Schottky field emission across narrow gaps and through thin films

The Schottky field enhanced emission equation appears to be applicable to a wide variety of structures. It has the following form, equation where A is Richardson´s constant, S the area, φ the work function, d is the separation distance, k is Boltzmann´s constant, T is in degrees Kelvin, ε₀ the permittivity constant, V the applied voltage, e the electronic charge and ε_r is the relative dielectric constant.