Figure 5: Impact of elliptic κ(E) on the tunnelling current through a Schottky barrier.
From: Analysing black phosphorus transistors using an analytic Schottky barrier MOSFET model
(a) Complex band structure κ(E) for Ev<E<Ec. The parabolic approximation is valid only close to the band edges. The elliptic κ(E) is parabolic near the band edges with the effective mass of the corresponding band. Near the branching point 
, the complex band becomes non-parabolic. (b) Band bending situation for a triangular barrier at a metal–semiconductor junction. The blue and red lines are stitched together according to the elliptic approximation in a. The open circle depicts the position of the branching point in the E−κ plane. The position of Eb in the E−x plane is shown using a dashed line. (c) Simulated Ids−Vgs curve for elliptic and parabolic κ(E) for specific metal line-up. For tall Schottky barriers, the more commonly employed parabolic κ(E) can severely underestimate the tunnelling current.
