The role of carbon-related traps in GaN-based ungated high-electron mobility transistor structures has been investigated both experimentally and by means of numerical simulations. A clear quantitative correlation between the experimental data and numerical simulations has been obtained. The observed current decrease in the tested structure during backgating measurements has been explained simply by means of a thermally activated hole-emission process with E-A = 0.9eV, corresponding to the distance of the acceptor-like hole-Trap level from the GaN valence band. Moreover, it has been demonstrated by means of electrical measurements and numerical simulations that only a low percentage of the nominal carbon doping levels induces the observed current reduction when negative substrate bias is applied to the tested structure.