Simplified calculation method of electron subband profile in ballistic nanowire MOSFET

We develop a simple method to calculate the electron subband profiles, which represent distributions of each discrete energy level along the channel, in a nanowire metal-oxide-semiconductor field-effect-transistor. The electrostatic potential distribution in the wire cross section is approximated by a quadratic function with a correction due to the depletion layer that spreads into the channel from the source and drain. The Schrodinger equation is solved analytically to derive the subbands, and their profiles are determined by numerically solving the coupled equation of charge densities derived from electrostatics or quantum mechanics. The obtained subband profiles are compared with simulation results calculated from the non-equilibrium Green´s function method, and our method demonstrates good accuracy. Using the Landauer formula with transmission probability calculated from the subband profiles, we finally calculate the drain current that shows good agreement with the simulation results.