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As an attempt to improve the description of the tunneling current that arises in ultrascaled nanoelectronic devices when charge carriers succeed in traversing the potential barrier between source and drain, an alternative and more accurate non-local formulation of the tunneling probability was suggested. This improvement of the probability computation might result of particular interest in the context of Monte Carlo simulations where the utilization of the conventional Wentzel-Kramers-Brillouin (WKB) approximation tends to overestimate the number of particles experiencing this type of direct tunneling. However, in light of the reformulated expression for the tunneling probability, it becomes of paramount importance to assess the type of potentials for which it behaves adequately. We demonstrate that, for ensuring boundedness, the top of the potential barrier cannot feature a plateau, but rather has to behave quadratically as one approaches its maximum. Moreover, we show that monotonicity of the reformulated tunneling probability is not guaranteed by boundedness and requires an additional constraint regarding the derivative of the prefactor that modifies the traditional WKB tunneling probability.

Analysis of the Reformulated Source to Drain Tunneling Probability for Improving the Accuracy of a Multisubband Ensemble Monte Carlo Simulator