ennaoui cours rabat part ii
DESCRIPTION
Prof. Dr. Ahmed Ennaoui Photovoltaic Solar Energy Conversion Advanced course 2 ENIM Rabat Morocco إنتاج الكهرباء من الطاقة الشمسيةTRANSCRIPT
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
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
Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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 =
Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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 =
Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
(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
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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
∇+=
+∇∂
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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=
Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
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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
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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
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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=→
⎪⎭
⎪⎬
⎫
=
==+
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
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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 ≈
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
⎟⎠
⎜⎝
+⎟⎠
⎜⎝
+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
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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−=
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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 x´c 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
0´c
´c
´c
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
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
Basic: PN junction Loss in Jph
⎟⎟⎠
⎞⎜⎜⎝
⎛
+−−= −αW
p
eαL111 R)(1 η
SEM image
⎠⎝ p
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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 ==
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
Dark current and photocurrent
1nkTqVexpII 0D ⎥⎦
⎤⎢⎣⎡ −= L
D0 I- 1
nkTqV
expII ⎟⎠⎞
⎜⎝⎛ −=
V (volt) V (volt)
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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 −−≈
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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↓
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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.
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
Role of Iph for the influence of RS
FF↓ and η↓ with increasing IFF↓ and η↓ with increasing ISC
Voltage (Volt)g ( )
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
⎟⎟⎠
⎞⎜⎜⎝
⎛
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
>
⎟⎟⎟⎟
⎠⎜⎜⎜⎜
⎝⎟⎟⎠
⎞⎜⎜⎝
⎛+=
⎟⎟⎠
⎞⎜⎜⎝
⎛=
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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 =⎟
⎠⎞
⎜⎝⎛ +=⎟⎟
⎠
⎞⎜⎜⎝
⎛+=⇒=−−= −
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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:
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
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)
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und EnergieSources: FU-Berlin
Lab. Work: ISC-VOC measurements
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und EnergieSources: FU-Berlin
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
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und EnergieSources: FU-Berlin
Consequence of EA: Temperature dependence of VOC
Lab-Work: Activation energyq A p p OC
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und EnergieSources: FU-Berlin
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
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und EnergieSources: FU-Berlin
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
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und EnergieSources: FU-Berlin
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
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
Solar cell efficiency under simulated sun light
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und EnergieSources: FU-Berlin
Principle of a sun simulator
solar cell
Reference cell
The unit of the photon flux
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und EnergieSources: FU-Berlin
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
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
From Cells to a Module
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
From Cells to a Module
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:
From Cells to a Module
p g g g
From Cells to a Module
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
From Module to array
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.
From Module to array
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
Standard conditions of your 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.
A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
• Module with Power of 240 WC
Standard conditions of your PV module
• 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
Standard conditions of your PV module
• 240 Wc and efficiency 14.8%• 1.64×0.99=1.6236 m².• ηSTC=240/(1000×1.6236) = 14.78 %≈ 14.8 %
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
Standard conditions of your PV module
• 240 Wc and efficiency 14.8%• 1.64×0.99=1.6236 m².• ηSTC=240/(1000×1.6236) = 14.78 %≈ 14.8 %
• 240 Wc and efficiency 14.8%• 1.64×0.99=1.6236 m².• ηSTC=240/(1000×1.6236) = 14.78 %≈ 14.8 %
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)
Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie
M. A. Green, Prog. Photovolt: Res. Appl. 17 (2009) 85