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This document was downloaded on April 03, 2014 at 16:24:47

Author(s) Garcia, Baldomero
Title Indium gallium nitride multijunction solar cell simulation using silvaco atlas
Publisher Monterey California. Naval Postgraduate School
Issue Date 2007-06
URL http://hdl.handle.net/10945/3423


NAVAL
POSTGRADUATE
SCHOOL

MONTEREY, CALIFORNIA



THESIS

Approved for public release; distribution is unlimited
INDIUM GALLIUM NITRIDE MULTIJUNCTION SOLAR
CELL SIMULATION USING SILVACO ATLAS

by

Bal domer o Gar ci a, J r .

J une 2007

Thesi s Advi sor : Sher i f Mi chael
Second Reader : Todd Weat her f or d
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i
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J une 2007
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4. TITLE AND SUBTITLE I ndi umGal l i umNi t r i de
Mul t i j unct i on Sol ar Cel l Si mul at i on Usi ng Si l vaco
At l as
6. AUTHOR(S) Bal domer o Gar ci a, J r .
5. FUNDING NUMBERS
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
Naval Post gr aduat e School
Mont er ey, CA 93943- 5000
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Appr oved f or publ i c r el ease; di st r i but i on i s unl i mi t ed
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13. ABSTRACT (maximum 200 words)
Thi s t hesi s i nvest i gat es t he pot ent i al use of wur t zi t e I ndi umGal l i umNi t r i de as
phot ovol t ai c mat er i al . Si l vaco At l as was used t o si mul at e a quad- j unct i on sol ar cel l .
Each of t he j unct i ons was made up of I ndi um Gal l i um Ni t r i de. The band gap of each
j unct i on was dependent on t he composi t i on per cent age of I ndi um Ni t r i de and Gal l i um
Ni t r i de wi t hi n I ndi um Gal l i um Ni t r i de. The f i ndi ngs of t hi s r esear ch show t hat I ndi um
Gal l i umNi t r i de i s a pr omi si ng semi conduct or f or sol ar cel l use.


15. NUMBER OF
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113
14. SUBJECT TERMS
Sol ar cel l , phot ovol t ai c devi ce, I ndi umGal l i umNi t r i de, Si l vaco
At l as.
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17. SECURITY
CLASSIFICATION OF
REPORT
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CLASSIFICATION OF THIS
PAGE
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ABSTRACT
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ABSTRACT

UL
NSN 7540- 01- 280- 5500 St andar d For m298 ( Rev. 2- 89)
Pr escr i bed by ANSI St d. 239- 18
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i i i
Approved for public release; distribution is unlimited


INDIUM GALLIUM NITRIDE MULTIJUNCTION SOLAR CELL SIMULATION
USING SILVACO ATLAS


Bal domer o Gar ci a, J r .
Li eut enant Commander , Uni t ed St at es Navy
B. S. , U. S. Naval Academy, 1995

Submi t t ed i n par t i al f ul f i l l ment of t he
r equi r ement s f or t he degr ee of


MASTER OF SCIENCE IN ELECTRICAL ENGINEERING


f r omt he


NAVAL POSTGRADUATE SCHOOL
June 2007




Aut hor : Bal domer o Gar ci a, J r .



Appr oved by: Sher i f Mi chael
Thesi s Advi sor



Todd Weat her f or d
Second Reader




J ef f r ey B. Knor r
Chai r man, Depar t ment of El ect r i cal and
Comput er Engi neer i ng
i v
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v
ABSTRACT
Thi s t hesi s i nvest i gat es t he pot ent i al use of wur t zi t e
I ndi um Gal l i um Ni t r i de as phot ovol t ai c mat er i al . Si l vaco
At l as was used t o si mul at e a quad- j unct i on sol ar cel l . Each
of t he j unct i ons was made up of I ndi umGal l i umNi t r i de. The
band gap of each j unct i on was dependent on t he composi t i on
per cent age of I ndi um Ni t r i de and Gal l i um Ni t r i de wi t hi n
I ndi um Gal l i um Ni t r i de. The f i ndi ngs of t hi s r esear ch show
t hat I ndi umGal l i umNi t r i de i s a pr omi si ng semi conduct or f or
sol ar cel l use.
vi
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vi i
TABLE OF CONTENTS
I. INTRODUCTION ............................................1
A. BACKGROUND .........................................1
B. OBJECTIVE ..........................................1
C. RELATED WORK .......................................1
D. ORGANIZATION .......................................2
1. Purpose of Solar Cells ........................2
2. Simulation Software ...........................2
3. Indium Gallium Nitride ........................3
4. Simulation ....................................3
II. SOLAR CELL AND SEMICONDUCTOR BASICS .....................5
A. SEMICONDUCTOR FUNDAMENTALS .........................5
1. Classification of Materials ...................5
2. Atomic Structure ..............................7
3. Electrons and Holes ...........................9
4. Direct and Indirect Band Gaps ................12
5. Fermi Level ..................................13
B. SOLAR CELL FUNDAMENTALS ...........................14
1. History of Solar Cells .......................14
2. The Photovoltaic Effect ......................15
a. The Electromagnetic Spectrum ............17
b. Band Gap ................................18
c. Solar Cell Junctions ....................19
d. Lattice Matching ........................20
e. AM0 Spectrum ............................22
f. Current-Voltage Curves ..................24
g. Electrical Output .......................25
C. CHAPTER CONCLUSIONS ...............................26
III. SILVACO ATLAS SIMULATION SOFTWARE ......................27
A. VIRTUAL WAFER FAB .................................27
B. SILVACO ATLAS .....................................28
C. INPUT FILE STRUCTURE ..............................29
1. Structure Specification ......................31
a. Mesh ....................................31
b. Region ..................................32
c. Electrodes ..............................34
d. Doping ..................................35
2. Materials Model Specification ................35
a. Material ................................36
b. Models ..................................36
c. Contact .................................37
d. Interface ...............................37
vi i i
3. Numerical Method Selection ...................38
4. Solution Specification .......................39
a. Log .....................................39
b. Solve ...................................40
c. Load and Save ...........................40
5. Results Analysis .............................41
D. CONCLUSION ........................................42
IV. INDIUM GALLIUM NITRIDE .................................43
A. A FULL SPECTRUM PHOTOVOLTAIC MATERIAL .............43
B. RADIATION-HARD SEMICONDUCTOR MATERIAL .............47
C. INDIUM GALLIUM NITRIDE CHALLENGES .................48
V. SIMULATION OF INDIUM GALLIUM NITRIDE IN SILVACO ATLAS ..49
A. SINGLE-JUNCTION SOLAR CELL ........................50
B. DUAL-JUNCTION SOLAR CELL ..........................52
C. THREE-JUNCTION SOLAR CELL .........................54
D. QUAD-JUNCTION SOLAR CELL ..........................57
VI. CONCLUSIONS AND RECOMMENDATIONS ........................67
A. RESULTS AND CONCLUSIONS ...........................67
B. RECOMMENDATIONS FOR FUTURE RESEARCH ...............67
APPENDIX A: SILVACO ATLAS INPUT DECK ........................69
A. TOP JUNCTION: IN
0.20
GA
0.80
N, EG=2.66 EV..............69
B. SECOND JUNCTION: IN
0.57
GA
0.43
N, EG=1.6 EV............73
C. THIRD JUNCTION: IN
0.68
GA
0.32
N, EG=1.31 EV............77
D. BOTTOM JUNCTION: IN
0.78
GA
0.22
N, EG=1.11 EV...........80
APPENDIX B: MATLAB CODE .....................................85
A. INDIUM GALLIUM NITRIDE BAND GAP CALCULATIONS ......85
B. CONVERSION FROM DIELECTRIC CONSTANTS (EPSILONS) TO
REFRACTION COEFFICIENTS (N, K) ....................86
C. CONVERSION FROM PHOTON ENERGY (EV) TO WAVELENGTH
(UM) ..............................................86
D. IV CURVE PLOTS FOR INDIUM GALLIUM NITRIDE QUAD
JUNCTION SOLAR CELL ...............................87
E. AIR MASS ZERO PLOTS ...............................90
LIST OF REFERENCES ..........................................91
INITIAL DISTRIBUTION LIST ...................................95

i x
LIST OF FIGURES
Fi gur e 1. Mat er i al s cl assi f i ed by conduct i vi t y ( Fr om
[ 6] ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Fi gur e 2. Par t i al per i odi c t abl e ( Af t er [ 7] ) . . . . . . . . . . . . . . . 6
Fi gur e 3. Si l i con at omi c st r uct ur e ( Fr om[ 8] ) . . . . . . . . . . . . . . 7
Fi gur e 4. Si l i con at omcoval ent bonds ( Fr om[ 1, p. 11] ) . . . . 8
Fi gur e 5. Band gap di agr ams ( Fr om[ 1, p. 8] ) . . . . . . . . . . . . . . . 9
Fi gur e 6. Dopi ng: n- t ype and p- t ype ( Fr om[ 1, p. 13] ) . . . . . 10
Fi gur e 7. Di r ect and i ndi r ect band gaps ( Af t er [ 1, p.
24] ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Fi gur e 8. Fer mi l evel : i nt r i nsi c case ( Af t er [ 9, p. 42] ) . . 14
Fi gur e 9. Fer mi l evel : n- t ype case ( Af t er [ 9, p. 42] ) . . . . . 14
Fi gur e 10. Fer mi l evel : p- t ype case ( Af t er [ 9, p. 42] ) . . . . . 14
Fi gur e 11. The el ect r omagnet i c spect r um( Fr om[ 13] ) . . . . . . . . 17
Fi gur e 12. Ef f ect of l i ght ener gy on di f f er ent band gaps
( Fr om[ 15] ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Fi gur e 13. Si mpl e cubi c l at t i ce st r uct ur e ( Fr om[ 16] ) . . . . . . 20
Fi gur e 14. Lat t i ce const ant s ( Fr om[ 17] ) . . . . . . . . . . . . . . . . . . . 21
Fi gur e 15. Lat t i ce const ant f or I nN and GaN ( Fr om[ 18] ) . . . . 22
Fi gur e 16. AM0 spect r um ( Wavel engt h vs I r r adi ance) ( Af t er
[ 19] ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Fi gur e 17. AM0 spect r um ( Ener gy vs I r r adi ance) ( Af t er
[ 19] ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Fi gur e 18. Sampl e I V cur ve used i n ef f i ci ency cal cul at i ons
( Af t er [ 20] ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Fi gur e 19. Sol ar cel l I V char act er i st i c ( Fr om[ 21] ) . . . . . . . . 26
Fi gur e 20. Si l vaco’ s Vi r t ual Waf er Fabr i cat i on Envi r onment
( Fr om[ 22] ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Fi gur e 21. At l as i nput s and out put s ( Fr om[ 23, p. 2- 2] ) . . . . 28
Fi gur e 22. At l as command gr oups and pr i mar y st at ement s
( Fr om[ 23, p. 2- 8] ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Fi gur e 23. At l as mesh ( Fr om2, p. 18] ) . . . . . . . . . . . . . . . . . . . . . . 31
Fi gur e 24. At l as r egi on ( Fr om[ 2, p. 19] ) . . . . . . . . . . . . . . . . . . 33
Fi gur e 25. At l as r egi ons wi t h mat er i al s def i ned ( Fr om [ 2,
p. 19] ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Fi gur e 26. At l as el ect r odes ( Fr om[ 2, p. 20] ) . . . . . . . . . . . . . . 34
Fi gur e 27. At l as dopi ng ( Fr om[ 2, p. 21] ) . . . . . . . . . . . . . . . . . . 35
Fi gur e 28. At l as mat er i al model s speci f i cat i on ( Af t er [ 23,
p. 2- 8] ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Fi gur e 29. At l as numer i cal met hod sel ect i on ( Af t er [ 23, p.
2- 8] ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Fi gur e 30. At l as sol ut i on speci f i cat i on ( Af t er [ 23, p. 2-
8] ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Fi gur e 31. At l as r esul t s anal ysi s ( Af t er [ 23, p. 2- 8] ) . . . . . 41
x
Fi gur e 32. Sampl e TonyPl ot I V cur ve. . . . . . . . . . . . . . . . . . . . . . . . 42
Fi gur e 33. I nGaN band gap as a f unct i on of I n composi t i on
( Af t er [ 25] ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Fi gur e 34. I nGaN band gap and sol ar spect r um compar i son
( Af t er [ 26] ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Fi gur e 35. Evi dence of 0. 7 eV band gap f or i ndi um ni t r i de
( Fr om[ 29] ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Fi gur e 36. I nGaN band gap as a f unct i on of I n
concent r at i on. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Fi gur e 37. Si mpl e si ngl e- j unct i on I nGaN sol ar cel l . . . . . . . . . 50
Fi gur e 38. Four si ngl e- j unct i on I V cur ves. . . . . . . . . . . . . . . . . . 51
Fi gur e 39. Si mpl e dual - j unct i on I nGaN sol ar cel l . . . . . . . . . . . 52
Fi gur e 40. Dual - j unct i on I nGaN sol ar cel l I V cur ve. . . . . . . . . 53
Fi gur e 41. Si mpl e t hr ee- j unct i on I nGaN sol ar cel l . . . . . . . . . . 55
Fi gur e 42. Thr ee- j unct i on I nGaN sol ar cel l I V cur ve. . . . . . . . 56
Fi gur e 43. Si mpl e quad- j unct i on I nGaN sol ar cel l . . . . . . . . . . . 58
Fi gur e 44. Quad- j unct i on I nGaN sol ar cel l I V cur ve. . . . . . . . . 59
Fi gur e 45. Spect r ol ab’ s sol ar cel l ef f i ci enci es ( Fr om
[ 34] ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Fi gur e 46. Compar i son of I nGaN band gap f or mul as. . . . . . . . . . . 62
Fi gur e 47. I V cur ve f or I n
0. 20
Ga
0. 80
N usi ng di f f er ent band
gaps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Fi gur e 48. Quad- j unct i on I nGaN sol ar cel l I V cur ve usi ng
cal cul at ed band gaps f r om[ 37] f or mul a. . . . . . . . . . 64

xi
LIST OF TABLES
Tabl e 1. Def i ni t i ons of n and p. . . . . . . . . . . . . . . . . . . . . . . . . . 11
Tabl e 2. n
i
f or f i ve semi conduct or s. . . . . . . . . . . . . . . . . . . . . . 11
Tabl e 3. Not abl e event s i n t he hi st or y of phot ovol t ai cs
( Fr om[ 12] ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Tabl e 4. Appr oxi mat e wavel engt h of var i ous col or s i n
vacuum( Af t er [ 14] ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Tabl e 5. Common semi conduct or band gaps ( Af t er [ 9, p.
31] ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Tabl e 6. Si l vaco At l as physi cal model s ( Fr om [ 23, p. 1-
2] ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Tabl e 7. Ef f i ci enci es of f our si ngl e- j unct i on I nGaN
cel l s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Tabl e 8. Dual - j unct i on I nGaN ef f i ci ency. . . . . . . . . . . . . . . . . . 54
Tabl e 9. Thr ee- j unct i on I nGaN ef f i ci ency. . . . . . . . . . . . . . . . . 56
Tabl e 10. Quad j unct i on I nGaN ef f i ci ency. . . . . . . . . . . . . . . . . . 59
Tabl e 11. I nGaN ef f i ci ency r esul t s ( Fr om[ 5] ) . . . . . . . . . . . . . 62
Tabl e 12. Quad j unct i on I nGaN ef f i ci ency usi ng band gaps
f r om[ 37] cal cul at i ons. . . . . . . . . . . . . . . . . . . . . . . . . . 64

xi i
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xi i i
ACKNOWLEDGMENTS
Fi r st , I woul d l i ke t o t hank Pr of essor Sher i f Mi chael
f or hi s hel p and gui dance dur i ng t he r esear ch pr ocess. Hi s
i nsi ght was i nval uabl e when f aced wi t h di f f i cul t pr obl ems.
Second, I woul d l i ke t o t hank Pr of essor Todd
Weat her f or d f or cl ar i f yi ng i ssues r egar di ng t he use of
Si l vaco At l as. He was al so cr i t i cal i n f i ndi ng poi nt s of
cont act at Lawr ence Ber kel ey Labor at or y.
Thi r d, I woul d l i ke t o t hank Dr . Wl adek Wal uki ewi cz
f r om t he Mat er i al Sci ences Di vi si on at Lawr ence Ber kel ey
Nat i onal Labor at or y. He and hi s t eam ar e t he wor l d- wi de
l eader s i n I ndi umGal l i umNi t r i de mat er i al sci ence r esear ch.
Thei r r esear ch was my i nspi r at i on t o st ar t t hi s r esear ch
pr oj ect .
Four t h, I woul d l i ke t o t hank Dr . Pet r a Specht f r om
Lawr ence Ber kel ey Nat i onal Labor at or y. She pr ovi ded key dat a
used i n t hi s r esear ch.
And l ast , but not l east , I woul d l i ke t o t hank my wi f e,
Nozomi and our chi l dr en, Oscar and Yuuki , f or t hei r pat i ence
and suppor t dur i ng my t i me at t he Naval Post gr aduat e School .
xi v
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xv
EXECUTIVE SUMMARY
One of t he pr i mar y goal s of sol ar cel l desi gn i s t o
i mpr ove ef f i ci ency. I ndi um Gal l i um Ni t r i de i s a mat er i al
t hat has under gone ext ensi ve r esear ch si nce 2002 as a
pot ent i al phot ovol t ai c mat er i al . By var yi ng t he composi t i on
of I ndi um Ni t r i de and Gal l i um Ni t r i de wi t hi n I ndi um Gal l i um
Ni t r i de, t he band gap of t hi s semi conduct or mat er i al can be
changed. The band gap r ange of I ndi um Gal l i um Ni t r i de
mat ches cl osel y t he vi si bl e sol ar spect r um f r equenci es.
Hence, a hi gh- ef f i ci ency sol ar cel l can be pot ent i al l y
devel oped by havi ng sever al I ndi um Gal l i um Ni t r i de
j unct i ons.
The use of Si l vaco At l as as a si mul at i on t ool can ai d
i n i dent i f yi ng whet her I ndi um Gal l i um Ni t r i de can be used
f or phot ovol t ai cs. Pr evi ous r esear ch at t he Naval
Post gr aduat e School has demonst r at ed t he vi abi l i t y of
Si l vaco At l as as a sol ar cel l model i ng mechani sm.
Fi ndi ng hi gh- ef f i ci ency sol ar cel l model s i s of gr eat
i nt er est i n space appl i cat i ons. By i ncr easi ng t he ef f i ci ency
of phot ovol t ai cs, t he number of sol ar panel s i s decr eased.
Ther ef or e, t he over al l wei ght t hat needs t o be l aunched i nt o
space i s r educed. A cost - r educt i on can be achi eved over t he
l i f e of t he space power syst em.
Resear ch at Lawr ence Ber kel ey Nat i onal Labor at or y
( LBNL) has been ongoi ng si nce 2002 i n t r yi ng t o devel op
hi gh- ef f i ci ency sol ar cel l s. One of t he mat er i al s LBNL has
been i nvest i gat i ng i s I ndi umGal l i umNi t r i de. I n addi t i on t o
t he band gap r ange, I ndi um Gal l i um Ni t r i de al so has ot her
char act er i st i cs t hat ar e benef i ci al f or space appl i cat i ons.
xvi
The r adi at i on l evel t hat I ndi um Gal l i um Ni t r i de i s abl e t o
wi t hst and i s appr oxi mat el y t wo or der s of magni t ude gr eat er
t han cur r ent mul t i j unct i on sol ar cel l mat er i al s. Ther ef or e,
i t i s of gr eat i nt er est t o cont i nue t o r esear ch I ndi um
Gal l i um Ni t r i de and i t s possi bi l i t i es as phot ovol t ai c
mat er i al .
The goal of t hi s r esear ch was t o i nvest i gat e t he
ef f i ci ency of I ndi um Gal l i um Ni t r i de sol ar cel l s usi ng t he
Si l vaco At l as TCAD si mul at i on sof t war e. No ot her TCAD
si mul at i ons have been per f or med on I nGaN sol ar cel l s. The
met hodol ogy of t hi s r esear ch pr ogr essed f r om si ngl e t o
mul t i - j unct i on cel l s. The si mul at i on r esul t s pr edi ct ed
ef f i ci enci es as hi gh as 41% f or a f our - j unct i on sol ar cel l .
Fur t her r ef i nement s of t he si mul at i on model ar e st i l l
possi bl e. Act ual pr oduct i on of a si ngl e- j unct i on sol ar cel l
i s t he next st ep r equi r ed t o event ual l y manuf act ur e hi gh-
ef f i ci ency, mul t i - j unct i on I nGaN sol ar cel l s.

1
I. INTRODUCTION
A. BACKGROUND
One of t he most i mpor t ant pr obl ems t o sol ve i n space
sol ar cel l desi gn i s ef f i ci ency. As ef f i ci ency i ncr eases,
t he r equi r ed number of cel l s decr eases t o f ul f i l l el ect r i cal
power r equi r ement s.
Sol ar cel l ef f i ci enci es have i mpr oved over t i me by
i ncr easi ng t he number of j unct i ons. Each j unct i on i s capabl e
of ext r act i ng ener gy f r oma por t i on of t he sol ar spect r um.
A new pat h t o i mpr ovi ng ef f i ci ency i s t o use new
phot ovol t ai c mat er i al s such as wur t zi t e I ndi um Gal l i um
Ni t r i de. I ndi um Gal l i um Ni t r i de possesses a band gap r ange
t hat can ext r act ener gy f r oma l ar ge por t i on of t he vi si bl e
sol ar spect r um.
B. OBJECTIVE
The obj ect i ve of t hi s t hesi s i s t o si mul at e I ndi um
Gal l i um Ni t r i de sol ar cel l s t o pr edi ct t hei r ef f i ci enci es.
Af t er obt ai ni ng t he ef f i ci enci es, a compar i son i s made wi t h
cur r ent sol ar cel l ef f i ci enci es. Si l vaco At l as TCAD
si mul at i on sof t war e i s used t o i nvest i gat e t hese
ef f i ci enci es.
C. RELATED WORK
Pr evi ous Si l vaco At l as sol ar cel l si mul at i ons have been
per f or med by Naval Post gr aduat e School r esear cher s.
Mi chal opoul os [ 1] i nvest i gat ed t he f easi bi l i t y of desi gni ng
sol ar cel l s usi ng Si l vaco At l as. To demonst r at e t he use of
2
Si l vaco At l as, Mi chal opoul os si mul at ed si ngl e- j unct i on sol ar
cel l s wi t h Gal l i um Ar seni de, dual - j unct i on sol ar cel l s wi t h
I ndi um Gal l i um Phosphi de and Gal l i um Ar seni de, and t r i pl e-
j unct i on cel l s wi t h I ndi um Gal l i um Phosphi de, Gal l i um
Ar seni de, and Ger mani um. The hi ghest ef f i ci ency obt ai ned
wi t h t he t r i pl e- j unct i on was 29. 5%. Thi s r esul t mat ched t he
29. 3% ef f i ci ency obt ai ned wi t h act ual t r i pl e- j unct i on sol ar
cel l s i n pr oduct i on. Bat es [ 2] pr ovi ded excel l ent backgr ound
on t he use of Si l vaco At l as. Gr een [ 3] and Canf i el d [ 4]
cont i nued t o wor k on Si l vaco At l as sol ar cel l desi gn. Mat l ab
f unct i ons and Si l vaco At l as code wer e modi f i ed f r om [ 1] - [ 4]
t o per f or msi mul at i ons i n t hi s r esear ch.
A pr evi ous I ndi um Gal l i um Ni t r i de si mul at i on has been
per f or med [ 5] usi ng f undament al semi conduct or physi cs
f or mul as. The r esul t s of t hi s r esear ch ar e compar ed wi t h
t hose of [ 5] .
D. ORGANIZATION
1. Purpose of Solar Cells
The pur pose of sol ar cel l s i s t o conver t l i ght ener gy
i nt o el ect r i cal ener gy. Li ght i s made up of phot ons. Phot ons
car r y ener gy t hat i s dependent on t he col or , or wavel engt h
of l i ght . El ect r i cal ener gy i s gener at ed when phot ons exci t e
el ect r ons f r omt he val ence band i nt o t he conduct i on band i n
semi conduct or mat er i al s. Chapt er I I cover s f undament al
concept s of sol ar cel l s and semi conduct or mat er i al s.
2. Simulation Software
Si l vaco At l as was used as t he si mul at i on sof t war e i n
t hi s t hesi s. Si l vaco of f er s a sui t e of sof t war e pr ogr ams
3
t hat can act as a Vi r t ual Waf er Fabr i cat i on ( VWF) t ool . The
Naval Post gr aduat e School has had mul t i pl e r esear cher s
publ i sh t heses on t he use of Si l vaco At l as f or t he pur pose
of sol ar cel l model i ng. Chapt er I I I cover s t he basi cs of
Si l vaco At l as.
3. Indium Gallium Nitride
Wur t zi t e I ndi um Gal l i um Ni t r i de ( I nGaN) i s a
semi conduct or t hat has t he pot ent i al t o pr oduce hi gh-
ef f i ci ency sol ar cel l s. Dr . Wl adek Wal uki ewi cz, of Lawr ence
Ber kel ey Nat i onal Labor at or y ( Sol ar Ener gy Mat er i al s
Resear ch Gr oup) , has been conduct i ng ext ensi ve I nGaN
r esear ch f or t he pur poses of pr oduci ng phot ovol t ai c
mat er i al . Chapt er I V cover s t he char act er i st i cs of I nGaN,
i t s pot ent i al , i t s mat er i al sci ence r esear ch st at us, and i t s
cur r ent l i mi t at i ons.
4. Simulation
Based on t he opt i cal char act er i st i cs of I nGaN,
si mul at i ons wer e per f or med usi ng Si l vaco At l as. Chapt er V
cover s t he f i ndi ngs of t he si mul at i ons. Chapt er VI cover s
t he concl usi ons and r ecommendat i ons. Fi nal l y, t he appendi ces
i ncl ude t he code used i n Si l vaco At l as as wel l as Mat l ab.
4
THI S PAGE LEFT I NTENTI ONALLY BLANK
5
II. SOLAR CELL AND SEMICONDUCTOR BASICS
Thi s t hesi s exami nes a novel pr ocess t o si mul at e I ndi um
Gal l i um Ni t r i de sol ar cel l s. Bef or e del vi ng i nt o t he
si mul at i on, t hi s chapt er cover s t he f undament al pr i nci pl es
of sol ar cel l s and semi conduct or s. The pr oper t i es of t he
semi conduct or mat er i al det er mi ne t he char act er i st i cs of t he
phot ovol t ai c devi ce.
A. SEMICONDUCTOR FUNDAMENTALS
1. Classification of Materials
Mat er i al s can be cat egor i zed accor di ng t o t hei r
el ect r i cal pr oper t i es as conduct or s, i nsul at or s or
semi conduct or s. The conduct i vi t y σ i s a key par amet er i n
i dent i f yi ng t he t ype of mat er i al .
Fi gur e 1 pr esent s a sampl e of mat er i al s based on
conduct i vi t y. The semi conduct or s f al l bet ween t he i nsul at or s
and t he conduct or s.

Fi gur e 1. Mat er i al s cl assi f i ed by conduct i vi t y ( Fr om[ 6] ) .
6
Semi conduct or s can be f ound i n el ement al or compound
f or m. Si l i con ( Si ) and Ger mani um ( Ge) ar e exampl es of
el ement al semi conduct or s. Bot h of t hese semi conduct or s
bel ong t o gr oup I V of t he per i odi c t abl e.
Fi gur e 2 shows an abbr evi at ed per i odi c t abl e. I n
addi t i on t o t he gr oup I V semi conduct or s, compounds can be
made wi t h el ement s f r om gr oups I I I and V, r espect i vel y.
Exampl es of I I I - V semi conduct or s i ncl ude Al umi num Phosphi de
( Al P) , Gal l i um Ni t r i de ( GaN) , I ndi um Phosphi de ( I nP) ,
Gal l i um Ar seni de ( GaAs) , among ot her s. I t i s al so possi bl e
t o make semi conduct or compounds f r om gr oups I I - VI , such as
Zi nc Oxi de ( ZnO) , Cadmi um Tel l ur i de ( CdTe) , Mer cur y Sul f i de
( HgS) , among ot her s. The subj ect of t hi s t hesi s i s t he
t er nar y al l oy wur t zi t e I ndi um Gal l i um Ni t r i de ( I nGaN) .
I ndi umand Gal l i umar e gr oup I I I el ement s, whi l e Ni t r ogen i s
a gr oup V el ement .



Fi gur e 2. Par t i al per i odi c t abl e ( Af t er [ 7] ) .

7
2. Atomic Structure
Si nce Si l i con i s t he most commonl y used semi conduct or
i n sol ar cel l s t oday, a br i ef anal ysi s of t hi s el ement i s
pr esent ed.
Si l i con has 14 pr ot ons and 14 neut r ons i n i t s nucl eus.
The 14 el ect r ons ar e di st r i but ed i n t hr ee shel l s.
Fi gur e 3 shows t he ar r angement of el ect r ons i n a
Si l i con at om. Ther e ar e t wo el ect r ons i n t he f i r st shel l ,
ei ght el ect r ons i n t he second shel l and f our el ect r ons i n
t he out er shel l . When Si l i con at oms ar e t oget her , t he at oms
f r omt he out er shel l s f or mcoval ent bonds. Hence, a Si l i con
at omf or ms bonds wi t h f our ot her Si l i con at oms.


Fi gur e 3. Si l i con at omi c st r uct ur e ( Fr om[ 8] ) .


As shown i n Fi gur e 4, t he coval ent bonds f or med by t he
si l i con at oms ar e r epr esent ed by t he el l i pt i cal dot t ed
l i nes. I n t he absence of an el ect r on, t he coval ent bond
ceases t o exi st . A hol e t akes t he pl ace of t he el ect r on.

8

Fi gur e 4. Si l i con at omcoval ent bonds ( Fr om[ 1, p. 11] ) .

Ener gy bands ar e a f undament al concept of semi conduct or
physi cs. These ener gy bands ar e t he val ence band, t he
conduct i on band, and t he f or bi dden gap or band gap [ 9, p.
27] . When an el ect r on i s i n t he val ence band, t he coval ent
bond exi st s. I n or der f or t he el ect r on t o move f r om t he
val ence band i nt o t he conduct i on band, ener gy i s r equi r ed t o
exci t e t he el ect r on. The band gap ener gy i s t he mi ni mum
ener gy r equi r ed f or t he el ect r on t o make t he move f r om t he
val ence band i nt o t he conduct i on band.
Fi gur e 5 shows t he band gap di agr ams f or conduct or s,
i nsul at or s, and semi conduct or s. Thi s f i gur e al so r ei nf or ces
t he di f f er ences among t he t hr ee t ypes of mat er i al s accor di ng
t o t hei r el ect r i c pr oper t i es. I n t he case of conduct or s, t he
band gap i s smal l or non- exi st ent . By cont r ast , i nsul at or s
have wi de band gaps. Ther ef or e, i t t akes much mor e ener gy
f or t he i nsul at or t o have el ect r ons i n t he conduct i on band.
9

Fi gur e 5. Band gap di agr ams ( Fr om[ 1, p. 8] ) .


Semi conduct or s have band gaps t hat ar e dependent on t he
mat er i al . Because band gap i s al so dependent on t emper at ur e,
i t shoul d be not ed t hat al l quot ed band gaps i n t hi s t hesi s
ar e at r oomt emper at ur e ( 300 K. )
3. Electrons and Holes
A semi conduct or at absol ut e zer o t emper at ur e i s unabl e
t o conduct heat or el ect r i ci t y [ 10, p. 44] . Al l of t he
semi conduct or ’ s el ect r ons ar e bonded. The el ect r ons acqui r e
ki net i c ener gy as t he t emper at ur e i s i ncr eased. Some of t he
el ect r ons ar e f r eed and move i nt o t he conduct i on band. These
el ect r ons ar e abl e t o conduct char ge or ener gy. The ar eas
l ef t by t hese el ect r ons i n t he val ence band ar e cal l ed
hol es. As t he t emper at ur e of t he semi conduct or i ncr eases,
t he number of f r ee el ect r ons and hol es i ncr eases as wel l .
Ther ef or e, t he conduct i vi t y of t he semi conduct or i s di r ect l y
pr opor t i onal t o t emper at ur e i ncr eases.
The conduct i vi t y of t he semi conduct or can be al t er ed by
exposi ng i t t o l i ght or by dopi ng i t . Phot oconduct i vi t y
consi st s of exposi ng t he semi conduct or wi t h phot on ener gy
10
l ar ger t han t he semi conduct or ’ s band gap. Dopi ng consi st s of
addi ng i mpur i t i es t o t he semi conduct or mat er i al .
Fi gur e 6 shows n- t ype and p- t ype dopi ng. The at om of
t he semi conduct or i s r epr esent ed by t he bl ue ci r cl e and a
+4. For exampl e, a si l i con at om has f our el ect r ons i n i t s
out er shel l . When si l i con at oms ar e n- doped, at oms f r om
gr oup V of t he per i odi c t abl e ar e added. Each added gr oup V
at om pr ovi des an ext r a el ect r on t o donat e. When si l i con
at oms ar e p- doped, t he at oms f r omgr oup I I I of t he per i odi c
t abl e ar e added. Each gr oup I I I at om has one l ess el ect r on
t han si l i con. Ther ef or e, a hol e i s added. Dopi ng i ncr eases
t he number of car r i er s i n t he semi conduct or mat er i al .

Fi gur e 6. Dopi ng: n- t ype and p- t ype ( Fr om[ 1, p. 13] ) .

An i nt r i nsi c semi conduct or i s a pur e semi conduct or wi t h
a negl i gi bl e amount of i mpur i t y at oms [ 9, p. 34] . By
def i ni t i on, t he number of el ect r ons and hol es i n a
semi conduct or ar e r epr esent ed by n and p. See Tabl e 1.
11
3
3
number of electrons
cm
number of holes
cm
n
p
=
=

Tabl e 1. Def i ni t i ons of n and p.

I n t he case of an i nt r i nsi c semi conduct or , t he
f ol l owi ng case occur s:
i n p n = =
For exampl e pur poses, n
i
i s gi ven f or GaAs, Si and Ge
and r oom t emper at ur e [ 9, p. 34] . Dat a f or I nN and GaN ar e
f r om[ 11] . See Tabl e 2.

6
3
10
3
13
3
22
3
22
3
2 10
1 10
2 10
6.2 10
8.9 10
GaAs
i
Si
i
Ge
i
InN
i
GaN
i
n
cm
n
cm
n
cm
n
cm
n
cm
×
=
×
=
×
=
×
=
×
=

Tabl e 2. n
i
f or f i ve semi conduct or s.


When sol ar cel l s ut i l i ze semi conduct or mat er i al s f r om
Tabl e 2, t he cur r ent l evel i s hi ghest f or Ge and l owest f or
GaAs. The cur r ent l evel s cor r espond i n r ank t o t he n
i
l evel s
pr ovi ded i n Tabl e 2. No dat a exi st s f or I nN or GaN cur r ent
l evel s as phot ovol t ai c mat er i al s.
12
4. Direct and Indirect Band Gaps
Si nce t he band gap i s t he mi ni mum ener gy r equi r ed t o
move an el ect r on f r om t he val ence band i nt o t he conduct i on
band, i t i s necessar y t o di st i ngui sh bet ween di r ect and
i ndi r ect band gaps.
Fi gur e 7 shows t he concept of di r ect and i ndi r ect band
gaps. The bl ue por t i on r epr esent s t he val ence band. The t an
por t i on r epr esent s t he conduct i on band.

Fi gur e 7. Di r ect and i ndi r ect band gaps ( Af t er [ 1, p. 24] ) .

When t he val ence band and t he conduct i on band coi nci de
i n wave vect or k, t he semi conduct or has a di r ect band gap.
When t he val ence band and t he conduct i on band have di f f er ent
wave vect or k, t he semi conduct or has an i ndi r ect band gap.
The k vect or r epr esent s a di f f er ence i n moment um. Phot ons
have negl i gi bl e moment um. I n or der t o exci t e an el ect r on
f r omt he val ence band t o t he conduct i on band i n an i ndi r ect
band gap semi conduct or , i n addi t i on t o a phot on, a phonon i s
r equi r ed. The phonon i s a l at t i ce vi br at i on. The phonon
13
t r ansf er s i t s moment um t o t he el ect r on at t he t i me t he
phot on i s absor bed. Ther ef or e, a di r ect band gap
semi conduct or i s gener al l y bet t er f or opt oel ect r oni cs.
Si l i con i s an exampl e of an i ndi r ect band gap semi conduct or .
Gal l i um Ar seni de and wur t zi t e I ndi um Gal l i um Ni t r i de ar e
exampl es of di r ect band gap semi conduct or s.
5. Fermi Level
The Fer mi f unct i on f ( E) speci f i es how many of t he
exi st i ng st at es at ener gy E ar e f i l l ed wi t h an el ect r on [ 9,
p. 42] . The Fer mi f unct i on i s a pr obabi l i t y di st r i but i on
f unct i on def i ned as f ol l ows:
( )
1
( )
1
F E E
kT
f E
e

=
+

Wher e E
F
i s t he Fer mi l evel , k i s Bol t zmann’ s const ant ,
and T i s t he t emper at ur e i n Kel vi n.
Fr omt he Fer mi f unct i on, i t can be det er mi ned t hat when
E=E
F
, t hen f ( E) =f ( E
F
) =0. 5.
Fi gur e 8 shows t he Fer mi l evel f or an i nt r i nsi c
semi conduct or . Fi gur e 9 shows t he Fer mi l evel f or n- t ype
semi conduct or . Fi gur e 10 shows t he Fer mi l evel f or p- t ype
semi conduct or . Fr om t hese Fi gur es, i t can be deduced t hat
t he n- t ype mat er i al has a l ar ger el ect r on car r i er
di st r i but i on and t he p- t ype mat er i al has a l ar ger hol e
car r i er di st r i but i on.

14
Fi gur e 8. Fer mi l evel : i nt r i nsi c case ( Af t er [ 9, p. 42] ) .


Fi gur e 9. Fer mi l evel : n- t ype case ( Af t er [ 9, p. 42] ) .


Fi gur e 10. Fer mi l evel : p- t ype case ( Af t er [ 9, p. 42] ) .

B. SOLAR CELL FUNDAMENTALS
Af t er cover i ng t he basi cs of semi conduct or s, t he
l ogi cal st ep i s t o cont i nue wi t h sol ar cel l f undament al s.
1. History of Solar Cells
Sol ar cel l r esear ch st ar t ed when Edmund Bequer el
di scover ed t he phot ovol t ai c ef f ect i n 1839. He r ecor ded t hat
an el ect r i c cur r ent was pr oduced when l i ght was appl i ed t o a
si l ver coat ed pl at i num el ect r ode i mmer sed i n el ect r ol yt e.
The next si gni f i cant st ep was per f or med by Wi l l i amAdams and
Ri char d Day i n 1876. They di scover ed t hat a phot ocur r ent
appear ed when sel eni um was cont act ed by t wo heat ed pl at i num
cont act s. However , cur r ent was pr oduced spont aneousl y by t he
act i on of l i ght . Cont i nui ng t o bui l d on t hese ef f or t s,
Char l es Fr i t t s devel oped t he f i r st l ar ge ar ea sol ar cel l i n
1894. He pr essed a l ayer of sel eni um bet ween gol d and
anot her met al . Pr ogr ess cont i nued as t he t heor y of met al -
15
semi conduct or bar r i er l ayer s was est abl i shed by Wal t er
Schot t ky and ot her . I n t he 1950s, si l i con was used f or sol i d
st at e el ect r oni cs. Si l i con p- n j unct i ons wer e used t o
i mpr ove on t he per f or mance of t he Schot t ky bar r i er . These
si l i con j unct i ons had bet t er r ect i f yi ng act i on and
phot ovol t ai c behavi or . I n 1954, Chapi n, Ful l er and Pear son
devel oped t he f i r st si l i con sol ar cel l , wi t h a r epor t ed
ef f i ci ency of 6%. However , t he cost per Wat t associ at ed wi t h
t hese sol ar cel l s made t hem pr ohi bi t i vel y expensi ve f or
t er r est r i al use. However , l ocat i ons wher e power gener at i on
was not f easi bl e ( i . e. , space) wer e sui t abl e f or sol ar
cel l s. Sat el l i t es wer e t he f i r st cl ear appl i cat i on f or
si l i con sol ar cel l s. Si nce t hat t i me, sol ar cel l s have
pr ogr essed st eadi l y bot h i n t er ms of ef f i ci ency as wel l as
mat er i al s used t hei r pr oduct i on [ 10, p. 2] .
Tabl e 3 shows a br i ef l i st of event s i n t he hi st or y of
phot ovol t ai cs f r om1939 unt i l 2002.
2. The Photovoltaic Effect
The phot ovol t ai c ef f ect i s t he pr ocess by whi ch a sol ar
cel l conver t s t he ener gy f r om l i ght i nt o el ect r i cal ener gy.
Li ght i s made up of phot ons. The ener gy of t hese phot ons
depends on t he col or ( wavel engt h) of l i ght . The mat er i al
t hat makes up t he sol ar cel l det er mi nes t he phot ovol t ai c
pr oper t i es when l i ght i s appl i ed [ 10, p. 1] .
When l i ght i s absor bed by mat t er , such as met al ,
phot ons pr ovi de t he ener gy f or el ect r ons t o move t o hi gher
ener gy st at es wi t hi n t he mat er i al . However , t he exci t ed
el ect r ons r et ur n t o t hei r or i gi nal ener gy st at e. I n
semi conduct or mat er i al s, t her e i s a bui l t - i n asymmet r y ( band
16
gap) . Thi s al l ows t he el ect r ons t o be t r ansf er r ed t o an
ext er nal ci r cui t bef or e t hey can r et ur n t o t hei r or i gi nal
ener gy st at e. The ener gy of t he exci t ed el ect r ons cr eat es a
pot ent i al di f f er ence. Thi s el ect r omot i ve f or ce di r ect s t he
el ect r ons t hr ough a l oad i n t he ext er nal ci r cui t t o per f or m
el ect r i cal wor k.

Tabl e 3. Not abl e event s i n t he hi st or y of phot ovol t ai cs ( Fr om
[ 12] ) .

17
a. The Electromagnetic Spectrum
Li ght i s el ect r omagnet i c r adi at i on. The f r equency
of l i ght det er mi nes i t s col or . Fi gur e 11 shows t he vi si bl e
par t of t he el ect r omagnet i c spect r um. Vi si bl e wavel engt hs
r ange f r om390 nm( vi ol et ) t o 780 nm( r ed) .

Fi gur e 11. The el ect r omagnet i c spect r um( Fr om[ 13] ) .

Tabl e 4 shows t he appr oxi mat e wavel engt h r ange of
vi si bl e col or s.

Col or Wavel engt h ( nm)
Red 780- 622
Or ange 622- 597
Yel l ow 597- 577
Gr een 577- 492
Bl ue 492- 455
Vi ol et 455- 390
Tabl e 4. Appr oxi mat e wavel engt h of var i ous col or s i n vacuum
( Af t er [ 14] ) .

18
The sun emi t s l i ght f r omul t r avi ol et , vi si bl e, and
i nf r ar ed wavel engt hs i n t he el ect r omagnet i c spect r um. Sol ar
i r r adi ance has t he l ar gest magni t ude at vi si bl e wavel engt hs,
peaki ng i n t he bl ue- gr een [ 10, p. 17] .
b. Band Gap
The band gap of t he semi conduct or mat er i al
det er mi nes how t he sol ar cel l r eact s t o l i ght . Tabl e 5 shows
a smal l sampl e of semi conduct or band gaps. Chapt er I V cover s
t he band gaps of I ndi umNi t r i de, Gal l i umNi t r i de, and I ndi um
Gal l i umNi t r i de.

Material Band gap (eV) at 300 K
Si 1. 12
Ge 0. 66
GaAs 1. 42
I nP 1. 34
Tabl e 5. Common semi conduct or band gaps ( Af t er [ 9, p. 31] ) .

The band gap of t he semi conduct or mat er i al
det er mi nes t he wavel engt h of l i ght t hat meet t he
r equi r ement s t o gener at e el ect r i cal ener gy. The conver si on
f or mul a bet ween band gap and wavel engt h i s:

( )
( )
1.24
( )
( )
hc
m
Eg eV
m
Eg eV
λ µ
λ µ
=
=

Wher e λ i s t he wavel engt h i n mi cr omet er s, h i s
Pl anck’ s const ant , c i s t he speed of l i ght i n vacuum, and Eg
19
i s t he band gap i n eV. One eV i s appr oxi mat el y equal t o
1. 6x10
- 19
J of ener gy. I n t he case of Gal l i um Ar seni de, t he
wavel engt h t hat cor r esponds t o 1. 42 eV i s 0. 873 m µ .
Fi gur e 12 hel ps vi sual i ze t he concept of l i ght
absor pt i on. When l i ght has ener gy gr eat er t han 1. 1 eV, t he
si l i con sol ar cel l gener at es el ect r i ci t y. Li ght wi t h l ess
t han 1. 1 eV of ener gy i s unused. Si mi l ar l y, l i ght wi t h
ener gy gr eat er t han 1. 43 eV exci t es t he out er shel l
el ect r ons of t he gal l i um ar seni de sol ar cel l . And f i nal l y,
l i ght wi t h ener gy gr eat er t han 1. 7 eV i s usef ul f or al umi num
gal l i umar seni de phot ovol t ai c mat er i al .


Fi gur e 12. Ef f ect of l i ght ener gy on di f f er ent band gaps
( Fr om[ 15] ) .

c. Solar Cell Junctions
The di scussi on i n t he pr evi ous sect i on di scussed
t he ef f ect of l i ght ener gy on di f f er ent band gaps. Tr eat ed
i ndi vi dual l y, each of t he phot ovol t ai c mat er i al s f r omFi gur e
12 woul d act as a si ngl e j unct i on sol ar cel l .
However , t o i ncr ease t he ef f i ci ency of t he sol ar
cel l , mul t i pl e j unct i ons can be cr eat ed. For exampl e, i n
20
Fi gur e 12, t he t op j unct i on woul d be made up of Al umi num
Gal l i um Ar seni de. Thi s j unct i on woul d absor b l i ght ener gy
gr eat er t han 1. 7 eV. Any unused phot ons woul d be f i l t er ed
t hr ough t o t he next j unct i on. The gal l i um ar seni de j unct i on
woul d t hen absor b t he phot ons wi t h ener gy gr eat er t han 1. 4
eV. The r emai ni ng phot ons woul d be absor bed by t he si l i con
j unct i on.
Al t hough t he above par agr aph descr i bed t he basi cs
of a mul t i j unct i on sol ar cel l , such devi ce may not pr oduce
t he desi r ed r esul t s due t o l at t i ce mi smat ch. The next
sect i on cover s t he basi cs of l at t i ce mat chi ng.
d. Lattice Matching
Semi conduct or s ar e t hr ee- di mensi onal i n t hei r cel l
st r uct ur e. The si mpl e cubi c st r uct ur e ser ves t o i l l ust r at e
t he concept of l at t i ce and i s pr esent ed i n Fi gur e 13.

Fi gur e 13. Si mpl e cubi c l at t i ce st r uct ur e ( Fr om[ 16] ) .


Fi gur e 13 shows t hat each si de of t he cube i s
r epr esent ed by t he l et t er “a”. The separ at i on “a” i s cal l ed
t he l at t i ce const ant . Each semi conduct or mat er i al has a
l at t i ce const ant . Ther ef or e, when cr eat i ng mul t i j unct i on
sol ar cel l s, t he l at t i ces must be mat ched.
21
Fi gur e 14 shows t he l at t i ce const ant s f or sever al
semi conduct or s. An exampl e gi ven by P. Mi chal opoul os [ 1, p.
87] shows how t o l at t i ce mat ch I ndi um Gal l i um Phosphi de t o
Gal l i umAr seni de.


Fi gur e 14. Lat t i ce const ant s ( Fr om[ 17] ) .


The al l oy I ndi um Gal l i um Phosphi de i s composed of
x par t s of Gal l i um phosphi de and 1- x par t s of I ndi um
Phosphi de. Ther ef or e, I ndi um Gal l i um Phosphi de i s
r epr esent ed as I n
1- x
Ga
x
P.
GaAs has a l at t i ce const ant α=5. 65Å, GaP has
α=5. 45Å and I nP has α=5. 87Å. The goal i s t o cr eat e I nGaP
wi t h a l at t i ce const ant t hat mat ches t hat of GaAs. The
f or mul a t o f i nd x i s gi ven as:
22
(1 )
InP GaAs
InP GaAs GaP
InP GaP
x x x
α α
α α α
α α

= ⋅ + ⋅ − ⇔ =


Wi t h x=0. 52, I n
0. 48
Ga
0. 52
P has α=5. 65Å. A r ough
appr oxi mat i on of t he r esul t i ng band gap of I n
0. 48
Ga
0. 52
P i s
gi ven as f ol l ows:
InGaP GaP InP
G G G
E E (1 )E x x = + −
The equat i on yi el ds a band gap of 1. 9 eV f or
I n
0. 48
Ga
0. 52
P. Ther ef or e, a dual - j unct i on sol ar cel l of I nGaP
at 1. 9 eV and GaAs at 1. 4 eV can be bui l t .
Fi gur e 15 shows t he l at t i ce const ant f or I ndi um
Ni t r i de and Gal l i umNi t r i de.

Fi gur e 15. Lat t i ce const ant f or I nN and GaN ( Fr om[ 18] ) .

e. AM0 Spectrum
The l ocat i on of t he sol ar cel l af f ect s t he i nput
sol ar r adi at i on spect r um. A sol ar cel l on Mar s r ecei ves a
23
di f f er ent ( smal l er ) spect r um t han a sol ar cel l on a
sat el l i t e t hat or bi t s Ear t h. The ener gy r ecei ved out si de
Ear t h’ s at mospher e i s appr oxi mat el y 1365 W/ m
2
. Thi s spect r um
i s cal l ed Ai r Mass Zer o or AM0. Ter r est r i al sol ar cel l s have
t o deal wi t h t he at t enuat i on of t he sol ar spect r um due t o
Ear t h’ s at mospher e. Thi s sol ar spect r umi s cal l ed AM1. 5. For
t he pur poses of t hi s t hesi s, AM0 i s used dur i ng si mul at i ons.
Fr om dat a obt ai ned f r om t he Nat i onal Renewabl e Ener gy
Labor at or y ( NREL) [ 19] , t he AM0 spect r umwas pl ot t ed usi ng a
Mat l ab scr i pt .
Fi gur es 16 and 17 show t he AM0 spect r um wi t h
r espect t o wavel engt h and ener gy, r espect i vel y. Fr om Fi gur e
17, i t can be seen t hat semi conduct or mat er i al s wi t h band
gaps of l ess t han 4 eV ar e abl e t o ext r act most of t he sol ar
spect r um.


Fi gur e 16. AM0 spect r um( Wavel engt h vs I r r adi ance) ( Af t er
[ 19] ) .
24

Fi gur e 17. AM0 spect r um( Ener gy vs I r r adi ance) ( Af t er [ 19] ) .

f. Current-Voltage Curves
A t ypi cal sol ar cel l cur r ent - vol t age ( I V) cur ve i s
pr esent ed i n Fi gur e 18.

Fi gur e 18. Sampl e I V cur ve used i n ef f i ci ency cal cul at i ons
( Af t er [ 20] ) .
25
Fr om Fi gur e 18, t her e ar e sever al poi nt s of
i nt er est . The shor t ci r cui t cur r ent ( I
SC
) occur s when t he
vol t age i s zer o. Thi s i s t he hi ghest absol ut e val ue cur r ent .
The open ci r cui t vol t age ( V
OC
) occur s when t he cur r ent i s
zer o. Thi s i s t he hi ghest vol t age. The di mensi ons of t he
l ar ger r ect angl e i n Fi gur e 18 ar e det er mi ned by V
OC
and I
SC
.
Si nce power ( P) i s det er mi ned by t he pr oduct of cur r ent
t i mes vol t age, t he maxi mumpower poi nt occur s at ( V
MP
, I
MP
) .
The cal cul at i ons f or sol ar cel l ef f i ci ency ar e as
f ol l ows:
max mp mp
max mp mp
sc oc sc oc
max mp mp
in in
P =I V
P I V
FF= =
I V I V
P I V
=
P P
η ≡

Wher e Pmax i s t he maxi mumpower poi nt , FF i s t he
f i l l f act or , and η i s t he ef f i ci ency. The f i l l f act or
measur es t he “squar eness” of t he I V cur ve.
g. Electrical Output
A sol ar cel l i s a p- n j unct i on phot odi ode. I n
or der t o obt ai n t he I V char act er i st i c of t he sol ar cel l , t he
dar k cur r ent needs t o be subt r act ed f r om t he phot ogener at ed
cur r ent .
L D I I I = −
The dar k cur r ent i s t he cur r ent t hr ough t he sol ar
cel l when bi as i s appl i ed i n t he dar k [ 10, p. 30] .
Gr aphi cal l y, t he I V char act er i st i c i s obt ai ned i n
Fi gur e 19.
26

Fi gur e 19. Sol ar cel l I V char act er i st i c ( Fr om[ 21] ) .




C. CHAPTER CONCLUSIONS
Thi s chapt er pr ovi ded basi c i nf or mat i on on
semi conduct or s and sol ar cel l s. The f oundat i on has been
est abl i shed f r om t he physi cs st and poi nt . The next st ep i s
t o cover an i nt r oduct i on t o t he si mul at i on sof t war e.
27
III. SILVACO ATLAS SIMULATION SOFTWARE
Thi s t hesi s uses Si l vaco At l as t o per f or m sol ar cel l
model i ng. Si l vaco I nt er nat i onal pr oduces a sui t e of sof t war e
pr ogr ams t hat t oget her become a Vi r t ual Waf er Fabr i cat i on
t ool . Thi s chapt er i nt r oduces Si l vaco At l as and some of i t s
f eat ur es.
A. VIRTUAL WAFER FAB
Si l vaco I nt er nat i onal pr ovi des sever al sof t war e t ool s
t o per f or mpr ocess and devi ce si mul at i on. Fr omFi gur e 20, i t
can be seen t hat Si l vaco of f er s power f ul si mul at i on
sof t war e.

Fi gur e 20. Si l vaco’ s Vi r t ual Waf er Fabr i cat i on Envi r onment
( Fr om[ 22] ) .

I n t hi s t hesi s, Si l vaco At l as was ext ensi vel y used. The
DeckBui l d r un- t i me envi r onment r ecei ved t he i nput f i l es.
Wi t hi n t he i nput f i l es, Si l vaco At l as was cal l ed t o execut e
t he code. And f i nal l y, TonyPl ot was used t o vi ew t he out put
of t he si mul at i on. Addi t i onal l y, out put l og f i l es wer e
pr oduced. The dat a ext r act ed f r om t he l og f i l es coul d t hen
28
be di spl ayed usi ng Mi cr osof t Excel or Mat l ab scr i pt s. Fi gur e
21 shows t he i nput s and out put s f or Si l vaco At l as.



Fi gur e 21. At l as i nput s and out put s ( Fr om[ 23, p. 2- 2] ) .


B. SILVACO ATLAS
At l as i s a sof t war e pr ogr am used t o si mul at e t wo and
t hr ee- di mensi onal semi conduct or devi ces. The physi cal model s
i ncl ude i n At l as ar e pr esent ed i n Tabl e 6.
29

Tabl e 6. Si l vaco At l as physi cal model s ( Fr om[ 23, p. 1- 2] ) .


C. INPUT FILE STRUCTURE
Si l vaco At l as r ecei ves i nput f i l es t hr ough DeckBui l d.
The code ent er ed i n t he i nput f i l e cal l s At l as t o r un wi t h
t he f ol l owi ng command:
go at l as
Fol l owi ng t hat command, t he i nput f i l e needs t o f ol l ow
a pat t er n. The command gr oups ar e l i st ed i n Fi gur e 22.
30

Fi gur e 22. At l as command gr oups and pr i mar y st at ement s ( Fr om
[ 23, p. 2- 8] ) .


At l as f ol l ows t he f ol l owi ng f or mat f or st at ement s and
par amet er s:
<STATEMENT> <PARAMETER>=<VALUE>
The f ol l owi ng l i ne of code ser ves as an exampl e.
DOPI NG UNI FORM N. TYPE CONCENTRATI ON=1. 0e16 REGI ON=1 \
OUTFI LE=my. dop
The st at ement i s DOPI NG. The par amet er s ar e UNI FORM,
N. TYPE, CONCENTRATI ON, REGI ON, and OUTFI LE. Ther e ar e f our
di f f er ent t ype of par amet er s: r eal , i nt eger , char act er , and
l ogi cal . The back sl ash ( \ ) ser ves t he pur pose of cont i nui ng
t he code i n t he next l i ne. Par amet er s, such as UNI FORM, ar e
31
l ogi cal . Unl ess a TRUE or FALSE val ue i s assi gned, t he
par amet er i s assi gned t he def aul t val ue. Thi s val ue can be
ei t her TRUE or FALSE. The Si l vaco At l as manual needs t o be
r ef er enced t o i dent i f y t he def aul t val ue assi gned t o
speci f i c par amet er s.
1. Structure Specification
The st r uct ur e speci f i cat i on i s done by def i ni ng t he
mesh, t he r egi on, t he el ect r odes and t he dopi ng l evel s.
a. Mesh
The mesh used f or t hi s t hesi s i s t wo- di mensi onal .
Ther ef or e, onl y x and y par amet er s ar e def i ned. The mesh i s
a ser i es of hor i zont al and ver t i cal l i nes and spaci ng
bet ween t hem. Fr om Fi gur e 23, t he mesh st at ement s ar e
speci f i ed.


Fi gur e 23. At l as mesh ( Fr om2, p. 18] ) .

32
The gener al f or mat t o def i ne t he mesh i s:
X. MESH LOCATI ON=<VALUE> SPACI NG=<VALUE>
Y. MESH LOCATI ON=<VALUE> SPACI NG=<VALUE>
For exampl e, t he x. mesh st ar t i ng at - 250 mi cr ons
has spaci ng of 25 mi cr ons. That means i t i s r el at i vel y
coar se. The x. mesh becomes f i ner bet ween - 25 and 25 mi cr ons
wi t h a spaci ng of 2. 5 mi cr ons. The y. mesh i s si mi l ar l y
def i ned. For exampl e, at y. mesh of - 2. 9 mi cr ons, t he spaci ng
i s 0. 01 mi cr ons. Then at l ocat i on y. mesh of - 2. 8 mi cr ons,
t he spaci ng changes t o 0. 03 mi cr ons. The mesh i s coar ser at
y. mesh l ocat i on of - 1, when t he spaci ng i s 0. 1.
A coar se or f i ne mesh det er mi nes t he accur acy of
t he si mul at i on. A coar se mesh pr oduces a f ast er si mul at i on,
but l ess accur at e r esul t s. A f i ne mesh pr oduces a sl ower
si mul at i on, but mor e accur at e r esul t s. The ar eas t hat have a
f i ner mesh, t her ef or e, ar e of gr eat est i nt er est i n t he
si mul at i on.
b. Region
Af t er def i ni ng t he mesh, i t i s necessar y t o def i ne
t he r egi ons. The f or mat t o def i ne t he r egi ons i s as f ol l ows:
REGI ON number =<i nt eger > <mat er i al _t ype> /
<posi t i on par amet er s>
Fr om Fi gur e 24, t he code t hat def i nes t he r egi ons
i s i dent i f i ed. Ther e ar e si x r egi ons def i ned. The l i mi t s of
each r egi on ar e expl i ci t l y i dent i f i ed i n t he x- and y- axi s.
The r egi ons must t hen be gi ven a mat er i al .
33

Fi gur e 24. At l as r egi on ( Fr om[ 2, p. 19] ) .

Fr om Fi gur e 25, t he code def i nes t he mat er i al f or
each r egi on. Not e t hat t he col or codi ng i dent i f i es t he
mat er i al . The r egi ons have ver t i cal and hor i zont al l i nes t o
mar k t hei r boundar i es.

Fi gur e 25. At l as r egi ons wi t h mat er i al s def i ned ( Fr om[ 2, p.
19] ) .
34
c. Electrodes
The next st r uct ur e speci f i cat i on cor r esponds t o
el ect r odes. Typi cal l y, i n t hi s si mul at i on t he onl y
el ect r odes def i ned ar e t he anode and t he cat hode. However ,
Si l vaco At l as has a l i mi t of 50 el ect r odes t hat can be
def i ned. The f or mat t o def i ne el ect r odes i s as f ol l ows:
ELECTRODE NAME=<el ect r ode name> <posi t i on_par amet er s>
Fr om Fi gur e 26, t he el ect r ode st at ement s ar e
def i ned f or t he anode and t he cat hode. Not e t hat t he cat hode
i s def i ned wi t h gol d as t he mat er i al . The x and y di mensi ons
cor r espond t o r egi on 6 pr evi ousl y def i ned. Meanwhi l e, t he
anode i s def i ned at t he bot t omof t he cel l f or t he ent i r e x-
r ange at y=0.


Fi gur e 26. At l as el ect r odes ( Fr om[ 2, p. 20] ) .





35
d. Doping
The l ast aspect of st r uct ur e speci f i cat i on t hat
needs t o be def i ned i s dopi ng. The f or mat of t he At l as
st at ement i s as f ol l ows:
DOPI NG <di st r i but i on t ype> <dopant _t ype> /
<posi t i on par amet er s>
Fr om Fi gur e 27, t he dopi ng t ypes and t he dopi ng
l evel s ar e def i ned. Dopi ng can be n- t ype or p- t ype. The
di st r i but i on t ype can be uni f or mor Gaussi an.


Fi gur e 27. At l as dopi ng ( Fr om[ 2, p. 21] ) .

2. Materials Model Specification
Af t er t he st r uct ur e speci f i cat i on, t he mat er i al s model
speci f i cat i on i s next . Fr om Fi gur e 28, t he mat er i al s model
speci f i cat i on i s br oken down i nt o mat er i al , model s, cont act ,
and i nt er f ace.
36

Fi gur e 28. At l as mat er i al model s speci f i cat i on ( Af t er [ 23, p.
2- 8] ) .

a. Material
The f or mat f or t he mat er i al st at ement i s as
f ol l ows:
MATERI AL <l ocal i zat i on> <mat er i al _def i ni t i on>
Bel ow ar e t hr ee exampl es of t he mat er i al
st at ement :
MATERI AL MATERI AL=Si l i con EG300=1. 1 MUN=1200
MATERI AL REGI ON=4 TAUN0=3e- 7 TAUP0=2e- 5
MATERI AL NAME=base NC300=4e18
I n al l exampl es, when MATERI AL appear s f i r st , i t
i s consi der ed t he st at ement . When MATERI AL appear s a second
t i me i n t he f i r st exampl e, i t i s consi der ed a l ocal i zat i on
par amet er . I n t he second and t hi r d exampl es, t he
l ocal i zat i on par amet er s ar e REGI ON and NAME, r espect i vel y.
Var i ous ot her par amet er s can be def i ned wi t h t he mat er i al
st at ement . Exampl es of t hese par amet er s ar e t he band gap at
r oom t emper at ur e ( EG300) , el ect r on mobi l i t y ( MUN) , el ect r on
( TAUN0) and hol e ( TAUP0) r ecombi nat i on l i f et i mes, conduct i on
band densi t y at r oomt emper at ur e ( NC300) , among ot her s.
b. Models
The physi cal model s f al l i nt o f i ve cat egor i es:
mobi l i t y, r ecombi nat i on, car r i er st at i st i cs, i mpact
37
i oni zat i on, and t unnel i ng. The synt ax of t he model st at ement
i s as f ol l ows:
MODELS <model f l ag> <gener al par amet er > /
<model dependent par amet er s>
The choi ce of model depends on t he mat er i al s
chosen f or si mul at i on.
The exampl e bel ow act i vat es sever al model s.
MODELS CONMOB FLDMOB SRH
CONMOB i s t he concent r at i on dependent model .
FLDMOB i s t he par al l el el ect r i c f i el d dependence model . SRH
i s t he Shockl ey- Read- Hal l model .
c. Contact
Cont act det er mi nes t he at t r i but es of t he
el ect r ode. The synt ax f or cont act i s as f ol l ows:
CONTACT NUMBER=<n> | NAME=<ename>| ALL
The f ol l owi ng i s an exampl e of t he cont act
st at ement .
CONTACT NAME=anode cur r ent
d. Interface
The semi conduct or or i nsul at or boundar i es ar e
det er mi ned wi t h t he i nt er f ace st at ement . The synt ax i s as
f ol l ows:
I NTERFACE [ <par amet er s>]
The f ol l owi ng exampl e shows t he usage of t he
i nt er f ace st at ement .
38
I NTERFACE X. MI N=- 4 X. MAX=4 Y. MI N=- 0. 5 Y. MAX=4 \
QF=1e10 S. N=1e4 S. P=1e4
The max and mi n val ues det er mi ne t he boundar i es.
The QF val ue speci f i es t he f i xed oxi de char ge densi t y ( cm
-
2
) . The S. N val ue speci f i es t he el ect r on sur f ace
r ecombi nat i on vel oci t y. S. P i s si mi l ar t o S. N, but f or
hol es.
3. Numerical Method Selection
Af t er t he mat er i al s model speci f i cat i on, t he numer i cal
met hod sel ect i on must be speci f i ed. Fr omFi gur e 29, t he onl y
st at ement t hat appl i es t o numer i cal met hod sel ect i on i s
met hod.

Fi gur e 29. At l as numer i cal met hod sel ect i on ( Af t er [ 23, p. 2-
8] ) .

Ther e ar e var i ous numer i cal met hods t o cal cul at e
sol ut i ons t o semi conduct or devi ce pr obl ems. Ther e ar e t hr ee
t ypes of sol ut i on t echni ques used i n Si l vaco At l as:
• decoupl ed ( GUMMEL)
• f ul l y coupl ed ( NEWTON)
• BLOCK
The GUMMEL met hod sol ves f or each unknowns by keepi ng
al l ot her unknowns const ant . The pr ocess i s r epeat ed unt i l
t her e i s a st abl e sol ut i on. The NEWTON met hod sol ves al l


39
unknowns si mul t aneousl y. The BLOCK met hod sol ves some
equat i ons wi t h t he GUMMEL met hod and some wi t h t he NEWTON
met hod.
The GUMMEL met hod i s used f or a syst em of equat i ons
t hat ar e weakl y coupl ed and t her e i s l i near conver gence. The
NEWTON met hod i s used when equat i ons ar e st r ongl y coupl ed
and t her e i s quadr at i c conver gence.
The f ol l owi ng exampl e shows t he use of t he met hod
st at ement .
METHOD GUMMEL NEWTON
I n t hi s exampl e, t he equat i ons ar e sol ved wi t h t he
GUMMEL met hod. I f conver gence i s not achi eved, t hen t he
equat i ons ar e sol ved usi ng t he NEWTON met hod.
4. Solution Specification
Af t er compl et i ng t he numer i cal met hod sel ect i on, t he
sol ut i on speci f i cat i on i s next . Sol ut i on speci f i cat i on i s
br oken down i nt o l og, sol ve, l oad, and save st at ement s, as
shown i n Fi gur e 30.

Fi gur e 30. At l as sol ut i on speci f i cat i on ( Af t er [ 23, p. 2- 8] ) .
a. Log
LOG saves al l t er mi nal char act er i st i cs t o a f i l e.
DC, t r ansi ent , or AC dat a gener at ed by a SOLVE st at ement
af t er a LOG st at ement i s saved.
40
The f ol l owi ng shows an exampl e of t he LOG
st at ement .
LOG OUTFI LE=myout put f i l e. l og
The exampl e saves t he cur r ent - vol t age i nf or mat i on
i nt o myout put f i l e. l og.
b. Solve
The SOLVE st at ement f ol l ows t he LOG st at ement .
SOLVE per f or ms a sol ut i on f or one or mor e bi as poi nt s. The
f ol l owi ng i s an exampl e of t he SOLVE st at ement .
SOLVE B1=10 B3=5 BEAM=1 SS. PHOT SS. LI GHT=0. 01 \
MULT. F FREQUENCY=1e3 FSTEP=10 NFSTEP=6
B1 and B3 speci f y t he opt i cal spot power
associ at ed wi t h t he opt i cal beam number s 1 and 3,
r espect i vel y. The beam number i s an i nt eger bet ween 1 and
10. BEAM i s t he beam number of t he opt i cal beam dur i ng AC
phot ogener at i on anal ysi s. SS. PHOT i s t he smal l si gnal AC
anal ysi s. SS. LI GHT i s t he i nt ensi t y of t he smal l si gnal par t
of t he opt i cal beam dur i ng si gnal AC phot ogener at i on
anal ysi s. MULT. F i s t he f r equency t o be mul t i pl i ed by FSTEP.
NFSTEPS i s t he number of t i mes t hat t he f r equency i s
i ncr ement ed by FSTEP.
c. Load and Save
The LOAD st at ement ent er s pr evi ous sol ut i ons f r om
f i l es as i ni t i al guess t o ot her bi as poi nt s. The SAVE
st at ement ent er s al l node poi nt i nf or mat i on i nt o an out put
f i l e.
41
The f ol l owi ng ar e exampl es of LOAD and SAVE
st at ement s.
SAVE OUTF=SOL. STR
I n t hi s case, SOL. STR has i nf or mat i on saved af t er
a SOLVE st at ement . Then, i n a di f f er ent si mul at i on, SOL. STR
can be l oaded as f ol l ows:
LOAD I NFI LE=SOL. STR
5. Results Analysis
Once a sol ut i on has been f ound f or a semi conduct or
devi ce pr obl em, t he i nf or mat i on can be di spl ayed gr aphi cal l y
wi t h TonyPl ot . Addi t i onal l y, devi ce par amet er s can be
ext r act ed wi t h t he EXTRACT st at ement , as shown i n Fi gur e 31.

Fi gur e 31. At l as r esul t s anal ysi s ( Af t er [ 23, p. 2- 8] ) .

I n t he exampl e bel ow, t he EXTRACT st at ement obt ai ns t he
cur r ent and vol t age char act er i st i cs of a sol ar cel l . Thi s
i nf or mat i on i s saved i nt o t he I Vcur ve. dat f i l e. Then,
TonyPl ot pl ot s t he i nf or mat i on i n t he I Vcur ve. dat f i l e.

EXTRACT NAME=" i v" cur ve( v. " anode" , I . " cat hode" ) /
OUTFI LE=" I Vcur ve. dat "

TONYPLOT I Vcur ve. dat

Fi gur e 32 shows t he sampl e I V cur ve pl ot t ed by
TonyPl ot .
42

Fi gur e 32. Sampl e TonyPl ot I V cur ve.


D. CONCLUSION
Thi s chapt er pr esent ed an i nt r oduct i on t o Si l vaco
At l as, t he st r uct ur e of t he i nput f i l es, and some of i t s
st at ement s. Wi t h t hese basi c t ool s, t he next chapt er
i nt r oduces some basi c i nf or mat i on on wur t zi t e I ndi umGal l i um
Ni t r i de bef or e pr oceedi ng t o t he t hesi s si mul at i on.
43
IV. INDIUM GALLIUM NITRIDE
A. A FULL SPECTRUM PHOTOVOLTAIC MATERIAL
Pr i or t o 2001, i t was t hought t hat wur t zi t e I ndi um
Ni t r i de had a band gap of appr oxi mat el y 1. 9 eV. I n 2001, i t
was di scover ed t hat I ndi um Ni t r i de had a much smal l er band
gap. Davydov, et al . , concl uded i n [ 24] t hat I ndi umNi t r i de
had a band gap of appr oxi mat el y 0. 9 eV. Addi t i onal l y,
Davydov, et al . , pr esent ed i n [ 25] t hat wur t zi t e I ndi um
Gal l i um Ni t r i de band gaps i n t he r ange x=0. 36 t o x=1
suppor t ed f i ndi ngs i n [ 24] . The band gaps f or I ndi umGal l i um
Ni t r i de, wi t h I ndi umNi t r i de concent r at i ons r angi ng f r om0. 0
t o 1. 0 ar e pr esent ed i n Fi gur e 33.

Fi gur e 33. I nGaN band gap as a f unct i on of I n composi t i on
( Af t er [ 25] ) .
44
Lat er on, r esear ch conduct ed at Lawr ence Ber kel ey
Nat i onal Labor at or y pr esent ed t hat t he I ndi um Ni t r i de
f undament al band gap was appr oxi mat el y 0. 77 eV at r oom
t emper at ur e. Si nce Gal l i um Ni t r i de has a band gap of
appr oxi mat el y 3. 4 eV at r oom t emper at ur e, t hen I ndi um
Gal l i umNi t r i de can have a band gap r angi ng f r om0. 77 eV t o
3. 4 eV by changi ng t he per cent composi t i on of I ndi um and
Gal l i um wi t hi n I ndi um Gal l i um Ni t r i de. Fi gur e 34 conf i r ms
t hat I ndi um Gal l i um Ni t r i de f ol l ows t he pat t er n of r angi ng
f r om0. 77 eV t o 3. 4 eV.

Fi gur e 34. I nGaN band gap and sol ar spect r umcompar i son
( Af t er [ 26] ) .

Fi gur e 34 al so pr esent s t he sol ar spect r umon t he l ef t -
hand si de. Ther ef or e, i t i s cl ear t hat t he vi si bl e spect r um
has a near - per f ect mat ch wi t h t he I ndi um Gal l i um Ni t r i de
r ange of band gaps.
I t shoul d be not ed t hat r esear ch conduct ed i n [ 27]
pr esent s a I ndi um Ni t r i de band gap of 1. 7± 0. 2 eV. I t i s
st at ed i n [ 27] , “These i nvest i gat i ons cl ar i f y t hat a band
45
t r ansi t i on ar ound 1. 7 eV does exi st i n wur t zi t e I nN al t hough
i n t hi s ener gy r ange opt i cal mat er i al r esponses ar e har dl y
ever f ound. I f t he 1. 7 eV band t r ansi t i on i s i ndeed t he
f undament al bandgap i n I nN at r oom t emper at ur e i t i s
concl uded t hat def ect bands, gr ai n boundar i es, di sl ocat i ons
and/ or t he ver y conduct i ve sur f ace ar e cont r i but i ng t o t he
l ower ener gy opt i cal r esponses i n I nN. The i dent i f i cat i on of
t he var i ous def ect s i n I nN wi l l be subj ect of f ut ur e
i nvest i gat i ons. ”
I n f ol l ow up r esear ch, [ 28] expl ai ns t he possi bl e
r eason f or t he hi gher I ndi um Ni t r i de band gap: “Owi ng t o
I nN’ s except i onal pr opensi t y f or n- t ype act i vi t y, i n many
i nst ances t he l ar ger appar ent val ues of t he band gap can be
at t r i but ed t o t he Bur st ei n–Moss shi f t of t he opt i cal
absor pt i on edge r esul t i ng f r om t he occupat i on of conduct i on
band st at es by f r ee el ect r ons. ”
Fi gur e 35 shows evi dence t hat t he f undament al band gap
of i ndi um ni t r i de i s appr oxi mat el y 0. 7 eV, and not near 2
eV. The opt i cal absor pt i on ( bl ue cur ve) has an onset at
appr oxi mat el y 0. 8 eV. Ther e i s no change i n absor pt i on
ar ound t he 2 eV r ange. The phot o l umi nescence ( r ed cur ve)
shows a peak at t he band edge of appr oxi mat el y 0. 8 eV.
Fi nal l y, t he phot o- modul at ed r ef l ect ance ( gr een cur ve)
pr esent s a t r ansi t i on cl ose t o 0. 8 eV. These t hr ee cur ves
suppor t a band gap f or i ndi um ni t r i de of appr oxi mat el y 0. 8
eV. The 1. 9- 2. 0 eV band gap i s not evi dent i n Fi gur e 35.
46

Fi gur e 35. Evi dence of 0. 7 eV band gap f or i ndi umni t r i de
( Fr om[ 29] ) .

The cont r over sy about i ndi umni t r i de’ s f undament al band
gap i s not t he subj ect of t hi s t hesi s. Thi s r esear ch
pr oceeded accept i ng t he f undament al band gap of 0. 77 eV f or
i ndi umni t r i de.
Accor di ng t o [ 30] , t he f ol l owi ng f or mul a pr ovi des an
appr oxi mat i on of I ndi umGal l i umNi t r i de band gap:
( ) 3.42 0.77(1 ) 1.43 (1 ) G E x x x x x = + − − −
Wher e E
G
i s t he I nGaN band gap, 3. 42 eV i s t he GaN band
gap, 0. 77 eV i s t he I nN band gap, 1. 43 eV i s t he bowi ng
par amet er b, x i s t he Ga concent r at i on, and ( 1- x) i s t he I n
concent r at i on.
When pl ot t i ng t he band gap f or mul a f or I nGaN usi ng a
Mat l ab scr i pt , t he Fi gur e 36 i s obt ai ned.
47

Fi gur e 36. I nGaN band gap as a f unct i on of I n concent r at i on.


The band gaps used i n t he Si l vaco At l as si mul at i ons
wer e f ound by modi f yi ng t he Mat l ab scr i pt f or Fi gur e 35.
B. RADIATION-HARD SEMICONDUCTOR MATERIAL
Radi at i on- har d mat er i al s ar e essent i al f or space
appl i cat i ons. When compar ed t o ot her Gal l i um Ar seni de and
I ndi um Gal l i um Phosphi de, I ndi um Gal l i um Ni t r i de i s abl e t o
wi t hst and a gr eat er amount of r adi at i on. Accor di ng t o [ 31] ,
I nGaN “r et ai ns i t s opt oel ect r oni c pr oper t i es at r adi at i on
damage doses at l east t wo or der s of magni t ude hi gher t han
t he damage t hr eshol ds of t he mat er i al s ( GaAs and GaI nP)
cur r ent l y used i n hi gh ef f i ci ency MJ cel l s”. Radi at i on
l evel s i n [ 31] wer e 1 MeV el ect r on, 2 MeV pr ot on, and 2 MeV
al pha par t i cl e i r r adi at i on.
48
Thi s i ndi cat es t hat I nGaN i s not onl y pot ent i al l y a
hi gh- ef f i ci ency phot ovol t ai c mat er i al , but i t i s al so abl e
t o wi t hst and t he har sh space envi r onment .
C. INDIUM GALLIUM NITRIDE CHALLENGES
Ther e ar e some si gni f i cant i ssues t hat cur r ent l y
pr event I nGaN f r om bei ng used as phot ovol t ai c mat er i al . As
of t hi s wr i t i ng, no PN j unct i on has been bui l t . The PN
j unct i on i s essent i al t o cr eat e phot odi odes. I ndi um Ni t r i de
has t he hi ghest el ect r on af f i ni t y among al l semi conduct or s
[ 32] . Hence, I ndi umNi t r i de has a t endency t o be n- t ype. I t
i s much mor e di f f i cul t t o bui l d p- t ype mat er i al wi t h I ndi um
Ni t r i de. However , evi dence of p- t ype dopi ng i n I ndi um
Ni t r i de and I ndi umGal l i umNi t r i de has been r epor t ed i n [ 33]
usi ng Magnesi um. Thi s i s a st ep i n t he r i ght di r ect i on.
Fur t her pr ogr ess i n t hi s ar ea di ct at es t he cr eat i on of
I ndi umGal l i umNi t r i de PN j unct i ons.
Havi ng r evi ewed t he char act er i st i cs of I ndi um Gal l i um
Ni t r i de, t he next chapt er cover s t he si mul at i on of I ndi um
Gal l i umNi t r i de usi ng Si l vaco At l as.




49
V. SIMULATION OF INDIUM GALLIUM NITRIDE IN SILVACO
ATLAS
One of t he pr i mar y mot i vat i ons behi nd t hi s r esear ch was
t o f i nd a way t o make sol ar cel l s si gni f i cant l y mor e
ef f i ci ent . When r esear chi ng hi gh- ef f i ci ency sol ar cel l s, t he
i mpr ovement s wer e t ypi cal l y i ncr ement al over pr evi ous
r esul t s. Sol ar cel l s wer e f i r st desi gned as si ngl e- j unct i on.
The most popul ar phot ovol t ai c mat er i al has been Si l i con due
t o i t s abundance and r el at i vel y l ow cost . The maxi mum
ef f i ci ency of pol ycr yst al l i ne Si l i con i s appr oxi mat el y
19. 8%. Commer ci al si l i con sol ar cel l s have a maxi mum
ef f i ci ency of appr oxi mat el y 13%. I mpr ovement s i n ef f i ci ency
can be obt ai ned i n si ngl e- j unct i on sol ar cel l s by usi ng
Gal l i um Ar seni de. Monocr yst al l i ne Gal l i um Ar seni de has a
maxi mumef f i ci ency of appr oxi mat el y 25. 1%[ 10, p. 195] .
By desi gni ng dual - j unct i on sol ar cel l s, t he ef f i ci ency
can agai n be i mpr oved. A dual - j unct i on cel l wi t h Gal l i um
Phosphi de as t he t op j unct i on and Gal l i um Ar seni de as t he
bot t omcel l can have an ef f i ci ency of 30. 3%[ 10, p 302] .
I ncr easi ng t he number of j unct i ons makes t he cel l s mor e
compl ex i n desi gn and t he gai ns begi n t o di mi ni sh. Tr i pl e-
j unct i on cel l s have ef f i ci enci es of appr oxi mat el y 31%. Quad-
j unct i on cel l s have ef f i ci enci es of appr oxi mat el y 33%. I t i s
expect ed t hat f i ve- and si x- j unct i on sol ar cel l s can have
ef f i ci enci es of appr oxi mat el y 35%[ 36] .
Thi s si mul at i on uses I ndi um Gal l i um Ni t r i de as
phot ovol t ai c mat er i al i n a si mul at i on. Wi t h i t s f ul l -
spect r um char act er i st i cs, t he ef f i ci ency of I ndi um Gal l i um
Ni t r i de has t he pot ent i al t o sur pass pr evi ous r esul t s.
50
A. SINGLE-JUNCTION SOLAR CELL
Fi gur e 37 shows a gr aphi cal r epr esent at i on of t he
si ngl e j unct i on sol ar cel l . The t hi ckness of t he emi t t er i s
0. 01 m µ and t he dopi ng i s 1x10
16
/ cm
3
. The t hi ckness of t he
base i s 3 m µ and t he dopi ng i s 1x10
16
/ cm
3
.

Fi gur e 37. Si mpl e si ngl e- j unct i on I nGaN sol ar cel l .

The f i r st st ep i s t o devel op si ngl e j unct i on sol ar
cel l s. Opt i cal dat a i n t he f or mof di el ect r i c const ant s was
f ound i n [ 34] f or I n
0. 20
Ga
0. 80
N. Thi s cor r esponds t o a
cal cul at ed band gap of 2. 66 eV. Addi t i onal opt i cal dat a was
f ound i n [ 35] f or I n
0. 57
Ga
0. 43
N ( cal cul at ed Eg=1. 60 eV) ,
I n
0. 68
Ga
0. 32
N ( cal cul at ed Eg=1. 31 eV) , and I n
0. 78
Ga
0. 22
N
( cal cul at ed Eg=1. 1 eV) . The di el ect r i c const ant s wer e t hen
conver t ed t o i ndex of r ef r act i on ( n) and ext i nct i on
coef f i ci ent ( k) usi ng a Mat l ab scr i pt ( Appendi x B) . The band
gap and t he opt i cal dat a wer e ent er ed i nt o t he i nput deck.
The si mul at i on r an i n Si l vaco At l as. Fr omt he l og f i l e, t he
cur r ent and vol t age dat a was ext r act ed.
I n t he si ngl e- j unct i on case, each of t he cel l s had AM0
as t he i nput spect r um. Fi gur e 38 shows t he I V cur ves of f our
si ngl e- j unct i on sol ar cel l s. The I V cur ve pat t er n
cor r esponds t o empi r i cal f i ndi ngs of ot her mul t i j unct i on
51
sol ar cel l s. Typi cal l y, t he cel l wi t h t he hi ghest vol t age
has t he l owest cur r ent . The cel l wi t h t he l owest vol t age has
t he hi ghest cur r ent .

Fi gur e 38. Four si ngl e- j unct i on I V cur ves.

Tabl e 7 shows I sc, Voc, f i l l f act or , and ef f i ci ency of
t he si ngl e- j unct i on sol ar cel l s pr esent ed i n Fi g. 36.

Mat er i al I sc
( mA/ cm
2
)
Voc ( V) Fi l l
f act or
Ef f i ci ency
I n
0. 20
Ga
0. 80
N 17. 613 2. 23 83. 72% 24. 32%
I n
0. 57
Ga
0. 43
N 18. 395 1. 15 78. 80% 12. 35%
I n
0. 68
Ga
0. 32
N 20. 453 0. 91 76. 38% 10. 52%
I n
0. 78
Ga
0. 22
N 20. 848 0. 72 73. 73% 08. 19%
Tabl e 7. Ef f i ci enci es of f our si ngl e- j unct i on I nGaN cel l s.

52
The ef f i ci enci es shown i n Tabl e 7 i ndi cat e t hat a hi gh-
ef f i ci ency, si ngl e- j unct i on cel l wi t h I n
0. 20
Ga
0. 80
N has good
pr ospect s. A 24. 32% ef f i ci ency compar es f avor abl y t o t he
si ngl e- j unct i on Gal l i um Ar seni de ef f i ci ency of 25. 1%. The
I nGaN cel l s si mul at ed can be opt i mi zed by changi ng t he
t hi ckness of t he j unct i on and changi ng t he dopi ng l evel s.
Addi ng a wi ndow, a back sur f ace f i el d ( BSF) and a buf f er can
al so hel p i n i mpr ovi ng t he ef f i ci ency r esul t s. These
i mpr ovement s can be t he subj ect of f ut ur e r esear ch.
B. DUAL-JUNCTION SOLAR CELL
Fi gur e 39 shows a gr aphi cal r epr esent at i on of a dual -
j unct i on I nGaN sol ar cel l . The t hi cknesses and dopi ng l evel s
r emai n i dent i cal t o t he si ngl e- j unct i on case.

Fi gur e 39. Si mpl e dual - j unct i on I nGaN sol ar cel l .

Fr om t he di scussi on i n t he si ngl e- j unct i on sol ar cel l
sect i on, i t shoul d be cl ear t hat t he best combi nat i on of
I nGaN band gaps i s 2. 66 eV and 1. 60 eV, si nce t hey have t he
53
hi ghest ef f i ci enci es. I t shoul d be not ed t hat f or t hi s
si mul at i on, t he AM0 spect r um was pr ovi ded f or t he t op
j unct i on I n
0. 20
Ga
0. 80
N ( Eg=2. 66 eV) . The bot t om j unct i on
I n
0. 57
Ga
0. 43
N ( Eg=1. 60 eV) r ecei ved t he AM0 spect r ummi nus t he
spect r umabsor bed by t he t op cel l .
Fi gur e 40 shows t he I V cur ves of t he dual - j unct i on
sol ar cel l . Not e t hat compar ed t o Fi gur e 38, t he I V cur ve of
Eg=2. 66 eV st ayed t he same, whi l e t he I V cur ve of Eg=1. 60 eV
had a cur r ent dr op. Thi s cur r ent decr ease was expect ed
because t he i nput spect r umwas di mi ni shed by t he t op cel l .

Fi gur e 40. Dual - j unct i on I nGaN sol ar cel l I V cur ve.

Si nce t he j unct i ons ar e i n ser i es, t he over al l I V cur ve
i s l i mi t ed i n i t s cur r ent l evel by t he I V cur ve wi t h t he
l owest cur r ent . The vol t ages ar e added accor di ngl y.
Tabl e 8 shows t he ef f i ci ency of t he dual - j unct i on sol ar
cel l .
54
Mat er i al I sc
( mA/ cm
2
)
Voc ( V) Fi l l
f act or
Ef f i ci ency
I n
0. 20
Ga
0. 80
N
I n
0. 57
Ga
0. 43
N
Dual
j unct i on
17. 11 3. 38 83. 25% 35. 58%
Tabl e 8. Dual - j unct i on I nGaN ef f i ci ency.

Ther e i s a si gni f i cant i ncr ease i n ef f i ci ency f r om
si ngl e- j unct i on ( 24. 32%) t o dual j unct i on ( 35. 58%) I nGaN
sol ar cel l s. Thi s i mpr ovement al one shoul d be enough t o
cont i nue t o pur sue t he devel opment of I nGaN sol ar cel l s.
Sear chi ng f or f ur t her i mpr ovement s, t hr ee- and f our -
j unct i on sol ar cel l s ar e exami ned next .
C. THREE-JUNCTION SOLAR CELL
Fi gur e 41 shows a gr aphi cal r epr esent at i on of a t hr ee-
j unct i on I nGaN sol ar cel l . Thi cknesses and dopi ng l evel s
st ayed t he same as t he si ngl e- and dual - j unct i on cases. Fr om
t he si ngl e- j unct i on sol ar cel l di scussi on, t he t hr ee most
ef f i ci ent cel l s wer e sel ect ed ( Eg=2. 66 eV, Eg=1. 60 eV,
Eg=1. 31 eV) . The t op cel l I n
0. 20
Ga
0. 80
N ( Eg=2. 66 eV) r ecei ved
t he AM0 spect r um. The cel l I n
0. 57
Ga
0. 43
N ( Eg=1. 60 eV) r ecei ved
t he AM0 spect r um mi nus t he spect r um absor bed by t he t op
cel l . The cel l I n
0. 68
Ga
0. 32
N ( Eg=1. 31 eV) r ecei ved t he AM0
spect r ummi nus t he spect r umabsor bed by t he t op t wo cel l s.
Fi gur e 42 shows t he I V cur ve of t he t hr ee- j unct i on
sol ar cel l . Not e t hat t he cur r ent l evel of t he t op t wo cel l s
i s i dent i cal t o t he dual - j unct i on case. However , t he cur r ent
55
l evel of t he bot t om cel l i s l ower t han t he si ngl e j unct i on
case f or t he same concent r at i on. Si mi l ar l y t o t he dual -
j unct i on case, t he cur r ent of t he over al l I V cur ve i s
l i mi t ed by t he i ndi vi dual j unct i on wi t h t he l owest I V cur ve.
The vol t ages ar e added accor di ngl y, si nce t he t hr ee
j unct i ons ar e i n ser i es.


Fi gur e 41. Si mpl e t hr ee- j unct i on I nGaN sol ar cel l .

56

Fi gur e 42. Thr ee- j unct i on I nGaN sol ar cel l I V cur ve.

Tabl e 9 shows t he ef f i ci ency of t he t hr ee- j unct i on
I nGaN sol ar cel l .

Mat er i al I sc
( mA/ cm
2
)
Voc ( V) Fi l l
f act or
Ef f i ci ency
I n
0. 20
Ga
0. 80
N
I n
0. 57
Ga
0. 43
N
I n
0. 68
Ga
0. 32
N
Thr ee
j unct i on
14. 12 4. 27 87. 23% 38. 90%
Tabl e 9. Thr ee- j unct i on I nGaN ef f i ci ency

The i ncr ease i n ef f i ci ency f r omdual - j unct i on t o t hr ee-
j unct i on i s 35. 58% t o 38. 90%. The modest i ncr ease i n
ef f i ci ency can be at t r i but ed t o t he dr op i n I sc f r om 17. 11
57
mA/ cm
2
t o 14. 12 mA/ cm
2
. However , t he i ncr ease i n Voc f r om
3. 38 V t o 4. 27 ensur ed t hat t he ef f i ci ency woul d i ncr ease.
The l ast case t o be exami ned i s t he quad- j unct i on I nGaN
sol ar cel l .
D. QUAD-JUNCTION SOLAR CELL
Fi gur e 43 shows a gr aphi cal r epr esent at i on of a quad-
j unct i on I nGaN sol ar cel l . Thi cknesses and dopi ng l evel s
r emai ned t he same as t he si ngl e- , dual - , and t hr ee- j unct i on
cases. Spect r umi nput f ol l owed t he pat t er n of t he dual - and
t hr ee- j unct i on cases. As expect ed, t he cur r ent dr opped f or
al l cases wher e AM0 had been r educed by t he t op cel l s.
Fi gur e 44 shows t he I V cur ve f or a quad- j unct i on I nGaN
sol ar cel l . Not e t hat t he I V- cur ves f or t he t op t hr ee cel l s
ar e i dent i cal t o t he t hr ee- j unct i on case. The bot t om cel l
has a l ower cur r ent l evel compar ed t o t he si ngl e j unct i on
case.
Tabl e 10 shows t he ef f i ci ency of t he quad- j unct i on
I nGaN sol ar cel l .








58



Fi gur e 43. Si mpl e quad- j unct i on I nGaN sol ar cel l

59

Fi gur e 44. Quad- j unct i on I nGaN sol ar cel l I V cur ve


Mat er i al I sc
( mA/ cm
2
)
Voc ( V) Fi l l
f act or
Ef f i ci ency
I n
0. 20
Ga
0. 80
N
I n
0. 57
Ga
0. 43
N
I n
0. 68
Ga
0. 32
N
I n
0. 78
Ga
0. 22
N
Quad-
j unct i on
12. 88 4. 98 87. 86% 41. 69%
Tabl e 10. Quad j unct i on I nGaN ef f i ci ency


For compl et eness, ef f i ci ency cal cul at i ons ar e pr ovi ded
bel ow f or t he quad- j unct i on case. These cal cul at i ons wer e
per f or med wi t h t he hel p of a Mat l ab scr i pt .
60
max mp mp
2 2
2
max mp mp
sc oc sc oc
2
2
max mp mp
in in
2
A W
P =I V =(0.0126 )(4.4736 V)=0.0564
cm cm
W
0.0564
P I V
cm
FF= = = =87.86%
A
I V I V
(0.0129 )(4.9793V)
cm
W
0.0564
P I V
cm
η = = =0.4169=41.69%
W
P P
0.1353
cm


I n or der t o get a per spect i ve on how t hi s r esul t
compar es t o act ual sol ar cel l s i n pr oduct i on, Fi gur e 45 i s
pr esent ed.

Fi gur e 45. Spect r ol ab’ s sol ar cel l ef f i ci enci es ( Fr om[ 34] ) .

61
The l abel nJ st ands f or new gener at i on f our t o si x-
j unct i on cel l s. XTJ i s a desi gnat i on f or a t r i pl e j unct i on
cel l . UTJ st ands f or Ul t r a Tr i pl e J unct i on. I TJ means
I mpr oved Tr i pl e J unct i on. TJ i s Tr i pl e J unct i on. DJ i s Dual
J unct i on. SJ i s si ngl e j unct i on.
Fi gur e 45 shows t he ef f i ci ency pr ogr essi on of a l eadi ng
sol ar cel l manuf act ur er ( Spect r ol ab) . The f i r st st ep
consi st s of si ngl e j unct i on si l i con sol ar cel l s. These cel l s
wer e i n pr oduct i on f r omt he mi d- 1960s unt i l t he ear l y 1990s.
Thei r ef f i ci ency was cl ose t o 15%. The next st ep consi st ed
of si ngl e j unct i on gal l i umar seni de sol ar cel l s. These cel l s
had ef f i ci enci es bet ween 15%and 20%. I n t he mi d- 1990s, dual
j unct i on sol ar cel l s appear ed. Ef f i ci enci es wer e sl i ght l y
above 20%. Tr i pl e j unct i on cel l s appear ed i n t he ear l y 2000s
wi t h ef f i ci enci es near i ng 30%. The pr oj ect i ons ar e t o
pr oduce quad- j unct i on sol ar cel l s wi t hi n t he next decade
wi t h ef f i ci enci es j ust under 35%.
Fur t her compar i sons can be made wi t h anot her
si mul at i on. Model i ng i n [ 5] used physi cs equat i ons t o
cal cul at e I sc and Voc. The i nput spect r um used i n t hat
si mul at i on was AM1. 5 i nst ead of AM0. The I nGaN band gap
f or mul a used was f r om [ 37] . Thi s t hesi s used t he band gap
f or mul a f r om [ 30] . Fi gur e 46 shows a compar i son of t he t wo
f or mul as. Bot h f or mul as seek t o dupl i cat e f i ndi ngs f r om
act ual band gap measur ement s. Ther ef or e, bot h f or mul as ar e
appr oxi mat i ons onl y.
The si mul at i on f r om [ 5] obt ai ned t he r esul t s pr esent ed
i n Tabl e 11. The hi ghest ef f i ci ency obt ai ned i n t hat
si mul at i on i s 40. 346%wi t h a si x- j unct i on I nGaN sol ar cel l .
62

Fi gur e 46. Compar i son of I nGaN band gap f or mul as



Tabl e 11. I nGaN ef f i ci ency r esul t s ( Fr om[ 5] ) .

The di f f er ences i n ef f i ci ency r esul t s can be par t l y
at t r i but ed t o t he di f f er ence i n band gap f or mul a used. For
exampl e, I n
0. 20
Ga
0. 80
N has a band gap of 2. 66 eV wi t h t he
f or mul a used i n t hi s t hesi s. The f or mul a f r om[ 37] yi el ds a
band gap of 1. 897 eV. I f t he I n
0. 20
Ga
0. 80
N band gap of 1. 897
eV i s subst i t ut ed i n t he si ngl e- j unct i on sol ar cel l
si mul at i on of t hi s t hesi s, t he ef f i ci ency decr eases
si gni f i cant l y. Fi gur e 47 compar es t he I V out put f or
I n
0. 20
Ga
0. 80
N at Eg=1. 897 eV and Eg=2. 66 eV.
63

Fi gur e 47. I V cur ve f or I n
0. 20
Ga
0. 80
N usi ng di f f er ent band gaps


The ef f i ci ency of t he I n
0. 20
Ga
0. 80
N ( 2. 66 eV) si ngl e-
j unct i on sol ar cel l si mul at ed i n t hi s t hesi s was 24. 32%.
Changi ng t he band gap t o 1. 897 eV yi el ds an ef f i ci ency of
14. 94%. Thi s i s a si gni f i cant decr ease. However , t he band
gap f or t he ot her t hr ee j unct i ons i ncr eases wi t h t he f or mul a
used i n [ 37] . The quad- j unct i on si mul at i on was r un wi t h t he
new band gaps. Fi gur e 48 shows t he I V cur ve f or t he quad-
j unct i on sol ar cel l . The ef f i ci ency f or t he quad- j unct i on
sol ar cel l i ncr eases t o 43. 62%. I t i s di f f i cul t t o st at e
whi ch band gap model i s mor e cor r ect .




64



Fi gur e 48. Quad- j unct i on I nGaN sol ar cel l I V cur ve usi ng
cal cul at ed band gaps f r om[ 37] f or mul a.




Mat er i al I sc
( mA/ cm
2
)
Voc ( V) Fi l l
f act or
Ef f i ci ency
I n
0. 20
Ga
0. 80
N
I n
0. 57
Ga
0. 43
N
I n
0. 68
Ga
0. 32
N
I n
0. 78
Ga
0. 22
N
Quad-
j unct i on
12. 9 5. 194 88. 06% 43. 62
Tabl e 12. Quad j unct i on I nGaN ef f i ci ency usi ng band gaps
f r om[ 37] cal cul at i ons.
65
A common f i ndi ng i n [ 5] and t hi s t hesi s i s t hat bot h
si mul at i ons show t hat I ndi um Gal l i um Ni t r i de mul t i j unct i on
sol ar cel l s can pr ovi de a si gni f i cant i mpr ovement i n sol ar
cel l ef f i ci ency. However , t hi s i s t he f i r st t i me t hat a
Technol ogy Comput er Ai ded Desi gn ( TCAD) , such as Si l vaco
At l as, has been used t o si mul at e I nGaN sol ar cel l s.
The r esul t s of t hi s t hesi s si mul at i on demonst r at e t hat
I ndi um Gal l i um Ni t r i de i s pot ent i al l y an excel l ent
semi conduct or phot ovol t ai c mat er i al . The mat er i al sci ence
r esear ch i n t he f ut ur e can conf i r m t hese out comes i n t he
f ut ur e.
Pr oduct i on of si ngl e- j unct i on sol ar cel l s appear s t o be
t he f i r st st ep t o be t aken. Once t he phot ovol t ai c pr oper t i es
ar e demonst r at ed wi t h act ual I ndi um Gal l i um Ni t r i de, t he
compl exi t y of dual - j unct i on sol ar cel l s can be addr essed.
Tunnel j unct i ons made up of I ndi umGal l i umNi t r i de may need
t o be expl or ed as wel l .
66
THI S PAGE LEFT I NTENTI ONALLY BLANK
67
VI. CONCLUSIONS AND RECOMMENDATIONS
A. RESULTS AND CONCLUSIONS
I ndi umGal l i umNi t r i de i s a semi conduct or mat er i al wi t h
pot ent i al t o be used i n phot ovol t ai c devi ces. A new
si mul at i on was per f or med usi ng Si l vaco At l as. The r esul t s of
t he quad- j unct i on I ndi umGal l i umNi t r i de sol ar cel l i ndi cat e
t hat a new hi gh- ef f i ci ency mat er i al shoul d be pr oduced.
Cur r ent st at e- of - t he- ar t mul t i j unct i on sol ar cel l s have
ef f i ci enci es i n t he 30- 33% r ange. The 41% ef f i ci ency
pr edi ct ed i n t hi s t hesi s i s t he hi ghest of al l si mul at i ons
per f or med at t he Naval Post gr aduat e School usi ng Si l vaco
At l as.
B. RECOMMENDATIONS FOR FUTURE RESEARCH
Ther e ar e mul t i pl e ar eas t hat can be expl or ed i n f ut ur e
r esear ch. Thi s t hesi s f ocused on t he devel opment of a sol ar
cel l model t hat emphasi zes t he use of opt i cal const ant s
( r ef r act i on and ext i nct i on coef f i ci ent s n and k) . The model
used def aul t set t i ngs f or ot her par amet er s, such as
per mi t t i vi t y, af f i ni t y, r adi at i ve r ecombi nat i on r at e,
el ect r on and hol e l i f et i mes, el ect r on and hol e densi t y of
st at es, and l at t i ce const ant s. One ar ea of f ut ur e r esear ch
i s t o obt ai n measur ed dat a f or t he above par amet er s. Thi s
subj ect i s cr i t i cal i n i mpr ovi ng t he model . The ot her opt i on
i s t o i nt er pol at e f r om known val ues. Addi t i onal l y, t he
i ncl usi on of t unnel j unct i ons i n t he si mul at i on i s of gr eat
val ue.
68
Ot her ar eas of r esear ch i ncl ude f i ndi ng di f f er ent
semi conduct or mat er i al s t hat of f er pot ent i al f or hi gh-
ef f i ci ency sol ar cel l s. Lawr ence Ber kel ey Nat i onal
Labor at or y i s al so wor ki ng wi t h mul t i band mat er i al s, such as
Zi nc Manganese Tel l er i um Oxi de ( ZnMnTeO) . Thi s t ype of
mat er i al of f er s a si ngl e j unct i on sol ar cel l , but t her e ar e
mul t i pl e band gaps wi t hi n t he si ngl e j unct i on.
One mor e r ecommended pat h i s t o opt i mi ze t he physi cal
par amet er s of t he sol ar cel l . The t hi ckness of each of t he
l ayer s can be opt i mi zed t o pr oduce a bet t er ef f i ci ency. The
band gap di st r i but i on f or a quad- j unct i on sol ar cel l can be
i mpr oved t o obt ai n hi gher ef f i ci ency. I t shoul d be not ed
t hat obt ai ni ng t he cor r ect opt i cal dat a f or t hese band gaps
i s essent i al .
69
APPENDIX A: SILVACO ATLAS INPUT DECK
The code f or t he quad- j unct i on I nGaN sol ar cel l was
br oken down i nt o f our si ngl e- j unct i on sol ar cel l s. Thi s was
done because t he mat er i al pr oper t i es of I nGaN had t o be
changed f or each of t he j unct i ons.
Or i gi nal code f or t he Si l vaco At l as i nput deck was
obt ai ned f r om Mi chal opol ous [ 1] , Bat es, [ 2] , Gr een [ 3] , and
Canf i el d [ 4] . Modi f i cat i ons t o t he code wer e made t o suppor t
t hi s t hesi s.
A. TOP JUNCTION: IN
0.20
GA
0.80
N, EG=2.66 EV
go at l as


set cel l Wi dt h=5. 000000e+002
set capWi dt hper cent =8. 000000e+000
set di vs=1. 000000e+001
set cont Thi ck=1. 000000e- 001
set capThi ck=3. 000000e- 001
set capDop=1. 000000e+020
set wi ndowThi ck=0. 01
set wi nDop=2. 15e17
set emi t t er Thi ck=0. 01
#changed emi t Dop f r om1e16 t o 1e20
set emi t Dop=1e16
set baseThi ck=3. 19467
#changed basDop f r om1e16 t o 1e20
set baseDop=1e16
set bsf Thi ck=0. 03533
set bsf Dop=2. 15e19

set cel l Wi dt hDi v=$cel l Wi dt h/ $di vs
set wi dt h3d=100e6/ $cel l Wi dt h
set capWi dt h=0. 01*$capWi dt hper cent *$cel l Wi dt h/ 2
set capWi dt hDi v=$capWi dt h/ ( $di vs/ 2)
set cel l Wi dt hHal f =$cel l Wi dt h/ 2

set bsf Lo=0
set bsf Hi =$bsf Lo- $bsf Thi ck
set bsf Di v=$bsf Thi ck/ $di vs

set baseLo=$bsf Hi
set baseHi =$baseLo- $baseThi ck
set baseMi d=$baseLo- $baseThi ck/ 2
set baseDi v=$baseThi ck/ $di vs

set emi t t er Lo=$baseHi
70
set emi t t er Hi =$emi t t er Lo- $emi t t er Thi ck
set emi t t er Di v=$emi t t er Thi ck/ $di vs

set wi ndowLo=$emi t t er Hi
set wi ndowHi =$wi ndowLo- $wi ndowThi ck
set wi ndowDi v=$wi ndowThi ck/ $di vs

set capLo=$wi ndowHi
set capHi =$capLo- $capThi ck
#set capDi v=$capThi ck/ $di vs

set cont Lo=$capHi
set cont Hi =$cont Lo- $cont Thi ck
set cont Di v=$cont Thi ck/ $di vs

set l i ght Y=$emi t t er Hi - 5

mesh wi dt h=$wi dt h3d
## X- Mesh
x. mesh l oc=- $cel l Wi dt hHal f spac=$cel l Wi dt hDi v
x. mesh l oc=- $capWi dt h spac=$capWi dt hDi v
x. mesh l oc=$capWi dt h spac=$capWi dt hDi v
x. mesh l oc=$cel l Wi dt hHal f spac=$cel l Wi dt hDi v

## Y- Mesh
# Top cont act
y. mesh l oc=$cont Hi spac=0
y. mesh l oc=$cont Lo spac=0
# Cap
# Wi ndow
y. mesh l oc=$wi ndowHi spac=$wi ndowDi v
y. mesh l oc=$wi ndowLo spac=$wi ndowDi v
# Emi t t er
y. mesh l oc=$emi t t er Lo spac=$emi t t er Di v
# Base
y. mesh l oc=$baseMi d spac=$baseDi v
# BSF
y. mesh l oc=$bsf Hi spac=$bsf Di v
y. mesh l oc=$bsf Lo spac=$bsf Di v


## Regi ons
# Cap
#r egi on num=8 mat er i al =Vacuum x. mi n=- $capWi dt h x. max=$capWi dt h y. mi n=$cont Hi
y. max=$cont Lo
r egi on num=1 mat er i al =I nGaN x. mi n=- $capWi dt h x. max=$capWi dt h y. mi n=$capHi
y. max=$capLo x. comp=0. 20
r egi on num=2 mat er i al =Vacuum x. mi n=- $cel l Wi dt hHal f x. max=- $capWi dt h
y. mi n=$cont Hi y. max=$capLo
r egi on num=3 mat er i al =Vacuum x. mi n=$capWi dt h x. max=$cel l Wi dt hHal f y. mi n=$cont Hi
y. max=$capLo
# Wi ndow [ f or Ge cel l , use Al GaAs wi t h x. comp=0. 2]
r egi on num=4 mat er i al =I nGaN x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f
y. mi n=$wi ndowHi y. max=$wi ndowLo x. comp=0. 20

#r egi on num=4 mat er i al =Al GaAs x. comp=0. 2 x. mi n=- $cel l Wi dt hHal f
x. max=$cel l Wi dt hHal f y. mi n=$wi ndowHi y. max=$wi ndowLo
# Emi t t er
r egi on num=5 mat er i al =I nGaN x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f
y. mi n=$emi t t er Hi y. max=$emi t t er Lo x. comp=0. 20
# Base
71
r egi on num=6 mat er i al =I nGaN x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f
y. mi n=$baseHi y. max=$baseLo x. comp=0. 20
# BSF
r egi on num=7 mat er i al =I nGaN x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f
y. mi n=$bsf Hi y. max=$bsf Lo x. comp=0. 20

## El ect r odes [ f or I nGaP cel l , add cat hode ( gol d) and r emove cat hode
( conduct or ) ]
el ect r ode name=cat hode mat er i al =Gol d x. mi n=- $capWi dt h x. max=$capWi dt h
y. mi n=$cont Hi y. max=$cont Lo
#el ect r ode name=cat hode x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f
y. mi n=$wi ndowHi y. max=$wi ndowHi
el ect r ode name=anode x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f y. mi n=$bsf Lo
y. max=$bsf Lo

## Dopi ng [ f or I nGaP cel l , uncomment cap dopi ng]
# Cap
dopi ng uni f or mr egi on=1 n. t ype conc=$capDop
# Wi ndow
dopi ng uni f or mr egi on=4 n. t ype conc=$wi nDop
# Emi t t er
dopi ng uni f or mr egi on=5 n. t ype conc=$emi t Dop
# Base
dopi ng uni f or mr egi on=6 p. t ype conc=$baseDop
# BSF
dopi ng uni f or mr egi on=7 p. t ype conc=$bsf Dop

## Mat er i al pr oper t i es
# Opaque cont act [ comment out f or I nGaP cel l ]
#mat er i al r egi on=8 r eal . i ndex=1. 2 i mag. i ndex=1. 8
# Vacuum ( f or zer o r ef l ect i on) [ change t o mat ch wi ndow mat er i al ( I nGaP use
Vacuum_Al I nP) ]
# [ f or I nGaP cel l , comment out r egi on 1]
#mat er i al r egi on=1 i ndex. f i l e=Vacuum_I nGaP. opt
mat er i al r egi on=2 i ndex. f i l e=VacuumI n20Ga80N. opt
mat er i al r egi on=3 i ndex. f i l e=VacuumI n20Ga80N. opt

#I nGaN
mat er i al mat er i al =I nGaN EG300=2. 6612 i ndex. f i l e=I n20Ga80N. opt

# Gol d
mat er i al mat er i al =Gol d r eal . i ndex=1. 2 i mag. i ndex=1. 8


## Model s [ I nGaP cel l , 1; GaAs cel l , 5&6; I nGaNAs cel l , 7]
model s r egi on=1 CONMOB
MODELS CHUANG CONMOB FLDMOB SRH OPTR PRI NT

## Li ght beams [ GaAs b1, 0. 55- 0. 75, 200 b2, 0. 75- 0. 88, 65] 0. 12- 2. 7, 50 [ 630, 825]
beam num=1 x. or i gi n=0 y. or i gi n=$l i ght Y angl e=90 back. r ef l
power . f i l e=AM0nr el . spec \
wavel . st ar t =0. 12 wavel . end=2. 4 wavel . num=50

st r uct out f i l e=Si ngl eCel l _webf . st r
#t onypl ot Si ngl eCel l _webf . st r

sol ve i ni t
met hod gummel newt on maxt r aps=10 i t l i mi t =25
sol ve b1=0. 9

## Get t i ng I sc f or I - V cur ve poi nt s
met hod newt on maxt r aps=10 i t l i mi t =100
72
sol ve b1=0. 95
ext r act name=" i sc" max( i . " cat hode" )
set i sc=$i sc*$wi dt h3d
set i 1=$i sc/ 10
set i 2=$i 1+$i sc/ 10
set i 3=$i 2+$i sc/ 10
set i 4=$i 3+$i sc/ 10
set i 5=$i 4+$i sc/ 10
set i 6=$i 5+$i sc/ 20
set i 7=$i 6+$i sc/ 20
set i 8=$i 7+$i sc/ 20
set i 9=$i 8+$i sc/ 20
set i 10=$i 9+$i sc/ 20
set i 11=$i 10+$i sc/ 40
set i 12=$i 11+$i sc/ 40
set i 13=$i 12+$i sc/ 40
set i 14=$i 13+$i sc/ 40
set i 15=$i 14+$i sc/ 40
set i 16=$i 15+$i sc/ 80
set i 17=$i 16+$i sc/ 80
set i 18=$i 17+$i sc/ 80
set i 19=$i 18+$i sc/ 80
set i 20=$i 19+$i sc/ 80
set i 21=$i 20+$i sc/ 80
set i 22=$i 21+$i sc/ 80
set i 23=$i 22+$i sc/ 80
set i 24=$i 23+$i sc/ 80
set i 25=$i 24+$i sc/ 80- 0. 00001
##

l og out f i l e=I n20Ga80N. l og

met hod newt on maxt r aps=10 i t l i mi t =100
sol ve b1=0. 95

cont act name=anode cur r ent
met hod newt on maxt r aps=10 i t l i mi t =100

## Pmax poi nt s [ I nGaP 18- 25; GaAs 15- 25; I nGaNAs 13- 25; Ge 11- 25]
sol ve i anode=- $i 25 b1=0. 95
sol ve i anode=- $i 24 b1=0. 95
sol ve i anode=- $i 23 b1=0. 95
sol ve i anode=- $i 22 b1=0. 95
sol ve i anode=- $i 21 b1=0. 95
sol ve i anode=- $i 20 b1=0. 95
sol ve i anode=- $i 19 b1=0. 95
sol ve i anode=- $i 18 b1=0. 95
sol ve i anode=- $i 17 b1=0. 95
sol ve i anode=- $i 16 b1=0. 95
sol ve i anode=- $i 15 b1=0. 95
sol ve i anode=- $i 14 b1=0. 95
sol ve i anode=- $i 13 b1=0. 95
sol ve i anode=- $i 12 b1=0. 95
sol ve i anode=- $i 11 b1=0. 95
sol ve i anode=- $i 10 b1=0. 95
sol ve i anode=- $i 9 b1=0. 95
sol ve i anode=- $i 8 b1=0. 95
sol ve i anode=- $i 7 b1=0. 95
sol ve i anode=- $i 6 b1=0. 95
sol ve i anode=- $i 5 b1=0. 95
sol ve i anode=- $i 4 b1=0. 95
sol ve i anode=- $i 3 b1=0. 95
73
sol ve i anode=- $i 2 b1=0. 95
sol ve i anode=- $i 1 b1=0. 95

sol ve i anode=0 b1=0. 95
l og of f
ext r act name=" i v" cur ve( v. " anode" , i . " cat hode" ) out f i l e=" I Vcur veI n20Ga80N. dat "
t onypl ot I Vcur veI n20Ga80N. dat

l og out f i l e=doneI n20Ga80N. l og
l og of f
B. SECOND JUNCTION: IN
0.57
GA
0.43
N, EG=1.6 EV
go at l as

set cel l Wi dt h=5. 000000e+002
set capWi dt hper cent =8. 000000e+000
set di vs=1. 000000e+001
set cont Thi ck=1. 000000e- 001
set capThi ck=3. 000000e- 001
set capDop=1. 000000e+020
set wi ndowThi ck=0. 01
set wi nDop=2. 15e17
set emi t t er Thi ck=0. 01
#changed emi t Dop f r om1e16 t o 1e20
set emi t Dop=1e16
set baseThi ck=3. 19467
#changed basDop f r om1e16 t o 1e20
set baseDop=1e16
set bsf Thi ck=0. 03533
set bsf Dop=2. 15e19

set cel l Wi dt hDi v=$cel l Wi dt h/ $di vs
set wi dt h3d=100e6/ $cel l Wi dt h
set capWi dt h=0. 01*$capWi dt hper cent *$cel l Wi dt h/ 2
set capWi dt hDi v=$capWi dt h/ ( $di vs/ 2)
set cel l Wi dt hHal f =$cel l Wi dt h/ 2

set bsf Lo=0
set bsf Hi =$bsf Lo- $bsf Thi ck
set bsf Di v=$bsf Thi ck/ $di vs

set baseLo=$bsf Hi
set baseHi =$baseLo- $baseThi ck
set baseMi d=$baseLo- $baseThi ck/ 2
set baseDi v=$baseThi ck/ $di vs

set emi t t er Lo=$baseHi
set emi t t er Hi =$emi t t er Lo- $emi t t er Thi ck
set emi t t er Di v=$emi t t er Thi ck/ $di vs

set wi ndowLo=$emi t t er Hi
set wi ndowHi =$wi ndowLo- $wi ndowThi ck
set wi ndowDi v=$wi ndowThi ck/ $di vs

set capLo=$wi ndowHi
set capHi =$capLo- $capThi ck
#set capDi v=$capThi ck/ $di vs

set cont Lo=$capHi
set cont Hi =$cont Lo- $cont Thi ck
74
set cont Di v=$cont Thi ck/ $di vs

set l i ght Y=$emi t t er Hi - 5

mesh wi dt h=$wi dt h3d
## X- Mesh
x. mesh l oc=- $cel l Wi dt hHal f spac=$cel l Wi dt hDi v
x. mesh l oc=- $capWi dt h spac=$capWi dt hDi v
x. mesh l oc=$capWi dt h spac=$capWi dt hDi v
x. mesh l oc=$cel l Wi dt hHal f spac=$cel l Wi dt hDi v

## Y- Mesh
# Top cont act
y. mesh l oc=$cont Hi spac=0
y. mesh l oc=$cont Lo spac=0
# Cap
# Wi ndow
y. mesh l oc=$wi ndowHi spac=$wi ndowDi v
y. mesh l oc=$wi ndowLo spac=$wi ndowDi v
# Emi t t er
y. mesh l oc=$emi t t er Lo spac=$emi t t er Di v
# Base
y. mesh l oc=$baseMi d spac=$baseDi v
# BSF
y. mesh l oc=$bsf Hi spac=$bsf Di v
y. mesh l oc=$bsf Lo spac=$bsf Di v


## Regi ons
# Cap
#r egi on num=8 mat er i al =Vacuum x. mi n=- $capWi dt h x. max=$capWi dt h y. mi n=$cont Hi
y. max=$cont Lo
r egi on num=1 mat er i al =I nGaN x. mi n=- $capWi dt h x. max=$capWi dt h y. mi n=$capHi
y. max=$capLo x. comp=0. 57
r egi on num=2 mat er i al =Vacuum x. mi n=- $cel l Wi dt hHal f x. max=- $capWi dt h
y. mi n=$cont Hi y. max=$capLo
r egi on num=3 mat er i al =Vacuum x. mi n=$capWi dt h x. max=$cel l Wi dt hHal f y. mi n=$cont Hi
y. max=$capLo
# Wi ndow [ f or Ge cel l , use Al GaAs wi t h x. comp=0. 2]
r egi on num=4 mat er i al =I nGaN x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f
y. mi n=$wi ndowHi y. max=$wi ndowLo x. comp=0. 57

#r egi on num=4 mat er i al =Al GaAs x. comp=0. 2 x. mi n=- $cel l Wi dt hHal f
x. max=$cel l Wi dt hHal f y. mi n=$wi ndowHi y. max=$wi ndowLo
# Emi t t er
r egi on num=5 mat er i al =I nGaN x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f
y. mi n=$emi t t er Hi y. max=$emi t t er Lo x. comp=0. 57
# Base
r egi on num=6 mat er i al =I nGaN x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f
y. mi n=$baseHi y. max=$baseLo x. comp=0. 57
# BSF
r egi on num=7 mat er i al =I nGaN x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f
y. mi n=$bsf Hi y. max=$bsf Lo x. comp=0. 57

## El ect r odes [ f or I nGaP cel l , add cat hode ( gol d) and r emove cat hode
( conduct or ) ]
el ect r ode name=cat hode mat er i al =Gol d x. mi n=- $capWi dt h x. max=$capWi dt h
y. mi n=$cont Hi y. max=$cont Lo
#el ect r ode name=cat hode x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f
y. mi n=$wi ndowHi y. max=$wi ndowHi
el ect r ode name=anode x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f y. mi n=$bsf Lo
y. max=$bsf Lo
75

## Dopi ng [ f or I nGaP cel l , uncomment cap dopi ng]
# Cap
dopi ng uni f or mr egi on=1 n. t ype conc=$capDop
# Wi ndow
dopi ng uni f or mr egi on=4 n. t ype conc=$wi nDop
# Emi t t er
dopi ng uni f or mr egi on=5 n. t ype conc=$emi t Dop
# Base
dopi ng uni f or mr egi on=6 p. t ype conc=$baseDop
# BSF
dopi ng uni f or mr egi on=7 p. t ype conc=$bsf Dop

## Mat er i al pr oper t i es
# Opaque cont act [ comment out f or I nGaP cel l ]
#mat er i al r egi on=8 r eal . i ndex=1. 2 i mag. i ndex=1. 8
# Vacuum ( f or zer o r ef l ect i on) [ change t o mat ch wi ndow mat er i al ( I nGaP use
Vacuum_Al I nP) ]
# [ f or I nGaP cel l , comment out r egi on 1]
mat er i al r egi on=2 i ndex. f i l e=VacuumI n57Ga43N. opt
mat er i al r egi on=3 i ndex. f i l e=VacuumI n57Ga43N. opt
# GaAs

#I nGaN
mat er i al mat er i al =I nGaN EG300=1. 559 i ndex. f i l e=I n57Ga43N. opt

# Gol d
mat er i al mat er i al =Gol d r eal . i ndex=1. 2 i mag. i ndex=1. 8



## Model s [ I nGaP cel l , 1; GaAs cel l , 5&6; I nGaNAs cel l , 7]
model s r egi on=1 CONMOB
MODELS CHUANG CONMOB FLDMOB SRH OPTR PRI NT

## Li ght beams [ GaAs b1, 0. 55- 0. 75, 200 b2, 0. 75- 0. 88, 65] 0. 12- 2. 7, 50 [ 630, 825]
beam num=1 x. or i gi n=0 y. or i gi n=$l i ght Y angl e=90 back. r ef l
power . f i l e=Post J unct i on1. spec. t xt \
wavel . st ar t =0. 12 wavel . end=2. 4 wavel . num=50

st r uct out f i l e=Si ngl eCel l _webf . st r
#t onypl ot Si ngl eCel l _webf . st r

sol ve i ni t
met hod gummel newt on maxt r aps=10 i t l i mi t =25
sol ve b1=0. 9

## Get t i ng I sc f or I - V cur ve poi nt s
met hod newt on maxt r aps=10 i t l i mi t =100
sol ve b1=0. 95
ext r act name=" i sc" max( i . " cat hode" )
set i sc=$i sc*$wi dt h3d
set i 1=$i sc/ 10
set i 2=$i 1+$i sc/ 10
set i 3=$i 2+$i sc/ 10
set i 4=$i 3+$i sc/ 10
set i 5=$i 4+$i sc/ 10
set i 6=$i 5+$i sc/ 20
set i 7=$i 6+$i sc/ 20
set i 8=$i 7+$i sc/ 20
set i 9=$i 8+$i sc/ 20
set i 10=$i 9+$i sc/ 20
76
set i 11=$i 10+$i sc/ 40
set i 12=$i 11+$i sc/ 40
set i 13=$i 12+$i sc/ 40
set i 14=$i 13+$i sc/ 40
set i 15=$i 14+$i sc/ 40
set i 16=$i 15+$i sc/ 80
set i 17=$i 16+$i sc/ 80
set i 18=$i 17+$i sc/ 80
set i 19=$i 18+$i sc/ 80
set i 20=$i 19+$i sc/ 80
set i 21=$i 20+$i sc/ 80
set i 22=$i 21+$i sc/ 80
set i 23=$i 22+$i sc/ 80
set i 24=$i 23+$i sc/ 80
set i 25=$i 24+$i sc/ 80- 0. 00001
##

l og out f i l e=I n57Ga43N. l og

met hod newt on maxt r aps=10 i t l i mi t =100
sol ve b1=0. 95

cont act name=anode cur r ent
met hod newt on maxt r aps=10 i t l i mi t =100

## Pmax poi nt s [ I nGaP 18- 25; GaAs 15- 25; I nGaNAs 13- 25; Ge 11- 25]
sol ve i anode=- $i 25 b1=0. 95
sol ve i anode=- $i 24 b1=0. 95
sol ve i anode=- $i 23 b1=0. 95
sol ve i anode=- $i 22 b1=0. 95
sol ve i anode=- $i 21 b1=0. 95
sol ve i anode=- $i 20 b1=0. 95
sol ve i anode=- $i 19 b1=0. 95
sol ve i anode=- $i 18 b1=0. 95
sol ve i anode=- $i 17 b1=0. 95
sol ve i anode=- $i 16 b1=0. 95
sol ve i anode=- $i 15 b1=0. 95
sol ve i anode=- $i 14 b1=0. 95
sol ve i anode=- $i 13 b1=0. 95
sol ve i anode=- $i 12 b1=0. 95
sol ve i anode=- $i 11 b1=0. 95
sol ve i anode=- $i 10 b1=0. 95
sol ve i anode=- $i 9 b1=0. 95
sol ve i anode=- $i 8 b1=0. 95
sol ve i anode=- $i 7 b1=0. 95
sol ve i anode=- $i 6 b1=0. 95
sol ve i anode=- $i 5 b1=0. 95
sol ve i anode=- $i 4 b1=0. 95
sol ve i anode=- $i 3 b1=0. 95
sol ve i anode=- $i 2 b1=0. 95
sol ve i anode=- $i 1 b1=0. 95
##

sol ve i anode=0 b1=0. 95

l og of f
ext r act name=" i v" cur ve( v. " anode" , i . " cat hode" ) out f i l e=" I Vcur veI n57Ga43N. dat "
t onypl ot I Vcur veI n57Ga43N. dat

l og out f i l e=doneI n57Ga43N. l og
l og of f

77
C. THIRD JUNCTION: IN
0.68
GA
0.32
N, EG=1.31 EV
go at l as


set cel l Wi dt h=5. 000000e+002
set capWi dt hper cent =8. 000000e+000
set di vs=1. 000000e+001
set cont Thi ck=1. 000000e- 001
set capThi ck=3. 000000e- 001
set capDop=1. 000000e+020
set wi ndowThi ck=0. 01
set wi nDop=2. 15e17
set emi t t er Thi ck=0. 01
#changed emi t Dop f r om1e16 t o 1e20
set emi t Dop=1e16
set baseThi ck=3. 19467
#changed basDop f r om1e16 t o 1e20
set baseDop=1e16
set bsf Thi ck=0. 03533
set bsf Dop=2. 15e19

set cel l Wi dt hDi v=$cel l Wi dt h/ $di vs
set wi dt h3d=100e6/ $cel l Wi dt h
set capWi dt h=0. 01*$capWi dt hper cent *$cel l Wi dt h/ 2
set capWi dt hDi v=$capWi dt h/ ( $di vs/ 2)
set cel l Wi dt hHal f =$cel l Wi dt h/ 2

set bsf Lo=0
set bsf Hi =$bsf Lo- $bsf Thi ck
set bsf Di v=$bsf Thi ck/ $di vs

set baseLo=$bsf Hi
set baseHi =$baseLo- $baseThi ck
set baseMi d=$baseLo- $baseThi ck/ 2
set baseDi v=$baseThi ck/ $di vs

set emi t t er Lo=$baseHi
set emi t t er Hi =$emi t t er Lo- $emi t t er Thi ck
set emi t t er Di v=$emi t t er Thi ck/ $di vs

set wi ndowLo=$emi t t er Hi
set wi ndowHi =$wi ndowLo- $wi ndowThi ck
set wi ndowDi v=$wi ndowThi ck/ $di vs

set capLo=$wi ndowHi
set capHi =$capLo- $capThi ck
#set capDi v=$capThi ck/ $di vs

set cont Lo=$capHi
set cont Hi =$cont Lo- $cont Thi ck
set cont Di v=$cont Thi ck/ $di vs

set l i ght Y=$emi t t er Hi - 5

mesh wi dt h=$wi dt h3d
## X- Mesh
x. mesh l oc=- $cel l Wi dt hHal f spac=$cel l Wi dt hDi v
x. mesh l oc=- $capWi dt h spac=$capWi dt hDi v
x. mesh l oc=$capWi dt h spac=$capWi dt hDi v
x. mesh l oc=$cel l Wi dt hHal f spac=$cel l Wi dt hDi v
78

## Y- Mesh
# Top cont act
y. mesh l oc=$cont Hi spac=0
y. mesh l oc=$cont Lo spac=0
# Cap
# Wi ndow
y. mesh l oc=$wi ndowHi spac=$wi ndowDi v
y. mesh l oc=$wi ndowLo spac=$wi ndowDi v
# Emi t t er
y. mesh l oc=$emi t t er Lo spac=$emi t t er Di v
# Base
y. mesh l oc=$baseMi d spac=$baseDi v
# BSF
y. mesh l oc=$bsf Hi spac=$bsf Di v
y. mesh l oc=$bsf Lo spac=$bsf Di v


## Regi ons
# Cap
#r egi on num=8 mat er i al =Vacuum x. mi n=- $capWi dt h x. max=$capWi dt h y. mi n=$cont Hi
y. max=$cont Lo
r egi on num=1 mat er i al =I nGaN x. mi n=- $capWi dt h x. max=$capWi dt h y. mi n=$capHi
y. max=$capLo x. comp=0. 68
r egi on num=2 mat er i al =Vacuum x. mi n=- $cel l Wi dt hHal f x. max=- $capWi dt h
y. mi n=$cont Hi y. max=$capLo
r egi on num=3 mat er i al =Vacuum x. mi n=$capWi dt h x. max=$cel l Wi dt hHal f y. mi n=$cont Hi
y. max=$capLo
# Wi ndow [ f or Ge cel l , use Al GaAs wi t h x. comp=0. 2]
r egi on num=4 mat er i al =I nGaN x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f
y. mi n=$wi ndowHi y. max=$wi ndowLo x. comp=0. 68

#r egi on num=4 mat er i al =Al GaAs x. comp=0. 2 x. mi n=- $cel l Wi dt hHal f
x. max=$cel l Wi dt hHal f y. mi n=$wi ndowHi y. max=$wi ndowLo
# Emi t t er
r egi on num=5 mat er i al =I nGaN x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f
y. mi n=$emi t t er Hi y. max=$emi t t er Lo x. comp=0. 68
# Base
r egi on num=6 mat er i al =I nGaN x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f
y. mi n=$baseHi y. max=$baseLo x. comp=0. 68
# BSF
r egi on num=7 mat er i al =I nGaN x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f
y. mi n=$bsf Hi y. max=$bsf Lo x. comp=0. 68

## El ect r odes [ f or I nGaP cel l , add cat hode ( gol d) and r emove cat hode
( conduct or ) ]
el ect r ode name=cat hode mat er i al =Gol d x. mi n=- $capWi dt h x. max=$capWi dt h
y. mi n=$cont Hi y. max=$cont Lo
#el ect r ode name=cat hode x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f
y. mi n=$wi ndowHi y. max=$wi ndowHi
el ect r ode name=anode x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f y. mi n=$bsf Lo
y. max=$bsf Lo

## Dopi ng [ f or I nGaP cel l , uncomment cap dopi ng]
# Cap
dopi ng uni f or mr egi on=1 n. t ype conc=$capDop
# Wi ndow
dopi ng uni f or mr egi on=4 n. t ype conc=$wi nDop
# Emi t t er
dopi ng uni f or mr egi on=5 n. t ype conc=$emi t Dop
# Base
dopi ng uni f or mr egi on=6 p. t ype conc=$baseDop
79
# BSF
dopi ng uni f or mr egi on=7 p. t ype conc=$bsf Dop

## Mat er i al pr oper t i es
# Opaque cont act [ comment out f or I nGaP cel l ]
#mat er i al r egi on=8 r eal . i ndex=1. 2 i mag. i ndex=1. 8
# Vacuum( f or zer o r ef l ect i on)
mat er i al r egi on=2 i ndex. f i l e=VacuumI n68Ga32N. opt
mat er i al r egi on=3 i ndex. f i l e=VacuumI n68Ga32N. opt

#I nGaN
mat er i al mat er i al =I nGaN EG300=1. 3068 i ndex. f i l e=I n68Ga32N. opt

# Gol d
mat er i al mat er i al =Gol d r eal . i ndex=1. 2 i mag. i ndex=1. 8


## Model s [ I nGaP cel l , 1; GaAs cel l , 5&6; I nGaNAs cel l , 7]
model s r egi on=1 CONMOB
MODELS CONMOB FLDMOB SRH OPTR PRI NT

## Li ght beams [ GaAs b1, 0. 55- 0. 75, 200 b2, 0. 75- 0. 88, 65] 0. 12- 2. 7, 50 [ 630, 825]
beam num=1 x. or i gi n=0 y. or i gi n=$l i ght Y angl e=90 back. r ef l
power . f i l e=Post J unct i on2. spec. t xt \
wavel . st ar t =0. 12 wavel . end=2. 4 wavel . num=50

st r uct out f i l e=Si ngl eCel l _webf . st r
#t onypl ot Si ngl eCel l _webf . st r

sol ve i ni t
met hod gummel newt on maxt r aps=10 i t l i mi t =25
sol ve b1=0. 9

## Get t i ng I sc f or I - V cur ve poi nt s
met hod newt on maxt r aps=10 i t l i mi t =100
sol ve b1=0. 95
ext r act name=" i sc" max( i . " cat hode" )
set i sc=$i sc*$wi dt h3d
set i 1=$i sc/ 10
set i 2=$i 1+$i sc/ 10
set i 3=$i 2+$i sc/ 10
set i 4=$i 3+$i sc/ 10
set i 5=$i 4+$i sc/ 10
set i 6=$i 5+$i sc/ 20
set i 7=$i 6+$i sc/ 20
set i 8=$i 7+$i sc/ 20
set i 9=$i 8+$i sc/ 20
set i 10=$i 9+$i sc/ 20
set i 11=$i 10+$i sc/ 40
set i 12=$i 11+$i sc/ 40
set i 13=$i 12+$i sc/ 40
set i 14=$i 13+$i sc/ 40
set i 15=$i 14+$i sc/ 40
set i 16=$i 15+$i sc/ 80
set i 17=$i 16+$i sc/ 80
set i 18=$i 17+$i sc/ 80
set i 19=$i 18+$i sc/ 80
set i 20=$i 19+$i sc/ 80
set i 21=$i 20+$i sc/ 80
set i 22=$i 21+$i sc/ 80
set i 23=$i 22+$i sc/ 80
set i 24=$i 23+$i sc/ 80
80
set i 25=$i 24+$i sc/ 80- 0. 00001
##

l og out f i l e=I n68Ga32N. l og

met hod newt on maxt r aps=10 i t l i mi t =100
sol ve b1=0. 95

cont act name=anode cur r ent
met hod newt on maxt r aps=10 i t l i mi t =100

## Pmax poi nt s [ I nGaP 18- 25; GaAs 15- 25; I nGaNAs 13- 25; Ge 11- 25]
sol ve i anode=- $i 25 b1=0. 95
sol ve i anode=- $i 24 b1=0. 95
sol ve i anode=- $i 23 b1=0. 95
sol ve i anode=- $i 22 b1=0. 95
sol ve i anode=- $i 21 b1=0. 95
sol ve i anode=- $i 20 b1=0. 95
sol ve i anode=- $i 19 b1=0. 95
sol ve i anode=- $i 18 b1=0. 95
sol ve i anode=- $i 17 b1=0. 95
sol ve i anode=- $i 16 b1=0. 95
sol ve i anode=- $i 15 b1=0. 95
sol ve i anode=- $i 14 b1=0. 95
sol ve i anode=- $i 13 b1=0. 95
sol ve i anode=- $i 12 b1=0. 95
sol ve i anode=- $i 11 b1=0. 95
sol ve i anode=- $i 10 b1=0. 95
sol ve i anode=- $i 9 b1=0. 95
sol ve i anode=- $i 8 b1=0. 95
sol ve i anode=- $i 7 b1=0. 95
sol ve i anode=- $i 6 b1=0. 95
sol ve i anode=- $i 5 b1=0. 95
sol ve i anode=- $i 4 b1=0. 95
sol ve i anode=- $i 3 b1=0. 95
sol ve i anode=- $i 2 b1=0. 95
sol ve i anode=- $i 1 b1=0. 95
##

sol ve i anode=0 b1=0. 95

l og of f
ext r act name=" i v" cur ve( v. " anode" , i . " cat hode" ) out f i l e=" I Vcur veI n68Ga32N. dat "
t onypl ot I Vcur veI n68Ga32N. dat

l og out f i l e=doneI n68Ga32N. l og
l og of f


D. BOTTOM JUNCTION: IN
0.78
GA
0.22
N, EG=1.11 EV
go at l as


set cel l Wi dt h=5. 000000e+002
set capWi dt hper cent =8. 000000e+000
set di vs=1. 000000e+001
set cont Thi ck=1. 000000e- 001
set capThi ck=3. 000000e- 001
set capDop=1. 000000e+020
81
set wi ndowThi ck=0. 01
set wi nDop=2. 15e17
set emi t t er Thi ck=0. 01
#changed emi t Dop f r om1e16 t o 1e20
set emi t Dop=1e16
set baseThi ck=3. 19467
#changed basDop f r om1e16 t o 1e20
set baseDop=1e16
set bsf Thi ck=0. 03533
set bsf Dop=2. 15e19

set cel l Wi dt hDi v=$cel l Wi dt h/ $di vs
set wi dt h3d=100e6/ $cel l Wi dt h
set capWi dt h=0. 01*$capWi dt hper cent *$cel l Wi dt h/ 2
set capWi dt hDi v=$capWi dt h/ ( $di vs/ 2)
set cel l Wi dt hHal f =$cel l Wi dt h/ 2

set bsf Lo=0
set bsf Hi =$bsf Lo- $bsf Thi ck
set bsf Di v=$bsf Thi ck/ $di vs

set baseLo=$bsf Hi
set baseHi =$baseLo- $baseThi ck
set baseMi d=$baseLo- $baseThi ck/ 2
set baseDi v=$baseThi ck/ $di vs

set emi t t er Lo=$baseHi
set emi t t er Hi =$emi t t er Lo- $emi t t er Thi ck
set emi t t er Di v=$emi t t er Thi ck/ $di vs

set wi ndowLo=$emi t t er Hi
set wi ndowHi =$wi ndowLo- $wi ndowThi ck
set wi ndowDi v=$wi ndowThi ck/ $di vs

set capLo=$wi ndowHi
set capHi =$capLo- $capThi ck
#set capDi v=$capThi ck/ $di vs

set cont Lo=$capHi
set cont Hi =$cont Lo- $cont Thi ck
set cont Di v=$cont Thi ck/ $di vs

set l i ght Y=$emi t t er Hi - 5

mesh wi dt h=$wi dt h3d
## X- Mesh
x. mesh l oc=- $cel l Wi dt hHal f spac=$cel l Wi dt hDi v
x. mesh l oc=- $capWi dt h spac=$capWi dt hDi v
x. mesh l oc=$capWi dt h spac=$capWi dt hDi v
x. mesh l oc=$cel l Wi dt hHal f spac=$cel l Wi dt hDi v

## Y- Mesh
# Top cont act
y. mesh l oc=$cont Hi spac=0
y. mesh l oc=$cont Lo spac=0
# Cap
# Wi ndow
y. mesh l oc=$wi ndowHi spac=$wi ndowDi v
y. mesh l oc=$wi ndowLo spac=$wi ndowDi v
# Emi t t er
y. mesh l oc=$emi t t er Lo spac=$emi t t er Di v
# Base
82
y. mesh l oc=$baseMi d spac=$baseDi v
# BSF
y. mesh l oc=$bsf Hi spac=$bsf Di v
y. mesh l oc=$bsf Lo spac=$bsf Di v

## Regi ons
# Cap
#r egi on num=8 mat er i al =Vacuum x. mi n=- $capWi dt h x. max=$capWi dt h y. mi n=$cont Hi
y. max=$cont Lo
r egi on num=1 mat er i al =I nGaN x. mi n=- $capWi dt h x. max=$capWi dt h y. mi n=$capHi
y. max=$capLo x. comp=0. 78
r egi on num=2 mat er i al =Vacuum x. mi n=- $cel l Wi dt hHal f x. max=- $capWi dt h
y. mi n=$cont Hi y. max=$capLo
r egi on num=3 mat er i al =Vacuum x. mi n=$capWi dt h x. max=$cel l Wi dt hHal f y. mi n=$cont Hi
y. max=$capLo
# Wi ndow [ f or Ge cel l , use Al GaAs wi t h x. comp=0. 2]
r egi on num=4 mat er i al =I nGaN x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f
y. mi n=$wi ndowHi y. max=$wi ndowLo x. comp=0. 78

#r egi on num=4 mat er i al =Al GaAs x. comp=0. 2 x. mi n=- $cel l Wi dt hHal f
x. max=$cel l Wi dt hHal f y. mi n=$wi ndowHi y. max=$wi ndowLo
# Emi t t er
r egi on num=5 mat er i al =I nGaN x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f
y. mi n=$emi t t er Hi y. max=$emi t t er Lo x. comp=0. 78
# Base
r egi on num=6 mat er i al =I nGaN x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f
y. mi n=$baseHi y. max=$baseLo x. comp=0. 78
# BSF
r egi on num=7 mat er i al =I nGaN x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f
y. mi n=$bsf Hi y. max=$bsf Lo x. comp=0. 78

## El ect r odes [ f or I nGaP cel l , add cat hode ( gol d) and r emove cat hode
( conduct or ) ]
el ect r ode name=cat hode mat er i al =Gol d x. mi n=- $capWi dt h x. max=$capWi dt h
y. mi n=$cont Hi y. max=$cont Lo
#el ect r ode name=cat hode x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f
y. mi n=$wi ndowHi y. max=$wi ndowHi
el ect r ode name=anode x. mi n=- $cel l Wi dt hHal f x. max=$cel l Wi dt hHal f y. mi n=$bsf Lo
y. max=$bsf Lo

## Dopi ng [ f or I nGaP cel l , uncomment cap dopi ng]
# Cap
dopi ng uni f or mr egi on=1 n. t ype conc=$capDop
# Wi ndow
dopi ng uni f or mr egi on=4 n. t ype conc=$wi nDop
# Emi t t er
dopi ng uni f or mr egi on=5 n. t ype conc=$emi t Dop
# Base
dopi ng uni f or mr egi on=6 p. t ype conc=$baseDop
# BSF
dopi ng uni f or mr egi on=7 p. t ype conc=$bsf Dop

## Mat er i al pr oper t i es
# Opaque cont act [ comment out f or I nGaP cel l ]
#mat er i al r egi on=8 r eal . i ndex=1. 2 i mag. i ndex=1. 8
# Vacuum( f or zer o r ef l ect i on)
mat er i al r egi on=2 i ndex. f i l e=VacuumI nGa22N. opt
mat er i al r egi on=3 i ndex. f i l e=VacuumI nGa22N. opt

#I nGaN
mat er i al mat er i al =I nGaN EG300=1. 1076 i ndex. f i l e=I nGa22N. opt

83
# Gol d
mat er i al mat er i al =Gol d r eal . i ndex=1. 2 i mag. i ndex=1. 8



## Model s [ I nGaP cel l , 1; GaAs cel l , 5&6; I nGaNAs cel l , 7]
model s r egi on=1 CONMOB
MODELS CONMOB FLDMOB SRH OPTR PRI NT

## Li ght beams [ GaAs b1, 0. 55- 0. 75, 200 b2, 0. 75- 0. 88, 65] 0. 12- 2. 7, 50 [ 630, 825]
beam num=1 x. or i gi n=0 y. or i gi n=$l i ght Y angl e=90 back. r ef l
power . f i l e=Post J unct i on3. spec. t xt \
wavel . st ar t =0. 12 wavel . end=2. 4 wavel . num=50

st r uct out f i l e=Si ngl eCel l _webf . st r
#t onypl ot Si ngl eCel l _webf . st r

sol ve i ni t
met hod gummel newt on maxt r aps=10 i t l i mi t =25
sol ve b1=0. 9

## Get t i ng I sc f or I - V cur ve poi nt s
met hod newt on maxt r aps=10 i t l i mi t =100
sol ve b1=0. 95
ext r act name=" i sc" max( i . " cat hode" )
set i sc=$i sc*$wi dt h3d
set i 1=$i sc/ 10
set i 2=$i 1+$i sc/ 10
set i 3=$i 2+$i sc/ 10
set i 4=$i 3+$i sc/ 10
set i 5=$i 4+$i sc/ 10
set i 6=$i 5+$i sc/ 20
set i 7=$i 6+$i sc/ 20
set i 8=$i 7+$i sc/ 20
set i 9=$i 8+$i sc/ 20
set i 10=$i 9+$i sc/ 20
set i 11=$i 10+$i sc/ 40
set i 12=$i 11+$i sc/ 40
set i 13=$i 12+$i sc/ 40
set i 14=$i 13+$i sc/ 40
set i 15=$i 14+$i sc/ 40
set i 16=$i 15+$i sc/ 80
set i 17=$i 16+$i sc/ 80
set i 18=$i 17+$i sc/ 80
set i 19=$i 18+$i sc/ 80
set i 20=$i 19+$i sc/ 80
set i 21=$i 20+$i sc/ 80
set i 22=$i 21+$i sc/ 80
set i 23=$i 22+$i sc/ 80
set i 24=$i 23+$i sc/ 80
set i 25=$i 24+$i sc/ 80- 0. 00001
##

l og out f i l e=I n78Ga22N. l og

met hod newt on maxt r aps=10 i t l i mi t =100
sol ve b1=0. 95

cont act name=anode cur r ent
met hod newt on maxt r aps=10 i t l i mi t =100

## Pmax poi nt s [ I nGaP 18- 25; GaAs 15- 25; I nGaNAs 13- 25; Ge 11- 25]
84
sol ve i anode=- $i 25 b1=0. 95
sol ve i anode=- $i 24 b1=0. 95
sol ve i anode=- $i 23 b1=0. 95
sol ve i anode=- $i 22 b1=0. 95
sol ve i anode=- $i 21 b1=0. 95
sol ve i anode=- $i 20 b1=0. 95
sol ve i anode=- $i 19 b1=0. 95
sol ve i anode=- $i 18 b1=0. 95
sol ve i anode=- $i 17 b1=0. 95
sol ve i anode=- $i 16 b1=0. 95
sol ve i anode=- $i 15 b1=0. 95
sol ve i anode=- $i 14 b1=0. 95
sol ve i anode=- $i 13 b1=0. 95
sol ve i anode=- $i 12 b1=0. 95
sol ve i anode=- $i 11 b1=0. 95
sol ve i anode=- $i 10 b1=0. 95
sol ve i anode=- $i 9 b1=0. 95
sol ve i anode=- $i 8 b1=0. 95
sol ve i anode=- $i 7 b1=0. 95
sol ve i anode=- $i 6 b1=0. 95
sol ve i anode=- $i 5 b1=0. 95
sol ve i anode=- $i 4 b1=0. 95
sol ve i anode=- $i 3 b1=0. 95
sol ve i anode=- $i 2 b1=0. 95
sol ve i anode=- $i 1 b1=0. 95
##

sol ve i anode=0 b1=0. 95

l og of f
ext r act name=" i v" cur ve( v. " anode" , i . " cat hode" ) out f i l e=" I Vcur veI n78Ga22N. dat "
t onypl ot I Vcur veI n78Ga22N. dat

l og out f i l e=doneI n78Ga22N. l og
l og of f
85
APPENDIX B: MATLAB CODE
The Mat l ab code pr ovi ded i n t hi s appendi x pr ovi ded
auxi l i ar y suppor t i n t he i nt er pr et at i on and di spl ay Si vaco
At l as l og f i l es.
Or i gi nal code f or some of t he Mat l ab f unct i ons and
scr i pt s was obt ai ned f r om Mi chal opol ous [ 1] , Bat es, [ 2] ,
Gr een [ 3] , and Canf i el d [ 4] . Modi f i cat i ons t o t he code wer e
made t o suppor t t hi s t hesi s.
A. INDIUM GALLIUM NITRIDE BAND GAP CALCULATIONS
%I nGaN Bandgap cal cul at i ons
%Bal domer o Gar ci a
cl c;

%Const ant s

EgGaN=3. 42;
EgI nN=0. 77;
b=1. 43;
x=[ 0: 0. 0001: 1] ;
%x=. 67;
%I nConcent r at i on=x
%GaConcent r at i on=1- x

%For mul a f or f i ndi ng EgI nGaN
EgI nGaN=( ( 1- x) . *EgGaN) +( x. *EgI nN) - ( b. *x. *( 1- x) )

%For mul a f or f i ndi ng x
sol ve( ' ( ( ( 1- x) *EgGaN) +( x*EgI nN) - ( b*x*( 1- x) ) ) - EgI nGaN' , ' x' ) ;

%The ot her EgI nGaN t hat we' r e sol vi ng f or i s EgI nGaN=1. 1
%EgI nGaN=2. 095
%Gacomp=1- ( 1/ 2/ b*( EgGaN- EgI nN+b- ( EgGaN^2- 2*EgI nN*EgGaN-
2*b*EgGaN+EgI nN^2- 2*EgI nN*b+b^2+4*b*EgI nGaN) ^( 1/ 2) ) )
%I ncomp=( 1/ 2/ b*( EgGaN- EgI nN+b- ( EgGaN^2- 2*EgI nN*EgGaN-
2*b*EgGaN+EgI nN^2- 2*EgI nN*b+b^2+4*b*EgI nGaN) ^( 1/ 2) ) )

%Pl ot
pl ot ( x, EgI nGaN, ' b' ) ;
xl abel ( ' I ndi umconcent r at i on ( uni t l ess r at i o) ' ) ;
yl abel ( ' I nGaN Band Gap ( eV) ' ) ;
t i t l e( ' I ndi umconcent r at i on vs I nGaN Band Gap' ) ;

86
B. CONVERSION FROM DIELECTRIC CONSTANTS (EPSILONS) TO
REFRACTION COEFFICIENTS (N, K)
Opt i cal dat a needed t o be pr ovi ded n- k f or mat . Some of
t he dat a obt ai ned was avai l abl e i n epsi l on f or m. Ther ef or e,
a conver si on needed t o be made. Mi chal opoul os gener at ed t he
f unct i on bel ow [ 1] .

% E2NK Conver t t he e1, e2 pai r s i nt o n, k pai r s.
%[ n k] = E2NK( e1, e2)

%( c) 2001 by P. Mi chal opoul os

f unct i on [ n, k] = e2nk( e1, e2)

ap = ( e1 + sqr t ( e1. ^2 + e2. ^2) ) / 2;
an = ( e1 - sqr t ( e1. ^2 + e2. ^2) ) / 2;

app = ap >= 0;
anp = an >= 0;
er r = ( app < 0) & ( anp < 0) ;
er r = sum( er r ) ;
i f er r ~= 0
di sp( ' ERROR! ' )
end

a = ap . * app + an . * anp;

n = sqr t ( a) ;

k = e2 . / ( 2 * n) ;

C. CONVERSION FROM PHOTON ENERGY (EV) TO WAVELENGTH (UM)
Dat a was f ound i n phot on ener gy and wavel engt h f or m.
I n or der t o make compar i sons, conver si on f r om one f or m t o
anot her was necessar y. Funct i ons by Mi chal opoul os [ 1] ar e
gi ven bel ow.
% EV2UM Conver t s phot on ener gy ( eV) i nt o wavel engt h ( um) .

%( c) 2001 by P. Mi chal opoul os

f unct i on um= ev2um( ev)
87

h = 6. 6260755e- 34;
eV = 1. 60218e- 19;
c = 2. 99792458e8;

ev = ev * eV;
f = ev / h;
wavel = c . / f ;
um= wavel / 1e- 6;

% UM2EV Conver t s phot on wavel engt h ( um) i nt o ener gy ( eV) .

%( c) 2001 by P. Mi chal opoul os

f unct i on ev = um2ev( um)

h = 6. 6260755e- 34;
eV = 1. 60218e- 19;
c = 2. 99792458e8;

wavel = um* 1e- 6;
f = c . / wavel ;
ev = h * f ;
ev = ev . / eV;

D. IV CURVE PLOTS FOR INDIUM GALLIUM NITRIDE QUAD
JUNCTION SOLAR CELL
%Code modi f i ed f r omCanf i el d' s sour ce code
%Dat a obt ai ned f r oml og f i l es f r omI nGaN quad- j unct i on sol ar cel l
%Bal domer o Gar ci a
cl c;
%I n20Ga80N wi t h AM0 spect r um
cur r ent 1=[ 0. 0176131398 0. 0176031407 0. 0175505986 0. 0174980573
0. 0173929742 0. 0171728094 0. 0169526469 0. 0167324843
0. 0165123158 0. 0162921532 0. 0160719881 0. 0158518253
0. 0156316602 0. 0154114983 0. 0149711686 0. 0145308402
0. 0140905121 0. 0136501825 0. 0132098541 0. 0123291993
0. 0114485415 0. 0105678837 0. 0096872266 0. 0088065691
0. 0070452558 0. 0052839419 0. 0035226276 0. 0017613142 -
0. 0000000001] ;
vol t age1=[ 0. 0000000000 0. 2970913579 1. 1822462140 1. 5075176680
1. 7472436590 1. 8900757790 1. 9378145180 1. 9663764170
1. 9875670060 2. 0047710060 2. 0194136280 2. 0322369610
2. 0436835120 2. 0540360290 2. 0722008890 2. 0877645130
2. 1013319790 2. 1132957310 2. 1239292560 2. 1419700890
2. 1566166780 2. 1686629450 2. 1786938920 2. 1871519430
2. 2006132650 2. 2108811030 2. 2190289820 2. 2257052930
2. 2313181110] ;

%I n57Ga43N wi t h post j unct i on1 spect r um
88
cur r ent 2=[ 0. 0171128720 0. 0171028783 0. 0168989671 0. 0166850573
0. 0164711457 0. 0162572338 0. 0160433258 0. 0158294126
0. 0156155026 0. 0154015923 0. 0151876797 0. 0149737698
0. 0145459485 0. 0141181240 0. 0136903032 0. 0132624807
0. 0128346588 0. 0119790166 0. 0111233713 0. 0102677280
0. 0094120828 0. 0085564398 0. 0068451513 0. 0051338641
0. 0034225761 0. 0017112879 - 0. 0000000001] ;
vol t age2=[ 0. 0000000000 0. 1305081858 0. 8192581792 0. 9015131674
0. 9331338594 0. 9534997163 0. 9689573887 0. 9815965012
0. 9923675261 1. 0017892410 1. 0101786220 1. 0177449700
1. 0309568480 1. 0422028240 1. 0519502020 1. 0605082500
1. 0680958050 1. 0809744750 1. 0915085520 1. 1002972060
1. 1077533400 1. 1141715070 1. 1247003520 1. 1330384420
1. 1398643710 1. 1456000250 1. 1505207070] ;

%I n68Ga32N wi t h post j unct i on2 spect r um
cur r ent 3=[ 0. 0141231105 0. 0141131184 0. 0140298496 0. 0139465807
0. 0137700408 0. 0135935022 0. 0134169620 0. 0132404230
0. 0130638854 0. 0128873465 0. 0127108077 0. 0125342689
0. 0123577303 0. 0120046521 0. 0116515739 0. 0112984952
0. 0109454185 0. 0105923395 0. 0098861822 0. 0091800273
0. 0084738721 0. 0077677158 0. 0070615601 0. 0056492474
0. 0042369367 0. 0028246240 0. 0014123119 0. 0000000001] ;
vol t age3=[ 0. 0000000000 0. 1311096030 0. 5441673681 0. 6320277025
0. 6842499725 0. 7083967768 0. 7248954021 0. 7377135412
0. 7483143199 0. 7574074704 0. 7653951663 0. 7725296065
0. 7789805527 0. 7902824668 0. 7999460470 0. 8083630634
0. 8157932979 0. 8224203640 0. 8337763994 0. 8431914560
0. 8511524069 0. 8579918718 0. 8639469242 0. 8738573284
0. 8818299562 0. 8884345077 0. 8940340114 0. 8988707325] ;

%I n78Ga22N wi t h pot j unct i on3 spect r um
cur r ent 4=[ 0. 0128841840 0. 0128741794 0. 0127231275 0. 0125620760
0. 0124010228 0. 0122399704 0. 0120789198 0. 0119178658
0. 0117568129 0. 0115957622 0. 0114347108 0. 0112736577
0. 0109515531 0. 0106294488 0. 0103073439 0. 0099852400
0. 0096631342 0. 0090189240 0. 0083747191 0. 0077305090
0. 0070862990 0. 0064420895 0. 0051536706 0. 0038652545
0. 0025768364 0. 0012884183 - 0. 0000000001] ;
vol t age4=[ 0. 0000000000 0. 1078032006 0. 4688474643 0. 5100668879
0. 5309258388 0. 5454971566 0. 5569116230 0. 5663876299
0. 5745324881 0. 5816962863 0. 5881009992 0. 5938970077
0. 6040640671 0. 6127739225 0. 6203776540 0. 6271079482
0. 6331288820 0. 6434973415 0. 6521554853 0. 6595301586
0. 6659109540 0. 6715037308 0. 6808929507 0. 6885228391
0. 6948948317 0. 7003322584 0. 7050534598] ;

%Combi ned
cur r ent 5=[ 0 0. 001991 0. 004011 0. 006003 0. 007994 0. 01001
0. 01178 0. 01198 0. 0126 0. 01275 0. 01286 0. 0128841840] ;
vol t age5=[ 4. 9793 4. 9542 4. 9195 4. 8744 4. 8185 4. 7271 4. 5995
4. 5723 4. 4736 4. 3906 4. 0906 0] ;

P1=cur r ent 1. *vol t age1;
[ a b] =max( P1) ;
89
Pmax1=vol t age1( b) *cur r ent 1( b) ;
Voc1=max( vol t age1) ;
I sc1=max( cur r ent 1) ;
FF1=Pmax1/ ( Voc1*I sc1)
Ef f 1=100*Pmax1/ ( . 1353)

P2=cur r ent 2. *vol t age2;
[ c d] =max( P2) ;
Pmax2=vol t age2( d) *cur r ent 2( d) ;
Voc2=max( vol t age2) ;
I sc2=max( cur r ent 2) ;
FF2=Pmax2/ ( Voc2*I sc2)
Ef f 2=100*Pmax2/ ( . 1353)

P3=cur r ent 3. *vol t age3;
[ e f ] =max( P3) ;
Pmax3=vol t age3( f ) *cur r ent 3( f ) ;
Voc3=max( vol t age3) ;
I sc3=max( cur r ent 3) ;
FF3=Pmax3/ ( Voc3*I sc3)
Ef f 3=100*Pmax3/ ( . 1353)

P4=cur r ent 4. *vol t age4;
[ g h] =max( P4) ;
Pmax4=vol t age4( h) *cur r ent 4( h) ;
Voc4=max( vol t age4) ;
I sc4=max( cur r ent 4) ;
FF4=Pmax4/ ( Voc4*I sc4)
Ef f 4=100*Pmax4/ ( . 1353)

P5=cur r ent 5. *vol t age5;
[ k l ] =max( P5) ;
Pmax5=vol t age5( l ) *cur r ent 5( l ) ;
Voc5=max( vol t age5) ;
I sc5=max( cur r ent 5) ;
FF5=Pmax5/ ( Voc5*I sc5)
Ef f 5=100*Pmax5/ ( . 1353)

pl ot ( vol t age1, cur r ent 1, ' r ' ) ;
%gr i d on;
hol d on;
%pl ot ( vol t age1( b) , cur r ent 1( b) , ' o' ) ;
hol d on;
pl ot ( vol t age2, cur r ent 2, ' r ' ) ;
hol d on;
%pl ot ( vol t age2( d) , cur r ent 2( d) , ' o' ) ;
hol d on;
pl ot ( vol t age3, cur r ent 3, ' r ' ) ;
hol d on;
%pl ot ( vol t age3( f ) , cur r ent 3( f ) , ' o' ) ;
hol d on;
pl ot ( vol t age4, cur r ent 4, ' r ' ) ;
hol d on;
%pl ot ( vol t age4( h) , cur r ent 4( h) , ' o' ) ;
hol d on;
90
pl ot ( vol t age5, cur r ent 5, ' b' ) ;
hol d on;
pl ot ( vol t age5( l ) , cur r ent 5( l ) , ' or ' ) ;
hol d of f ;
xl abel ( ' Vol t age ( V) ' )
yl abel ( ' Cur r ent Densi t y ( A/ cm^2) ' )
t i t l e( ' Sol ar Cel l I V Cur ve' )
axi s( [ 0 5. 5 0 0. 020] )

E. AIR MASS ZERO PLOTS
Ai r Mass Zer o ( AM0) dat a was obt ai ned f r om NREL [ 19]
and pl ot t ed usi ng t he Mat l ab f unct i on pr ovi ded by
Mi chal opoul os [ 1] . I t was modi f i ed t o pr ovi de an addi t i onal
pl ot .

% AMSPECTRUMS Pl ot t he dat a cont ai ned i n spect r ums. mat
%Check t he sour ce code and uncomment t he r equi r ed l i nes.
%( c) 2001 by P. Mi chal opoul os
h = 6. 6260755e- 34;
eV = 1. 60218e- 19;
c = 2. 99792458e8;
l oad( ' Dat a\ spect r ums' )
pl ot ( AM0_wavel , AM0_i nt 1, ' b' , AM15a_wavel , AM15a_i nt 1, ' r ' ) , gr i d on
t i t l e( ' AM 0 and AM 1. 5 spect r a' ) , xl abel ( ' Wavel engt h [ um] ' ) ,
yl abel ( ' I r r adi ance [ W/ cm^2*um] ' )
axi s( [ 0 3 0 0. 23] )

The code above was modi f i ed t o di spl ay AM0 wi t h r espect
t o phot on ener gy and wavel engt h, r espect i vel y.
Fi gur e ( 1)
pl ot ( um, i r adi ance, ' r ' ) ;
xl abel ( ' Wavel engt h ( um) ' )
yl abel ( ' I r r adi ance W/ cm^2*um' )
t i t l e( ' AM0' )
axi s( [ 0 2. 5 0 0. 25] )
Fi gur e ( 2)
pl ot ( ev, i r adi ance, ' b' ) ;
xl abel ( ' Ener gy ( eV) ' )
yl abel ( ' I r r adi ance W/ cm^2um' )
t i t l e( ' AM0' )
axi s( [ 0 6. 0 0 0. 25] )
91
LIST OF REFERENCES
[ 1] P. Mi chal opoul ous, “A novel appr oach f or t he devel opment
and opt i mi zat i on of st at e- of - t he- ar t phot ovol t ai c
devi ces usi ng Si l vaco”, Mast er ’ s Thesi s, Naval
Post gr aduat e School , Mont er ey, Cal i f or ni a, 2002.
[ 2] A. D. Bat es, “Novel opt i mi zat i on t echni ques f or
mul t i j unct i on sol ar cel l desi gn usi ng Si l vaco At l as”,
Mast er ’ s Thesi s, Naval Post gr aduat e School , Mont er ey,
Cal i f or ni a, 2004.
[ 3] M. Gr een, “The ver i f i cat i on of Si l vaco as a sol ar cel l
si mul at i on t ool and t he desi gn and opt i mi zat i on of a
f our - j unct i on sol ar cel l ”, Mast er ’ s Thesi s, Naval
Post gr aduat e School , Mont er ey, Cal i f or ni a, 2003.
[ 4] B. J . Canf i el d, “Advanced model i ng of hi gh t emper at ur e
per f or mance of I ndi umGal l i umAr seni de
t her mophot ovol t ai c cel l s”, Mast er ’ s Thesi s, Naval
Post gr aduat e School , Mont er ey, Cal i f or ni a, 2005.
[ 5] A. S. Bouazzi , H. Hamzaoui , B. Rezi g, “Theor et i cal
possi bi l i t i es of I nGaN t andemPV st r uct ur es”, Solar
Energy Materials & Solar Cells, Vol . 87, 595- 603, 2004.
[ 6] S. M. Sze, Semiconductor Devices, 2nd edi t i on, J ohn
Wi l ey & Sons, I nc, 2001.
[ 7] Per i odi c t abl e of el ement s, 21 Mar ch 2007,
ht t p: / / www. nr c- cnr c. gc. ca/ st udent - sci ence- t ech/ .
[ 8] Si l i con at omi c st r uct ur e, 13 Mar ch 2007,
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95
INITIAL DISTRIBUTION LIST
1. Def ense Techni cal I nf or mat i on Cent er
Ft . Bel voi r , Vi r gi ni a

2. Dudl ey Knox Li br ar y
Naval Post gr aduat e School
Mont er ey, Cal i f or ni a

3. Sher i f Mi chael
Naval Post gr aduat e School
Mont er ey, Cal i f or ni a

4. Todd Weat her f or d
Naval Post gr aduat e School
Mont er ey, Cal i f or ni a

5. Wl adek Wal uki ewi cz
Lawr ence Ber kel ey Nat i onal Labor at or y
Ber kel ey, Cal i f or ni a

6. Pet r a Specht
Lawr ence Ber kel ey Nat i onal Labor at or y
Ber kel ey, Cal i f or ni a

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