Conversion efficiency (η)
&
quantum efficiency (QE)
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Overview
• A standardized sun
• Solar cell models
• Conversion efficiency
• Definitions
• Limits
• Measurements
• Quantum efficiency measurements
• Definitions
• Limits
• Measurements
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A standardized sun
•
•
The spectral distribution and the intensity of the Sunlight incident on a given
location is determined by how much of the light is absorbed in the atmosphere.
The absorption depends on two factors:
• The local composition of the atmosphere.
• The path length of the Sunlight through the atmosphere.
•
The effect of the atmospere is quantified using the parameter air mass (AM).
AM =
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The actual path length of the sunlight through the atmosphere
The thickness of the atmosphere
Air mass
•
The path length of sunlight through
the atmosphere is determined the
angle θ between the sunlight and
the normal of the horizon:
AM = 1/cos(θ)
•
Example values:
• θ = 0o
• θ = 48o
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: AM1.0
: AM1.5
Air mass
•
•
Solar cell characterization is
performed using AM1.5 spectra
normalized to 1 kW/m2.
Commonly used solar spectra:
• AM1.5: the industry standard for
terrestrial solar cell applications.
• AM0: a spectrum more relevant for
space applications.
•
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For theoretical calculations, the
black body spectrum is sometimes
used, since it allows for analytical
solutions.
A standardized sun: AM1.5
Visible light
1800
1600
1400
Irradiance
1200
1000
800
600
400
200
0
0
0,5
1
1,5
2
2,5
Wavelength [um]
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3
3,5
4
4,5
Solar cell operation
Ephot = hc/λ > Eg
-
Eg
+
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V
Solar cells and power generation
(The electrician’s point of view)
•
A solar cell is a two terminal
device, which
1. Acts as a diode in the dark.
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Diode I-V characteristics
Solar cells and power generation
(The electrician’s point of view)
•
A solar cell is a two terminal
device, which
1. Acts as a diode in the dark.
2. Generates photovoltage V and a
photogenerated current ISC when
illuminated. The photocurrent is
determined by the irradiance
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Illuminated solar cell
JSC
Solar cells and power generation
(The electrician’s point of view)
•
A solar cell is a two terminal
device, which
1. Acts as a diode in the dark.
2. Generates photovoltage V and a
photogenerated current ISC when
illuminated. The photocurrent is
determined by the irradiance
•
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The total current-voltage (I-V)
relationship of an illuminated solar
cell is a superposition of the I-V
characteristics of the diode and the
photocurrent.
Illuminated solar cell
JSC
Simple equivalent circuit diagram
•
A good model for simple evaluation of solar cell efficiency
+
JSC
Jdark
Vout
-
JTOT = Jdark – JSC = J0(eeV/kT – 1) – JSC
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Ideality factor
•
Real diodes rarely exhibit an ideal diode behaviour described by
JTOT = J0(eeV/kT – 1)
•
A better description can be obtained by introducing an ideality factor (m)
JTOT = J0(eeV/mkT – 1)
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Two-diode model
•
The most commonly used model in the solar cell research community and industry
Rseries
+
JSC
J0,1
J0,2
Rshunt
Vout
-
JTOT = J0,1(eq(V+JARseries)/kT – 1) + J0,2(eq(V+JARseries)/2kT – 1) – JSC + (V + JARseries)/Rshunt
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Important solar cell parameters
•
•
•
•
•
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Open circuit voltage
Short circuit current
Efficiency
Fill factor
Quantum efficiency
VOC
JSC
η
FF
QE
Open circuit voltage: VOC
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Short circuit current: ISC
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Conversion efficiency: η
•
The efficiency (η) of a solar cell is
defined as the ratio between the
output electrical power and the
power of the light falling upon it in
the following manner:
η = Pcell / Psun
• Pcell is given by
Pcell = I·V
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Psun
Pcell
Conversion efficiency: η
• η is defined at the maximum power
point of the solar cell.
η = Pmp/Psun
= Imp·Vmp/Psun
• η is sometimes called the conversion
efficiency of a solar cell.
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FF
•
The fill factor (FF) is
defined as the ratio
FF = Im·Vm / ISC·VOC
• η can be related to ISC
and VOC through FF
η = ISC·VOC ·FF / Psun
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FF
• FF is determined by the
shape of the I-V curve
•
•
•
•
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Ideality factor
Series resistance
Shunt resistance
…
Measuring η
• η is extracted from I-V measurements of illuminated solar cells.
• Solar cell characteristics depend on T and irradiance.
• Solar cell efficiency must be measured under standard testing
conditions (STC) for comparison.
• Spectrum = AM1.5
• Irradiance = “1 Sun” = 1 kW / m2 UNLESS OTHERWISE SPECIFIED
• Cell temperature (Tc) = 25 oC
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The solar simulator
Light
bulb
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Measuring η
• I-V curves are fitted to a two-diode model
• Several different algorithms for curve fitting
• Speed is of the essence
• In-line measurements of every cell and module
• Heating an issue
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Measuring η
• Controlled and calibrated measurements required
• Effect of irradiance (G)
JSC(G) ~ (JSC,ref/Gref) · G
• Effect of temperature
VOC(Tc) = VOC,ref + (Tc – Tc,ref) · (dVOC(T)/dT)
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Typical solar cell characteristics
40
SETTINGS:
Cell Area: 156,25 cm2
Temperature: 25 oC
Sun Intensity: 100 mW/cm2
30
20
CELL PARAMETERS:
10
0
-0,1
0,1
-10
-20
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0,3
0,5
0,7
Efficiency:
Voc:
Jsc:
FF:
Vmp:
Jmp:
J01:
J02:
Rs
Rsh:
17,1 %
615 MV
36,4 mA/cm2
76,4 %
511 MV
33,5 mA/cm2
5,6∙10-10 mA/cm2
1,3 ∙10-4 mA/cm2
2,5 ∙10-3 Ω
26,2 Ω
I-V signatures: shunt resistance
0
0,1
0,2
0,3
0,4
0,5
0
-0,5
-1
Current [A]
-1,5
-2
-2,5
-3
0,1
0,5
1
-3,5
-4
-4,5
10
Rshunt
-5
Voltage [V]
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0,6
0,7
0,8
I-V signatures: series resistance
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0
-0,5
-1
1
Rseries
Current [A]
-1,5
-2
-2,5
0,1
-3
0,05
-3,5
0,01
-4
-4,5
-5
Voltage [V]
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What else is there?
• Temperature-dependent I-V measurements
• Temperature coefficient extraction
• Time-dependent I-V measurements
• Light-induced degradation
• Indirect I-V measurements
•
•
•
•
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• Suns-Voc / «quasi-I-V curves»
Concentrated I-V
Spectrally dependent I-V
Local I-V
…
Record efficiencies + uncertainties
Solar cell
Efficiency
Theoretical limit for Si homojunction solar cell
~ 29.4 %
Monocrystalline Si (Panasonic)
25,6 % ± 0,5
Multicrystalline Si (FhG-ISE)
20,4 % ± 0,5
Thin film transfer Si (Solexel, 43 um)
20,1 % ± 0,4
Large area mc-Si (Q-cells, LFC)
19,5 % ± 0,4
Large area sc-Si (Panasonic, HIT)
24,7% ± 0,5
Si solar panel Si (UNSW)
22,9 % ± 0,6
CIGS (NREL)
19,6 % ± 0,4
Si (Amonix, 92 Suns)
27,6 % ± 1,0
CdTe (GE Global Research)
19,6 % ± 0,4
Perovskite (EPFL)
14,1% ± 0,3
Si thin film (LG, nc-Si-based 3J)
13,4 %± 0,4
GaAs thin film (Alta devices)
28,8 % ± 0,9
GaInP/GaAs/Ge (Sharp, 1 Sun)
37,9 % ± 1,2
GaInP/GaAs/GaInNAs (Sharp, 302 Suns)
44,4 % ± 2,6
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Prog. Photovolt. Solar Cell Efficiency Tables 39 (2012)
Quantum efficiency
• ”Particles out per particles in”
• A diagnostic tool
• Very important for determining loss mechanisms in real solar
cells
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Photogenerated current
•
The photocurrent depends on
several factors
• The incident irradiation (bs(E))
• The amount of reflected light from
the solar cell
• Reflectance (R(E))
• The amount of light absorbed
within the solar cell
• Absorbance (a(E))
• The probability of collecting
photogenerated charge carriers at
an external terminal
• Collection efficiency (ηcoll(E))
• The area (A) of the solar cell
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bs(E)
R(E)
a(E), ηcoll(E)
Photogenerated current
bs(E)
R(E)
a(E), ηcoll(E)
ISC(E) = q · A · ([1 – R(E)] · ηcoll(E) · a(E) · bs(E))
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QE
•
•
The quantum efficiency (QE(E)) is a measure of the probability of an incident
photon generating one electron that is successfully collected at the terminals
The external quantum efficiency (EQE(E)) is given by
EQE(E) = [1 – R(E)] · ηcoll(E) · a(E)
ISC(E) = q · A · EQE(E) · bs(E)
•
The internal quantum efficiency (IQE(E)) neglects reflective losses, and is
given by
IQE(E) = ηcoll(E) · a(E)
ISC(E) = q · A · [1 – R(E)] IQE(E) · bs(E)
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Measuring IQE and EQE
Lamp
PC
Monochromator
Chopper
Reference
diode
Integrating
sphere
Mirror
Solar cell
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EQE and IQE
Rear surface and bulk
recombination, transmission
IQE/EQE [%]
Front surface and emitter
recombination
Optical
losses
Band gap
energy
Wavelength [λ]
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Wikipedia
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Example: lifetime (PC1D)
100
90
80
IQE [%]
70
60
50
40
30
20
IQE 1
IQE 100
IQE 10000
IQE 10
10
0
300
400
500
600
700
800
900
1000
1100
1200
Wavelength [nm]
Marstein (2012)
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Predicting solar cell efficiency (PL)
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342
351
(15.3%)
(16.5%)
Predicting solar cell efficiency (EL)
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342
351
(15.3%)
(16.5%)
Tandem
King et al.APL 90 183516 (2007)
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IQE/EQE [%]
Up- and down conversion (UC/DC)
DC
Band gap
energy
Wavelength [λ]
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UC