An Analytical Model for the Electrostatics of Reverse-Biased Al/SiO₂/Si(p) MOS Capacitors With Tunneling Oxide

Abstract

An analytical model for the electrostatics of Al/SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /Si(p) MOS tunnel structures under reverse bias has been proposed in this work by formulating and balancing minority carrier current equations. The model was validated by experimental and technology computer-aided design (TCAD) simulation data under a wide range of oxide thicknesses with minor deviations. Moreover, for ultrathin oxides, it manages to predict the deep depletion phenomenon, while the ordinary MOS electrostatics model does not. Collectively, an approximate closed-form expression for the critical gate voltage as the starting point of deep depletion phenomena has also been formulated. Future corrections and more delicate assumptions may help improve the model’s accuracy in accordance with experimental values of critical voltage. This model is believed to be a convenient and comprehensive approach for evaluating the electrostatics of the MOS(p) tunnel structures.