The fabrication and electrical characterization of Metal‐Insulator‐Metal (MIM) structures, using a‐C:H films as the insulating material, are presented in this work. These PECVD carbon films show a very low dielectric constant and a very high resistivity. The current conduction mechanisms were analyzed before and after the post deposition annealing in pure argon ambient at 400°C. For as‐deposited films, the experimental J ‐U curves showed that under low biasing regime (|U | < 8 V) the space charge limited current conduction is the main transport mechanism, whereas under higher biasing regime (|U | > 8 V)) the current transport is dominated by the Schottky mechanism. For annealed structures, under low and high biasing the ohmic and Schottky mechanisms were identified as the main processes for the electrical transport. Finally, we found that both parameters, the dielectric constant and resistivity, decrease slightly after the thermal annealing. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)