An Analytical Gate Tunneling Current Model for MOSFETs Having Ultrathin Gate Oxides

In this paper, we present a completely analytical model for the gate tunneling current, which can be used to get a first-order estimate of this parameter in present-generation MOSFETs, having ultrathin gate oxides and high substrate doping concentrations. The model has been developed from first principles, and it does not use any empirical fitting and/or correction parameters. It takes into account the quantization of the electron energy levels within the inversion layer of a MOSFET, which behaves similar to a potential well. Several interesting simplifications regarding this well structure have been made, and all these assumptions have been rigorously justified, both based on physical arguments as well as through numerical quantifications. An extremely interesting and important outcome of this procedure is a nonzero value of the wavefunction at the semiconductor-insulator interface, which is physically justified, however, contrary to what other existing literatures in this area assume. This procedure also led to a closed-form analytical expression for the inversion layer thickness. The interface wavefunction was used, in association with the tunneling probability through the gate oxide, and the carriers in transit model in the gate metal, to find the resultant gate tunneling current density as a function of the applied gate-to-body voltage. The results obtained from our simple and completely analytical model were compared with the experimental results reported in the literature, and the match is found to be excellent for varying oxide thicknesses and substrate doping concentrations, which justifies the authenticity of the model developed in this work here.