On the Tunneling Energy within the Full-Band Structure Approach

The aim of this paper is to generalize the well-known formula used for the computation of the Fowler-Nordheim tunneling current of cold electrons to the case of hot-electron full-band transport. The same framework of approximations is employed which was successful in the simulation of the erasing mechanism in flash memory cells. For the WKB tunneling probability, an approximation for the tunneling energy within the fullband structure approach is proposed which consists of weighting the total electron energy by the ratio between the square of the group velocity component normal to the interface to the square of the total group velocity. The difference of the gate current when using either the total or the "perpendicular" energy for tunneling is about two orders of magnitude with decreasing tendency for higher gate voltage, similar to previous results with a more elaborated model in the literature.