Thermodynamic and Kinetic Criteria for Light-Driven Water Splitting

2 Thermodynamic and Kinetic Criteria for Light-Driven Water Splitting 

In semiconductor physics, the equilibrium free energies of electrons and holes are expressed in terms of the corresponding Fermi energies or (equivalently) their electrochemical potentials. In order to enable comparison with the electron energy levels in the electrolyte, it is useful to define the redox Fermi levels on the vacuum scale using the approximate relationship 

The Fermi-Dirac function can be approximated by the Boltzmann function if Ep - E) is much greater than kpT. The Fermi energy Ep determines n and p, the concentrations of 

In photoelectrolysis cells, the concentrations of electrons and holes are changed from their dark equilibrium values due to creation of electron-hole pairs by absorption of photons. Since thermal equilibration with lattice vibrations is much faster than the electron-hole recombination of electrons, electrons and holes can be considered to be in thermal equilibrium with the lattice, even though they are metastable states. Therefore, Fermi-Dirac statistics can still be used by defining quasi-Fermi levels ( Ep and pEp) for electrons and holes in terms of their steady-state concentrations under illumination, n and p.  

It is these quasi-Fermi levels that are important in defining the thermodynamic criteria for light-driven water splitting. In the case of an n-type semiconductor such as rutile, the concentration of electrons in the dark is high (typically 10 cm ), whereas the concentration of holes is vanishingly small since the law of mass action applies. 

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