a method to rapidly predict the injection rate in dye sensitized solar cells

A method to rapidly predict the injection rate in Dye Sensitized Solar Cells

Daniel R. Jones and Alessandro TroisiPG Symposium 2009

Outline

1. Introduction • What is a dye sensitized solar cell?• How can theory help?

2. Theory• How do we compute the rate of electron transfer?

3. Results• The rate of injection by this method.

4. Continuations• Where do we go from here?

Dye Sensitized Solar Cell

Load Voltage

Conductive Glass Electrode

3 I−

Dye CoatedNanocrystalline TiO2

CounterElectrode

I3−

Dye Sensitized Solar Cell

+ Attractive “third-generation” solar technology offering up to 11% IPCE

+ Cheap material and processing costs mean that it may compete with fossil fuels in terms of W/$

− Ideally needs to be more efficient to increase uptake.− Liquid electrolyte is not ideal

How can theory help?

Designing the optimum chromophore is still an active area of research

Screen candidate molecules for their potential Minimize efficiency losses Better understanding of the electron transfer reaction

mechanisms Aspire to a multiscale model of the functioning cell

Goal

To provide a method to screen candidate molecules for their potential in dye sensitized solar cells (DSSC) which is:

– computationally inexpensive– not reliant on experimental parameterization

Compute the rate of electron transfer from the photoexcited chromophore into the conduction band of the TiO2

For example…

Li et al investigated Anthraquinone dyes1

Found they produced cells with efficiency worse than that of naked TiO2

Chemical intuition does not always work Can we do better by computational screening?

1 Li et al. Solar Energy Materials and Solar Cells 2007, 91, 1863-1871.

Outline

1. Introduction • What is a dye sensitized solar cell?• How can theory help?

2. Theory• How do we compute the rate of electron transfer?

3. Results• The rate of injection by this method.

4. Continuations• Where do we go from here?

The Method

1)

2)

3)

Chromophore dye system modelled by separating into 3 subsystems

The Method

It can be shown that the effective Hamiltonian for the state can be written

The self energy, Σ, is complex, and can be separated into real and imaginary components

The imaginary part of self energy, Γs, can be calculated using l

s

slV

s

i ( ) exp( )ss sP t t

*2( ) ( )s sl ls l

l

E V V E E

0effH H

The Method

To compute the coupling terms, Vsl, the states on the semiconductor and the states on the chromophore are recast in an atomic basis set

The energy dependent density matrix ρkk’.

The self energy on the molecule in an atomic basis set

The self energy on the first excited state

* *' '

, '

( ) 2 ( )mn mk k n lk lk ll k k

E V V C C E E

*' '( ) ( )kk kl k l l

l

E C C E E

*' '

'

2( ) ( )mn mk k n kk

kk

E V V E

smm

s c m

,

( ) ( )r mn rm rnm n

E E c c

The Method

1)

2)

3)

Chromophore dye system modelled by separating into 3 subsystems

Csm, E

Vmk

ρkk’

Γmn

Coupling - Vsm

Rutile (110) surface Ti-O(mol) 2.07 Å Ti-Ti-O(mol) 80˚

Anatase (101) surfaceTi-O(mol) 2.16 ÅTi-Ti-O(mol) 70˚

Computing ρkk’

*' '( ) ( )kk kl k l l

l

E C C E E

•Electronic structure computed using B3LYP/6-31G*.•Clusters embedded in a volume of point charges to model bulk electrostatics.

Chromophore

• Chromophore’s electronic structure and geometry computed using B3LYP/6-31G*

• csm comes from the DFT output• The energy of injection, E, can be

approximated in one of 2 ways.1. Using the energy of the LUMO2. Take the difference between the energy

of the 1st excited state from TD-DFT and the energy of the cation.

Outline

1. Introduction • What is a dye sensitized solar cell?• How can theory help?

2. Theory• How do we compute the rate of electron transfer?

3. Results• The rate of injection by this method.

4. Continuations• Where do we go from here?

Variation of rate with injection energy

E in this range

Real Chromophores – realistic rates?

Dye rutile (110)/ fs anatase(101) / fs

a 2.83 1.43

b 56.7 53.9

c 2.25 0.18

d 1.81 5.96

e 3.58 6.20

f 9.99 4.09

a) b)

c) d)

e) f)

Molecular Engineering?

Perylene derivatives Substitution at the 2 position means the LUMO

is less localised on the carboxylic acid group. Rutile (110) lifetimes

7.99 fs 12.3 fs 27.3 fs

Importance of injection energy

•Rapid variation of injection rate with changing energy.•Energy of injection computed using the LUMO energy of the neutral chromophore compared to that computed using ETDDFT−ECation differ by ~1.5 eV

•Computed rate using ELUMO and ETDDFT−ECation

•Qualitatively different, the more sophisticated computation matches much better with experimental evidence

2.83 fs

2260 fs

56.5 fs

195 fs

Conclusions and closing remarks

We have developed a method to rapidly compute the rate of electron transfer from chromophore to semi-conductor in DSSC

We note the importance of choosing the correct injection energy

Our method may be improved by aligning the energy levels with experiment

This method is modular, so may be improved relatively easily if more accurate computations for any of the subsystems are available

Outlook

All chromophores considered so far have been connected by a carboxylic bridge, consider other anchoring groups

Compute the rate of recombination, where an electron in the conduction band neutralises the chromophore+, more difficult to guess qualitatively

Try to find “better ways” to treat the semiconductor surface

Write a thesis…

Acknowledgements

Alessandro Troisi

His group, past and present:Dave Cheung, Natalia Martsinovich, Arijit Bhattacharyay, Sara Fortuna, Dave McMahon, Jack Sleigh, Konrad Diwold

EPSRC and University of Warwick for funding.

… and you for your attention