how solar cells work -...
Post on 18-May-2020
9 Views
Preview:
TRANSCRIPT
How Solar Cells Work
Basic theory of photovoltaic energy conversion
Peter WürfelUniversity of Karlsruhe, Germany
Three Messages
Sun is a heat source, solar cells must be heat engines
Important conversion stepsolar heat chemical energy of electron-hole pairslimited by thermodynamics
Conversion of chemical energy electrical energycan be 100% efficient and needs more than a pn-junction
Important: generation of (entropy-) Free Energy by cooling
F = E - TS
Carnot process
P
V
isothermal
isothermal adiabatic
adiabatic
1
2
3
4
isothermal
isothermal
adiabaticadiabatic
1 2
34
T
S
TA
T0
Solar cells are heat engines
Principle
I = T IE,in S S,in
IS,in
T I0 S,outI IS,out S,in≥
I I (1 - T /T )E,out E,in 0 S£
The solar cell as a heat engine?
Questions:
What is the working medium (the gas)?
What kind of free energy is produced?
Conversion of solar heat into chemical energy of electrons and holes
Energy per photon ħω→ chemical energy µeh per e-h pair by thermalisation
εC εFCεF
εVεFV
εe
gdn /dh eε
dn /de eε
10 s-14 10 s-12
> meh
energy gap is necessary
Maximum chemical energyReduce entropy generation during thermalisation by
reducing the energy range, for which Fermi-distribution is established
ideal: isoenergetic thermalisation in narrow energy ranges is isentropic
DeC eFCeF
DeVeFV
ee
ω
dn /dh ee
dn /de ee
10 s-14 10 s-12
μeh
e
h
tandem cells
Tandem cells2 cells → 4 Fermi-energies for 4 energy ranges
4-level system3 Fermi-energies for connection in series
eF1
eF2
eF3
eF4
Recombinationrecombination
at the surface in the materialnon-radiative non-radiative
radiative
surface recombination bulk lifetimevelocity
effective lifetime
RecombinationDirect optical transitions in 2-level system
drup drspont drstim
[ ]212 1 2
d ( )d ( ) ( ) 1 ( ) d( )
d( )up
jr M D f f γ ω
ω ε ε ωω
= −
e1
e2
[ ]212 2 1
d ( )d ( ) ( ) 1 ( ) d( )
d( )stim
jr M D f f γ ω
ω ε ε ωω
= −
[ ]2 012 2 1
cd ( ) ( ) ( ) 1 ( ) d( )nspontr M D D f fγω ω ε ε ω= −
( )3
23 3 3
0
( )4
nDcγ ω ω
πΩ
=
density of states for photons
2 1ε ε ω− =
⎫⎪⎪⎬⎪⎪⎭
upwards
downwards
Absorption coefficient
[ ]212 1 2
12
d ( ) d ( ) d ( )
( ) ( ) d ( )( ) d ( )
abs up stimr r r
M D f f jj
γ
γ
ω ω ω
ε ε ω
α ω ω
= −
= −
=
absorption coefficient [ ]212 12 1 2( ) ( ) ( )M D f fα ω ε ε= −
12 2 1( ) 0 for ( ) ( )f fα ω ε ε< >
( ) ( )12( , ) ( ,0) 1 ( ) exp ( )j x j r xγ γω ω ω α ω= − −
amplificationj xg( )
x
Spontaneous emissionreplace in spontaneous emission rate
[ ][ ]
1 2012
1 2
1 ( ) ( )d ( ) ( ) ( ) d
( ) ( )spont
f fcr Dn f fγ
ε εω α ω ω ω
ε ε−
=−
[ ]2 12
121 2
( )( ) ( )
M Df fα ωε ε
=−
1 21 2
1 1( ) and ( )exp 1 exp 1FV FC
f f
kT kT
ε εε ε ε ε
= =− −⎛ ⎞ ⎛ ⎞+ +⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
2 1ε ε ω− =with and
0 d( )d ( ) ( ) ( )( )exp 1
spontFC FV
cr Dn
kT
γωω α ω ω
ω ε ε=
− −⎛ ⎞ −⎜ ⎟⎝ ⎠
Production of chemical energy
2
3 3 2
( )( ) ( )( )4 exp 1FC FV
dj a dc
kT
γωω ω ω
ω ε επΩ
=− −⎡ ⎤ −⎢ ⎥⎣ ⎦
djg,abs
djg,emit
djeh = djg,abs – djg,emit
only radiative recombination, monochromatic
generalized Planck law
Sun: T = TS εFC – εFV = 0Semiconductor: T = T0 εFC – εFV ≠ 0
eFC – eFV = meh
absorptance ( ) ( ){ }( ) 1 ( ) 1 exp ( )a R dω ω α ω= − − −
djeh = dgeh – dreh
Characteristic for production of chemical energyby monochromatic lightdjeh(meh) = djg,abs – djg,emit(meh)
djg,abs
djeh
djg,emitdjg
wmeh,mp
mehmeh,ocmeh,sc
h =
Production of chemical energy frommonochromatic radiation
0 1 2 3 4 50
102030405060708090
100
ef
ficie
ncy
/ %
photon energy / eV
maximum concentration
no concentration
Infinite tandem: η = 86% max. concentration
Production of chemical energyin wide band semiconductor with total solar spectrum(Shockley-Queisser)
0 1 2 30
0.1
0.2
0.3
0.4
η
εG / eV
max. concentration
no concentration
AM0 spectrum
Optimal materials
full absorption above energy threshold (in a thin film)
minimum recombination for given difference of Fermi-energies:
radiative recombination
good materials for solar cells should be luminescingadvantage for organic materials?
difference of the Fermi-energies (chemical energy per eh-pair) is obtained from luminescence intensity
Chemical energy → electrical energy
Charge current
-ej
eFV
eFC
eV
eC
ee
0 xjQ
G R µehjQ = - e (G - R)
Separation of electrons and holes withsemi-permeable membranes← H2 , O2 →
Voltage: eV = eF,right - eF,left = μeh
O2
O2
O2
O2 O2
O2
O2
O2
O2
O2
H2
H2 H2
H2 H2H2
H2
H2
H2
← e , h →
ee
eF,C eF,V
eV
eC
x
-ej0
absorbern-type p-type
eF,lefteF,rightµeh
Transport properties, drift current
acceleration ii
i
z e Eam∗=
,mobility C ii
i
eb
mτ∗=
drift current
Diffusion currentdiffusion current
Einstein relation
chemical potential of particles i,0 ln ii i
i
nkTN
μ μ⎛ ⎞
= + ⎜ ⎟⎝ ⎠
Fick‘s law of diffusion
total charge current
i i iz eη μ ϕ= +
for electrons (zi = -1) and holes (zi = +1)
electrochemical potential
e e FC
h h FV
ee
η μ ϕ εη μ ϕ ε
= − == + = −
field and diffusion currents do not exist
Dye Solar Cell
Problem: e and h bound in exciton
e
h
Problems with excitons in organicsemiconductors
�e
�exciton
�exciton
�C
�V
electron bound to free hole hole bound to free electron
lumo
homo
large exciton binding energy
1 2
0
exciton dissociation
Requirements for solar cell structures
+-
Le
n+
p+
absorbern+
p+
Sufficient condition:Le, Lh >> ta >> 1/a
rules out low mobility absorbers
ta
Necessary condition:Le, Lh >> distance betweenmembranes
1/α
Conditions for optical and electrical properties of absorberssplitting of Fermi-energies selective transport
ta >> 1/a
bulk heterojunction
Advantage of nano-structures in conventional solar cells
distance between membranes on nm-scale
absorbers can have poor transport properties
Problem: large interface area may increaserecombination
luminescence as a tool to proveenergy conversion efficiencyspectral intensity of luminescence
( )( ) ( )
2
3 3 2
0
2
, 3 3 2
0
( )( )4
exp 1
spectral emission of photons through surface of homogeneous system( )( )
4 ( )exp 1
(
emissioneh
FC FV
emissionemit
FC FV
dR x dc x x
kT
dj a dc
kT
a
γ
ωα ω ωπ ω ε ε
ωω ωπ ω ε ε
Ω=
⎛ ⎞− −⎡ ⎤⎣ ⎦ −⎜ ⎟⎜ ⎟⎝ ⎠
Ω=
⎛ ⎞− −−⎜ ⎟
⎝ ⎠
[ ] ( )) 1 ( ) 1 exp ( ) eR Lω ω α ω= − −⎡ ⎤⎣ ⎦
Luminescence as a characterization tool
16000
14000
12000
10000
8000
6000
4000
2000
16000
14000
12000
10000
8000
6000
4000
2000
l < 1000 nmElectroluminescence
counts per pixel
Physics of Solar Cells
top related