARAM N.H., ERMER J.H., HADDAD N., COLTER P., ISSHİKİ T.,

YOON H., COTAL H.L., JOSLIN D.E., KRUT D.D., SUDHARSANAN

R., EDMONDSON K., CAVICCHI B.T., LILLINGTON D.R., 2000 .

“Next-generation, high-efficiency III-V multijunction solar cells”,

Photovoltaic Specialists Conference. Conference Record of the Twenty-

Eighth IEEE , , pp. 998 -1001

Light Spectrum, Cited on 26 August 2010,

http://www.photobiology.info/Visser-Rolinski_files/Fig2.png

Light Energy Absorption With Respect To Band Gap, Cited on 26 August 2010.

http://www1.eere.energy.gov/solar/bandgap_energies.html

MICHALOPOULOUS P., 2002. A novel approach for the development and

optimization of state-of-the-art photovoltaic devices using Silvaco,

Master’s Thesis, Naval Postgraduate School, Monterey, California.

MICHAEL S., GREEN M., 2003. Innovative approach for the design and

optimization for multijunction photovoltaic devices, NCPV and Solar

Program Review Meeting.

National Renewable Energy (NREL) Air Mass Zero (AM0) solar spectrum, Cited on

01 September 2010,

http://rredc.nrel.gov/solar/spectra/am0/

NELSON J., 2003. The Physics of Solar Cells, Imperial College Press, London,

England.

Parameters Of Semiconductor Compounds atoms per cm3, Cited on 25 August 2010,


Periodic Table Of Elements, Cited on 25 August 2010,

http://www.nrc-cnrc.gc.ca/eng/education/elements/index.html

PIERRET R. F., 1996. Semiconductor Device Fundamentals,

http://www.physics.purdue.edu/research/ugrad_rsch/maccall/

http://www.photobiology.info/Visser

http://www1.eere.energy

http://www.ioffe.ru/SVA/NSM/Se

http://www.nrc

85

Addison-Wesley Publishing, Reading, Massachusetts, 1996.

POH B.N., 2002,.“Use of SILVACO TCAD Software For Teaching Silicon

Processing Technology “, Submitted for the degree of Bachelor of

Engineering (Honours) Electrical Engineering, Department of

Information Technology and Electrical Engineering University of

Queensland, Australia.

Science Help Online Chemistry Lesson 3-6 Electron Configuration, Cited on 25

August 2010,

http://www.fordhamprep.org/gcurran/sho/sho/lessons/lesson36.htm

Silicon Electron Shell Diagram, Cited on 25 August 2010,

http://commons.wikimedia.org/wiki/File:Electron_shell_014_silicon.png

SILVACO International, Cited on 26 August 2010,


Simple Cubic Lattice Structure, Cited on 26 August 2010,

http://en.wikipedia.org/wiki/File:Lattic_simple_cubic.svg

SZE S. M., 2001. Semiconductor Devices, 2nd edition, John Wiley & Sons, Inc,.

SZE, S. M., 1981. Physics of Semiconductor Devices, 2nd edition, John Wiley &

Sons, Inc,

UTSLER J., 2006. Genetic Algorithm Based Optimization Of Advanced Solar Cell

Designs Modeled In Silvaco Atlas, Master’s Thesis, Naval Postgraduate

School, Monterey, California.

http://www.fordhamprep.org/gcurran/sho/sho/lessons/lesson36.htm

http://commons.wikimedia.org/wiki/File:Electron_shell_014_silicon.png


87

CURRICULUM VITAE

Faruk KÜRKER was born in Adana, in 1975. He completed his elementary

educationat Sıdıka Sabancı Ilkokulu, Adana. He went to high school at Adana 19

Mayıs Lisesi, Adana. He completed this education in 1992. He graduated from

Department of Electrical Electronics Engineering, Gaziantep University in 2000. He

is married and has two children. His interest areas are automatic control systems, PLC…

89

APPENDIX Atlas Source Codes A. Simple Inp Cell Main Structure go atlas


# Mesh

# X-Mesh

# Y-Mesh

# Regions

# Electrodes

# Doping


# Models

# Light beams

# Solving

#Mesh and X-Mesh

mesh space.mult=1





#Y-Mesh

# Vacuum

90


# Emitter (0.1 um)


# Base (3 um)

y.mesh loc=1.5 spac=0.3


#Regions

# Emitter

region num=1 material=InP x.min=-250 x.max=250 y.min=-0.1 y.max=0

# Base

region num=2 material=InP x.min=-250 x.max=250 y.min=0 y.max=3

#Electrodes

electrode name=cathode x.min=-250 x.max=250 y.min=-0.1 y.max=-0.1

electrode name=anode x.min=-250 x.max=250 y.min=3 y.max=3

#Doping

# Emitter


# Base


#Material Properties

# Vacuum


# InP




91



#Models

models BBT.KL TATUN TRAP.TUNNEL

#Light Beams



struct outfile=zInP.str

tonyplot zInP.str

#Solving

solve init

method gummel newton maxtraps=10 itlimit=25

solve b1=0.9

## Getting Isc for I-V curve points

method newton maxtraps=10 itlimit=100

solve b1=0.95

extract name="isc" max(i."cathode")

set isc=$isc

set i1=$isc/10

set i2=$i1+$isc/10

set i3=$i2+$isc/10

set i4=$i3+$isc/10

set i5=$i4+$isc/10

set i6=$i5+$isc/20

set i7=$i6+$isc/20

set i8=$i7+$isc/20

set i9=$i8+$isc/20

92

set i10=$i9+$isc/20

set i11=$i10+$isc/40














set i25=$i24+$isc/80-0.00001

##

log outfile=zInP.log


solve b1=0.95

contact name=anode current


## Pmax points

solve ianode=-$i25 b1=0.95








93


















##

solve ianode=0 b1=0.95

log off

extract name="iv" curve(v."anode", i."cathode") outfile="IVcurvezInP.dat"

tonyplot IVcurvezInP.dat

quit

94

B. Heterojunction Solar Cell Main Structure go atlas


# Mesh

# X-Mesh

# Y-Mesh

# Regions

# Electrodes

# Doping


# Models

# Light beams

# Solving

#Mesh and X–Mesh

mesh space.mult=1





#Y–Mesh

# Vacuum


# Window (0.03 um)


# Emitte (0.05 um)

95


# Base (0.55 um)


# BSF (0.03 um)


# Tunnel emitter (0.015 um)


# Tunnel base (0.015 um)


# Window (0.05 um)


# Emitter (0.1 um)


# Base (3 um)


# BSF (0.1) um)


# Tunnel emitter (0.015 um)


# Tunnel base (0.015 um)


# Window (0.05 um)


# Emitter (0.1 um)


# Substrate (300 um)

y.mesh loc=303.4 spac=50

#Regions

# Window

region num=1 material=AlGaAs x.min=-250 x.max=250 y.min=-0.72 y.max=-0.69

96

# Emitter

region num=2 material=InGaAs x.min=-250 x.max=250 y.min=-0.69 y.max=-0.64

# Base

region num=3 material=InGaAs x.min=-250 x.max=250 y.min=-0.64 y.max=-0.09

# BSF InAlAsP(AlInGaP)

region num=4 material=InAlAsP x.min=-250 x.max=250 y.min=-0.09 y.max=-0.06

# Tunnel emitter

region num=5 material=InP x.min=-250 x.max=250 y.min=-0.06 y.max=-0.045

# Tunnel base

region num=6 material=InP x.min=-250 x.max=250 y.min=-0.045 y.max=-0.03

# Window

region num=7 material=InGaAs x.min=-250 x.max=250 y.min=-0.03 y.max=0.02

# Emitter

region num=8 material=InP x.min=-250 x.max=250 y.min=0.02 y.max=0.12

# Base


# BSF

region num=10 material=InGaAs x.min=-250 x.max=250 y.min=-3.12 y.max=3.22

# Tunnel emitter


# Tunnel base


# Window


# Emitter

region num=14 material=Ge x.min=-250 x.max=250 y.min=3.3 y.max=3.4

# Substrate

region num=15 material=Ge x.min=-250 x.max=250 y.min=3.4 y.max=303.4

#Electrodes

electrode name=cathode x.min=-250 x.max=250 y.min=-0.72 y.max=-0.72

97

electrode name=anode x.min=-250 x.max=250 y.min=303.4 y.max=303.4

#Doping

# Window

doping uniform region=1 n.type conc=1.95e18

# Emitter


# Base

doping uniform region=3 p.type conc=1.5e17

# BSF


# Tunnel emitter


# Tunnel base


# Window


# Emitter


# Base


# BSF


# Tunnel emitter


# Tunnel base


# Window


# Emitter


98

# Substrate


#Material Properties

# Vacuum


# Ge


material material=Ge EG300=0.661 PERMITTIVITY=16.2 AFFINITY=4

material material=Ge MUN=3900 MUP=1900

material material=Ge NC300=1.0e19 NV300=5.0e18

material material=Ge index.file=Ge.opt

# InP






# InGaAs

material TAUN=1 TAUP=1 COPT=0 AUGN=0 AUGP=0

material material=InGaAs EG300=0.571 PERMITTIVITY=14.2 AFFINITY=4.13

material material=InGaAs MUN=5400 MUP=200

material material=InGaAs NC300=1.15e17 NV300=8.12e18

material material=InGaAs index.file=InGaAs.opt

#AlGaAs

material TAUN=1e-9 TAUP=1e-8 COPT=1.8e-10 AUGN=5.0e-30 AUGP=1e-31

material material=AlGaAs EG300=2.14 PERMITTIVITY=10.202 AFFINITY=3.507

material material=AlGaAs MUN=256.15 MUP=116.35

material material=AlGaAs NC300=2.77e19 NV300=1.615e18

material material=AlGaAs index.file=AlGaAs9.opt

# AlInGaP (=InAlAsP)

99


material material=InAlAsP EG300=2.4 PERMITTIVITY=11.7 AFFINITY=4.2

material material=InAlAsP MUN=2150 MUP=141

material material=InAlAsP NC300=1.2e20 NV300=1.28e19

material material=InAlAsP index.file= AlGaAs0.opt

#Models

models BBT.KL

TATUN TRAP.TUNNEL

#Light Beams



#Solving

solve init

method gummel newton maxtraps=10 itlimit=25

solve b1=0.9

## Getting Isc for I-V curve points


solve b1=0.95

extract name="isc" max(i."cathode")

log outfile=heterocell.log


solve b1=0.95

contact name=anode current


solve ianode=3.1654e-7 b1=0.95




100





solve ianode=0 b1=1

log off

extract name="iv" curve(v."anode", i."cathode") outfile="IVcurveheterocell.dat"

tonyplot IVcurveheterocell.dat

quit

Çukurova university institute of natural and ... - cu …library.cu.edu.tr/tezler/8116.pdf · this...

Documents