Self-consistent three-dimensional models for quantum ballistic transport in open systems

A quasi-three-dimensional model for quantum ballistic transport in nanostructures is proposed. The model goes beyond the Thomas-Fermi approximation and is numerically more tractable than the full three-dimensional Schr\"odinger-Poisson model. Its derivation relies on the strong confinement of electrons at the heterojunction which allows us to split the three-dimensional Schr\"odinger equation into a one-dimensional Schr\"odinger equation for the confined direction and a two-dimensional Schr\"odinger equation in the transport direction. The space charge effects are taken into account in a three-dimensional framework. Numerical simulations of quantum waveguide devices such as T stubs and directional couplers are used to illustrate the accuracy of the quasi-3D model versus the fully 3D model and to show the importance of quantum effects.