Ennaoui cours rabat part ii

Photovoltaic Solar Energy Conversion (PVSEC)الشمسية الطاقة من الكهرباء يإنتاج ن ا ا ء هرب ج ا إ

Courses on photovoltaic for Moroccan academic staff; 23-27 April, ENIM / Rabat

PVSEC P t II Ingot crystal

Courses on photovoltaic for Moroccan academic staff; 23 27 April, ENIM / Rabat

PVSEC-Part II Fundamental and application of Photovoltaic solar cells

and system

crystal

Ahmed EnnaouiHelmholtz-Zentrum Berlin für Materialien und Energie

[email protected]

Wafer

Solar cell

Highlight:Photovoltaic Solar Energy Conversion (PVSEC)

HighlightsBasic of solar cells and ModulesLight absorption and band to band transition

Highlights

g pQuantum efficiency and absorption coefficientGeneration and recombination processesShockley-Read Hall Recombination (SRH) Shockley-Read Hall Recombination (SRH) Continuity equation and Transport processSilicon to binary and ternary compoundsF ili l ll l f PN j tiFrom silicon solar cell as example of PN junctionPerformance of solar cells Equivalent Circuit model: series (Rs) and shunt resistance (Rsh) s shChange in cell performance with Rs and RshChange in short circuit current and open-circuit with solar radiationChange in short circuit current and open-circuit with the temperature

Prof. Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie

Change in short circuit current and open circuit with the temperaturePerformance measurement standard conditions

Basic of solar cells and Modules

Solar cell has roughly T = 300 KSun has roughly T = 5800 K Solar cell has roughly T 300 KSun has roughly T 5800 K

Two basic functions of a solar cell1 Light absorption: generation of free excess charge carriers 1. Light absorption: generation of free excess charge carriers

photocurrent, I2. Charge separation: separate/extraction of excess electrons and holes

photovoltage, V

PowerI x V

Conversion of the Sun light in the „Black Box“• To absorb the solar spectrum as efficient as possible• To collect photogenerated charge carriers

p g ,

Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie

To collect photogenerated charge carriers• Charge transport must be possible• To make electron go to one side and holes to another current flow

Key aim is to generate electricity from solar spectrumBasic: Task of Photovoltaic

y g y pPower = Voltage x Current

Two challenges

J [A/cm2]

. (Jm,Vm)Jm

. Jm x Vm[Volt ] [A/cm2][Watt/cm2]

Two challengesGenerating a large current.Generating a large voltage.

V [Volt ]

Vm

High current.But low voltageE l t t h t

High voltageBut low current

Excess energy lost to heat Sub-band gap light is lost


Basic: Absorption-Separation-CollectionPhotons absorbed Electron flow Electrical currentPhoton flux gives number of photons/unit time/unit area/wavelength

x)).exp(R).(1( x).exp( λ)R(

λλ

λ −−λ=λ⎯⎯ →⎯−=λ αΦ)(ΦαΦ)(Φ 00

Electrons collectedLoadxe

dxdxG αα −Φ=Φ

−=)(

ceptor

EJ σ= dxdpD p

μP = Voltage x Current

V lt Δ

dx

Acc

Vocor

Rec

μeVoltage Δμ = μe – μhμ = chemical potential

0 La= 1/αLnW

Don

o μh


Basic: Quantum efficiency• Photoccurrent = how much light converted? This ratio can be measured Maximum short circuit current

• Limited information on the electronic properties• Information on the optical properties of the device

[ ][ ]Coulombe

A/cmJN2

electronsout =

Electrons collected / Photons absorbed

L d

[ ][ ]Joulehν

Watt/cmΦN2

photonsin =

[ ]Coulombe

)(1239)(nm

eVEhchν G λλ=⇒=

ccep

tor

EJ σ=dxdpD p

LoadExternal Quantum Efficiency, EQE

λhc)(J

)(Φ1

NNEQE photons

electronout λ

λ==

Ac

VR

μeE→ p∇

→

Internal Quantum Efficiency EQEIQE

λe)(ΦNQ photons

in λ

Voc

x = 0 L = 1/αor

Rec

μh

)(R λ−=

1IQE

Origine of the photovoltageChemical potentialx = 0 La= 1/α

x = Lnx = W

Don

o Chemical potentialEF,n = μe EF,h = μh


Basic: Quantum efficiency measurementselectron 1 ofarge current/chEQE""EfficiencyQuantumExternal =

Beam splitter

photon1ofrgy photon/eneofpower TotalEQEEfficiencyQuantum External

Monochromator equipped with more gratings*Chopper

EG

EQE vs. λ

2 – Cell Measurement

*Gratings should have line density as high as possible for achieving high resolution and high power throughput. (600 – 3000 lines/mm).

1 - Reference measurement

2CELLCELLsc .Φq.EQEJ =

2MONMON,2sc .aΦq.EQEJ =

3 – Final Result

REFREF

MON,1sc

MON,2

CELLsc

CELL EQEJ

J.JJEQE =

1REFREFsc .Φq.EQEJ =

1MONMON,1sc .aΦq.EQEJ = 2MONsc q Q

.a.EQEJJ.aEQE MONMON,2

sc

CELLsc

CELL =

scsc JJ1MONsc q Q

1

MON,1sc

MON qΦJ.aEQE =


Basic: EQE and and absorption coefficientPhoton absorption in a E(k)

E

pdirect band-gapsemiconductorConduction

Band

( )

2G )E(h

hνB

−= να

GaAs e.g.

Direct Bandgap Eg

EC

EV

Photon

Valence

( ) GG21

E)E(hν vs. .hν →−α

hν

∫Φ= λλλ dEQEq Jsc )()(+k-k

ValenceBand

E(k)

Cut-off λ vs. EG

[eV]E1.24m][μλG

G = ∫λ

Photon absorption in an indirect band-gap

ConductionBand

E(k)

Si e.g.

[eV]G

PhotonEg

EC

EV

semiconductorPhononEG+Ep

E ( )2

21

G )E(hhA

−= νν

α

+k-k

ValenceBand

Ep ( ) GG2 E)E(h vs. .h →−ννα


Basic: absorption coefficient and absorption lengthLight absorption

A.f(T)(0)E(T)E gG −=Si Ge GaAs

E (eV) 1 12 0 66 1 42Temperature changes:

EG ↑ as T ↓, Changing the absorption edge

EG (eV) 1.12 0.66 1.42

hν

Absorption ↔ Generationx

0 ).eR.(1ΦΦ αλ

−−=

Φ0(E)ΦA(E) Φt(x)

)R.(1ΦΦln .

d1 α

λ0 −−=λ

dΦ αx-o R).α).-(E).(1Φ

dxdΦx)G(E, =−=

ΦΦΦΦ TAR0 ++=

Depth xx =1/αΦr(E)

Surface

Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energieλλλ ++= TAR100%

Φ

Basic: absorption coefficient and absorption length

100 nm100 nm


Basic: improuvement, Light traping

Influence of the layer thickness on the photocurrent of SiInfluence of the layer thickness on the photocurrent of Si

Realization:• Etching and texturing of semiconductors.• Implementation of particles for scatteringd i i h d f


deposition on rough or structured surfaces

Basic: Challenging parameters

Reflection Loss Important cost factorAll device parameters

[ ]∫ λ−= λ0λsc dλ.dα-exp.)().ΦR(1.η(λ). qJ

Reflection LossAll device parameters Material parameter €

[ ]∫GE

λ0λsc p)()(η( )qDecisive Material parameter Light trapping

%=↑η(λ) EQE or η or IPCE - incident photon to electron conversion efficiency)

λ

hc.q

JΦ(λ)

1EQE ph=

η p y)

Reflection loss

Resistive loss

Top contact“loss”

Recombination loss

loss


Back contact„Loss“

Basic: Close look to EQE

hcJ1 )(λ

λhc

qJ

Φ(λ)1EQEη(λ) ph .

)(λ==

(2) Losses due to reflection and low diffusion length

(3) Losses due to rear surface passivation and reduced absorption at long wavelengths and low diffusion lengthand low diffusion length

(4) Complete loss due to missing absorption

(1) Losses due to front surfacerecombination and absorptionin passivation and antirection

Wavelength atthe band gap [eV]E

1.24m][μλG

G =


in passivation and antirectioncoating layers

the band gap [eV]EG

Basic: PN junction Loss in Jph

Good surface passivation. Texturing in the form of pyramids so that Good surface passivation.Antireflection coatings.Low metal coverage of the top surface.Light trapping or thick material

Texturing in the form of pyramids so that light is trapped at the surface (<60nm)

Light trapping or thick material (but not thicker than diffusion length).High diffusion length in the material.Junction depth optimized for absorption Junction depth optimized for absorption in emitter and base.

Low reflection by texturing

Reflection loss

Resistive loss

Top contact“l ”

Recombination loss

“loss”

Back contact„Loss“

Generation vs. recombination processesGeneration (g) requires an input of energy given to an electron:

El t

(g) gy g- Phonons - vibrational energy of the lattice - Photons - Light, or electromagnetic waves - Kinetic energy from another carrier (Impact ionization )

Electron thermalizes

to band edge

CEEK.E. −=

EC

Ekin

Generation

energy = Eenergy > EG

C

ECEVGeneration

Ekin energy = EG energy < EG

EV

kin

- Impact ionizationThe electron hits an atom, and break a covalent bond to generate anelectron-hole pair, if the kinetic energy is larger than the energy neededt t th i Th ti ith th l t d


to generate the pair. The process continues with the newly generatedelectrons, leading to avalanche generation (e-h).

Recombination (r) is the opposite of generation, leading to voltage and current loss.

Generation vs. recombination processes

Non-radiative recombination phonons, lattice vibrations. Radiative recombination photons (dominating in a direct bandgap materials ) Auger recombination charge carrier may give its energy to the other carrier.R bi ti h t i d b th i it i lif ti Recombination processes are characterized by the minority carrier lifetime τ.Equilibrium: charge distributions np = ni

2

Out of equilibrium: The system tries to restore itself towards equilibrium through R-GSteady-state rates: deviation from equilibriumy q

( ) npnBgrRBnnB.pg

.pn Br 2

i2i00

−=−=⎭⎬⎫

==

=/scm102B(Si) 315−×=

E bina

tion

y give

n rri

er in

d E

Electron thermalizes to band edge

ERadiative

recombination

ECAu

ger r

ecom

bxc

ess e

nerg

yo

anot

her c

arhe

sam

e ban

d EC

E(eV

) Non-radiative recombination

Phonon

EC

EV

A Ex to th

EV


Phonon

EV

Shockley-Read Hall Recombination (SRH) The impurities create deep-level-traps (ET) within the bad gap

(1)+(3): one electron reduced from Conduction bandand one‐hole reduced from valence‐band and

(1) (2)

ET

ECThe electron in transition between bands passes through ET

(2)+(4): one hole created in valence band andone electron created in conduction band

(3) (4)EV

Steady-state rates: R = A (np-ni2) = deviation from equilibrium:

11nnpR

2i

⎞⎛⎞⎛−

=

Steady state rates: R A (np ni ) deviation from equilibrium:n, p and NT inside Δx are held constant by the balancing effect of distinct different process

cp,n: capture coefficient of the recombination processNT: density of the recombination levels.σn,p: capture cross sections for e and h. ET: energy levels inside the energy gap.

)p(pNc1)n(n

Nc1

1Tn

1Tp

+⎟⎟⎠

⎞⎜⎜⎝

⎛++⎟

⎟⎠

⎞⎜⎜⎝

⎛

Tn,tn Nvσ1

=↑ nτ↑=Th,tp Nvσ

1pτ

ET: energy levels inside the energy gap.vth: average thermal velocity of e and h.pT, nT: number of empty states availablen, p: number of electrons or holesn1 , p1: number of electrons and holes at ET

Tn,tn

Tk)EE(

i1Tk

)EE(

i1B

iT

B

iT

enen−−−

== p nL l l i j ti


n1 , p1: number of electrons and holes at ETLow level injection

pSRH

nSRH τ

ΔpR materialtype p τΔnR materialtype -n =−=

Summary: Generation & RecombinationAuger recombination

(dominant effect at high carrier concentration) Ekin= -qELsc

Shockley-Read Hall recombination

Direct recombination

direct band

(dominant effect at high carrier concentration)

EV

EC

Ekin

kin q sc

Loss to thermal vibrations

Impact ionization is ageneration mechanism.When the electron hits anatom, it may break a⎟

⎟⎠

⎞⎜⎜⎝

⎛++Δ=++=

111nτττ

RRRR AugerDirectSRH atom, it may break acovalent bond to generatean electron-hole pair.

The process continues with the newlygenerated electrons leading to avalanche

( )2DAugern,DTn .NcBNNcΔn ++=

⎟⎠

⎜⎝ AugerDirectSRH τττ

( ) 1−++=⇒ 2NcBNNcτ generated electrons, leading to avalanche

generation of electrons and holes.

τ : average time it takes an excess minority carrier to recombine(1 ns to 1 ms) in Si

( )eff ++=⇒ DAugern,DTn .NcBNNcτ


(1 ns to 1 ms) in Siτ : depends on the density of metallic impurities and the density

of crystalline defects.t/teff

τ

What we have learned?

Photo absorption and photo generation, Direct and indirect band gap, EQE, IQE absorption coefficient, absorption length, excess minority carrier , carrier lifetimeRecombination: Non Radiative, Radiative, Auger Recombination: Non Radiative, Radiative, Auger Shockley-Read Hall Recombination (dominant process in Si) There are wide variety of generation‐recombination events that allow restoration of equilibrium once the stimulus is removed.Direct recombination is photon‐assisted, indirect recombination phonon assisted.Recombination lifetime in Si is controlled by Auger recombination at high carrierRecombination lifetime in Si is controlled by Auger recombination at high carrierconcentrationRecombination life time in Si is controlled by SRH at low carrier densities and depends on the amount of impurities and defects.

Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energiehttp://en.wikipedia.org/wiki/Main_Page

Basic: Continuity equation and Transport processContinuity equation for minority carriers:( ) x . r . Ax . g . A dx)(x J. A -(x) J. A

tn .x . A

nnnn Δ−Δ+

−+

=∂Δ∂

q

y q y

αx)).exp(R.(1ΦΦ λ0 −−=

Light flux

nnn rgJ. −+∇=−+Δ

+=

∂∂ 1r gdx)(x J-(x)J n

nnnn

nnn g.q Δ−∂ q

gxt nn

( ) =⋅∇∂∂+⋅∇=×∇⋅∇ cond t

DJH 0

( ) ( )

⎪⎨

⎧ −+⋅∇=∂∂

−+−=ρ=∂ρ∂

++⋅∇

nnn

ADpn

RGqt

n

NNnpqtJ

JJ

1

,0

Maxwell

⎪⎩

⎪⎨

−+⋅∇−=∂∂∂⇒

ppp RGqt

pqt

J1


rain Evaporation

Basic: Continuity equation and Transport process

rain

In flow

p

= (in flow – out flow) + Rain - EvaporationOut flowRate of

increase of t l l 1

dtdn

water level in lake r -g .J

q1 nnn +∇=

dt

nnn r-g.J1n+∇=

∂r-g.J1p

+∇=∂

nnnn

nnn

qDEqnμJ

r g .Jq

t

∇+=

+∇∂

pppp

ppp

qDEqnμJ

r g .Jqt

∇+=

+∇∂


Carriers are collected when they are: G t d l t th j ti

Basic: Continuity equation and Transport process

Generated closer to the junctionGenerated within a diffusion length of the junctionKey parameters for high collection are:Minority carrier diffusion

tn 0=

∂∂

ySurface recombinationDifficult to achieve high collection near front surface and also rear

Differential equation is simple only when G = constant. 2 2

conditions Bondary GτL

xBexpL

xAexpΔn(x) n ←++

+−

=n

2n

2

2

Dx)G(λ(

LΔn

dxΔnd

−=p

2p

2

2

Dx)G(λ(

LΔp

dxΔpd

−=

Acce

ptor

ΕF,n=μeΕF,p=μh

Dono

rLL nn

p(-α

x)

A

Vocor

Rec

Ε

Rec

Ε

D

Acce

ptor

=Φ0(

1-R

)exp

0 La= 1/αLnW

Dono ΕF,p=μh

0WLpLa= 1/α

ΕF,n=μe

A

Φ=


Basic Diode J-V equationApplying the same boundary conditions as in the ideal diode case pd

qDJ nΔ=

VDD ⎞⎛

Applying the same boundary conditions as in the ideal diode case. Differentiating to find the currentEquating the currents on the n-type and p-type sides, we get:

dxqDJ pp =

dxnd

qDJ pnn

Δ=

)( 1Tk

qVexp pLD

qnLDqJ

Bn,0

p

pp,0

n

n −⎟⎟⎠

⎞⎜⎜⎝

⎛+=

0J

W)LqG(L pn ++−

LJnt Photocurre

+ JD

0J

LTn.k

qV

0 J1expJJ B −⎟⎟⎞

⎜⎜⎛

−=- JL

L

L

Jcurrent, Dark

0 J1expJJ

D

⎟⎠

⎜⎝ 44 344 21

J : saturation current

nDnDqJ

2ip

2in

0 ⎥⎤

⎢⎡

+=

J0 : saturation currentkB : Boltzmann`s constant, 1.381 10-23 J/Kelvinn : ideality factorni: carrier concentration

NLNLq

DpAn0

⎥⎥⎦⎢

⎢⎣

iNA,ND. Doping concentration


Silicon (Diamond) to Chalcopyrite (Tetragonal)

IV Grimm-Sommerfeld-ruleaDiamond structure 4=+mqnq MN

SiIV Grimm Sommerfeld rulea 4

...=

++mnN,M elements, n,m atoms/unit cell and qN, qM valence electrons

III-V II-VIzincblende structure

sp3 hybrid bonds

Epitaxial film: GaAs , InP…

Polycrystalline thin film: CdTe, ZnS

I-III-VI2II-IV-V2

Polycrystalline thin film: Cu(In,Ga)(Se,S)2

(Chalcopyrite and related compounds)

Epitaxial film: ZnGeAs, …

I-III-VI2 Alloy: Group I= Cu, Group III= In and Ga, Group VI = Se and S


SiIIB IIIB IVB VB VIBIB

Basic: how to make a solar cell: The p-n junction

Si

C6

B5

O8

N7

Periodic Table Ge

GaAs

Si14

3231 33P

15

Al13

29 3431

CB

30S

16ON GaAs

CdTe

I PGeGa As

Cd48

Te52

In49

Sb51

Cu Se

In49

Zn

Sn50

CIGS

InP

AlSb

CIGS

CZTS

NMetallurgical Junction

N

PP NN-- -- -- -- -- ---- -- -- -- -- ---- -- -- -- -- --

-- -- -- -- -- --

+ + + + ++ + + + ++ + + + ++ + + + ++ + + + ++ + + + +

+ + + + ++ + + + +

NA

Space

ND

SpaceCharge Regionionized acceptors ionized donors

E-Fieldh+ diffusion = h+ drift e- diffusion = e- drift

Basic: PN junction at equilibrium⎪⎨⎧ ≈ Dno Nn⎪

⎨⎧ ≈

2

Ap0 Np

CE

iEbiqV

inpn ==kTE32

iGeBTn −=

⎪⎩

⎪⎨

≈D

2i

n0 Nnp⎪⎩

⎨≈

A

2i

p0 Nnn

VE

iFE

W

i

310i cm101.5n :300K −×≅

W)(xρ

N

qND+- ( ) ( )+= FFb EEEEqV

Built-in voltage Vbi

x-qNA)(xV

biV

- ( ) ( )( )[ ][ ]−=

−=

−+−=

0

0exp

exp

BFiip

BiFin

niFpFibi

TkEEnpTkEEnn

EEEEqV

x)(xE

px− nx

[ ]

⎟⎟⎠

⎞⎜⎜⎝

⎛≈⎟

⎟⎠

⎞⎜⎜⎝

⎛= 22

00

0

lnln

p

i

DAT

i

npBbi

BFiip

nNNV

n

npqTkV

p

A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie

xmaxE⎠⎝⎠⎝ ii

Depletion region width:Basic: PN junction in the dark

Depletion region width:Solve 1D Poisson equation using depletion charge approximation, subject to the following boundary conditions:

p-side:

0)()(,)(,0)( ==−==− pnbinp xExEVxVxV

( )202

)( ps

Ap xx

kqNxV +

ε=

n-side:

02 sk ε

( ) bins

Dn Vxx

kqNxV +−

ε−= 2

02)(

Use the continuity of the two solutions at x=0, and charge neutrality, to obtain the expression for the depletion region width W:

Wxx ⎫=+

DA

biDAs

DA

np

pn

NqNVNNkW

xNxNVVWxx

)(2)0()0( 0 +ε=→

⎪⎭

⎪⎬

⎫

=

==+


nDpA xNxN ⎭

Depletion layer capacitance:Basic: PN junction in the dark

Depletion layer capacitance:Consider a p+n, or one-sided junction, for which:

( )bis VVkW m02 ε=

The depletion layer capacitance is calculated using:

DqNW =

02

0 )(21)(2 ε

=→ε

===sD

bi

bi

sDDckqNVV

CVVkqN

dVdWqN

dVdQC m

m21 C

DNslope 1

∝Measurement setup:

WdW

VVV

Forward biasReversebias

dW

~

V

vac


VVbi − V

Ideal Current-Voltage Characteristics:

Basic: PN junction in the dark

Ideal Current-Voltage Characteristics:Assumptions:• Abrupt depletion layer approximation

Low level injection injected minority carrier density much smaller than the • Low-level injection injected minority carrier density much smaller than the majority carrier density

• No generation-recombination within the space-charge region (SCR)

D l ti lDepletion layer:

EW ( )T

2i V/Vexpnp.n =

CE

FEqV

( )Ti V/Vexpnp.n( )Tn0nn V/Vexpn)(xp =

VE

FnEFpE ( )Tp0pp V/Vexpn)x(n =−

Tk B


px−nx q

TkV BT =

Basic: PN junction in the dark

Reverse bias:Forward bias:

CE

qV ( )VVq bi +Ln

CEW

( )VV

VEFnE

FpE

FnEqV

FpE

( )VVq bi −

WLp

VEp

Reverse saturation current is due to minority carriers being collected

over a distance on the order of the diffusion length.

Quantitative p-n Diode Solution / Little MATHBasic: PN junction in the dark

Q. neutral RegionP-typeE = 0

Q. neutral RegionN-typeE = 0

Depletion RegionE ≠ 0

-∞ +∞-xp +xnElectrical field existe in the depletion

region the minority i diff i

Ln

p2

p2

np G

ndx

ndD

tn

+τ

Δ−

Δ=

∂

Δ∂L

p

n2

n2

pn G

pdx

pdD

tp

+τ

Δ−

Δ=

∂Δ∂

carrier diffusionDoes not apply here

n

p2

p2

n

ndx

ndD0

τ

Δ−

Δ=

p

n2

n2

pp

dxpd

D0τ

Δ−

Δ=

0)x( =−∞→Δ pncondition Boundary

?)xx( p =−→Δ pncondition Boundary

?)xx( n =→Δ npconditionBoundary

0)x( =+∞→Δ npconditionBoundary

⎟⎟⎠

⎞⎜⎜⎝

⎛−=−= 1

TkqVexp

Nn

)x(xΔnBA

2i

pp ⎟⎟⎠

⎞⎜⎜⎝

⎛−== 1

TkqVexp

Nn

)x(xΔpBD

2i

pn⎠⎝ ⎠⎝

Total current density:Basic: PN junction in the dark

y• Total current equals the sum of the minority carrier diffusion currents defined at the

edges of the SCR:)(I)(II diffdiff

( )1eLnD

LpD

qAI

)x(I)(xII

TV/Vp0nn0pD

pdiffnn

diffptot

−⎟⎟⎠

⎞⎜⎜⎝

⎛+=

−+=

• Reverse saturation current density:

LL np⎟⎠

⎜⎝

current

A. JI 00 =

2inp ≈

2in

currentarea

V (volt)Current density

⎟⎟⎞

⎜⎜⎛

+=⎟⎟⎞

⎜⎜⎛

+= np2i

p0nn0p0

DDqAn

nDpDqAI

D

i0n Np ≈

A

i0p Nn ≈


⎟⎠

⎜⎝

+⎟⎠

⎜⎝

+AnDp

inp

0 NLNLqAn

LLqAI

Ph t t C tN PΦ(x)

Basic: How to make a solar cell: Dark current + Dark current

Photocurrent Current:

• Diffusion courant (electron, region 1)31

2

Φ(x)

Φe-αx

• Generation current in SCR (region 2)

• Diffusion current (holes region3)Ohmiccontact

OhmiccontactE

xp xn

phTk

qV

0 J1expJJ B −⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−=n-typep-type

12 3

contact

⎟⎠

⎜⎝

CEW

)x(J)x(J)x(JJ ++=

E

FnEqV

FpE

2 3

)x(J)x(J)x(JJ pdiff,nnGndiff,pph ++=1


VE

px−nx

G ti t i h i N P

Basic: PN junction under illumination (Space Charge Region, SCR)

2Generation current in space charge region 2

N PΦ(x)

Φe-αx

C ti it ti (f l t )

p,Gn,G JJ =

Lp

nn Gp

dxdJ

q1

tn

+τ

Δ−=

∂∂

31

xp xnOhmiccontact E

Continuity equation (for electron)

pq

nxn-typep-type

12 3

contact Ohmiccontact

E

Steady-state

dJ1

x)Φαexp(G(x) α=

∫=n

pxG G(x)dxqJL

n GdxdJ

q10 +=

W x)Φαexp(-G(x) α=W

( ) ( )Wxx e1eqeq)x( pn α−α−α−α Φ== px-eΦJ ( ) ( )nn,G e1eqeq)x( pn −Φ=−= peΦJ


N PΦ( )

Basic: PN junction under illumination (diffusion current)Neutral region 3 n-type

dxpdqDJ p.dff,p

Δ=

2

N PΦ(x)

Φe-αx

Neutral region 3 n type Diffusion current: holes

dx

2p

2pL/xL/x

L1BeAep pp

α−

ατΦ++=Δ +−

31

xp xn

Oh i E Boundary conditions

0B/1d0p n =⇒α<<+∞→==Δ ; L xx pcn-typep-type

12 3

Ohmiccontact

Ohmiccontact

E

)0E(xx0p n ===Δ p

pnn L/xx2p

eL

+α−

α

ατΦ=⇒ 2

p

-1A

p

Lα

( )pnnn L/)xx()xx(x2p

2p eeeL1

p −−−α−α− −α−

ατΦ=Δ

nxp.diff,p e

L1L

qJ α−

α−

αΦ−=


Neutral region p-type1

Basic: PN junction under illumination

ndΔ

Neutral region p type1

2

N PΦ(x)

Φe-αx

Diffusion current: electron

dxndqDJ n.dff,n

Δ=

22nL/xL/x

L1BeAen pn

αατΦ

++=Δ −

31

xp xnOhmic xć xcnL1 α−

Boundary conditionsn-typep-type1

2 3

contact Ohmiccontact

E

)(S ionrecombinat surface on depends)Δn(x

)Δn(x xx

E field electrical xx

0ć

ć

ć

p

→=

=Δ= )(0n

)(p)( 0c

⎟⎟⎞

⎜⎜⎛

+ −− pnpnp αxn2

/Lxn/Lxn eτΦα

eB

eA

qDJ )x(

Surface recombinationS0

⎟⎟⎠

⎜⎜⎝ −

−+−= pnpnp

2n

2n

n

n

n

nndiff.n, e

Lα1e

Le

LqDJ )x( n


Basic: PN junction under illumination

0J α1d junction N-Pefficient anFor diff.n,p ≈⇒<<

( )

⎪⎩

⎪⎨

⎧

α+

αΦ−=

−−==

== α−

−

J

e1qΦJ Wx and 0xat Origine

diff.p,

αWG

np W22

pn

n

eL1

Lq)x(

)Wx(

⎪⎩ α+ pL1

⎟⎞

⎜⎛ W1

j tii)1(W1WfJM i

J ph ⎟⎟⎠

⎞⎜⎜⎝

⎛

α+−Φ−= α− W

p

eL1

11q

junction-pin e.g. )(W 1Wfor J Maximum ph →α

>>>>α


PN junction under illumination / Efficient p-n diode

⎟⎞

⎜⎛

⎟⎞

⎜⎛

αΦΦα W)R1(W 11

A.JIarea cellA phph ⎟⎟⎠

⎞⎜⎜⎝

⎛

α+−−Φ==→= α− W

p0 e

L111)R1(Aq

J J phph0

⎟⎟⎠

⎜⎜⎝ α+

−−Φ=⎯⎯⎯⎯ →⎯⎟⎟⎠

⎜⎜⎝ α+

−Φ−= α−−Φ=Φα− W

p0

)R1(W

p

eL1

11)R1(qeL1

11q

⎠⎝ p

Φ0 = Number of photon per unit area, per unit time, per wavelength incrementincident power: Pinput = hν . Φ0 . A

EQE . 1239λ(nm)

⎟⎟⎠

⎞⎜⎜⎝

⎛

α+−−

ν=⎟

⎟⎠

⎞⎜⎜⎝

⎛

α+−

Φν−Φ

= α−α− W

p

W

p0

0

input

ph eL1

11)R1(hqe

L111

A.h)R1(Aq

PI

.

1239

Multimeter

⎟⎟⎠

⎞⎜⎜⎝

⎛

α+−−== α− W

i

ph

eL1

11)R1(P

qI

EQE geometry

⎟⎠

⎜⎝ α+

νpinput L1

hP

reflexion Absorptioncoefficient

Minority carrier diffusion length)nm(1 λ

==1

Pyranometer

coefficient g1239

qh

=

λ

=ν

qhc


Basic: PN junction Loss in Jph

⎟⎟⎠

⎞⎜⎜⎝

⎛

+−−= −αW

p

eαL111 R)(1 η

SEM image

⎠⎝ p


Basic: Open circuit Voltage, VOC

⎟⎟⎞

⎜⎜⎛

⎥⎤

⎢⎡

1JlTnkV0J1qVJJJJ LB⎟⎟⎠

⎜⎜⎝

+=⇒=−⎥⎦

⎢⎣

−=+= 1J

lnq

V 0 J1Tnk

qexpJJJJ0

LBOCL

B0phD

J0 : saturation current , n : ideality factor, kB : Boltzmann ´s constant, VOC: open circuit voltage JL or J h photocurrentVOC: open circuit voltage, JL or Jph photocurrent

+ JD - JL O i it ltJL

⎟⎟⎠

⎞⎜⎜⎝

⎛+= 1

JJln

qTnkV

0

LBOC

Open circuit voltage

⎠⎝ Jq 0


Open circuit Voltage, VOCFor a given band gap EG, we need trade-offs

⎟⎟⎠

⎞⎜⎜⎝

⎛+= 1

JJln

qTnkV

0

LBOC

For a given band gap EG, we need trade offs

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

Dp

2ip

An

2in

0 NLnD

NLnDqJ

⎠⎝

Diffusion lengthDoping

TB

G

pn

i

An

n

Dp

pVC0 k

E-]exp

ττwqn)

N1

τD

N1

τD

(N[qNJ ++=

kTDD )25mV (V q

kTVμD

μD

300KTTp

p

n

n ==== =

VOC


Power output characteristics

FFVJ .VJ RJ

mpp = Maximum Power Point

Sun

OCSC

P.FF.VJ

EFF.=OCSC

mppmpp

.VJ

.VJ RmppJ

P=I.V

Pmpp= Impp x VmppV

Fill Factor

OCSC

mppmpp

.VJVx J

Vmpp

VOCSC

mppmpp V . JEFF=

Inverse of slope Vmpp/Impp

is characteristic resistance

SunP

Jsc VOC Pmax

is characteristic resistance

Jmpp mmp


Importance of mobility μ and Diffusion length, Lp,n

The higher mobility μ, the better is the carrier extractiong y μ,L : Mean free length of path (L2 = D.τ) gives how long charge carrier (Lp or Ln) can travel in a volume of a crystall lattice before recombination takes place

dxdnqDnEqμJ nn +=

vvelocity

dx

Ev

FieldvelocityMobility μ ==


Dark current and photocurrent

1nkTqVexpII 0D ⎥⎦

⎤⎢⎣⎡ −= L

D0 I- 1

nkTqV

expII ⎟⎠⎞

⎜⎝⎛ −=

V (volt) V (volt)


Limitation of VOC by I0 and JSCAt room temperature: VT = kBT/q = 26 mV VOC increases by 0.06 V if I0 decreases by one order of magnitudeVOC increases by 0.06 V if ISC increases by one order of magnitude

V (volt) V (volt)Diode saturation current density for nearly ideal Si solar cellsDiode saturation current density for nearly ideal Si solar cells

2130 A.cm10(Si)I −−≈


Energy conversion efficiency of a solar cell

I.VPPointPowerMaximum ==

Sun

SCOC

PI . V

EFFICIENCY LIGHT SUN OFPOWER

MPP INPOWER EFFICIENCY ==

MPMPMPP I . VPPointPower Maximum ==

V

MP

MPMPPL I

VR MPP the in resistance load Optimal = Importance of the solar cell efficiency

↑

W/c

m2 )

EFFECIENCY↑

m2 )

x V

(W MATERIAL + AREA↓

I(A

/cm

COST FOR PV↓

V (volt)€/Wp↓


One diode model / Equivalent CircuitJD

Ideal diode (dark current , ID) J. RS (Voltage drop)

JJDD

(Shockley diode equation)

⎥⎦⎤

⎢⎣⎡ −= 1exp0 nkT

qVJJ D

D

PRLoadVD

SD RJVV .+=add a serie resistance RS

jsh . RshCurrent loss

JL

VP

N

LS

D JnkT

RJVqJJ −⎥⎦

⎤⎢⎣⎡ −

−= 1

).(exp0 Solar cell under illumination

Solar cell in the dark

⎥⎦⎤

⎢⎣⎡ −

−= 1

).(exp0 nkT

RJVqJJ S

D

add a shunt resistance

nk ⎦⎣

J = I/A

⎦⎣

⎥⎥⎦

⎤

⎢⎢⎣

⎡+=

Dp

ip

An

in

NLnD

NLnDqJ

22

0

Dark characteristics being shifted down by photocurrent which depend on light intensity.

add a shunt resistance

RJVRi +=

VOC

4TH Q d tVReverse

Forward0

J0Photogenerated carriers can also flow through the crystal surfaces or grain boundaries in polycrystalline devices

R

J.RVJ-

Sh

SL

++⎥⎦

⎤⎢⎣⎡ −

−= 1

nkT)R.JV(q

expJJ S0

Sshsh RJVRi .. += JSC

- JL

4TH Quadrant

Two diodes model / Equivalent Circuit4th Quadrant

R

J.RV

Sh

S++⎥

⎦

⎤⎢⎣

⎡−

−+⎥

⎦

⎤⎢⎣

⎡−

−= 1

).(exp1

).(exp

202

101 kTn

RJVqJ

kTnRJVq

JJ SSLJ -

J + RSJ

RLoadVJ01,n1

J02,n2

RshJL

1st Quadrant

J

-1st Quadrant

4th Quadrant V

R

J.RV

Sh

S+−⎥

⎦

⎤⎢⎣

⎡−

−−⎥

⎦

⎤⎢⎣

⎡−

−−= 1

).(exp1

).(exp

202

101 kTn

RJVqJ

kTnRJVq

JJJ SSL

1 Quadrant


During operation, the efficiency of solar cells is reduced by the dissipation of power across

Role of Rsh (Rp) for I-V-characteristics of solar cells

internal resistances which can be modeled as a parallel shunt resistance (RSH) and series resistance (RS). For an ideal cell, RSH would be infinite and would not provide an alternate path for current to flow, while RS would be zero, resulting in no further voltage drop before the load.

V lt (V lt)Voltage (Volt)

Voltage (Volt)

Using LabVIEW analysis capabilities you can assess the main performance parameters for PV cells and modules.


Role of Iph for the influence of RS

FF↓ and η↓ with increasing IFF↓ and η↓ with increasing ISC

Voltage (Volt)g ( )


The efficiency increases with increasing light intensity.Basic: solar cell is a sensor for solar radiation

y g g yWe Compare the efficiency at two light intensities P P and P 0

SunSun0Sun >

No additional heating Linearity PI SunSun ∝ I(T)I)(TI 00000 ==

0SC

0OC

Sun

SCOC

I .VFF

PI . V

FFη =

0Sun

SCOC00 P

FFη =

SCphB I 1

IlnTnk

⎟⎟⎞

⎜⎜⎛

+

0Sun

0SC

00

0ph0B

Sun0

00

PI

1II

lnq

Tnk

P1

Iln

qFFFF

ηη

⎟⎟⎠

⎞⎜⎜⎝

⎛+

⎟⎟⎠

⎜⎜⎝

+

=⇒

XII

PP

PI

II

ln

TT

FFFFη

0ph

0Sun

00Sun

SC

0

ph

==⎞⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛

≈

Sun0q ⎠⎝

IP

PI

II

lnTFFη 0

ph0Sun

0Sun

0SC

00

0ph000

⎟⎟⎠

⎞⎜⎜⎝

⎛


Basic: solar cell is a sensor for solar radiationThe efficiency increases with increasing light intensity.y g g y

Two light intensitiesPPandP 0

SS0S >

+⎟⎟⎠

⎞⎜⎜⎝

⎛ 0ph

0

0ph

II

lnlnFFI

IXln

FFηX

PPandP SunSunSun >

⎟⎟⎠

⎞⎜⎜⎝

⎛=

⎟⎟⎠

⎞⎜⎜⎝

⎛⎠⎝=

0

0ph

0

0

0

0ph

0

00

II

ln

IFFFF

II

ln

I

FFFF

ηη

lnXFFII

lnlnXFFη

0ph

⎟⎟⎟⎞

⎜⎜⎜⎛

+1

II

ln

lnX1FFFF

II

ln

IFFFF

ηη

0

0ph0

0

0ph

0

00

>

⎟⎟⎟⎟

⎠⎜⎜⎜⎜

⎝⎟⎟⎠

⎞⎜⎜⎝

⎛+=

⎟⎟⎠

⎞⎜⎜⎝

⎛=


Basic: solar cell is a sensor for solar radiationAs light intensity changesg y g

αxαΦedxdΦG(x) −=−=

Φ: Photon flux photons/sec/cm²

• JSC change much greater than VOC.• Low light intensity still produces voltage.• JSC increases proportionally with irradiance.

dx

SC p p y• MPP indicates Rload to achieve maximum power use.

II.RV

1qVII S+⎤⎡1 sun

0.8 sun0 6

MPPI-

R 1

nkTqVexp.II L

Sh

S0 +⎥⎦

⎤⎢⎣⎡ −=

LS

0 I- 1Tn k

)I.Rq(Vexp II ⎥

⎦

⎤⎢⎣

⎡−

−= .

JSC

0.6 sun

1JJln

qnkTV

0

LOC ⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

⎤⎡ 22

B .Tn.k ⎦⎣

W)LqG(LJ pnL ++=⎥⎥⎦

⎤

⎢⎢⎣

⎡+=

Dp

2ip

An

2in

0 NLnD

NLnDqJ

A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und EnergieVOC

Basic: Temperature EffectsSolar cell operate best at lower temperature.As the temperature decreases, the output voltage and efficiency increase.

The output voltage Voc, when Voc >> nkBT/q,

00

ln1lnJJ

qnkT

JJ

qnkTV LL

OC ≈⎟⎟⎠

⎞⎜⎜⎝

⎛+=

JL increase proportionally with irradiance

⎞⎛⎞⎛ KIVKIkT

JL = K . I

J0 is reverse saturation current and strongly

⎟⎟⎠

⎞⎜⎜⎝

⎛=⇒⎟⎟

⎠

⎞⎜⎜⎝

⎛=

00

lnlnJKI

nkTeV

JKI

enkTV oc

oc

0 g ydepend on temperature:

kTE

iipin

G

eTnpnnDnDqJ

−≈=⎥

⎤⎢⎡

+= 3222

0 . iDpAn

pNLNL

q⎥⎥⎦⎢

⎢⎣

0


Basic: Temperature EffectsJnkTJnkT ⎟

⎞⎜⎛

00

ln1lnJJ

qnkT

JJ

qnkTV LL

OC ≈⎟⎟⎠

⎞⎜⎜⎝

⎛+=

Assuming n = 1, at two different temperatures T1 and g , p 1T2 and the same illumination:

⎟⎟⎠

⎞⎜⎜⎝

⎛≈⎟⎟

⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=− 2

210112 lnlnlnln iococ

nn

JJ

JKI

JKI

kTeV

kTeV - ⎟

⎠⎜⎝

⎟⎠

⎜⎝

⎟⎠

⎜⎝

⎟⎠

⎜⎝ 202010212 inJJJkTkT

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−=−⇒−=

121

1

2

22 11expTTk

EkTeV

kTeV

kTENNn gococgvci

⎟⎟⎠

⎞⎜⎜⎝

⎛−+⎟⎟

⎠

⎞⎜⎜⎝

⎛=

1

2

1

212 1

TT

eE

TTVV g

ococ

0.493V

Example, Si solar cell has Voc1 = 0.55 V at 20 oC (T1 = 293 K), at 50 oC (T2 = 323 K),

V V V 49303231)11(323)550( ⎟⎞

⎜⎛

⎟⎞

⎜⎛V V V V 493.0

2931)1.1(

293)55.0(2 =⎟

⎠⎞

⎜⎝⎛ −+⎟

⎠⎞

⎜⎝⎛=ocV


Basic: ExamplesConsider a p–n junction diode at 25 °Cwith a reverse saturation current of 10−9 A. Find the voltage drop across the diode when it is carrying the following: (a) no current (open-circuit voltage), (b) 1 A, (c) 10 A.q =1.602 × 10−19 C, k =1.381 × 10−23 J/K), n = 1 and T=25°C(a) In the open-circuit condition ID = 0 and VD = 0(a) In the open circuit condition, ID 0, and VD 0.(b) With ID = 1 A, we can find VD by rearranging the Shockley diode equation

⎥⎦

⎤⎢⎣

⎡−=⎥

⎦

⎤⎢⎣

⎡−=⎥⎦

⎤⎢⎣⎡ −= −

−

1)(

600.11exp110381.110602.1exp1exp 023

19

00 KTVJ

TVJ

nkTqVJJ DDD

D xx [ ]19.38

0 −=°= DVD eJJC 25T at

⎦⎣⎦⎣

532.0110

1ln9.38

11ln9.38

19

0

=⎟⎠⎞

⎜⎝⎛ +=⎟⎟

⎠

⎞⎜⎜⎝

⎛+= −J

JV DD (b)

592.0110ln19 =⎟

⎠⎞

⎜⎝⎛ +=DV (c)

Consider a 100 cm2 PV cell photovoltaic cell with reverse saturation current I0 = 10−12 A/cm2. In full sun, it produces a short-circuit

t f 40 A/ 2 t 25°C Fi d th i it lt t f ll d i f 50% li ht Pl t

109.38 9 ⎟⎠

⎜⎝ −D( )

current of 40 mA/cm2 at 25°C. Find the open-circuit voltage at full sun and again for 50% sunlight. Plot the results.The reverse saturation current J0 is 10−12 A/cm2 × 100 cm2 = 1 × 10−10 A. At full sun JSC is 0.040 A/cm2 × 100 cm2 = 4.0 A. The open-circuit voltage isSC p g

[ ] VJJ

VeJJJ ScOC

VL

D 627.0110

4ln0257.01ln0257.001 100

9.380 =⎟

⎠⎞

⎜⎝⎛ +=⎟⎟

⎠

⎞⎜⎜⎝

⎛+=⇒=−−= −


Basic: One diode model / Equivalent CircuitSince short-circuit current is proportional to solar intensity, at half sun ISC = 2 A and the open-circuit Since short circuit current is proportional to solar intensity, at half sun ISC 2 A and the open circuit voltage is

Plotting the relation belo gi es s the follo ing

VVOC 610.0110

2ln0257.0 10 =⎟⎠⎞

⎜⎝⎛ += −

Plotting the relation below gives us the following:


Lab. work

V i d d d tVaried and measured parameterscurrentvoltagetemperaturetemperaturelight intensitywavelength of the light

phsh

SS0 I-

RI.RV

1n.k.T

)R . Iq(Vexp.II

++⎥⎦

⎤⎢⎣⎡ −

−=

Solar cell parameters: diode saturation current densityideality factorseries resistanceparallel resistanceshort circuit current density

Derived parameters: fill factor FF energy conversion efficiency thermalDerived parameters: fill factor, FF energy , conversion efficiency thermalactivation energy, Ea

A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und EnergieSources: FU-Berlin

Lab. Work: ISC-VOC measurementsVery simple measurement no need for a load resistance with one multimeter only

⎤⎡ qV1

y p yLight intensity variation: ideality, I0 and Rp from ISC-VOC – characteristicsTemperature variation: thermal activation energy of I0

decade

⎥⎤

⎢⎡ −= 1

qVexpII 2

02D

nkTqVexp

nkTqV

exp

101

II

2

1

2D

1D ≈=

⎥⎦⎤

⎢⎣⎡ −= 1

nkTqV

expII 101D

decade

⎥⎦⎢⎣1

nkTexpII 02D nkT

UUΔU/decade =

26mVq

Tk 2.3ln10 B ==

12 UUΔU/decade −=

n.60mV .ln10q

Tkn B →=

Room T: ΔU/decade = n.60mV (Si: n = 1.1 – 1.3)


Lab. Work: ISC-VOC measurements


Lab-Work: Activation energyDetermination of EA from the slope in Arrhenius plotsDetermination of EA from the slope in Arrhenius plots

EA = 0.5 eV corresponds toabout 2 orders of magnitudefor T1 = 300 K and T2 = 400 K


Consequence of EA: Temperature dependence of VOC

Lab-Work: Activation energyq A p p OC


Lab-Work: Measurements with loadsWhat is RL ? RL is the power taken from the illuminated solar cell.

V.IP and IVR L ==

What is RL ? RL is the power taken from the illuminated solar cell.

I

Each RL corresponds to one point on I-V curve.Simplest way: RL known, V measured.Simplest way: RL known, V measured.

(high accuracy for low cost)Set-up: just using a voltmeter variation of known RGood for ranges of RL between 1 Ω and 100 kΩ

(Si l ll ith ll thi fil i i d l )(Si solar cells with small area, thin film mini-modules)

Voltage (Volt)sources of errors: accuracy of RL: i t f i d t t

g ( )resistances of wires and contactsinternal resistance of the voltmeter


Choice of load resistance (RL) for simplest I-V measurements

Lab-Work: Measurements with loadsChoice of load resistance (RL) for simplest I V measurements

1. VOC and ISC are measured with a multimeter2. RL* is calculated RL* = VOC / ISC (RL* is close to Maximum Power Point, MPP)3. RL is changed towards ISCL SC

RL is decreased by taking about 10 values up to RL ≤ RL*/104. RL is changed towards VOC

RL is increased by taking about 10 values up to RL ≥ 10 RL*

Determination of RpDetermination of Rp

IV

ΔΔ

−=pR0VI →Δp

Voltage (Volt)A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und EnergieSources: FU-Berlin

Lab-Work: Measurements with loads

Determination of RMeasurement at two light intensitiesRp large enoughdetermination of the potentials

Determination of RS

determination of the potentials U1 at currents I1 = ISC1 - ΔI U2 at currents I2 = ISC2 - ΔI

( )⎥⎦

⎤⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛ −= 1

Tk.RIUq.

expIΔI S110.

Voltage (Volt)

⎦⎣ ⎠⎝ Tk B

( )⎥⎦

⎤⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛ −= 1

Tk.RIUq.

expIΔIB

S220.

Voltage (Volt)

21S

UUR

−= Works well for conventional solar cells

FF i l ti l l12

S II − FF is relatively large


The power conversion efficiencies (PCE) dependent the light source.

Performance measurement standard conditions

p ( ) p gSunlight varies in intensity and spectral distribution depending on thelocation on the earth and time of day and year. Researchers have adopted two common irradiance spectra: Air Mass 0 and Air Mass 1.5. Standard Reporting Conditions (SRC) has been defined as a radiant density of 1000 W/m2Standard Reporting Conditions (SRC) has been defined as a radiant density of 1000 W/m2

with a spectral distribution defined as “AM1.5G” (ASTM G173) at a cell temperature of 25°C.Acronym AM1.5 “stands for air mass 1.5” represents the typical spectrum that wouldbe expected after sunlight travels through one and a half “typical” Earth atmospheres.

Calibration laboratories: NREL (US), FhG ISE (Germany), AIST (Japan)ASTM = American Society for Testing and Materialshttp://rredc.nrel.gov/solar/spectra/am1.5/ASTMG173/ASTMG173.html

Solar cell efficiency under simulated sun light

ChallengesChallengesTo simulate a spectrum as similaras possible to the sun spectrumwith excellent homogeneity overwith excellent homogeneity overrelatively large areas

AM1 AM0AM0

AM1.5

d=1.5 atmos d=1 atmos

Earth´s Surface


Solar cell efficiency under simulated sun light


Principle of a sun simulator

solar cell

Reference cell

The unit of the photon flux


From

Performance measurement standard conditions

Contactgrid

0.5 cm

1 cm

Iluminated Area (1)

0.5 cmmonochromator

TotalAreaIl i t d

1 cm( )

1 cm

Area Including

grid

Iluminated Area (2)

JSC is rather accurately determined by EQE measurements

(1) effective area or (2) total area

∫Φ=λ

λλλ dEQEq )( )( J 0sc


From Cells to a Module


The basic building block for PV applications is a module consistingThe basic building block for PV applications is a module consistingof a number of pre-wired cells in series.Typical module: 36 cells in series referred to as 12V.Large 72-cell modules are now quite common.Multiple modules can be wired in series to increase voltage and in parallel to increase current. in parallel to increase current.

Such combinations of modules are referred to as an array

Cells wired in series


1

4 cells

Adding cells in series

4 x 0.6V36 x36 x 0.6V = 21.6 V

0.6 V each cell

36

Vmodule = n (Vd – I.RS)

Cell 1 Cell 2 Cell 36

module ( d S)Series resistance RS

PV module made up of 36 identical cells all wired in series With 1 sun insolation

Voltage and Current from a PV Module PV module made up of 36 identical cells, all wired in series. With 1-sun insolation (1 kW/m2), each cell has short-circuit current ISC = 3.4 A and at 25°C its reverse saturation current is I0 = 6 × 10−10 A. Parallel resistance RP = 6.6 Ω and series resistance RS = 0.005Ω..a) Find the voltage, current, and power delivered when the junction voltage of each cell is 0.50 V.b) Set up a spreadsheet for I and V and present a few lines of output to show how it works.) p p p p

R

I.RV 1

n.k.T)I . Rq(V

exp.-IIIp

SS0ph

+−⎥⎦

⎤⎢⎣⎡ −

−=

[ ] V

Using Vd = 0.50 V along with the other data

[ ]p

dV9.380ph R

V 1e .-III d −−=

[ ] 50

The voltage produced by the 36-cell module:V = n(V − I x R ) = 36(0 50 − 3 16 x 0 005) = 17 43 V

[ ] A6.36.65.0 1e .10x6-4.3I 5.0x9.3810 =−−= −

Vmodule = n(Vd I x RS ) = 36(0.50 3.16 x 0.005) = 17.43 VPower dilevred: P(watts) = Vmodule x I = 17.43 × 3.16 = 55.0 W

A spreadsheet might look something like the following:


p g g g


A parallel association of n cells is possible and enhances the output current of the A parallel association of n cells is possible and enhances the output current of the generator created. In a group of identical cells connected in parallel, the cells are subjected to the same voltage and the the resulting group is obtained by adding currents

n Cells

n x ISC

n Cells

in parallele

VSC,nCell n

Cell 1ISC,n

From Module to array

For modules in series the I V curves are simply added along the voltage axis at any given For modules in series, the I –V curves are simply added along the voltage axis at any given current which flows through each of the modules), the total voltage is just the sum of the individual module voltages.

For modules in parallel, the same voltage is across each module and the total


For modules in parallel, the same voltage is across each module and the totalcurrent is the sum of the currents at any given voltage, the I –V curve of the parallel combination is just the sum of the individual module currents at that voltage.

Two ways to wire an array with three modules in series and two modules in parallel.


Two ways to wire an array with three modules in series and two modules in parallel.

V VThe series modules may be wired as strings, and the strings wired in parallel.

The parallel modules may be wired together first and those units combined in series

If an entire string is removed from service for some reason, the array can still deliver whatever voltage is needed by the load, though the current is diminished, which is not the case when a parallel

f d l i dgroup of modules is removed.

Standard conditions of your PV module Standard Test Conditions:

C20NOCT ⎞⎛ °• 1 kW/m2, AM 1.5, 25°C Cell Temperature• Solar irradiance of 1 kW/m2 (1 sun)• Air mass ratio of 1.5 (AM 1.5).

.S0.8

C20NOCTTT ambCell ⎟⎠⎞

⎜⎝⎛ °−

+=

cell temperature (°C)• Key parameter: rated power PDC,STC• I –V curves at different insolation and cell temperature• NOCT: Nominal Operating Cell Temperature

2

cell temperature ( C)ambient temperature (°C)

Insolation(1 kW/m2 )(T = 20°C,Solar Irradiation= 0.8 kW/m2, winds speed 1 m/s.) (1 kW/m )

MPPMPP

VMPPVMPP V

Standard conditions of your PV module

Impact of Cell Temperature on Power for a PV Module


Impact of Cell Temperature on Power for a PV Module.Estimate cell temperature, open-circuit voltage, and maximum power output for the150-W BP2150S module under conditions of 1-sun insolation and ambienttemperature 30°C. The module has a NOCT of 47°C.temperature 30 C. The module has a NOCT of 47 C.

C64.10 8

C2043.S0 8

C20NOCTTT ambCell °=⎟⎠⎞

⎜⎝⎛ °−

+=⎟⎠⎞

⎜⎝⎛ °−

+=70

0.80.8 ⎠⎝⎠⎝From The table for this module at the standard T = 25°C, VOC = 42.8VVOC drops by about 0.37% per °C , the new VOC = 42.8[1 − 0.0037(64 − 25)] = 36.7 Vwith decrease in maximum power available of about 0.5%/°C.with decrease in maximum power available of about 0.5%/ C.With maximum power expected to drop about 0.5%/°C, this 150-W module atits maximum power point will deliver:

Pmax = 150 W· [1 − 0.005(64 − 25)] = 121 WThi i i ifi t d f 19% f it t d This is a significant drop of 19% from its rated power.


• Module with Power of 240 WC


• 240 Wc and efficiency 14.8%• 1.64×0.99=1.6236 m².• ηSTC=240/(1000×1.6236) = 14.78 %≈ 14.8 %

• Module with Power of 240 WC Siliken modules were awarded the



Number one test modules 2010 and Number two test modules 2011.

• Module with Power of 240 WC• Module with Power of 240 WC Siliken modules were awarded the




K (P) 0 41 %/°C P d b (0 41% × 240W)

Number one test modules 2010 and Number two test modules 2011.

• KT(P) = -0.41 %/°C Power decreases by (0.41% × 240W) = 0.984 W /°C

• KT(Uco) = -0.356 %/°C Load voltage decreases by (0 356 × 37V) = 0 13 V / °C

NOCT terms:Level of illumination: 800 W / m²Outdoor temperature: 20 ° C(0.356 × 37V) = 0.13 V / C.

• KT(Icc) = 0.062 %/°C Isc enhanced by(0.062% × 8.61 = 0.0053 A / °C

• NOCT = 49°C (±2°C). )S(kW/mC20C249C)(TC)(T 2⎟⎞

⎜⎛ °−°±

+°°

Outdoor temperature: 20 CWind speed: 1 m / sAir mass AM = 1.5

NOCT 49 C (±2 C). ).S(kW/m0.8

C)(TC)(T ambCell ⎟⎠

⎜⎝

+°=°

NEXTNEXTPVSEC-3:

Fundamental and application of ppPhotovoltaic solar cells and system

Q-Dots

ZnO NRs

Q Dots

ZnO NRsDSSC

O iOrganic

Introduction: Photovoltaic Solar Energy Conversion (PVSEC)Solar Cell Efficiency Tables (Version 33)


M. A. Green, Prog. Photovolt: Res. Appl. 17 (2009) 85

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