3-D self-consistent Schrodinger-Poisson solver : the spectral element method

In this paper, we developed an efficient threedimensional (3-D) nanoelectronic device simulator based on a self-consistent Schrodinger-Poisson solver to simulate quantum transport. An efficient and fast algorithm, the spectral element method (SEM), is developed in this simulator to achieve spectral accuracy where the error decreases exponentially with the increase in the sampling density and the order of the polynomial basis functions, thus significantly reducing the CPU time and memory usage. Perfectly matched layer (PML) boundary method, as an alternative to the open-boundary conditions in NEGF, is applied in this solver to simplify the numerical implementation. The validity of the Schrodinger and Poisson solvers are illustrated by a multiple-terminal device and a spherical charge example, respectively. The utility of the self-consistent Schrodinger-Poisson solver is illustrated by a nanotube example.