Simple method to incorporate nonparabolicity effects in the Schrodinger equation of a quantum dot

摘要

In this work we formulate the nonparabolic Schrodinger equation for a quantum dot in order to explore the main features of the carriers in these systems. In addition, we present a fast iterative numerical algorithm to solve it, obtaining the energy levels and envelope functions. We also model the electrostatic potential profile in a manner that makes it possible to discuss the effects of stronger confinements on the results. To demonstrate a practical implementation of this algorithm, we carry out an investigation into the effects of nonparabolicity of the valence band on the eigenstates of a Si quantum dot. Finally, we fit our results, using power expressions to relate the energy levels to the size of the cubic quantum dots, thus demonstrating the relevance of nonparabolicity.