From Fowler-Nordheim to Non-Equilibrium Green's Function Modeling of Tunneling

In this work, an analytic model is proposed which provides in a continuous manner the current-voltage characteristic (I-V) of high performance tunneling field-effect transistors (TFETs) based on direct bandgap semiconductors. The model provides closed-form expressions for I-V based on: 1) a modified version of the well-known Fowler-Nordheim (FN) formula (in the ON-state), and 2) an equation which describes the OFF-state performance while providing continuity at the ON/OFF threshold by means of a term introduced as the "continuity factor". It is shown that traditional approaches such as FN are accurate in TFETs only through correct evaluation of the total band bending distance and the "tunneling effective mass". General expressions for these two key parameters are provided. Moreover, it is demonstrated that the tunneling effective mass captures both the ellipticity of evanescent states and the dual (electron/hole) behavior of the tunneling carriers, and it is further shown that such a concept is even applicable to semiconductors with nontrivial energy dispersion. Ultimately, it is found that the I-V characteristics obtained by using this model are in close agreement with state-of-the-art quantum transport simulations both in the ON- and OFF-state, thus providing validation of the analytic approach.