Hopping conductivity and dielectric relaxation in Schottky barriers on GaN

A study of the current and capacitance dependences on the forward voltage in Au/$n$-GaN Schottky diodes, the sub-band optical absorption spectra, and the defect photoluminescence in $n$-GaN bulk crystals and thin layers is reported. It is shown that defect-assisted tunneling is the dominant transport mechanism for forward-biased Schottky contacts on $n$-GaN. The dependences of the current and capacitance on forward bias reflect the energy spectrum of defects in the band gap of $n$-GaN: the rise in the density of deep states responsible for yellow photoluminescence in GaN with increasing energy and the steep exponential tail of states with an Urbach energy of $E_{\operatorname{U}}$ = 50 meV near the conduction-band edge. A decrease in the frequency of electron hops near the Au/$n$-GaN interface results in a wide distribution of local dielectric relaxation times and in a dramatic transformation of the electric-field distribution in the space-charge region under forward biases.