Numerical simulaon of the performance of the dye‐sensized solar … · 2011-05-03 · Numerical simulaon of the performance of the dye‐sensized solar cell 1 Departamento de Física

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


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


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


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


€

∂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)


€

∂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


€

∂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):


€

∂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


€

∂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


€

V = −(EF − EF

0 )e

=kBTαe

lnnV0

n00

n(x)

n00

nV0

0 d

a

b

x

JSC

VOC

J

V

Electron density profile


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


Use the experimental current transient to obtain the trap

distribution parameter α

Villanueva et al., J. Phys. Chem. C 2009, 113, 19722–19731.


Use open-circuit voltage versus light intensity and time decay to obtain charge transfer parameters from TCO substrate

(J0TCO , b)

slope = 78 mV


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


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%


TiO2 (brookite)/N719/organic electrolyte

eff = 4.0%

α = 0.28

slope = 33 mV


ZnO/D149/organic solvent electrolyte

R = 30 Ohm cm2

α = 0.2 kR

0 = 3.3 10-3 s-1

eff = 2.8%


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


“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


€

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



γ ≈ 0.75 for NPs

ZnO/D149/organic solvent electrolyte


γ = α + b α = 0.2 b = 0.55

Non-ideality in Voc vs. light intensity curve


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


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


PROYECTO DE EXCELENCIA P06-FQM-01869

CONSOLIDER-INGENIO 2010 CSD2007-00007

Acknowledgements

FPU fellowships

Grant No. 80002-Y

Red Temática en Fuentes de Energía


Documents

Numerical simulaon of the performance of the dye‐sensized solar … · 2011-05-03 · Numerical simulaon of the performance of the dye‐sensized solar cell 1 Departamento de Física