Shockley diode equation.Shockley diode equation.Photovoltaic effect.Photovoltaic effect.

Solar cell output parameters.Solar cell output parameters.

VVBB II00

VVBB ; Breakdown voltage

II0 ;0 ; Reverse saturation current

Forward BiasForward Bias

Reverse BiasReverse Bias

Current

Voltage

Jn1 Jn2

Jn1Jn2

At equilibrium, the diffusion and generation are equal in magnitude and opposite in direction. The diffusion current from n to p is a small fraction of the large number of majority electrons, while the generation currentfrom p to n is a large fraction of the small number of minority electrons.

)()( generationJdiffusionJJ rrr +=

VVBB II00

VVBB ; Breakdown voltage

II0 ;0 ; Reverse saturation current

Forward BiasForward Bias

Reverse BiasReverse Bias

Current

Voltage

Band diagram and carrier flow Band diagram and carrier flow under biasunder bias

Band diagram and carrier flow Band diagram and carrier flow under biasunder bias

Calculation of the current through Calculation of the current through the junction.the junction.

EenneDJJJ nnnnnrrrrr

+=+= 21

EeppeDJJJ ppppprrrrr

+=+= 21

(1)

(2)

Deducir Deducir eqeq....

Thus the total current density is the sum of the two, as follows:

)1()1( 0 =

+=+= kT

eVkT

eV

n

pon

p

noppn

FF

eJeL

neDL

peDJJJ

J0 is called the saturation current density.

pn is the minority hole density in the neutral n region, pn0 is the equilibrium hole density in the neutral n region, np is the minority electron density in the neutral p region, np0 is the equilibrium minority electron density in the neutral p region, and p and n are the minority hole and minority electron lifetimes, respectively.

The quantity:The quantity:

2/1)( ppD has the dimensions of a length, and we define has the dimensions of a length, and we define the diffusion length the diffusion length LLpp for holes by:for holes by:

ppp DL =2

The diffusion length is a measure of the distance a carrier diffuses in its lifetime. It can be shown that the diffusion length is the average distance a carrier diffuses before recombining.

J0 is called the saturation current density and is expressed as:

An

in

Dp

ip

n

pon

p

nop

NLneD

NLneD

LneD

LpeDJ

22

0 +=+=

When a reverse bias voltage VR is applied to the p-n junction, the current-voltage characteristic under a reverse bias is given by:

)1(0 =

kTeVR

eJJ

Shockley diode equationShockley diode equation

)1(0 = kTeVa

eJJ

VVBB II00

VVBB ; Breakdown voltage

II0 ;0 ; Reverse saturation current

Forward BiasForward Bias

Reverse BiasReverse Bias

Current

Voltage

Effects of generation and Effects of generation and recombination.recombination.

It is difficult to fabricate pIt is difficult to fabricate p--n junctions n junctions with an ideal currentwith an ideal current--voltage voltage characteristic.characteristic.In the practical pIn the practical p--n junction solar cell, it n junction solar cell, it is necessary is necessary to consider the to consider the generation and recombination of generation and recombination of carriers in the depletion region.carriers in the depletion region.At the forward bias, the carriers will At the forward bias, the carriers will recombine through energy states at recombine through energy states at the forbidden energy gap.the forbidden energy gap.The recombination current is The recombination current is approximately given by:approximately given by:The forward current density of the The forward current density of the practical ppractical p--n junction is represented n junction is represented empirically by:empirically by:n is called the ideality factor.n is called the ideality factor.In the case of the ideal pIn the case of the ideal p--n junction, n junction, when the diffusion current dominates, when the diffusion current dominates, n=1 and when the recombination n=1 and when the recombination dominates, n=2, that is dominates, n=2, that is n has a value n has a value between 1 and 2. between 1 and 2.

)1(0 = kTeVa

eJJ)1(0 = kT

eVaeJJ

kTeV

rec

F

eJ 2

)1(0 = nkTeVF

eJJ

Photovoltaic devicePhotovoltaic device

Photovoltaic devicePhotovoltaic deviceThe separated The separated photogeneratedphotogenerated carriers set up an electric carriers set up an electric field field EE which is opposite in direction to the builtwhich is opposite in direction to the built--in in electric field electric field EE..The net electric field across the junction is reduced to the The net electric field across the junction is reduced to the value value EE--E.E.VVoo is reduced to a smaller value is reduced to a smaller value VVoo--VVff..The effect is the same as if a forwardThe effect is the same as if a forward--bias voltage bias voltage VVffwere applied to the junction.were applied to the junction.The overall result is the development of an The overall result is the development of an openopen--circuit circuit voltage voltage VVff, in the forward direction across the , in the forward direction across the illuminated junction.illuminated junction.The appearance of this voltage across an illuminated pThe appearance of this voltage across an illuminated p--n n junction is called the junction is called the photovoltaic effectphotovoltaic effect..

We can see that the maximum value of the We can see that the maximum value of the openopen--circuit voltage circuit voltage VVff is the diffusion is the diffusion potential Vpotential Voo, obtained when the , obtained when the illumination is intense, enough that the illumination is intense, enough that the photogenetatedphotogenetated electric field electric field EE cancels cancels completely the builtcompletely the built--in field in field EE..The maximum value of VThe maximum value of Voo in a given in a given semiconductor is semiconductor is EEgg/e/e..

)()( pEnEeV FFo =

LkT

eVJeJJ

a

= )1(0)( pnL LWLeGJ ++=

Solar cell output parametersSolar cell output parametersShortShort--circuit current, circuit current, IIscsc..OpenOpen--circuit voltage, circuit voltage, VVococ..Fill factor, Fill factor, FFFF..EnergyEnergy--conversion efficiency, conversion efficiency, ..

ShortShort--circuit current, circuit current, IIscsc..

LSC JJ =

OpenOpen--circuit voltage, circuit voltage, VVococ..

Setting J=0 in Setting J=0 in Shockley Shockley eqeq. gives . gives the ideal value:the ideal value:VVoc oc is determined by is determined by the properties of the the properties of the semiconductor by semiconductor by virtue of its virtue of its dependence on Jdependence on Joo. .

+= 1ln

0JJ

qkTV LOC

Fill factor, Fill factor, FFFF..

It is a measure of how It is a measure of how square the output square the output characteristics are.characteristics are.For cells of For cells of reasonably efficiency, reasonably efficiency, it has a value in the it has a value in the range range 0.7 to 0.850.7 to 0.85..

scoc

mpmp

JVJV

FF =

Fill factor, Fill factor, FFFF..Ideally, it is a Ideally, it is a function only of the function only of the openopen--circuit circuit voltage, Vvoltage, VOCOC..Defining a Defining a normalized normalized voltage, vvoltage, vococ as as VVococ/(/(kT/qkT/q), the ), the ideal (maximum) ideal (maximum) value of FF is value of FF is shown in Figure.shown in Figure.An empirical An empirical expression expression describing this describing this relationship to relationship to about four about four significant digits significant digits for vfor vococ>10 is:>10 is:

1)72.0ln(

+

+=

oc

ococ

v

vvFF

EnergyEnergy--conversion efficiency, conversion efficiency, ..

in

scoc

in

mpmp

PFFJV

PJV

==

FINFIN