Solar Cells 2
shoomoosh
class05SolarCells2020-08Resistanceeffectsonfillfactor.pptxResistance effects on fill factor
Prof. Richard R. King
Solar Cells
EEE 565
Arizona State University
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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)
FF
Solar Cell Efficiency
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(a) Generation-recombination current region
(b) Diffusion current region (g = 1)
(c) High-injection region (g = 2)
(d) Series resistance effect
(e) Reverse leakage current
Ref.: S. M. Sze, Physics of Semiconductor Devices, 2nd Ed., Wiley, New York, 1981.
Dark I-V
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γ = 1, ρs = 0 Ωcm2, σsh = 0 Ω-1cm-2
γ = 2, ρs = 0 Ωcm2, σsh = 0 Ω-1cm-2
γ = 1, ρs = 2 Ωcm2, σsh = 0 Ω-1cm-2
γ = 1, ρs = 0 Ωcm2, σsh = 0.007 Ω-1cm-2
γ = 1, ρs = 2 Ωcm2, σsh = 0.007 Ω-1cm-2
Effects of diode ideality factor, series resistance, and shunt conductance on FF
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Fill factor
A useful approximation for FF when you know
Voc and g , in the absence of series resistance and shunt conductance, is:
M. A. Green, High Efficiency Silicon Solar Cells, Trans Tech Publications, Brookfield, VT, 1987.
M. A. Green, "Accuracy of Analytical Expressions for Solar Cell Fill Factors," Solar Cells 8, 3 (1983)
where:
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Diode equation with non-ideal shunt,
series resistance effects
ρs = specific series resistance [Ωcm2]
σsh = specific shunt conductance [Ω-1cm-2]
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Diode Equation with Non-Ideal Shunt, Series Resistance Effects (series after shunt)
rs = specific series resistance [Wcm2]
ssh = specific shunt conductance [W-1cm-2]
Go crazy, include everything:
1-diode model, with series, with shunt
1-diode model, with series resistance
2-diode model, no series, no shunt
1-diode model, no series, no shunt
ρs
hν
σsh
Joγ
+V
0
J
(V + Jρs )
Jo1
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High series resistance affects both the dark I-V and the light I-V, degrading the fill factor and reducing efficiency
Effect of high series resistance
Rs= 10
Rs= 1
A= 1 cm2
Effect of Rseries
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8
High series resistance and low shunt resistance degrade primarily FF, but in severe cases, Voc and possibly Jsc. Due to edge leakage, defects shorting the junction, etc.
Effect of low shunt resistance
Effect of Rshunt
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9
γ = 1, ρs = 0 Ωcm2, σsh = 0 Ω-1cm-2
γ = 2, ρs = 0 Ωcm2, σsh = 0 Ω-1cm-2
γ = 1, ρs = 2 Ωcm2, σsh = 0 Ω-1cm-2
γ = 1, ρs = 0 Ωcm2, σsh = 0.007 Ω-1cm-2
γ = 1, ρs = 2 Ωcm2, σsh = 0.007 Ω-1cm-2
Effects of diode ideality factor, series resistance, and shunt conductance on FF
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Effects of diode ideality factor, series resistance, and shunt conductance on FF
Diode ideality factor > 1 results in a more rounded “knee” of the light J-V curve, near Vmp and Jmp
High series resistance results in a sloped voltage leg of the light J-V curve, near Voc
High shunt conductance results in a sloped current leg of the light J-V curve, near Jsc
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Example for a (very) good silicon solar cell
Note that Voc and Jsc stay the same or change very little for the different values of diode ideality factor, specific series resistance, and specific shunt conductance shown here
Effects of diode ideality factor, series resistance, and shunt conductance on FF
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Resistance in different cell regions
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Typical solar cell structure
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Base resistance
Emitter spreading resistance
Contact resistance
Metal grid resistance
Sources of series resistance
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Base resistance is just the resistance due to flow of current in the neutral base region
where b is the resistivity of the base region, typically 0.5- 5.0 -cm, and Wb is the width of the base.
For a 200 m base length cell, and 1 -cm resistivity material, for a 1 cm2 cell, the base resistance would be 0.02 , quite small
Base resistance
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Emitter spreading resistance is due to distributed resistance along the emitter to the front grid contacts
The emitter is typically quite thin. Therefore its more usual to talk about the sheet resistance of the emitter in terms of
where sh is the sheet resistance in ohms/square (/)
Emitter spreading resistance
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The incremental power loss in a section dy is
The current flowing into the left finger is zero in the middle and increases linearly as y increases
The total power loss due to the current flowing into the left finger is
Emitter spreading resistance
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At the maximum power point, the generated power is given by
Therefore, the fractional power loss is given by
As S increases as well as sheet resistance, so does fractional power loss. For sh = 40 /, Jmp = 30 mA/cm2, Vmp = 450 mV, S < 4 mm for less than 4% total power loss
Optimal grid design minimizes power loss while simultaneously minimizing shading loss
Emitter spreading resistance
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Due to non-ideal nature of metal semiconductor contact
Usually characterized in terms of the specific contact resistance
Typical values on the order of 10-4-10-6 -cm2
Contact resistance reduced by heavy doping under contact: tunnel contact
Contact resistance
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0.000.010.020.030.040.0500.10.20.30.40.50.60.70.8Current Density (A/cm2)Voltage (V)g=1, Rs=0, Ssh=0g=2, Rs=0, Ssh=0g=1, Rs=2, Ssh=0g=1, Rs=0, Ssh=0.007g=1, Rs=2, Ssh=0.007
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