With the continuous progress of microelectronics, the featured structure size has been scaled down to the nanometer regime. Therefore, quantum mechanical effects significantly influence the characteristics of state-of-the-art devices. This poses new challenges to the modeling and simulation of semiconductor devices, since semi-classical models only allow the incorporation of empirical quantum corrections. The wavelike nature of the electrons in quantum mechanical systems requires proper treatment by the Schrödinger equation. Very elaborate physical models posing open boundary conditions have been developed for quantum transport.
Green's functions are a general concept used to solve inhomogeneous differential equation systems. The numerical treatment of steady-state transport is achieved within the Non-Equilibrium Green's Functions (NEGF) formalism. The intersection of a general quantum transport theory using Green's functions and its numerical implementation within a computer simulation requires careful treatment of all assumptions and approximations. The Vienna Schrödinger Poisson (VSP) solver has been extended by the addition of a one-dimensional NEGF solver. The effective mass Schrödinger equation is treated within this framework and solved self-consistently with the Poisson equation. Numerical integration methods are necessary to obtain the physical quantities of interest, such as the electron or current density. Adaptive quadrature routines that allow the resolution of problematic areas in the energy spectrum, i.e., narrow resonances and contact potentials, have been investigated. Additionally, a sophisticated resonance finder has been implemented to determine the quasi-bound states within resonant tunneling diodes and MOS structures in advance.