Recent advances in the fabrication technology of heterojunction semico
nductor nanostructures have made possible the realization of systems w
ith extremely small sizes. In these devices, electrons are confined al
ong some directions and are free to move in others. Semiconductor nano
structures have become so small that we have to take into account quan
tum effects. The two dimensional physical model consists of Poisson's
equation for the electrostatic potential phi, coupled with an eigenval
ue problem for Schrodinger's equation. Proposes a comparison between a
nodal finite element method and a mixed finite element method for a s
elf-consistent solution of Schrodinger-Poisson equation.