ITERATION SCHEME FOR THE SOLUTION OF THE 2-DIMENSIONAL SCHRODINGER-POISSON EQUATIONS IN QUANTUM STRUCTURES

A fast and robust iterative method for obtaining self-consistent solut ions to the coupled system of Schrodinger's and Poisson's equations is presented. Using quantum mechanical perturbation theory, a simple exp ression describing the dependence of the quantum electron density on t he electrostatic potential is derived. This expression is then used to implement an iteration scheme, based on a predictor-corrector type ap proach, for the solution of the coupled system of differential equatio ns. We find that this iteration approach simplifies the software imple mentation of the nonlinear problem, and provides excellent convergence speed and stability. We demonstrate the approach by presenting an exa mple for the calculation of the two-dimensional bound electron states within the cross section of a GaAs-AlGaAs based quantum wire. For this example, the convergence is six times faster by applying our predicto r-corrector approach compared to a corresponding underrelaxation algor ithm. (C) 1997 American Institute of Physics.