Finite Element Method Linear Triangular Element for Solving Nanoscale InAs⁄GaAs Quantum Ring Structures

Abstract

This paper concerned with the solution of the nanoscale structures consisting of the with an effective mass envelope function theory, the electronic states of the quantum ring are studied. In calculations, the effects due to the different effective masses of electrons in and out the rings are included. The energy levels of the electron are calculated in the different shapes of rings, i.e., that the inner radius of rings sensitively change the electronic states. The energy levels of the electron are not sensitively dependent on the outer radius for large rings. The structures of quantum rings are studied by the one electronic band Hamiltonian effective mass approximation, the energy- and position-dependent on electron effective mass approximation, and the spin-dependent on the Ben Daniel-Duke boundary conditions. In the description of the Hamiltonian matrix elements, the Finite elements method with different base linear triangular element is adopted. The non-linear energy confinement problem is solved approximately by using the Finite elements method with linear triangular element, to calculate the energy of the electron states for the quantum ring.