Electrical transport across the barrier

For simplicity, only electron transport across the interface is considered. At zero applied voltage, the equilibrium current fluxes in 

The application of a bias changes the current from the semiconductor by a factor e eVJkT), because the Fermi energy is raised or lowered by with respect to the metal Fermi energy. Thus, 

In forward bias (positive V ) the current increases exponentially with (when kT) and in reverse bias the current saturates at J. The forward bias current is more usually written as 

The temperature dependence of J, measured by extrapolation of the forward J-V data, is shown is Fig. 9.3. The saturation current density is given in the thermionic emission model by 

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. 

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