At low forward biases, a high current flows in Esaki junctions due to band-to-band tunnelling. At sufficiently high biases the current flows by normal forward injection. Between these two bias ranges, the current is unexpectedly high and has been called the excess current. A comprehensive experimental study has been made of this excess current in silicon junctions. It is shown that the properties of the excess current observed so far can be accounted for by a mechanism originally suggested by Yajima and Esaki, in which carriers tunnel by way of energy states within the forbidden gap. Based on this model, the following expression for the excess current, $I_x$, is proposed: $I_x\sim D_x\exp \{-(\frac{{\alpha }_x{W}_1{e}^{\frac{1}{2}}}{2}\left)\right[\epsilon -e{V}_x+0.6e(V_n+V_p)\left]\right\},$ where $D_x$ is the density of states in the forbidden gap at an energy related to the forward bias, $V_x$, and the Fermi energies on the $n$ and $p$ sides are $V_n$ and $V_p$, respectively, $e$ is the electron charge, $\epsilon$ is the energy gap, $W_1$ is the junction width constant, and ${\alpha }_x$ is a constant containing a reduced effective mass, $m_x$. This formula describes the observed dependence of $I_x$ (i) on $D_x$, observed by introducing states associated with electron bombardment, (ii) on $\epsilon$, studied by the temperature variation of the diode characteristics, (iii) on $V_x$, verified from semilogarithmic plots of the forward characteristics, and (iv) on $W_1$, tested by using junctions of different widths. From these experiments, $m_x=0.3\mathrm{}{m}_0$ to within a factor of 2.

The origins of the states in the band gap are not known for certain though they are most likely the band edge tails inherent to heavily doped semiconductors. It is probable that the tunnelling-via-local-states model for the excess current in silicon is applicable to excess currents in other materials.

• Received 6 June 1960

DOI:https://doi.org/10.1103/PhysRev.121.684