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

An outstanding problem of a quantitative description of electronic properti es of a vertical gated quantum dot has been solved by a self-consistent app roach to the Poisson and Schrodinger equations. We have calculated the conf inement potential and determined the conditions for single-electron tunneli ng. A good agreement with experiment has been obtained for the 12 single-el ectron current peaks as a function of gate voltage V-g for source-drain vol tage V-sd = 0, the bounds on diamond-shaped regions in the V-g - V-sd plane , for which the flow of current is blocked; and the current-gate voltage ch aracteristics in an external magnetic field.