We derive general formulae for calculating the transport of free charge carriers in a MOS structure with a thin insulating layer. In particular, we obtain relationships for boundary concentrations of free charge carriers on the insulator-semiconductor interface and for the current densities flowing through the MOS structure. Our direct tunnelling-diffusion approach makes the well known thermionic emission-diffusion theory for the Schottky interface applicable also to metal-insulator-semiconductor barriers with a very thin insulator layer. We demonstrate how direct tunnelling through the insulating layer and drift-diffusion of free charge carriers in the semiconductor affect the I-V and C-V curves and the boundary concentrations needed to numerically solve the continuity equations. (C) 2008 Elsevier Ltd. All rights reserved.