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Vertical current conduction in a 1.3-μm-thick semi-insulating (SI) C-doped GaN grown on a GaN substrate is analyzed. During the growth, pressure was varied from 100 to 20 mbar in order to increase C concentration from ~ 1 × 1017 cm−3 to ~ 6 × 1018 cm−3; SI GaN is sandwiched between two n-GaN layers. Optical transitions suggest two acceptor levels: ~0.9 eV above the valence band and ~0.6 eV below the conduction band. Current–voltage characterizations reveal a space-charge-limited-current conduction with an impact-ionization-assisted filling of traps in a moderately C-doped sample. On the other hand, highly compensated SI GaN forms a ~0.5-eV potential barrier at the interface with n-GaN, whereas the breakdown voltage exceeds 350 V. As the model explains, deep acceptors above the valence band compensate residual donors and lead to an electron mobility collapse. On the other hand, depending on C concentration, acceptors below the conduction band play a different role. In the moderately doped SI GaN, they act as electron traps and define the breakdown voltage. On the other hand, acceptors below the conduction band in highly compensated SI GaN are responsible for the barrier-controlled conduction and reaching of the avalanche. [ABSTRACT FROM AUTHOR]