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 Schrödinger 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 $V_g$ for source-drain voltage $V_{\mathrm{sd}}=0,$ the bounds on diamond-shaped regions in the $V_g-V_{\mathrm{sd}}$ plane, for which the flow of current is blocked; and the current-gate voltage characteristics in an external magnetic field.