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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