Quantum Transport Beyond the Effective Mass Approximation

A three-dimensional full band simulator for nanowire field-effect transistors (FETs) is presented in this thesis. At the nanometer scale the classical drift-diffusion transport theory reaches its limits; quantum transport (QT) phenomena govern the motion of electrons and holes. The development of a QT simulator requires the assembly of several physical models and the choice of appropriate simplifications. In the first part, the Non-Equilibrium Green’s Function (NEGF) formalism is reviewed, a method extensively used for the description of nanostructures. It is applied to the simulation of a two-dimensional ultra-thin-body (UTB) transistor and of a three-dimensional nanowire FET, both treated within the effective mass approximation (EMA) and in a coupled mode-space. However, the strong quantization effects that characterize structures with dimensions below five nanometers oblige an accurate QT simulator to go beyond the EMA. The semi-empirical sp3d5s∗ tight-binding (TB) method is chosen as bandstructure model because (1) it reproduces the complete bulk (E−k) relation of a wide range of semiconductor materials, (2) it uses an atomic grid, and (3) its extension to nanostructures is straightforward. The integration of the TB method into a transport code is only possible, if open boundary conditions (OBC) are introduced. The available procedures to apply OBC in a three-dimensional multiband QT simulator are computationally too intensive since they represent a generalized eigenvalue problem or require iterative solvers. Therefore, a new method based on the scattering-boundary approach is developed in this work. It significantly reduces the computational burden associated with the OBC calculation. Furthermore, it can be formulated either in the NEGF or in the Wave Function formalism, and