Pseudo-spectral methods for the efficient simulation of quantization effects in nanoscale MOS transistors

This paper presents an in-detail investigation of the 6 possible advantages related to the use of the pseudospectral (PS) 7 method for the efficient description of the carrier quantization 8 in nanoscale n- and p-MOS transistors. To this purpose, we 9 have implemented, by using both the finite-difference (FD) and 10 PS methods, self-consistent Schrödinger–Poisson solvers for both 11 a 2-D hole gas described by a k · p Hamiltonian (suitable for 12 p-MOSFETs) and a 1-D electron gas in the effective-mass ap- 13 proximation (for n-type fin-shaped FETs and nanowire FETs). 14 The PS and FD methods have been systematically compared in 15 terms of the CPU time and the number of discretization points by 16 monitoring not only the subband energies in the low-dimensional 17 carrier gas but also the calculation of some scattering-matrix 18 elements that are critically important for the transport modeling. 19 Our results indicate a remarkable reduction in the CPU time for 20 the PS method with respect to the FD method, which makes the PS 21 method very attractive for the modeling of the carrier quantization 22 in nanoscale MOSFETs.