Simple Method for Calculating the Tunneling Current of an Esaki Diode

The exact solution of Esaki's equation for the tunneling current is extremely complicated. A method is presented allowing a simple solution. Under the assumption that the distances between the Fermi level and the band edges $E_1$ and $E_2$ on both sides of the junction do not exceed $2kT$, the Fermi function is approximated by a straight line. The resulting equation indicating the voltage dependence of the tunneling current is as follows: $I=A^{\prime \prime \prime }V{(E_1+E_2-qV)}^2$.