numerical simulaon of the performance of the dye‐sensized solar … · 2011-05-03 · numerical...
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Numericalsimula,onoftheperformanceofthedye‐sensi,zedsolarcell
1 Departamento de Física Aplicada, CINVESTAV‐IPN, Mérida, Yucatán, México
2Departamento de Sistemas Físicos, Químicos y Naturales, Universidad Pablo de Olavide, 41013 Sevilla, Spain
* Current address: Chemical & Materials Science Center, NaQonal Renewable Energy Laboratory, Golden, CO 80401, USA
JulioVillanueva‐Cab1,*,ElenaGuillén2,JuanAntonioAnta2andGerkoOskam1
I Taller de Innovación Fotovoltaica y Celdas Solares; March 8 – 10, 2011, CIE – UNAM, Temixco.
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
• photoelectrochemical cell • porous, high surface area metal oxide film • light absorption by adsorbed sensitizer molecules • electron transport in solid and ion transport in solution
3 I -
3 I -
I -
I -
I -
+
e -
dye
donor acceptor
CB
E redox
E
TCO TiO 2 electrolyte solution
h ν
D0/D+
D*/D+
recombination
Objectives
Numerical tool to simulate the current-voltage curve in Dye Sensitized Solar Cells (DSSC)
Make a connection with microscopic theories on transport and recombination so the model is as rigorous as possible (but not too complex!!) Make a connection with experimental techniques to obtain the relevant parameters
I Taller de Innovación Fotovoltaica y Celdas Solares; March 8 – 10, 2011, CIE – UNAM, Temixco.
Dye solar cells: generation, transport and recombination
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
Absorbance
x
e-e-e-gl
ass
TCO
light
electron density
x
electron acceptors
ionsions
Electron density
• Particles are too small for band bending • Solution with ions provide shielding • Electron transport is impeded by transfer
to electron acceptor in the solution
steady-state measurements (Lindquist et al.): photocurrent is dominated by diffusion
Short circuit
Open circuit
∂n∂t=1e∂J∂x
− R +G
J = enµn∂φ
∂x+ eD ∂n
∂x
Continuity equation
n is the electron density under illumination J is the current density in the film G and R are generation and recombination rates
Current density µn is the electron mobility φ is the electrical potential D is the electron diffusion coefficient
€
∂n(x, t)∂t
= D ∂2n(x, t)∂x2
+n(x, t)− n0
τ0+Γα exp(−αx) = 0
Diffusion transport equation
electron injection recombination flux
Thediffusioncoefficientandrecombina,ontermaredependenttothelightintensitytransportequa,onismorecomplex:numericalmethodstomodelelectrontransport
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
Band diagram showing trap states in the band gap. The rate constants k1 and k-1 denote trapping and de-trapping of electrons, respectively. The Fermi energy determines which traps dominate the transport kinetics.
Conduction Band
Valence Band
EF,n k1 k-1
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
D is a power law function of the light intensity, i.e, the electron density
Electron Transport in Porous Nanocrystalline TiO2 Photoelectrochemical Cells F Cao, G Oskam, G J Meyer, and P C Searson J. Phys. Chem. 1996, 100, 17021-17027.
€
∂n(x, t)∂t
=G(x) +∂∂x
D(n) ∂n(x, t)∂x
− kR (n) n(x, t) − n0
0( ) +JTCOed
Continuity equation for electrons
GENERATION
DIFFUSION RECOMBINATION
CHARGE TRANSFER FROM TCO SUBSTRATE
1-dimensional problem (x is the distance to the substrate)
n(x,t) is the total electron density
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
€
∂n(x, t)∂t
=G(x) +∂∂x
D(n) ∂n(x, t)∂x
− kR (n) n(x, t) − n0
0( ) +JTCOed
GENERATION
€
G(x) = φinj I0 λ( ) εCell (λ) exp −εCell (λ) x[ ] dλλmin
λmax∫
Dye absorption coefficient
Injection quantum
yield
(0 < φinj < 1)
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
€
∂n(x, t)∂t
=G(x) +∂∂x
D(n) ∂n(x, t)∂x
− kR (n) n(x, t) − n0
0( ) +JTCOed
DIFFUSION
€
D(n) = Dref f (n) = Drefnnref
1−αα
Density-dependent (Fermi-level dependent)
diffusion coefficient
€
g(E) =αNt
kBTexp − αE
kBT
€
EF (x, t) = −kBTαln n(x, t)
Nt
α = 0.2-0.5
Multiple trapping mechanism
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
€
∂n(x, t)∂t
=G(x) +∂∂x
D(n) ∂n(x, t)∂x
− kR (n) n(x, t) − n0
0( ) +JTCOed
€
kR = kRref f (n) = kR
ref nnref
β
€
EF (x, t) = −kBTαln n(x, t)
Nt
β = (1-α)/α
The same as for diffusion
RECOMBINATION from nanostructured film
Rate constant is f(EF):
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
€
∂n(x, t)∂t
=G(x) +∂∂x
D(n) ∂n(x, t)∂x
− kR (n) n(x, t) − n0
0( ) +JTCOed
RECOMBINATION from nanostructured film
Rate is f(V):
€
kR = kRref f (V ) = kR
ref exp beVkT
b ≈ 0.5
€
kR = kRref n(x)
nref
bα
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
€
∂n(x, t)∂t
=G(x) +∂∂x
D(n) ∂n(x, t)∂x
− kR (n) n(x, t) − n0
0( ) +JTCOed
CHARGE TRANSFER FROM TCO SUBSTRATE
€
JTCO = JTCO0 exp −(1− b)eV
kBT
− exp
beVkBT
Butler-Volmer equation
bTCO ≈ 0.5
TCO
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
€
V = −(EF − EF
0 )e
=kBTαe
lnnV0
n00
n(x)
n00
nV0
0 d
a
b
x
JSC
VOC
J
V
Electron density profile
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
J
V
Use the experimental short-circuit current to fit either the injection yield or the dye concentration in cell
Use the experimental open-circuit voltage to obtain a
first estimate of the recombination constant pre-
factor
Practical procedure
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
Use the experimental current transient to obtain the trap
distribution parameter α
Villanueva et al., J. Phys. Chem. C 2009, 113, 19722–19731.
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
Use open-circuit voltage versus light intensity and time decay to obtain charge transfer parameters from TCO substrate
(J0TCO , b)
slope = 78 mV
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
J
V
Use the current at maximum power point to obtain the
total series resistance in the cell
Numerical Method: Forward Time Centered Space (FTCS) with the Lax scheme
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
TiO2/N719/organic electrolyte ZnO/N719/solvent-free electrolyte
Numerical Simulation of the Current-Voltage Curve in Dye-Sensitized Solar Cells Julio Villanueva, Juan A. Anta, Elena Guillén, and Gerko Oskam J. Phys. Chem. C 2009, 113, 19722–19731.
eff = 6.5% eff = 1.5%
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
TiO2 (brookite)/N719/organic electrolyte
eff = 4.0%
α = 0.28
slope = 33 mV
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
ZnO/D149/organic solvent electrolyte
R = 30 Ohm cm2
α = 0.2 kR
0 = 3.3 10-3 s-1
eff = 2.8%
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
Parameter ZCell(ZnO) TCell(TiO2)BrookiteCellZnO/D149
CCell (M) 0.140.25 0.24
kR0 (s‐1) 9.010‐7 3.110‐97.310‐93.310‐3
α 0.18 0.200.28 0.2
blocking layer no no yes yes
J0(TCO) (A cm‐2) 1.010‐4 1.110‐5 1.510‐9
bTCO 0.500.550.55
dVoc /dLn(Int) (mV) 52 78 3334
R (Ω cm2) 37.511.3 15.330
L (µm) 10.5180 117
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
“Influence of the recombination mechanism on the IV-curve of dye-sensitized solar cells” J Villanueva, G Oskam and J A Anta, Solar Energy Materials & Solar Cells, 94 (2010) 45–50.
“Transport-limited” or “transfer-limited recombination”
Model 1: Transport-limited recombination
€
kR = kRref exp beV
kT
€
kR = kRref n
nref
1−αα
Model 2: Transfer-limited recombination
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
€
D(n) = Drefnnref
1−αα
€
kR = kRref n
nref
1−αα
€
kR = kRref exp beV
kT
€
VOC ∝kBTeLn I
€
VOC ∝kBT
(α + b)eLn I
Model 1: Transport-limited recombination
Model 2: Transfer-limited recombination
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
γ ≈ 0.75 for NPs
ZnO/D149/organic solvent electrolyte
Model 2: Transfer-limited recombination
γ = α + b α = 0.2 b = 0.55
Non-ideality in Voc vs. light intensity curve
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
Comparison “total electron” and “free electron” density models
Steady-state conditions
€
0 =G(x) + D ∂2ncb∂x 2
− kR ncb − n0( )γ
€
0 =G(x) +∂∂x
D(ntot )∂ntot∂x
− kR (ntot ) ntot − n0( )
If γ < 1, we have the case of non-first order recombination • light intensity dependence of the electron diffusion length • discrepancy results from steady-state & modulation methods
Free electron
Total electron
For γ = 1, both equations are formally identical
€
kR = kRref exp beV
kT
Model 2: Both models are identical with γ = α + b
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
Conclusions Numerical solution of the continuity equation in DSSC was obtained with explicit consideration of recombination via the oxide and the substrate
The model can fit simultaneously current and voltage transients, open-circuit voltage vs. light intensity and the full IV curve The model was tested for several very different kind of cells and different types of recombination kinetics The total electron density model compares well with the free electron model to describe transport & recombination kinetics
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).
PROYECTO DE EXCELENCIA P06-FQM-01869
CONSOLIDER-INGENIO 2010 CSD2007-00007
Acknowledgements
FPU fellowships
Grant No. 80002-Y
Red Temática en Fuentes de Energía
I Taller de Innovación Fotovoltaica y Celdas Solares, CIE–UNAM (2011).