Tunneling current in oppositely connected Schottky diodes formed by contacts between degenerate $n$-GaN and a metal

The nonlinear behavior of the I – V characteristics of symmetric contacts between a metal and degenerate n -GaN, which form oppositely connected Schottky diodes, is investigated at free-carrier densities from 1.5 $\times$ 10$^{19}$ to 2.0 $\times$ 10$^{20}$ cm$^{-3}$ in GaN. It is demonstrated that, at an electron density of 2.0 $\times$ 10$^{20}$ cm$^{-3}$, the conductivity between metal (chromium) and GaN is implemented via electron tunneling and the resistivity of the Cr–GaN contact is 0.05 $\Omega$ mm. A method for determining the parameters of potential barriers from the I – V characteristics of symmetric opposite contacts is developed. The effect of pronounced nonuniformity of the current density and voltage distributions over the contact area at low contact resistivity is taken into account. The potential-barrier height for Cr–$n^+$-GaN contacts is found to be 0.47 $\pm$ 0.04 eV.