Solar Cells
Solar cell device physics (2)
Prof. Richard R. King
Solar Cells
EEE 565
Arizona State University
‹#›
h =
Iinc
Voc
Jsc
FF
h = solar cell efficiency (unitless)
Voc = open-circuit voltage (V)
Jsc = short-circuit current (A/cm2)
FF = fill factor (unitless)
Iinc = incident light intensity (W/cm2)
Voc
Solar Cell Efficiency
‹#›
How is the open-circuit voltage Voc related to bandgap Eg ?
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Energy Transitions in
Semiconductors
Note:
Since this is an electron energy band diagram:
Something good to know about band diagrams:
Electron energy increases in upward direction
Electric potential φ increases in downward direction
EC
EV
hn
Eg
EFC = -qφn
qV
EFV = -qφp
V = voltage of solar cell
= quasi-Fermi level splitting
= φp - φn
E
φ
‹#›
EC
EV
hn
Eg
EFC = -qφn
qV
EFV = -qφp
V = voltage of solar cell
= quasi-Fermi level splitting
= φp - φn
Energy Transitions in
Semiconductors
E
φ
‹#›
EC
EV
hn
Eg
EFC = -qφn
qV
EFV = -qφp
V = voltage of solar cell
= quasi-Fermi level splitting
= φp - φn
Energy Transitions in
Semiconductors
E
φ
→
‹#›
EC
EV
hn
Eg
EFC = -qφn
qV
EFV = -qφp
V = voltage of solar cell
= quasi-Fermi level splitting
= φp - φn
Energy Transitions in
Semiconductors
E
φ
→
→
‹#›
Voltage depends on non-equilibrium concentrations of electrons and holes
Bandgap-voltage offset (Eg/q) – V is a useful parameter for gauging solar cell quality, especially when dealing with semiconductors of many different bandgaps
Basically a measure of how close electron and hole quasi-Fermi levels are to conduction and valence band edges
Solar Cell Voltage
Bandgap-voltage offset formulation
Standard formulation
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How is the open-circuit voltage Voc related to bandgap Eg ?
Surprising constancy of bandgap-voltage offset
Woc ≡ (Eg/q) - Voc
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Experimental and Theoretical Bandgap-Voltage Offset Woc
Bandgap-voltage offset at open circuit = Woc ≡ (Eg /q) – Voc lower is better
Difference between bandgap and quasi-Fermi level splitting strikingly similar across wide range of III-V, group-IV, II-VI, I-III-VI, and other semiconductors
R. R. King et al., Prog. in PV, doi: 10.1002/pip.1044 (2010)
‹#›
Solar Cell Efficiency
h =
Iinc
Voc
Jsc
FF
h = solar cell efficiency (unitless)
Voc = open-circuit voltage (V)
Jsc = short-circuit current (A/cm2)
FF = fill factor (unitless)
Iinc = incident light intensity (W/cm2)
Iinc
‹#›
Standard Solar Spectra
AM0 – Extraterrestrial solar spectrum
AM1.5G – Global solar spectrum, for flat plate panels
AM1.5D – Direct solar spectrum, for concentrators
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Standard Solar Spectra
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Standard Solar Spectra
‹#›
h =
Iinc
Voc
Jsc
FF
h = solar cell efficiency (unitless)
Voc = open-circuit voltage (V)
Jsc = short-circuit current (A/cm2)
FF = fill factor (unitless)
Iinc = incident light intensity (W/cm2)
Jsc
Solar Cell Efficiency
‹#›
External quantum efficiency (EQE) =
Find short circuit current density of a solar cell by integrating:
Quantum efficiency QE(E) as a function of photon energy E
Weighted by the incident spectral photon flux per unit energy
Over all photon energies 0 to ∞
Short-Circuit Current Density Jsc
Quantum efficiency of subcells in a 3-junction solar cell, with solar spectra
‹#›
Jph of solar cell is the sum of current densities coming from each component of cell:
Base quasi-neutral region
Space-charge region
Emitter quasi-neutral region
Integrate over wavelength, weighted by incident spectrum, to get Jph
Current is collected by diffusion in the quasi-neutral base and emitter regions, and by drift in the space-charge region (SCR)
Base diffusion current typically dominates; emitter and SCR are thin
Window should be included in AR coating design
Small amounts of photogenerated current can come from window, BSF
AR coating
window (n-type)
emitter
quasi-neutral region
(n-type)
back-surface field (BSF) (p-type)
p-side tunnel junction
emitter
space-charge region
base
space-charge region
base
quasi-neutral region
(p-type)
n-side tunnel junction
photogenerated current density
hn
Current Components in
Solar Cells
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AR coating
window (n-type)
emitter
quasi-neutral region
(n-type)
back-surface field (BSF) (p-type)
p-side tunnel junction
emitter
space-charge region
base
space-charge region
base
quasi-neutral region
(p-type)
n-side tunnel junction
photogenerated current density per unit cell thickness
hn
Ref.: H. J. Hovel, Solar Cells, in R. K. Willardson and A. C. Beer, Eds., Semiconductors and Semimetals, Vol. 11, Academic, New York, 1975.
xj
W
H'
Current Components in
Solar Cells
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Anti-reflection (AR) coatings
Coating must not damage semiconductor surface
Coatings must be broad-band
Coatings must not degrade
For ideal two-layer coat: n1n2 = n3n0 and thickness = λ/4
Heterojunction surface layers, adhesives, and coverglasses must be considered when designing coatings
Losses are greater for non-normal incidence of radiation
For high-efficiency cells, multilayer coatings make sense
Courtesy S. Kurtz and D. Friedman
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Multilayer anti-reflection coatings
More layers give wider and deeper minimum
Courtesy S. Kurtz and D. Friedman
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0.0
0.5
1.0
1.5
2.0
0.6 1 1.4 1.8 2.2
Band Gap E
g
(eV)
E
g
/q, V
oc
, and (E
g
/q) - V
oc
(V)
measured Voc
meas. Eg from EQE
Woc = (Eg/q) - Voc
radiative recomb. only
detailed balance model
d-AlGaInP
GaAs
1.4 - eV GaInAs
o-GaInP
AlGaInAs d-AlGaInP d-GaInP
d-AlGaInP0.97-eV GaInAs
GaInNAs
1.10-eV GaInAs1.24-eV GaInAs1.30-eV GaInAs
Ge (indirect gap)
AlGaInAs
V
oc
and band gap-voltage offset W
oc
= (E
g
/q) - V
oc
of solar cells with wide range of band gaps
Si (indirect gap)
0.79-eV GaInAs
0
0.5
1
1.5
2
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
Wavelength (nm)
Intensity per Unit Wavelength =
Spectral Irradiance (W/m
2 .
nm)
AM0, ASTM E490-00a, 1366.1 W/m2
AM1.5G, ASTM E892-87, 1000 W/m2
AM1.5D, ASTM G173-03, 1000 W/m2
0
0.5
1
1.5
2
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
Wavelength (nm)
Intensity per Unit Wavelength =
Spectral Irradiance (W/m
2 .
nm)
AM0, ASTM E490-00a, 1366.1 W/m2
AM1.5G, ASTM E892-87, 1000 W/m2
AM1.5D, ASTM G173-03, 1000 W/m2
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
Wavelength (nm)
Current Density per Unit Wavelength
(mA/cm
2 .
nm)
AM0, ASTM E490-00a, 1366.1 W/m2
AM1.5G, ASTM E892-87, 1000 W/m2
AM1.5D, ASTM G173-03, 1000 W/m2
0
100
200
300
400
500
600
700
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Photon Energy (eV)
Intensity per Unit Photon Energy
(W/m
2 .
eV)
AM0, ASTM E490-00a, 1366.1 W/m2
AM1.5G, ASTM E892-87, 1000 W/m2
AM1.5D, ASTM G173-03, 1000 W/m2
0
10
20
30
40
50
60
70
80
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Photon Energy (eV)
Current Density per Unit Photon Energy
(mA/cm
2 .
eV)
AM0, ASTM E490-00a, 1366.1 W/m2
AM1.5G, ASTM E892-87, 1000 W/m2
AM1.5D, ASTM G173-03, 1000 W/m2
0
10
20
30
40
50
60
70
80
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Photon Energy (eV)
Current Density per Unit Photon Energy
(mA/cm
2 .
eV)
AM0, ASTM E490-00a, 1366.1 W/m2
AM1.5G, ASTM E892-87, 1000 W/m2
AM1.5D, ASTM G173-03, 1000 W/m2
0
10
20
30
40
50
60
70
80
90
100
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Photon Energy (eV)
External Quantum Efficiency (%)
0
10
20
30
40
50
60
70
80
90
100
Current Density per Unit Energy
(mA/(cm
2
eV))
GaInP top cell
GaInAs middle cell
Ge bottom cell
AM1.5G
AM0
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