MODIFIED THOMAS-FERMI APPROXIMATION - A SURPRISINGLY GOOD TOOL FOR THE TREATMENT OF SEMICONDUCTOR LAYER STRUCTURES INCLUDING VARIOUS 2-DIMENSIONAL SYSTEMS

In this paper the calculational procedure of the electronic structure of delta-doped quantum well HEMTs is studied with emphasis on the calculation rather than on the results. It will be shown that a modified Thomas-Fermi approximation yields very accurate results which differ from the exact solutions of the Kohn-Sham equations by only percents while the CPU time is reduced drastically and convergence problems are avoided. The question hinges on the point of an appropriate rho(V(r), r) in the Poisson equation. The construction of this charge density is discussed in detail. Care is taken on the nonseparability of the Schrodinger-like equation with a position dependent mass.