A new solution method of the 1D open-boundary Schrödinger equation for transport in NW-FETs including band effects

The importance of full-band structure effects in ultra-scaled silicon nanowire (NW) FETs has been fully recognized, both on the device electrostatics and I-V characteristics. Though a full 3D atomistic approach based on tight-binding has been recently demonstrated, its use in NW-FETs is still very time consuming. Therefore the most common approach consists in separating the problem in the transverse and longitudinal directions. Longitudinal transport is treated by means of a 1D open-boundary Schrödinger equation (SE) for each subband, with the Hamiltonian built upon the 1DEG energy dispersion relation and the bottom energy profile of each subband calculated from a 2D SE in the transverse direction for each cross-section, coupled with the 3D Poisson equation. Non parabolic corrections based on atomistic calculations can be taken into account both in the transverse 2D SE and in the 1D transport SE. In this work we focus on the 1D transport SE, and propose a solution method that goes beyond the non-parabolic corrections introduced in [3], also circumventing the numerical difficulties related with the high-order differential terms in the Hamiltonian. The approach takes into account the full 1DEG subband structure including its periodic nature.