CHAPTER TWOCHAPTER TWO

THE PHOTOVOLTAIC EFFECTTHE PHOTOVOLTAIC EFFECT

2e A G.I. Module Energie Solaire

Copyright, 2006 © Ahmed S. Bouazzi

المدرسة الوطنية

للمهندسين بتونس

The Photovoltaic Effect (1)The Photovoltaic Effect (1)The p-n Junction

E c

E v

E F

p

n

Electrons Light HHHooollleeesss

E c

E v

E f

Electrons current

Holes current

The photocurrent under illumination

PHOTOVOLTAIC EFFFECT PHOTOVOLTAIC EFFFECT (2)(2)

The Photovoltaic Effect (3)The Photovoltaic Effect (3)The photovoltage under illumination

Ec

Ev

EF

p

nThe

photovoltage

I-V Characteristic of a p-n I-V Characteristic of a p-n junctionjunction

J (A/cm2)

V (mV)

-JL

Illumination

Dark

1exp

kT

qVJJJ oL

Voltage (V)

Vco

Jsc

Current (A/cm2)

(J,V)

I-V Characteristic of a PV I-V Characteristic of a PV GeneratorGenerator

1exp

kT

qVJJJ oL

The slope is 1/R

Hole density in the n side:

Electron density in the p side:

2

2

x

pDp

2

2

x

nDn

Minority Carrier Minority Carrier ConcentrationConcentration

x

pFµp

p

p

)(xG = 0

x

nFµn

n

n

)(xG = 0

G (x,) = ()()exp{-()x}

(): flux of the incident light

The Generation FunctionThe Generation Function

wavelength of the light

(): absorption coefficient

Holes current (n side):

Electrons current (p side):

Fpqµx

pqDJ nppp

Fnqµx

nqDJ pnnn

PhotocurrentPhotocurrent

p

n

d d+w l x

h

0

n= 0 p= 0

qpSx

pqDp

'qnSx

nqDn

Boundary ConditionsBoundary Conditions

dxpp x

pqDJ

•Holes current (n side):

wdxnn x

nqDJ

•Electrons current (p side):

Pseudo-neutral Regions Pseudo-neutral Regions Photocurrent DerivationPhotocurrent Derivation

Jw = qo{exp(-d) - exp[-(d+w)]}

= qoexp(-d)[1 - exp(-w)]

Depletion Region Depletion Region PhotocurrentPhotocurrent

0.275 0.475 0.675 0.875 1.075 1.275

107

Absorption coefficient (cm-1)

Wavelength (µm)

10-3

10-2

10-1

1

10

102

103

104

106

105

Absorption CoefficientAbsorption Coefficient

dp

p

pop eL

L

LqJ

221

ppp

p

ppp

pdp

p

p

Ld

Ld

D

SL

Ld

Ld

D

SLeL

D

SL

coshsinh

sinhcosh

n-side Photocurrentn-side Photocurrent

nnn

n

nn

nn

n

n

Lwdl

Lwdl

DLS

Lwdl

DLS

wdlLD

LS

coshsinh'

exp'

1)(exp'

11 22

)(

nn

wdno

n LL

eLqJ

p-side Photocurrentp-side Photocurrent

)(

)()(

o

TQ q

JR

For a given wavelength

Quantum ResponseQuantum Response

Quantum response

0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

S = 102

S = 103

S = 104

S = 105

S = 106

wavelenth (µm)

The Effect of the Surface The Effect of the Surface Recombination VelocityRecombination Velocity

0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

d = 0.2 d = 0.6 d = 1.2

Quantum response

wavelength (µm)

The Effect of the Junction The Effect of the Junction DepthDepth

200

160

120

80

4020

0.0 0.4 0.8 1.2 1.6 2.0 2.4

6.04.0

3.0 2.0 1.5 1.0 0.8 0.6 0.5

(µm)

(eV)

WevelengthEnergy

Radiation intensity (W/m2/µm)

Spectrum out of theatmosphere

Sea levelspectrum by clearday

The Solar SpectrumThe Solar Spectrum

spectrum

solarTheQoL dRqJ )()(

The total photocurrent:

The Total Solar CurrentThe Total Solar Current

1exp

kT

qVJJJ oL

I-V Characteristic of the I-V Characteristic of the PV GeneratorPV Generator

Current (mA)

Voltage (V) VocV

Isc

I

IxV

1exp1

o

Lmm

J

J

kT

qV

kT

qV

Maximum VoltageMaximum Voltage

Current (mA)

Voltage (V) VocVm

IscIm

1exp

kT

qVJJJ m

oLm

Maximum PhotocurrentMaximum Photocurrent

Current (mA)

Voltage (V) VocVm

IscIm

1Log

o

Lco J

J

q

kTV

Open Circuit VoltageOpen Circuit Voltage

Current (mA)

Voltage (V) VocVm

IscIm

ocL

mmc VJ

VJF

Current (mA)

Voltage (V) VocVm

IscIm

The Fill FactorThe Fill Factor

i

cocL

P

FVJ

The EfficiencyThe Efficiency

Current (mA)

Voltage (v)

Outputpower(mW)

Current (mA)

Voltage (V) VocV

Isc

I

IxV

The Output PowerThe Output Power

J

J

V L

RC

Js

The Ideal Equivalent The Ideal Equivalent CircuitCircuit

J

J

VL shR

sR

Rc

The Real Equivalent The Real Equivalent CircuitCircuit

sh

ssOL R

IRVIRVAIII

1)](exp[

The Real Circuit EquationThe Real Circuit Equation

ocL

mmc VJ

VJF

Current (mA)

Voltage (V) VocVm

Isc

Im

The Fill FactorThe Fill Factor

The Series Resistance The Series Resistance EffectEffect

The Shunt Resistance The Shunt Resistance EffectEffect

0 4 8 12 16 20 24 28

Voltage (V)

Current (A)

0.2

0.4

0.60.8

1.0

1.2

1.4

1.6

1.82.0

2.2

2.4

2.6

T = 75°C

T = 50°C

T = 25°C

T = 0°C

The Cell Temperature The Cell Temperature EffectEffect