Scattering matrix approach to direct solution of the Schrödinger equation

Abstract

We discuss a numerically stable method, the Usuki method, which is closely related to both the scattering matrix approach and recursive Green's functions. This approach provides a viable approach to directly solving the Schrödinger equation in simulations of semiconductor devices. It has a major advantage over the Green's function in that the electron density can be obtained far more efficiently for use in the self-consistent loop. Various applications of this approach have been studied, although here we focus upon the application of the method to study MOSFETS.

Numerical formulation of three-dimensional scattering problems for optical structures

“…To solve the above Eq. ( 20), we can establish a stable iterative procedure [16,17] by using the 4LM ×4LM column operator P j . This procedure does not entail solving multi-slice eigenvalue problems for the region with scattering and absorption, which has advantages in both computational time and numerical precision over the other procedure [20,21] that can be applied to optical scattering [12][13][14][15].…”

“…This paper proposes a numerical method that can produce precise S-matrices for designing the silicon photonics devices. The method exploits a numerical procedure for quantum transport [16,17]. The numerical precision of the method is evaluated in terms of the S-matrix properties.…”