Mesoscopic approach to the soft breakdown failure mode in ultrathin SiO2 films

We present an analytic model for the soft breakdown failure mode in ultrathin
SiO2 films based on the conduction theory through quantum point contacts. The breakdown path across the oxide is represented by a three-dimensional constriction in which, due to the lateral confinement of the electron wave functions, discrete transverse energy levels arise. In the longitudinal direction, such levels are viewed by the incoming electrons as effective potential barriers, which can be treated using the one-dimensional tunneling formalism. In addition, it is shown that our mesoscopic approach is also consistent with the hard breakdown conduction mode.