Transmission through potential barriers with a generalised Fermi-Dirac current

We study the effect of the shape of different potential barriers on the transmitted charged current whose fermionic population is not monoenergetic but is described by means of an energy spectrum. The generalised Kappa Fermi-Dirac distribution function is able to take into account both equilibrium and non-equilibrium populations of particles by changing the kappa index. Moreover, the corresponding current density can be evaluated using such a distribution. Subsequently, this progressive charged density arrives at the potential barrier, which is considered under several shapes, and the corresponding transmission factor is evaluated. This permits a comparison of the effects for different barriers as well as for different energy states of the incoming current.