The tunnel current models based on the Franz dispersion relation for carriers in the involved insulators are tested for several types of metal-insulator-silicon structures. The features related to the application of this alternative dispersion relation are analysed. Simplified approaches for tunneling current models are also examined. The positive and negative aspects of the Franz model are described. Special attention is paid to the tunneling of carriers with energies far from the insulator conduction band edge. The results of the new tunneling models are compared to those of the conventional models adopting the parabolic dispersion laws. It turns out that the physically well justified Franz relation yields typically a better agreement with experiments compared to the parabolic relation despite offering less freedom in term of adjustable parameters. (C) 2009 Elsevier Ltd. All rights reserved.