Solution of the Poisson-Schrödinger problem for a single-electron transistor

An outstanding problem of a quantitative description of electronic properties of a vertical gated quantum dot has been solved by a self-consistent approach to the Poisson and Schr\"odinger equations. We have calculated the confinement potential and determined the conditions for single-electron tunneling. A good agreement with experiment has been obtained for the 12 single-electron current peaks as a function of gate voltage Vg for source-drain voltage Vsd=0, the bounds on diamond-shaped regions in the Vg-Vsd plane, for which the flow of current is blocked; and the current-gate voltage characteristics in an external magnetic field.