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2002-03
A novel approach for the development and
optimization of state-of-the-art photovoltaic
devices using Silvaco
Michalopoulos, Panayiotis
Monterey, California. Naval Postgraduate School
http://hdl.handle.net/10945/5609
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Dudley Knox Library / Naval Postgraduate School
411 Dyer Road / 1 Univefsity Circle
Monterey, California USA 93943
NAVAL POSTGRADUATE SCHOOL
Monterey, California
THESIS
A NOVEL APPROACH FOR THE DEVELOPMENT AND
OPTIMIZATION OF STATE-OF-THE-ART
PHOTOVOLTAIC DEVICES USING SILVACO
by
Panayiotis Michalopoulos
March 2002
Thesis Advisor: Sheiif Michael
Bret Michael
Second Reader: Todd Weatherford
Approved for public release; distribution is unlimited.
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2. REPORT DATE
March 2002
6. AUTHOR(S) Panayiotis Michalopoulos
11. SUPPLEMENTARY NOTES The views expressed in this thesis are those of the author and do not reflect the official
policy or position of the Department of Defense or the U.S. Government.
13. PiSST'RACT (maximum 200 words)
In this thesis, 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. The major stages of the process are explained
and the simulation results are compared to published experimental data. 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.
16. PRICE CODE
NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)
Prescribed by ANSI Std. 239-18
20. LIMITATION
OE ABSTRACT
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15. NUMBER OE
PAGES
187
14. SUBJECT TERMS
Solar cell, multijunction, simulation, model, development, Silvaco, Atlas, InGaP, GaAs, Ge
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Naval Postgraduate School
Monterey, CA 93943-5000
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4. TITLE AND SUBTITLE: Title (Mix case letters)
k Novel Approach for the Development and Optimization of State-of-the-Art
i’hotovoltaic Devices Using Silvaco
3. REPORT TYPE AND DATES COVERED
Master’s Thesis
1. AGENCY USE ONLY (Leave blank)
1
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Approved for public release; distribution is unlimited.
A NOVEL APPROACH FOR THE DEVELOPMENT AND OPTIMIZATION OF
STATE-OF-THE-ART PHOTOVOLTAIC DEVICES USING SILVACO
Panayiotis Michalopoulos
Lieutenant, Hellenic Navy
B.S., Hellenic Naval Academy, 1993
Submitted in partial f ulfillm ent of the
requirements for the degree of
MASTER OF SCIENCE IN ELECTRICAL ENGINEERING
and
MASTER OF SCIENCE IN COMPUTER SCIENCE
from the
NAVAL POSTGRADUATE SCHOOL
March 2002
Author: Panayiotis Michalopoulos
Approved by: Sheiif Michael
Thesis Advisor
Bret Michael
Co-Advisor
Todd Weatherford
Second Reader
Christopher Eagle
Chairman Department or Computer Science
Jeffrey B. Knorr
Chairman Department or Electrical and Computer Engineering
iii
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IV
ABSTRACT
In this thesis, a new method for developing reahstic 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 facihtate and enhance the modehng process. Furthermore, specific
models of an InGaP/GaAs and of an InGaP/GaAs/Ge multi-junction solar cells are
prepared and are fully simulated. The major stages of the process are explained and the
simulation results are compared to pubhshed experimental data. 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.
V
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VI
TABLE OF CONTENTS
I. INTRODUCTION.1
A. BACKGROUND.1
B. OBJECTIVE.2
C. REEATED WORK.3
D. ORGANIZATION.3
II. INTRODUCTION TO SEMICONDUCTORS.5
A. BASIC PHYSICS.5
B. CRYSTAE STRUCTURES.9
C. CARRIERS.10
D. EERMIEEVEE.15
E CARRIER TRANSPORT.19
E. MOBIEITY.20
G. RECOMBINATION.22
H. TUNNEEING.25
III. SEMICONDUCTOR JUNCTIONS.27
A. P-N JUNCTION.27
1. Eormation.27
2. Eorward Bias.30
3. Reverse Bias.32
4. Breakdown.34
5. Capacitance, Ohmic Eosses and Overview.35
B. M-S JUNCTION.36
C. OHMIC CONTACT.39
D. TUNNEE JUNCTION.40
E DIRECT AND INDIRECT TUNNEEING.43
E. HETEROJUNCTIONS.44
IV. SOLAR CELLS.49
A. SOLAR ENERGY.49
B. OPTICAL PROPERTIES.51
C. EUNDAMENTALS.54
D. TEMPERATURE AND RADIATION EEFECTS.57
E CELL TYPES.58
E. CONTACTS.60
G. ARRAYS.62
vii
V. MULTIJUNCTION SOLAR CELLS.63
A. BASICS.63
B. MONOLITHIC MULTIJUNCTION CELLS.66
C. CURRENT DEVEEOPMENTS.67
VI. SIMULATION SOFTWARE.71
A. MODELING TODAY.71
B. SILVACO.72
C. WORKING WITH ATLAS.74
1. Mesh.74
2. Regions.75
3. Electrodes.76
4. Doping.76
5. Material Properties.77
6. Models.77
7. light.77
8. Simulation Results.77
D. SIMULATION SOURCE CODE.78
E. EXCHANGING DATA WITH MATLAB.80
1. Creating SUvaco input files.81
2. Extracting results.81
VIL MATERIAL PROPERTIES.85
A. CURRENT STATUS.85
B. SILVACO LIBRARY.86
C. LATTICE MATCHING AND ALLOY PROPERTIES.87
D. OTHER CALCULATIONS.88
E. RESULTS.89
E. MOBILITY VS DOPING.91
G. OPTICAL PARAMETERS.93
VIIL BUILDING A MULTIJUNCTION CELL.97
A. THE PROCESS.97
B. THE SIMPLE GaAs CELL.99
C. IMPROVING THE CELL.102
D. THE COMPLETE InGaP CELL.104
E THE TUNNEL JUNCTION.106
E. THE InGaP/GaAs MECHANICALLY STACKED TANDEM CELL.107
G. THE InGaP/GaAs DUAL MULTUUNCTION CELL.110
H. THE COMPLETE InGaP / GaAs CELL.112
viii
IX. DEVELOPING AND OPTIMIZING A STATE-OF-THE-ART
MULTIJUNCTION CELL.115
A. HRST STAGE OF DEVELOPMENT.115
B. PARAMETRIC ANALYSIS AND OPTIMIZATION.120
C. FURTHER OPTI MIZA TIONS.128
X. CONCLUSIONS AND RECOMMENDATIONS.129
A. RESULTS AND CONCLUSIONS.129
B. FURTHER OPTI MIZA TIONS AND RECOMMENDATIONS.130
APPENDIX A. LIST OF SYMBOLS.131
APPENDIX B. GREEK ALPHABET.133
APPENDIX C. SOME PHYSICAL CONSTANTS.135
APPENDIX D. UNITS.135
APPENDIX E. MAGNITUDE PREFIXES.137
APPENDIX F. ATLAS SOURCE CODE.139
APPENDIX G. MATLAB SOURCE CODE.159
LIST OF REFERENCES.167
INITIAL DISTRIBUTION LIST.171
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X
ACKNOWLEDGMENTS
Many people have contributed to the completion of this thesis. I would first like to
express my deep appreciation to my advisor Dr Sherif Michael for his continuous
guidance and support, my co-advisor Dr Bret Michael and my second reader Dr Todd
Weatherford for providing valuable insights, improving this work. I have also benefited
from the significant advice of Dr Gamani Kamnasiri. Additionally, I am grateful to the
professors of the Naval Postgraduate School for their outstanding tutoring. They were
always a source of inspiration.
Furthermore, I am thankful to my country, Hellas, and the Hellenic Navy for
making this educational experience possible. I am indebted to my parents, Theofanis and
Sofia, whose love, patience, excellent example, motivation and encouragement were
always by my side, even from thousands of miles away. Finally, I would especially like
to express my gratitude to my dear wife, Elpida, who was always loving, supporting and
encouraging, even during my long hours of study.
XI
EXECUTIVE SUMMARY
One of the major limiting factors in space missions and applications is the
production of electric power. Even though a plethora of energy sources have been
invented and are widely used in terrestrial apphcations, most of them are not practical for
use in space apphcations: their large volume, weight and coohng requirements are only
some of the forbidding reasons. An abundant, renewable, smaU, and lightweight power
source has yet to be discovered.
The use of solar ceUs is currently the best solution to this energy problem. They
are light, they require almost no maintenance and they are totally renewable. However,
their efficiency is lim ited and that has resulted to the constmction and deployment of
solar arrays spanning many cubic meters. This alone is the cause of many problems of
mostly mechanical nature, like stowage volume, aerodynamic drag and maneuverabihty.
Advances in semiconductor design and fabrication has lead to the development of
tandem ceUs in complex monohthic stmctures caUed multijunction ceUs. Their high level
of efficiency ahows significant reduction in array sizes. Such an advance in the design of
solar cells could open up new vistas for the design of spacecraft.
Although many analytical models of solar cells have been created and pubhshed,
almost aU research on the design of solar cells is currently conducted using
experimentation. This is in part due to the lack of computer-based tools with a complete
design environment and a fuU set of models to simulate aU aspects of an advanced solar
ceU, except for the Silvaco Virtual Wafer Fabrication (VWF) suite of tools. Despite the
capabilities of VWF, to date there are no pubhshed accounts of its use to develop
multijunction solar ceUs.
hr this thesis, a methodology is introduced for using VWF - and in particular
Atlas within that suite of tools - to model advanced solar cells. It simplyfies the process
by abstracting fabrication details and focusing on the device itself. Additionahy, the
software developed to post-process the output of Atlas in another tool cahed Matlab, is
discussed. This software was also used to adjust and cahbrate parameter values for use by
Atlas in modeling advanced solar cells. Such parameters include electrical and optical
properties of exotic materials, often used in high-end cells. As most of them remain to be
studied by the photovoltaic community, their properties must be interpolated from the
properties of their components. Due to the non-linearity involved, several bowing
parameters are used in more complex interpolation functions.
As a first attempt to verify the correctness of this approach for designing
advanced solar cells, an InGaP/GaAs cell is developed. The first step is to model and
simulate a simple GaAs cell. Voltage, current, IV characteristic and frequency response
results are collected and compared with pubhshed experimental values. Although the
similarity observed is remarkable, several parameters were tuned to attain better
accuracy. The improved model is simulated again and new results are obtained. This
process is repeated until the desired level of accuracy is obtained. Additional layers (e.g.
BSF, buffers, windows) are added to the basic device to create a more advanced
stmcture. Each step is followed by a comparison and evaluation of results.
Using the same approach, an InGaP cell is formed. Both cells are then placed in a
mechanically stacked configuration to investigate shadowing phenomena. An appropriate
tunnel junction is also developed to electrically interconnect the two cells, resulting in a
creation of a multijunction cell. The dimensions and stmctural characteristics used are
identical to those in pubhshed cells. The fact that the results also match is a good
indication of the vahdity of this methodology.
The final case study reported in this thesis is of a triple InGaP/GaAs/Ge
multijunction cell. This stmcture is only vaguely described in the hterature, therefore
requiring some modehng decisions. Those are made based on the experience gained from
previous steps in this research. The simulation results closely approximate pubhshed
results from experimentation. Finally, an optimization process is used for determining the
best combination of thicknesses of the three cells involved. The results obtained from the
optimization process correspond to those obtained for the original design.
1. INTRODUCTION
A. BACKGROUND
We live in the age of space exploration and conquest. Deep space missions, space
stations, shuttles and sateUites are currently everyday news. As technology advances and
space applications become more and more demanding, their requirement for more energy
becomes imperative.
On the other hand, one of the most significant factors, in any kind of space
mission, is weight. This is due in part to both technological li mitations and cost
considerations. With an average cost exceeding $20,000 per pound and electric power
systems (EPSs) constituting almost 30% of the total spacecraft’s weight, the need for
efficient and renewable power sources is cmcial.
Solar cells outweigh all these energy sources due to their small weight and their
relatively high power density. However, solar arrays are stiU very large and fa some cases
have a surface of more than 30m . This causes many problems due to their increased
stowage volume, aerodynamic drag, and radar cross-section. The abihty to maneuver
such a large array and the vibrations that accompany an operation fake that are also
limiting factors.
Advances in semiconductor design and fabrication are very rapid and everyday
provide new ideas and means for improving cell performance. After the impressive
evolution of the 1839’s primitive Selenium to the currently most popular Silicon cell,
cutting-edge technology has presented state-of-the-art triple and quadmple
multijunction cells. These advances provided for a reduction of solar array size by a
factor of two, while more recent developments are expected to achieve even greater
reductions. Therefore, innovative solar cell design is of the utmost importance to the
design of new spacecraft.
A number of significant pubhcations fuUy describe various aspects of device
characteristics and modehng. However, all of them were focused on very specific issues,
lacking the breadth of a complete simulation tool.
1
Today, experts solely utilize the above analytic models. Despite their credibihty,
they only describe a small fraction of the phenomena that take place in a complex solar
cell, providing very httle insight into the characteristics of the final product. For this
reason, current research on the development and optimization of solar cells rehes
primarily on the use of experimentation. However, in such experiments, many undesired
factors are involved. Most of them have to do with the details of the fabrication process
used. This may result in confusion and misleading conclusions. Other important side
effects are the long time required to set up the experiments (e.g., fabrication,
development of instmmentation) and the high cost associated with conducting
experiments.
The Silvaco Software Package is a suite of integrated simulation and analysis
tools for use in electronic design. One of its major components of this suite of tools b the
Virtual Wafer Fabrication package (VWF). Within VWF, the ATLAS tool aids in the
design and development of all types of semiconductor and VLSI devices, from simple
bipolar transistors to EEPROMs. The phenomena modeled start from simple electrical
conductivity and extend to such things as thermal analysis, radiation, and laser effects. A
wide variety of detailed layer-growth processes and material properties (e.g. mobihties,
recombination parameters, ionization coefficients, optical parameters) add to the fidelity
of the simulation. However, no effort to utihze this powerful tool for the modehng of
advanced solar cells has been reported in the hterature by researchers or the
manufacturers of solar cells.
B. OBJECTIVE
The research issues addressed in this thesis research are as follows: whether
ATEAS can be successfully used for simulating complex solar cell stmctures, how to
prepare the necessary infrastmcture for such tasks, and how to simulate devices of
different levels of complexity. In addressing the last issue, the results obtained via
simulation, are compared with published experimental data.
2
C. RELATED WORK
As it was mentioned earlier, no published papers were found in conferences or
journals about fuUy modeling and simulating ah major aspects in the behavior of an
advanced solar cell. This is the reason why this methodology is considered to be novel.
However, interest in this area was seen by students at the Naval Postgraduate School. The
most remarkable work exists in Ref. 30 and 34.
In Ref. 34, modehng of a simple one-junction cell, using Silvaco, was performed
and its IV characteristic was produced. No other results were shown and no comparison
to experimental data was presented.
In Ref. 30, dark-current analysis of solar cells was mainly performed. An
indication of the usage of Silvaco for their simulation was also briefly provided. Within
this, there was an attempt to simulate a triple MJ cell, but little results were presented and
no comparison with experimental results was done.
D. ORGANIZATION
Chapters 2 and 3 are an introduction to semiconductor physics and basic
electronic devices. The principles and major functional characteristics of both simple and
advanced solar cells are explained in chapters 4 and 5. In chapter 6, a novel methodology
for simulating state-of-the-art cells is introduced and is continued throughout chapter 7
with the research of material properties. They both form the basis of the fohowing two
chapters. In chapter 8, a dual multijunction ceh is constmcted, simulated and the results
are verified against pubhshed experiments. The first part of chapter 9 simulates a cutting-
edge ceh and also verifies its results with pubhshed experiments. Finahy, an optimization
of this ceh is performed in the second part of this chapter.
Chapter 10 concludes the thesis with a summary and recommendations for future
work.
3
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4
11. INTRODUCTION TO SEMICONDUCTORS
This chapter contains introductory information about semiconductors and the
physics surounding their nature and functionality. It is addressed to students not very
familiar with such concepts. Readers well versed in this area might rather go directly to
Chapter 3 or 4.
A. BASIC PHYSICS
The various materials can be categorized according to their electrical properties as
conductors, semiconductors and insulators. Resistivity p and its reciprocal conductivity a
are two of the most important electrical properties. Table 2.1 displays the resistivity and
conductivity for various types of materials:
Resi.stivit>' p (il - cm)
10'» 10*® 10'^ 10'** 10'® 10® 10® 10^ lO^ 1 10-2 10-4 10-6 lo-H
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“1-^ 1 ^
Silver
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(pure)
Silicon (Si)
Copper
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Diamond
(pure)
Gallium arsenide (GaAs)
Gallium phosphide (GaP)
Aluminum
•
Platinum
•
Fused
Cadmium sulfide (CdS)
Bismuth
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Conductivity’ a (S/cm)
Insulator
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Table 2.1. Resistivity for various material types [from Ref. l:p. 18].
It is well known that materials are comprised of atoms. Each atom has a nucleus
and electrons revolving around it. The nucleus consists of protons and neutrons. The
5
attractive force between the positive charged protons and the negative charged electrons
are responsible for holding this structure together.
According to Niels Bohr, electrons exist in specific orbits or shells around the
nucleus, the outermost of which is called a valence shell. They can transition to a shell of
higher (or lower) energy level by absorbing (or losing) energy, equal to the difference of
the two levels (Figure 2.1). This energy can have the form of a photon or heat.
Figure 2.1. Transition of an electron from one shell to another.
Inside a material, however, things are a bit different. At 0°K all electrons are
tightly held by their atoms and the material has zero conductivity. As temperature rises,
heat increases the energies of valent electrons and some of them break free from their
atoms. Those are called free electrons. Their number increases drastically with
temperature. Free electrons are directly responsible for the electrical conductivity of a
material and actually participate in current flow. Hence, as temperature increases, so does
conductivity. This is true up to a certain temperature. Above that, there are no more
electrons to become free and the conductivity stops to increase.
On the other hand, atoms oscillate due to heat. As temperature increases, this
oscillation becomes larger. Free electrons moving in the material bounce on the
oscillating atoms and reduce their speed. The larger the oscillation, the bigger the
difficulty of movement for the free electrons. This way temperature decreases
conductivity. The balance between the two factors is shown in Figure 2.2:
6
0 Temperature [“K]
Figure 2.2. Conductivity vs. Temperature.
Free electrons are affected by electrostatic forces produced by nearby atoms. In
order to achieve chemical stabihty, every atom requires a full valence shell. This is
always done with eight electrons, except for the first shell, which only requires two.
Elements with five or more valence electrons hold those tightly in their atoms and attract
others in an attempt to reach a chemically stable state. The additional electrons wrh
increase the negative charge of the atoms. These atoms now have an overall negative
charge and are called negative ions. On the contrary, elements with three or less valence
electrons allow them to escape, using one shell bellow as valent, again reaching a stable
state. This loss will result in an excessive positive charge. These atoms are now called
positive ions. The produced positive and negative ions are electrostatically attracted and
an ionic bond is created. Elements with four valence electrons do not receive or offer any
of them. Instead, they share them with other atoms. This way a covalent bond is created.
Electrons existing in the inner shells require so much more energy to change energy level
that they will not concern us.
Eree electrons have higher energies and are said to exist in the conduction band.
Electrons not freed from their atoms have lower energies and are said to exist in the
valence band. Energies between the conduction and the valence bands form the bandgap
Eg. Electrons can exist in the conduction or the valence band, but not in the bandgap. In
conductors, the conduction and the valence bands overlap, thus there is no bandgap, as
illustrated in Eigure 2.3. Eor this reason, electrons can easily move from one band to the
other. EinaUy, Eg tends to decrease with temperature.
7
A
E^
^ E^
Conduction band
Conduction band
Conduction band
i
Bandgap ^ Eg
Bandgap
E
Valence band
r
Valence band
Valence band
Conductors Semiconductors Insulators
Figure 2.3. Energy bands in various material types.
The number of free electrons, and thus conductivity, can be increased by offering
amounts of energy to them at least equal to the bandgap. Obviously conductors do not
require any such energy. On the contrary, in order to reach noticeable conductivity levels,
insulators require large amounts due to their large Eg. Semiconductors with much less
energy reach levels almost as good as conductors.
While electrical systems use exclusively conductors and insulators, electronic
systems are entirely based on semiconductors. That is because of their unique abihty to
behave as conductors and as insulators according to our needs. All diodes, transistors and
thyristors are built using semiconductive materials. The most common semiconductors
are stiicon (Si) and Germanium (Ge) whose atomic stmcture is shown in Eigure 2.5.
Those are also called group IV materials due to the number of valent electrons.
Additionally, compound semiconductors can also be used tike GaUium Arsenide (GaAs)
and Indium Phosphide (InP). Those are called group IH-V materials. Other types may be
n-VI like CdS and ZnO, IV-IV tike SiC or IV-VI tike PbS and PbTe. Most of them can
be seen in the brief periodic table of Eigure 2.4.
8
H
He
Li
Be
B
C
N
0
F
Ne
Na
Mg
A1
Si
P
S
Cl
Ar
K
Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
Gs
Ge
As
Se
Br
Kr
Rb
Sr
Y
Zr
Nb
Mo
Tc
Ru
Rh
Pd
Ag
Cd
In
Sn
Sb
Te
I
Xe
Figure 2.4. Abbreviated Periodic Table of elements.
Figure 2.5. Atomic structure of Si and Ge.
B. CRYSTAL STRUCTURES
As mentioned earlier, electrostatic forces of neighboring atoms attract electrons
and form ions, in their attempt to reach chemical stabUity. Electrostatic forces among
these ions form symmetric lattices that are called crystals. One of the simplest crystals is
that of O 2 and Ga, producing a simple cubic stmcture. Si and Ge form a more complex
crystal called cubic face centered as shown in Figure 2.6. Each crystal stmcture is
completely defined by a number called lattice constant a.
9
Figure 2.6. Examples of crystal structures.
The crystaUine stmcture is necessary and very important in the production of
wafers. Badly-matched stmctures may display unforeseen electrical behavior and very
poor mechanical properties.
Production of crystalline materials in large sizes can be very expensive. Materials
composed of very small crystals or grains are called polycrystalline. These have inferior
properties than crystalline, but are much cheaper to produce. Materials with no crystal
uniformity are called amorphous and their properties are far inferior, but they are very
cheap. They are used where large areas of cheap semiconductive material is needed, such
as displays, imagers and terrestrial solar cells etc.
C. CARRIERS
Another way to represent the structure of a semiconductor in two-dimensions is
illustrated in Figure 2.7. In this, the valent electrons, being shared among atoms with
covalent bonds, are clearly shown. Also shown is the charge of the nucleus (protons)
related to those electrons. Since each atom has all four of its valent electrons, it is not
electrically charged.
AH electrons, initially, exist in the valence band. If an electron somehow absorbs
enough energy to enter the conduction band, it breaks the covalent bond, leaves the
crystalline stmcture and becomes free. The atom that owned that electron is now left with
an excessive positive charge. This charge is called hole. It has a positive charge equal to
10
the absolute value of the electron’s charge and is located where the free electron used to
be. Both the free electron and the hole form a pair called electron-hole pair (EHP). The
above descibed phenomenon is called ionization or generation. The production rate of
EHP’s is a strong function of temperature. On the other hand, electrons moving freely
through the crystal tend to recombine with holes. This way EHP’s disappear. This
phenomenon is called recombination and its rate is proportional to the number of existing
holes and free electrons. In thermal equUibrium the ionization and the recombination rate
are equal keeping the number of EHP’s constant.
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■
1 1
1 t
1 t
1 1
1 t
1 1
H
H
H
■
+4. •
•_ +4 T •
__*-'+4
•
■
+4
• :+4 T*
• +4
■
«
•
•
•
•
•
: nucleus • : electron o : hole : covalent bond
Eigure 2.7. Stmcture of a semiconductor.
Pure semiconductor crystals, that do not contain any foreign atoms, are called
intrinsic. In an intrinsic semiconductor at CK there are no EHP’s. As temperature rises,
however, the heat absorbed by the material will create a number of EHP’s and the
conductivity of the material will increase. Since EHP’s are responsible for conductivity,
they are called intrinsic carriers. Their number increases logarithmically. Eor Si, Ge and
GaAs this is shown in Eigure 2.8.
11
Temperature [°K]
Figure 2.8. Intrinsic carrier density vs. Temperature [after Ref 2:p. 19].
This number, although it seems large, is actually a very small percentage of the
total atoms in the semiconductor. This is better shown in Table 2.2.
Semiconductor
atoms/cm^
Intrinsic
carriers /cm^
ratio
Bandgap [eV]
Ge
4.42-10^^
2.4-10^^
1 : 1.810‘^
0.66
Si
5-10^^
1.45-10'°
1 : 3.4-10^^
1.12
GaAs
4.42-10^^
1.7910'^
1 : 2.5-10^^
1.424
Table 2.2 Carrier concentration in intrinsic semiconductors at 300°K
[after Ref. 2:p. 850].
Elements other than semiconductors also have carriers. If an element has three or
less electrons in the valence band, then its predominant carriers are holes and it is called
an acceptor. Usually, acceptors have three valence electrons ((rivalent). If an element has
five or more valent electrons, then its predominant carriers are electrons and it is called a
donor. Usually, donors have five valent electrons (pentavalent). The process of adding
12
impurities in an intrinsic semiconductor is called doping. This way the semiconductor
becomes extrinsic and obtains new, very important electrical properties.
As a donor atom enters the crystal, it forms covalent bonds with the
semiconductor atoms, but also has a number of electrons involved in no bonds with other
atoms. Those are loosely held within the donor atom and become free electrons. Because
of this excessive number of electron carriers, the material is called n-type. Any material
can be used as a donor as long as its atom has more valent electrons than the
semiconductor atom it replaces. N-type materials are said to have electrons as majority
carriers and holes as minority carriers. On the contrary, acceptor atoms wiU not have
enough valent electrons to share with neighboring semiconductor atoms and a hole will
be created. As there is now an excessive number of holes, the material is called p-type.
Any material can be used as an acceptor as long as its atom has less valent electrons than
the semiconductor atom it replaces. P-type materials are said to have holes as majority
carriers and electrons as minority carriers. Both types of semiconductors can be seen in
Figure 2.9.
• •
•
•
•
•
•
+4 ._«
’"•V+4
•
•
+4 r > ’
•.-'+4 •
• +4 •
iti iSi
1 > 1 1
1 1
/•'>
1 1
!m\
I 1
lm\
1 1
1 1 1 1
!•; !•; *
H
H
H
•
+4 +5
”V:+4
•
•
+4 :y
• +4 •
ill ISI
1 > 1 1
1 1
1 1
1 1
1 1
1 1 1 1
H
H
H
•
+4 _ _ A'>4 ! '•_
+4
•
•
+4 'XI
IK +4 rx]
» '
IK +4 •
• •
•
m
•
•
n-doped
p-doped
: nucleus •
: electron
o : hole
m
• 3-' : covalent bond
Figure 2.9. Structure of doped semiconductors.
The number of majority carriers is analogous to the doping in a material, while
the number of minority carriers is analogous to temperature. Note that both p- and n-type
13
materials remain neutral. However, the effect of doping is great to the electrical
properties of the material even at very small concentrations (1 : 10^). Adding to the
previous table, it is shown that the effect on the conductivity and the bandgap is
significant:
Semicond.
atoms/cmP
Intrinsic
Extrinsic
carriers /cm^
ratio
Eg [eV]
carriers /cm"
ratio
Eg [eV]
Ge
4.42-10""
2.4-10'"
1:1.8-10’
0.66
4.42-10'®
1:10"
0.01
Si
5-10""
1.45-10“'
1:3.4-10'"
1.12
5-10'®
1:10"
0.05
GaAs
4.42-10""
1.79-10®
1:2.5-10'®
1.424
4.42-10'®
1:10"
Table 2.3 Carrier concentration in intrinsic and extrinsic semiconductors at 300°K
[after Ref. 2:p. 850].
In a material, the concentration of majority carriers (rino for electrons in n-type or
PpO for holes in p-type materials) is equal to the concentration of carriers created by the
semiconductor plus the concentration of carriers created by the impurity. According to
the above table this will be approximately equal to the concentration of impurity atoms
(Nd for donor or Na for acceptor).
On the other hand, the concentration of minority carriers (ripo for electrons in p-
type or pno for holes in n-type materials) times the concentration of majority carriers is
constant (p n = ni ) in thermal equihbrium. According to the above:
n-type
p-type
majority carriers
Hno = Nd
PpO = Na
minority carriers
Pno = rii^ / Nd
Hpo = rii^ / Na
product p n
rii^
rii^
Table 2.4 Carrier concentration relations.
14
D. FERMI LEVEL
All the above phenomena are deseribed as very preeise and distinet. However, in
reality they are mled by Heisenberg's prineiple of uncertainty. Thus, any reference to the
direction, concentration, energy etc of electrons or holes should more precisely be done
using probabUistic expressions.
In an intrinsic semiconductor at O^K, all electrons have energies below a certain
level called Fermi level Ep. As temperature rises and EHP’s are created, electrons of
energies higher than Ep appear, populating the conduction band. This is described in the
Fermi-Dirac distribution function that is equal to:
Where E is the electron energy, is the Eermi level, k is Boltzmann’s constant and T is
the absolute temperature. A plot of f(E) is shown in Eigure 2.10.
1
0.9
0.8
0.7
0.6
0.5 h
0.4
0.3
0.2
0.1
0
_ _— J
- 1 --
-1
-1
- To
-i
-1
—
1
\ \ L
- T,
....
.-Ti..
■
\ ; \ 1
Ik
Iv
lo = 0“K
.... To< Ti< T2<
_i_i_
T, ..
_
_
_
1- —^—
Ep
Eigure 2.10. Eermi distribution.
As doping takes place, the carrier concentrations change and so do the
populations on the various energy levels and the Ep. Dopants introduce more energy
levels within the energy bands. This is shown in Eigures 2.11 and 2.12.
15
Figure 2.11. Band diagram, density of states, Fermi-Dirac distribution and carrier
concentrations [after Ref. 2:p.23].
16
Figure 2.12. Ionization energies for various impurities in Ge, Si and GaAs
[Ref. 2:p.21].
If a donor introduces energy levels close to the conduction band, then a very small
amount of energy is needed to ionize its electrons to the conduction band. This is called
shallow donor. Similarly, acceptors that introduce energy levels close to the valence
band, require tittle energy to ionize its holes into the valence band. This is called shallow
acceptor. Dopants away from their corresponding bands are called deep dopants. Some
materials (tike Si) can behave as donors or as acceptors depending on which site (Ga or
As in GaAs) of the semiconductor they occupy. Other materials (tike Cu and Au) have a
very complicated behavior and introduce multiple energy levels. These are called
amphoteric.
In reality, even the purest semiconductors contain a significant number of both
donor and acceptor impurities. Their conductivity type is determined by the prevailing
concentration of dopants, as the effect of one dopant is countered (compensated) by the
effect of another. Even though all semiconductive materials fall into this category, the
ones that contain significant amounts of both dopants are called compensated
semiconductors. Compensation is used to counter the effects of “unwanted” impurities in
a material.
If the concentrations of both dopants are very large and equal, the material is
called strongly compensated. In spite of the fact that impurities are spread throughout the
material, their distribution is not absolutely even. Therefore, energy fluctuations versus
position are observed. In some cases, small portions of the conduction band exist below
Ep {electron droplets) and in others, small portions of the valence band exist above
{hole droplets). This will introduce unique properties where the material behaves tike an
insulator containing conductive spots. Also, electrons with low energies and holes with
high energies are trapped within the droplets and cannot move around the material tike
the rest of the carriers (Eigure 2.13). As a result the material’s conductivity is affected.
18
electron droplet
Figure 2.13. Strongly compensated material [after Ref. 3:p. 66].
E. CARRIER TRANSPORT
If there is a higher concentration of carriers in a part of a doped semiconductor,
then those carriers will tend to diffuse, spreading evenly aU over the material. This is
analogous to a gas expanding evenly in a container. The current produced by this
movement of carriers is called diffusion current (Id) and is analogous to the majority
carrier concentration and thus the doping. The carriers (holes) shown in the following
example (Figure 2.14) move to the right, where their concentration is smaller, producing
Id. Note that if the carriers displayed were electrons. Id would be reversed.
19
Current can also be produced by the movement of carriers by an external force,
like an electric or a magnetic field. This will produce a current called drift current (Is)
and is analogous to the minority carrier concentration and thus the temperature. Is will
obviously be proportional to the intensity of the field, too. Again in the following
example (Figure 2.15) the carriers displayed are holes.
F. MOBILITY
We mentioned before that under thermal equfiibrium, the population of energy
levels is given by the Fermi-Dirac distribution. However, when an electric field is
apphed, or when fight produces EHP’s etc, the material is not under equilibrium. In this
case the equations of table 2.4 do not apply. Instead of the Fermi energy level Ep, the
electron and hole Quasi-Fermi energy levels Epp, Epn must now be used. In equilibrium
conditions we have Ep = Epn = Epp. The new distributions become:
1
In vacuum, an electron that exists inside an electric field wifi accelerate
constantly. On the contrary, inside a material, the electron wifi originally accelerate, but
as its speed increases it wifi cofiide more and more often with the atoms of the lattice.
20
Additionally, it will be affected by the charge of ionized impurities in the material. These
coUisions wiU decelerate it. Thus, the electron will soon stop accelerating and will reach a
constant average speed called drift speed. The ratio of that speed to the applied field is
called mobility |l. MobUity decreases with temperature and impurity concentration
(Figure 2.16) due to the carrier scattering mentioned above.
MobiUty is also reduced near the surface of the material due to surface or
interface scattering mechanisms. In order to avoid this, a carrier density gradient can be
created by varying the doping density in the semiconductor. Finally, mobihty is
analogous to the permittivity 8s.
,4
Pi,: electron mobihty
Pp: hole mobihty
21
G. RECOMBINATION
Energy-band levels vary as a function of the momentum of electrons. There are
materials that have their minimum Ec and their maximum Ey at the same momentum k.
Some of them are GaAs, InP etc and are called direct. All the others like Si, Ge etc are
called indirect. In Eigure 2.15, E-k diagrams of Ge, Si and GaAs are shown.
WAVE VECTOR
Eigure 2.15. Energy-band stmctures vs. momentum of Ge, Si and GaAs
[after Ref. 2:p. 17].
A hole is actually a position in the lattice missing an electron. As seen in
paragraph C, during recombination this empty space becomes occupied by some electron
and so this particular EHP disappears. Thus, both electron and hole cease being carriers.
During this phenomenon the electron transits into a state of lower energy. In order to do
that it must release an energy quantum equal to the difference of its original and its final
state. This can be done in three ways:
22
• emit a photon (radiative reeombination)
• emit a phonon (non-radiative reeombination)
• kinetieally exeite another eleetron (Auger reeombination)
Recombination can be characterized as:
• band-to-band or direct recombination
• band-to-impurity, trap-assisted or indirect recombination
• surface recombination
• Auger recombination
Direct recombination is when an electron in the conduction band combines with a
hole in the valence band, without change in the electron’s momentum. This type of
recombination occurs in direct materials such as Ge and GaAs. Since no momentum is
required the recombination rate is the highest. The lifetime of a carrier is the reciprocal of
its recombination rate, therefore in this case this hfetime is very short.
Indirect recombination occurs in indirect materials like Si. Impurities, stmctural
defects of the lattice and interface phenomena can create energy levels inside the
bandgap. Those are called recombination centers Er. E is fi ll ed at equilibrium, however,
an electron from there may jump down to the valence band combining with a hole. The
energy E-Ev emitted is usually offered to the lattice as heat. This way a hole is created in
Ef. In a quite similar fashion, an electron from the conduction band may drop down to E
occupying the hole and releasing energy Ec-E-. Macroscopically, two carriers, a free
electron and a hole, have recombined and energy E-Ev has being released. The result is
the same as direct recombination, but the process is different. This is also known as
Shockley-Read-Hall (SRH) recombination. Direct and indirect recombination graphs can
be seen in Eigure 2.18.
As E approaches the middle of the bandgap, the recombination rate increases
since the energy required for the completion of each step is less. Besides, more than one
recombination center may exist in a material. Many of them can participate in an indirect
recombination done in multiple steps. This is called multiple-level recombination (Eigure
23
2.19). Since the energy required now for the eompletion of each step is even less, the
reeombination rate increases further.
Figure 2.18. Direct and indirect recombination.
Figure 2.19. 2-level indirect recombination.
Sometimes when an electron moves from F to D, or from F to F, it is thermally
re-excited back to its original state. Sinee the phenomenon was not eompleted,
recombination did not occur. This is called temporary trapping and F is called trapping
24
level Et- The opposite phenomenon of recombination is the generation of carriers and is
called ionization. This was discussed in paragraph A.
Surface recombination is due to the danghng bonds at the surface of a
semiconductor. This abmpt discontinuity of the lattice introduces a large number of
energy states called surface states. These serve as recombination centers and thus
increase the recombination rate.
We have seen that during impact ionization an electron with high kinetic energy
collides with a stationary one and produces an EHP. Auger recombination is observed at
very highly doped materials and is exactly the opposite. The energy produced by the
recombination of an EHP is given to a third carrier. Usually, this energy is later lost to the
lattice as phonons.
H. TUNNELING
Assume two isolated semiconductive materials being brought very close to each
other. Their band diagram would look hke the one in Eigure 2.20. According to
conventional physics, carriers can move from one material to the other only by going
over such energy barrier. This can only be done by obtaining equal or larger energy. On
the contrary, quantum physics view the behavior of carriers as probabihty functions.
Consequently, there is always a probabihty of a carrier going through the energy barrier
without changing its energy as in Eigure 2.21. Tunneling is a phenomenon tightly related
to quantum theory. According to this, a carrier with low energy has a probabihty of
jumping to the other side of an energy barrier without increasing its energy. The carrier
does not go over the barrier, since that would require energy absorption, rather it goes
through the energy barrier (is tunneled) and retains its original energy. This is a
phenomenon with many apphcations in electronics and solar cehs, as wih be explained in
later chapters.
25
Figure 2.20. Band diagram of two close-by semiconductors.
(a)
(b)
Figure 2.21. Tunneling (a) as probability, (b) as wave function.
26
III. SEMICONDUCTOR JUNCTIONS
A. P-N JUNCTION
The p-n junction was invented and explained by W. Shockley in “The
theory of p-n Junctions in Semiconductors and p-n Junction Transistors” in 1949 [Ref.
2 ].
1. Formation
It is known that doped semiconductors at equihbiium have no charge and no
diffusion current. Assume two such materials, one p-type and one n-type. If they are
brought in contact with each other, a series of phenomena are observed.
First of all, holes (majority carriers) from the p-type will begin to diffuse into the
n-type. Similarly, electrons from the n-type will begin to diffuse into the p-type. Both
will contribute to the development of a large dijfusion current Id, which is obviously
analogous to the number of majority carriers and thus the doping. During this process,
holes diffusing across the junction into the n-type material, will recombine with the
existing electrons and both carriers will disappear from the scene. Similarly, electrons
diffusing across the junction into the p-type material will recombine with the existing
holes and wiU, again, disappear. This carrier depletion will lead to the formation of an
area near the junction where no carriers will be present. This area is called the depletion
region.
At the same time, impurity atoms, in the depletion region, that have lost their
carriers are either positively (donors) or negatively (acceptors) charged. Consequently, a
negative charge will be built up at the p-doped side of the junction and a positive charge
at its n-doped side. This, in turn, will form an electrostatic field that will oppose the
diffusion of carriers. Also, minority carriers on each side will be forced by this field to
their opposite ends creating a small drift current Is due to thermal generation. This is
obviously analogous to the number of minority carriers and thus the temperature. As time
progresses, the charge build-up (and therefore the field and the depletion region)
27
becomes bigger and so does Is, while Id decreases. A steady state is reached when J
becomes equal in magnitude to Id-
A voltage differential Vq of about 0.7V for Si or O.IV for Ge is developed
between the two materials with its negative side on the p-doped material. This is a
barrier voltage that is responsible for the reduction of Id. However, this voltage cannot
be measured physically. If we attempt to attach electrodes on the materials to measure it,
then another junction will be created between each electrode and the semiconductor.
These will develop voltages equal, but opposite to the original. So, the total voltage and
the external current will be zero. If that was not the case, then the p-n junction could be
used as a power source producing electricity out of nothing. This would be against the
energy conservation principle. A p-n junction is shown in Figure 3.1.
Depletion region
9 Hole Electron recombining with a hole
0 Electron Hole recombining with an electron
• Electrostatic field
I I Neutral charge
I I Positive charge
I I Negative charge
Eigure 3.1. Schematic of p-n junction formation.
28
From an energy-level point of view, the p- and the n-type materials have
different Fermi levels. As the two materials become connected, the exchange of carriers
win equalize the Fermi levels. Also, a gradual interface is formed between the two
conduction and valence energy levels, as shown in Figure 3.2.
E I
Ec
Ef-
Ev
—
p-type
En
Ec
Ef-
Ev
—
n-type
E A
Ec
Ef
Ev
Drift
Diffusion
Diffusion
--
p-type
Drift
-N'-
n-type
Ec
Ev
Figure 3.2. Band diagram of p-n junction formation.
29
2. Forward Bias
Assume that a voltage is applied externally to the junction as illustrated in figure
3.3. A large number of majority carriers will be constantly provided on both ends. These
carriers will tend to diffuse towards their opposite ends. Additionally, the external voltage
apphed will force inject) majority carriers to their opposite ends. In the process, they will
neutr aliz e the charge in the depletion region, narrowing it. Therefore, the barrier voltage
across the junction becomes smaller and so b increases greatly. At the steady state, b -
Is = I or I = Id, which is very large. This is called forward bias. A representation is shown
in Figure 3.3 and the band diagram in Figure 3.4.
Is
Id
^ ^
** ^ ^ ^ ^
^ ^ ^ ^
••
I
I
V
' Hole
' Electron
Electron recombining with a hole
Hole recombining with an electron
• • Electrostatic field
I I Neutral charge
I I Positive charge
I I Negative charge
Eigure 3.3. Schematic of a forward biased p-n junction.
30
E
▲
Ec
Ef
Ev
I q(Vo-V)
I qV
p-type
C
o
o
c
3
n-type
Ec
Ef
Ev
Eigure 3.4. Band diagram of the forward biased p-n junction.
If we record the current I over the voltage V, we get the characteristic curve of
the forward biased p-n junction. This looks tike the on in Eigure 3.5, where Vd = Vq is
equal to 0.7V for Si or O.IV for Ge. Note that I increases greatly for only a small increase
of V after Vd.
Eigure 3.5. Characteristic curve of the forward biased p-n junction.
31
3. Reverse Bias
Assume now that voltage is applied externally to the junction in the opposite way,
as shown in figure 3.6. In this case the external source will draw majority carriers from
both sides and provide them with excessive minority carriers. This will increase the
imbalance of charges near the junction, widening the depletion region, increasing the
barrier voltage and therefore decreasing fc. At the steady state Is - Id = I or I = Is which
is very small. This is called reverse bias. A representation is shown in Figure 3.6 and the
band diagram in Figure 3.7.
Is
◄-
Id
-►
0 Hole Electron recombining with a hole I I Neutral charge
9 Electron Hole recombining with an electron | | Positive charge
• Electrostatic field I I Negative charge
Eigure 3.6. Schematic of a reverse biased p-n junction.
32
3.8.
Eu
Ec
Ef
Ev
p-type
qV
q(Vo+V)
c
.2
’•w
o
c
:3
n-type
Ec
Ef
Ev
Eigure 3.7. Band diagram of the reverse biased p-n junction.
The characteristic curve for the reverse biased p-n junction can be seen in Figure
I
►
V
Eigure 3.8. Characteristic curve of the reverse biased p-n junction.
33
4. Breakdown
Assume a reverse-biased p-n junction. It is explained that for any external
voltage V the current I is small and approximately equal to Is. However, if V increases
above a certain threshold, the current suddenly becomes very large as if the junction was
forward-biased. This threshold is called breakdown voltage Vz. There are two
phenomena that are responsible for this behavior. For instance in Si, if \^ < 5V then the
predominant mechanism is the zener effect, if Vz > 7V it is the avalanche effect and if 5V
< Vz < 7V then either or both effects occur and contribute to the breakdown
phenomenon.
In the zener effect (or tunneling effect), the electrostatic field in the depletion
region is strong enough to break covalent bonds and generate EHP’s. From an energy
point of view, an electron is tunneled from the valence to the conduction band,
penetrating through the bandgap. Due to the same field, created minority carriers will be
swept to the opposite side. Thus, electrons will be forced to the n-doped and holes to the
p-doped region. This exchange of minority carriers is so intense that creates a large
current equal to I. With only small changes in V the current I varies greatly.
In the avalanche effect (or avalanche multiplication), the minority carriers that go
through the depletion region have very large kinetic energy. As they coUide with atoms
they are able to break covalent bonds and create EHP’s (impact ionization). This is also
called ionizing collision. The new carriers created may have sufficient energy to repeat
this phenomenon and create more EHP’s. This continues in the form of an avalanche.
Again, minority carriers are swept to their opposite sides and this creates a large current I
with only small changes in V.
The avalanche effect is more sudden and abmpt than the zener effect. However,
neither is destmctive as long as the power dissipated is less than the maximum allowed
by the physical characteristics of the device.
34
5. Capacitance, Ohmic Losses and Overview
The existence of charge in the depletion region also behaves like a capacitor.
Since this charge is more when the junction is reverse-biased, its capacitance is also
higher. There are many applications (ie tuning) that make use of this property. However,
in most cases it is parasitic and designers try to e lim inate it because it lim its high-
frequency operation.
Like every non-ideal material, p-n junctions have inherent ohmic resistances
throughout aU their mass. These are usually very small and most times neghgible due to
the high doping of the materials. However, this is still a factor when very small signals
are applied.
Overall, the p-n junction has a characteristic that looks like the one in Figure 3.9:
Figure 3.9. Characteristic curve of the p-n junction.
35
B. M-S JUNCTION
The first semiconductor device was actually the metal-semiconductor junction
(M-S), which was invented by Braun as early as 1874. Its concept is simpler than the p-n
junction explained before.
The energy difference between the Fermi level Ep and the energy level of the
vacuum fyacuum level) is called the work function. When two materials make contact, at
equUibrium, the Fermi levels become equalized. The work function of each material
remains unchanged except near the junction. There, the vacuum levels become
continuous with a gradual interface, thus affecting the work function. In our case, when a
metal and a semiconductor make contact, their energy bands are shown below. Note the
energy barrier formed which obstmcts the exchange of carriers across the junction
(Figure 3.10).
E k
vacuum
level
Ev
Ep
Ec
C
v
metal -2
o
1
t f
vacuum
vacuum
level
level
Ec
Ev
Ep
- Ev
Ep
Ep -
Ec
Ev
Ec
}
-vx-^ V-
metal
n-doped
semiconductor
Ec
Ep
-V-
n-doped
c semiconductor
3
Y
metal
E
vacuum
level
Ev
Ep
Ec
A
Y
3
metal -2
o
Ec
Ep
Ev
p-doped
semiconductor
Ec
Ep
Ev
- 'Y -
p-doped
s semiconductor
3
Figure 3.10. Band diagram of M-S junction formations.
36
If a voltage is applied to an M-S junetion, the energy bands ehange levels.
Assume a junetion with n-doped semieonduetor. If the potential of the metal is more
positive than the potential of the semieonduetor, then the barrier beeomes smaller and
eleetrons move from the semieonduetor to the metal easier. This is an ohmic junction. On
the eontrary, if the potential of the metal beeomes more negative, the barrier inereases
and eleetrons ean no longer move from the semiconductor to the metal. This is a
rectifying junction.
The same is also illustrated below using current densities. For the non-biased
junction with n-doped semiconductor, the current densities in the metal and in the
semiconductor are balanced. The current from the metal to the semiconductor (M^S)
and the one from the semiconductor to the metal (S^M) are equal and so no total current
is observed.
In ohmic mode, the semiconductor energy levels are raised. The M^S current
remains the same since the barrier height is unchanged in that side. However, the barrier
height becomes smaller on the semiconductor side and therefore, the S^M current
largely increases and prevails over the M^S.
Similarly, in rectifying mode, the M^S current remains the same, but now the
S^M current decreases and the total current observed is very small. Using the same
reasoning, corresponding conclusions can be derived for a junction with p-doped
semiconductor. All three cases are shown in Figure 3.11.
The general characteristic and use of the M-S junction is very similar to those of
the p-n junction. Its big advantage, however, is the fact that its capacitance is much
smaller - due to the absence of minority carriers - and that makes it ideal for high-
frequency apphcations. The M-S junction is also called a Schottky junction.
37
E
vacuum
level
Ev
Ef
Ec
E
vacuum
level
Ev
Ef
Ec
fqv
s
s
i L
c
o
~V"
Ec
Ef
Ec
Ef
Ev
metal -a n-doped
c semiconductor
E
+
vacuum
(b)
E ,
vacuum
/•
: /
level
i
t- ^
Ec
Ev
i
_
Ef
Ef
A
Ev
Ec
(c)
Y
v*
metal
p-doped
c semiconductor
3
M —> S electron flow | | Conduction band
S —> M electron flow I I Valence band
^ Current density □ Overlapping bands
Eigure 3.11. Band diagram and currents of: (a) non-biased,
(b) forward-biased and (c) reverse-biased M-S junctions [after Ref. 1].
38
C. OHMIC CONTACT
If the interface region of an M-S junction is highly doped, then the barrier region
developed is quite narrow. When any kind of bias is apphed to the junction, dectrons do
not go over the barrier, instead, they are tunneled through it. This changes its behavior
totally making it resemble a regular small ohmic resistance. This is called a tunneling
ohmic contact. It is represented in Figure 3.12 and is characteristic can be seen in Figure
3.13.
E n
vacuum
level
Ev
Ef ■
Ec
Ec
Ef
Ev
E
vacuum
level
Ev
Ef -
Ec
Ec
Ef
Ev
Y
metal •,
A-.
c
o
u
c
3
-V-
n-doped
semiconductor
Y
3
metal
o
3
3
__^
'V
highly n-doped
semiconductor
(a) (b)
Eigure 3.12. Band diagram of: (a) Schottky and (b) tunneling ohmic junction.
Eigure 3.13. Characteristic curves of an ohmic (red) and a Schottky (blue) junction.
39
D. TUNNEL JUNCTION
The regular p-n junction as described earlier is built using tightly doped
materials. The concentration of impurities is around 1:10^ atoms of semiconductor. In
1958, the Japanese scientist Leo Esaki created a p-n junction using highly doped
materials with impurity concentration around 1000:10 making them degenerate. The
new junction develops a region of differential negative resistance, not seen in any other
device. This is called tunnel junction.
As shown in the energy diagram of Figure 3.14, the Fermi levels exist within the
bands themselves, due to the heavy doping. This creates a unique formation of the bands’
interface around the junction. For the same reason, the depletion region is far narrower
than this of a regular p-n junction. This enables electrons to be tunneled through the
barrier, without any change in their energy, instead of going over it. This is called band-
to-band tunneling. The tunneling phenomenon was explained in the previous chapter.
E A
Ec
Ev
Ef
Ec
Ev
highly p-doped
semiconductor
highly n-doped
c semiconductor
3
Figure 3.14. Band diagram of a tunnel junction.
40
In the characteristic I-V curve (Figure 3.15), the forward current is increasing to a
peak ]p at Vp and then is decreasing to a smaller valley current Iv at Vv, only to increase
again like a regular p-n junction. The region between Vp and Vy is that of negative
resistance.
Figure 3.15. Characteristic curves of a tunnel (red) and a regular (blue) p-n junction.
From the carrier transport point of view the TV curve is formed in the following
way. When the junction is reverse-biased, tunneling of electrons from the p-side valence
band to the n-side conduction band is observed (Figure 3.16a). If the bias is zero the
electrons tunneled from the p- to the n- side are in balance with those tunneled the
opposite direction and so no current is observed (Figure 3.16b). If forward bias is applied,
electrons are tunneled from the n-side conduction band to the p-side valence band
increasing the current (Figure 3.16c). As the bias increases, the common energy levels of
the n-side conduction band and the p-side valence band are reduced and so the current
decreases (Figure 3.16d). As the bias increases further, a point is reached when there are
no more common energy levels and so tunneling can no longer occur. Electrons now flow
from the n-side to the p-side conduction bands, absorbing energy and going over the
barrier like a regular p-n junction (Figure 3.16e).
41
w [if [^[Ij
Figure 3.16. Tunnel junction energy diagrams for each section of the I-V curve
[after Ref. 2:p. 518].
42
Characteristic curves of the so common Ge and GaAs are shown in Figure 3.17.
Other ways to build tunneling junctions are by using metal-insulator-semiconductor or
metal-insulator-metal technologies. Tunnel junctions have many apphcations in high
frequency circuits as well as multijunction solar cells as explained in the next chapter.
Figure 3.17. Characteristic curves of a Ge (blue) and a GaAs (blue) tunnel junction
[after Ref. 2:p. 530].
E. DIRECT AND INDIRECT TUNNELING
In the previous chapter the direct and indirect materials were defined and their
recombination differences were explained. Similar differences exist in tunneling, too.
Electrons are tunneled from the minimum of the conduction band energy-momentum (E-
k) curve to the maximum of the valence band E-k curve. In direct tunneling, those two
points have the same momentum. Direct tunnehng occurs in direct bandgap materials, but
also in indirect materials when the applied voltage is large enough to accelerate electrons
sufficiently to transition between the bandgap at equal point of momentum.
When the minimum of the conduction band E-k curve is not the same as the
maximum of the valence band E-k curve, the phenomenon is called indirect tunneling.
This difference in momentum Ak is supphed by phonons or impurities. In phonon-
assisted tunneling, the sum of the phonon energy plus the initial electron energy must
equal the final electron energy after the tunneling.
43
Ee (init) Eph — Eg (fin)
Similarly, the sum of the phonon momentum plus the initial electron momentum must
equal the final electron momentum after the tunneling.
ke (init) kph — kg (fin)
This way, both energy and momentum are conserved.
Direct tunneling, when possible, has a larger probabihty of occurrence than
indirect. Also, indirect tunneling with only one phonon is more probable than with
several phonons (Figure 3.18).
(a)
(b)
Figure 3.18. Direct (a) and indirect (b) tunneling [after Ref. 2:p. 519].
F. HETEROJUNCTIONS
A junction created by the same semiconductive material is called homojunction.
As both sides of the junction have the same lattice constant, the crystal atoms form
smooth chemical bonds in the interface area. 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.
44
Junctions created using different materials are eaUed heterojunctions. Sinee now
the lattiee eonstants do not mateh, the atoms ereate ehemieal bonds in the heterointerface
by adjusting their positions. This ereates strain and eauses erystal disloeations and
stmeture imperfeetions in depth. This wiU inerease earner seattering and henee decrease
their mobUity. Additionally, atoms with dangling bonds will form earner traps acting as
recombination centers, whieh wiU deerease earner lifetime (Figure 3.19).
Figure 3.19. Crystal disloeation in heterojunction.
For this reason, materials with similar lattice constants are used, tike GaAs with
AlAs. The use of ternary eompounds, like GaP + InP, is also recommended, as their
proportion ean adjust their lattiee eonstant to the required levels. (GaP)o. 5 i(InP)o .49 =
Gao. 51 Ino. 49 P is matched to GaAs.
Another way is to choose a substrate erystal plane that is shghtiy offset from a
major crystal plane so that the distance between the atoms on the substrate surface
approximates the distance between the atoms in the deposited fi lm of another
semiconductor material. This may also lead to a deflection of the dislocations, so that
they are primarily located near the heterointerfaee [Ref. 3 p. 222].
45
From an energy point of view, the formation of the heterointerface uses the
vacuum and Fermi energy levels in a way very similar to that of the M-S junction
explained in paragraph B and is illustrated in Figure 3.20.
vacuum
level
Ec
Ef
Ev
"V
n
j \_
n
u
c
3
“V"
p
J
o
c
3
P
Ec
Ef
Ev
o
c
3
Eigure 3.20. Band diagram of heterojunction formations.
The use of heterostructure fi lm s on porous Si has been proposed. The microscopic
islands and grooves of the Si surface reheve the strains and reduce dislocations. Einahy,
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 mobihty
of the device. Eor example, GaAs has a bandgap of 1.42eV and Alo. 3 Gao. 7 As 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 stmcture will look like in figure 3.21a.
Si can be used to dope the AlGaAs and make it n-type while the GaAs remains undoped.
46
This will raise the Fermi level and change the energy diagram like in figure 3.21b.
Electrons from the donor (Si) in AlGaAs will move into the GaAs layers because of their
lower energy conduction band. Now the donor atoms that would cause carrier scattering
are separated from the carriers (Figure 3.21), hence the electron mobility in GaAs is
increased. This increase is far greater than that of the bulk material and thus the carrier
mobihty is substantially improved.
c/ii
<
C/D
<
C/D
<
lyD
<
C/D
<
C/D
<
C/D
<
C/D
<
C/D
<
C/D
<
cd
cd
cd
cd
cd
o
o
o
o
o
a
o
a
o
a
<
<
<
<
(a)
(b)
Figure 3.21. Band diagram of superlattice formation
(a) undoped and (b) AlGaAs doped [after Ref. 2:p.l28].
Some heterojunction applications include photonic devices like photodetectors,
photodiodes, semiconductor lasers and solar cells.
47
THIS PAGE INTENTIONALLY LEET BLANK
48
IV. SOLAR CELLS
A. SOLAR ENERGY
The sun’s very high temperature is due to the nuclear fusion reaction of hydrogen
into hehum. Every second, 6T0 Kg H 2 is converted to 410 Kg He. The difference in
mass is called mass loss. It is converted into energy which, according to Einstein’s
relation E=mc , is equal to 4-10 J. This energy is emitted as electromagnetic radiation.
Its wavelength spans the ultraviolet and infrared region (0.2 to 3|im) [after Ref. 2:p. 791].
This energy arrives outside the earth’s atmosphere with an intensity of 1365W/m
and a specific spectral distribution called air mass zero (AMO). As it approaches the
surface, it is attenuated by infrared absorption due to water-vapor, ultraviolet absorption
due to ozone and scattering due to airborne dust and aerosols. The various solar energy
spectral distributions are specified in detail in the ISO standards, a brief summary of
which is shown in the Table 4.1:
Height
Sun’s position
Incident solar
power [W/m?]
Weather
conditions
Spectral
distrihution
outside atmosphere
-
1365
-
AMO
surface
0=90“ (zenith)
925
optimum
AMI
surface
0=48“
963
USA average
AM 1.5
surface
0=60“
691
average
AM2
Table 4.1. Solar energy spectral distribution conditions [after Ref. 1, 2, 3, 4].
Eor space apphcations AMO is used, while for terrestrial apphcations both AMI and
AM 1.5 (most common) are used. Both are shown in Eigure 4.1.
49
Irradiance [W/ cm^*um] Irradiance [W/ cnn^*um]
AMO and AMI.5 Spectrums
AMO and AMI .5 Spectrums
Figure 4.1. AMO (blue) and AM 1.5 (red) solar energy spectral distributions
[data after Ref. 31].
50
B. OPTICAL PROPERTIES
A beam of light is shined at a semiconductor (incident beam) with a certain angle.
If this angle is large enough, part of this electromagnetic energy whl be reflected back by
the semiconductor’s surface with an equal angle (Sneh’s law). The rest of it whl be
refracted inside the material with a smaher angle (Figure 4.2). The ratio of the incident
and the refractive angles is equal to the ratio of the speed of hght outside and inside the
material. This ratio is cahed refraction index nr.
^incident _ ^outside _
r
From the energy refracted in the semiconductor again only a part is absorbed. The
rest of it goes through and exits the material from its other side with an angle equal to the
incident angle. The amount of energy absorbed is described by the absorption index %.
The complex index of refraction rt* is defined as:
n* = nr x(1 -i?)
incident
beam
Figure 4.2. Path of hght beam through semiconductor.
51
Another way to describe the optical properties of a material is the dielectric
function £. This is given by:
6 = 6 ^ ±102 =(n±ik)^ from which -k^ and ©2 =2nk
Finally, reflectivity R is given by:
R_ (n-1)^+k^
(n+1 )^+k^
The values of Ei, E 2 , n and k vary according to the material and the wavelength of
the hght shined. For Si £ 1 and £2 can be seen in Figure 4.3.
Figure 4.3. £1 (blue) and £2 (red) for Si [after Ref. 6].
It is obvious that the hght that is reflected or not absorbed (passed through)
contains energy that is lost for the solar cell. In order to increase absorption, the
material’s thickness is increased. However, the reduction of reflection is not that easy.
The simplest method is the use of very thin layers of anti-reflective coating (ARC)
52
materials like MgF 2 and ZnS. More sophisticated and expensive methods involve the
creation of microgrooves on the surface of the semiconductor. Light rays reflected from
one groove hit another and finally enter the material. This is shown in Figures 4.4 and
4.5.
Figure 4.5. Light path in microgroove.
StiU, not all photons entering a solar cell are used. A number of them just happen
to go through it unaffected. A technique to Educe this number is using a very well shined
metallic plate as the bottom contact of the cell. Photons not used are now reflected by it
and re-enter the cell layers. This way, the probabihty of them not being used is reduced
by half. An improvement of that introduces a thin oxide layer above the bottom contact to
increase its reflectivity (Figure 4.6).
53
oxide
n
p
- 1 ^ _1 1_1
bottom contact
Figure 4.6. Improved reflective bottom contact.
The energy produced by a solar cell is directly proportional to the intensity of
light shining on it. In order to increase this amount, various lens and mirror constmctions
{concentrators) are used. These are much cheaper than cells and can greatly reduce the
total cost of produced energy, since less cells are now required. However, in space
apphcations, their weight is very high and the cost related to it largely exceeds that of the
cells. This restricts their use only to terrestrial apphcations.
C. FUNDAMENTALS
We have seen earlier that electrons can be excited with heat and that atoms can be
ionized to produce EHP’s. Another way to offer such energy to a material is photons
{photogeneration), thus hght. In a single type semiconductor this creation of carriers
leads to an increase in conductivity.
In a p-n junction, however, those carriers will become separated {carrier
separation) and minority carriers wiU be swept across the junction, due to the
electrostatic field of the depletion region. This way, an excess of electrons (negative
charge) whl be observed in the n-type semiconductor and similarly, an excess of holes
(positive charge) whl be observed in the p-type. This excess of majority carriers whl
develop a voltage differential on the two sides of the device (figure 4.1). This voltage is
quite large for the M-S junctions of the contacts to counter and therefore, can be eashy
measured. If a resistance is connected to the device, current {photocurrent) whl flow.
This phenomenon is cahed photovoltaic.
54
In order to create an EHP, a specific minimum quantum of energy is required.
This is equal to the bandgap Eg of the semiconductor. A photon entering the ceU with
energy less than Eg wiU not be absorbed and wiU pass through it. A photon with energy
equal to Eg is ideal for the creation of an EHP. EinaUy, a photon with larger energy wiU
create an EHP offering energy equal to E and waste the remaining amount as heat to the
lattice. Such heat, however, will deteriorate the electrical properties of the material.
As the amount of photons entering the material becomes larger, so does the
number of generated EHPs. Hence, the photocurrent increases and the produced power
increases, too. Unfortunately, a number of carriers recombine inside the material before
they are collected at the contacts. This number becomes very large in semiconductors
with significant amount of recombination centers. A schematic of a ceU is shown in
Eigure 4.7.
V*
Depletion region
# Hole EHP generation I-1 Neutral charge
# Electron • Electrostatic field I I Positive charge
I I Negative charge
Eigure 4.7. Schematic of a simple solar ceU.
55
The derived I-V curve {illuminated characteristic) is illustrated in Figure 4.8a
with the red hne. It mainly exists in the 4th quadrant, which means that it produces
energy. Note the similarity to the I-V shown in the same figure in blue. This is the
characteristic in the absence of hght and is called dark current characteristic. As a power
supply, the illuminated characteristic can be presented inverted like in Figure 4.8b. V)c is
the open circuit voltage and Isc is the short circuit current. The blue rectangle is called
maximum power rectangle and corresponds to the values of V and I for which the power
produced (P=V I) becomes maximum. The ratio of the maximum power rectangle to the
Voc-Isc rectangle is called/////actor FF.
The power conversion efficiency n of the solar cell is the ratio of the maximum produced
power Pmax to the incident power Pine of the hght.
max
me
(a)
(b)
Figure 4.8. Dark (blue) and hluminated (red) characteristic curve of the solar ceU.
56
If the light propagates towards the y-axis, then its intensity ean be expressed by
F(y). The hght absorption would then be dF(y)/dy. This leads to the following equation:
where a is called absorption coefficient. The distance 1/a is called light penetration
depth and its relation to F is show in Figure 4.9:
F
F/e
1 /a (hght penetration depth) y
Figure 4.9. Light intensity F in semicondactor vs distance from surface y [Ref. 3].
dF(y)
dy
D. TEMPERATURE AND RADIATION EFFECTS
The effects of temperature on the resistivity of materials were explained in
previous chapters. In solar cells and in semiconductors in general, it was shown that a
small increase in temperature facilitates EHP generation and hence is beneficial to the
electrical properties of the materials. However, further rising of temperature causes an
unwanted increase in their resistivity, drasticaUy deteriorating their behavior.
In addition to that, the phenomenon of diffusion becomes more intense as
temperature rises. This leads to an increase of fc- However, \()c decreases exponentially
with temperature, countering the benefit of the higher Isc and further reducing the
maximum power produced by the cell.
The knee of the cell’s I-V curve also becomes more round (soft) with
temperature. This way, the maximum power rectangle and the fill factor are decreased. It
is obvious now that, overall, the efficiency of the cell is greatly reduced as temperature
rises (Figure 4.10).
57
V T
(a) (b)
Figure 4.10. Effect of temperature on the I-V curve (a)
and the normalized efficiency (b) of solar cells.
For space apphcations, radiation that exists outside the earth’s atmosphere can
also have a significant effect on solar cells. High-energy particles, entering the cell,
create imperfections in the lattice stmcture that act as recombination or trapping centers.
This particle bombardment is continuous and thus, the cell output decreases with time.
Various materials are affected differently by radiation. For example Si is more sensitive
than Ge. Also, p-on-n cells are also more sensitive than n-on-p. In order to cope with
this problem, several techniques are used. Introducing Fi to the lattice is one of them. Fi
can diffuse to and combine with the created defects and so prevent the degradation of the
cell. Another method is the placement of a thin cover (usually cerium-doped) in front of
the cell to filter out some of the high-energy particles (Ref. 2).
E. CELL TYPES
Photovoltaic phenomena were first observed and studied by the French scientist
Henri Becquerel in 1839. The first material used was selenium in 1877. Better
understanding of the mechanics involved was provided by Einstein in 1905 and by
Schottky in 1930. Chapin, Pearson and Fuller were the first to develop a Si solar cell, in
1954, with 6% efficiency. (ACREWeb, http://acre.murdoch.edu.au)
58
One way to categorize solar cells is by their substrate material. The most common
materials used are Si, Ge and GaAs. Si is actually sand and so it is very cheap. It also has
better efficiency than Ge or GaAs, but is more sensitive to radiation. Even though Ge and
GaAs are not very efficient, their combination in a multijunction cell (discussed later) can
produce much better results, but with a big increase in fabrication cost. Finally, Si is non¬
toxic and non-poisonous, in contradiction to GaAs. For all these reasons it is widely used
for terrestrial apphcations while Ge and GaAs are more used for space apphcations.
According to the amount of material crystaUization, a cell can be amorphous,
polycrystaUine or single-crystal. The easiest and cheapest method for creating solar cells
is by using non-crystalhne or amorphous semiconductors (Figure 4.11c). The problem
with such materials is the existence of many danghng bonds that act as recombination
centers. To cope with this problem, semiconductor-hydrogen alloys, with fairly large
concentration of H 2 , are used. li tends to tie up those bonds and reduce the number of
recombination centers. Si-H (a-Si), Ge-H and Si-C-H have been built and are used in
cells. Maybe the most important advantage of this type is its combination with thin-film
technology. This provides the abihty to produce large-area cells, using small amounts of
semiconductive material. It also allows their fabrication on various, even flexible,
substrates (glass, plastic etc) at very low cost. Their efficiencies are not very high,
reaching only up to 15%, therefore they are mostly used in commercial apphances and
terrestrial apphcations.
Polycrystalhne ceUs are produced from thin (approx 300|im) shoes of
semiconductive material that contains a number of large crystallites separated by grain
boundaries (Figure 4.11b). This is done by pouring molten material into a cyhndrical or
rectangular mold and ahowing it to set. A significant number of recombination centers
exist on the borders of the crystahites. The fabrication cost is a little higher, but the
efficiency of the ceh is much better reaching 20%. Much of the cost increase is attributed
to the material lost as sawdust during the shcing process.
Single crystal cehs (Figure 4.11a) are produced from shoes of a large (usuahy 6-
8 “) single crystal ingot cahed boule. This ingot is grown by slowly hfiting a smah crystal
over a highly-pure melt of the same semiconductive material. The wafer produced is an
almost perfect lattice with very tittle impurities or defects. The efficiency of these cells is
59
the highest available reaching 25%, but the whole process of growing the crystal, added
to the slicing loss, makes these cells very expensive. Single crystal cells are mostly used
for space apphcations where the need for high-density and hghtweight power sources is
more important than fabrication cost.
I I I I I I
(a)
\/
dangling
bonds
/\
/\
/
(c)
(b)
Figure 4.11. (a) Single-crystal, (b) polycrystaUine and (c) amorphous material.
F. CONTACTS
Since the efficiency of aU types of solar cells is not high, it is essential to
mi nim ize losses wherever possible. One area is the method used to collect the produced
current. Electrical contacts may introduce junction voltages and ohmic resistances. In
order to e lim inate the first, layers of metal-semiconductor alloys on top of highly-doped
semiconductive material are introduced between the contact and the cell. Ohmic
resistance can be eliminated by using very low-resistivity metals tike gold (Au).
60
The bottom contacts of a cell are easier to develop as the only additional
consideration is that they have a good reflective surface, as seen in paragraph B. On the
contrary, top contacts require more examination as they block photons from entering the
cell (^hadowing effect). For this reason, various grid stmctures have been developed. On
one hand, these grids need to be thick enough for good conductivity and dense enough for
collecting as much photogenerated carriers as possible. On the other hand, they need to
be thin and sparse enough to avoid casting too much shadow on the cell. A very common
compromise is a shadowing (or shadow loss) of 10% for single crystal cells. Some
contact configurations can be seen in Figure 4.12.
However, amorphous cells would require a much more dense grid. This is due to
the fact that their carriers display very small horizontal movement. Such a grid would
cast too much shadow over the cell, making it unusable. For this reason transparent
contacts, with smaller conductivity, have been developed. These are made by using a
transparent conducting oxide (TCO) such as tin oxide (Sn02). Amorphous cells are
usually built the opposite way. First the TCO layer is created in the form of a glass
61
superstrate. All the cell layers are then built on it from top to bottom using thin-film technology.
In the end, the bottom metal contact is added.
G. ARRAYS
As seen before, a cell usually has a Vos less than 2V and a Isc of a few mA
providing a total power of 2-3Watts. In order to use solar cells in a wider range of
applications, a number of cells is connected in series to increase the voltage and then in
parallel to increase the current provided. Those constructions are called modules. Thin-
fihn modules can be bruit directly, bypassing the single-cell stage. Furthermore, modules
can be connected together to form much larger power arrays in the range of several
MWatts (Figure 4.13).
Figure 4.13. (a) Solar cell, (b) module and (c) array
[after Ref. 32].
62
V. MULTUUNCTION SOLAR CELLS
A. BASICS
We have seen previously that a material can be ionized by photons with energies
higher than its bandgap, or in other words with wavelengths lower than the wavelength
corresponding to this bandgap. The equations connecting photon energy and wavelength
are the following:
E=h-f and c= ?-f
where E is the photon energy, X is its wavelength, f is its frequency, c is the speed of hght
and h is Plank’s constant. Photons with energies lower than the bandgap go through the
material unaffected and unused (Figure 5.1).
Figure 5.1. Absorption energies and wavelengths for Ge, GaAs and GalnP
on AMO spectrum.
63
This might lead to creating only Ge cells, since they can absorb most of the solar
spectmm. Another reason that might lead to the same conclusion is shown in the I-V
curves of the individual cells in Figure 5.2. Obviously, Ge cells produce much more
current per cm than others. However, its voltage is much smaller and so the power
output per area unit of Ge is smaller than this of Si.
Figure 5.2. I-V curves for Si, Ge, GaAs and GalnP cells.
An optimal combination is the mechanical stacking of aU these types (one over
the other) and connected in series. This is called tandem cell. Cells with the higher
bandgap are placed above cells with lower bandgap. This way, a cell will absorb the
higher-energy photons and will produce electric power. At the same time, it will allow
the lower-energy photons to pass through it. These will enter the next cell in line and so
on... There is virtually no lim itation to the number of cells stacked, as long as their
bandgaps are different. In theory, the efficiency of such cell can reach 60%. The sum of
the cells’ individual spectmm responses produces the response of the tandem cell. This
method is called spectrum separation (Figures 5.3 and 5.4).
64
Figure 5.3. Tandem cells.
65
B. MONOLITHIC MULTUUNCTION CELLS
Mechanically stacked cells have a lot of additional volume and weight due to the
stacking mechanisms used. This is a serious disadvantage for space applications. In
addition, a significant amount of energy is lost due to reflection as hght goes from one
cell to the other. In an attempt to e lim inate these problems, the monolithic tandem cells
were created. In these cells, oxide layers are used to provide electrical insulation between
cells. A number of internal contacts were also used to perform the in-series connection of
cells. These contacts were also made external to provide valuable information of the
individual cells (Figure 5.5).
□
GalnP
□
GaAs
□
Ge
n
oxide
□
contact
Figure 5.5. Monohthic tandem cell.
However, significant loss and shadowing led to the creation of what is now called
monolithic multijunction cell (Ml cell). The problem with simply connecting cells
together hes to the fact that new junctions would be created between cells. Those
junctions would be reversed-biased and their depletion-region electrostatic field would
oppose the flow of carriers towards the contacts. This would prevent the cell from
producing any current.
Instead, specially prepared tunnel junctions can be used to solve this problem. A
reverse-biased tunnel junction will conduct current the desirable way, due to the
tunneling phenomenon explained in earher chapters. The tunnel layers are always more
heavily-doped than the cell layers. For this reason, intermediate junctions formed
between the tunneling junctions and the cells will conduct current from the p to the p"^
regions and from the if to the n regions. This will allow current flow instead of hindering
it. Although the tunneling junction layers introduce considerable losses that affect the
66
overall efficiency of the cells, they are currently the most attractive technique for
connecting cells (Figure 5.6).
top
ceU
bottom
ceU
r
)
n
\
T T ▼ T ▼
>
P
A A A A A
• • • « •
• • • • •
1
n
T ▼ ▼ ▼ ▼
P
V
(a)
▲ depletion region
: electrostatic field
top ceU
junction
parasitic
junction
bottom ceU
junction
top
ceU
tunneling
layers
bottom
ceU
A tunneling region
; electrostatic field
T ▼ T ▼ ▼
P
▼ ▼ ▼ ▼ T
P"
▼ ▼ T ▼ ▼
n+
• • • • •
T ▼ T ▼ ▼
n
T ▼ T ▼ T
P
(b)
top ceU
junction
intermediate
junction
tunnel
junction
intermediate
junction
bottom ceU
junction
Figure 5.6. (a) Simple connection of cells and (b) connection using tunneling junction.
C. CURRENT DEVELOPMENTS
We have seen previously that layers of different materials, grown on top of each
other, create danghng bonds that act as recombination centers. For this reason, the need
for using lattice-matched layers is apparent. Unary semiconductors like Ge and binary
like InP have fixed lattice constants and therefore cannot be matched directly. On the
other hand, ternary hke GalnP and quaternary like AlGalnP alloys can easily be
constmcted to have almost any desirable lattice constant.
When non-matching materials (i.e. unary and binary) are required to be placed in
contact together, a method called windowing can be used. According to this, a thin layer
67
(window) of an alloy is grown between them to eliminate the unwanted surface
recombination. The window creates a gradient that smoothes-out the lattice difference.
Its bandgap is carefully selected to be higher than the bandgap of the cells beUow it.
Additionally, with its small thickness, the window does not consume valuable photons.
As photogeneration takes place, minority carriers diffuse towards the junction of
the ceU. However, some of them tend to diffuse the opposite way, towards the back
surface of the ceU, introducing more losses. To avoid that, a thin highly-doped layer is
placed right below the ceU, creating an electrostatic field that will push minority carriers
towards the junction. This is called back surface field (BSF). Thicker BSFs are often used
above the substrate, forming what is called a high-low junction.
At this moment, the triple MJ ceU (Figure 5.7) with the highest efficiency (29.3%)
published is built by Spectrolab [Ref. 19]. It is built on a Ge substrate, which also acts as
a base for the bottom cell. On top of it is the Ge emitter and an AlGaAs window. Two
heavUy-doped n and p GaAs layers follow, forming the tunnel junction between the
bottom and the middle cell. On top of it is a GalnP BSF and then the GaAs middle ceU
with its GalnP window. Another GaAs tunnel junction foUows and above that the
AlGalnP BSF of the top cell, the top GalnP ceU itself and its Alln P window. The surface
of the cell is covered with an ARC to eliminate reflection. Below the contacts only, there
is a GaAs layer. This is caUed cap and is used to faciUtate current movement to the
fingers. It also protects the underlying layers from being damaged when the contacts are
heated during bonding. In foUowing chapters we wiU model the parts of this
configuration individuaUy and then combine them to form the whole stmcture. The same
company is also experimenting with a quadmple AlGaInP/GaAs/GaInNAs/Ge MJ ceU
with even higher efficiency.
68
top
cell
tunnel
junction
middle
cell
tunnel
junction
bottom
cell
Figure 5.7. Spectrolab’s triple MJ cell [after Ref. 19].
69
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70
VI. SIMULATION SOFTWARE
After a thorough review of the existing modehng and analysis tools, along with
related pubhcations, the suite of tools and reusable models developed by Silvaco [Ref.
14] was selected. In this chapter, the strategy and methodology, for modehng solar ceUs
using Silvaco, is discussed. An overview is also given of the software that was developed
or reused in order to enhance its functionality and to meet the modehng and simulation
needs for researching advanced solar cells.
A. MODELING TODAY
There is a very large number of pubhcations available that document the
modehng of almost every aspect of solar ceh function and behavior. These span from the
macroscopic electrical to the microscopic molecular level and have very high accuracy
and credibihty.
However, they ah address individual solar ceh viewpoints, without providing a
complete coverage of the complex combination of phenomena that actuahy take place.
Thus, there is a need to select and use a large number of different models, in order to
study an actual complete ceh stmcture. An important consideration is the fact that not ah
of these models are compatible with each other. This makes their selection prone to
errors, quite hard, and time consuming. In addition, each one exposes the researcher to
many detailed parameters that usuahy create a lot of unnecessary confusion. Ah the
above make complete simulation of advanced solar cehs a forbidding task.
As a consequence, solar ceh research today is conducted by actuahy fabricating
cehs and experimenting with them. Then, researchers theorize about the cohected results.
Although that methodology provides the most credible results, it may also lead to some
confusion. The reason hes in the huge number of factors that always need to be
considered, most of which are more relevant to the fabrication process used and not the
ceh itself. Therefore, many combinations of parameters need to be materiahzed lik e
material types and characteristics, doping, dimensions, fabrication conditions and
71
processes. This is not only a time and personnel consuming task, but can also be
expensive to carry out. The number of experiments, needed to answer questions, is also
very large, due to the fact that experts are not allowed to focus on a certain issue. Instead,
they need to consider and develop the design and the complete fabrication process of the
cell under study. Additionally, in any kind of experiment there is always a number of
unpredictable factors that may introduce deviation among results.
Extensive research, of the existing hterature and COTs, revealed that no
methodology, copping with these problems, currently exists. Small attempts were found
to lack the breadth of a complete simulation tool. For this reason, they have not been
adopted by the Photovoltaic community. In this thesis, a new method for developing a
reahstic model of any type of solar cell is presented.
B. SILVACO
Silvaco is a company that specializes in the creation of simulation software
targeting almost every aspect of modem electronic design. In their TCAD suite of tools,
the company provides modehng and simulation capabihties for simple Spice-type
circuits all the way to detailed VLSI fabrication (Figure 6.1). User-friendly environments
are used to facihtate design and a vast number of different modehng options. The tools
provide for creating complex models and 3D stmctural views.
The phenomena modeled range from simple electrical conductivity to such things
as thermal analysis, radiation and laser effects. A wide variety of detailed layer-growth
processes and material properties (e.g. mobihties, recombination parameters, ionization
coefficients, optical parameters) add to the accuracy of the simulation. However, todate
thesre is no publicly available documentation of efforts by researchers or solar ceU
manufacturers to utihze this powerful tool for the modeling of advanced solar ceUs, but
only of simple stmctures.
72
Figure 6.1. Silvaco’s TCAD suite of tools [after Ref. 14].
For this purpose, Adas is a good combination of sophisticated in-depth device
analysis in 2D or 3D. In addition, it abstracts away all fabrication details, shifting the
focus of the modeler to the actual design. Like the rest of TCAD apphcations, it is based
on hundreds of widely accepted pubhcations, verified for their accuracy and correctness
73
by numerous researchers. This variety provides for features such as the following and
others [Ref. 10 p. 1.4]:
• DC, AC small- signal, and full time-dependency
• Drift-diffusion transport models
• Energy balance and Hydrodynamic transport models
• Lattice heating and heatsinks
• Graded and abmpt heterojunctions
• Optoelectronic interactions with general ray tracing
• Amorphous and polycrystaUine materials
• General circuit environments
• Stimulated emission and radiation
• Fermi-Dirac and Boltzmann statistics
• Advanced mobihty models
• Heavy doping effects
• Full acceptor and donor trap dynamics
• Ohmic, Schottky, and insulating contacts
• SRH, radiative. Auger, and surface recombination
• Impact ionization (local and non-local)
• Floating gates
• Band- to- band and Fowler- Nordheim tunneling
• Hot carrier injection
• Thermionic emission currents
C. WORKING WITH ATLAS
Atlas can accept stmcture description files from Athena and DevEdit, but also
from its own command files. Since, for the purposes of this thesis, detailed process
description is not required, the later is the more attractive choice. The development of the
desired stmcture in Atlas is done using a declarative programming language. This is
interpreted by the Atlas simulation engine to produce results. A brief walk-through of
how a stmcture is built and simulated follows.
1. Mesh
The first thing that needs to be specified s the mesh on which the device will be
constmcted (Figure 6.2). This can be 2D or 3D and can be comprised of many different
sections. Orthogonal and cylindrical coordinate systems are available. Several constant or
variable densities can be specified, while scaling and automatic mesh relaxation can also
74
be used. This way, a number of minimum triangles is created; this determines the
resolution of the simulation. The correct specification of the mesh is very important for
the final accuracy of the results. If the number or density of triangles is not high enough
in regions, such as junctions or material boundaries, the results of the simulation will be
cmde and possibly misleading. On the other hand, use of too many triangles will likely
lead to significant and unnecessary increases in execution time.
-60 -«0 -20 0 20 40 60
Width [|j.m]
Figure 6.2. Typical mesh.
2. Regions
The material regions need to be specified next. Here, all parts of the grid are
assigned to a specific material (Figure 6.3). This can be selected out of SHvaco’s own
hbrary or can be custom-made by the user. In addition, heterojunction grading between
materials can also be described.
75
Figure 6.3. Regions specified.
3. Electrodes
To define the electrodes of the device, their position and size need to be entered.
Additional information about their materials and workfunctions can be supphed if
needed.
4. Doping
Each material can be doped by any dopant to the desired concentration. This can
be done in a regular uniform way, in a linear or even a Gaussian distribution. Non¬
standard doping profiles can also be inputted from other TCAD programs or from custom
ASCn files. More advanced doping can be used by using the built-in C interpreter.
Automatic optimizations of the mesh according to doping can be performed afterwards.
76
5. Material Properties
Materials used throughout the simulation can be selected from a hbrary that
includes a number of common elements, compounds and alloys. These have their most
important parameters already defined. However, in solar cells the use of exotic materials
is not unusual. For such purposes, there is the abihty to fuUy define already existing or
brand new materials, down to their smallest detail. Such properties range from the
essential bandgap and mobihty all the way to laser absorption coefficients. Contact
information and workfunctions can also be entered here.
6. Models
More than seventy models can be used to achieve better description of a full range
of phenomena. Each model can be accompanied by a full set of its parameters, when
these differ from the default. Again new models can be described using the C interpreter
capabihty.
7. Light
When hghting is important for a device (hke in solar cells), there is the abihty to
use a number of hght sources and adjust their location, orientation and intensity. The
spectmm of the hght can be described in ah the necessary detail. Polarization, reflectivity
and raytrace are also among the simulator’s features.
8. Simulation Results
Once everything is defined the user can take unbiased measurements, bias certain
contacts, short others and take more measurements (Figure 6.4). This way fc, Vqc and
other values can be read. Additionahy, I-V curves and frequency responses may be
obtained. From these, a variety of diagrams can be displayed using a program called
TonyPlot. An additional feature is the abihty to take measurements from any part of the
device and see a 2D or 3D picture of various metrics such as carrier and current densities,
photogeneration, potential and e-fields. These pictures are invaluable for the insights
they offer.
77
D. SIMULATION SOURCE CODE
The full set of souree eode used to program the simulations deseiibed in the
following chapters can be found in Appendix F. In order to enhance understanding, aid
further development by others and avoid unnecessary repetitions and confusion, the
following scheme has been used to present the code. All the files contain main sections
structured the same way:
78
go atlas
# Definition of constants
# Mesh
# X-Mesh
# Y-Mesh
# Regions
# Electrodes
# Doping
# Material properties
# Models
# Light beams
# Solving
Each commented seetion is filled using eode from its eorresponding subseetions.
For example for deriving the Isc and Vqc of a simple GaAs eell, the eode beeomes:
go atlas
# Definition of constants
# Mesh
mesh space.mult=l
# X-Mesh: surface=500 um2 = 1/200,000 cm2
x.mesh loc=-250 spac=50
x.mesh loc=0 spac=10
x. mesh loc=250 spac=50
# Y-Mesh
# Vacuum
y. mesh loc=-0.1 spac=0.01
# Emitter (0.1 urn)
y.mesh loc=0 spac=0.01
# Base (3 um)
y.mesh loc=3 spac=0.3
# Regions
# Emitter
region num=l material=GaAs x.min=-250 x.max=250 y.min=-0.1 y.max=0
# Base
region num=2 material=GaAs x.min=-250 x.max=250 y.min=0 y.max=3
# Electrodes
79
electrode name=cathode top
electrode name=anode bottom
# Doping
# Emitter
doping uniform region=l n.type conc=2el8
# Base
doping uniform region=2 p.type conc=lel7
# Material properties
material TAUN=le-7 TAUP=le-7 COPT=1.5e-10 AUGN=8.3e-32 AUGP=1.8e-31
if GaAs
material material=GaAs EG300=1.42 PERMITTIVITY=13 . 1 AFFINITY=4 . 07
material material=GaAs MUN=8800 MUP=400
material material=GaAs NC300=4.7el7 NV300=7el8
material material=GaAs index . file=GaAs . opt
# Models
models BBT.KL
# Light beams
beam num=l 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 bl=l
contact name=cathode current
solve icathode=0 bl=l
If now, the IV characteristic must be produced, only the “Solving” section needs
to be changed with code from the corresponding subsection. This could very well be
handled by using object-oriented programming. Unfortunately, VWF does not support
such functionaUty. The scheme used here is an attempt to provide a substitute even
though it is a primitive one.
E. EXCHANGING DATA WITH MATLAB
In spite of the functionahty provided by TonyPlot, there is often the need to
exchange data between TCAD and more flexible and general environments such as
80
Matlab. Since this functionality is not supported by the program, part of this thesis
involved the development of several Matlab functions to provide this. The source code
can be found in Appendix G.
1. Creating Silvaco input files
Before mnning a simulation, several input data must be provided to the program.
One set of inputs consists of solar spectmm power files and material optical parameter
files. VEC2SPEC creates the power file for any solar spectmm specified in its input.
Using this function, power files for AMO, AM 1.5 and AM2 were created.
Function name: VEC2SPEC
Input arguments: wavel: An array with the wavelengths to be saved.
int: An array with the corresponding intensities,
filename: The name of the file to be saved.
Output arguments: none
Syntax: VEC2SPEC(wavel, int, filename)
OPT2SILV creates n and k optical parameter files for various materials. This was
used to produce files for all the materials used in this research (i.e. Ge, GaAs, GaP, InP
etc).
Eunction name: OPT2SIEV
Input arguments: filename: The name of the .mat file that contains the data.
t: The type of data, “e” for el and e2 vs. energy [eV] and “n” for
n and k vs. wavelength [pm]
Output arguments: none
Syntax: OPT2SIEV(filename, t)
2. Extracting results
AH Silvaco numerical data may be saved at log files. These may contain totally
different types of data. DISPLOG scans a log file and displays the types of its contents.
Eunction name: DISPEOG
Input arguments: filename: The name of the .log file to be read.
Output arguments: none
Syntax: DISPEOG(filename)
81
An example of its output is:
>> displog('GaAs-l-IV')
ATLAS
Electrodes:
1. cathode
2. anode
Values :
1. Light Intensity beam 1
2. Available photo current
3. Source photo current
4. Optical wavelength
5. cathode Voltage
6. cathode Int. Voltage
7. cathode Current
8. anode Voltage
9. anode Int. Voltage
10. anode Current
Various log files have a peculiar format. PARSELOG translates this and parses all
existing data.
Function name: PARSELOG
Input arguments: filename: The name of the .log file to be read.
Output arguments: prog: The name of the program that originally created the file.
numOfElec: The number of electrodes for which data is provided.
elecName: A cell containing the name of these electrodes,
val: The number of different types of values in the file.
vafName: A cell containing the names of those types,
data: A matrix containing the actual data. Columns contain data
of the same type.
Syntax: [prog, numOfElec, elecName, val, valName, data] =
PARSELOG(filename)
82
PLOTLOG creates plots of data that exist in a log file.
Function name: PLOTLOG
Input arguments: filename: The name of the .log file to be read.
x-axis: The number of the data type to appear on the x-axis. This
is the number that is shown by the DISPLOG function.
y-axis: The number of the data type to appear on the y-axis. This
is the number that is shown by the DISPLOG function.
style: The style of the line to be used for the plot. See PLOT
function for the supported styles.
xmult: Multiphcation factor for the values on the x-axis.
ymult: Multiphcation factor for the values on the y-axis.
Output arguments: none
Syntax: PLOTLOG(filename, x-axis, y-axis, style, xmult, ymult)
EV2UM , UM2EV and E2NJ are also written to implement unit transormations for
supporting the above files.
83
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84
m MATERIAL PROPERTIES
The next portion of thesis study contains the research related to how various
materials and their physical and electrical properties are modeled. This was a challenging
task as most of the materials used in advanced solar cell technology are exotic and httle
published research exists.
A. CURRENT STATUS
Analytical modehng rehe on the use of equations to approximate the actual
behavior of - in our case - solar cells. As such, they require a detailed description of the
device to be simulated and the materials that are used in its constmction. It will become
apparent in later chapters that the selection of the appropriate material type and
composition as well as its electrical properties are very important to the efficiency of both
real and simulated cells.
According to the existing hterature, the materials mostly used are the single
element semiconductors Si and Ge and the binary compounds GaAs and InP. In addition
to those, many ternary and quaternary compounds are also used in most cases. These are
alloys of three or four of the Al, As, Be, Cd, Ga, Hg, In, N, P, Pb, S, Sb, Sc, Se, Te, Zn
and other, less common, elements. The large number of these combinations provides
electronic device researchers with a valuable abundance of choices.
However, the electrical and physical properties of each material cannot be
theoretically calculated with enough accuracy. Instead, they need to be measured in very
precise and expensive experiments. Therefore, the material abundance, mentioned earher,
creates a huge task for physicists. The single element semiconductors and the binary
GaAs have been studied exhaustively. However, for the rest of the binaries, only their
major and most important properties are published. For the ternaries and quaternaries,
very httle is available and most of the times, the only solution is provided by
interpolating the properties of their binary components.
85
B. SILVACO LffiRARY
Silvaco maintains a property library of many materials common to electronic
devices. However, in an effort to push solar ceU efficiency to higher levels, researchers
tend to use many exotic materials. For them, Silvaco’s hbrary is under development and
mostly incomplete.
The models used in this thesis are heavily dependent on the following properties:
• Bandgap Eg
• Electron and hole density of states Nc and Ny
• Electron and hole motihties MUN and MUP
• Eattice constant a
• Permittivity
• Electron and hole hfetimes TAUN and TAUP
• Electron affinity
• Radiative recombination rate COPT
• Electron and hole Auger coefficients AUGN and AUGP
• Optical parameters n and k
Values for most of these have been provided by various publications. As another part of
this thesis, a large number of such pubhcations has been researched. Theis collection of
information has been identified, categorized and compared. EinaUy, the best have been
selected and used in the simulations described in this thesis. Parameters, for materials not
found in pubhcations, have been mathematicahy approximated. In addition, several weU-
studied cells were also used as references to provide calibration for these unknown
values.
Eurthermore, a very large number of additional parameters can still be specified.
However, they mostly represent secondary phenomena. These wiU be approximated by
values of weU-known materials hke Si, Ge or GaAs. Due to the secondary agnificance of
the properties, bad approximations wiU only lead to errors within acceptable noise
margins.
86
C. LATTICE MATCHING AND ALLOY PROPERTIES
An alloy is created with a combination of binary compounds under eertain
proportions. Thus, one part of the ternary GalnP is aetuaUy x parts GaP plus 1-x parts
InP. A way to represent this is (GaP)x(InP)i_x or simpler GaxIni_xP.
The properties of the alloy have values between those of the properties of its
eomponents. This is rarely a linear l:x relationship, as shown in Figure 7.1, but most of
the times it can be approximated as such. For example, GaAs has a lattiee constant
a=5.65A, GaP has a=5.45A and InP has a=5.87A. In order to lattice match GaxIni_xP to
GaAs we need
^GaAs ~^GaP ' X -
'^GaP '^InP
whieh returns ?e0.52 (Gao. 52 Ino. 48 P)- GaP has ^=2.35eV and InP has ^=1.42eV so, in
this ease, its bandgap will be
-x)-Eg"^
whieh returns Eg=1.9eV. Other properties ean also be ealculated the same way for
ternaries and quaternaries.
87
When higher aecuracy is required, sets of bowing parameters have been pubhshed
to produce a better approximation to this non-linearity. For ternaries the quadratic form
E°‘‘"'’'=x-E°‘‘’'+(I-x)-Ep''-x-(I-x)-Ba,„„p [Ref. 33]
is used where BQ^inp is the bowing parameter for GaInP. For quaternaries like the
AlxGai-xIUyPi-y the expression
j^AlGalnP
[Ref. 33]
jc • (1 - Jc)[(l - y) • + y ■ ] + y • (1 - y)[jc • Ef^^ + (1 -x) •
x-{l-x) + y{l-y)
can be used where and are the bandgaps for AkGai-xP and AlxGai-xIn
respectively and Eg"^*^"^ and Eg'^^^"^ are the bandgaps for Al[iy,Pi_y and GaInyPi_y
respectively as calculated above.
D. OTHER CALCULATIONS
Temperature compensation for the bandgap can be calculated by using the
following equation:
£,(7-) = i.,(0)-^
where a, (3 and either Fg(T) or Eg(0) can easily be found in existing research.
The effective density of states of electrons Nc and holes Ny can be found using
Nc=2-
^600-71-ml-k
3
32
and Ny — 2-
^eOO-n-mrk
_ h
3
32
[after Ref. 10:p. 3.5]
V y \ j
where rn is the effective mass of the carrier in question, h is Plank’s constant and k is
Boltzmann’s constant.
88
E. RESULTS
A detailed set of major material parameters has been produced by literature
research and calculations as well as cahbration from well-known cells. Tables 7.1 to 7.5
show the values that were finally produced and used for the purposes of this research. All
Nitrides are zinc blende. Numbers in blue color indicate that the values were found in
existig hterature, while numbers in green have been calculated. All properties are at
300°K unless other wise indicated. Values indicated with a “NR” were not found
anywhere in published research. The optical parameters n and k are different for every
wavelength. Due to the large quantity of numbers, they are not shown here.
Material
^ o
g,®
1 >
re ",
OQ
a(r)
[meV/K]
CCL '—'
X
^ o
re®
?>
re ",
OQ
a(r)
[meV/K]
CQ_ “
O
re®
?>
re ",
OQ
a(r)
[meV/K]
CCL “
Bandgap Eg
[eV] @300° K
Si
1.12
Ge
0.67
GaAs
1.519
0.5405
204
1.981
0.46
204
1.815
0.605
204
1.42
AlAs
3.099
0.885
530
2.24
0.7
530
2.46
0.605
204
2.16
AIN
4.9
0.593
600
6
0.593
600
9.3
0.593
600
6.28
AlP
3.63
0.577
372
2.52
0.318
588
3.57
0.318
588
2.45
GaN
3.299
0.593
600
4.52
0.593
600
5.59
0.593
600
3.45
GaP
★
NR
NR
2.35
0.577
372
2.72
0.577
372
2.27
In As
0.417
0.276
93
1.433
0.276
93
1.133
0.276
93
0.35
InN
1.94
0.245
624
2.51
0.245
624
5.82
0.245
624
2
InP
1.424
0.363
162
★★
NR
NR
2.014
0.363
162
1.35
* 2.886 + 0.1081 [1 -coth(164/T)]
** 2.384-3.7-10 T
Table 7.1. Bandgap parameters for unary and binary materials.
89
Material
Latice const
a [A]
>.
■>
5 a?
E "S’
0)
Q.
Affinity ?
[eV]
Heavy e effective mass
[me*/mo]
Heavy effective mass
[mh*/mo]
e mobility
MUN [cm^/V s]
h* mobility
MUP [cm^/V s]
e density of states
NC [cm^]
h* density of states
NV [cm”^]
Si
5.43
11.9
4.17
0.92
0.54
1500
500
2.8e19
1.04e1
9
Ge
5.66
16
4
1.57
0.28
3900
1800
1.04e19
6e18
GaAs
5.65
13.1
4.07
0.063
0.5
8800
400
4.7e17
7e18
AlAs
5.66
10.1
2.62
1.1
0.41
1200
420
3.5e19
6.6e18
AIN
4.38
NR
NR
NR
NR
NR
14
NR
NR
AlP
5.45
9
NR
3.61
0.51
60
450
2.1 e20
9.2e18
GaN
4.5
12.2
NR
0.22
0.96
380
130
3.1e18
2.4e19
GaP
5.45
11.1
4
4.8
0.67
160
135
3.2e20
1.4e19
In As
6.06
14.6
4.54
0.021
0.43
33000
450
9.2e16
7.1e18
InN
4.98
NR
NR
0.12
0.5
250
-
1.3e18
8.9e18
InP
5.87
12.4
4.4
0.325
0.6
4600
150
5.6e18
1.2e19
Table 12. Major parameters for unary and binary materials.
Material
Bowing parameter
[eV] @0°K
Bowing parameter Eg’^
[eV] @0°K
Bowing parameter Eg*"
[eV] @0°K
AIGaAs
-0.127+1.31X
0.055
0
AIGaP
0
0.13
NR
Alin As
0.7
0
NR
AllnP
-0.48
0.38
NR
GaAsP
0.19
0.24
0.16
GalnAs
0.477
1.4
0.33
GalnP
0.65
0.2
1.03
Table 7.3. Bowing parameters for ternary materials.
90
Material
Bowing parameter Eg
[eV] @0°K
(only for the bandgap)
Bowing parameter
[eV] @0°K
(for quantities other than
the bandgap)
Bowing parameter Eg*"
[eV] @0°K
(for quantities other than
the bandgap)
AIGaN
0
0.61
0.8
AlInN
16-9.1X
NR
NR
GaAsN
120.4^1 OOx
NR
NR
GaInN
3
0.38
NR
InAsN
4.22
NR
NR
Table 7.4. Bowing parameters for ternary Nitrides.
Materiai
Bandgap Eg
[eV] @300°K
Latice const
a [A]
>.
■>
E "S’
0)
Q.
Affinity ?
[eV]
Heavy e effective
mass [me /mo]
Heavy effective
mass [mh /mo]
e mobiiity
MUN [cm^/V s]
h* mobiiity
MUP [cm^/V s]
e density of states
NC [cm"^]
h* density of states
NV [cm“^]
AIGalnP
2.3
5.65
11.7
4.2
2.85
0.64
2150
141
1.2e20
1.28e19
AllnP
2.4
5.65
11.7
4.2
2.65
0.64
2291
142
1.08e20
1.28e19
GalnP
1.9
5.65
11.6
4.16
3
0.64
1945
141
1.3e20
1.28e19
Table 7.5. Major parameters for the ternary (Alo. 52 Ino. 48 P, Gao. 51 Ino. 49 P) and
quaternary (Alo. 25 Gao. 25 Ino. 5 P) lattice matched to GaAs materials used.
F. MOBILITY VS DOPING
The mobihty values mentioned above are for undoped materials. However,
mobihty changes very much with doping. The values for GaAs are in Table 7.6 and
Figure 7.2. For the purposes of this thesis, the GaAs mobihty values used are interpolated
from this table. For other materials mobihty values are derived using this table as a
guideline.
91
Doping concentration [cm e mobiiity MUN [cm^/V s] h* mobiiity MUP [cm^/V s]
1.0e14
8000.0
390.0
2.0e14
7718.0
380.0
4.0e14
7445.0
375.0
6.0e14
7290.0
360.0
8.0e14
7182.0
350.0
1.0e15
7300.0
340.0
2.0e15
6847.0
335.0
4.0e15
6422.0
320.0
6.0e15
6185.0
315.0
8.0e15
6023.0
305.0
1.0e16
5900.0
302.0
2.0e16
5474.0
300.0
4.0e16
5079.0
285.0
6.0e16
4861.0
270.0
8.0e16
4712.0
245.0
1.0e17
4600.0
240.0
2.0e17
3874.0
210.0
4.0e17
3263.0
205.0
6.0e17
2950.0
200.0
8.0e17
2747.0
186.9
1.0e18
2600.0
170.0
2.0e18
2060.0
130.0
4.0e18
1632.0
90.0
6.0e18
1424.0
74.5
8.0e18
1293.0
66.6
1 .0e20
1200.0
61.0
Table 7.6. Mobility vs doping concentration [data after Ref. 10].
92
Figure 7.2. Mobility vs doping concentration [data after Ref. 10].
G. OPTICAL PARAMETERS
The meaning of optical parameters was explained in chapter 4. The values
required for the purposes (f this research are the n and k for wavelengths in the range of
0.2nm to 6nm. Adas can receive this input, separately for each material, from an ASCII
file of specific format. Non-existent values are automatically interpolated.
This data can only be derived by experiments and measurements performed on the
each material, under very strict conditions. These have been pubhcized among others in
93
Ref. 5. The materials covered in those are most of the unaries and binaries, but only a
small number of ternaries aid quaternaries. Hence, the only way to produce the necessary
numbers is interpolation.
In Figure 7.3, the k parameter for Ino. 5 Gao. 5 P (red) has been interpolated from GaP
(blue) and InP (violet) using a simple algorithm. Photons are absorbed by the material
when k is greater than zero. Therefore, the wavelength where k first becomes non-zero,
corresponds to energy approximately equal to the bandgap This can easily be verified
for GaP and InP from Table 7.1. However, the result for InGaP does not seem correct.
For this reason, a more sophisticated and enhanced algorithm (OPTINTERP) was
implemented in Matlab and used throughout the simulations. Figure 7.4 shows the correct
results. The full source code can be seen in Appendix G.
Function name: OPTINTERP
Input arguments: fI: The name of the first .mat file to be used in the interpolation.
f2: The name of the second .mat file to be used in the
interpolation.
r: The ratio f 1 :f2 of the interpolation.
Output arguments: wavel: An array with the wavelengths of the resulting parameters,
n: An array with the n optical paramater.
k: An array with the k optical paramater.
Syntax: [wavel n k] = OPTINTERP(fl, f2, r)
94
Figure 7.3. Optical parameter k vs wavelength and energy
(simple interpolation).
95
Figure 7.4. Optical parameter k vs wavelength and energy
(enhanced interpolation).
96
Vni. BUILDING A MULTIJUNCTION CELL
This chapter uses the methodology introduced in chapter 6 and the results on
material properties of chapter 7 to provide a complete simulation of an actual solar ceU.
This particular ceU is studied very much by researchers and a large number of
publications provide valuable experimental data. This data is used to verify the
simulation results and thus validate the process.
A. THE PROCESS
Even though TCAD is a tool with many features and varied fiinctionahty, the fact
that it has not been used to model advanced solar cells might raise doubts about the
vahdity of its output when it is used for such a purpose. The plethora of stiU unexplored
material and optical parameters involved, are also a cause of valid concern about the
accuracy of the produced results. For the third and major part of this thesis, these issues
have been addressed and resolved.
The development of a complete model starts with the building of a p-n junction
which is the simplest possible device. This involves a thorough verification process. The
device is fuUy simulated and the results are compared to published experimental results
of similar devices. Various parameters and characteristics of the model are then tweaked,
to approximate the results in those pubhcations more closely. The whole process is
repeated, as in a spiral (Figure 8.1), until a satisfactory level of accuracy is reached. For
the sake of simplicity and briefness, only the results of this process are presented here.
97
Accuracy
Process
Figure 8.1. Verification process.
After the device is fuUy developed and its behaviour is verified, additional layers
are added to it. The new structure then goes through the same verification process
described earher, thus allowing for starting with a simple model and incrementally
adding and accessing successive layers of complexity. Many of these devices are later
combined to create an advanced solar cell (Figure 8.2).
Figure 8.2. Cell development process.
B. THE SIMPLE GaAs CELL
A very common material used in solar cells is GaAs. It produces relatively high
current (Isc = 25mA/cm2) and a voltage of 'Vbc = 0.9V. On this first attempt, the cell will
have the basic n-on-p stmcture shown in Figure 8.3:
I
Emitter n+GaAs 0.1pm 2el8cm“^
Base p+ GaAs 3pm lelVcm”^
Figure 8.3. Simple GaAs cell.
In the beginning, the mesh (Figure 8.4) is created, taking special care to make it
denser near the junction and to have enough divisions per layer.
99
Microns
After the material regions and the doping levels are specified, a fuU set of material
properties is defined. For simplicity, at this step, the electrodes are considered to be ideal
and transparent. Finally, several types of results are programmed to be calculated. One of
them is the potential build-up, as weU as the electrostatic field of the depletion region at
the junction, both of which can be seen in Figure 8.5.
Figure 8.5. (a) Potential and (b) Electrostatic field.
'y
At this stage of development the ceU has a 'Vbc = 0.93V and an Isc = 25.2mA/cm
which are very close to the expected values. Furthermore, the I-V characteristic can be
plotted (Figure 8.6) to aid in the determination of the cell’s operating point, fill factor,
efficiency etc.
100
30
The frequency response (Figure 8.7) can be used in researching ways to improve
performance. The goal is to expand the frequency range in which the multijunction cell is
active and thus produces current. To succeed in this, cells that respond to different
frequency ranges must be identified and used. The normalized current - used here and
throughout this thesis - is actually the short-circuit current produced by the cell, for a
single optical wavelength of the AMO light shined upon it. This is normalized to its
maximum value, in order to facUitate comparison.
101
Another impressive graph allows the viewing of the current as it is created by the
various wavelengths (Figure 8.8).
Figure 8.8. Electron current density per wavelength.
C. IMPROVING THE CELL
As discussed in chapter 8, the addition of a BSF below the ceU is one of the most
important improvements. It should shghdy increase Isc and voltage to Vqc = IV. The
material selected is InGaP lattice matched to GaAs.
For purposes of mechanical strength, the ceU should also be built on a much
thicker ^0.3mm) substrate. GaAs is a good material to use. However, the junction of the
substrate and the BSF should not create a field that opposes the movement of carriers
towards the electrodes. For this reason, a heavily doped GaAs buffer layer is grown
between them. Together with its window layer the ceU becomes Uke in Figure 8.9 and
8 . 10 :
102
i
Window
n-i-AUnP
0.05|im
lel9cm ^
Emitter
n-i- GaAs
0.1 |im
2el8cm“^
Base
p-i- GaAs
3|im
lel7cm“^
BSF
p-i- InGaP
0.1 |im
2el8cm“^
Buffer
p-i- GaAs
0.3|im
7el8cm“^
Substrate p-i- GaAs
300|im
lel9cm“^
\
Figure 8.9. Improved GaAs ceU.
The mesh of the cell now becomes:
- 200-100 0 100 200
Microns
- 200-100 0 100 200
Microns
- 200-100 0 100 200
Microns
(whole ceU) (upper part) (top cell)
Figure 8.10. The mesh of the improved ceU.
- 200-100 0 100 200
Microns
(bottom ceU)
103
Microns
The additional electrostatic field of the BSF can also be seen in Figure 8.11:
'y
Now the cell has a \()c = IV and an Isc = 27.6mA/cm . These values are almost
the same as those publicized of actual GaAs cells in Ref. 15-18.
D. THE COMPLETE InGaP CELL
A similar ceU can be built using InGaP. This material, when lattice-matched to
GaAs, has higher bandgap (Eg = 1.9eV). Therefore, its Voc is also expected to be larger.
This also agrees with Figure 5.2. According to the same figure, Isc is expected to be
lower. Using the same process utilized before, the ceU is simulated and is found to
‘•y
produce Voc = 1-3V and Isc = IlmA/cm .
With its own BSF, buffer and window layers the ceU looks like in Figure 8.12:
104
Figure 8.12. The complete InGaP cell.
The complete ceU now has Vqc = 1-4V and Isc = 19.1mA/cm . Taking into
account that shadow losses, caused by an actual opaque contact, are not considered at this
point, the results are very similar to those in Ref. 15-18. The IV characteristic and the
frequency response of the cell can be compared to the ones of the GaAs cell as follows in
Figure 8.13.
30
25
20
2 15
3
o
0)
o 10
jr
05
U
cathode Voltage [V]
Optical wavelength [uml
Figure 8.13. The IVs of the complete individual InGaP and GaAs cells.
105
E.
THE TUNNEL JUNCTION
As seen in earlier chapters a tunnel junction (Figure 8.12) is actually a very thin
and heavily doped p-n junction.
1
^ 1
p+ InGaP 0.015|im
8el8cm“^
n+ InGaP O.OlSpm
lel9cm“^
I
Figure 8.12. A tunnel junction.
When simulated, it produces the dark IV characteristic of Figure 8.14. Obviously
the created junction can easily handle the current produced by the above cells.
106
F. THE InGaP / GaAs MECHANICALLY STACKED TANDEM CELL
In a first attempt to create a tandem ceU, the mechanically stacked stmcture
(Figure 8.15) was used for simphcity. This is the placement of the InGaP over the GaAs
cell. The two cells are not in contact. Instead, they are separated by a thin layer of
vacuum. Vacuum is a very good insulator for the voltage levels used here. Also it does
not absorb or alter light as it goes hrough it. Each cell has its own ideal and transparent
contacts.
t
Window
n+AUnP
0.03|im
<2el8cm ^
Emitter
n+ InGaP
0.05|im
2el8cm“^
Base
p+ InGaP
0.55|im
1.5el7cm“^
BSE
p+ InGaP
0.03|im
2el8cm“^
Buffer
p+AUnP
0.03|im
lel8cm“^
!>
f
Window
n+AUnP
0.05|im
lel9cm ^
Emitter
n+ GaAs
0.1 |im
2el8cm“^
Base
p+ GaAs
3|im
lel7cm“^
BSE
p+ InGaP
0.1 |im
2el8cm“^
Buffer
p+ GaAs
0.3|im
7el8cm“^
Substrate
p+ GaAs
300|J.m
lel9cm“^
r
Figure 8.15. The mechanically stacked tandem cell.
107
The actual stmcture is illustrated in Figure 8.16:
Microns
Microns
Microns
(a) (b) (c)
Figure 8.16. The mechanically stacked tandem cell in Silvaco:
(a) The whole stmcture, (b) expanded view of the two cells,
(c) expanded view of the two cell junctions.
As expected, both cells produce the same voltage as before. The top cell is totally
unaffected. On the contrary, the bottom one produces less current, due to the fact that
higher energy photons have been absorbed by all the layers over it. This current becomes
almost equal to the current produced by the top cell (purrent matching). This can be seen
in the new frequency response (Figure 8.17). The electrical characteristics of the top cell
are the same, so Vqc = 1.4V and Isc = 19.1mA/cm^. The bottom cell is changed and now
‘j
has Voc = IV and Isc = 19mA/cm .
108
Figure 8.17. Frequency response of the stacked cells
compared to that of the individual cells.
The potential build-up can be seen in Figure 8.18.
0 —
50 —
100 —
150 —
200 —
250 —
300—1
-1—
1—
V
_
■ 0.8
-
-
2 —
■
-
■
3 —
WM
■ -1.9
_
I I I I I I I I I I I M I I I I I I
200-100 0 100 200
Microns
I I I I 11 I I 11 I I 11 I I I I I
- 200-100 0 100 200
Microns
I I I I I I I I 1 1 I I 1 1 I I I I I ^
200-100 0 100 200
Microns
Figure 8.18. The potential build-up.
109
G. THE InGaP / GaAs DUAL MULTUUNCTION CELL
The next step is to connect the two cells using the tunnel diode developed earlier.
'y
The simulated cell produced Voc = 2.49V and Isc = 19mA/cm .
top ,
cell
tunnel
junction
bottom
cell
t
Window
n+AllnP
0.03|im
<2el8cm ^
Emitter
n+ InGaP
0.05|im
2el8cm“^
Base
p+ InGaP
0.55|im
1.5el7cm“^
BSF
p+ InGaP
0.03|im
2el8cm“^
Buffer
p+AllnP
0.03|im
lel8cm“^
p+ InGaP 0.015|im 8el8cm ^
n+InGaP 0.015|im lel9cm“^
Window
n+AllnP
O.OSpm
lel9cm ^
Emitter
n+ GaAs
0.1 |im
2el8cm“^
Base
p+ GaAs
3|im
lel7cm“^
BSE
p+ InGaP
0.1 |im
2el8cm“^
Buffer
p+ GaAs
0.3|im
7el8cm“^
Substrate p+ GaAs
300|im
lel9cm“^
r
Figure 8.19. The multijunction ceU.
The rv characteristic (Figure 8.20) is changed as expected and the frequency
response (Figure 8.21) is actually the sum of the responses of each cell. Both are in
agreement with experimental data found in Ref. 15-18.
110
Figure 8.20. IV characteristic of the multijunction ceU.
Figure 8.21. Frequency response of the multijunction cell,
(experimental data after Ref. 15-18)
Even though this ceU is stUl not exactly the same as the one presented in Ref 15-
18, the close agreement of simulated and experimental results observed here is a strong
indication that the methodology used is correct. Encouraged by this, further additions and
111
improvements to the eell can be modeled to improve the design. This is done in the
following sections where the modeled cell becomes almost identical to those referenced.
H. THE COMPLETE InGaP / GaAs CELL
The final step (Figure 8.22) is to add an ARC layer on top to minimize reflections.
A cap layer and real golden contacts are also added. The bottom contact is shined and
becomes a back surface reflector (BSR) to reflect photons back into the cell.
Cap n+ GaAs 0.3|im
top
cell
tunne
junction
bottom
cell
Window
n+AUnP
0.03|im
<2eI8cm ^
Emitter
n+ InGaP
0.05|im
2eI8cm“^
Base
p+ InGaP
0.55|im
I.5eI7cm“^
BSF
p+ InGaP
0.03|im
2eI8cm“^
Buffer
p+AllnP
0.03|im
IeI8cm“^
p+ InGaP 0.015|im 8el8cm ^
n+InGaP 0.015|im lel9cm“^
Window
n+AUnP
0.05|im
IeI9cm ^
Emitter
n+ GaAs
0.1|im
2eI8cm“^
Base
p+ GaAs
3|im
leI7cm“^
BSF
p+ InGaP
0.1|im
2eI8cm“^
Buffer
p+ GaAs
0.3|im
7eI8cm“^
Substrate p+ GaAs
300|im
IeI9cm“^
r
Figure 8.22. Final version of the multijunction cell.
112
The final IV characteristic (Figure 8.23) reflects those improvements.
Figure 8.23. Final IV characteristic of the multijunction cell.
(experimental data after Ref. 15-18)
The simulated cell produced Voc = 2.49V and Isc = 24mA/cm . This result is very
similar to the Voc = 2.488V and Isc = 23mA/cm^ found in Ref. 15-18. The I-V
characteristic and the frequency response are also in agreement.
Another interesting graph shows the photogeneration rate (Figure 8.25 and 8.26)
vs. the wavelength of the light (Figure 8.24). Note how the top and the bottom cells are
active and produce current in different wavelengths, according to their frequency
response.
113
Microns Microns
-200 -lOO □ lOO 200 -200 -lOO O lOO 200 -200 -lOO O lOO 200
Microns Microns Microns
Microns
Microns
Microns
Figure 8.25. Photogeneration in the MJ cell (expanded view of the top cell).
Figure 8.26. Photogeneration in the MJ cell (expanded view of the bottom cell).
114
IX. DEVELOPING AND OPTIMIZING A
STATE-OE-THE-ART MULTIJUNCTION CELL
This final chapter has two major parts. The first part is the modeling of a state-of-
the-art triple multijunction solar cell. It is a successful attempt to simulate a device
currently on the cutting edge of technology. This way, the demonstrated methodology is
used as a high-end research tool. On the second part, parametric analysis is used, to
optimize the cell, adding to the value of the proposed process.
A. FIRST STAGE OF DEVELOPMENT
The cell with the highest efficiency ever published has been built by Spectrolab
Inc and is described in Ref. 19. Under AMO, this cell is measured to produce Vqc =
2.651V, = 17.73mA/cm^, to have efficiency = 29.3% and FF = 84.3%. Unhke the cell
studied in the previous chapter, all recent pubhcations on advanced cells treat stmctural
details as proprietary information. Therefore, layer thicknesses and doping levels are not
revealed.
Using the process explained earher and experience gained from the research of cell
development, a set of probable values has been produced in order to simulate this cell.
This was used as a first estimation.
Ge is a material with very low bandgap (Eg = 0.67eV). This means that it can
produce energy even with very low-energy photons. As upper cells absorb most of the
high-energy photons, Ge is ideal for a bottom cell in a multijunction configuration. As
seen in figure 5.2, Ge cells can produce very high current. Unfortunately, this advantage
will largely remain unused, as this current will be choked by the above cells in the stack.
Its \bc is quite small (only 0.3V) and does not seem to be very important. However, the
cell developed in the previous chapter produced only a total Vqc = 2.49V. An increase of
0.3V would lead to the significant power increase by 12%.
The double cell studied in the previous chapter is used again and a Ge cell is
simply attached below it. Small changes have been implemented to match the design of
Ref. 19. Hence, the tunnel junctions are now created using GaAs, aU the buffer layers
115
have been removed and some materials used for the window layers are ehanged. The new
stmcture ean be seen in Figure 9.1:
top
cell
tunnel
junction
middle
cell
tunnel
junction
bottom
cell
Cap n+ GaAs 0.3|im
Window
n+AUnP
0.03|im
<2el8cm ^
Emitter
n+ InGaP
0.05|im
2el8cm“^
Base
p+ InGaP
0.55|im
1.5el7cm“^
BSF
p+AlInGaP 0.03|im
2el8cm“^
p+GaAs 0.015|im 8el8cm^
n+ GaAs 0.015|im lel9cm“^
Window
n+ InGaP
0.05|im
lel9cm ^
Emitter
n+ GaAs
O.I|im
2el8cm“^
Base
p+ GaAs
3|im
lel7cm“^
BSE
p+ InGaP
0.1 |im
2el8cm“^
p+GaAs 0.015|im 8el8cm^
n+ GaAs 0.015|im lel9cm“^
Window
n+ AlGaAs
0.05|im
7el8cm ^
Emitter
n+ Ge
0.1 |im
2el8cm“^
Substrate p+ Ge
300|im
lel7cm“^
r
Figure 9.1. Triple MJ cell prototype.
The simulation returned Vqc = 2.655V and Isc = 17.6mA/cni2 which are
obviously very close to the results pubhshed in Ref. 19. Great similarity also exists in the
116
rv characteristic (Figure 9.2) and in the frequeney response shown below. This leads to
the behef that the eonfiguration simulated is very elose to the actual configuration built
and published by Speetrolab.
15
<N
£
o
I 10
0 ^
o 5
0
0 0.5 1 1.5 2 2.5 3
Voltage [V]
Figure 9.2. IV eharaeteristie of the prototype triple MJ eeU.
(experimental data after Ref. 19)
Like before, the frequeney responses of both the individual and staeked eells have
been produeed and ean be seen in Figures 9.3 and 9.4. Also the response of the total
multijunetion eeU is provided and eompared to the experimental results.
Figure 9.3. Frequeney response of all eeUs.
117
Figure 9.4. Frequency response of the total MJ cell,
(experimental data after Ref. 19)
Even though - unlike in chapter 8 - the cell is not described in detail in Ref. 19 or
in any other pubhcations, the close agreement of simulated and experimental results
suggests that the structure developed here is not far from the stmcture crigmaHy buUt and
tested by Spectrolab in the reference.
The photogeneration rate (Figure 9.6) for various wavelengths of the AMO
spectmm (Figure 9.5), seen in the previous chapter, is also created here.
118
Figure 9.6. Photogeneration rate vs. optical wavelength.
119
B. PARAMETRIC ANALYSIS AND OPTIMIZATION
The current produced by a single ceU is in direct analogy with its thickness and
more specifically with the thickness of its base. As the base becomes thicker, the current
produced becomes larger. In multijunction cells this principle is also tme. However, the
thicker a ceU is, the more photons it absorbs and thus, less photons are aUowed to pass
through to the other ceUs beUow it. This “shadowing” affects greatly the lower ceUs and
may lead them to photon starvation. Therefore, a thick top ceU wiU cause the current
produced by lower cells to decrease. The various thicknesses have tittle effect on the
open-circuit voltages of the cells, thus, the selection of the open-circuit current alone can
be used as a factor for overall power optimization.
In a multijunction configuration, each cell behaves tike a current source. AU these
current sources are connected in series (Figure 9.7). Consequently, the total current
produced by the stmcture is equal to the smallest current produced by the individual cells.
Hence, a cell that is too thin or too shadowed wtil result in lower overall performance,
creating a bottleneck for the others.
Figure 9.7. A multijunction solar cell as a set of current sources connected in series.
The top cell, obviously, cannot be shadowed and absorbs almost all photons in the
range of 0.2 to 0.6|im. The remaining photons enter the middle cell where wavelengths
120
from 0.6 to 0.9|J.m are absorbed. Finally, the remaining photons in the range of 0.9 to
1.6|im are absorbed by the bottom eeU (Figure 9.8).
Optical Wavelength [um]
InGaP
Figure 9.8. Light propagation through cells.
From pubhshed research, it is known that top cells usually have thicknesses in the
range of 0.5 to O.Vpm, while middle cells have around 2 to 4|im. A number of
121
simulations have been executed and the thicknesses of those cells have been varied in a
bit wider ranges. The first result shown is the short-circuit current of the top cell vs. its
thickness (Figure 9.9). Note that no other parameter affects this cell.
Top cell thickness [um]
Figure 9.9. Top cell short-circuit current vs. top cell thickness.
Because of its position, the shadow casted by the bottom cell does not affect any
parts of the structure. Therefore, its thickness will be chosen to be as high as possible to
increase the current produced. However, the thickness of the middle cell will greatly
affect it as shown in Figure 9.10.
Figure 9.10. Bottom cell short-circuit current vs. middle cell thickness.
122
Finally, for designing the middle cell, both its thickness (due to the shadowing on
the bottom cell) and the thickness of the top cell need to be considered. For this reason,
the family of curves of Figure 9.11 is produced.
Figure 9.11. Middle cell short-circuit current vs. top and middle cell thickness.
In order to derive a conclusion, the above graphs are combined. The total current
is the minimum current of the three cell currents. This is also the actual current produced
by the multijunction combination of the three cells, due to their in-series connection.
Therefore, the total short-circuit current is the best indication of the output power and the
efficiency of the whole cell and that is why it is also plotted. First, a set of graphs of aU
the currents vs. the thickness of the top cell can be seen in Figure 9.12. There, all the
above-mentioned theory becomes evident. In this set, the optimum point seems to be for
top cell thickness equal to 0.55|im and middle cell thickness equal to A similar set
of graphs, but this time, vs. middle cell thickness, follows in Figure 9.13. The optimum
point is also found at the same combination of cell thicknesses. Another way to locate the
optimum point is by using the contour plot of the total current seen in Figure 9.14 or the
3D surface plot in Figure 9.15.
123
Current [mA/cm^] Current [mA/cm^] Current [mA/cm^]
20
Top cell thickness [urn]
Top cell thickness [urn]
Top cell thickness [urn]
Top cell thickness [urn]
Top cell thickness [urn]
Top cell short-circuit current
Middle cell short-circuit current
Bottom cell short-circuit current
Total MJ short-circuit current
Figure 9.12. All short-circuit currents vs. top cell thickness.
124
Current [mA/cm^] Current (mA/cm^] Current [mA/cm^]
20
Middle cell thickness [urn]
top cell
thickness = 0.3|im
Middle cell thickness [urn]
125
Current [mA/cm^] Current [mA/cm^]
Top cell short-circuit current
Middle cell short-circuit current
Bottom cell short-circuit current
Total MJ short-circuit current
Figure 9.13. All short-circuit currents vs. middle cell thickness.
126
Middle cell thickness [urn]
6
5.5
5
4.5
4
3.5
3
2.5
2
1.5
1
0.2 0.3 0.4 0.5 0.6 0.7 0.8
Top cell thickness [um]
Figure 9.14. Total short-circuit current vs. top and middle ceU thicknesses.
17.5
-16.5
-16
^^ 15.5
Figure 9.15. Total short-circuit current vs. top and middle ceU thicknesses.
127
Total short-circuit current [mA/cm^]
An interesting observation is that, even though the thickness of the middle ceU has
a major effect on the bottom ceU current (as seen in Figure 9.10), the multijunction
combination of cells is httle affected by it. This conclusion is very reasonable and is due
to the fact that the bottom cell rarely becomes the limiting current source in the stmcture.
Therefore, the thickness of the middle ceU has httle effect on the total current produced.
The bottom cell is a Ge one and due to its small bandgap, will absorb more photons and
wiU produce more current than ah other ceUs (see Figure 5.2). AdditionaUy, its frequency
response shows that it wiU mainly work in a region of optical wavelengths very different
and larger than the GaAs or InGaP cells (see Figure 9.3). Therefore, the shadowing of the
upper ceUs wiU not reduce its current enough to make it a limiting factor in the design.
The results of the optimization process point towards the results obtained in the
previous section and are very similar to the ones in Ref. 19. This indicates that the
stmcture tested earUer was already optimized. This choice is not attributed to luck. As it
was explained in the beginning of this chapter, the two upper ceUs were almost identical
to the dual ceU tested in chapter 8. That ceU was expeiimentaUy optimized by its creators
and aU the details of its stmcture were fully described in their pubUcation. These
parameters were also used in this simulation. The addition of the bottom ceU did not
change the optimum point of the triple-ceU stmcture due to the reasons mentioned in the
previous paragraph.
128
X. CONCLUSIONS AND RECOMMENDATIONS
A. RESULTS AND CONCLUSIONS
A novel methodology was presented for modeling and developing state-of-the-
art solar cells. It is beheved that it will be of great value to the photovoltaic industry and
the developers of spacecrafts. Since almost all research on advanced solar cells is
currently conducted via expensive and complex experimentation, the proposed simulation
method is expected to help reduce that cost, simphfy the design process, and allow the
designer to focus on the final result.
In this thesis, as a first step, the exotic materials used in such designs were
identified and all their major electrical and optical parameters were researched or derived.
In addition, software code was developed to adjust and calibrate ATLAS for the task of
simulating solar cells. More software was also developed to exchange data between
ATLAS and MatLab, thus enhancing the abihties of the package.
An InGaP/GaAs dual multijunction cell was built and was fuUy simulated. The
whole process was done in stages and detailed explanations were provided. Every result
was also compared with pubhshed experimental results to verify the close agreement and
accuracy of this methodology. This has formed a paper that has been submitted for
publication in the 9th IEEE International Conference on Electronics, Circuits and
Systems - ICECS 2002 September 15-18, 2002, in Dubrov nik Croatia.
A state-of-the-art InGaP/GaAs/Ge triple multijunction cell was also built and
simulated. Although the stmctural details of the cell were not available, the cell was
tweaked according to the experience gained on solar cells and the results matched the
experiments very closely. Another paper was written and has already been accepted for
pubhcation in the 6th WSEAS International Conference on CIRCUITS - July 7-14, 2002
in Rethymna Beach, Rethymnon, Crete, Greece.
Additional optimization was finally done on the triple cell attempting to further
improve its efficiency. The modeling, simulation and optimization of the triple cell has
been submitted, as a paper, for publication in the 29th IEEE Photovoltaic Speciahsts
Conference (PVSC) - May 20-24, 2002 in New Orleans, Eouisiana USA.
129
B. FURTHER OPTIMIZATIONS AND RECOMMENDATIONS
There are several elements that might improve the performance of the
configuration tested. One of these is the addition of buffer layers below each cell, to
achieve better lattice matching of cells and tunnel junctions. Another very important
improvement could be the addition of a BSF layer for the Ge cell. An attempt was made
to incorporate both enhancements and the result was an increase in the Voc by 0.15V
(5.6%) and a total efficiency of 30.5%. This is a proposal to researchers for further
development. However, due to the time li mitations of this thesis, detailed results were not
presented here. They may be researched in future work.
Another topic, that may be the subject of further research, is the investigation of
various doping concentration effects on the electrical and optical properties of materials,
with the aim of attaining higher levels of accuracy.
Additionally, in this thesis, the layer boundaries are treated as being strictly
defined and their doping is assumed to be uniform. However, during any fabrication
process, material diffusion and gradually varying doping are the dominant characteristics
in a device. Their study wiU allow the simulation and modeling of both the basic cell
stmcture and the actual fabricated implementation.
The possibihty of radiation effects on solar cells and whether these can be
simulated using VWF may be investigated in the future. This is a very important field for
space applications.
Shining laser beams on cells may also be researched. Lasers can be used for
providing additional photons to the cell, but also for countering some of the radiation
effects.
Finally, modehng of secondary phenomena could also increase the accuracy of
the results produced.
130
APPENDIX A. LIST OF SYMBOLS
Symbol
Description
Unit
a
Angle
deg
a
Absorption coefficient
m-i
a
Eattice constant
0
A
UGN/AUGP
Electron / hole Auger coefficients
crn^/s
C
Capacitance
E
c
Speed of light
m/s
COPT
Radiative recombination rate
cm^/s
E
Energy
eV
8
Dielectric function
-
8 i, 82 , n,k
Optical constants
-
es
Permittivity
E/cm
Ec
Bottom of conduction band
eV
Ef
Eermi energy level
eV
Eg
Energy bandgap
eV
Ev
Top of valence band
eV
f
Erequency
Hz
f(E)
Eermi-Dirac distribution function
-
h
Plank’s constant
Is
hv
Photon energy
eV
I
Current
A
Id / Is
Diffusion / drift current
A
Isc
Short circuit current
A
k
Boltzmann’s constant
J/K
kT
Thermal energy
eV
*
m
Effective mass
rUe
131
|ln (MUN) / |ip (MUP)
n
V
Nc/Nv
Nd/Na
UnO / PpO
UpO / PnO
Vk ! rC
p
R
p
a
T
TAUN / TAUP
V
Voc
%
%
Electron / hole mobility
Power conversion efficiency
Photon frequency
Electron / hole density of states
Donor / acceptor impurity atom concentration
Majority ■ minority carrier concentration product
Majority carrier (electrons / holes) concentration
Minority carrier (electrons / holes) concentration
Refraction / complex refraction index
Power
Reflectivity
Resistivity
Conductivity
Absolute temperature
Electron / hole hfetimes
Voltage
Open circuit current
Absorption index
Affi nity
crn^ -s
Hz
-3
cm
-3
cm
-3
cm
-3
cm
-3
cm
W
Om
S/m
"K
s
V
V
eV
132
APPENDIX B. GREEK ALPHABET
Letter
Pronounciation
Uppercase
Lowercase
Alpha
‘alpha
A
a
Beta
‘veeta
B
P
Gamma
‘yama
r
Y
Delta
‘delta
A
5
Epsilon
‘epsilon
E
8
Zeta
‘zeeta
Z
C
Eta
‘eeta
H
Theta
‘theeta
0
0
Iota
‘yota
I
i
Kappa
‘kapa
K
K
Eambda
‘lamda
A
1
Mu
mee
M
P
Nu
nee
N
V
Xi
ksee
M
Omicron
‘omikron
o
0
Pi
pee
n
7C
Rho
rho
p
P
Sigma
‘siyma
z
o
Tau
taf
T
X
Upsilon
‘ipseelon
Y
V)
Phi
fee
9
Chi
hee
X
%
Psi
psee
'P
¥
Omega
om’eya
a
0)
The phenotic ‘y’
is pronounced like in
‘y-es’ or ‘y-eUow’.
The phonetic ‘d’
is pronounced like in
‘th-is’ or ‘th-ere’
The phonetic ‘th’
is pronounced hke in
‘th-ank’ or ‘th-ink’
133
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134
APPENDIX C. SOME PHYSICAL CONSTANTS
Quantity
Symbol
Value
Boltzmann’s constant
k
1.38066-10“^^ J/K
Electron charge
qe
1.60218 10“^‘^Cb
Electronvolt
eV
1.60218 10“^‘^ J
Electron mass at rest
me
0.91093897-10“^° Kg
Proton mass at rest
rup
1.6726231-10“^^ Kg
Plank’s constant
h
6.6260755-10“^^ J-s
Eight speed in vacuum
c
2.99792458-10“^ m/s
APPENDIX D. UNITS
Fundamental Units
Quantity
Unit
Symbol
Eength
meter
m
Mass
kilogram
Kgr
Time
second
s
Current
ampere
A
Temperature
degree Kelvin
K
Eight intensity
candela
Cd
Additional Units
Quantity
Unit
Symbol
Angle
radian
rad
Solid angle
steradian
sr
Matter quantity
mole
mol
135
Produced Units
Quantity
Unit
Symbol
Equivalence
Surface
square meter
m^
m^
Volume
cube meter
m'
m'
Velocity
-
m/s
m/s
Acceleration
-
m/s^
m/s^
Density
-
Kg/m^
Kg/m^
Momentum
-
Kgm/s
Kgm/s
Force
Newton
N
Kg-m/s^
Frequency
Hertz
Hz
1/s
Pressure
Pascal
Pa
N/m^
Viscocity
-
N-s/m^
N-s/m^
Energy
Joule
J
Kg-m^/s^
Heat
-
J
Kg-m^/s^
Power
Watt
W
N-m/s
Electric charge
Coulomb
Cb
A-s
Electric potential
Volt
V
Kg-m^ / As^
Electric resistance
Ohm
a
Kg-m^ / A^-s^
Electric conductivity
Siemens
s
m^ A^-s^ / Kg
Electric capacitance
Earad
E
A^-s^ / Kg-m^
Electric iductance
Henry
H
Kg-m^ / A^-s^
Magnetic flux
Weber
Wb
Kgm^/A-s^
Magnetic induction
Tesla
T
Kg / A^-s^
light flux
Eumen
cd-sr
Blumination
Eux
lx
cd/ m^
136
APPENDIX E. MAGNITUDE PREEIXES
Magnitude prefix
Symbol
Multiple factor
yotta
Y
1x10^+24
zetta
Z
1x10^+21
exa
E
1x10^+18
peta
P
1x10^+15
tera
T
1x10^+12
giga
G
lxlO^+9
mega
M
lxlO^+6
kilo
K
lxlO^+3
hecto
h
lxlO^+2
deka
da
lxlO^+1
-
-
1x10^0
deci
d
1x10^-1
centi
c
lxlO^-2
miDi
m
lxlO^-3
micro
P
lxlO^-6
nano
n
lxlO^-9
pico
P
1x10^-12
femto
f
1x10^-15
atto
a
1x10^-18
zepto
z
1x10^-21
yocto
y
1x10^-24
137
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138
APPENDIX F. ATLAS SOURCE CODE
A. MAIN STRUCTURE
go atlas
# Definition of constants
# Mesh
# X-Mesh
# Y-Mesh
# Regions
# Electrodes
# Doping
# Material properties
# Models
# Light beams
# Solving
B. COMMON SECTIONS
1. Mesh and X-Mesh
mesh space.mult=l
# X-Mesh: surface=500 um2 = 1/200,000 cm2
x.mesh loc=-250 spac=50
x.mesh loc=0 spac=10
x.mesh loc=250 spac=50
2. Material Properties
material TAUN=le-7 TAUP=le-7 COPT=1.5e-10 AUGN=8.3e-32 AUGP=1.8e-31
# Vacuum
material material=Vacuum real.index=3.3 imag.index=0
# Ge
material material=Ge EG300=0.67 PERMITTIVITY=16 AFFINITY=4
material material=Ge MUN=3900 MUP=1800
material material=Ge NC300=1.04el9 NV300=6el8
material material=Ge index.file=Ge.opt
GaAs
material material=GaAs EG300=1.42 PERMITTIVITY=13.1 AFFINITY=4.07
material material=GaAs MUN=8800 MUP=400
material material=GaAs NC300=4.7el7 NV300=7el8
material material=GaAs index.file=GaAs.opt
# InGaP
material material=InGaP EG300=1.9 PERMITTIVITY=11.62 AFFINITY=4.16
material material=InGaP MUN=1945 MUP=141
material material=InGaP NC300=1.3e20 NV300=1.28el9
material material=InGaP index.file=InGaP-l.9.opt
139
# AllnP (=InAsP)
material material=InAsP EG300=2.4 PERMITTIVITY=11.7 AFFINITY=4.2
material material=InAsP MUN=2291 MUP=142
material material=InAsP NC300=1.08e20 NV300=1.28el9
material material=InAsP index.file=AlInP.opt
# AlInGaP (=InAlAsP)
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=1.28el9
material material=InAlAsP index.file=AlInP.opt
3. Models
models BBT.KL TATUN TRAP.TUNNEL
4. Light Beams
beam num=l x.origin=0 y.origin=-5 angle=90 \
power.file=AMOsilv.spec wavel.start=0.21 wavel.end=4 wavel.num=50
B. InGaAs/GaAsCELL
1. Bottom Cell
a. Y-Mesh
# Vacuum
y.mesh loc=-0.15 spac=0.001
# Window (0.05 urn)
y.mesh loc=-0.1 spac=0.01
# Emitter (0.1 urn)
y.mesh loc=0 spac=0.01
# Base (3 urn)
y.mesh loc=1.5 spac=0.3
y.mesh loc=3 spac=0.01
# BSE (0.1 urn)
y.mesh loc=3.1 spac=0.01
# Buffer (0.3 urn)
y.mesh loc=3.4 spac=0.05
# Substrate (300 urn)
y.mesh loc=303.4 spac=50
b. Regions
# Window AllnP (=InAsP)
region num=l material=InAsP x.min=-250 x.max=250 y.min=-0.15 y.max=-0.1
# Emitter
region num=2 material=GaAs x.min=-250 x.max=250 y.min=-0.1 y.max=0
# Base
region num=3 material=GaAs x.min=-250 x.max=250 y.min=0 y.max=3
# BSE
region num=4 material=InGaP x.min=-250 x.max=250 y.min=3 y.max=3.1
# Buffer
region num=5 material=GaAs x.min=-250 x.max=250 y.min=3.1 y.max=3.4
140
# Substrate
region num=6 material=GaAs x.min=-250 x.max=250 y.min=3.4 y.max=303.4
c. Electrodes
electrode name=cathode x.min=-250 x.max=250 y.min=-0.15 y.max=-0.15
electrode name=anode x.min=-250 x.max=250 y.min=303.4 y.max=303.4
d. Doping
# Window
doping uniform region=l n.type conc=lel9
# Emitter
doping uniform region=2 n.type conc=2el8
# Base
doping uniform region=3 p.type conc=lel7
# BSF
doping uniform region=4 p.type conc=2el8
# Buffer
doping uniform region=5 p.type conc=7el8
# Substrate
doping uniform region=6 p.type conc=lel9
e. Solving
(1) IscandVoc
# Get Isc and Voc
solve init
method gummel maxtraps=10 itlimit=25
solve bl=0.9
method newton maxtraps=10 itlimit=100
solve bl=l
contact name=cathode current
method newton maxtraps=10 itlimit=100
solve icathode=17.404e-8 bl=l
solve icathode=0 bl=l
(2) Frequency response
# Get frequency response
solve init
log outfile=freq-bot.log
solve bl=0.1 lambda=0.2
solve bl=0.1 lambda=0.25
solve bl=0.1 lambda=0.3
solve bl=0.1 lambda=0.35
solve bl=0.1 lambda=0.4
solve bl=0.1 lambda=0.45
solve bl=0.1 lambda=0.5
solve bl=0.1 lambda=0.6
solve bl=0.1 lambda=0.65
solve bl=0.1 lambda=0.675
solve bl=0.1 lambda=0.7
solve bl=0.1 lambda=0.75
solve bl=0.1 lambda=0.8
141
solve bl=0.1 lambda=0.83
solve bl=0.1 lambda=0.84
solve bl=0.1 lambda=0.85
solve bl=0.1 lambda=0.9
solve bl=0.1 lambda=0.95
solve bl=0.1 lambda=l
solve bl=0.1 lambda=1.2
2. Top Cell
a. Y-Mesh
# Vacuum
y.mesh loc=-0.87 spac=0.003
# Window (0.03 um)
y.mesh loc=-0.84 spac=0.003
# Emitter (0.05 um)
y.mesh loc=-0.79 spac=0.003
# Base (0.55 um)
y.mesh loc=-0.5 spac=0.1
y.mesh loc=-0.24 spac=0.003
# BSF (0.03 um)
y.mesh loc=-0.21 spac=0.003
# Buffer (0.03 um)
y.mesh loc=-0.18 spac=0.002
b. Regions
# Window AllnP (=InAsP)
region
0.84
num=l
material=InAsP
X.min=-250
X.max=250
y.min=-0.8 7
y. max=
# Emitter
region
0.79
num=2
material=InGaP
X.min=-250
X.max=250
y.min=-0.8 4
y. max=
# Base
region
0.24
# BSF
num=3
material=InGaP
X.min=-250
X.max=250
y.min=-0.7 9
y. max=
region
0.21
num=4
material=InGaP
X.min=-250
X.max=250
y.min=-0.2 4
y. max=
# Buffer AllnP
(=InAsP)
region
num=5
material=InAsP
X.min=-250
X.max=250
y.min=-0.21
y. max=
0.18
c. Electrodes
electrode name=cathode x.min=-250 x.max=250 y.min=-0.87 y.max=-0.87
electrode name=anode x.min=-250 x.max=250 y.min=-0.18 y.max=-0.18
d. Doping
# Window
doping uniform
# Emitter
doping uniform
# Base
doping uniform
region=l n.type
region=2 n.type
region=3 p.type
conc=l.95el8
conc=2el8
conc=l.5el7
142
# BSF
doping uniform region=4 p.type conc=2el8
# Buffer
doping uniform region=5 p.type conc=0.95el8
e. Solving
(1) IscandVoc
# Get Isc and Voc
solve init
method gummel maxtraps=10 itlimit=25
solve bl=0.9
method newton maxtraps=10 itlimit=100
solve bl=l
contact name=cathode current
method newton maxtraps=10 itlimit=100
solve icathode=14.364e-8 bl=l
solve icathode=0 bl=l
(2) Frequency response
# Get frequency response
solve init
log outfile=freq-top.log
solve
bl=0.1
lambda=0.2
solve
bl=0.1
lambda=0.25
solve
bl=0.1
lambda=0.3
solve
bl=0.1
lambda=0.35
solve
bl=0.1
lambda=0.4
solve
bl=0.1
lambda=0.4 5
solve
bl=0.1
lambda=0.5
solve
bl=0.1
lambda=0.6
solve
bl=0.1
lambda=0.65
solve
bl=0.1
lambda=0.675
solve
bl=0.1
lambda=0.7
solve
bl=0.1
lambda=0.7 5
solve
bl=0.1
lambda=0.8
solve
bl=0.1
lambda=0.83
solve
bl=0.1
lambda=0.84
solve
bl=0.1
lambda=0.85
solve
bl=0.1
lambda=0.9
solve
bl=0.1
lambda=0.95
solve
bl=0.1
lambda=l
solve
bl=0.1
lambda=l.2
3. :
Stacked Cell
a. Y-Mesh
# Vacuum
y.mesh loc=-0.87 spac=0.003
# Window (0.03 urn)
y.mesh loc=-0.84 spac=0.003
# Emitter (0.05 urn)
y.mesh loc=-0.79 spac=0.003
143
# Base (0.55 um)
y.mesh loc=-0.5 spac=0.1
y.mesh loc=-0.24 spac=0.003
# BSF (0.03 um)
y.mesh loc=-0.21 spac=0.003
# Buffer (0.03 um)
y.mesh loc=-0.18 spac=0.002
# Vacuum (0.015 um)
y.mesh loc=-0.165 spac=0.002
# Vacuum (0.015 um)
y.mesh loc=-0.15 spac=0.001
# Window (0.05 um)
y.mesh loc=-0.1 spac=0.01
# Emitter (0.1 um)
y.mesh loc=0 spac=0.01
# Base (3 um)
y.mesh loc=l.5 spac=0.3
y.mesh loc=3 spac=0.01
# BSF (0.1 um)
y.mesh loc=3.1 spac=0.01
# Buffer (0.3 um)
y.mesh loc=3.4 spac=0.05
# Substrate (300 um)
y.mesh loc=303.4 spac=50
b. Regions
# Window AllnP (=InAsP)
region
0.84
num=l
material=InAsP
X.min=-250
X.max=250
y.min=
-0 .87
y. max=
# Emitter
region
0.79
# Base
num=2
material=InGaP
X.min=-250
X.max=250
y.min=
-0 .84
y. max=
region
0.24
# BSF
num=3
material=InGaP
X.min=-250
X.max=250
y. min=
-0.79
y. max=
region
0.21
num=4
material=InGaP
X.min=-250
X.max=250
y. min=
-0.24
y. max=
# Buffer AllnP (=InAsP)
region
0.18
num=5
material=InAsP
X.min=-250
X.max=250
y.min=
-0.21
y. max=
# Vacuum
region
0.165
num=6
material=Vacuum
X.min=-250
X.max=250
y.min=
00
\ —1
o
1
y. max=
region
num=7
material=Vacuum
X.min=-250
X.max=250
y.min=-
■0.165
y. max=
0.15
# Window AllnP (=InAsP)
region num=8 material=InAsP x.min=-250 x.max=250 y.min=-0.15 y.max=-0.1
# Emitter
region num=9 material=GaAs x.min=-250 x.max=250 y.min=-0.1 y.max=0
# Base
region num=10 material=GaAs x.min=-250 x.max=250 y.min=0 y.max=3
# BSF
region num=ll material=InGaP x.min=-250 x.max=250 y.min=3 y.max=3.1
# Buffer
region num=12 material=GaAs x.min=-250 x.max=250 y.min=3.1 y.max=3.4
144
# Substrate
region num=13 material=GaAs x.min=-250 x.max=250 y.min=3.4 y.max=303.4
c. Electrodes
electrode name=cathode x.min=-250 x.max=250 y.min=-0.87 y.max=-0.87
electrode name=cc x.min=-250 x.max=250 y.min=-0.18 y.max=-0.18
electrode name=ee x.min=-250 x.max=250 y.min=-0.15 y.max=-0.15
electrode name=anode x.min=-250 x.max=250 y.min=303.4 y.max=303.4
d. Doping
# Window
doping uniform region=l n.type conc=1.95el8
# Emitter
doping uniform region=2 n.type conc=2el8
# Base
doping uniform region=3 p.type conc=1.5el7
# BSF
doping uniform region=4 p.type conc=2el8
# Buffer
doping uniform region=5 p.type conc=0.95el8
# Window
doping uniform region=8 n.type conc=lel9
# Emitter
doping uniform region=9 n.type conc=2el8
# Base
doping uniform region=10 p.type conc=lel7
# BSF
doping uniform region=ll p.type conc=2el8
# Buffer
doping uniform region=12 p.type conc=7el8
# Substrate
doping uniform region=13 p.type conc=lel9
e. Solving
(1) IscandVoc
# Get Isc and Voc
solve init
method gummel maxtraps=10 itlimit=25
solve bl=0.9
method newton maxtraps=10 itlimit=100
solve bl=l
contact name=emitter current
method newton maxtraps=10 itlimit=100
#solve iemitter=3.67113e-8 icathode=14.3731e-8 bl=l
solve iemitter=3.67113e-8 bl=l
solve iemitter=0 bl=l
(2) Frequency response
# Get frequency response
solve init
145
log outfile=
InGaP-GaAs-stack-freq. log
solve
bl=0.1
lambda=0.2
solve
bl=0.1
lambda=0.22
solve
bl=0.1
lambda=0.24
solve
bl=0.1
lambda=0.2 6
solve
bl=0.1
lambda=0.28
solve
bl=0.1
lambda=0.3
solve
bl=0.1
lambda=0.32
solve
bl=0.1
lambda=0.34
solve
bl=0.1
lambda=0.3 6
solve
bl=0.1
lambda=0.38
solve
bl=0.1
lambda=0.4
solve
bl=0.1
lambda=0.42
solve
bl=0.1
lambda=0.4 4
solve
bl=0.1
lambda=0.4 6
solve
bl=0.1
lambda=0.4 8
solve
bl=0.1
lambda=0.5
solve
bl=0.1
lambda=0.52
solve
bl=0.1
lambda=0.54
solve
bl=0.1
lambda=0.5 6
solve
bl=0.1
lambda=0.58
solve
bl=0.1
lambda=0.6
solve
bl=0.1
lambda=0.62
solve
bl=0.1
lambda=0.64
solve
bl=0.1
lambda=0.66
solve
bl=0.1
lambda=0.68
solve
bl=0.1
lambda=0.7
solve
1—1
o
II
;—1
lambda=0.7 5
solve
bl=0.1
lambda=0.8
solve
bl=0.1
lambda=0.83
solve
bl=0.1
lambda=0.84
solve
bl=0.1
lambda=0.85
solve
bl=0.1
lambda=0.8 6
solve
bl=0.1
lambda=0.87
solve
bl=0.1
lambda=0.88
solve
bl=0.1
lambda=0.8 9
solve
bl=0.1
lambda=0.9
solve
bl=0.1
lambda=0.92
solve
bl=0.1
lambda=0.95
solve
bl=0.1
lambda=l
solve
bl=0.1
lambda=l.2
4. Tunnel Junction
a. Y-Mesh
y.mesh loc=-0.18 spac=0.002
# Tunnel emitter (0.015 um)
y.mesh loc=-0.165 spac=0.002
# Tunnel base (0.015 um)
y.mesh loc=-0.15 spac=0.001
b. Regions
region num=l material=InGaP x.min=-250 x.max=250 y.min=-0.18 y.max
0.165
146
region num=2 material=InGaP x.min=-250 x.max=250 y.min=-0.165 y.max
0.15
c. Electrodes
electrode name=cathode x.min=-250 x.max=250 y.min=-0.18 y.max=-0.18
electrode name=anode x.min=-250 x.max=250 y.min=-0.15 y.max=-0.15
d. Doping
doping uniform region=l p.type conc=8el8
doping uniform region=2 n.type conc=lel9
e. Solving
(1) rv characteristic
solve init
solve vcathode=0
solve vcathode=-0.5
solve vcathode=-l
solve vcathode=-l.5
log outfile=InGaP-td-IV.log
solve vcathode=-2
solve vcathode=-l.75
solve vcathode=-l.5
solve vcathode=-l.25
solve vcathode=-l
solve vcathode=-0.75
solve vcathode=-0.5
solve vcathode=-0.3
solve vcathode=-0.2
solve vcathode=-0.1
solve vcathode=0
solve vcathode=0.1
solve vcathode=0.2
solve vcathode=0.3
solve vcathode=0.4
solve vcathode=0.5
solve vcathode=0.6
solve vcathode=0.7
solve vcathode=0.8
solve vcathode=0.9
5. MJ Cell
a. Y-Mesh
# Vacuum
y.mesh loc=-0.87 spac=0.003
# Window (0.03 urn)
y.mesh loc=-0.84 spac=0.003
# Emitter (0.05 urn)
y.mesh loc=-0.79 spac=0.003
# Base (0.55 urn)
y.mesh loc=-0.5 spac=0.1
147
y.mesh loc=-0.24 spac=0.003
# BSF (0.03 um)
y.mesh loc=-0.21 spac=0.003
# Buffer (0.03 um)
y.mesh loc=-0.18 spac=0.002
# Tunnel emitter (0.015 um)
y.mesh loc=-0.165 spac=0.002
# Tunnel base (0.015 um)
y.mesh loc=-0.15 spac=0.001
# Window (0.05 um)
y.mesh loc=-0.1 spac=0.01
# Emitter (0.1 um)
y.mesh loc=0 spac=0.01
# Base (3 um)
y.mesh loc=1.5 spac=0.3
y.mesh loc=3 spac=0.01
# BSF (0.1 um)
y.mesh loc=3.1 spac=0.01
# Buffer (0.3 um)
y.mesh loc=3.4 spac=0.05
# Substrate (300 um)
y.mesh loc=303.4 spac=50
b. Regions
# Window AllnP (=InAsP)
region
0.84
num=l
material=InAsP
X.min=-250
X.max=250
y.min=
-0 .87
y. max=
# Emitter
region
0.79
# Base
num=2
material=InGaP
X.min=-250
X.max=250
y.min=
-0 .84
y. max=
region
0.24
# BSF
num=3
material=InGaP
X.min=-250
X.max=250
y.min=
-0.79
y. max=
region
0.21
num=4
material=InGaP
X.min=-250
X.max=250
y.min=
-0.24
y. max=
# Buffer AllnP
(=InAsP)
region
0.18
num=5
material=InAsP
X.min=-250
X.max=250
y.min=
-0.21
y. max=
# Tunnel emitter
region
0.165
num=6
material=InGaP
X.min=-250
X.max=250
y.min=
CO
\— 1
o
1
y, max=
# Tunnel base
region
num=7
material=InGaP
X.min=-250
X.max=250
y.min=-
0.165
y. max=
0.15
# Window AllnP (=InAsP)
region num=8 material=InAsP x.min=-250 x.max=250 y.min=-0.15 y.max=-0.1
# Emitter
region num=9 material=GaAs x.min=-250 x.max=250 y.min=-0.1 y.max=0
# Base
region num=10 material=GaAs x.min=-250 x.max=250 y.min=0 y.max=3
# BSF
region num=ll material=InGaP x.min=-250 x.max=250 y.min=3 y.max=3.1
# Buffer
148
region num=12 material=GaAs x.min=-250 x.max=250 y.min=3.1 y.max=3.4
# Substrate
region num=13 material=GaAs x.min=-250 x.max=250 y.min=3.4 y.max=303.4
c. Electrodes
electrode name=cathode x.min=-250 x.max=250 y.min=-0.87 y.max=-0.87
electrode name=anode x.min=-250 x.max=250 y.min=303.4 y.max=303.4
d. Doping
# Window
doping uniform
# Emitter
doping uniform
# Base
doping uniform
# BSF
doping uniform
# Buffer
doping uniform
# Tunnel
doping uniform
# Tunnel
doping uniform
# Window
doping uniform
# Emitter
doping uniform
# Base
doping uniform
# BSF
doping uniform
# Buffer
doping uniform
# Substrate
doping uniform
region=l
n.type
conc=l.95el8
region=2
n.type
conc=2el8
region=3
p.type
conc=l.5el7
region=4
p. type
conc=2el8
region=5
p. type
conc=0.95el8
region=6
p. type
conc=8el8
region=7
n. type
conc=lel9
region=8
n. type
conc=lel9
region=9
n. type
conc=2el8
region=10 p.type conc=lel7
region=ll p.type conc=2el8
region=12 p.type conc=7el8
region=13 p.type conc=lel9
e. Solving
(1) IscandVoc
# Get Isc and Voc
solve init
method gummel maxtraps=10 itlimit=25
solve bl=0.9
method newton maxtraps=10 itlimit=100
solve bl=l
contact name=cathode current
method newton maxtraps=10 itlimit=100
solve icathode=8.17e-8 bl=l
solve icathode=0 bl=l
149
B. InGaAs / GaAs / Ge CELL
1. Bottom Cell
a. Definition of Constants
set botLo=0
set botWindowThick:=0.05
set botEmitterThick=0.1
set botBaseThick=300
set botBaseLo=$botLo
set botBaseMid=$botBaseLo-$botBaseThick/2
set botEmitterLo=$botBaseLo-$botBaseThick
set botWindowLo=$botEmitterLo-$botEmitterThick
set botHi=$botWindowLo-$botWindowThick
set botBaseDiv=$botBaseThick/20
set botEmitterDiv=$botEmitterThick/20
set botWindowDiv=$botWindowThick/20
set lightY=$botHi-5
b. Y-Mesh
# Vacuum
y.mesh loc=$botHi spac=$botWindowDiv
# Window
y.mesh loc=$botWindowLo spac=$botWindowDiv
# Emitter
y.mesh loc=$botEmitterLo spac=$botEmitterDiv
# Base
y.mesh loc=$botBaseMid spac=$botBaseDiv
y.mesh loc=$botBaseLo spac=$botEmitterDiv
c. Regions
# Window
region num=l material=GaAs x.min=-250 x.max=250 y.min=$botHi
y.max=$botWindowLo
# Emitter
region num=2 material=Ge x.min=-250 x.max=250 y.min=$botWindowLo
y.max=$botEmitterLo
# Base
region num=3 material=Ge x.min=-250 x.max=250 y.min=$botEmitterLo
y.max=$botBaseLo
d. Electrodes
electrode name=cathode x.min=-250 x.max=250 y.min=$botHi y.max=$botHi
electrode name=anode x.min=-250 x.max=250 y.min=$botLo y.max=$botLo
e. Doping
# Window
doping uniform
# Emitter
doping uniform
# Base
doping uniform
region=l n.type
region=2 n.type
region=3 p.type
conc=lel9
conc=2el8
conc=lel7
150
/. Light Beams
beam num=l x.origin=0 y.origin=$lightY angle=90 \
power.file=AMOsilv.spec wavel.start=0.21 wavel.end=4 wavel.num=50
g. Solving
(1) IscandVoc
# Get Isc and Voc
solve init
method gummel maxtraps=10 itlimit=25
solve bl=0.9
method newton maxtraps=10 itlimit=100
solve bl=l
contact name=cathode current
method newton maxtraps=10 ltlimit=100
solve icathode=3.1654e-7 bl=l
solve icathode=0 bl=l
(2) Frequency response
solve Inlt
log outfile=InGaP-GaAs-Ge-bot-freq.log
solve bl=0.1 lambda=0.22
solve bl=0.1 lambda=0.3
solve bl=0.1 lambda=0.4
solve bl=0.1 lambda=0.5
solve bl=0.1 lambda=0.6
solve bl=0.1 lambda=0.7
solve bl=0.1 lambda=0.8
solve bl=0.1 lambda=0.9
solve bl=0.1 lambda=l
solve bl=0.1 lambda=l.1
solve bl=0.1 lambda=1.2
solve bl=0.1 lambda=l.3
solve bl=0.1 lambda=l.4
solve bl=0.1 lambda=l.5
solve bl=0.1 lambda=1.6
solve bl=0.1 lambda=l.7
solve bl=0.1 lambda=l.8
solve bl=0.1 lambda=l.9
solve bl=0.1 lambda=2.1
solve bl=0.1 lambda=2.2
solve bl=0.1 lambda=2.3
solve bl=0.1 lambda=2.4
solve bl=0.1 lambda=2.5
solve bl=0.1 lambda=2.6
solve bl=0.1 lambda=2.7
solve bl=0.1 lambda=2.8
solve bl=0.1 lambda=2.9
solve bl=0.1 lambda=3
solve bl=0.1 lambda=3.1
solve bl=0.1 lambda=3.2
solve bl=0.1 lambda=3.3
151
solve bl=0.1 lambda=3.4
solve bl=0.1 lambda=3.5
solve bl=0.1 lambda=3.6
solve bl=0.1 lambda=3.7
solve bl=0.1 lambda=3.8
solve bl=0.1 lambda=3.9
2. Middle Cell
a. Definition of Constants
set midLo=0
set midWindowThick=0.03
set midEmitterThick=0.05
set midBaseThick=0.55
set midBsfThick=0.03
set midBsfLo=$midLo
set midBaseLo=$midBsfLo-$midBsfThick
set midBaseMid=$midBaseLo-$midBaseThick/2
set midEmitterLo=$midBaseLo-$midBaseThick
set midWindowLo=$midEmitterLo-$midEmitterThick
set midHi=$midWindowLo-$midWindowThick
set midBsfDiv=$midBsfThick/20
set midBaseDiv=$midBaseThick/20
set midEmitterDiv=$midEmitterThick/20
set midWindowDiv=$midWindowThick/20
b. Y-Mesh
# Vacuum
y.mesh loc=$midHi spac=$midWindowDiv
# Window
y.mesh loc=$midWindowLo spac=$midWindowDiv
# Emitter
y.mesh loc=$midEmitterLo spac=$midEmitterDiv
# Base
y.mesh loc=$midBaseMid spac=$midBaseDiv
y.mesh loc=$midBaseLo spac=$midBsfDiv
# BSE
y.mesh loc=$midBsfLo spac=$midBsfDiv
c. Regions
# Window
region num=l material=InGaP x.min=-250 x.max=250 y.min=$midHi
y.max=$midWindowLo
# Emitter
region num=2 material=GaAs x.min=-250 x.max=250 y.min=$midWindowLo
y.max=$midEmitterLo
# Base
region num=3 material=GaAs x.min=-250 x.max=250 y.min=$midEmitterLo
y.max=$midBaseLo
# BSE
region num=4 material=InGaP x.min=-250 x.max=250 y.min=$midBaseLo
y.max=$midBsfLo
152
d.
Electrodes
electrode name=cathode x.min=-250 x.max=250 y.min=$midHi y.max=$midHi
electrode name=anode x.min=-250 x.max=250 y.min=$midLo y.max=$midLo
e. Doping
# Window
doping uniform region=l n.type conc=1.95el8
# Emitter
doping uniform region=2 n.type conc=2el8
# Base
doping uniform region=3 p.type conc=1.5el7
# BSF
doping uniform region=4 p.type conc=2el8
/. Solving
(1) Isc^ndVoc
# Get Isc and Voc
solve init
method gummel maxtraps=10 itlimit=25
solve bl=0.9
method newton maxtraps=10 itlimit=100
solve bl=l
contact name=cathode current
method newton maxtraps=10 itlimit=100
solve icathode=l.376e-7 bl=l
solve icathode=0 bl=l
3. Top Cell
a. Definition of Constants
set topLo=0
set topWindowThick=0.03
set topEmitterThick=0.05
set topBaseThick=0.55
set topBsfThick=0.03
set topBsfLo=$topLo
set topBaseLo=$topBsfLo-$topBsfThick
set topBaseMid=$topBaseLo-$topBaseThick/2
set topEmitterLo=$topBaseLo-$topBaseThick
set topWindowLo=$topEmitterLo-$topEmitterThick
set topHi=$topWindowLo-$topWindowThick
set topBsfDiv=$topBsfThick/20
set topBaseDiv=$topBaseThick/20
set topEmitterDiv=$topEmitterThick/20
set topWindowDiv=$topWindowThick/20
b. Y-Mesh
# Vacuum
y.mesh loc=$topHi spac=$topWindowDiv
# Window
153
y.mesh loc=$topWindowLo spac=$topWindowDiv
# Emitter
y.mesh loc=$topEmitterLo spac=$topEmitterDiv
# Base
y.mesh loc=$topBaseMid spac=$topBaseDiv
y.mesh loc=$topBaseLo spac=$topBsfDiv
# BSE
y.mesh loc=$topBsfLo spac=$topBsfDiv
c. Regions
# Window AllnP (=InAsP)
region num=l material=InAsP x.min=-250 x.max=250 y.min=$topHi
y.max=$topWindowLo
# Emitter
region num=2 material=InGaP x.min=-250 x.max=250 y.min=$topWindowLo
y.max=$topEmitterLo
# Base
region num=3 material=InGaP x.min=-250 x.max=250 y.min=$topEmitterLo
y.max=$topBaseLo
# BSE AlInGaP (=InAlAsP)
region num=4 material=InAlAsP x.min=-250 x.max=250 y.min=$topBaseLo
y.max=$topBsfLo
d. Electrodes
electrode name=cathode x.min=-250 x.max=250 y.min=$topHi y.max=$topHi
electrode name=anode x.min=-250 x.max=250 y.min=$topLo y.max=$topLo
e. Doping
# Window
doping uniform
# Emitter
doping uniform
# Base
doping uniform
# BSE
doping uniform
region=l
region=2
region=3
region=4
n.type
n.type
p.type
p.type
conc=l.95el8
conc=2el8
conc=l.5el7
conc=2el8
/. Solving
(1) IscandVoc
# Get Isc and Voc
solve init
method gummel maxtraps=10 itlimit=25
solve bl=0.9
method newton maxtraps=10 itlimit=100
solve bl=l
contact name=cathode current
method newton maxtraps=10 itlimit=100
solve icathode=8.4714e-8 bl=l
solve icathode=0 bl=l
154
3. Stacked Cell
a. Definition of Constants
set divs=10
set topBaseThick=0.55
set midBaseThick=0.55
set topWindowThick=0.03
set topEmitterThick=$topBaseThick/10
set topBsfThick=0.03
set midWindowThick=0.03
set midEmitterThick=$midBaseThick/10
set midBsfThick=0.03
set botWindowThick=0.05
set botEmitterThick=0.1
set botBaseThick=300
set tunnelThick=0.015
# Bottom
set botLo=0
set botBaseLo=$botLo
set botBaseMid=$botBaseLo-$botBaseThick/2
set botEmitterLo=$botBaseLo-$botBaseThick
set botWindowLo=$botEmitterLo-$botEmitterThick
set botHi=$botWindowLo-$botWindowThick
set botBaseDiv=$botBaseThick/$divs
set botEmitterDiv=$botEmitterThick/$divs
set botWindowDiv=$botWindowThick/$divs
# Bot Tunnel
set botTunnelLo=$botHi
set botTunnelMid=$botTunnelLo-$tunnelThick
set botTunnelHi=$botTunnelMid-$tunnelThick
set tunnelDiv=$tunnelThick/$divs
# Middle
set midLo=$botTunnelHi
set midBsfLo=$midLo
set midBaseLo=$midBsfLo-$midBsfThick
set midBaseMid=$midBaseLo-$midBaseThick/2
set midEmitterLo=$midBaseLo-$midBaseThick
set midWindowLo=$midEmitterLo-$midEmitterThick
set midHi=$midWindowLo-$midWindowThick
set midBsfDiv=$midBsfThick/$divs
set midBaseDiv=$midBaseThick/$divs
set midEmitterDiv=$midEmitterThick/$divs
set midWindowDiv=$midWindowThick/$divs
# Top Tunnel
set topTunnelLo=$midHi
set topTunnelMid=$topTunnelLo-$tunnelThick
set topTunnelHi=$topTunnelMid-$tunnelThick
# Top
set topLo=$topTunnelHi
set topBsfLo=$topLo
set topBaseLo=$topBsfLo-$topBsfThick
set topBaseMid=$topBaseLo-$topBaseThick/2
set topEmitterLo=$topBaseLo-$topBaseThick
set topWindowLo=$topEmitterLo-$topEmitterThick
set topHi=$topWindowLo-$topWindowThick
set topBsfDiv=$topBsfThick/$divs
155
set topBaseDiv=$topBaseThick/$divs
set topEmitterDiv=$topEmitterThick/$divs
set topWindowDiv=$topWindowThick/$divs
# Light
set lightY=$topHi-5
b. Y-Mesh
# Vacuum
y.mesh loc=$topHi spac=$topWindowDiv
# Window
y.mesh loc=$topWindowLo spac=$topWindowDiv
# Emitter
y.mesh loc=$topEmitterLo spac=$topEmitterDiv
# Base
y.mesh loc=$topBaseMid spac=$topBaseDiv
y.mesh loc=$topBaseLo spac=$topBsfDiv
# BSE
y.mesh loc=$topBsfLo spac=$tunnelDiv
# Vacuum
y.mesh loc=$topTunnelMid spac=$tunnelDiv
# Vacuum
y.mesh loc=$midHi spac=$tunnelDiv
# Window
y.mesh loc=$midWindowLo spac=$midWindowDiv
# Emitter
y.mesh loc=$midEmitterLo spac=$midEmitterDiv
# Base
y.mesh loc=$midBaseMid spac=$midBaseDiv
y.mesh loc=$midBaseLo spac=$midBsfDiv
# BSE
y.mesh loc=$midBsfLo spac=$tunnelDiv
# Vacuum
y.mesh loc=$botTunnelMid spac=$tunnelDiv
# Vacuum
y.mesh loc=$botHi spac=$tunnelDiv
# Window
y.mesh loc=$botWindowLo spac=$botWindowDiv
# Emitter
y.mesh loc=$botEmitterLo spac=$botEmitterDiv
# Base
y.mesh loc=$botBaseMid spac=$botBaseDiv
y.mesh loc=$botBaseLo spac=$botEmitterDiv
c. Regions
# Window AllnP (=InAsP)
region num=l material=InAsP x.min=-250 x.max=250 y.min=$topHi
y.max=$topWindowLo
# Emitter
region num=2 material=InGaP x.min=-250 x.max=250 y.min=$topWindowLo
y.max=$topEmitterLo
# Base
region num=3 material=InGaP x.min=-250 x.max=250 y.min=$topEmitterLo
y.max=$topBaseLo
# BSE AlInGaP (=InAlAsP)
156
region num=4 material=InAlAsP x.min=-250 x.max=250 y.min=$topBaseLo
y.max=$topBsfLo
# Vacuum
region num=5 material=Vacuum x.min=-250 x.max=250 y.min=$topTunnelHi
y.max=$topTunnelMid
#Vacuum
region num=6 material=Vacuum x.min=-250 x.max=250 y.min=$topTunnelMid
y.max=$topTunnelLo
# Window
region num=7 material=InGaP x.min=-250 x.max=250 y.min=$midHi
y.max=$midWindowLo
# Emitter
region num=8 material=GaAs x.min=-250 x.max=250 y.min=$midWindowLo
y.max=$midEmitterLo
# Base
region num=9 material=GaAs x.min=-250 x.max=250 y.min=$midEmitterLo
y.max=$midBaseLo
# BSE
region num=10 material=InGaP x.min=-250 x.max=250 y.min=$midBaseLo
y.max=$midBsfLo
# Vacuum
region num=ll material=Vacuum x.min=-250 x.max=250 y.min=$botTunnelHi
y.max=$botTunnelMid
#Vacuum
region num=12 material=Vacuum x.min=-250 x.max=250 y.min=$botTunnelMid
y.max=$botTunnelLo
# Window
region num=13 material=GaAs x.min=-250 x.max=250 y.min=$botHi
y.max=$botWindowLo
# Emitter
region num=14 material=Ge x.min=-250 x.max=250 y.min=$botWindowLo
y.max=$botEmitterLo
# Base
region num=15 material=Ge x.min=-250 x.max=250 y.min=$botEmitterLo
y.max=$botBaseLo
d. Electrodes
electrode name=gate x.min=-250 x.max=250 y.min=$topHi y.max=$topHi
electrode name=drain x.min=-250 x.max=250 y.min=$topLo y.max=$topLo
electrode name=collector x.min=-250 x.max=250 y.min=$midHi y.max=$midHi
electrode name=emitter x.min=-250 x.max=250 y.min=$midLo y.max=$midLo
electrode name=cathode x.min=-250 x.max=250 y.min=$botHi y.max=$botHi
electrode name=anode x.min=-250 x.max=250 y.min=$botLo y.max=$botLo
e. Doping
# Window
doping uniform region=l n.type conc=1.95el8
# Emitter
doping uniform region=2 n.type conc=2el8
157
# Base
doping uniform region=3 p.type conc=1.5el7
# BSF
doping uniform region=4 p.type conc=2el8
# Window
doping uniform region=7 n.type conc=1.95el8
# Emitter
doping uniform region=8 n.type conc=2el8
# Base
doping uniform region=9 p.type conc=1.5el7
# BSF
doping uniform region=10 p.type conc=2el8
# Window
doping uniform region=13 n.type conc=lel9
# Emitter
doping uniform region=14 n.type conc=2el8
# Base
doping uniform region=15 p.type conc=lel7
/. Light Beams
beam num=l x.origin=0 y.origin=$lightY angle=90 \
power.file=AMOsilv.spec wavel.start=0.21 wavel.end=4 wavel.num=50
158
APPENDIX G. MATLAB SOURCE CODE
A. VEC2SPEC
% VEC2SPEC Converts spectrum data to a Silvaco spec file.
% VEC2SPEC(wavel, int, filename) creates the file filename.spec
% and stores the wavel and int information of the spectrum.
% (c)2001 by P. Michalopoulos
function vec2spec(wavel, int, filename)
% Error checking
len = length(wavel);
if (len ~= length(int))
disp('ERROR! Vector lengths must agree.')
break;
end
% Initialize output file
file = fopen([filename '.spec'], 'w');
fprintf(file, '%d', len);
% Save data to file
for i = 1:len,
fprintf(file, '\n%e %e' , wavel(i), int(i));
end
fclose(file);
B. OPT2SILV
0PT2SILV Convert an optical parameter mat file into a Silvaco
f ile .
% 0PT2SILV(filename, t) Creates the Silvaco optical parameter file
filename.opt
% from the filename.mat file.
% If t='e' then filename.mat must contain eV-el-e2 data
% If t='n' then filename.mat must contain wavel-n-k data
% (c)2001 by P. Michalopoulos
function opt2silv(filename, t)
% Load data
load(['Data\' filename '.mat'])
% Convert to common units
if t == 'e'
wavel = ev2um(eV);
159
[n k] = e2nk(el, e2);
end
% Initialize file
file = fopen(['Data\' filename '.opt']? 'w');
len = length(wavel) ;
fprintf(flie, '%d\n', len);
% Save data to file
for i = 1:len
fprintf(file, '%d %d %d\n', wavel(i), n(i), k(i));
end
fclose(file);
C. DISPLOG
% DISPLOG Displays the properties of a Silvaco log file.
% DISPLOG(filename) prints the major properties of a Silvaco log file.
% (c)2001 by P.Michalopoulos
function displog(filename)
[program, numOfElectrodes, electrodeName, values, valueName, data] =
parselog(filename) ;
disp(program)
disp ( 'Electrodes: ')
for 1 = 1:numOfElectrodes,
disp ( [' ' num2str(i) '. ' electrodeName{i}])
end
disp('Values:')
for 1 = l:values,
disp ( [' ' num2str(i) '. ' valueName{i}])
end
D. PARSELOG
% PARSELOG Parses a Silvaco log file.
% [prog, numOfElec, elecName, val, valName, data]=PARSELOG(filename)
% parses filename.log and returns:
% prog : the program that generated the log file
% numOfElec : the number of electrodes
% elecName : a cell with the names of the electrodes
% val : the number of different types of values contained
% valName : a cell with the names of those values
% data : a matrix with the actual data (each column is a value)
% (c)2001 by P. Michalopoulos
function [program, numOfElectrodes, electrodeName, values, valueName,
data] = parselog(filename)
data = [];
160
% Read log file
file = fopen([filename '.log']);
while 1
line = fgetl(file);
if ~ischar(line), break, end
% Translate data codes and parse data
switch line (1)
case 'v' % program used
[token, line] = strtok(line);
[token, line] = strtok(line);
program = token;
case '#' % comments
case 'y'
case 'z '
case 'f' % electrode names
[token, line] = strtok(line);
[token, line] = strtok(line);
numOfElectrodes = strlnum(token);
electrodeName = cell(numOfElectrodes, 1) ;
for 1 = 1:numOfElectrodes,
[token, line] = strtok(line);
electrodeName{1} = token;
end
case 'p' % data properties
[token, line] = strtok(line);
[token, line] = strtok(line);
values = strlnum(token);
valueName = cell(values,1);
for 1 = l:values,
[token, line] = strtok(line);
token = strlnum(token);
switch token
case 2
valueName]1} = [electrodeName{1} ' Voltage'];
case 3
valueName]1} = [electrodeName]!} ' Voltage'];
case 4
valueName]!} = [electrodeName]3} ' Voltage'];
case 5
valueName]!} = [electrodeName]4} ' Voltage'];
case 6
valueName]!} = [electrodeName]5} ' Voltage'];
case 7
valueName]!} = [electrodeName]6} ' Voltage'];
case 20
valueName]!} = [electrodeName]!} ' Current'];
case 21
valueName]!} = [electrodeName]!} ' Current'];
case 22
valueName]!} = [electrodeName]!} ' Current'];
case 23
valueName]!} = [electrodeName]4} ' Current'];
case 24
valueName]!} = [electrodeName]!} ' Current'];
case 25
161
valueName{i} = [electrodeName{6} ' Current'];
case 85
valueName]i} = 'Available photo current';
case 86
valueName]1} = 'Source photo current';
case 87
valueName]!} = 'Optical wavelength';
case 91
valueName]!} = 'Light Intensity beam 1';
case 601
valueName]!} = [electrodeName]!} ' Int. Voltage'];
case 602
valueName]!} = [electrodeName]!} ' Int. Voltage'];
case 603
valueName]!} = [electrodeName]3} ' Int. Voltage'];
case 604
valueName]!} = [electrodeName]4} ' Int. Voltage'];
case 605
valueName]!} = [electrodeName]5} ' Int. Voltage'];
case 606
valueName]!} = [electrodeName]6} ' Int. Voltage'];
otherwise
disp('Unknown value name')
end
end
case 'd' % data values
dataLine = [];
[token, line] = strtok(line);
for 1 = l:values,
[token, line] = strtok(line);
value = str2double(token);
dataLine = [dataLine value];
end
data = [data; dataLine];
otherwise
disp('Unknown command')
end
end
fclose(file);
E. PLOTLOG
% PLOTLOG Plots a Silvaco log file.
% PLOTLOG(filename, x-axis, y-axis, style, xmult, ymult) Creates
% a plot of the value in y-axis vs the value in x-axis with values
% and data derived from filename.log. The line style used is specified
% after that. The x and y values are scaled according to xmult and
% ymult accordingly.
% (c)2001 by P.Michalopoulos
function plotlog(filename, x, y, p, mx, my)
[program, numOfElectrodes, electrodeName, values, valueName, data] =
parselog(filename) ;
162
sx = sign(x) ;
sy = sign(y);
X = abs(x);
y = abs(y);
if (x > values) | (y > values),
disp('ERROR! Axis parameter can not be found.')
else
plot(sx*data(:,x)'*mx, sy*data(:,y)'*my, p), grid on
title([filename '.log from ' program]);
Xlabel(valueName{x});
ylabel(valueName{y}) ;
end
F. OPTINTERP
% OPTINTERP Interpolates optical parameters.
% OPTINTERP(fl, f2, r) Interpolates the optical parameters found in
% fl.mat and f2.mat with a ratio of r and returns the wavel, n
% and k of the result.
% (c)2002 by P. Michalopoulos
function [wavel, n, k] = optinterp (file2, filel, ratio)
% Load optical parameters for material 1
load(['Data\' filel '.mat'])
wavelCompl = ev2um(eV);
[nCompl kCompl] = e2nk(el, e2);
% Load optical parameters for material 2
load(['Data\' file2 '.mat'])
wavelComp2 = ev2um(eV);
[nComp2 kComp2] = e2nk(el, e2);
% Perform simple interpolation
wavelResultl = wavelCompl;
nResult = nCompl*(1-ratio) + nComp2*ratio;
kResult = kCompl*(1-ratio) + kComp2*ratio;
kResultlen = length(kResult);
wavelResult = wavelCompl;
% Locate the area where only kl or k2 is zero
kComp2ch = (kComp2 ~= 0);
kComplch = (kCompl ~= 0);
kResultch = xor(kComp2ch, kComplch);
area = find(kResultch) ;
arealen = length(area);
% Implement correction in material 2
kComp2ch = kComp2;
index = find(~kComp2ch) ;
163
kComp2ch(index) = [];
kComp2chlen = length(kComp2ch);
kComp2ch = kComp2ch(kComp2chlen - arealen + 1 : kComp2chlen);
wavelComp2ch = wavelComp2;
wavelComp2ch(index) = [];
wavelComp2chlen = length(wavelComp2ch);
wavelComp2ch = wavelComp2(wavelComp2chlen - arealen + 1 :
wavelComp2chlen) ;
% Implement correction in material 1
kComplch = kCompl;
index = find(~kComplch);
kComplch(index) = [];
kComplchlen = length(kComplch);
kComplch = kComplch(kComplchlen - arealen + 1 : kComplchlen);
wavelComplch = wavelCompl;
wavelComplch(index) = [];
wavelComplchlen = length(wavelComplch);
wavelComplch = wavelCompl(wavelComplchlen - arealen + 1 :
wavelComplchlen) ;
% Combine corrections
kResultch = kComplch*(1-ratio) + kComp2ch*ratio;
% Smooth-out result
kResultchl = kResultch(1);
[h index] = min(abs(kResult - kResultchl));
ratio = linspace(0, 1, arealen);
kResult(index + 1 : index + arealen) = kResultch.*ratio + kResult(index
+ 1 : index + arealen) .*(1-ratio) ;
kResult(index + arealen + 1 : kResultlen) = kResult(index + arealen + 1
: kResultlen)*0;
wavel = wavelResult;
n = nResult;
k = kResult;
F. EV2UM
% EV2UM Converts photon energy (eV) into wavelength (urn).
% (c)2001 by P. Michalopoulos
function urn = ev2um(ev)
h = 6.6260755e-34;
eV = 1.60218e-19;
c = 2.99792458e8;
ev = ev * eV;
f = ev / h;
wavel = c ./ f;
urn = wavel / le-6;
164
G.
UM2EV
% UM2EV Converts photon wavelength (um) into energy (eV).
% (c)2001 by P. Michalopoulos
function ev = um2ev(um)
h = 6.6260755e-34;
eV = 1.60218e-19;
c = 2.99792458e8;
wavel = um * le-6;
f = c ./ wavel;
ev = h * f;
ev = ev ./ eV;
H. E2NK
% E2NK Convert the el, e2 pairs into n, k pairs.
% [n k] = E2NK(el, e2)
% (c)2001 by P. Michalopoulos
function [n,k] = e2nk(el, e2)
ap = (el + sqrt(el.^2 + e2.^2)) / 2;
an = (el - sqrt(el.^2 + e2.^2)) / 2;
app = ap >= 0;
anp = an >= 0;
err = (app < 0) & (anp < 0);
err = sum(err);
if err ~= 0
disp('ERROR!')
end
a = ap .* app + an .* anp;
n = sqrt(a);
k = e2 ./ (2 * n);
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166
LIST OF REFERENCES
1. Sze, S. M., Semiconductor Devices, 2nd edition, John Wiley & Sons, Inc, 2001.
2. Sze, S. M., Physics of Semiconductor Devices, 2nd edition, John Wiley & Sons, Inc,
1981.
3. Shur, M., Physics of Semiconductor Devices, Prentice-Hall, Inc, 1990.
4. Messenger, G. C., Ash, M. S., The Effects of Radiation on Electronic Systems, Van
Nostrand Reinhold Company Inc, 1986.
5. Pahk, E. D., Handbook of Optical Constants of Solids, Academin Press, Inc, 1985.
6. Palik, E. D., Gorachand, G., Electronic Handbook of Optical Constants of Solids,
Academin Press, Inc, 1999.
7. Sze, S. M., Modern Semiconductor Device Physics, John Wiley & Sons, Inc, 1998.
8. Eraser, D. A., The Physics of Semiconductor Devices, Clarendon Press - Oxford,
1986.
9. Bolz, R. E., Tuve, G. E., CRC Handbook of Tables for Applied Engineering Science,
The Chemical Rubber Co, 1973.
10. ATLAS User’s Manual, vols 1-2, SIEVACO International, 2000.
11. ATHENA User’s Manual, SIEVACO International, 2000.
12. DEVEDIT User’s Manual, SIEVACO International, 2000.
13. PC Interractive Tools User’s Manual, SIEVACO International, 1999.
14. SIEVACO International, www.silvaco.com
15. T. Agui, T. Takamoto, E. Ikeda, H. Kurita, “High-efficient dual-junction
InCaP/CaAs solar cells with improved tunnel interconnect”. Indium Phosphide and
Related Materials, 1998 International Conference on, pp 203-206, 1998
16. T. Takamoto, E. Ikeda, H. Kurita, M. Ohmori, “High efficiency InCaP solar cells for
InCaP/CaAs tandem cell apphcation”. Photovoltaic Energy Conversion, 1994.,
Conference Record of the Twenty Eourth. IEE E Photovoltaic Speciahsts Conference -
1994, 1994 IEEE Eirst World Conference on , Volume: 2, pp 1729 -1732 vol.2, 1994
167
17. H. Kurita, T. Takamoto, E. Ikeda, M. Ohmoii, “High-efficiency monolithic
InGaP/GaAs tandem solar cells with improved top-cell back-surface-field layers”, Indium
Phosphide and Related Materials, 1995. Conference Proceedings., Seventh International
Conference on, pp 516-519,1995
18. B.T. Cavicchi, D.D. Krut, D.R. Lilhngton, S.R. Kurtz, J.M. Olson, “The design and
evaluation of dual-junction GaInP/sub 2//GaAs solar cells for space apphcations”.
Photovoltaic Speciahsts Conference, 1991., Conference Record of the Twenty Second
IEEE, pp 63-67 vol. 1 , 1991
19. R.R. King, N.H. Karam, J.H. Ermer, N. Haddad, P. Colter, T. Issh iki , H. Yoon, H.E.
Cotal, D.E. Joslin, D.D. Krut, R. Sudharsanan, K. Edmondson, B.T. Cavicchi, D.R.
EiUington, “Next-generation, high-efficiency IH-V multijunction solar cells”.
Photovoltaic Specialists Conference, 2000. Conference Record of the Twenty-Eighth
IEEE , 2000, pp. 998-1001
20. D. Eilhngton, H. Cotal, J. Ermer, D. Eriedman, T. Moriarty, A. Duda, “32.3%
efficient triple junction GaInP/sub 2//GaAs/Ge concentrator solar cells”. Energy
Conversion Engineering Conference and Exhibit, 2000. (lECEC) 35th Intersociety ,
Volume: 1,2000, pp. 516 -521
21. J.E. Granata, J.H. Ermer, P. Hebert, M. Haddad, R.R. King, D.D. Krut, J. Eovelady,
M.S. GiUanders, N.H. Karam, B.T. Cavicchi, ‘Triple-junction GaInP/GaAs/Ge solar
cells-production status, quahfication results and operational benefits”. Photovoltaic
Specialists Conference, 2000. Conference Record of the Twenty-Eighth IE EE , 2000, pp.
1181 -1184
22. N.H. Karam, R.R. King, B.T. Cavicchi, D.D. Krut, J.H. Ermer, M. Haddad, Ei Cai,
D.E. Joslin, M. Takahashi, J.W. Eldredge, W.T. Nishikawa, D.R. Eilhngton, B.M. Keyes,
R.K. Ahrenkiel, “Development and characterization of high-efficiency Ga/sub 0.5/In/sub
0.5/P/GaAs/Ge dual- and triple-junction solar ceUs”, Electron Devices, IEEE
Transactions on , Volume: 46 Issue: 10 , Oct. 1999, pp. 2116 -2125
23. Reinhardt K.C, Mayberry C.S, Eewis B.P, Kreifels T.E, “Multijunction solar ceU
iso-junction dark current study”. Photovoltaic Specialists Conference, 2000, Conference
Record of the Twenty-Eighth IEE E , 2000, pp 1118-1121
24. King R.R, Karam N.H, Ermer J.H, Haddad N, Colter P, Isshiki T, Yoon H, Cotal
H.E, Joshn D.E, Kmt D.D, Sudharsanan R, Edmondson K, Cavicchi B.T, EiUington
D.R., “Next-generation, high-efficiency III-V multijunction solar ceUs”, Photovoltaic
Specialists Conference, 2000, Conference Record of the Twenty-Eighth IEE E , 2000, pp
998-1001
168
25. Van Kerschaver E, Nijs J, Mertens R, Ghannam M, “Twodimensional solar cell
simulations by means of circuit modelling”, Photovoltaic Specialists Conference, 1997.,
Conference Record of the Twenty-Sixth IEEE , 1997, pp 175-178
26. Jain R.K, Elood D.J, “Simulation of high-efficiency n/sup -t/p indium phosphide
solar cell results and future improvements”. Electron Devices, IEEE Transactions on ,
Volume: 41 Issue: 12 , Dec. 1994, pp 2473-2475
27. Kurtz S, Geisz J.E, Eriedman D.J, Olson J.M, Duda A, Karam N.H, King R.R,
Ermer J.H, Joshn D.E, “Modeling of electron diffusion length in GaJnAsN solar cells”.
Photovoltaic Specialists Conference, 2000, Conference Record of the Twenty-Eighth
IEEE, 2000, pp 1210-1213
28. Walters R.J, Summers G.P, Messenger S.R, “Analysis and modehng of the radiation
response of multijunction space solar cells”. Photovoltaic Specialists Conference, 2000,
Conference Record of the Twenty-Eighth IE EE , 2000, pp 1092 -1097
29. Pause P, Sankaranarayanan H, Narayanaswamy R, Shankaradas M, Ying Y,
Eerekides C.S, Morel D.E, “Evaluation and modehng of junction parameters in
Cu(In,Ga)Se/sub 2/ solar cells”. Photovoltaic Specialists Conference, 2000, Conference
Record of the Twenty-Eighth IEEE , 2000, pp 599 -602
30. Eewis, B. P., Dark current analysis and computer simulation of triple-junction solar
cells. Naval Postgraduate School, 1999.
31. Renewable Resource Data Center (rredc.nrel.gov)
32. US Department of Energy - Photovoltaics Program (http://www.eren.doe.gov/pv)
33. I. Vurgaftman, J.R. Meyer, E.R. Ram-Mohan, “Band parameters for III-V
compound semiconductors and their aUoys”, Applied Physics Review, Journal of Apphed
Physics, vol 89, number 11, 1 June 2001, pp. 5815-5875
34. McCloy, D. J., High efficiency solar ceUs: a model in Silvaco, Naval Postgraduate
School, 1999.
169
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