Self-consistent Calculation Of Electron States In III-V Multilayer Structures

Two different algorithms have been developed for calculating one-dimensional self-consistent numerical solutions to the Schrodinger and Poisson equations for electron states in III-V multi-layer structures. The Schrodinger equation is solved by a spectral or a finite-difference method. The Poisson equation is solved with a finite element method together with a Newton linearization scheme. The latter makes it necessary to evaluate the derivative of the charge density with respect to the electrostatic potential. In a first approach we have approximated this derivative by its classical expression. In a second approach, which is more consistent with the physical model, we have evaluated the derivative by making use of the quantum mechanical perturbation theory. Both methods lead to convergence of the over-all solution. An important feature of the self-consistent solution is that it guarantees global charge neutrality and that it leads to the "true" electron states. In the most spectacular cases the states with the lowest energy are localized states in the self-consistent solution and extended states in the non self-consistent solution.