Current conduction mechanisms through a metal-oxide semiconductor capacitor with a 9.6 nm thick SiO2 dielectric layer are characterized via Fowler-Nordheim (FN) and Poole-Frenkel (PF) plots, as well as through the analysis of the power exponent parameter α = d(log I)/d(log V). It is shown that the evaluation by means of α is much more sensitive in the accurate identification of different current conduction mechanisms. If FN tunneling and PF conduction occur simultaneously, evaluation using the α-voltage (α-V) plot actually allows one to determine the fraction of each conduction mechanism quantitatively. Even a slight current saturation due to minority carrier depletion, which cannot be detected through the evaluation of the current-voltage characteristics using FN or PF plots, can be detected by the α-V plot.