Scattering matrix approach to direct solution of the Schrödinger equation

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.