1. Lecture 4
Solar Cells: Theory I

2. Lecture 4. Solar cells: Motivation (examples) and Theory
pn junctions under illumination
Homojunctions
Open-circuit voltage, short-
circuit current
IV curve, fill factor, solar-to-
electric conversion efficiency
Carrier generation and
recombination
Defects and minority carrier
diffusion
Current due to minority carrier
diffusion:
Solution to the diffusion
differential equation under
Spatially-homogeneous
generation, and
under Inhomogeneous
generation
Effect of an electric field
Heterojunctions

4. Celdas Solares

7. LA TECNOLOGIA FOTOVOLTAICA ESTA
CONTEMPLADA PARA APLICACIÓN
AUTONAMA. ELECTRIFICACION RURAL,
BOMBEO DE AGUA, ILUMINACION DE
CARRATERAS, MONITOREO DE NIVELS DE
AGUA EN RIOS ETC. SON ALGUNOS
EJEMPLOS
ESTA TECNOLOGIA CONVIERTE LA
ENERGIA SOLAR DIRECTO A ENERGIA
ELECTRICA DC UTILIZABDO MODULOS
FOTOVOLTAICOS (CELDAS SOLARES)
EL MATERIAL DE CONSTRUCCION DE
CELDA SOLAR SE LLAMA
“SEMICONDUCTOR”

16. Example: PV-Roof and Front,
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17. Alwitra Solar-foil
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18. Example: Sports-Center Tübingen
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19. Example:
Fire-brigade
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20. Example: BP Showcase
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21. Crystalline Silicon
• Polycrystalline Si
– Made from melting Si into ingots, slicing off
wafers
– Cell efficiencies of 14% - 15%
– Widest use
• Monocrystalline Si
– “Grown” crystals, more uniform structure
– Higher cell efficiencies (17% - 22%)
– Higher cost and better space utilization
• Most often manufactured in framed modules

22. Amorphous Thin-Film Si
• Si solution layered onto various
substrates
• Conversion efficiencies of 9% to
12%
• Some framed module products,
others bonded to flexible roofing
materials
• Very uniform appearance, but less
effective space utilization
• Less costly to produce than
crystalline modules

23. Building Integrated PV
• Roof tile replacements
• Solar glass
• Thin film bonded to single-ply membrane
roofing material

24. Solar-roof shingle
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26. 25 m2

28. 300 m2

31. Concentrating Solar Panels
• Fresnel lenses in tracking panels concentrate
light 500:1 on smaller amount of Si (Xerox
PARC Research)
• Tracking mirrors focus sunlight on stationary Si
(Energy Innovations “Sunflower”)

32. Energía Fotovoltaica
Efecto Fotovoltaico
LUZ SOLAR
El Efecto Fotovoltaico (FV):
es la generación de un voltaje en
las terminales de un captador
solar cuando éste es iluminado. Si CELDA
a las terminales del captador se le SOLAR
conecta un aparato eléctrico, por
ejemplo, un foco, entonces el foco
se enciende debido a la corriente Voltaje fotogenerado
eléctrica que circula por él. Esta es
la evidencia física del fenómeno
fotovoltaico.
Corriente eléctrica fotogenerada

33. History
• 1839: Discovery of the photoelectric effect
by Bequerel
• 1873: Discovery of the photoelectric effect
of Selen (change of electrical resistance)
• 1954: First Silicon Solar Cell as a result of
the upcoming semiconductor technology (
= 5 %)
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35. energy-states in solids:
Band-Pattern
Atom Molecule/Solid
• • • • • • • •
energy-states
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36. energy-states in solids:
Insulator
electron-energy
conduction-band
Fermi- bandgap EG
level EF (> 5 eV)
valence-band
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37. energy-states in solids :
metal / conductor
electron-energy
Fermi-
level EF
conduction-band
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38. energy-states in solids:
semiconductor
electron-energy
conduction-band
Fermi- bandgap EG
level EF ( 0,5 – 2 eV)
valence-band
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39. energy-states in solids:
energy absorption and emission
electron-energy
conduction-band
- x
-
EF h
h
+ x
+
Generation Recombination
valence-band
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40. doping of semiconductors
In order to avoid recombination of photo-induced charges and to „extract“
their energy to an electric-device we need a kind of internal barrier. This can
be achieved by doping of semiconductors:
IIIB IVB VB
„Doping“ means in this case the replacement of
original atoms of the semiconductor by different ones 5
(with slightly different electron configuration). B
Semiconductors like Silicon have four covalent 14 15
electrons, doping is done e.g. with Boron or Si P
Phosphorus:
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41. N - Doping
crystal view energy-band view
conduction-band
Si Si Si
-
- - - - - - majority carriers
P+ P+ P+ P+ P+
Si Si+
P Si EF
Donator level
Si Si Si
n-conducting Silicon
valence-band
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42. P - Doping
crystal energy-band view
conduction band
Si Si +
Si
Si B
Si- + Si EF Acceptor level
B- B- B- B- B-
+ + + + + majority carriers
Si Si Si
p-conducting Silicon valence-band
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43. p/n-junction without light
Band pattern view
depletion-zone
Diffusion
-
Ud - - - - -
P+ P+ P+ P+ P+ EF
B- B- B- B- B-
+ + + + +
+
Diffusion
Ed
+ - p – type region
n – type region internal electrical field
Clemson Summer School
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44. irradiated p/n-junction
band pattern view (absorption p-zone)
E = h depletion-zone
photocurrent
-
Ud - - - - -
P+ P+ P+ P+ P+ EF
B- B- B- B- B-
+ + + + +
+
Ed
+ - p–type region
n–type region Internal electrical field
Clemson Summer School
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45. p/n–junction with irradiation
crystal view
h
+
+ + + + + + + + + + + +
+
- + + + + + + + + + + + +
+ p-Silizium
-
+ + + + + + + + + + + +
+
diffusion
+ - - + + + + + + + + +- +-
+ + - - - - - - - -
+ - - - - - - - -
- + + + + + + + + +- +- +- E electrical field
- -
- - - - - - - - - - - -
- n-Silizium
- - -- - - - - - - - - -
- - - - - - - - - - - - depletion zone
-
Clemson Summer School
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46. The real Silicon Solar-cell
Front-contact
-
Antireflection- h n-region
coating
p-region
~0,2µm + + + + + + + + + + +
- - - - - - - - - -
~300µm
depletion zone
Backside contact
Clemson Summer School
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53. Practical Considerations

55. This is for an “ideal cell”.
In reality, there are other effects which can
often be accounted for by introduction of a
multiplier “A” (larger than 1) in front of the kT/q
term on the right.

62. Next we calculate the light-generated
short circuit current for using the
relevant differential equations.
Consider the p-region where the
minority carriers are electrons.
Also assume that the minority current
is diffusion-dominated.

64. We now solve this differential
equation under various boundary
conditions:
1)uniform generation, semi-infinite
geometry
2) generation decaying exponentially
with position, semi-infinite geometry
3)uniform generation, finite thickness
4)generation decaying exponentially
with position, finite thickness

65. n=0
x=0 x
N P

74. Heterojunctions

76. Efficiency Losses in Solar Cell
1 = Thermalization loss
2 and 3 = Junction and contact voltage loss
4 = Recombination loss

80. Clemson Summer School
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