Helmholtz layer flat band potential

Fig. V-14. Energy level diagram and energy scales for an n-type semiconductor pho-toelectrochemical cell Eg, band gap E, electron affinity work function Vb, band bending Vh, Helmholtz layer potential drop 0ei. electrolyte work function U/b, flat-band potential. (See Section V-9 for discussion of some of these quantities. (From Ref. 181.)...

For the flat band potential situation, i.e. at E = Epb and for eAtpsc = e(Es — Eb) = 0, one obtains an appropriate relation for the Fermi level of the oxide Ep,ox in dependence of pb and the potential drop in the Helmholtz layer Es — Eso (Eq. (23)). The potential drop Aadsorption equilibrium at the oxide surface, i.e. from its isoelectric point. The flat band potential Epb may be determined by extrapolation of the potential dependence of the photocurrent as will be shown in Fig. 40 of Section 6.2 for passivating CU2O on Cu. With these data the positions of the energy bands of Fig. 39 have been determined, however with the assumption of an energy difference of the Fermi level from the conduction or the valence band of 0.25 eV, respectively. For the anodic oxides of Cu, the position of the bands has been determined independently by UPS measurements (Section 6.2). 

Relationships are shown between the electrolyte redox couple (H /H2), the Helmholtz layer potential drop (V ), the semiconductor band gap (Eg), electron affinity Of), work function (sc), band bending (V0), and flat-band potential (Uf ). The electrochemical and solid state energy scales are shown for comparison. is the electrolyte work function. 

The effect of the Helmholtz layer on the semiconductor band bending is contained within the flat-band potential. This important parameter is a property both of the semiconductor bulk and the electrolyte, as seen from the following relation ... 

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