Analytic modeling of leakage current through multiple breakdown paths in SiO₂ films

We have investigated the multiple-event dielectric breakdown of ultra-thin SiO₂ films used as gate insulators in MOS devices. A theoretical framework, based on the physics of mesoscopic conducting systems, which explains the post-breakdown current-voltage characteristics is presented. In this approach, the breakdown path is treated as a three dimensional quantum point contact in which an effective potential barrier arises as a consequence of the quantization of the transverse momentum of the passing electrons. Hard breakdown corresponds to large spot areas and therefore to completely open conducting channels between the electrodes. On the contrary, soft breakdown is associated with smaller areas and therefore with more restricted conducting paths. An adiabatic formulation of the charge transport process not only yields an analytic expression for the gate leakage current, which improves our understanding of the oxide breakdown physics, but also a compact model well suited for incorporation in circuit simulators. In addition, it is shown that the model accounts for the so-called nonlinear hard breakdown conduction mode in a consistent manner and how its conceptual framework might be adapted to cover the stress-induced leakage current regime.