# Transmission through potential barriers with a generalised Fermi-Dirac current

## TL;DR

This paper investigates how various potential barrier shapes affect the transmission of charged currents with non-monoenergetic fermionic populations described by a generalized Kappa Fermi-Dirac distribution, considering both equilibrium and non-equilibrium states.

## Contribution

It introduces a method to evaluate transmission through different barriers using a generalized distribution that accounts for non-equilibrium populations, extending traditional models.

## Key findings

- Transmission varies with barrier shape and energy distribution.
- The generalized Kappa Fermi-Dirac distribution effectively models non-equilibrium populations.
- Comparison shows significant differences in transmission for different barrier geometries.

## Abstract

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.