ABSTRACT
This chapter shows that the electron-electron interaction leads to an effect called “Coulomb degeneracy” that results from a collapse of states on the Fermi level due to electron-electron interaction. It investigates the influence of the confining potential and the role of electron-electron interaction in the formation of shell structure in planar quantum dots achieved by confining a two-dimensional electron gas by means of patterned gates. It is worth mentioning that the experimental data show more peaks than the theory because of spin effects and Hund’s rule in shell filling. The chapter discusses the computational model and reviews the iterative extraction orthogonalization method for solving Schrodinger equation. It also discusses the boundary conditions imposed on the potential and the wave functions in the various regions of the device. Solving rigorously the Poisson equation by imposing the equipotential boundary conditions at the gates eliminates the need to include explicitly the effect of the image charge as a correction to the electron-electron interaction.
