A compact model for gate tunneling currents in undoped cylindrical surrounding-gate metal-oxide-semiconductor field-effect transistors

We present a compact model of the gate tunneling current in cylindrical surrounding-gate (SG) metal-oxide-semiconductor field-effect transistors (MOSFETs) based on quantum mechanical correction. The model is physics-based and is given in an analytical closed form. We start by deriving a quadratic approximation of the quantum electrostatic potential with the two lowest energy levels using quantum perturbation theory. In addition, small-diameter cylindrical SG MOSFETs can be described excellently by taking both structural and electrical confinement effects into account. A self-consistent Schrodinger-Poisson simulation was used as a benchmark to assess the proposed model. It was found that the calculated gate tunneling currents determined using the model matched well with the corresponding currents derived using self-consistent calculations. The model is thus useful for fast analysis of gate tunneling currents within the context of a circuit simulator.