Solar Energy: The Semiconductor - NPTEL · 2019. 2. 21. · Allowed energy and wave vectors of...
Transcript of Solar Energy: The Semiconductor - NPTEL · 2019. 2. 21. · Allowed energy and wave vectors of...
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Solar Energy:The Semiconductor
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Learning objectives:
1)To plot the band diagrams of materials2)To explain the interaction of bands with
radiation3)To understand the different ways in
which band diagrams can be plotted.
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Band gap Eg
Filled Valence Band
Overlapping bands: Metal
Partially filled bands: Metal
Band gap less than 2eV:
Semiconductor
Band gap greater than
2eV: Insulator
Filled Valence Band
Empty Conduction
Band
Empty Conduction
Band
Band gap Eg
(a) (b) (c) (d)
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Visible Spectrum Wavelength: 400 nm (violet) to 700 nm (red)
Corresponding band gaps: 3.1 eV to 1.8 eV
UV3%
Visible44%Infra Red
53%
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Band gap Eg
Filled Valence Band
Overlapping bands: Metal
Partially filled bands: Metal
Band gap less than 2eV:
Semiconductor
Band gap greater than
2eV: Insulator
Filled Valence Band
Empty Conduction
Band
Empty Conduction
Band
Band gap Eg
Visible Spectrum Wavelength: 400 nm (violet) to 700 nm (red)
Corresponding band gaps: 3.1 eV to 1.8 eV
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Filled Valence Band
Intrinsic semiconductor
Empty Conduction
Band
(a) (b) (c)
Filled Valence Band
n-type extrinsic semiconductor
Empty Conduction
Band
Filled Valence Band
p-type extrinsic semiconductor
Empty Conduction
Band
Ef
Ef
Ef
Acceptor LevelsDonor Levels
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Temperature
Ch
arge
car
rier
co
nce
ntr
atio
n
Extrinsic regime
Intrinsic regimeLow TemperatureCharge Carriersfrozen
Intrinsic semiconductorExtrinsic semiconductor
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2 2
2
h kE
m
l = ph
E = hn Planck
de Broglie
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Ene
rgy
Ek
0 π/a 2π/a 3π/a-3π/a -2π/a -π/a-4π/a 4π/a
Allowed energy and wave vectors of nearly free electrons
Brillouin zone boundaries
Brillouin zones and allowed
electron energy levels
identified, but interaction
between them not shown
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d
dSinq dSinq
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O A
B
S
S0
l
l
S
l
S0
l- = Hhkl
b1
b2
Ewald sphere
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Ene
rgy
Ek
0 π/a 2π/a 3π/a-3π/a -2π/a -π/a
Brillouin zone boundaries
Interaction between Brillouin
zones and allowed nearly free
electron energy levels –
Extended zone representation
E Vs k of nearly free electrons, without accounting for the Brillouin ZonesE Vs k of nearly free electrons, distorted due to interaction with Brillouin Zones
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Ene
rgy
Ek
0 π/a 2π/a 3π/a-3π/a -2π/a -π/a
Brillouin zone boundaries
Interaction between Brillouin
zones and allowed nearly free
electron energy levels –
Extended zone representation
E Vs k of nearly free electrons, without accounting for the Brillouin ZonesE Vs k of nearly free electrons, distorted due to interaction with Brillouin Zones
Resulting
flat band
diagrams
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Ene
rgy
Ek
0 π/a 2π/a 3π/a-3π/a -2π/a -π/a
Brillouin zone boundaries
Interaction between Brillouin
zones and allowed nearly free
electron energy levels –
Extended zone representation
E Vs k of nearly free electrons, without accounting for the Brillouin ZonesE Vs k of nearly free electrons, distorted due to interaction with Brillouin Zones
Resulting
flat band
diagrams
Ef
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Ene
rgy
E
k0 π/a 2π/a 3π/a-3π/a -2π/a -π/a
Brillouin zone boundaries
Interaction between Brillouin
zones and allowed nearly free
electron energy levels –
Repeated zone representation
E Vs k of nearly free electrons, without accounting for the Brillouin ZonesE Vs k of nearly free electrons, distorted due to interaction with Brillouin Zones
Corresponding
flat band
diagrams
Ef
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Ene
rgy
Ek
0 π/a 2π/a 3π/a-3π/a -2π/a -π/a
Brillouin zone boundaries
Interaction between
Brillouin zones and allowed
nearly free electron energy
levels – Reduced zone
representation
E Vs k of nearly free electrons, without accounting for the Brillouin ZonesE Vs k of nearly free electrons, distorted due to interaction with Brillouin Zones
Corresponding
flat band
diagrams
Ef
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Ene
rgy
E
k0 π/a-π/a
Corresponding flat band diagrams
Ene
rgy
E
k0 π/a-π/b
Corresponding flat band diagrams
EgEg
Direct bandgap semiconductor Indirect bandgap semiconductor
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Ene
rgy
E
k
Eg
Ph
oto
n
Phonon
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Conclusions:
1) There is significant variation in the band diagrams of different types of materials
2) Interaction of a material with radiation depends strongly on its band diagram
3) Visible spectrum is a small fraction of solar radiation4) There is a difference in the effectiveness with which
direct and indirect bandgap semiconductors interact with radiation
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Solar Energy:The p-n junction
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Learning objectives:
1)To describe the material features as well as characteristics of the p-n junction
2)To explain the functioning of the p-n junction
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Charge carrier concentration depends only temperature
Conductivity depends only on Temperature
Examples: Elemental: Group IV A: Si (1.1 eV), Ge (0.7 eV) Compound:
Group III A and Group V A (III-V) GaAs, InSb
Group II B and Group VI A (II-VI) CdS, ZnTe
Filled Valence Band
Intrinsic semiconductor
Empty Conduction
Band
Ef
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Filled Valence Band
p-type extrinsic semiconductor
Empty Conduction
Band
Ef
Acceptor Levels
Charge carrier concentration depends on dopant concentration
Conductivity depends on dopant concentration
Examples: Group IV A elements doped with small
quantities of Group III A elements: B, Al, Ga, In, Tl
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Filled Valence Band
n-type extrinsic semiconductor
Empty Conduction
Band
Ef
Donor Levels
Charge carrier concentration depends on dopant concentration
Conductivity depends on dopant concentration
Examples: Group IV A elements doped with small
quantities of Group V A elements: N, P, As, Sb, Bi
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Valence Band
Intrinsic semiconductor
Conduction Band
Ef
Hole in valence band
Electron in conduction band
𝐸𝑔 = ℎ𝑣 Stability of electron-hole pair?
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Metal
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The p-n junction
+ + + + + + +
+ + + + + + +
+ + + + + + +
+ + + + + + +
+ + + + + + +
+ + + + + + +
- - - - - - -
- - - - - - -
- - - - - - -
- - - - - - -
- - - - - - -
- - - - - - -
Si doped with B Si doped with P
𝜎 = 𝑛 𝑒 𝜇𝑒 + 𝑝 𝑒 𝜇ℎ
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The space charge regionDepletion region
+ + + + ++ +
+ + + + ++ +
+ + + + ++ +
- -- - - - -
- -- - - - -
- -- - - - -
+ + + + ++ +
+ + + + ++ +
+ + + + ++ +
- -- - - - -
- -- - - - -
- -- - - - -
𝐸
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space charge regiondepletion region
+ + + + ++ +
+ + + + ++ +
+ + + + ++ +
- -- - - - -
- -- - - - -
- -- - - - -
+
+
+
- - - -
- - - -
- - - -
- - -
- - -
- - -
++ +
++ +
++ +
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+ + + + ++ +
+ + + + ++ +
+ + + + ++ +
- -- - - - -
- -- - - - -
- -- - - - -
+ + +
+ + +
+ + +
- - -
- - -
- - -
+ + + +
+ + + +
+ + + +
-
-
-
space charge regiondepletion region
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EVac
EC
EFp
EV
EC
EFn
EV
EFi EFi
p- type n- type
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EVac
EC
EFp
EV
EC
EFn
EV
EFi
EFi
pn-junction
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EVac
EC
EFp
EV
EC
EFn
EV
EFi
EFi
pn-junction
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The space charge region
+ + + + ++ +
+ + + + ++ +
+ + + + ++ +
- -- - - - -
- -- - - - -
- -- - - - -
Charge density 𝜌
𝜌
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The space charge region
+ + + + ++ +
+ + + + ++ +
+ + + + ++ +
- -- - - - -
- -- - - - -
- -- - - - -
𝜕𝐸
𝜕𝑥=𝜌
𝜀
𝐸
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𝜕2𝑉
𝜕𝑥2= −
𝜌
𝜀
The space charge region
+ + + + ++ +
+ + + + ++ +
+ + + + ++ +
- -- - - - -
- -- - - - -
- -- - - - -
𝜕𝑉
𝜕𝑥= −𝐸
𝑉
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𝜌
𝐸
𝑉
𝜕𝐸
𝜕𝑥=𝜌
𝜀
𝜕2𝑉
𝜕𝑥2= −
𝜌
𝜀
𝜕𝑉
𝜕𝑥= −𝐸
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Forward bias
+ + + + ++ +
+ + + + ++ +
+ + + + ++ +
- -- - - - -
- -- - - - -
- -- - - - -
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Forward bias
+ + + + ++ +
+ + + + ++ +
+ + + + ++ +
-- - - - - -
-- - - - - -
-- - - - - -
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Reverse bias
+ + + + ++ +
+ + + + ++ +
+ + + + ++ +
- -- - - - -
- -- - - - -
- -- - - - -
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Reverse bias
+ + + +++ +
+ + + +++ +
+ + + +++ +
- --- - - -
- --- - - -
- --- - - -
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I-V characteristics
I
V
Forward biasReverse bias
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Conclusions:
1) A p-n junction can be formed using appropriately doped materials that are processed carefully
2) Charge, Field and Potential depend on the location in a p-n junction
3) A p-n junction has interesting I-V characteristics
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I-V characteristics
I
V
Forward biasReverse bias
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Solar Cell:Growing the single crystal
and making the p-n junction
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Learning objectives:
1)To become familiar with the techniques used to make single crystal as well as amorphous Si
2)To understand the method to manufacture the p-n junction
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Czochralski process
Float Zone process
Zone refining
Cutting wafers
Amorphous Si
Manufacturing p-n junctions
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A
(a) (b)
(c) (d)
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Quartzite(relatively pure sand)
Metallurgical Grade Silicon (MGS)
Metallurgical Grade Silicon (MGS)98% purity
Electronic Grade Silicon (EGS)ppm (C, O) to ppb (metals)
Si (solid) + 3HCl SiHCl3 (gas) + H2
Si converted to Trichlorosilane, which is purified and reduced back to Si
SiO2 + Coke + Heat
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Molten Silicon(Melting point 1414 oC)
Heating coilsRF currentsInduction1425 oC
Rotating Chuck
Quartz Crucible
GrowingCrystal
SeedCrystal
Czochralski process
200-300mm
25 mm/hrSemiconductor grade SiliconQuartz (SiO2) crucible (1670 oC)Inert atmosphere of ArB or P added before melting
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Introduction of seed crystal
Melting of polycrystalline
Silicon and adding of dopants
Growth of crystal
Completed crystal
Czochralski process
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Float zone process
Polycrystalline Si rod
Molten Zone
Moving Heating coils
Upper chuck
Lower chuck
SeedCrystal
Ar Smaller diameter
(150mm) due to surface tension
Higher purity
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Zone refining
Composition % B
Tem
per
atu
re
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Inner diameter slicing of Si ingot
Diamond cutting edge
Silicon ingot
Sliced wafer
Can produce one wafer at a timeWire saw uses fast moving thin wire with abrasive slurry, can cut several wafers at the same time
Silicon wafers are 0.2 to 0.75 mm thick
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p{100)
n{111}
P{111}
n{100}
Notches typically used to indicate orientation and doping
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Amorphous Si
CVD process
Has dangling bonds (defects)
Hydrogenated amorphous Silicon, a-Si:H by deposition from Silane gas SiH4
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p-n junction
Ion implantation: Low temperature process, ionized dopants accelerated using electric fields. Annealing required
Diffusion: Vapour phase deposition followed by high temperature diffusion
Epitaxy: Under high vacuum, gaseous elements condense on substrate wafer
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Conclusions:
1) It is quite challenging to produce single crystal Si2) Multiple process steps involved 3) Purity and dimensions can have significant impact
on costs4) Amorphous Si is an option
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Solar Energy:Interaction of p-n junction
with radiation
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Learning objectives:
1)To describe the interaction of a p-n junction with radiation
2)To explain the functioning of the p-n junction solar cell
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Forward bias
+ + + + ++ +
+ + + + ++ +
+ + + + ++ +
- -- - - - -
- -- - - - -
- -- - - - -
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𝜌
𝐸
𝑉
𝜕𝐸
𝜕𝑥=𝜌
𝜀
𝜕2𝑉
𝜕𝑥2= −
𝜌
𝜀
𝜕𝑉
𝜕𝑥= −𝐸
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Forward bias
+ + + + ++ +
+ + + + ++ +
+ + + + ++ +
-- - - - - -
-- - - - - -
-- - - - - -
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Reverse bias
+ + + + ++ +
+ + + + ++ +
+ + + + ++ +
- -- - - - -
- -- - - - -
- -- - - - -
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Reverse bias
+ + + +++ +
+ + + +++ +
+ + + +++ +
- --- - - -
- --- - - -
- --- - - -
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I-V characteristics
I
V
Forward biasReverse bias
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EC
EFp
EV
EC
EFn
EV
EFi
EFi
pn-junction
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EVac
EC
EFp
EV
EC
EFn
EV
EFi
EFi
pn-junction
Incoming Solar Radiation
- --
- --
++ +
++ +
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EVac
EC
EFp
EV
EC
EFn
EV
EFi
EFi
pn-junction
Incoming Solar Radiation
- --- --
++ +++ +
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EVac
EC
EFp
EV
EC
EFn
EV
EFi
EFi
pn-junction
Incoming Solar Radiation
- --- --
++ +++ +
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EVac
EC
EFp
EV
EC
EFn
EV
EFi
EFi
pn-junction
Incoming Solar Radiation
- --- --
++ +++ +
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EVac
EC
EFp
EV
EC
EFn
EV
EFi
EFi
pn-junction
Incoming Solar Radiation
- --- --
++ +++ +
Need to minimize recombinationEffect of DefectsSingle Crystalline SiPolycrystalline SiAmorphous Si Trade off between cost and efficiency
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Solar Cell is a current source
Charge carriers created by sunlight received: Photocurrent Iph
Without external load, the pn junction is forward biased, and internally shorts
Iph
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RL
RL
RS
Iph
Iph Iph
RL
RS
RShIph
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Conclusions:
1)The p-n junction stabilizes the electron-hole pair
2)The p-n junction solar cell is a current source and has to be used accordingly
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Solar Energy:Solar cell characteristics
and usage
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Learning objectives:
1)To determine the operational characteristics of a p-n junction based solar cell
2)To understand the best way to use the solar cell
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I-V characteristics
I
V
Forward biasReverse bias
𝐼𝑑 = 𝐼0(𝑒𝑞𝑉𝑑𝛾𝑘𝑇 − 1)
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RL
RS
RShIph
(Assuming recombination current is low)𝐼𝑝ℎ − 𝐼𝑑 = 𝐼𝐿
𝐼𝑑 = 𝐼0(𝑒𝑞𝑉𝑑𝛾𝑘𝑇 − 1)
𝑉𝑑 = 𝑉𝐿 + 𝐼𝐿𝑅𝑆
𝑉𝐿 =𝛾𝑘𝑇
𝑞ln
𝐼𝑝ℎ − 𝐼𝐿
𝐼0+ 1 − 𝐼𝐿𝑅𝑆
𝐼𝑝ℎ − 𝐼𝑑 − 𝐼𝑆ℎ = 𝐼𝐿
𝐼𝐿 = 𝐼𝑝ℎ − 𝐼0 𝑒𝑞(𝑉𝐿+𝐼𝐿𝑅𝑆)
𝛾𝑘𝑇 − 1 −𝑉𝐿 + 𝐼𝐿𝑅𝑆
𝑅𝑆ℎ
𝑉𝑂𝐶 =𝛾𝑘𝑇
𝑞ln
𝐼𝑝ℎ
𝐼0+ 1
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I-V characteristics
IL
VL
Isc
Voc
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I-V characteristics
IL
VL
Isc
Voc
Maximum Power Point
𝐹𝑖𝑙𝑙 𝐹𝑎𝑐𝑡𝑜𝑟 =𝑉𝑀𝑃𝑃 × 𝐼𝑀𝑃𝑃
𝑉𝑂𝐶 × 𝐼𝑆𝐶
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I-V characteristics
IL
VL
Isc
Voc
Comparing Solar Panels
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I-V characteristics
IL
VL
Isc
Voc
Variation with Sunlight
𝑉𝑂𝐶 =𝛾𝑘𝑇
𝑞ln
𝐼𝑝ℎ
𝐼0+ 1
𝐼𝑝ℎDepends linearly on incident sunlight
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I-V characteristics
IL
VL
Isc
Voc
AgingRL
RS
RShIph
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Conclusions:
1)The solar cell is a current source2)I- V relationship is complicated3)OCV is not the most important parameter4)Fill factor of a solar cell is important5)Solar cell must be coupled with an end
use that utilizes the MPP
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Solar Energy:Solar cell construction
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Learning objectives:
1)To describe how solar cells are constructed2)To indicate the limitations of single junction
solar cells3)To describe the functioning of tandem solar
cells
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Shockley-Quiesser limit
Air Mass Coefficient: Optical path length relative to path length vertically upward AM 1.5 typically used for evaluating panels
In unconcentrated, AM 1.5 Solar radiation with a band gap of 1.34 eV, 33.4 % efficiency is obtained
Si, 1.1 eV, 32 % efficiency is the best. Practically 24% accomplished
Blackbody radiation 7% (At room T, actual T~ 75 oC)Recombination losses 10% Spectrum losses 19% unabsorbed, 33% excess n, total 52%
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Negative terminal
Positive terminal
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Negative terminal
Positive terminal
Anti-reflective coatings necessary
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Negative terminal
Positive terminal
Single crystalline: 25%Poly crystalline: 15%Amorphous: 5%
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Low bandgap cell
High bandgap cell
Tandem Cells
With several tandem cells and concentrated sunlight, theoretically > 80% efficiency possible
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Visible Spectrum Wavelength: 400 nm (violet) to 700 nm (red)
Corresponding band gaps: 3.1 eV to 1.8 eV
PbS, a direct bandgap semiconductor
Bandgap of bulk PbS: 0.41 eV (3020 nm)Bandgap of nanocrystalline PbS: Can be varied to 4.0 eV
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Conclusions:
1)Parts of a solar cell are designed to increase the efficiency of the solar cell
2)Shockley-Quiesser limit indicates the limitation of a single junction solar cell
3)Tandem solar cells can overcome these limitations