A numerical solution of the Poisson-Schrodinger problem for a vertical gated quantum dot

We present a numerical solution of the Poisson-Schrodinger problem for a semiconductor nanostructure containing a single quantum dot. The main outcome of our work is the lateral confinement potential, which determines the electronic properties of the nanodevice. We study the real nanodevice with cylindrical symmetry, which allows us to solve the three-dimensional problem on a two-dimensional mesh. We discuss the self-consistency of the solution with respect to the distribution of ionized donors inside the nanodevice.