Fermi hole contact mechanism

Although the reverse current of an ideal Schottky barrier is J, in practice there are other current soitfces. Imperfect contacts have a leakage current which generally increases exponentially with bias. Even with an ideal contact, there is a thermal generation current caused by the excitation of electrons and holes from bulk gap states to the band edges. This mechanism determines the Fermi energy position under deep depletion conditions. The current density is the product of the density of states and the excitation rate and is approximately. 

The Andreev reflection is the second-order quantum mechanical process by which an electron-like particle incident on a superconductor with a quasi-particle excitation energy E above the Fermi energy may be transmitted as a Cooper pair in the superconductor, if a hole-like particle (-E) is reflected along the path of the incoming electron [12], For a superconductor-semiconductor interface with low contact resistance (high transparency) and with a negligible Schottky barrier, the Andreev scattering leads to an increased conductance. 

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