Solar cell operating principles · 2016. 2. 22. · Solar cell operating principles. PVI ffVImax mp mp oc sc= = η=PPffVIPmax I oc sc I= Short circuit current Isc [A] Open circuit

1. Absorption of photons ⇒ generation of electron-hole pairs

2. Separation of carriers in the internal electric field created by p-n junction and collection at the electrodes ⇒potential difference and current in the external circuit

3. Potential difference at the electrodes of a p-n junction ⇒injection and recombination of carriers ⇒ losses

The resulting current in the external circuit: I = IL - ID (V)• photocurrent IL• dark (diode) current ID

Solar cell operating principles

P V I ff V Imax mp mp oc sc= =η = =P P ff V I Pmax I oc sc I

Short circuit current Isc [A]

Open circuit voltage Voc [V]

Peak PowerPmax [Wp]

External parameters:• Short circuit current Isc [A]• Open circuit voltage Voc [V]• Fill factor ff• Maximum (peak) power Pmax [Wp]• Efficiency η

I-V measurementStandard test conditions:• AM1.5 spectrum• irradiance 1000 W/m2

• temperature 25°C

External parameters of a solar cell

- 56% colour mismatch

- 9% reflection & transmission

- 13% fundamental recombination

- 7% excess recombination, resistance, etc

15%

Typical commercial c-Si solar cellsunlight

solar cell

electricity

waste

heat

Solar cell performanceSingle junction solar cell:

Optical losses:Non-absorptionThermalizationReflectionTransmissionArea loss

Solar cell performanceCollection losses:Recombination- bulk- surface

( )λΦ 0 ( )R1−

g optη QE

t

f

AA

elQE

Optical losses: Non-absorption

( )∫∞

=0

0I dλλ

hcλΦP

( )λΦ 0 Photon flux density: number of photons per unit area per unit time and unit wavelength

Non-absorption Eph

( )

( ) dλλchλΦ

dλλΦE

λ

0

0

λ

0

0g

g

g

∫

∫

EC

EV

EphEG

Thermalization Eph>EGOptical losses: Thermalization

( )∫∞

=0

0I dλλ

hcλΦP

( )λΦ 0 Photon flux density: number of photons per unit area per unit time and unit wavelength

gλ

Thermalization

g phλ λ>

Solar cell performance

EC

EV

EphEG

Thermalization Eph>EG

EC

EV

EphEG

Non-absorption Eph

( )λΦ 0 ( )R1−

elQE

Optical losses: Reflection and transmission

Reflection:• Different refractive indices

Transmission:• finite thickness of a cell• absorption coefficient

Area loss:• metal electrode coverage

t

f

AA

g optη QE


( )λΦ 0 ( )R1− Recombination:• bulk recombination (minority carrier lifetime)

• surface recombination (surface recombination velocity)

g optη QE

t

f

AA

Collection losses: Recombination

elQE

( )t

felgoptmaxsc A

AQEηQER1JJ −=

( )∫=gλ

0

0max dλλΦqJ


I

ocsc

PffVJη =

( )0I0

hcP Φ λ dλλ

∞

= ∫

( ) ( )gλ

0fsc opt g el

t 0

AJ 1 R QE η QE q Φ λ dλA

= − ∫

Efficiency:

( )

( )( )

gλ0

0 fg opt el oc

0 t

0

q Φ λ dλAη= 1-R η QE QE V ffAhcΦ λ dλ

λ

∞

∫

∫

( )

( )

( )

( )( )

g g

g

λ λ0 0

G0 0 ocf

g opt elλ0 t G0

0 0

h cE Φ λ dλ Φ λ dλλ q VAη= 1-R η QE QE ff

A Ehc h cΦ λ dλ Φ λ dλλ λ

∞

∫ ∫

∫ ∫


8. Fill factor

7. Voltage factor

6. Loss due to recombination

5. Loss by incomplete absorption due to the finite thickness

4. Loss by reflection

3. Loss by metal electrode coverage

2. Loss by excess energy of photons

1. Loss by long wavelengths

( )

( )

( )

( )( ) ff

EVq

QEQEηR1AA

dλλchλΦ

dλλΦE

dλλchλΦ

dλλchλΦ

ηg

oceloptg

t

fλ

0

0

λ

0

0g

0

0

λ

0

0

g

gg

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

∫

∫

∫

∫∞

Solar cell performance limits

Overstraeten, Mertens: Physics, technology and Use of Photovoltaics, Adam Hilger 1986

Optical losses:Non-absorptionThermalizationReflectionTransmissionArea loss


Collection losses:Recombination- surface- bulk

Optical gapOptical gapRefractive indicesAbsorption coefficientMetal grid design

Surface recombination velocityMinority carriers lifetimeDiffusion coefficient

Properties:

Total current: ( ) LkTqV0T I1eII −−=Short circuit current (V=0):

LSC II −=

Open circuit voltage (I=0):

⎟⎟⎠

⎞⎜⎜⎝

⎛+= 1lnV

0OC I

Iq

kT L

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

Dp

ip

An

in

NLnDq

NLnDqAI

22

0

Low I0:• High doping densities• Low surface recombination

velocities• Large diffusion lengths

Optimal design

High Isc :• Minimize front surface reflection

- antireflection coatings• Minimize transmission losses

- thick absorber • Minimize surface recombination

- passivation layers• Minimize bulk recombination

- large diffusion lengths- high electronic quality material


p++ p++

Al

Al Al

SiO2 n+

p-typec-Si

Solar cell performanceOptimal thickness of the absorber layer:

Absorption versus collection:- Thickness of the absorber layer- Minority carrier diffusion length

c-Si (300 µm)Al

Le

p++ p++

Al

Al Al

SiO2 n+

p-typec-Si



Le

Le



p++ p++

Al

Al Al

SiO2 n+

p-typec-Si

Le

p++ p++

Al



p++ p++

Al

Al Al

SiO2 n+

p-typec-Si

Solar cell performanceThin absorber layer:

Increase absorption:- Surface texture- Antireflection coating

Avoid surface recombination:- Surface passivation

SiO2 n+

p++ p++

Al

AlAl

IL 1 2 V+

-

I

Equivalent circuit:

• current source IL• diode diffusion current• diode recombination current


1

2

I-V characteristics

Voltage

Cur

rent

IL

ID

IT

ISC

VOC

RS

RshIL 1 2 V

+

-

IEquivalent circuit:


• series resistor RS• parallel resistor Rsh

RP

RS

Series resistance (RS)• Bulk resistance of semiconductor• Bulk resistance of metal electrodes• Contact resistance between semiconductor and metal

Shunt (parallel) resistance (RP)• Leakage across the p-n junction around the edge

• Crystal defects, pinholes, impurity precipitates


Total current:( ) ( )( ) LkTRIVqT IeTII ST −−= + 10

Saturation current:kTEgeTKI 030

−=

Open circuit voltage:

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−=

L

gOC I

kTq

kTq

ETV

30 ln

( )⎥⎦

⎤⎢⎣

⎡−−= TV

qE

TdTdV

OCgOC 01

CmVdTdVOCo3.2−=Si

1.0

0.9

0.8

0.7

0.6

0 100 200 300

VOC [V]

ff

η

Temperature [oC]

External parameters

11

10

9

8

7

6

[%]


n-type Si

p-type Si

(+) (+)

(-)

Fabricated in 1954• wrap-around structure• p-n junction formed by B

dopant diffusion• high resistive losses in the p-

layer• efficiency 6%

First c-Si solar cell

First c-Si solar cell

University of New South Wales (Australia)

c-Si solar cell: Efficiency improvement

c-Si solar cell

Passivated Emitter and Rear Locally diffused

External parameters (1994):• Jsc =40.9 mA/cm2• Voc =0.709 V• ff = 0.827• η = 24.0 %

c-Si solar cell: PERL structure (UNSW)

Record c-Si solar cell

Key attributes for high efficiency solar cells:

• Surface texture (inverted pyramids for light trapping)

• Selective emitter (n+-layer for contact, n-layer for active part of surface)

• Passivation of surface (SiO2 on both sides of solar cell)

• Thin metal fingers on the front side

• Back side metalization with small contact area to the base material

• Locally diffused regions under contact points at the back(BSF field)

• Minority diffusion lengths well in excess of device thickness

Record c-Si solar cell

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Solar cell operating principles · 2016. 2. 22. · Solar cell operating principles. PVI ffVImax mp mp oc sc= = η=PPffVIPmax I oc sc I= Short circuit current Isc [A] Open circuit