Description of an Exciton in a Quantum Dot Within the Effective-Mass Approximation

Abstract

In the following description a quantum dot is modeled as a local perturbation of the periodic crystal field of a semiconducting structure that surrounds the dot. In the description of such a system, the effective-mass approximation can be applied if the perturbation potential varies slowly over the interatomic distance. In the case of quantum dots with sizes a few tens of nanometers, this assumption is expected to be satisfied. This also seems doubtless the case for the dots created by means of interlayer diffusion or by the application of a modulated electric field. It is probably a good approach for lens-shaped self-assembled dots. However, the cases of dots in the form of compact bubbles embedded in another semiconductor are disputable, since their sharply defined geometrical shapes may lead to a more rapid jump of the potential at the interface.