Tunneling Current in Esaki Diodes

The integral giving the net tunneling current flowing across the junction in an Esaki diode, I=A∫Ec^Eᵥfc(E)-fᵥ(E)Zρc(E)ρᵥ(E)dE is evaluated under the normal assumptions that (ξc-Ec) and (Eᵥ-ξᵥ) are of the order of $2kT$. The resulting expression is $I={-}{A}^{{'}{'}}{{({E}ᵥ{-}{E}c)}²(1{-}{e}qV/kT)}{(m+n){e}a/2+(1+{e}qV/kT)},$ where ${A}^{{'}{'}}$ is an arbitrary constant and $m$, $n$, and $a$ are functions of the Fermi levels on both sides of the junction, the location of the band edges and the absolute temperature. This expression is plotted as a function of the applied voltage for temperatures of 200^∘{}K, 300^∘{}K, and 350^∘{}K for donor and acceptor concentrations of 10¹⁹ cm^-3 and 1.6×{}10¹⁹ cm^-3, respectively. The resulting curves compare quite favorably with those of Esaki's.