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.
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