Unified tunnelling-diffusion theory for Schottky and very thin MOS structures

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.