Schottky diodes were fabricated by thermal evaporation of nickel on phase-pure cubic GaN(c-GaN) layers grown by plasma assisted molecular beam epitaxy on freestanding 3C-SiC. Detailed analysis of the I-V characteristics revealed the existence of a thin surface barrier at the Ni-semiconductor interface. Thermal annealing in air at 200°C alters the composition of this thin surface barrier, reduces the leakage current by three orders of magnitude, and increases the breakdown voltage. The dependence of the breakdown voltage on the doping density of the c-GaN layers is in good agreement with calculated values. We obtain a critical electric-field strength of Ecrit≅2.5×106V∕cm for c-GaN.