Eigenstate modelling in arbitrary shaped nanostructres with gradual heterointerfaces

We consider the problem of evaluating the energy levels and envelope wavefunctions of electrons in semiconductor nanostructures with a smooth confining potential, such as inter- diffused quantum dots or quantum wells. We show how Gaussian functions can be used to model various confinement potentials in 1D, 2D and 3D. We develop a fast and accurate numerical algorithm for solving the one-particle Schrodinger equation with a position-dependent effective mass for this type of potential. We examine the convergence and accuracy of our algorithm. This method can be used to analyze experimental data, such as the PL spectra of quantum wells, wires and dots and the charge carrier transport through various nanostructures. GaAs/Al0.3Ga0.7As system is used in calculations.