In this paper, we present the derivation and the simulation of an effective mass model, describing the quantum motion of electrons in an ultra-scaled confined nanostructure. Due to the strong confinement, the crystal lattice is considered periodic only in the one-dimensional transport direction and an atomistic description of the entire cross-section is given. Using an envelope function decomposition, an effective mass approximation is obtained. It consists of a sequence of one-dimensional device-dependent Schrödinger equations, one for each energy band, in which quantities retaining the effects of the confinement and of the transversal crystal structure are inserted. In order to model a gate-all-around field effect transistor, self-consistent computations include the resolution, in the whole domain, of a Poisson equation describing a slowly varying macroscopic potential. Simulations of the electron transport in a simplified one-wall carbon nanotube are presented.
Effective-mass model and magneto-optical properties in hybrid perovskites