21 Solar Cells II

7/27/2019 21 Solar Cells II

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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).


10/18

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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Lifetime p

and diffusion length Lp

of holes inn-type Si vs.

donor density. T = 300 K.



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Lifetime n

and diffusion length Ln

of electrons inp-type Si vs.

acceptor density. T = 300 K.



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The absorption coefficient vs. photon energy


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Theoretical max. efficiency as a function of semiconductor band gap


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21 Solar Cells II