Fermi Dirac distribution surface states

The question of how the p factor enters in relation to the applicability of the Fermi-Dirac distribution in electron transfer processes appears to require further exploration. The problem arises from the way change of Fermi-level energy is assumed just to shift the potential energy surface up or down by VF and hence cause a change of (1 - p)VF in the transition-state energy according to the Br0nsted principle. 

The energy states of the surface, denoted by Es, are located with respect to the Fermi energy value Ep, which corresponds to the reference state of the solid. In a similar way to the bulk states, each surface state can be empty or occupied by an electron. The ratio of surface states Es occupied by electrons, denoted by ft (Es), is given by the Fermi-Dirac distribution function ... 

At absolute zero, the highest occupied energy level is referred to as the Fermi level (in 3-D Fermi surface), derived from Fermi-Dirac statistics.The Fermi-Dirac distribution function, f(E), describes the probability that a given available energy state will be occupied at a given temperature ... 

The calculation of /rec requires a stipulation of the surface states that are occupied. Since surface states exchange electrons both with the conduction band and the electrolyte, the statistics are more complex than in a bulk trap. The occupation of the surface states is determined by a demarcation level and in general it is not possible to define a Fermi level [180, 215]. For simplicity we assume here that the trapping-release rate is sufficiently fast, so that the surface state is in equilibrium with the transport states, and the occupancy of both is described by Fermi-Dirac distribution, with a single Fermi level. 

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