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1S Ph
qV
I I IkTexp
=
Solar cell I-V curves and equivalent circuit
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Open-circuit solar cell
the current is zero; the solar cell delivers maximum voltage;
The output power P = I V =0
1 0ocS phqV
I I IkT
exp
= =
The open-circuit voltage, at I=0:
Note, the maximum achievable VOCmax = Vbi
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Short-circuit solar cell
the voltage across the diode is zero;the solar cell provides maximum current into the circuit;
The output power P = I V =0
The short-circuit current, at V=0:
0
1
V
sc S phqVI I IkT
exp
=
=
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Solar cell with an arbitrary load
The dashed region shows the range of external bias where the
energy isgenerated: Pdis=V
I < 0
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Equivalent circuit of the solar cell with active load.
VL
1S PhqVI I IkT
exp =
Diode equation:
0L LV V or V V ;+ = =
Load equation:
L L LI V R V R/ /= =
Kirchhoff voltage law:
Load line
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The output power of the solar cell
The condition for maximum power
This leads to the equation:
(Here kB is the Boltzmann constant, same as k)
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1
m m
m
qV kT qV kT mS S ph
qV kT mph S
qVI e I e IkT
qVI I e
kT
/ /
/
;+
+
Compare Vm to the open-circuit voltage VOC:
From this, 1 mm OCqVkT
V V lnq kT
= +
Note that
From this, the optimal voltage can be estimated:
OCqV kT ph SI I e
/=
( )1 0 026 1 1 0 026 0 096mqVkT
ln Vq kT
. ln / . .
+ + =
Also, note that ln(x) is a slow function of x. Hence,
1 1m OCqV qV
ln lnkT kT
+ +
The optimal voltage is then: 1 OCm OCqVkTV V ln
q kT +
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The optimal current of the solar cell(corresponding to the maximum output power)
Given the optimal voltage is Vm,
the corresponding maximum current can be found as
1mm S PhqVI I IkT
exp =
1 OCm OCqVkTV V ln
q kT = +
Where andph
OCS
IkTV ln
q I
after transformations, 1m phm
kTI I
qV
=
Note that kT/q y0.026 Vand hence, under strong excitation
kT/(qVm)
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Measured current-voltage characteristics of a high efficiency silicon
solar cell. Open circle voltage, Voc = 0.6411 V, short-circuit current
density,Jsc = 35.48 mA/cm2, fill factor 0.822, efficiency 18.70%.
Open circle denotes the maximum power point.
(after M. A. Green, A. W. Blakers, J. Shi, E. M. Keller, and S. R. Wenham, IEEETrans. Electron. Dev., ED-31, No. 5, p. 679, 1984, IEEE, 1984).
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Solar cell fill factor
The maximum voltage that the solarcell can develop is VOC;
The maximum current of the solar
cell is ISC.If the solar cell could simultaneously
deliver the maximum voltage and the
maximum current, the maximum
power would be PMM = VOCISCThe actual power is given by
Pm = VmIm
The solar cell fill factor is thusdefined as
VOC
ISC PMM
m m
SC OC
I VFFI V
=
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Solar cell conversion efficiency
The "standard" solar radiation (known as the "air mass 1.5 spectrum")has a power density of 1000 watts per square meter. Thus, a 12%
efficiency solar cell having 1 m of surface area in full sunlight (at
solar noon at the equator) will produce 120 watts of power.
A solar cell's energy conversion efficiency (, "eta"), is the percentage
of power converted from absorbed light to electrical energy
S l ll d i i
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Solar cell design issues
A schematic of a simple conventional solar cell.
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Effect of series resistance on the I-V characteristic of a solar cell
S l ll d i i
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Solar cell design issues
Lifetime p
and diffusion length Lp
of holes inn-type Si vs.
donor density. T = 300 K.
Solar cell design issues
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Solar cell design issues
Lifetime n
and diffusion length Ln
of electrons inp-type Si vs.
acceptor density. T = 300 K.
Solar cell design issues
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Solar cell design issues
The absorption coefficient vs. photon energy
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Theoretical max. efficiency as a function of semiconductor band gap
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