Pseudospectral Methods for the Efficient Simulation of Quantization Effects in Nanoscale MOS Transistors

Abstract

This paper presents an in-detail investigation of the possible advantages related to the use of the pseudospectral (PS) method for the efficient description of the carrier quantization in nanoscale n- and p-MOS transistors. To this purpose, we have implemented, by using both the finite-difference (FD) and PS methods, self-consistent Schrödinger-Poisson solvers for both a 2-D hole gas described by a <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</b> · <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</b> Hamiltonian (suitable for p-MOSFETs) and a 1-D electron gas in the effective-mass approximation (for n-type fin-shaped FETs and nanowire FETs). The PS and FD methods have been systematically compared in terms of the CPU time and the number of discretization points by monitoring not only the subband energies in the low-dimensional carrier gas but also the calculation of some scattering matrix elements that are critically important for the transport modeling. Our results indicate a remarkable reduction in the CPU time for the PS method with respect to the FD method, which makes the PS method very attractive for the modeling of the carrier quantization in nanoscale MOSFETs.