Fermi levels versus vacuum energy level

The semiconductor solid-state physics community has adopted the electron energy in vacuum as a reference whereas electrochemists have traditionally used the standard hydrogen electrode (SHE) scale. Although estimates vary [23-25, SHE appears to lie at —4.5 eV with respect to the vacuum level. We are now in a position to relate the redox potential, Eredox (as defined with reference to SHE), with the Fermi level, Ep,redox, expressed versus the vacuum reference (Figure 5a) ... 

Furthermore, it has been found that the Fermi level of an iron cathode when the breakdown occurs in water is around — 1.3eV versus a vacuum. This value is in fairly good agreement with the energy of the conduction band of water, which is —1.2 eV. This correlation justified the proposition" that the free electrons are transferred from a cathode to an anode through the conduction band of a solvent. 

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