Constraints to the flat band potential of hematite photo-electrodes

Abstract

We revisit the fundamental constraints that apply to flat band potential values at semiconductor photo-electrodes. On the physical scale, the Fermi level energy of a non-degenerate semiconductor at the flat band condition, E_F(FB), is constrained to a position between the conduction band, E_C, and the valence band, E_V,: |E_C| < |E_F(FB)| < |E_V| throughout the depth of the semiconductor. The same constraint applies on the electrode potential scale, where the values are referenced against a common reference electrode: U_C(FB) < U_F(FB) < U_V(FB). Some experimentally determined flat band potentials appear to lie outside these fundamental boundaries. In order to assess the validity of any determined flat band potential, the boundaries set by the conduction band and the valence band must be computed on both scales a priori, where possible. This is accomplished with the aid of an analytical reconstruction of the semiconductor|electrolyte interface in question. To illustrate this approach, we provide a case study based on synthetic hematite, α-Fe₂O₃. The analysis of this particular semiconductor is motivated by the large variance in the flat band potential values reported in the literature.