Modeling of the electronic properties of vertical quantum dots by the finite element method

We investigate the quantum mechanical properties and single-electron charging effects in vertical semiconductor quantum dots by solving the Schrödinger and Poisson (SP) equations, self-consistently. We use the finite element method (FEM), specifically the Bubnov-Galerkin technique to discretize the SP equations. Owing to the cylindrical symmetry of the structure, the mesh is generated from hexahedral volume elements. The fine details of the electron spectrum and wavefunctions in the quantum dot are obtained as a function of macroscopic parameters such as the gate voltage, device geometry and doping level. The simulations provide comprehensive data for the analysis of the experimental data of Tarucha, Austing, Honda, van der Hage, and Kouwenhoven (1996).