CHEM01200604009 Sreejith Kaniyankandy - Homi Bhabha ...

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1. 7. 1. Electron Injection
ET in dye-semiconductor system involves reactant state mostly localized on dye LUMO and
product state consisting of electron in CB of the semiconductor. While reactant state in dye
molecule are mostly consists of only one orbital while the product states are a continuum in a
semiconductor. Therefore Franck-Condon overlap with weighted DOS should be considered
for electron transfer rates. In the case of an adiabatic coupling, the problem is nontrivial due
to involvement of several strongly interacting potential energy surfaces (PES). In
nonadiabatic case, Marcus et al [1.45] showed ET rates as given below
2 0 2
4
1 2 ( G
E)
kET
dE( E)(1 f( E, EF
) H( E) exp
h 4kT
(1.37)
4k B
BT
0
In the above equation, free energy ( G ) is given as = ECB Eox
( E
CB
= energetic
position of conduction band and
E = oxidation potential of adsorbate LUMO; ( E)
is the
ox
DOS at energy E. ( E)
has contribution from CB and surface states. H( E) is the strength of
electronic coupling between adsorbate LUMO and states in the semiconductor at the same
energy E; and λ the total reorganization energy. The Fermi occupancy factor f( E E F
) is
introduced to include only unoccupied states. It is generally neglected due to assumption that
at room temperature electron population is negligible at room temperature in a wide band gap
semiconductor.
In real systems the electronic interaction between semiconductor and adsorbate is
inhomogeneous leading to a distribution of electronic coupling, H , which in turns leads to a